ANSYS FLUIDS

Fluids Analysis Guide

Release 13.0ANSYS, Inc.November 2010Southpointe

275 Technology DriveCanonsburg, PA 15317 ANSYS, Inc. is

certified to ISO9001:2008.

[email protected]://www.ansys.com(T) 724-746-3304(F) 724-514-9494

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Table of Contents

I. CFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Overview of FLOTRAN CFD Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.Types of FLOTRAN Analyses .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.1. Laminar Flow Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.2. Turbulent Flow Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.3. Thermal Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.4. Compressible Flow Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.5. Non-Newtonian Fluid Flow Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.6. Multiple Species Transport Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.1.7. Free Surface Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2. About GUI Paths and Command Syntax .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42. The Basics of FLOTRAN Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1. Characteristics of the FLOTRAN Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.1. Other Element Features .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2. Considerations and Restrictions for Using the FLOTRAN Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1. Limitations on FLOTRAN Element Use .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3. Overview of a FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.1. Determining the Problem Domain .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2. Determining the Flow Regime .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.3. Creating the Finite Element Mesh .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.4. Applying Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.5. Setting FLOTRAN Analysis Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.6. Solving the Problem ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.7. Examining the Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4. Files the FLOTRAN Elements Create .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.1.The Results File ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.2. The Print File (Jobname.PFL ) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.3. The Nodal Residuals File ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.4. The Restart File ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.5. The Domain File ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.6. Restarting a FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5. Convergence and Stability Tools ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.1. Relaxation Factors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.2. Inertial Relaxation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.3. Modified Inertial Relaxation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.4. Artificial Viscosity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5.5. DOF Capping .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.5.6. The Quadrature Order .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6. What to Watch For During a FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.6.1. Deciding How Many Global Iterations to Use .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.6.2. Convergence Monitors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.6.3. Stopping a FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.6.4. Pressure Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.7. Evaluating a FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.8. Verifying Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3. FLOTRAN Laminar and Turbulent Incompressible Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1. Activating the Turbulence Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1.1. The Role of the Reynolds Number .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.2. Determining Whether an Analysis Is Turbulent .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.3. Turbulence Ratio and Inlet Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

iiiRelease 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

3.1.4. Turbulence Models ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.4.1. Standard k-epsilon Model (default) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.1.4.2. Zero Equation Turbulence Model (ZeroEq) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.4.3. Re-Normalized Group Turbulence Model (RNG) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.4.4. k-epsilon Model Due to Shih (NKE) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.4.5. Nonlinear Model of Girimaji (GIR) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.1.4.6. Shih, Zhu, Lumley Model (SZL) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.4.7. k-omega Turbulence Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.4.8. Shear Stress Transport Model (SST) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2. Meshing Requirements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.3. Flow Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4. Strategies for Difficult Problems .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.5. Example of a Laminar and Turbulent FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4. FLOTRAN Thermal Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.1. Meshing Requirements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2. Property Specifications and Control ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.3. Thermal Loads and Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3.1. Applying Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.3.1.1. Applying Loads Using Commands .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3.1.2. Applying Loads Using the GUI .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.3.1.3. Solutions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.4. Solution Strategies .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.4.1. Constant Fluid Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4.2. Forced Convection, Temperature Dependent Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4.3. Free Convection, Temperature Dependent Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4.4. Conjugate Heat Transfer ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.5. Heat Balance .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.6. Surface-to-Surface Radiation Analysis Using the Radiosity Method ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.6.1. Procedure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.6.2. Heat Balances .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.7. Examples of a Laminar, Thermal, Steady-State FLOTRAN Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.7.1. The Example Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.7.2. Doing the Buoyancy Driven Flow Analysis (GUI Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.7.3. Doing the Buoyancy Driven Flow Analysis (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.8. Example of Radiation Analysis Using FLOTRAN (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.9. Where to Find Other FLOTRAN Analysis Examples .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5. FLOTRAN Transient Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.1. Time Integration Method .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.2. Time Step Specification and Convergence .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.3.Terminating and Getting Output from a Transient Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.4. Applying Transient Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6. Volume of Fluid (VOF) Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.1. VFRC Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.1.1. Initial VFRC Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.1.2. Boundary VFRC Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

6.2. Input Settings .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2.1. Ambient Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.2.2. VFRC Tolerances .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.2.3. VOF Time Steps .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

6.3. Postprocessing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.4.VOF Analysis of a Dam ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.4.1. The Problem Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.iv


6.4.2. Building and Solving the Model (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706.5. VOF Analysis of Open Channel with an Obstruction .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5.1. The Problem Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.5.2. Building and Solving the Model (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.6. VOF Analysis of an Oscillating Droplet ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.6.1. The Problem Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.6.2. Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.6.3. Building and Solving the Model (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.6.4.Where to Find Other Examples .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

7. Arbitrary Lagrangian-Eulerian (ALE) Formulation for Moving Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.1. Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.2. Mesh Updating .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.3. Remeshing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.4. Postprocessing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.5. ALE Analysis of a Simplified Torsional Mirror ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

7.5.1. The Problem Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.5.2. Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.5.3. Forces and Moments .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.5.4. Building and Solving the Model (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

7.6. ALE/VOF Analysis of a Vessel with a Moving Wall ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947.6.1. The Problem Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947.6.2. Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.6.3. Building and Solving the Model (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.7. ALE Analysis of a Moving Cylinder .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.7.1. The Problem Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.7.2. Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.7.3. Building and Solving the Model (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

8. FLOTRAN Compressible Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.1. Property Calculations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1038.2. Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1048.3. Structured vs. Unstructured Mesh .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1058.4. Solution Strategies .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

8.4.1. Inertial Relaxation .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068.5. Example of a Compressible Flow Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8.5.1. The Example Described .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068.5.1.1. Fluid Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068.5.1.2. Approach and Assumptions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8.6. Doing the Example Compressible Flow Analysis (GUI Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078.7. Doing the Example Compressible Flow Analysis (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

9. Specifying Fluid Properties for FLOTRAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1179.1. Fluid Property Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9.1.1. Property Types for Specific Heat .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189.1.2. Property Types for Density and Thermal Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.1.3. Property Types for Viscosity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.1.4. Property Types for Surface Tension Coefficient .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.1.5. Property Types for Wall Static Contact Angle .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.1.6. General Guidelines for Setting Property Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

9.1.6.1. Using a Fluid Property Table .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1209.1.6.2. Specifying Property Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

9.1.7. Density .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1229.1.8. Viscosity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1239.1.9. Specific Heat .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

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9.1.10. Thermal Conductivity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1259.1.11. Surface Tension Coefficient .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1259.1.12. Wall Static Contact Angle .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

9.2. Initializing and Varying Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1269.2.1. Activating Variable Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

9.3. Modifying the Fluid Property Database .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1279.4. Using Reference Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1299.5. Using the ANSYS Non-Newtonian Flow Capabilities ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

9.5.1. Activating the Power Law Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1309.5.2. Activating the Carreau Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1319.5.3. Activating the Bingham Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9.6. Using User-Programmable Subroutines .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13210. FLOTRAN Special Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

10.1. Coordinate Systems .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13310.2. Rotating Frames of Reference .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13510.3. Swirl .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13610.4. Distributed Resistance/Source .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

11. FLOTRAN CFD Solvers and the Matrix Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13911.1. Tri-Diagonal Matrix Algorithm ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14011.2. Semi-Direct Solvers ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

11.2.1. Preconditioned Generalized Minimum Residual (PGMR) Solver ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14111.2.2. Preconditioned BiCGStab (PBCGM) Solver ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

11.3. Sparse Direct Method .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14312. Coupling Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

12.1. Algorithm Settings .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14512.1.1. Advection Scheme .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14512.1.2. Solver ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14612.1.3. Relaxation Factors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

12.2. Performance .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14613. Multiple Species Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

13.1. Mixture Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14913.1.1. Dilute Mixture Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14913.1.2. Composite Mixture Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15013.1.3. Composite Gas Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

13.2. Doing a Multiple Species Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15113.2.1. Establish the Species .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15113.2.2. Choose an Algebraic Species .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15113.2.3. Adjust Output Format .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15113.2.4. Set Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15213.2.5. Specify Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15313.2.6. Set Relaxation and Solution Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

13.3. Doing a Heat Exchanger Analysis Using Two Species .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15413.4. Example Analysis Mixing Three Gases .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

14. Advection Discretization Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16114.1. Using SUPG and COLG .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16114.2. Strategies for Difficult Solutions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

II. Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1631. Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

1.1. Solving Acoustics Problems ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1651.2. Building the Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

1.2.1. Harmonic Acoustic Analysis Guidelines .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1661.2.1.1. FLUID29, FLUID30, FLUID220, and FLUID221 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

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1.2.1.2. FLUID129 and FLUID130 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1671.3. Meshing the Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

1.3.1. Step 1: Mesh the Interior Fluid Domain .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1691.3.2. Step 2: Generate the Infinite Acoustic Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1691.3.3. Step 3: Specify the Fluid-Structure Interface .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

1.4. Applying Loads and Obtaining the Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1711.4.1. Step 1: Enter the SOLUTION Processor .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1711.4.2. Step 2: Define the Analysis Type .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1711.4.3. Step 3: Define Analysis Options .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1711.4.4. Step 4: Apply Loads on the Model ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

1.4.4.1. Applying Loads Using the GUI .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1731.4.4.2. Applying Loads Using Commands .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1731.4.4.3. Load Types .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

1.4.5. Step 5: Specify Load Step Options .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1751.4.5.1. Dynamics Options .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1751.4.5.2. General Options .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1751.4.5.3. Output Controls ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

1.4.6. Step 6: Back Up Your Database .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1761.4.7. Step 7: Apply Additional Load Steps (Optional) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1761.4.8. Step 8: Finish the Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

1.5. Reviewing Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1761.6. Fluid-Structure Interaction .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1771.7. Sample Applications .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

1.7.1. Example 1: Fluid-Structure Coupled Acoustic Analysis (Command Method) .... . . . . . . . . . . . . . . . . . 1771.7.2. Example 2: Room Acoustic Analysis (Command Method) .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1791.7.3. Example 2: Radiation From Two Waveguides .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

III. Thin Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1831. Thin Film Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

1.1. Elements for Modeling Thin Films .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1851.2. Squeeze Film Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

1.2.1. Static Analysis Overview .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1871.2.2. Harmonic Response Analysis Overview .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1871.2.3. Transient Response Analysis Overview .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1881.2.4. Flow Regime Considerations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1881.2.5. Modeling and Meshing Considerations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1891.2.6. Analysis Settings and Options .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1891.2.7. Loads and Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1901.2.8. Review Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1901.2.9. Sample Harmonic Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1911.2.10. Simplified Transient Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1941.2.11. Complex Transient Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

1.3. Modal Projection Method for Squeeze Film Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2011.3.1. Modal Projection Method Overview .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2011.3.2. Steps in Computing the Damping Parameter Using the Modal Projection Technique .... . . . 202

1.3.2.1. Modeling and Meshing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031.3.2.2. Perform Modal Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031.3.2.3. Extracting Eigenvectors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2031.3.2.4. Performing a Harmonic Response Analysis and Extracting Damping Parameters ... . . 203

1.3.3. Example Problem Using the Modal Projection Method .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2041.3.4. Damping Extraction for Large Signal Cases .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

1.4. Slide Film Damping .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2091.4.1. Slide Film Damping Example .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

viiRelease 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information



Index .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

List of Figures

2.1. Convergence Monitors Displayed by the GST Feature .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1. Internal Flow .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2. External Flow .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3. Structured Mesh .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.4. Unstructured Mesh .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1. Diagram of the Square Cavity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2. Plot of the Temperature Solution .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.3. Plot of Streamline Contours .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.4. Plot of Velocity Vectors ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.5. Plot of Flow Trace .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.1. Instantaneous Pressure Distributions at 0.001 ms .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.2. Instantaneous Pressure Distributions at 0.012 ms .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767.1.Torsional Mirror at t = 0 Seconds .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.2. Torsional Mirror at t = 2.5 Seconds .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.3. Torsional Mirror at t = 7.5 Seconds .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.4. Boundary Conditions for Moving Walls ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.5. Torsional Mirror Problem Description .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.6. Torsional Mirror Problem - Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.7. Square Vessel with a Moving Wall ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947.8. Left Wall Displacement and Velocity .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.9. Moving Cylinder .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.10. Elements at 0 Seconds .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.11. Elements at 22 Seconds .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.12. Elements at 44 Seconds .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988.1. Three Types of Meshing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10510.1. Direction of Positive Swirl Velocity VZ for Axisymmetric Models ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13410.2. Rotating Flow Problem ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13510.3. Problem Schematic with Rotating Coordinate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13611.1. Typical Debug Files ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14113.1. Environment for a Typical Heat Exchanger Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1541.1. Example of a 2-D Acoustic Model (Fluid Within a Structure) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1671.2. Example of Absorption Element Application .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1681.3. Submerged Cylindrical Shell .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1681.4. Mesh the Fluid Domain .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1691.5. Add the Absorption Element on the Boundary .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1701.6. Specify Fluid-Structure Interface .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1711.1. Moving Plate above a Fixed Wall ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1861.2. Perforated Plate Structure .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1861.3. Pressure Distribution on a Plate at a Low Driving Frequency .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1871.4. Damping and Squeeze Stiffness Coefficients vs. Frequency .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1871.5. Coupling of Nodes at the Hole Periphery with the Center Node of a FLUID138 Element .... . . . . . . . . . . . . . . . . . . . . 1891.6. Pressure Distribution (Real Component) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1921.7. Pressure Distribution (Imaginary Component) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1921.8. Applied Voltage .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1971.9. Displacement Time History .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1971.10. Pressure Time History .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1981.11. Modal Projection Technique for Damping Characterization .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

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1.12. Damping and Squeeze Stiffness Parameters for a Rectangular Plate .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2021.13. Fluidic Cross-Talk between Transverse and Rotational Motion .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2041.14. Time-Transient Response from Voltage Pulse .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2081.15. Slide Film Damping at Low and High Frequencies .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2101.16. Viscous Slide Film Element FLUID139 .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2111.17. Comb Drive Resonator .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2121.18. Displacement of Central Mass .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2121.19. Real and Imaginary Current .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

List of Tables

2.1. 2-D Solid Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.1. Boundary Conditions at Intersections .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.1. Command Family and GUI Path Used to Apply Loads .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2. Load Commands for a FLOTRAN Thermal Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1. Specifying Values for Time Steps .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605.2. Saving Analysis Results for Processing .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617.1. Interface Boundary Conditions .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.2. Element Qualities ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.3. Remeshing Limitations .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.4. Quality Requirements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979.1. Units for Thermal Quantities ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189.2. Energy Units for Incompressible Analyses with Viscous Heating .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1189.3. Units for the AIR Property Type .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199.4. Property types for Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1209.5. Property Database Format .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12810.1. Coordinate System Specification .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13412.1. Advection Scheme Defaults ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14612.2. SIMPLEF and SIMPLEN Performance Results ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1461.1. Loads Applicable in an Acoustic Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1721.2. Commands for Applying Loads in Acoustic Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1731.3. Load Step Options for a Harmonic Acoustic Analysis ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1751.1.Thin Film Fluid Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1851.2. Load Options for Thin Film Fluid Elements .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1901.3. Beam Model Results Considering Perforated Holes .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1911.4. Modal Damping Parameters for First Two Eigenfrequencies .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

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CFD

Chapter 1: Overview of FLOTRAN CFD Analyses

The ANSYS FLOTRAN derived product and the FLOTRAN CFD (Computational Fluid Dynamics) option to theother ANSYS products offer you comprehensive tools for analyzing 2-D and 3-D fluid flow fields. Using eitherproduct and the FLOTRAN CFD elements FLUID141 and FLUID142, you can achieve solutions for the following:

• Lift and drag on an airfoil

• The flow in supersonic nozzles

• Complex, 3-D flow patterns in a pipe bend

In addition, you can use the features of ANSYS and ANSYS FLOTRAN to perform tasks including:

• Calculating the gas pressure and temperature distributions in an engine exhaust manifold

• Studying the thermal stratification and breakup in piping systems

• Using flow mixing studies to evaluate potential for thermal shock

• Doing natural convection analyses to evaluate the thermal performance of chips in electronic enclosures

• Conducting heat exchanger studies involving different fluids separated by solid regions

The following FLOTRAN CFD analysis topics are available:1.1.Types of FLOTRAN Analyses1.2. About GUI Paths and Command Syntax

1.1. Types of FLOTRAN Analyses

You can perform these types of FLOTRAN analyses:

• Laminar or turbulent

• Thermal or adiabatic

• Free surface

• Compressible or incompressible

• Newtonian or Non-Newtonian

• Multiple species transport

These types of analyses are not mutually exclusive. For example, a laminar analysis can be thermal or adia-batic. A turbulent analysis can be compressible or incompressible.

To solve any analysis involving the flow of fluid, use either of the following:

Command(s): FLDATA1,SOLU,FLOW,TRUEGUI: Main Menu> Solution> FLOTRAN Set Up> Solution Options

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1.1.1. Laminar Flow Analysis

In these analyses, the velocity field is very ordered and smooth, as it is in highly viscous, slow-moving flows.The flow of some oils also can be laminar.

1.1.2. Turbulent Flow Analysis

Turbulent flow analyses deal with problems where velocities are high enough and the viscosity is low enoughto cause turbulent fluctuations. The two-equation turbulence model in ANSYS enables you to account forthe effect of the turbulent velocity fluctuations on the mean flow.

Laminar and turbulent flows are considered to be incompressible if density is constant or if the fluid expendslittle energy in compressing the flow. The temperature equation for incompressible flow neglects kineticenergy changes and viscous dissipation.

1.1.3. Thermal Analysis

Often, the solution for the temperature distribution throughout the flow field is of interest. If fluid propertiesdo not vary with temperature, you can converge the flow field without solving the temperature equation.In a conjugate heat transfer problem, the temperature equation is solved in a domain with both fluid andnon-fluid (that is, solid material) regions. In a natural convection problem, the flow results mainly or solelyfrom density gradients brought about by temperature variations. Most natural convection problems, unlikeforced convection problems, have no externally applied flow sources.

1.1.4. Compressible Flow Analysis

For high velocity gas flows, changes in density due to strong pressure gradients significantly influence thenature of the flow field. ANSYS uses a different solution algorithm for compressible flow.

1.1.5. Non-Newtonian Fluid Flow Analysis

A linear relationship between the stress and rate-of-strain cannot describe many fluid flows adequately. Forsuch non-Newtonian flows, the ANSYS program provides three viscosity models and a user-programmablesubroutine.

1.1.6. Multiple Species Transport Analysis

This type of analysis is useful in studying the dispersion of dilute contaminants or pollutants in the bulkfluid flow. In addition, you can use multiple species transport analysis for heat exchanger studies where twoor more fluids (separated by walls) may be involved.

1.1.7. Free Surface Analysis

Free surface analyses deal with problems involving a unconstrained gas-liquid surface. You can use this typeof analysis to solve two dimensional planar and axisymmetric problems such as flow over a dam and tanksloshing.

1.2. About GUI Paths and Command Syntax

Throughout this document, you will see references to ANSYS commands and their equivalent GUI paths.Such references use only the command name, because you do not always need to specify all of a command's

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Chapter 1: Overview of FLOTRAN CFD Analyses

arguments, and specific combinations of command arguments perform different functions. For completesyntax descriptions of ANSYS commands, consult the Command Reference.

The GUI paths shown are as complete as possible. In many cases, choosing the GUI path as shown will performthe function you want. In other cases, choosing the GUI path given in this document takes you to a menuor dialog box; from there, you must choose additional options that are appropriate for the specific task beingperformed.

For the thermal related analyses described in this guide, specify the material you will be simulating usingan intuitive material model interface. This interface uses a hierarchical tree structure of material categories,which is intended to assist you in choosing the appropriate model for your analysis. See Material Model In-terface in the Basic Analysis Guide for details on the material model interface.



1.2. About GUI Paths and Command Syntax


Chapter 2: The Basics of FLOTRAN Analysis

Before running a FLOTRAN analysis, you need to understand the behavior of the FLOTRAN elements, thesteps to running a FLOTRAN analysis, the tools available, and how to evaluate an analysis.

The following FLOTRAN analysis topics are available:2.1. Characteristics of the FLOTRAN Elements2.2. Considerations and Restrictions for Using the FLOTRAN Elements2.3. Overview of a FLOTRAN Analysis2.4. Files the FLOTRAN Elements Create2.5. Convergence and Stability Tools2.6.What to Watch For During a FLOTRAN Analysis2.7. Evaluating a FLOTRAN Analysis2.8.Verifying Results

2.1. Characteristics of the FLOTRAN Elements

The ANSYS FLOTRAN elements, FLUID141 and FLUID142, solve for 2-D and 3-D flow, pressure, and temper-ature distributions in a single phase viscous fluid. For these elements, the ANSYS program calculates velocitycomponents, pressure, and temperature from the conservation of three properties: mass, momentum, andenergy.

Table 2.1 2-D Solid Elements

DOFsShape or CharacteristicDi-

mens.

Element

Fluid velocity, pressure, temperature,turbulent kinetic energy, turbulent

Quadrilateral, four nodes or triangle,three nodes

2-DFLUID141

energy dissipation, multiple speciesmass fractions for up to six fluids

Fluid velocity, pressure, temperature,turbulent kinetic energy, turbulent

Hexahedral, eight nodes or tetrahed-ral, four nodes or wedge, six nodes

3-DFLUID142

energy dissipation, multiple speciesmass fractions for up to six fluids

or pyramid, five nodes; tetrahedraland hexahedral elements can becombined by pyramids

2.1.1. Other Element Features

Other features of the FLOTRAN elements include:

• A two-equation turbulence model for simulating turbulent flows.

• Derived results, such as Mach number, pressure coefficient, total pressure, shear stress, y plus at walls,and stream function for fluid analyses and heat flux and heat transfer (film) coefficient for thermalanalyses.

• Fluid boundary conditions, including velocities, pressures, and the turbulence quantities kinetic energyand kinetic energy dissipation rate. You may supply specific values of the turbulence quantities at the



inlet, but the FLOTRAN default boundary conditions suffice if the entrance is not close to the regionsof primary interest.

• Thermal boundary conditions, including temperature, heat flux, volumetric heat sources, and heattransfer (film) coefficient.

You can solve problems in Cartesian, cylindrical, polar, and axisymmetric coordinate systems. If a problemis axisymmetric, activating a swirl option allows you to calculate a velocity component normal to theaxisymmetric plane.

2.2. Considerations and Restrictions for Using the FLOTRAN Elements

The FLOTRAN elements have some limitations:

• You cannot change the problem domain during a single analysis.

• Certain features of the ANSYS program do not work with the FLOTRAN elements.

• You cannot use certain commands or menu paths with the FLOTRAN elements.

• If you use the ANSYS GUI, only the features and options called for in the FLOTRAN SetUp portion of themenus and dialog boxes will appear.

2.2.1. Limitations on FLOTRAN Element Use

When you are using the FLOTRAN elements, you should avoid using certain ANSYS features and commands,or if you do choose to use them, be aware that they have slightly different uses with the FLOTRAN elements.This does not mean that every command not listed here will work with FLOTRAN elements. ANSYS informs youif you try to issue a command that is invalid.

When using the FLOTRAN elements, keep the following points in mind:

• FLOTRAN elements cannot be combined with other elements except when using the ANSYS Multi-fieldsolver.

• The nodal coordinate system must be identical to the global coordinate system.

• The /CLEAR command does not destroy an existing FLOTRAN results file (Jobname.RFL ), thus preventingyou from inadvertently destroying a results file that took much time and effort to create. Existing Job-name.RFL file names will become Jobname.RFO file names if the number of nodes in the model haschanged since the Jobname.RFL file creation. You should remove unwanted results files at the systemlevel.

• In FLOTRAN, the CP command enforces periodic boundary conditions by coupling all degrees of freedombetween two nodes. You should not use the CP command to couple more than two nodes or to couplea subset of the degrees of freedom. You should only use this command to couple all degrees of freedomof one node on a periodic boundary face to one other node on another periodic boundary face.

You cannot couple nodes on the same element, and you may have difficulty coupling nodes on adjacentelements.

• The ADAPT macro does not work with FLOTRAN.

• You cannot use the ANTYPE command to invoke a transient analysis with the FLOTRAN element. (SeeFLOTRAN Transient Analyses (p. 59).)

• FLOTRAN analyses do not support automatic time stepping. For more information, see FLOTRAN Transient

Analyses (p. 59).


Chapter 2:The Basics of FLOTRAN Analysis

• If you specify nodal heat generation loads via commands BFCUM, BFDELE, or BFUNIF, ANSYS uses loadvalues specified with the BFE command instead.

• The commands CE, CECMOD, CEDELE, and CEINTF do not work with FLOTRAN.

• The CNVTOL command does not set convergence tolerances with FLOTRAN as it does for other analyses.For information about FLOTRAN convergence, see Deciding How Many Global Iterations to Use (p. 17).

• The symmetry and antisymmetry conditions that the DSYM command specifies are not appropriate forFLOTRAN. FLOTRAN Laminar and Turbulent Incompressible Flow (p. 23) explains how to specify flowsymmetry boundary conditions for FLOTRAN.

• FLOTRAN does not support angular acceleration vectors for rotating coordinate systems.

• In a FLOTRAN analysis, the command FLDATA4,TIME (rather than the DELTIM command) specifies atime step for a load step.

• For FLOTRAN, you cannot use the DESOL command or the PRESOL command to modify HEAT, FLOW,or FLUX nodal results.

• FLOTRAN does not permit extrapolation of integration point results to nodes (via the ERESX command).

• FLOTRAN does not allow you to generate elements through reflections. Although not recommended,FLOTRAN will execute properly if you generate reflected elements using a different element type andyou subsequently switch to the FLOTRAN element type.

• In FLOTRAN analyses, you cannot ramp loads via the KBC command. The FLOTRAN commandFLDATA4,TIME,BC, however, is analogous to the ANSYS command KBC, except that the default forFLOTRAN is a step change.

• Load case operations, such as those performed by the LCCALC, LCDEF, LCFACT, and LCFILE commands,are not allowed in a FLOTRAN analysis.

• Do not use the LSWRITE or LSSOLVE command in a FLOTRAN analysis. Use the SOLVE command tostart a FLOTRAN solution.

• The convergence tool invoked with the NCNV command does not apply to the FLOTRAN segregatedsolver.

• Do not use the NEQIT command, which defines the number of equilibrium iterations for a nonlinearsolution, in a FLOTRAN analysis.

• FLOTRAN requires the nodal and global Cartesian coordinate systems to be the same. Therefore, youcannot use the rotational fields on the N, NMODIF, and NROTAT commands.

• In a FLOTRAN analysis, the commands FLDATA2,ITER, FLDATA4,TIME, and FLDATA4A,STEP controlitems written to the results files (Jobname.RFL and Jobname.PFL

• FLOTRAN does not permit user programmable elements, such as those specified via the NSVR command.

• In a FLOTRAN analysis, the commands FLDATA2,ITER and FLDATA4,TIME control items written to thedatabase.

• The PRNLD command does not apply to FLOTRAN, because it does not store boundary conditions asprintable element nodal loads.

• Node reaction solutions, such as those produced by the PRRSOL command, are not available for FLOTRAN.

• The partial and predefined solution option (called by the PSOLVE command) does not apply to theFLOTRAN segregated solver.

• The TIME command, which associates boundary conditions with a particular time value, does not applyto FLOTRAN.



2.2.1. Limitations on FLOTRAN Element Use

• FLOTRAN analyses use the FLDATA1,SOLU command instead of the TIMINT command to specify tran-sient load steps.

• FLOTRAN analyses use the FLDATA4,TIME command instead of the TRNOPT command to specifytransient analysis options.

• The RESCONTROL command does not apply to FLOTRAN. Some of the functionality of RESCONTROL

is provided with the FLDATA32,REST command.

• For FLOTRAN, you cannot use the DK command to define DOF constraints at keypoints.

2.3. Overview of a FLOTRAN Analysis

A typical FLOTRAN analysis consists of several main steps:2.3.1. Determining the Problem Domain2.3.2. Determining the Flow Regime2.3.3. Creating the Finite Element Mesh2.3.4. Applying Boundary Conditions2.3.5. Setting FLOTRAN Analysis Parameters2.3.6. Solving the Problem2.3.7. Examining the Results

2.3.1. Determining the Problem Domain

You need to determine the proper domain for each problem you analyze. Locate the boundaries of theproblem where conditions are known. If you do not know precise conditions and must make assumptionsabout them, do not locate boundaries too close to the regions of greatest interest or near regions that havesteep gradients in the solution variables.

Sometimes, you may not realize that steep gradients occur too near the outlet or in some other region untilyou see the analysis results. Should this happen, you can re-analyze the problem with a different problemdomain.

For specific recommendations on determining problem domain, see the sections discussing the various flowphenomena.

2.3.2. Determining the Flow Regime

You need to estimate the character of the flow. The character is a function of the fluid properties, geometry,and the approximate magnitude of the velocity field.

Fluid flow problems that FLOTRAN solves will include gases and liquids, the properties of which can varysignificantly with temperature. The flow of gases is restricted to ideal gases. You must determine whetherthe effect of temperature on fluid density, viscosity, and thermal conductivity is important. In many cases,you can get adequate results with constant properties.

To assess whether you need the FLOTRAN turbulence model, use an estimate of the Reynolds number, whichmeasures the relative strengths of the inertial and viscous forces. (See FLOTRAN Laminar and Turbulent Incom-

pressible Flow (p. 23) for more information.)

To determine whether you need to use the compressible option, estimate the Mach number. (See FLOTRAN

Compressible Analyses (p. 103)) The Mach number at any point in the flow field is the ratio of the fluid speedand the speed of sound. At Mach numbers above approximately 0.3, consider using the compressible solutionalgorithm. At Mach numbers above approximately 0.7, you can expect significant differences between in-



compressible and compressible results. You may want to compare results from each algorithm for a repres-entative problem.

2.3.3. Creating the Finite Element Mesh

You will need to make assumptions about where the gradients are expected to be the highest, and youmust adjust the mesh accordingly. For example, if you are using the turbulence model, then the region nearthe walls must have a much denser mesh than would be needed for a laminar problem. If it is too coarse,the original mesh may not capture significant effects brought about through steep gradients in the solution.Conversely, elements may have very large aspect ratios with the long sides along directions with very lowgradients.

For the most accurate results, use mapped meshing. It more effectively maintains a consistent mesh patternalong the boundary. You can do this by issuing the command MSHKEY,1 (Main Menu> Preprocessor>

Meshing> Mesh> entity> Mapped).

In some cases, you may wish to use hexahedral elements to capture detail in high-gradient regions andtetrahedral elements in less critical regions. As described in Creating Transitional Pyramid Elements in theModeling and Meshing Guide you can instruct ANSYS to automatically create pyramid elements at the interface.

For flow analysis, especially turbulent, you should not use pyramid elements in the region near the wallsbecause it may lead to inaccuracies in the solution.

Wedge elements can be useful when a complex area can be easily meshed with triangles that are then ex-truded. For a quick solution, you can use wedge elements in the region near the walls. However, for accurateresults, you should use hexahedral elements in those regions.

Wedge elements are considered to be degenerate hexahedral elements. When using the ANSYS MeshTool(Main Menu> Preprocessor> Meshing> MeshTool) to sweep triangles into wedges, you must select Hexelements.

2.3.4. Applying Boundary Conditions

You can apply boundary conditions before or after you mesh the domain. Consider every model boundary.If a condition is not specified for a dependent variable, a zero gradient of that value normal to the surfaceis assumed.

You can change boundary conditions between restarts. If you need to change a boundary condition or acci-dentally omit it, you do not need to restart your analysis unless the change causes instabilities in the analysissolution.

2.3.5. Setting FLOTRAN Analysis Parameters

In order to use options such as the turbulence model or solution of the temperature equation, you mustactivate them. Specific items to be set, such as fluid properties, are a function of the type of flow problemat hand. Other sections in this document recommend parameter settings for various types of flow.

2.3.6. Solving the Problem

You can monitor solution convergence and stability of the analysis by observing the rate of change of thesolution and the behavior of relevant dependent variables. These variables include velocity, pressure, tem-perature, and (if necessary) turbulence quantities such as kinetic energy (degree of freedom ENKE), kineticenergy dissipation rate (ENDS), and effective viscosity (EVIS).



2.3.6. Solving the Problem

An analysis typically requires multiple restarts.

2.3.7. Examining the Results

You can postprocess output quantities and examine the results in the output files. Use your engineeringjudgment when examining the results to evaluate the plausibility and consistency of the overall analysisapproach, how specific properties are used, and the conditions imposed.

Note

Results tracking via the NLHIST command is not available with FLOTRAN analyses.

2.4. Files the FLOTRAN Elements Create

You perform most fluid flow analyses in ANSYS by stopping the analysis job and then restarting it multipletimes. Often, analysts change parameters such as relaxation factors or turn options (such as solution of thetemperature equation) on or off between restarts. Each time you continue a job, the ANSYS program appendsdata to all of the files that its FLOTRAN element creates.

The following list explains all files that a FLOTRAN element creates. A discussion of the residual file appearsat the end of this section.

• The results file, Jobname.RFL , contains nodal results.

• The print file, Jobname.PFL , contains input convergence monitors, and inlet/outlet summaries.

• The wall file, Jobname.RSW, contains wall shear stress and Y-plus information.

• The residual file, Jobname.RDF , contains the nodal residuals.

• The debug file, Jobname.DBG, contains information about algebraic solver performance.

• The results backup file, Jobname.RFO , contains a copy of the results file data.

• The restart file, Jobname.CFD , contains FLOTRAN data structures.

• The domain file, (jobname.pv_0000 n) for use by ICEM CFD's PV3 postprocessing visualization tool.

2.4.1. The Results File

The results of a FLOTRAN analysis are not stored in the ANSYS database automatically. At the end of everysolution, the ANSYS program adds a set of results to the results file, Jobname.RFL . You have some controlover the content of the results file and how often ANSYS updates it. The defaults given in the descriptionof the FLDATA5,OUTP command in the Command Reference reflect FLOTRAN's determination of what theresults file should store based on the options you choose.

The ANSYS program is flexible about how many sets of results you can store for a steady-state FLOTRANanalysis. Keeping sets of results from earlier executions has advantages: you can compare changes that oc-curred between sets of results, and you can continue an analysis from its earlier stages using different optionsor relaxation parameters.

The ANSYS program stores a set of results when you begin an analysis (before the first iteration), then storesresults again when one of the termination criteria is reached. Between those events, you can append theresults to the Jobname.RFL file. Storing intermediate sets of results enables you to continue the analysisfrom an earlier stage with different options and features activated, for example to enhance stability.



We recommend that you use ANSYS' overwrite frequency option because it allows you to periodically storeand update a temporary set of results. Using this option ensures that a useful set of results will exist shouldyou need to restart an analysis after a power failure or other system interruption. The next regularly scheduledoutput of results overwrites the temporary results set. You can accomplish the same thing by instructingANSYS to append data to the results file more often; however, this method inflates the size of the resultsfile.

To set the overwrite frequency, use either of the following:

Command(s): FLDATA2,ITER,OVER,ValueGUI: Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl

To set the append frequency, use either of the following:

Command(s): FLDATA2,ITER,APPE,ValueGUI: Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl

2.4.2. The Print File (Jobname.PFL)

The Jobname.PFL file contains a complete record of all FLOTRAN input parameters, including propertiesand solution options. This information is recorded each time a SOLVE is issued so as to provide a completeaccount of the analysis history. In addition, all convergence monitors are recorded for all active values. Aresults summary, showing maximum and minimum values of each property and degree of freedom, isprovided at a user-determined frequency. Average values are also recorded. The mass flow boundaries areidentified and a mass balance is calculated. Finally, all heat transfer information is summarized for all heattransfer and heat sources.

2.4.3. The Nodal Residuals File

The nodal residuals file, Jobname.RDF , shows you how well the current solution is converged. At everystage in the solution procedure, the flow, property, and temperature fields are used to calculate coefficientmatrices and forcing functions for each DOF. If a solution is converged completely, these matrices and forcingfunctions will produce the same velocity field used to generate them and the residuals of the matrix equationwill be very small. You must request at least one global iteration to obtain a nodal residual file.

If a solution oscillates, however, the magnitude of the residuals shows where the maximum errors are. (Themain diagonal entries of the matrix normalize the residuals.) This normalization enables you to comparedirectly the value of the DOF and the value of its residual.

To calculate residuals for every active degree of freedom and output them to the residuals file, do either ofthe following:

Command(s): FLDATA5,OUTP,RESI,TRUEGUI: Main Menu> Solution> FLOTRAN SetUp> Additional Out> Residual File

To read the residuals file, either issue the FLREAD command (Main Menu> General Postproc> FLOTRAN

2.1A). The residuals are postprocessed with the label associated with the DOF (for instance, TEMP or PRESfor the temperature or pressure residuals).

2.4.4. The Restart File

By default, FLOTRAN calculates data structures at the beginning of a restart of an analysis. These calculationsmay take considerable time for large models. To avoid recalculation, you can opt to have FLOTRAN store



2.4.4.The Restart File

the data structures in the Jobname.CFD file. FLOTRAN creates this file from information in the ANSYSdatabase (but the file is not required for restarts).

To write to or read from the Jobname.CFD file, use either of the following methods before the restart:

Command(s): FLDATA32,REST,RFIL,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Restart Options> CFD Restart File

You can toggle the RFIL state on (TRUE) or off (FALSE). If is on, ANSYS reads the restart file when FLOTRANbegins to execute. If no restart file exists, one will be created.

If you are restarting an analysis with updated boundary conditions, you must overwrite an existing .CFDfile in order to use the new conditions. To overwrite the file, use either of the following methods:

Command(s): FLDATA32,REST,WFIL,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Restart Options> CFD Restart File

This will cause FLOTRAN to create a new restart file during the next load step, and automatically sets theRFIL state to False. After the restart that has created the new file completes, issue theFLDATA32,REST,RFIL,TRUE command so that subsequent restarts use the new Jobname.CFD restart file.

2.4.5. The Domain File

Domain files are used by ICEM CFD's PV3 postprocessor visualization tool. In addition to nodal results thesefiles contain information to define the finite element model, including node locations, element topology,element connectivity, and family information concerning predefined ANSYS components. They also containload step, substep, cumulative iteration, and time point values.

2.4.6. Restarting a FLOTRAN Analysis

You can restart the FLOTRAN analysis from any set of results in the Jobname.RFL file or from a different.RFL file. You can base the restart on the set number (Label = NSET), the global iteration number (Label= ITER), the load step/subset numbers (Label = LSTP), or the transient analysis time (Label = TIME). Youdetermine the restart criteria by doing either of the following:

• Issue the command FLDATA32,REST,Label,Value. Specify one of the labels listed above in place ofLabel. The Value argument causes values associated with the other criteria to be zeroed. Once invoked,the behavior is turned off in the database by setting all the criteria to zero. If you are restarting from adifferent results file, you also need to specify the filename, extension, and directory of that file.

• Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Restart Options> Restart/Iteration

(or Restart/Load step, Restart/Set, etc.)

If you specify invalid criteria, ANSYS notifies you and (if the program is operating in batch mode) terminatesthe analysis.

When you restart an analysis, ANSYS copies the original results file to the file Jobname.RSO and places therestart point, all previous results sets, and all subsequent results sets in the new Jobname.RFL file. If theValue input on the FLDATA32,REST command is negative, creation of the Jobname.RSO file is blocked.FLOTRAN uses the absolute value of the number specified for Value.

If a results file name is entered in the Fname field of the FLDATA32,REST command, FLOTRAN interpolatesthose results onto the current mesh in the database, regardless of whether or not the mesh has changed.This causes the convergence monitors to start again from zero. This restart is different than a restart withouta file name specification. However, the results quickly converge to the original solution.



2.5. Convergence and Stability Tools

2.5.1. Relaxation Factors

The ANSYS program offers several tools to help with convergence and solution stability. The Theory Reference

for the Mechanical APDL and Mechanical Applications explains how they are implemented.

The relaxation factor is the fraction of the change between the old solution and the newly calculated solutionthat is added to the old solution, giving the results for the new global iteration. The relaxation factors forevery component must be between 0.0 (resulting in no update to the degree of freedom or property) and1.0 inclusive. You set relaxation factors via either of the following:

Command(s): FLDATA25,RELX,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> DOF Relaxation

Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> DOF Relaxation

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation

Note

See the description of the FLDATA25,RELX command in the Command Reference for lists of degreeof freedom and property component names.

2.5.2. Inertial Relaxation

Inertial relaxation of the equation set for a DOF provides diagonal dominance to make a solution stable.Hypothetically, when a solution is converged in the absence of round off-error, the inertial relaxation applieddoes not affect the value of the answer. However, in real situations, some round off-error always occurs, sothe inertial relaxation may affect your solution.

You can apply inertial relaxation to the momentum equations (MOME), turbulence equations (TURB), thepressure equation (PRES), and the temperature equation (TEMP). To do so, use either of these methods:

Command(s): FLDATA26,STAB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms

The inertial relaxation factor is in the denominator of the term added, so smaller values have a greater effect.

Typical useful values range between 1.0 (mild) and 1.0 x 10-7 (severe).

2.5.3. Modified Inertial Relaxation

Modified inertial relaxation adds a local positive value to the diagonal term to guarantee a positive diagonal.

You can apply modified inertial relaxation to the momentum equations (MOME), turbulence equations (TURB),and the temperature equation (TEMP). To do so, use either of these methods:

Command(s): FLDATA34,MIR,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization



2.5.3. Modified Inertial Relaxation

A larger modified inertial relaxation factor gives a more robust scheme, but it may yield a slower convergence.The recommended range is 0.1 to 1.0.

You should consider inertial relaxation and modified inertial relaxation to be mutually exclusive.

2.5.4. Artificial Viscosity

Artificial viscosity smooths the velocity solution in regions of steep gradients. It has proven useful in aidingconvergence of compressible problems and in smoothing velocity solutions in incompressible problemswith distributed resistances. For incompressible analyses, you should keep the artificial viscosity within anorder of magnitude of the effective viscosity.

To apply artificial viscosity, use either of these methods:

Command(s): FLDATA26,STAB,VISC,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms


2.5.5. DOF Capping

DOF capping allows you to prevent variables from going out of boundaries you specify. You can limit thevelocities, pressure, and temperature degrees of freedom (VY, VY, VZ, PRES, TEMP). To do this, use either ofthese methods:

Command(s): FLDATA31,CAPPGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Results Capping

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Results Capping

Velocity capping eliminates the effects of velocity spikes on properties, which may occur in the early stagesof convergence. Capping is especially suited to compressible analyses, where velocity spikes can cause kin-etic energy terms great enough to produce negative static temperatures. When a degree of freedom iscapped, ANSYS prints a message along with the convergence monitor printout.

The pressure value calculated by the solution of the pressure equation is capped, not the relaxed value.Therefore, if you introduce pressure capping upon restarting an analysis, pressure values may still be outsidethe caps.

Capping applies to relative values of pressure and absolute values of temperature.

You should cap the total temperature when performing compressible thermal analyses. It will help ensurenegative properties do not enter the calculations.

Caution

When velocities are capped, conservation of mass may not be enforced.

2.5.6. The Quadrature Order

You have control over the quadrature order. In axisymmetric problems, the quadrature order automaticallyis set to 2 upon solution. This is because quadrature orders of 2 produce more accurate results for problemswith irregularly shaped elements. The quadrature order is also automatically set to 2 upon solution for 3-Dproblems using cylindrical coordinates.



If you notice anomalous results near a region of skewed hexahedral elements, reset the quadrature orderto 2. There might be a problem with the results when the included angles of the hexahedra exceed 120degrees.

You can change the quadrature order for momentum diffusion or source, pressure diffusion or source,thermal diffusion or source, turbulent diffusion or source, using either of the following:

Command(s):

FLDATA30,QUAD,Label,Value

(Label is the element integral to change quadrature for, and Value is the number of integration points).

GUI:

Main Menu> Preprocessor> FLOTRAN Set Up> Mod Res/Quad Ord> CFD Quad Orders

Main Menu> Solution> FLOTRAN Set Up> Mod Res/Quad Ord> CFD Quad Orders

For more information on quadrature order, refer to the description of the FLDATA30,QUAD command inthe Command Reference.

2.6. What to Watch For During a FLOTRAN Analysis

This section describes what happens in a FLOTRAN analysis and how to evaluate how the analysis is proceed-ing.

2.6.1. Deciding How Many Global Iterations to Use

A FLOTRAN analysis is nonlinear and uses a sequential solution, so the first thing you must do is decide howmany global iterations should be executed. A global iteration is the solution, in sequence, of all relevantgoverning equations followed by any fluid property updates that are needed.

In a transient simulation, a time step loop exists around the global iteration loop.

During a global iteration, the ANSYS Multiphysics program or ANSYS FLOTRAN obtains approximate solutionsto the momentum equation and uses them as forcing functions to solve a pressure equation based onconservation of mass. ANSYS uses the resulting pressures to update the velocities so that the velocity fieldconserves mass. If you request it, the ANSYS program solves the temperature equation and updates temper-ature dependent properties.

Finally, if you have activated the turbulence model, the equations are solved and the program uses theturbulent kinetic energy and dissipation rate to calculate the effective viscosity and thermal conductivity.Effective viscosity and thermal conductivity replace, respectively, the laminar viscosity and thermal conduct-ivity to model the effect of turbulence on the mean flow.

To specify how many global iterations a FLOTRAN analysis should execute, use either of the following:

Command(s): FLDATA2,ITER,EXEC,Value (Value is the number of iterations.)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl

Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl

2.6.2. Convergence Monitors

As a FLOTRAN simulation proceeds, ANSYS calculates convergence monitors for each degree of freedom everyglobal iteration. Convergence monitors are computed for velocities (VY, VY, VZ), pressure (PRES), temperature



2.6.2. Convergence Monitors

(TEMP), turbulent kinetic energy (ENKE), kinetic energy dissipation rate (ENDS), and any active speciestransport equations (SP01-SP06).

The convergence monitors are a normalized measure of the solution's rate of change from iteration to iter-ation. Denoting by the general field variable, Φ, any DOF, the convergence monitor is defined as follows:

ConvMon=− −

=

=

∑

∑

φ φ

φ

ik

ik

i

N

ik

i

N

1

1

1

The convergence monitor represents the sum of changes of the variable calculated from the results between

the current kth iteration and the previous (k-1)th iteration, divided by the sum of the current values. Thesummation is performed over all n nodes, using the absolute values of the differences.

Available in both batch and interactive sessions, the Graphical Solution Tracking (GST) feature displays thecomputed convergence monitors while the solution is in process. Be default, GST is ON for interactive sessionsand OFF for batch runs. To turn GST on or off, use either of the following:

Command(s): /GST

GUI: Main Menu> Solution> Load Step Opts> Output Ctrls> Grph Solu Track

Figure 2.1 (p. 18) shows two typical GST displays:

Figure 2.1 Convergence Monitors Displayed by the GST Feature



(a) Steady-state simulation, (b) Transient simulation

In Figure 2.1 (p. 18) (b), a plot of a transient FLOTRAN solution, each "spike" on the plot indicates the beginningof a new time step.

After perhaps some initial fluctuations, convergence monitors will decrease as the analysis approachesconvergence. How small the numbers become depends on several factors, such as:

• Complexity of the geometry

• Adequacy of the finite element mesh in regions with steep gradients

• The severity of the turbulence levels, indicated by the flow Reynolds number

• Development of the flow near outlet boundaries

Points to remember when using graphical solution tracking include:

• The GST feature is available for FLOTRAN analyses and also for structural, thermal, and electromagneticanalyses containing nonlinearities. For information about using GST to track convergence in non-FLOTRANanalyses, see the Thermal Analysis Guide, the Low-Frequency Electromagnetic Analysis Guide, and theStructural Analysis Guide.

• GST can display up to ten curves at the same time. (Your model can include more than ten DOFs, butonly the first ten will be displayed.)

• When the GST begins its plotting, ANSYS displays a dialog box with a STOP button. You can stop thesolution at any time by clicking on this button. To restart it, issue SOLVE or choose Main Menu>

Solution> Run FLOTRAN.

• The time label which is positioned above the graph reveals the time at the last iteration.

2.6.3. Stopping a FLOTRAN Analysis

You can choose a target value for terminating a FLOTRAN analysis, based on the convergence monitors foreach degree of freedom falling below a certain value. To specify these values, use the following:

Command(s): FLDATA3,TERM,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


See the Command Reference for the default values. Termination checks do not include inactive degrees offreedom or degrees of freedom set to a negative value.

The analysis must satisfy convergence criteria for all active degrees of freedom, or complete the specifiednumber of global iterations requested. FLOTRAN terminates on the first condition satisfied. For information onterminating transient analyses, see FLOTRAN Transient Analyses (p. 59).

To stop a FLOTRAN batch or background job in progress, place a file named Jobname.ABT in the subdir-ectory from which the ANSYS job has been executed. The first line of this file should contain the word "ter-minate," and should be left-justified. On Windows systems, you should also add a blank line at the end ofthe Jobname.ABT file. FLOTRAN looks for the Jobname.ABT file during every global iteration. If it findsthe file and reads the word "terminate," it will finish that global iteration and terminate normally, writingthe results to the Jobname.RFL file and extending the Jobname.PFL file.



2.6.3. Stopping a FLOTRAN Analysis

2.6.4. Pressure Results

For locked tetrahedral elements (those at a corner where two walls meet) there is a slight pressure anomaly.ANSYS takes those elements out of the solution domain because all the nodes have boundary conditions.The solution is correct in the domain. Use hexahedral elements to avoid this pressure anomaly.

2.7. Evaluating a FLOTRAN Analysis

The two basic questions an analyst must answer are:

1. When is the analysis completed?

2. Has it been done correctly?

These questions are interrelated, since convergence may not be achieved it you have not set up and executedthe analysis correctly.

If you have set the input parameters and boundary conditions correctly, the analysis is complete when theconvergence monitors for all variables stop decreasing and the average, maximum, and minimum values ofthe solution variables no longer increase or decrease. There is no guarantee, however, that you will achievea single exact answer because nature does not guarantee that a single exact answer exists. Oscillatoryproblems (for example, vortex shedding behind a cylinder) may not yield stationary results from a steady-state or a transient solution algorithm. You may wish to continue executing the analysis to verify whethera solution has a stable or a fluctuating nature.

The ANSYS program stores the average, minimum, and maximum values of the solution variables in the fileJobname.PFL . This file also records the FLOTRAN input plus the convergence monitors which have beencalculated. The results summary includes all the DOF, as well as laminar and effective properties. You determinehow often ANSYS issues the results summary by using one of these methods:

Command(s): FLDATA5,OUTP,SUMF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Additional Out> RFL Out Derived

Main Menu> Solution> FLOTRAN Set Up> Additional Out> RFL Out Derived

The Value argument is the number of global iterations that pass before ANSYS issues the next resultssummary.

You may also want to map your results onto a path through your model. See Mapping Results onto a Pathin the Basic Analysis Guide for more information on reviewing results along a path.

2.8. Verifying Results

You, the analyst, are responsible for verifying results. If your FLOTRAN analysis produces unexpected results,take the actions listed below. You can accomplish many of these actions at the beginning of the analysis.ANSYS creates a Jobname.PFL file and checks inputs even if the number of iterations executed is zero.

1. Check the mass balance printed as part of the results summary. Internal checks will determine if anymass flow can potentially cross a model boundary. Boundary conditions admitting mass flow are:

• Specified velocity boundaries

• Specified pressure boundaries

• Unspecified boundaries (These can result if you inadvertently omit a boundary condition.)

The ANSYS program tabulates the number of inlets/outlets, which should correspond to expectations.



2. Check boundary conditions within ANSYS to ensure that they are accurate.

3. Check that you specified the properties correctly and that they can vary with temperature and pressureif necessary. The results summary in the Jobname.PFL file is a convenient place to check this.

4. Check that the length units used to build the model are consistent with those used in specifyingproperties.

5. In some cases, you need to verify that equations associated with the options chosen are solved correctly(for instance, the pressure equation in compressible flow).

6. If the unexpected result of your analysis is divergence, the finite element mesh may not have sufficientresolution, or significant gradients may exist near outlets. To resolve this, you may need to use conver-gence aids such as relaxation. Later sections in this document discuss various relaxation techniques.

7. If you get a diverged solution for a particular variable, you can re-initialize that variable to a singlevalue and continue. To do so, use one of these methods:

Command(s): FLDATA29,MODVGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Mod Res/Quad Ord> Modify Results

Main Menu> Solution> FLOTRAN Set Up> Mod Res/Quad Ord> Modify Results



2.8.Verifying Results


Chapter 3: FLOTRAN Laminar and Turbulent Incompressible Flow

A laminar or turbulent flow analysis calculates the flow and pressure distribution in a 2-D or 3-D geometry.Flow problems require you to specify density and viscosity. Problems may be internal or external in nature.For internal flows, wall or symmetry planes bound the flow (for example, flow in a pipe), except for the inletand outlet boundaries. (Figure 3.1 (p. 23) shows an example). The boundaries of external problems generallyare either far-field velocity or pressure boundary conditions. The flow surrounding an airfoil is an externalflow (See Figure 3.2 (p. 23)).

Figure 3.1 Internal Flow

Wall

Wall

Figure 3.2 External Flow

Free Stream Conditions

Free Stream Conditions

The distinction between incompressible and compressible flow lies in both the equation of state and thesolution algorithm.

• In an incompressible flow, density variations can drive the flow only through gravitational acceleration.Temperature changes cause variations of density.



• In a compressible flow, the density changes caused by pressure variations significantly affect the mo-mentum and temperature equations.

In any event, the incompressible algorithm can measure flow of an ideal gas, complete with small densitychanges due to pressure. See FLOTRAN Compressible Analyses (p. 103) for more information.

The following FLOTRAN laminar and turbulent incompressible flow topics are available:3.1. Activating the Turbulence Model3.2. Meshing Requirements3.3. Flow Boundary Conditions3.4. Strategies for Difficult Problems3.5. Example of a Laminar and Turbulent FLOTRAN Analysis

3.1. Activating the Turbulence Model

The distinction between laminar and turbulent flow lies in the ratio of the inertial transport to the viscoustransport. As this ratio increases, instabilities develop and velocity fluctuations begin to occur. A turbulentmodel accounts for the effect of these fluctuations on the mean flow by using an increased viscosity, theeffective viscosity, in the governing equations. The effective viscosity is the sum of the laminar viscosity(which is a property of the fluid) and turbulent viscosity (which is calculated from a turbulence model).

µe = µ + µt

Generally, the more turbulent the flow field, the higher the effective viscosity.

3.1.1. The Role of the Reynolds Number

The dimensionless Reynolds number measures the ratio of inertial and viscous forces to help determinewhether or not the turbulence model should be activated. The Reynolds number is defined in terms of theproperties of the fluid, a characteristic velocity, and a characteristic dimension:

RE =ρ

µVLc

The density ρ (mass/length3) and absolute viscosity µ (mass/length-time) are properties of the fluid. For in-ternal flow problems, the characteristic dimension is the hydraulic diameter, defined as:

L =D =4 (Cross-Sectional Flow Area)

Wetted Perimeterc h

For example, the hydraulic diameter of a pipe is simply the diameter. As a general guideline for internal flowproblems such as flow in pipes, the turbulence model should usually be activated if the Reynolds numberis in excess of about 2300.

For an external flow problem, such as the flow over an airfoil, the characteristic length is a parameter suchas the length of the airfoil (wing cross section for a 2-D analysis).

For flow over a flat plate, the dimension is the length along the plate from the leading edge, with thetransition to turbulence occurring at a Reynolds number of approximately 500,000.

For more information, see Turbulence in the Theory Reference for the Mechanical APDL and Mechanical Applic-

ations.



3.1.2. Determining Whether an Analysis Is Turbulent

Determining if an analysis is laminar or turbulent is your responsibility. What happens if turbulence is notactivated when it should be, or vice versa? What are the indications and the consequences?

If turbulence is needed but not activated, the analysis probably will diverge. If this occurs, the momentumand pressure convergence parameters will approach 1.0 and the values of velocities and pressure will becomevery large. You should start over with the turbulence model activated.

In some cases, convergence occurs even without the turbulence model. This can happen if no geometricalfeatures such as bends disturb the flow. Physically, some flows retain laminar characteristics unless they areslightly disturbed in some fashion.

Conversely, although the turbulence models are not low Reynolds number models and do not "automatically"resort to laminar behavior at low Reynolds numbers, in such cases the turbulence models predict low valuesof effective viscosity. If the final average effective viscosity is less than five times greater than the laminarvalue, you should rerun the case without the turbulence model and evaluate the differences.

You can postprocess the effective viscosity with the label EVIS. It is also tabulated in the results summaryoutput provided in the Jobname.PFL file. Therefore, you can observe the average behavior of effectiveviscosity as the solution proceeds. You also can postprocess it to see its variation throughout the flow field.

3.1.3. Turbulence Ratio and Inlet Parameters

Be aware that when an analysis begins, the effective viscosity initializes as a multiple of the laminar value.This initialization occurs whether a turbulence model is or is not active. The default value of this multiple(also called the turbulence ratio) is 1000; a reasonable value for most turbulent analyses. The algorithm cal-culates lower or higher values as conditions dictate. However, the accuracy of the initial estimate affectshow long the program takes to compute the final value.

To set the turbulence ratio, use either of these methods:

Command(s): FLDATA24,TURB,RATI,Value

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

The two-equation turbulence models require boundary conditions for the turbulent kinetic energy (ENKE)and turbulent kinetic energy dissipation rate (ENDS) at an inlet. If known values are available at the inlet,you can specify ENKE and ENDS, Otherwise, you must specify an inlet intensity (ININ), which is the ratio ofthe fluctuating velocity to the inlet velocity, and an inlet scale factor (INSF), which is the ratio of a lengthscale inlet region to the hydraulic diameter of the inlet. ININ and INSF default to 0.01.

To set the inlet intensity and inlet scale factor, you use either of the following:

Command(s): FLDATA24,TURB,ININ,Value FLDATA24,TURB,INSF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

3.1.4. Turbulence Models

FLOTRAN offers several turbulence models:3.1.4.1. Standard k-epsilon Model (default)3.1.4.2. Zero Equation Turbulence Model (ZeroEq)3.1.4.3. Re-Normalized Group Turbulence Model (RNG)3.1.4.4. k-epsilon Model Due to Shih (NKE)3.1.4.5. Nonlinear Model of Girimaji (GIR)



3.1.4.Turbulence Models

3.1.4.6. Shih, Zhu, Lumley Model (SZL)3.1.4.7. k-omega Turbulence Model3.1.4.8. Shear Stress Transport Model (SST)

Turbulence modeling is activated by either of the following:

Command(s): FLDATA1,SOLU,TURB,TGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution Options

Main Menu> Solution> FLOTRAN Setup> Solution Options

To select a model, you use either of the following:

Command(s): FLDATA24,TURB,MODL,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence Model

Main Menu> Solution> FLOTRAN Setup> Turbulence> Turbulence Model

Normally, the Standard k-ε Model is the first model to apply. It usually provides a realistic picture of the flow.It is fine for the analysis of turbulent flow in pipes and channels. However, it over predicts the amount ofturbulence in a number of situations. For example, the flow in a converging nozzle undergoes significantnormal strain and the Standard k-ε Model over predicts the amount of turbulence. The resulting kinetic energyis over predicted, and the resulting effective viscosity prevents simulation of shock waves in some cases.

In general, the RNG, NKE, GIR, and SZL turbulence models produce significantly more realistic and reliableresults in regions of large strain. This is particularly important for cases where the flow is strongly acceleratedor decelerated (e.g. a converging nozzle) or where there is significant separation or recirculation (e.g. a ductthat goes through a 180 degree change of direction). Other situations where the Standard k-ε Model encoun-ters difficulties include flows with stagnation points.

The RNG, NKE, GIR, and SZL turbulence models control the excess turbulence by applying adjustments toC µ and the source term of the dissipation equation. The adjustments are made in accordance with the localrate of strain.

The k-ω turbulence model has the advantage near the walls to accurately predict the turbulence lengthscale in the presence of an adverse pressure gradient. The k-ω model is much more sensitive to the free-stream turbulence levels than the k-ε model. The Shear Stress Transport model (SST) combines the k-ωmodel near the wall and the k-ε model away from the wall to overcome the deficiencies of both models.

See the Command Reference and Turbulence in the Theory Reference for the Mechanical APDL and Mechanical

Applications for more information on the models.

3.1.4.1. Standard k-epsilon Model (default)

The Standard k-ε Model, the Zero Equation Turbulence Model, and the k-ω Model are the simplest models.The other models are all extensions of the Standard k-ε Model and the k-ω Model. The Standard k-ε Modelis the default model.

To select the Standard k-ε Model, you use either of the following:

Command(s): FLDATA24,TURB,MODL,1GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence Model


Cµ, C1, C2, SCTK, and SCTD are Standard k-ε Model constants that are defined as follows:



Cµ - Value is the k-ε turbulence model constant

µρ

εµt Ck

=2

which is used in the update of the turbulent viscosity.

C1 - Value is the k-ε turbulence model C1 constant. It is the multiplier of the shear rate generation term

of the turbulent kinetic energy dissipation rate equation.

C2 - Value is the k-ε turbulence model C2 constant. It is the multiplier of the dissipation source term in the

turbulent kinetic energy dissipation rate equation.

SCTK - Value is the Schmidt number for the turbulent kinetic energy. The diffusion term in the turbulentkinetic energy equation is divided by this factor.

SCTD - Value is the Schmidt number for the kinetic energy dissipation rate. The diffusion term in the dis-sipation rate equation is divided by this factor.

To set the Standard k-ε Model constants Cµ, C1, C2, SCTK, and SCTD, you use either of the following:

Command(s): FLDATA24,TURB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence Model


The following five wall parameters control turbulence wall modeling. The wall parameters apply for all tur-bulence models except the Zero Equation Turbulence Model.

KAPP - Value is the law of the wall constant. It is the slope of the plot of normalized shear velocity (u+)

versus the nondimensionalized distance from the wall (y+). See Near-Wall Treatment in the Theory Reference

for the Mechanical APDL and Mechanical Applications for details.

EWLL - Value is the law of the wall constant. It is related to the y intercept value for a plot of normalized

shear velocity (u+) versus the nondimensionalized distance from the wall (y+). See Near-Wall Treatment inthe Theory Reference for the Mechanical APDL and Mechanical Applications for more details.

WALL - Value is the choice of wall conductivity model. The default model is the Van Driest model (Value= VAND), used most often for high Prandtl number fluids. The second choice is the Spalding model (Value= SPAL), applicable to low Prandtl number fluids. The third choice is the Equilibrium model (Value = EQLB).The equilibrium model is also automatically invoked for the wall viscosity by this command.

VAND - Value is the constant A in the Van Driest wall conductivity model, as described in Equation 7–61and Near-Wall Treatment in the Theory Reference for the Mechanical APDL and Mechanical Applications.

TRAN - Value is the magnitude of y+ marking the outer boundary of the laminar sublayer. Used only forthe Equilibrium Wall model.

To set the wall parameters KAPP, EWILL, WALL, VAND and TRAN, you use either of the following:

Command(s): FLDATA24,TURB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Wall Parameters

Main Menu> Solution> FLOTRAN Setup> Turbulence> Wall Parameters




The following three buoyancy terms control buoyancy modeling. The buoyancy terms apply for all turbulencemodels except the Zero Equation Turbulence Model.

BUC3 - Value is the k-ε buoyancy model constant. A value of zero means that there is no contribution tothe turbulent kinetic energy dissipation rate equation. The default value of one is appropriate for stablethermally stratified flows. A value of zero is appropriate for unstable thermally stratified flows.

BUC4 - Value is the k-ε multiplier applied to the buoyancy term of the turbulent kinetic energy equation.A value of 1.0 is appropriate for the calculation of stable thermally stratified flows. The default value is zero.

BETA - Value is β, the coefficient of thermal expansion

βρ

ρ=

∂∂

1

T

This term is used in the buoyancy terms of the k-ε model.

To set the buoyancy terms BUC3, BUC4, and BETA, you use either of the following:

Command(s): FLDATA24,TURB,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Buoyancy Terms

Main Menu> Solution> FLOTRAN Setup> Turbulence> Buoyancy Terms

See Standard k-epsilon Model in the Theory Reference for the Mechanical APDL and Mechanical Applications

and the Command Reference for more information.

3.1.4.2. Zero Equation Turbulence Model (ZeroEq)

The Zero Equation Turbulence Model (ZeroEq) is the simplest and fastest turbulence model. It applies toproblems with fairly simple geometry and flow characteristics. The model does not give accurate results ifthere is significant separation or recirculation.

To select the Zero Equation Turbulence Model, you use either of the following:



The Zero Equation Turbulence Model contains an automatic calculation of the length scale or you can specifythe length scale. Generally, the turbulence ratio can be set to 2.0 when you are using the Zero EquationTurbulence Model.

See Zero Equation Model in the Theory Reference for the Mechanical APDL and Mechanical Applications andthe Command Reference for more information.

3.1.4.3. Re-Normalized Group Turbulence Model (RNG)

The Re-Normalized Group Turbulence Model (RNG) is effective where the geometry has a strong curvature(e.g., a duct that goes through a 180 degree change in direction. If you have tried the SZL Model and theresults are unsatisfactory, it is generally recommended that you try the RNG Model.

To select the RNG Model, you use either of the following:

Command(s): FLDATA24,TURB,MODL,3



GUI: Main Menu> Preprocessor> FLOTRAN Setup> Turbulence> Turbulence Model


To set the constants for the RNG Model, you use either the FLDATA24A,RNGT command or the foregoingGUI.

The RNG Model is an extension of the Standard k-ε Model. Seven constants are assigned values. The Cµ, C1,

C2, SCTK, and SCTD constants are assigned values that are separate from the Standard k-ε Model. The following

two constants are added:

BETA -Value is the RNG model constant, β∞

ETAI -Value is the asymptotic value of the strain rate parameter eta.

Inlet parameters and wall parameters are the same as the Standard k-ε Model.

See RNG Turbulence Model in the Theory Reference for the Mechanical APDL and Mechanical Applications andthe Command Reference for more information.

3.1.4.4. k-epsilon Model Due to Shih (NKE)

The k-ε Model due to Shih (NKE) features a variable Cµ term which helps to reduce the excess normal strain

terms in the Standard k-ε Model. The NKE model also employs a different dissipation source term than theStandard k-ε Model.

The NKE and GIR models are recommended for rotating flows.

To select the NKE Model, you use either of the following:



To set the constants for the NKE Model, you use either the FLDATA24B,NKET command or the foregoingGUI.

The NKE Model is an extension of the Standard k-ε Model. Four constants are assigned values. The C2, SCTK,

and SCTD constants are assigned values that are separate from the Standard k-ε Model. The following constantis added:

C1MX - Value is the maximum allowed value of the C1 constant in the turbulent kinetic energy dissipation

rate equation.


See NKE Turbulence Model in the Theory Reference for the Mechanical APDL and Mechanical Applications andthe Command Reference for more information.

3.1.4.5. Nonlinear Model of Girimaji (GIR)

The Nonlinear Model of Girimaji (GIR) is suggested for cases with secondary vortices in the flow. The GIRand NKE models are recommended for rotating flows.

To select the GIR Model, you use either of the following:






To set the constants for the GIR Model, you use either the FLDATA24C,GIRT command or the foregoing GUI.

The GIR Model is an extension of the Standard k-ε Model. Seven constants are assigned values. The SCTK,and SCTD constants are assigned values that are separate from the Standard k-ε Model. The following fiveconstants are added:

G0 - Value is the C10

constant.

G1 - Value is the C11

constant.G2 - Value is the C2 constant.

G3 - Value is the C3 constant.

G4 - Value is the C4 constant.


See GIR Turbulence Model in the Theory Reference for the Mechanical APDL and Mechanical Applications andthe Command Reference for more information.

3.1.4.6. Shih, Zhu, Lumley Model (SZL)

The SZL Model is simpler than the NKE and GIR models. It produces the lowest level of turbulence. The SZLmodel is numerically efficient, but in some cases the resulting low effective viscosity has an adverse effecton stability. Generally, if the SZL model does not give satisfactory results, it is recommended that you trythe RNG model.

If conditions of large strain exist in the flow field, you may want to try the SZL Model after trying the RNG,NKE or GIR models. If the SZL Model gives significantly different results, it is recommended that you refinethe mesh in the regions where the turbulence field is strongly altered.

To select the SZL Model, you use either of the following:



To set the constants for the SZL Model, you use either the FLDATA24D,SZLT command or the foregoingGUI.

The SZL Model is an extension of the Standard k-ε Model. Five constants are assigned values. The SCTK, andSCTD constants are assigned values that are separate from the Standard k-ε Model. The following threeconstants are added:

SZL1 - Value is the numerator constant used in the calculation of Cµ. It is the Aszl1 constant.

SZL2 - Value is the denominator constant used in the calculation of Cµ. It is the Aszl2 constant.

SZL3 - Value is the strain rate multiplier. It is the Aszl3 constant.


See SZL Turbulence Model in the Theory Reference for the Mechanical APDL and Mechanical Applications andthe Command Reference for more information.



3.1.4.7. k-omega Turbulence Model

The k-ω model is one of the simplest turbulence models. It provides better modeling of the turbulentboundary layer than the standard k-ε model, but is more sensitive to the free-stream turbulence levels.

To select the k-ω Model, you use either of the following:



To set the constants for the k-ω Model, use either the FLDATA24E,SKWT command or the foregoing GUI.

The k-ω Model solves for the ω equation rather than the ε equation in the standard k-ε Model. Four constantsare assigned values. The SCTK constant is an assigned value that is separate from the Standard k-ε Model.The following three constants are added:

SCTW - Value is the Schmidt number for the specific dissipation rate.BETA - Value is the BETA factor.GAMA - Value is the GAMMA factor.


See Standard k-omega Model in the Theory Reference for the Mechanical APDL and Mechanical Applications

and the Command Reference for more information.

3.1.4.8. Shear Stress Transport Model (SST)

The SST Model combines advantages of both the Standard k-ε Model and the k-ω Model. It automaticallyswitches to the k-ω Model in the near region and the Standard k-ε Model away from the walls.

To select the SST Model, you use either of the following:



To set the constants for the SST Model, use the FLDATA24F,SST1, FLDATA24G,SST1 and FLDATA24H,SST2commands, or the foregoing GUI. Similar to the k-ω Model, the SST Model solves for the ω equation ratherthan the ε equation in the Standard k-ε Model. Nine constants are assigned values. The SCTK1 and the SCTK2

constants are assigned values that are separate from the Standard k-ε Model. The following seven constantsare added.

CLMT - Value is the turbulent production clip factor.SCTW1 - Value is the Schmidt number for the specific dissipation rate in the k-ω regime.

SCTW2 - Value is the Schmidt number for the specific dissipation rate in the k-ε regime.

BETA1 - Value is the BETA factor in the k-ω regime.

BETA2 - Value is the BETA factor in the k-ε regime.

GAMA1 - Value is the GAMMA factor in the k-ω regime.

GAMA2 - Value is the GAMMA factor in the k-ε regime.





See SST Turbulence Model in the Theory Reference for the Mechanical APDL and Mechanical Applications andthe Command Reference for more information.

3.2. Meshing Requirements

The meshing requirements for turbulence are more restrictive than those for laminar flow. The most importantareas obviously are those with the higher gradients, in particular the regions near walls.

Structured meshes, as contrasted with free meshes, can provide more consistent representation at the walls.Figure 3.3 (p. 32) and Figure 3.4 (p. 32) compare the structured and unstructured meshes for a region nearthe wall.

Figure 3.3 Structured Mesh

This mesh was produced with MSHAPE,0,2D and MSHKEY,1 commands.

Figure 3.4 Unstructured Mesh

This mesh was produced with MSHAPE,1,2D and MSHKEY,0 commands.

You can evaluate the adequacy of the mesh near the walls. Applying the turbulence model near walls involves

the "Log Law of the Wall," the relationship between a nondimensionalized distance from the wall Y+, andthe log of a nondimensionalized velocity in a region near the wall. This law calculates a near wall viscosity

that is consistent with experimentally determined velocity profiles near the wall. Values of Y+ are relevantonly for wall nodes and are available for postprocessing (YPLU).



Optimum values of Y+ are between approximately 30 and 1000. If the pressure is decreasing in the direction

of flow, values up to 5000 are acceptable. FLOTRAN handles the case where Y+ is less than 30 for the nearwall node by assuming that the near wall node is in the laminar sublayer or the overlap region. In the formercase, the near wall viscosity is simply the laminar value.

If Y+ is very small, perhaps below 1, more elements than necessary are being used to resolve the flow distri-

bution field. If Y+ is greater than 5000, decrease the mesh spacing near the wall.

Caution

Use enough elements to resolve the flow field in the regions of interest. You should use at leastfour elements to span the cross sections of long thin channels. Use more than four elementswhere thin channels connect to larger regions.

3.3. Flow Boundary Conditions

Each boundary of the problem domain requires treatment. You specify some combination of DOF (VX, VY,VZ and PRES) at the boundary types listed below. (If suitable values are available, you can specify turbulentkinetic energy (ENKE) and turbulent kinetic energy dissipation rate (ENDS) at an inlet.) The derivative of alldependent variables normal to the surface is zero if you apply no conditions at the boundary surface.

To set DOF constraints at nodes, use either of the following:

Command(s): D

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> boundary condition type

You can set boundary conditions on the solid model using any of the following:

Command(s): DA and DL

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> boundary condition type>

On Areas

Main Menu> Solution> Define Loads> Apply> boundary condition type> On Areas

Main Menu> Preprocessor> Loads> Define Loads> Apply> boundary condition type> On

Lines

Main Menu> Solution> Define Loads> Apply> boundary condition type> On Lines

This enables you to redo the analysis with a different mesh, without reapplying boundary conditions on anodal basis. These commands or GUI paths allow you to specify the condition on the endpoints of a line orthe edge of an area.

Take care to ensure that the proper conditions are applied at intersecting boundaries. You have control overwhether or not boundary conditions are applied at the ends of lines or at the edges of areas. A nonzerovelocity component at the end of a line or at the edge of an area will not replace an existing zero velocitycondition at the associated nodes. Where a wall intersects an inlet, the wall condition will automaticallyprevail.

If you apply new (and different) boundary conditions to a solid model of a finite element mesh, you shoulddelete existing nodal boundary conditions before transferring the new loads.

Specified Flow: You specify all velocity components at the boundary. Use this method to specify a flow atan inlet. Knowledge of the mass flow at the inlet requires you to know the density.




Specified Pressure: Typically, you apply a relative pressure (usually zero) as an outlet boundary condition.In the absence of gravity and a rotating reference frame, the absolute pressure is the sum of the FLOTRAN(relative) pressure and the reference pressure. See the Theory Reference for the Mechanical APDL and Mechan-

ical Applications for a more complete discussion of pressure. A problem may also be pressure driven, inwhich case one of the pressure boundaries is an inlet.

Note

If significant gradients are calculated near a boundary, a mass imbalance can occur. This is dueto the implied condition of fully developed flow for a constant pressure boundary. If the flow hasnot fully developed, FLOTRAN is forced to adjust it across the last row of elements to satisfy theboundary condition. Occasionally, this adjustment may cause a mass imbalance.

To prevent this from occurring, you can add a development length to the exit. This addition does not actuallyneed to match the physical flow geometry. You can subtract the pressure drop in this "chimney" to obtainthe desired pressure drop. The pressure drop in the "chimney" will vary over its full cross section. You willhave to choose a representative value of the pressure drop to match the desired outlet conditions. You willnot know this pressure drop, of course, until after you examine the results from the chimney. You can optto apply an exit pressure profile, based on these results, to the original geometry.

You can calculate the required length of the chimney (L) using the characteristic diameter (D) from the de-velopment length formula:

Laminar flow: L/D ~ 0.06 Re

Turbulent flow: L/D ~ 4.4 Re1/6

Typically, a chimney 20 to 25 diameters long will be sufficient. Although the mesh in this region may becoarse, you should avoid drastic changes in element size by using a size ratio in the chimney. The importantfeature is the chimney length, not the number of nodes in it.

Symmetry Boundary: The velocity component normal to the boundary is specified as zero. Leave all otherdegrees of freedom unspecified.

Generalized Symmetry Boundary Conditions: You can also apply generalized symmetry boundary conditions.Velocity components are set tangential to the symmetry surface if the ALE formulation is not activated. Theyare set equal to the mesh velocity if the ALE formulation is activated. To apply generalized symmetryboundary conditions, use one of the following commands or the GUI equivalent:

D,NODE,ENDS,-1DL,LINE,AREA,ENDS,-1,Value2DA,AREA,ENDS,-1,Value2

With one exception, if any velocity component is specified at the same boundary, the generalized symmetryboundary conditions are overwritten. In a 2-D swirl problem, specification of a velocity component VZ doesnot overwrite generalized symmetry conditions.

Stationary Wall: This is also referred to as a no-slip condition. All the velocity components are set to zero.

Moving Wall: Specify the velocity component tangent to the wall and set all other velocity components tozero. As a flag to indicate this is a moving wall, set the turbulent kinetic energy to -1 on a moving wall. Thisspecification is as a flag only; it does not affect the performance of the wall turbulence model. If you areusing the GUI, indicate a moving wall when specifying the velocities.



Unspecified Boundary: In this case, neither the relative pressure nor the velocities are known. The mostcommon application for this is at downstream boundaries in compressible supersonic flow.

Periodic Boundary: Conditions are unknown but identical at two boundaries. You select the nodes at oneboundary and then issue the macro PERI,DX, DY, DZ, where DX, DY, and DZ are the offsets of the secondboundary from the first. The offsets are input in the established FLOTRAN coordinate system. The meshes at

the two boundaries must be identical.

Intersections: At the intersection of surfaces where two different boundary conditions are applied, eitherthe boundary conditions are merged or one takes precedence over the other. The following table providesguidance on what boundary conditions are applied at the intersection.

Table 3.1 Boundary Conditions at Intersections

ActionIntersecting Boundary

2

Intersecting Boundary

1

Overwrite inflow with wallWall:VX, VY, VZ = 0

Inflow:VX, VY, VZ values specified

Combine inflow with symmetrySymmetry:VX or VY or VZ = 0


Enforce inflow condition, not outflowOutflow:P = 0


Combine symmetry and outflowOutflow:P = 0

Symmetry:VX or VY or VZ = 0

Overwrite symmetry with the wallWall:X, VY, VZ = 0

Symmetry:VX or VY or VZ = 0

Combine wall and outflow conditionsOutflow:P = 0

Wall:VX, VY, VZ = 0

Combine the generalized symmetry and out-flow conditions

Outflow:P = 0

Generalized Symmetry

Note

Inflow, symmetry , and wall boundary conditions all overwrite generalized symmetry conditions.

Inlet Values: If you activate the turbulence model, boundary conditions are required. The ANSYS programsupplies default values based on the inlet velocity and a scale factor. Given an inlet velocity magnitude V,the inlet kinetic energy is specified as:

k [(ININ)V]inlet2=

3

2

The default value of the factor ININ is 0.01, corresponding to a level of turbulence of 1 percent at the inlet.The inlet value of the kinetic energy dissipation rate ε is calculated from:




ε µinlet

INSF L=

C k

3

2

( )

The INSF value is a user-controlled scale factor. To specify the factors ININ and INSF, use either of the followingmethods:

Command(s): FLDATA24,TURB,ININ,Value and FLDATA24,TURB,INSF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

Main Menu> Solution> FLOTRAN Set Up> Turbulence> Turbulence Param

You can set specific values of the turbulent kinetic energy (ENKE) or the dissipation rate (ENDS) using eitherthe FLDATA24 command or the menu paths in Determining Whether an Analysis Is Turbulent (p. 25).

Occasionally, you may wish to activate the turbulence model for the case, but deactivate it for certain regions.To deactivate the turbulence model in regions, set the kinetic energy (ENKE) to zero and the dissipation rate(ENDS) to 1.0. It is never valid to set the dissipation rate to zero, and FLOTRAN prohibits it. ENDS will be setto 1.0, if ENKE is set to zero.

Wall Roughness:

The FLOTRAN default condition is smooth walls. To specify wall roughness values, you must use the equilib-rium wall turbulence model. You activate it using the FLDATA24,TURB,WALL,EQLB command.

To apply a uniform wall roughness in length units to all walls, you can use the FLDATA24,TURB,KS,Valuecommand. In addition to being the actual roughness, the KS parameter determines the regime of roughness(smooth, transitional, or fully rough). The default value of 0.0 implies a smooth wall.

You can also apply an empirical dimensionless factor (CKS) between 0.5 and 1.0 that specifies the degreeof nonuniformity of the surface. The default value of 0.5 means that the roughness signified by KS is uniformlydistributed. Higher values increase the roughness losses without changing the flow regime implied by thevalue of KS. You can use the FLDATA24,TURB,CKS,Value command to specify this factor.

The following two methods are available if you have surfaces that require different roughness values.

The first method utilizes real constants for all the wall elements. You apply suitable KS and CKS values tothe near wall elements as real constants. A different real constant set will exist for each set of wall roughnesses.Note that roughness constants applied to elements that are not near wall will be ignored. Also, any KS andCKS values specified by the FLDATA24,TURB command will be ignored.

The second method is for cases where most of the surfaces have the same roughness condition and only afew are different. First, set the values appropriate for most of the surfaces with the FLDATA24,TURB command.Then use real constants to apply roughnesses to the walls that have different conditions. The real constantswill overwrite the FLDATA24,TURB values. Note that if the same value of CKS is applied to all the surfaces(as is typical), it can be controlled with the FLDATA24,TURB command and the real constant can be omitted.

3.4. Strategies for Difficult Problems

The most common problems are divergence or oscillation of the pressure and/or velocity field.

The following strategies have proven helpful in getting difficult turbulent problems to converge.

1. Activate the turbulence option if you have not done so.



Turbulence modeling is activated by either of the following:

Command(s): FLDATA1,SOLU,TURB,TGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution Options


2. Use a mapped mesh if a free mesh has given poor results. Resolve the boundary layer so that the value

of Y+ is less than 5000.

To set the Y+ output option, use the following:

Command(s): FLDATA5,OUTPUT,YPLU,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Additional Out> RFL Out Derived

Main Menu> Solution> FLOTRAN Setup> Additional Out> RFL Out Derived

3. Set the turbulence inertial relaxation factor to 1.0. Values as low as 1.0-2 may help. (For incompressibleflow problems, you may not need to vary this factor.)

To set the turbulence inertial relaxation factor, use the following:

Command(s): FLDATA26,STAB,TURB,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms


4. Use pressure and momentum relaxation factors less than 0.5. If values as low as 0.2 do not help, goinglower probably will not help either.

To set the pressure and momentum relaxation factors, use the following:

Command(s): FLDATA25,RELX,PRES,Value FLDATA25,RELX,VX (or VY, VZ),ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> DOF Relaxation

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> DOF Relaxation

5. Begin the problem with a higher turbulence ratio (meaning a higher initial effective viscosity). Do not

set values for this parameter, which takes effect only at problem startup, above 1.0 x 107. The ratio setcontrols the initial effective viscosity no matter when you activate the turbulence model.

To set the turbulence ratio, use either of these methods:

Command(s): FLDATA24,TURB,RATI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

Main Menu> Solution> FLOTRAN Set Up> Turbulence> Turbulence Param

6. After initializing with the correct properties, solve the problem with a higher viscosity and the turbulencemodel turned off. When the flow field is partially converged, the turbulence model is activated. Youmay need to reduce the relaxation factor of the effective viscosity to 0.1 or 0.0 for some global iterationsto allow partial convergence of the turbulence equations. Refer to the foregoing strategies for commandinformation.

7. Difficulties can involve large changes in properties due to large fluctuations in pressure or temperature.Preventing property variations early in the analysis (until the large fluctuations calm down) can stabilizethe analysis significantly.

You also can invoke velocity capping to prevent large values of velocities or pressures. This is particularlyuseful in compressible analyses, where velocity spikes can cause negative static temperatures.

To implement velocity capping, use either of the following methods:



3.4. Strategies for Difficult Problems

Command(s): FLDATA31,CAPP,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Results Capping

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Results Capping

If you use the FLDATA31 command, Label represents a capping parameter such as VELO (velocity),or TEMP (temperature). Value is either the capping flag (T or F) or the capping parameter value.Pressure capping applies to relative values of pressure. Temperature capping applies to absolute valuesof temperature.

8. Problems involving pyramid, wedge or in particular tetrahedral element shapes may require tighterconvergence of the pressure equation. Values as low as 1.E-18 may be required(FLDATA21,CONV,PRES,1.E-18). You should reduce the convergence criterion until, from one globaliteration to the next, the number of iterations required to solve the equation varies by less than 10percent (as per the Jobname.DBG file).

9. The solution of the pressure equation may affect the mass balance. The mass balance may be incorrect(as per the Jobname.PFL file) if large aspect ratio elements are near significant flow area changes.Mass imbalances may also occur if inlet or outlet regions are too coarsely meshed or if the flow tendsto exit at an angle at outlets.

10. If FLOTRAN displays a message stating that the coefficient matrix has a negative diagonal and thesolution is probably divergent, try turning on modified inertial relaxation in the momentum equationor turbulence equation. Set the Value between 0.1 and 1.0. To achieve a faster convergence rate, usethe smallest Value possible.

To set the turbulence inertial relaxation factor, use the following:

Command(s): FLDATA34,MIR,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization


11. If you notice anomalous results for 3-D problems, you should increasing the quadrature order to 2.

12. Specifying the Streamline Upwind/Petrov-Galerkin (SUPG) approach for momentum may help conver-gence. Specifying the SUPG approach for temperature may also yield more accurate energy solutionsand hence more accurate energy balances. For more information on the SUPG approach, see Advection

Discretization Options (p. 161).

3.5. Example of a Laminar and Turbulent FLOTRAN Analysis

Before you begin the laminar/turbulent example, note the following:

• The example problem is only one of many possible FLOTRAN analyses. It does not illustrate everytechnique you might use in a FLOTRAN analysis, and is intended only to show the kinds of tasks aFLOTRAN analysis typically requires.

• You can use many techniques in a FLOTRAN analysis that are not shown in this problem. For example,you can integrate pressure and shear stress on an airfoil to determine the lift and drag forces (see thedescription of the INTSRF command in Integrating Surface Results in the Basic Analysis Guide).

• The values you enter in this example are specific values for this example only. The characteristics of theindividual problem you are solving dictate what values you should specify for a particular FLOTRANanalysis.



Chapter 4: FLOTRAN Thermal Analyses

In a thermal analysis, you solve the temperature equation to determine temperature. Even if the temperatureitself is not important, the variation of fluid properties with temperature may be important enough to warranta thermal analysis.

In addition to calculating a temperature field, a thermal analysis provides heat fluxes at problem boundariesand heat transfer coefficients based on an assumed bulk or ambient temperature.

You activate solution of the temperature equation via one of the following:

Command(s): FLDATA1,SOLU,TEMP,TRUEGUI: Main Menu> Solution> FLOTRAN Set Up> Solution Options

FLOTRAN automatically includes viscous heating for compressible flows. For information on activating viscousheating for incompressible flows, see Forced Convection, Temperature Dependent Properties (p. 43) and thedescription of the FLDATA1 command in the Command Reference.

The following FLOTRAN thermal analysis topics are available:4.1. Meshing Requirements4.2. Property Specifications and Control4.3.Thermal Loads and Boundary Conditions4.4. Solution Strategies4.5. Heat Balance4.6. Surface-to-Surface Radiation Analysis Using the Radiosity Method4.7. Examples of a Laminar,Thermal, Steady-State FLOTRAN Analysis4.8. Example of Radiation Analysis Using FLOTRAN (Command Method)4.9.Where to Find Other FLOTRAN Analysis Examples

4.1. Meshing Requirements

The ANSYS program has no formal criteria for evaluating the finite element mesh. However, thermal gradientsare often extremely high near thermal boundaries, especially heat flux boundaries. Therefore, the meshshould usually be denser near thermal boundaries.

4.2. Property Specifications and Control

In addition to density and viscosity, thermal flow problems require the specification of thermal conductivityand specific heat. You must determine whether or not fluid properties should vary with temperature.

To set properties for non-fluid regions, use one of these methods:

Command(s): MP

GUI: Main Menu> Preprocessor> Loads> Load Step Opts> Other> Change Mat Props

Main Menu> Preprocessor> Material Props> Material Models> CFD> Conductivity> Isotropic

Main Menu> Preprocessor> Material Props> Material Models> CFD> Specific Heat

Main Menu> Solution> Load Step Opts> Other> Change Mat Props



4.3. Thermal Loads and Boundary Conditions

The ANSYS program supports six types of thermal boundary conditions:

1. Constant temperatures

2. Constant heat fluxes

3. Applied heat transfer (film) coefficients with associated ambient temperatures

4. Ambient radiation with associated surface emissivities and ambient temperatures

5. Surface-to-surface radiation with associated emissivities and enclosure number.

6. Adiabatic boundaries (the default condition)

In addition, constant volumetric heat sources may be located in both fluid and non-fluid regions.

The applicable commands are summarized below.

You can apply your boundary conditions via TABLE type array parameters (see Applying Loads Using TABLEType Array Parameters in the Basic Analysis Guide). You can also apply your boundary conditions usingfunction boundary conditions (see "Using the Function Tool" in the Basic Analysis Guide).

You can define a TABLE type array parameter to apply your boundary conditions in a FLOTRAN analysis.Attempting to use tabular boundary conditions in a FLOTRAN analysis will create erroneous results.

4.3.1. Applying Loads

The table below lists the loads you can apply in a thermal FLOTRAN analysis.

Table 4.1 Command Family and GUI Path Used to Apply Loads

GUI PathCmd

Fam-

ily

CategoryLoad Type

Main Menu> Solution> Define Loads> Apply>

Temperature

DConstraintsTemperature(TEMP)

SFSurfaceLoads

Convection (CONV),Heat Flux (HFLU),


Thermal> Convection

Radiation (RAD), Main Menu> Solution> Define Loads> Apply>

Thermal> Heat FluxSurface-to-surface radiation (RDSF) Main Menu> Solution> Define Loads> Apply>

Thermal> Ambient Rad


Thermal> Surface Rad


Fluid/CFD> Heat Generat

BFBodyLoads

Heat GenerationRates (HGEN)

In an analysis, you can apply, remove, operate on, or list loads.



4.3.1.1. Applying Loads Using Commands

The table below lists all the commands in detail you can use to apply loads in a FLOTRAN thermal analysis.

Table 4.2 Load Commands for a FLOTRAN Thermal Analysis

Apply

Settings

OperateListDeleteAp-

ply

EntitySolid

Model or

FE

Load Type

--DLISTDDELEDNodesFinite Ele-ment

Temperature

---SFLDELESFLLinesSolid Mod-el

Convection,Heat Flux, Ambi-ent Radiation, or SFGRADSFTRANSFALISTSFADELESFAAreasSolid Mod-

elSurface-to- sur-face Radiation

--SFLISTSFDELESFNodesFinite Ele-ment

-SFS-

CALE

SFELISTSFEDELESFEEle-ments

Finite Ele-ment

-SFS-

CALE

SFELISTSFEDELESFEEle-ments

Finite Ele-ment

Heat GenerationRates

-BFTRANBFLLISTBFLDELEBFLLinesSolid Mod-el

-BFTRANBFALISTBFADELEBFAAreasSolid Mod-el

-BFTRANBFVLISTBFVDELEBFVVolumesSolid Mod-el

--BFLISTBFDELEBFNodesFinite Ele-ment

-BFS-

CALE

BFELISTBFEDELEBFEEle-ments

Finite Ele-ment

Note

You must use tabular boundary conditions if you are applying tapered heat flux or convectionloads.

4.3.1.2. Applying Loads Using the GUI

You access all operations except List through a series of cascading menus. From the Solution Menu, youchoose the operation (Apply, Delete, etc.), then the load type (temperature, heat flux, etc.), and then theobject (node, line, or area) to which you are applying the load.

For example, to apply a temperature load to lines, follow this GUI path:

Main Menu> Solution> Define Loads> Apply> Thermal> Temperature> On Lines

To list loads, follow this GUI path:



4.3.1. Applying Loads

Utility Menu> List> Loads> load type

4.3.1.3. Solutions

The following list describes what is known and what is calculated as a function of the type of boundaryspecified.

• For temperature boundary conditions, heat flux and heat transfer coefficient are calculated.

• For heat flux boundary conditions, temperature and heat transfer coefficient are calculated.

• For ambient radiation boundary conditions, temperature and heat flux are calculated.

• For surface-to-surface radiation boundary conditions, temperature and heat flux are calculated.

• For heat transfer boundary conditions, temperature and heat flux are calculated.

• For adiabatic boundary conditions, temperature is calculated.

When you apply a heat transfer (film) coefficient, you also specify an associated ambient temperature. TheANSYS program uses this along with the surface temperature to calculate the heat flux at that boundary.

You specify heat flux and heat transfer coefficients at external model boundaries. You cannot specify themat general internal surfaces. You can specify heat flux and heat transfer coefficients at internal boundaryfaces (such as fluid/solid interface surfaces), but FLOTRAN will issue a warning because they are probablyincorrect. In a standard FLOTRAN analysis the heat transfer at a fluid/solid boundary is a desired result, nota boundary condition. If you wish to apply a heat flux or a heat transfer coefficient, you should apply it atthe external solid material boundary, or at the edge of the fluid region without modeling the solid materialin the analysis. If you specify a film coefficient or a heat flux at an internal fluid/solid interface, FLOTRANinterprets it to be a line/area heat source or sink. You can prescribe temperatures anywhere.

In cases where you must calculate the heat transfer coefficient at a surface, ANSYS uses the surface temper-ature along with the bulk temperature you specify using either of the following methods:

Command(s): FLDATA14,TEMP,BULK,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions

Main Menu> Solution> FLOTRAN Set Up> Flow Environment> Ref Conditions

If the analysis is compressible, boundary condition temperatures are in terms of total temperature, and thetemperature equation is formulated and solved in terms of total temperature.

The FLOTRAN ambient radiation load simulates radiation heat transfer to space at a constant temperature.You specify the constant temperature with the SF command. You specify the Stefan-Boltzmann constant

with the STEF command (defaults to 0.119E-10 Btu/hr/in2/ °R4). The form factor is 1.0 by assumption.

Since radiation can pass through a fluid region and impact on a solid, you can apply the ambient radiationload on a fluid/solid interface, as well as on external model boundaries. In this case, you should apply thesurface load to either the fluid or solid element faces, or the solid model entity defining the interface. If youapply the load to more than one face, FLOTRAN applies the boundary conditions on only one face and issuesa message that it skipped duplicate boundary conditions.

4.4. Solution Strategies

The most efficient way to solve thermal-flow problems depends on the degree to which the fluid propertiesdepend on the temperature.



4.4.1. Constant Fluid Properties

In this case, the flow solution does not depend at all on the temperature field and can be converged withoutactivating the temperature equation solution.

Once the flow solution is complete, the temperature equation become linear. You can then solve it in oneglobal iteration after you set the relaxation factor for temperature to 1 using either method shown below:

Command(s): FLDATA25,RELX,TEMP,1.0GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap/DOF Relaxation

Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap/Prop Relaxation

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap/DOF Relaxation

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap/Prop Relaxation

This is often best accomplished with a semi-direct solution algorithm.

See FLOTRAN CFD Solvers and the Matrix Equation (p. 139) for more information.

The flow equations need not be solved during the solution of the temperature equation. Executing twoglobal iterations should result in a very small change, if any, in the answer during the second calculation.This will be reflected in a large decrease in the convergence monitors for temperature in the second iteration.

4.4.2. Forced Convection, Temperature Dependent Properties

The flow pattern will be a mild function of the temperature field. You can choose to solve the temperatureequation every global iteration or converge the flow field calculations before activating solution of thetemperature equation. In the latter case, you will still need to solve the flow and temperature equationstogether to refine the flow field with the property variations. If difficulties with the temperature equationare encountered early in the solution, it is then best to start over and partially converge the flow solutionbefore allowing the properties to vary with temperature.

For incompressible flows, viscous heating is generally not important for cases with low Prandtl numbers orlow to moderate velocities. However, you should turn on viscous heating whenever the Prandtl number isgreater than 2 or the velocities are high (e.g., greater than 100 m/s in air). FLOTRAN automatically includesviscous heating for compressible flows. To include viscous heating for incompressible flows, use one of thefollowing:

Command(s): FLDATA1,SOLU,IVSH,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options

Main Menu> Solution> FLOTRAN Set Up> Solution Options

For information on the energy units required for thermal quantities when an incompressible analysis includesviscous heating, refer to Fluid Property Types (p. 117).

4.4.3. Free Convection, Temperature Dependent Properties

In this case, the driving force for the flow is the density change brought about by temperature variations.You must turn on both options.

You also must do the following:

• Specify acceleration due to gravity, using one of the following:

Command(s): ACEL



4.4.3. Free Convection,Temperature Dependent Properties

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Gravity

Main Menu> Solution> FLOTRAN Set Up> Flow Environment> Gravity

• Activate the variable density option using one of the following:

Command(s): FLDATA13,VARY,Label,TRUE (Label = fluid property)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid properties

Main Menu> Solution> FLOTRAN Set Up> Fluid properties

Buoyancy property types, which use a constant pressure to evaluate the density from the ideal gas law areprovided for AIR. (See Specifying Fluid Properties for FLOTRAN (p. 117).) Pressure fluctuations are thus preventedfrom causing instabilities in density calculations. Natural convection cases converge slowly, and may bemore stable if the TDMA algorithm is used for pressure and temperature. The number of sweeps used maybe set to Number of Nodes/10, but should be at least 100.

4.4.4. Conjugate Heat Transfer

When the thermal properties of the non-fluid material are several orders of magnitude different from thoseof the fluid, this is called an ill-conditioned conjugate heat transfer problem. In this situation, the TDMAmethod probably will not yield useful results, no matter how many sweeps you specify. You access the TDMAmethod using either of the following:

Command(s): FLDATA18,METH,TEMP,1GUI: Main Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> Temp Solver CFD

The Conjugate Residual method offers more functionality and requires little more memory than the Tri-Di-agonal Matrix Algorithm (TDMA) method. To access it, use either of the following:


You can control several parameters, such as convergence criteria and the number of search vectors used,to enhance performance. (See the discussion of FLDATA18 in the Command Reference for more informationabout these parameters.) However, the conjugate residual method, although fairly fast, is not suited for dif-ficult problems.

A more robust choice for solving ill-conditioned heat transfer problems is the Preconditioned ConjugateResidual method, which requires much more memory than either the TDMA or Conjugate Residual methods.The PCR method allows you to control the number of search vectors used, up to a maximum of 30. To useit, use either of the following:


Note

For nodes connected only to solid nodes, the value stored in the Jobname.RFL file under thedensity (DENS) label is the product of the density and specific heat.

You can evaluate performance of the Conjugate Residual and Preconditioned Conjugate Residual methodsby looking at the Jobname.DBG file (described in FLOTRAN CFD Solvers and the Matrix Equation (p. 139)).

The most robust, but most memory-intensive, method for solving conjugate heat transfer problems is thePreconditioned Generalized Minimum Residual method. You can access it via either of the following:




The Preconditioned Generalized Minimum Residual (PGMR) solution method is the default choice for tem-perature.

Although the same user controls exist for the PGMR method as for the PCCR solver, the default values aredifferent. For PGMR, the least restrictive convergence criterion allowed is 1.E-10. If you try to use a less re-strictive convergence criterion, FLOTRAN will change it to 1.E-10. A convergence criterion as low as 1.E-20may be necessary for some problems. In addition, you should use at least 12 search vectors, and FLOTRANensures this. For the PGMR solver, 12 search vectors is the default and the allowable range is 12 to 20.

FLOTRAN non-fluid elements support both temperature dependence and orthotropic variation. That is, KXX,KYY, and KZZ can assume different values and temperature variations. FLOTRAN considers conductivity asan element quantity, evaluated at the quadrature points in the element. However, in fluid elements, FLOTRANconsiders thermal conductivity to be a nodal quantity.

To specify the variable and orthotropic conductivities, you use the following commands or GUI paths:

Command(s): MP or MPDATA

GUI: Main Menu> Preprocessor> Loads> Load Step Opts> Other> Change Mat Props

Main Menu> Preprocessor> Material Props> Material Models> CFD> Conductivity> Orthotropic

Main Menu> Solution> Load Step Opts> Other> Change Mat Props

Main Menu> Preprocessor> Loads> Load Step Opts> Other> Change Mat Props

Note

Thermal analysis problems having variable thermal conductivity are nonlinear and require multipleiterations to solve. Variable solid thermal conductivities are not relaxed.

For a conjugate heat transfer problem, it is wise to obtain an initial temperature solution before solving thecoupled energy/momentum equations. To achieve the temperature solution, use the following:

Command(s): FLDATA1,SOLU,FLOW,FGUI: Main Menu> Solution> FLOTRAN Set Up> Solution Options

Command(s): FLDATA1,SOLU,TEMP,TGUI: Main Menu> Solution> FLOTRAN Set Up> Solution Options

Command(s): FLDATA25,RELX,TEMP,1.0GUI: Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> DOF Relaxation

Command(s): FLDATA2,ITER,EXEC,1GUI: Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl

Command(s): FLDATA18,METH,TEMP,3GUI: Main Menu> Solution> FLOTRAN Set Up> CFD Solver Contr> TEMP Solver CFD

In the above steps, an initial temperature solution is obtained from a solution of the heat conductionequation.

FLOTRAN can calculate film coefficients at walls in conjugate heat transfer problems. Two algorithms areavailable for this purpose: the conductivity matrix algorithm and the temperature field algorithm. The con-ductivity matrix algorithm uses the thermal conductivity matrix to calculate heat fluxes and film coefficients.



4.4.4. Conjugate Heat Transfer

It is the default. Generally, it produces satisfactory results for well shaped elements. However, if the elementsare not well shaped, it can produce non-smooth results. You should then switch to the temperature fieldalgorithm. It calculates film coefficients directly from thermal gradients. To set the algorithm, use the following:

Command(s): FLDATA37,ALGR,HFLM,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Algorithm Ctr

Main Menu> Solution> FLOTRAN Set Up> Algorithm Ctr

4.5. Heat Balance

Using information in the Jobname.PFL file, you can calculate a heat balance for your problem. For anyflow problem with the thermal option activated, the energy flow into and out of the problem domain atthe inlets/outlets is calculated and tabulated. Also calculated for the flow boundaries is the heat conductionacross the boundary faces. The difference between the energy flow into the system and out of the systemat the flow boundaries should equal the total energy added through sources and sinks.

The accuracy of the energy balance depends on the approach used to discretize the advection term in theenergy equation. In general, the Streamline Upwind/Petrov-Galerkin (SUPG) approach provides a more ac-curate energy balance than the Monotone Streamline Upwind (MSU) approach. If you desire an exact energybalance, use the Collocated Galerkin (COLG) approach. For steady-state incompressible flows, it provides anexact energy balance, even with a coarse mesh. However, SUPG or COLG may suffer from oscillatory thermalsolution near walls with a coarse mesh. Use the FLDATA40,WADV command to minimize such spatial oscil-lation.

Energy flowing into or out of the system at mass flow boundaries is equal to the product of the mass flow,the specific heat, and the temperature. A temperature offset specified by the TOFFST command does notenter this calculation. Positive numbers mean heat flows into the system.

Energy sources include volumetric heat sources in either fluids or solids. Specified wall temperatures andspecified film coefficient boundaries are either sources or sinks, depending on the temperature gradient.Heat fluxes are sources or sinks depending on the sign.

Heat transfer to/from wall faces refers to boundaries of fluid regions which are not inlets or outlets.

Heat transfer at wall faces refers to fluid boundaries, regardless of whether or not the boundary is a no-fluidelement or simply a no-slip condition. Positive numbers mean heat flows into the fluid.

Volumetric heat generation can be applied to solid regions or fluid regions. Be careful, when calculating theenergy balance to avoid accounting for heat generation in solids twice.

For example, suppose a conjugate heat transfer problem featured a volumetric heat source in a solid regionwhich is cooled by a fluid flow. The difference between the energy flow in and out should equal heattransfer to wall faces. This number should also match the volumetric heat generation in the solid.

For all cases, the difference between the energy flowing into the system at flow boundaries and flowing outat the boundaries should equal heat transfer to wall faces plus fluid volumetric heat sources plus the heatconduction effects normal to the flow direction at the flow boundaries.

Essentially, FLOTRAN performs a heat balance on the fluid region only. Heat fluxes and film coefficients aresolution outputs for the external fluid boundaries only. Heat fluxes applied on external boundaries are notpart of the solution output.

The effects of viscous dissipation on a heat balance are not explicitly tabulated. The associated heat gener-ation is manifested in terms of an increased temperature, which in turn affects the energy departure at the



outlet and the heat transfer at wall faces if applicable. With adiabatic walls, for example, the temperatureof the fluid will increase from viscous dissipation, even though no heat sources will be apparent.

4.6. Surface-to-Surface Radiation Analysis Using the Radiosity Method

Surface-to-surface radiation analysis in FLOTRAN can be used for solving generalized radiation problemsinvolving two or more radiating surfaces in single or multiple open or closed enclosures. The method issupported for both 3-D and 2-D FLOTRAN elements FLUID141 and FLUID142. The thermal solution optionhas to be on for radiation analysis. You can switch radiation analysis off using the FLDATA1, SOLU, RDSFcommand. The command defaults to on.

Surface-to-surface radiation analysis in 2-D is supported for planar and axisymmetric geometry about YRand XR coordinate systems. Radiation analysis is not supported for 3-D/2-D compressible flow thermal ana-lysis and for R-θ and R-θ-Z coordinate system in 2-D and 3-D analysis respectively.

Elements supported for the radiosity method include:

FLOTRAN

FLUID141FLUID142

4.6.1. Procedure

The Radiosity Solution method consists of four steps:

1. Define the radiating surfaces.

2. Define Solution options.

3. Define View Factor options.

4. Calculate and query view factors.

See Using the Radiosity Solver Method in the Thermal Analysis Guide for a detailed explanation of thesesteps.

4.6.2. Heat Balances

Jobname.PFL file provides information of the net positive and negative radiation heat transfer from bothsolid and fluid surfaces.

See Example of Radiation Analysis Using FLOTRAN (Command Method) (p. 56)

4.7. Examples of a Laminar, Thermal, Steady-State FLOTRAN Analysis

This chapter describes a laminar, thermal, steady-state fluid flow problem and two ways to solve it: bychoosing items on the ANSYS GUI menus or by issuing a series of ANSYS commands.

Before you begin reading about the example, note the following:

• The example problem described is only one of many possible FLOTRAN analyses. It does not illustrateevery technique you might use in a FLOTRAN analysis, and is intended only to show the kinds of tasksa FLOTRAN analysis typically requires.



4.7. Examples of a Laminar,Thermal, Steady-State FLOTRAN Analysis

• The values you enter in this example via commands or dialog boxes are specific values for this example

only. The characteristics of the individual problem you are solving dictate what values you should specifyfor a particular FLOTRAN analysis.

4.7.1. The Example Described

This example evaluates buoyancy-driven flow in a square cavity with differentially heated vertical sides. Itis a laminar steady-state analysis that uses the FLUID141 2-D element. The physics modeled in this problemgovern a number of practical problems, including solar energy collection, the ventilation of rooms, and soon.

Figure 4.1 Diagram of the Square Cavity

L = .03m

Insulated

Insulated

T = 320K T = 280Kg = 9.81 m/s2

Density variations resulting from the temperature difference across the cavity drive the laminar flow. TheRayleigh number for this flow is 1.01E+05, and is defined as follows:

Ra = g β ∆TL3 ρ2

Cp/k µ

The symbols in this equation are:

g = gravitational accelerationβ = 1/T∆T = THOT - TCOLD

L = cavity lengthρ = densityCp = specific heat

k = thermal conductivityµ = viscosity

Other example analysis conditions are:

• Cavity: dimensions 0.03m x 0.03m; gravitational acceleration 9.81 m/s2



• Operating conditions: nominal temperature 193K; reference pressure 1.0135E+05 Pa

• Fluid: Air in SI units

• Loads: no slip walls (Vx = Vy = 0); left wall of cavity maintained at THOT = 320K; right wall of cavity

maintained at TCOLD = 280K

4.7.2. Doing the Buoyancy Driven Flow Analysis (GUI Method)

To do the example buoyancy-driven flow analysis using the menus, perform the steps discussed in the nextfew sections.

Step 1: Establish an Analysis Title and Preferences

When you have entered the ANSYS program, do these tasks:

1. Choose menu path Utility Menu> File> Change Title. The Change Title dialog box appears.

2. Enter the text "Buoyancy driven flow in a square cavity."

3. Click on OK.

4. Choose menu path Main Menu> Preferences. The Preferences for GUI Filtering dialog box appears.

5. Click the button for FLOTRAN CFD to "On."

6. Click on OK. You have just instructed the ANSYS program to do a FLOTRAN analysis.

Step 2: Define Element Types

Next, you need to specify which elements your analysis will use. The example uses only one element, FLUID141.To define it:

1. Choose menu path Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Typesdialog box appears.

2. Click on Add. The Library of Element Types dialog box appears.

3. In the two scrollable lists, highlight (click on) FLOTRAN CFD and "2D FLOTRAN 141."

4. Click on OK. ANSYS returns you to the Element Types dialog box.

5. Click on Close.

Step 3: Create Areas

Next, create the areas you need. Our example requires an area representing the square cavity. To create it,perform these tasks:

1. Choose menu path Main Menu> Preprocessor> Modeling> Create> Areas> Rectangle> By Dimen-

sions. The Create Rectangle by Dimensions dialog box appears.

2. Enter the X coordinates from 0.0 to 0.03.

3. Enter the Y coordinates from 0.0 to 0.03.

4. Click on OK. The square area you have just created will appear in the Graphics Window.

Step 4: Define Lines, Mesh, and Plot Elements

This step meshes the square cavity area so that you can apply temperature loads to it. Follow these steps:



Step 4: Define Lines, Mesh, and Plot Elements

1. Choose menu path Main Menu> Preprocessor> Meshing> MeshTool. Under the Size Controls sectionof the MeshTool, click Lines,Set. The Element Size on Picked Lines picking menu appears.

2. Click Pick All. The Element Size on Picked Lines dialog box appears.

3. Set the number of element divisions to 25.

4. Click on OK.

5. In the MeshTool, select Areas from the Mesh drop down menu. Then click Quad and Free. Then clickMESH. The Mesh Areas picking menu appears.

6. Click on Pick All to generate the mesh.

7. Click on Close on the MeshTool.

8. Click SAVE_DB on the ANSYS Toolbar.

Step 5: Apply Velocity Boundary Conditions

In this step and Step 6, you apply boundary conditions to your model, starting with the exterior nodes. Dothe following:

1. Choose menu path Utility Menu> Select> Entities. The Select Entities dialog box appears.

2. Select Nodes and Exterior.

3. Click on OK.

4. Choose menu path Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Velocity>

On Nodes. The Apply V on Nodes picking menu appears.

5. On the picking menu, click on Pick All. The Velocity Constraints on Nodes dialog box appears.

6. Set the VX velocity component and VY velocity component fields to 0.

7. Click on OK.

Step 6: Apply Thermal Boundary Conditions

Now you need to apply temperature loads on the left and right edges of the model. To do so:

1. Choose menu path Main Menu> Preprocessor> Loads> Define Loads> Apply> Thermal> Temper-

ature> On Nodes. The Apply TEMP on Nodes picking menu appears.

2. Click on Box. Doing this enables you to select the nodes to which you are applying loads by drawinga box around them.

3. Press and drag your left mouse button to draw a box around the nodes on the left edge of the meshedarea.

4. Click on OK.

5. In the Apply TEMP on Nodes dialog box, enter 320 as the temperature value.

6. Click on OK.

7. Choose menu path Main Menu> Preprocessor> Loads> Define Loads> Apply> Thermal> Temper-

ature> On Nodes. The Apply TEMP on Nodes picking menu appears.

8. On the menu, click on Box. Doing this enables you to select the nodes to which you are applying loadsby drawing a box around them.

9. Press and drag your left mouse button to draw a box around the nodes on the right edge of themeshed area.



10. Click on OK.

11. In the Apply TEMP on Nodes dialog box, enter 280 as the temperature value.

12. Click on OK.

13. Choose menu path Utility Menu> Select> Everything. This step is important; it ensures that ANSYSincludes all nodes and elements in the analysis.

14. Click on the SAVE_DB button on the Toolbar.

Step 7: Set FLOTRAN Solution Options and Execution Controls

In this step and the next few steps, you set up conditions for the FLOTRAN analysis. You first specify whattype of FLOTRAN analysis you are doing and what values will control FLOTRAN execution.

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options. The FLOTRANSolution Options dialog box appears.

2. Set the "Adiabatic or thermal?" field to Thermal.

3. Click on OK.

4. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl. The Steady StateControl Settings dialog box appears.

5. Set the Global Iterations (EXEC) field to 200.

6. Set the .RFL File Overwrite Freq field to 50.

7. Set the Output summary frequency (SUMF) field to 50.

8. Click on OK.

Step 8: Set Fluid Properties

To set the fluid properties for the example analysis, do the following:

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties. The FluidProperties dialog box appears.

2. Set the "Density," "Viscosity," "Conductivity," and "Specific heat" fields to AIR-SI.

3. Set the "Allow density variations?" field to Yes.

4. Click on Apply. The CFD Flow Properties dialog box appears.

5. Read the information about how coefficients will be calculated, then click on OK.

Step 9: Set FLOTRAN Flow Environment Parameters

To set the flow environment parameters, follow these steps:

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Gravity.The Gravity Specification dialog box appears.

2. Set the "Accel in Y direction" field to 9.81.

3. Click on OK.

Step 10: Solve the Problem

Set controls for the FLOTRAN solver before you initiate the solution process. Follow these steps:



Step 10: Solve the Problem

1. Choose menu path Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Contr> PRES Solver

CFD. The PRES Solver CFD dialog box appears.

2. Choose TDMA.

3. Click on OK. The TDMA Pressure dialog box appears.

4. Make sure that the value of the "No. of TDMA sweeps for pressure" field is 100. If so, click on OK.

5. Click on the SAVE_DB button in the Toolbar.

6. Choose menu path Main Menu> Solution> Run FLOTRAN.

7. Wait for the solution to finish, then review the information in the ANSYS Output Window. Click Closein the Solution is done window.

Step 11: Read In Results and Plot the Temperature Solution

Perform these steps:

1. Choose menu path Main Menu> General PostProc> Read Results> Last Set.

2. Choose menu path Main Menu> General PostProc> Plot Results> Contour Plot> Nodal Solu. TheContour Nodal Solution Data dialog box appears.

3. In the "Item to be Contoured" list, click on (highlight) DOF Solution.

4. In the scrollable list, scroll down and choose TEMP.

5. Click on OK. The Graphics Window shows you the following contour plot:

Figure 4.2 Plot of the Temperature Solution

Step 12: Plot Streamline Contours

1. Choose menu path Main Menu> General PostProc> Plot Results> Contour Plot> Nodal Solu. TheContour Nodal Solution Data dialog box appears.

2. Click on (highlight) "Other quantities."

3. In the scrollable list, select "Strm func2D STRM" (stream function).



4. Click on OK. The Graphics Window shows you the following contour plot:

Figure 4.3 Plot of Streamline Contours

Step 13: Plot Velocity Vectors

For better viewing of the analysis results for the example, switch to vector plotting as described below:

1. Choose menu path Utility Menu> PlotCtrls> Device Options. The Device Options dialog box appears.

2. Set Vector mode (wireframe) to "On."

3. Click on OK.

4. Choose menu path Main Menu> General PostProc> Plot Result> Vector Plot> Predefined. TheVector Plot of Predefined Vectors dialog box appears.

5. Verify that the items "DOF solution" and "Velocity" are highlighted. If so, click on OK. The display inthe Graphics Window now looks similar to the one below.



Step 13: Plot Velocity Vectors

Figure 4.4 Plot of Velocity Vectors

Step 14: Plot Particle Traces Contoured by Temperature

In the example analysis, the dimensions of the problem are small (.03 x .03). Therefore, before plottingparticle trace points, you should change the working plane to give a better view from which to choose thosepoints.

1. Choose menu path Utility Menu> WorkPlane> WP Settings. The WP Settings dialog box appears.

2. Set Snap Increment to 0.0005.

3. Set Spacing to 0.0001.

4. Set Tolerance to 0.00005.

5. Click on OK.

6. Choose menu path Utility Menu> Plot> Elements.

7. Choose menu path Main Menu> General Postproc> Plot Results> Flow Trace> Defi Trace Pt.

8. Using your mouse, pick five or six points anywhere within the upper half of the problem domain.

9. Click on OK in the picking menu.

10. Choose menu path Main Menu> General Postproc> Plot Results> Flow Trace> Plot Flow Trace.The Plot Flow Trace dialog box appears.

11. In the scrollable list, click on (highlight) "Temperature TEMP".

12. Click on OK. The Graphics Window shows a plot that resembles the plot shown below. Your plot maylook different, depending on the location of the points you picked. If a warning message appears telling

you that the maximum number of loops has been exceeded, review it and click Close. For the purposes of

this problem, the particle trace is stuck in a loop by definition, so you can ignore this message.



Figure 4.5 Plot of Flow Trace

Step 15: Plot Particle Traces Contoured by Velocity Magnitude

1. Choose menu path Main Menu> General PostProc> Plot Results> Flow Trace> Plot Flow Trace.The Plot Flow Trace dialog box appears.

2. In the scrollable list, choose "VSUM."

3. Click on OK. The plot shown in the Graphics Window is now contoured by velocity magnitude. Howyour plot looks will depend on the location of the points you picked. If you receive another warningmessage about the maximum number of loops being exceeded, click Close.

4. If you wish, you can use animation to enhance your analysis of particle flow. Choose menu path Util-

ity Menu> PlotCtrls> Animate> Particle Flow. When the Animate Flow Trace dialog box appears,enter the desired animation data and click OK. (To animate particle flow, you must have at least onetrace point defined. To complete the sample analysis, simply take the defaults and click on OK.)

5. When you are done viewing the animation, click Stop and then Close in the Animation Controller. Ifadditional warning messages appear, close them.

6. To exit ANSYS, click Quit on the ANSYS Toolbar. Choose an exit option and then click on OK.

See Section 5.10, Doing the Sample Analysis (Command Method), for an example problem.

4.7.3. Doing the Buoyancy Driven Flow Analysis (Command Method)

To do the example buoyancy-driven flow analysis, you issue these ANSYS commands:

/TITLE,Buoyancy driven flow in a square cavity/PREP7ET,1,FLUID141 ! Set 2-D fluid element typeRECTNG,,0.03,,0.03 ! Create square areaLPLOTLESIZE,ALL, , ,25,1,0 ! Define line divisions and mesh areaAMESH,1EPLOTNSEL,S,EXT ! Apply velocity b.c. on exterior nodes



4.7.3. Doing the Buoyancy Driven Flow Analysis (Command Method)

D,ALL,,,,,,VX,VYNSEL,S,NODE,,1 ! Apply thermal b.c. on left edgeNSEL,A,NODE,,52NSEL,A,NODE,,77,100D,ALL,TEMP,320NSEL,S,NODE,,2 ! Apply thermal b.c. on right edgeNSEL,A,NODE,,27,51D,ALL,TEMP,280NSEL,ALLESEL,ALLFLDATA1,SOLU,TEMP,1 ! Set solution option to thermalFLDATA2,ITER,EXEC,200 ! Set FLOTRAN execution controlsFLDATA2,ITER,OVER,50FLDATA5,OUTP,SUMF,50!*FLDATA13,VARY,DENS,1 ! Set fluid propertiesFLDATA7,PROT,DENS,AIR-SIFLDATA7,PROT,VISC,AIR-SIFLDATA7,PROT,COND,AIR-SIFLDATA8,NOMI,COND,-1FLDATA7,PROT,SPHT,AIR-SI!*ACEL,0,9.81,0 ! Set flow environment gravityFLDATA18,METH,PRES,1 ! Set FLOTRAN solver controlsFLDATA19,TDMA,PRES,100FINISH/SOLUSOLVE ! Solve modelFINISH/POST1SET,LASTPLNSOL,TEMP ! Plot temperature solutionPLNSOL,STRM ! Plot streamline contours/DEVICE,VECTOR,1!*PLVECT,V, , , ,VECT,ELEM ! Plot velocity vectorswpstyle,0.0005,0.0001,-1,1,0.00005,0,2,,5EPLOTTRPOIN,P ! The P argument enables graphical picking ! of trace points via the GUIPLTRAC,FLUID,TEMP ! Plot particle traces contoured byPLTRAC,FLUID,V,SUM ! temperature and velocity magnitudeFINISH

4.8. Example of Radiation Analysis Using FLOTRAN (Command Method)

The following is an example of a laminar, thermal, steady-state FLOTRAN analysis with surface-to-surfaceradiation using the radiosity solution method (command method). In this example a buoyancy-driven flowin a square cavity with differentially heated vertical walls is considered. All walls of the cavity are radiatingsurfaces with an emissivity of 0.9. The final temperature distribution in the cavity effected by the presenceof the radiating walls in the fluid domain.

To do the surface-to-surface radiation problem, you issue these ANSYS commands:

/prep7et, 1, 141 ! 2-D Fluid elementrectng, , .027744, , .027744 ! Create square cavityesize, , 20 ! Set number of elementsamesh, all ! Mesh areansel, s, ext ! Select external nodesd, all,,,,,,vx,vy ! Set all external wall velocities to zero allsel lsel, s, loc, x, 0.0nsll, s, 1d, all, temp, 500 ! Set wall temperature at x = 0.0 to 500 Klsel, s, loc, x, .027744nsll, s, 1d, all, temp, 200 ! Set wall temperature at x = 0.027744 to 200 Knsel, all



esel, allfldata1, solu, temp, 1 ! Set solution option to thermalfldata2, iter, exec, 200 ! Set FLOTRAN execution controlfldata2, iter, over, 50 fldata5, outp, sumf, 50! fldata13, vary, dens, 1 ! Set fluid propertiesfldata7, prot, dens, air-sifldata7, prot, visc, air-sifldata7, prot, cond, air-sifldata8, nomi, cond, -1fldata7, prot, spht, air-si!acel, 0, 9.81, 0 ! Set flow environment gravityfldata18, meth, pres, 1fldata19, tdma, pres, 100fldata18, meth, temp, 6stef,5.67e-8 ! Set Stefan-Boltzmann constanttoff,0 ! Set temperature offset to zero radopt,.5,0.0001 ! Set radiosity solver optionsfinish/soluallselnsel,s,ext ! Select all external nodessf, all, rdsf, 0.9, -1 ! Apply radiation on external faces facing inwardsallselsolve ! Solvefinish/post1set lastplnsol, temp ! Plot temperature solutionplnsol, strm ! Plot streamline contours

4.9. Where to Find Other FLOTRAN Analysis Examples

The Verification Manual contains several examples of FLOTRAN analyses. The Verification Manual examplesinclude:

VM46 - Flow Between Rotating Concentric CylindersVM121 - Laminar Flow Through a Pipe with Uniform Heat FluxVM178 - Plane Poiseuille FlowVM209 - Multiple Species Flow Entering A Circular PipeVM219 - Non-Newtonian Pressure Driven Sector Flow



4.9.Where to Find Other FLOTRAN Analysis Examples


Chapter 5: FLOTRAN Transient Analyses

You activate the transient algorithm by setting the solution option, using one of these methods:

Command(s): FLDATA1,SOLU,TRAN,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options


You must make decisions regarding the time step, the method of converging the analysis during a timestep, the length of execution of the job and the frequency of output.

What you specify via one of the following methods determines the transient execution and output:

Command(s): FLDATA4,TIME and FLDATA4A,STEPGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


The final section of this chapter explains how to apply transient boundary conditions for FLOTRAN.

The following FLOTRAN transient analysis topics are available:5.1.Time Integration Method5.2.Time Step Specification and Convergence5.3.Terminating and Getting Output from a Transient Analysis5.4. Applying Transient Boundary Conditions

5.1. Time Integration Method

There are two methods available for the time integration: Backward (the default) and Newmark. The Newmarkmethod is more accurate than the Backward method. To specify the Newmark method, use one of the fol-lowing:

Command(s): FLDATA4,TIME,METH,NEWMGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Transient Contrl> Time Integration Meth

Main Menu> Solution> FLOTRAN Set Up> Transient Contrl> Time Integration Meth

When using the Newmark method, you can introduce numerical damping to stabilize the solution.

Command(s): FLDATA4,TIME,DELT,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Transient Contrl> Time Integration Meth

Main Menu> Solution> FLOTRAN Set Up> Transient Contrl> Time Integration Meth

The Newmark parameter must be ≥ 0.5. It defaults to 0.5. The recommended range is 0.5 to 0.6. Highervalues are more stable because there is more damping. Lower values result in more accurate results with0.5 corresponding to second order accuracy. For more information on the Newmark method, see TransientAnalysis in the Theory Reference for the Mechanical APDL and Mechanical Applications.



There are two mass types that you can set for the transient analysis: lumped (the default) and consistent.The consistent type is more dissipative than the lumped type. To specify the consistent type, use one of thefollowing:

Command(s): FLDATA38,MASS,Label,CONS MSMASS,SPNUM,CONSGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Transient Contrl> Mass Type

Main Menu> Solution> FLOTRAN Set Up> Transient Contrl> Mass Type

Main Menu> Solution> FLOTRAN Set Up> Multiple Species

5.2. Time Step Specification and Convergence

Because the algorithm is implicit in nature, no stability restrictions exist on the time step size. You specifya time step or elect to have FLOTRAN calculate a time step. To do so, use either of the following:

Command(s): FLDATA4A,TIME,STEP,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


The graphical user interface will require you to set the time step if you choose the User Defined option.

The table below shows the values you can specify. A brief description of the FLOTRAN calculation followsthe table.

Table 5.1 Specifying Values for Time Steps

MeaningValue to Specify

User Specified Time StepAny value > 0

Advection Limit-1

Pressure Wave Limit-2

Smaller of Pressure wave and Advection-3

Conduction Limit-4

The advection limit prevents a particle of fluid from passing completely through a finite element during atime step.

The pressure wave limit means the time step is chosen small enough to prevent a pressure wave frompassing all the way through a finite element during a single time step. This option is active only if you choosethe compressible solution algorithm.

The choice of -3 (again valid only for compressible analyses) means that the more restrictive (that is, smaller)time step criterion will be imposed.

The conduction limit is calculated to prevent the conductive diffusion of a parcel of energy completelythrough an element during a time step. The limit applies only to problems that include conduction, and isvalid for problems with both fluid and non-fluid elements.

FLOTRAN must execute global iterations to converge within a time step. The time step terminates wheneither of the following happens:

• The convergence criteria are met.

• The maximum number of global iterations allowed per time step executes.



You set the maximum number of global iterations per time step using one of the following:

Command(s): FLDATA4A,TIME,GLOB,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


The convergence criteria are values below which the convergence monitors for each active degree of freedommust drop to cause the time step to terminate. You specify these values using the following commands ormenu paths:

Command(s): FLDATA4,TIME,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


As soon as all the convergence criteria are met, the time step terminates. The time step terminates on thenumber of global iterations allowed if the convergence monitor criteria are not met.

If the problem is adiabatic, only the pressure equation monitor is checked. Both the pressure and temperatureequation monitors must be reduced below the convergence criteria values if the temperature equation alsois solved.

As soon as the convergence monitor criteria are met, the time step terminates. The time step terminates onthe number of global iterations allowed if the convergence monitor criteria are not met.

5.3. Terminating and Getting Output from a Transient Analysis

You can either specify an end time for a transient FLOTRAN analysis or have it end after a specified numberof time steps. To specify an end time, use either method shown below.

Command(s): FLDATA4,TIME,TEND,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


To specify a number of time steps, either use one of the menu paths listed above or issue the followingcommand:

Command(s):

FLDATA4,TIME,NUMB,Value

The event that occurs first (end time or reaching the time step threshold) terminates the analysis.

You determine how often ANSYS saves the analysis results for processing and how often it writes informationto the Jobname.PFL file. You do this by choosing from the following commands or menu paths:

Command(s): FLDATA4,TIME,Label,Value and FLDATA4A,STEP,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Execution Ctrl


The table below shows you how the values you specify affect analysis output:

Table 5.2 Saving Analysis Results for Processing

Meaning of ValueName, Label, Value

Output results to Jobname.RFL every n time stepsSTEP,APPE,n



5.3.Terminating and Getting Output from a Transient Analysis

Meaning of ValueName, Label, Value

Output results to Jobname.RFL every x secondsTIME,APPE,x

Add output summary to Jobname.PFL every n time stepsSTEP,SUMF,n

Add output summary to Jobname.PFL every x secondsTIME,SUMF,x

Overwrite the temporary results set every n time stepsSTEP,OVER,n

Overwrite the temporary results set every x secondsTIME,OVER,x

If you wish to control the output based on time, you must first defeat the default controls which set APPEand SUMF to ten steps.

5.4. Applying Transient Boundary Conditions

When any boundary conditions are changed, FLOTRAN assumes either a step change (default) or a rampchange. The ramp is chosen by setting the BC label in the TIME item to 1 via one in the following:

Command(s): FLDATA4,TIME,BC,1GUI: Main Menu> Preprocessor> FLOTRAN Setup> Execution Control

The ramp will occur for the next execution over the period of time for execution specified by the user. Thisis the difference between the current time (i.e., the beginning in the execution) and the end time as specifiedby the following:

Command(s): FLDATA4,TIME,TEND,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Execution Control

The ramp is between the "old" boundary conditions and the "new" boundary conditions. A boundary conditionis considered old as soon as FLOTRAN has gone through the calculational loop. This means that to use aramped condition at the beginning of an analysis, a zero iteration execution (which may be accomplishedwith the FLOCHECK command) should be done with the initial condition (applied as a boundary condition)and then the boundary condition value(s) are changed to those at the end in the ramp.

Note that the ramp is calculated with the value of TEND as specified above, NOT the actual ending time inthe case. For this reason, it is recommended that the user terminate the case with the TIME controls ratherthan the STEP controls. Ensure that the case will not terminate prematurely due to an insufficient numberof time steps. If the case terminates before the time specified by TEND, upon restart the boundary conditionswill be immediately changed from where they were when the run terminated to what the current boundarycondition setting is. If you use the STEP controls in the GUI to set the number of time steps, you need to

set TEND in that same dialog box. Otherwise, TEND defaults to 1.0 x 106 and the ramp is almost nonexistent.

Transient boundary conditions on velocity DOF (VX, VY, and VZ) must not be ramped from zero to a nonzerovalue. A very small velocity must be used instead of zero so that FLOTRAN recognizes the face as an inletor outlet rather than a wall.

At any time, you can change the applied boundary conditions to the "old" state with one of the following:

Command(s): FLOCHECK,2GUI: Main Menu> Preprocessor> FLOTRAN Setup> Flocheck

FLOCHECK,2 has no effect on the Jobname.RFL file.



Caution

FLOTRAN has no record of boundary conditions at earlier times. That is, if you want to restartfrom an earlier point in time and simulate a ramped boundary condition it is necessary to applythe boundary condition appropriate for the beginning of the ramp, make it an old condition viathe FLOCHECK command, and then apply the condition at the end of the ramp.



5.4. Applying Transient Boundary Conditions


Chapter 6: Volume of Fluid (VOF) Analyses

In a Volume of Fluid (VOF) analysis, FLOTRAN uses an advection algorithm for the volume fraction (VFRC)to track the evolution of the free surface. The VFRC value for each element varies from zero to one, wherezero denotes an empty or void element and one denotes a full or fluid element. The values between zeroand one indicate that the corresponding elements are the partially full or surface elements (henceforth calledpartial elements), and the free surface can thus be determined by the distribution of the VFRC field.

For the dynamic behavior at the interface between a gas and liquid, FLOTRAN uses a continuum surfaceforce (CSF) method to model the surface tension. Surface tension is an inherent characteristic of materialinterfaces. It is a localized surface force acting on the interface. FLOTRAN reformulates this surface force intoan equivalent volumetric force in the momentum equation. This force consists of two components: a normalcomponent to the interface due to local curvature and a tangential component to the interface due to localvariations of the surface tension coefficient.

Currently, VOF capability is available only for quadrilateral elements for two dimensional planar or axisym-metric analyses. For a VOF analysis, boundary conditions are required for boundary nodes that belong to atleast one non-empty (partial or full) element.

To activate a VOF analysis in FLOTRAN and model the surface tension effect, use the following commandsor GUI menu paths:

Command(s): FLDATA1,SOLU,VOF,Value FLDATA1,SOLU,SFTS,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution Options


In FLOTRAN, the VOF algorithm first computes the motion of the polygon of fluid in a Lagrangian sense andthen utilizes the computational geometry of the intersection of two polygons to determine the VFRC fluxes.This method is referred to as the Computational Lagrangian-Eulerian Advection Remap (CLEAR) method.See CLEAR-VOF Advection in the Theory Reference for the Mechanical APDL and Mechanical Applications forinformation on the theoretical background. This CLEAR-VOF method tracks the free surface explicitly in time,and it is therefore necessary to activate the transient solution option for a VOF analysis. Refer to FLOTRAN

Transient Analyses (p. 59) for information on the selection of the transient parameters, such as the time step,converging method, execution length and the output frequency. For accuracy, you should use the StreamlineUpwind Petrov-Galerkin (SUPG) approach described in Advection Discretization Options (p. 161). If you encountera convergence difficulty, the time increment may be reduced, and the modified inertial relaxation (MIR)scheme may also be activated for robustness.

Caution

You should avoid using quadrilateral elements with only one node on the inflow or outflowboundary.

The following VOF topics are available:6.1.VFRC Loads6.2. Input Settings6.3. Postprocessing



6.4.VOF Analysis of a Dam6.5.VOF Analysis of Open Channel with an Obstruction6.6.VOF Analysis of an Oscillating Droplet

6.1. VFRC Loads

When performing a VOF analysis, you need to apply both initial and boundary VFRC loads. In most cases,default values are appropriate.

6.1.1. Initial VFRC Loads

You impose initial conditions for the velocity and other degrees of freedom in the usual manner. For theinitial VFRC field, you can define each element as initially full, partially full or empty. Take care when initiallysetting partial elements. Each partial element must be adjacent to at least one full element and one emptyelement. During the analysis, if a partial element does not have any full elements as neighbors, it will bereset to empty. You should also include at least one layer of empty elements above the free surface to allowthe surface to evolve in time.

To set the initial volume fraction field, use one of the following:

Command(s): ICE,ELEM,VFRC,ValueGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Volume Fract> Init

Loads> On Elements

Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Fract> Init Loads> On Elements

By default, the volume fraction is zero. Therefore, if there is fluid initially inside the problem domain, youmust set the VFRC field accordingly.

To set the initial volume fraction for a given geometry, use one of the following:

Command(s): ICVFRC,GEOM,VAL1,VAL2,VAL3,VAL4GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Volume Fract> Init Loads> By

Geom

Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Frac> Init Loads> By Geom

ICVFRC automatically calculates the volume fraction value for all selected elements that are either insidethe given geometry or intersect with it. The volume fraction is:

• One for elements completely within the geometry

• A fraction equal to the element area within the geometry for elements intersected by the boundary ofthe geometry

Currently, there are two valid geometries: circle (CIRC) and ellipse (ELPT). For a circle or ellipse, VAL1 andVAL2 are the x and y coordinates of the center, respectively. For a circle, VAL3 is the radius and VAL4 is notused. For an ellipse, VAL3 and VAL4 are the x and y semiaxes, respectively.

To display the initial volume fraction loads, use the following:

Command(s): /PICE,VFRC,,KEYGUI: Utility Menu> PlotCtrls> Symbols

The /PBF and /PSF commands override the /PICE command.



6.1.2. Boundary VFRC Loads

You impose boundary conditions for the velocity and other degrees of freedom in the usual manner. Althoughboundary conditions outside the fluid region have no physical meaning initially, these conditions will becomeactive if the fluid touches these boundaries. Accordingly, you should apply all appropriate boundary conditionson all boundaries potentially touched by the fluid. FLOTRAN treats unspecified boundaries with naturalconditions.

Boundary conditions for VFRC loads consist of the boundary VFRC value and the wetting status. FLOTRANonly allows zero (empty) and one (full) values for the boundary VFRC values. By default, boundary VFRCvalues are set to one (full). FLOTRAN uses the boundary VFRC values to determine the normal surface directionin the VOF reconstruction stage, when the boundary is adjacent to the surface elements. The wetting statusspecifies whether the fluid can be advected into the problem domain. A zero value indicates a non-wettingboundary, whereas a unity value indicates a wetting boundary. By default, wetting status is set to zero (non-wetting boundary). On a wetting boundary, fluid advection into the problem domain takes place. The cor-responding boundary VFRC value must be set to unity to be meaningful. On a non-wetting boundary, ad-vection of the fluid or void elements into the problem domain does not take place. The boundary VFRCvalue only acts passively to help determine the normal surface direction.

To set boundary VFRC loads, use one of the following:

Command(s): SFL,LINE,VFRC,VALI,VALJ,VAL2I,VAL2J SFE,ELEM,LKEY,VFRC,KV-AL,VAL1,VAL2,VAL3,VAL4GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Volume Fract> Bound

Loads> On Lines

Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Volume Fract> Bound Loads>

On Elements

Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Fract> Bound Loads> On Lines

Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Volume Fract> Bound Loads> On Elements

For the SFL command, VALI specifies the boundary VFRC value and (defaults to 1) VAL2I specifies thewetting status (defaults to non-wetting). If Lab = VFRC, a VAL2I setting of 1 indicates a wetted boundary.For the SFE command, VAL1 specifies the boundary VFRC value (defaults to 1) when KVAL = 0 or 1, andVAL1 specifies the boundary wetting status (defaults to non-wetting) when KVAL = 2. If Lab = VFRC andKVAL = 2, a VAL1 setting of 1 indicates a wetted boundary. At a wetted boundary, the fluid upstream keepsthe associated elements full.

6.2. Input Settings

When performing a VOF analysis, you may set the environmental conditions regarding the ambient conditions,the VFRC tolerances, and the time stepping strategy.

When studying surface tension effects, you need set the proper values for the surface tension coefficientand the wall static contact angle. Refer to Specifying Fluid Properties for FLOTRAN (p. 117) for information onthese property types.

6.2.1. Ambient Conditions

Set the ambient nodal values outside the fluid region for the following variables:

VX - U velocityVY - V velocityVZ - W velocity



6.2.1. Ambient Conditions

TEMP - TemperatureENKE - Turbulent Kinetic EnergyENDS - Turbulent Dissipation Rate

using one of the following:

Command(s): FLDATA36,AMBV, Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> VOF Environment> Ambient Condit'n

Main Menu> Solution> FLOTRAN Setup> VOF Environment> Ambient Condit'n

When a boundary node with Dirichlet Condition lies outside the fluid region, the assigned ambient valueson this node are ignored. The prescribed Dirichlet Condition will become active once its associate elementbecomes partially full or full. Except for pressure, the ambient values are only set for postprocessing purposes.Pressure acts as an actual boundary condition.

Unlike other FLOTRAN analyses, the pressure field for a VOF analysis will include both the dynamic pressureand the static pressure and the static pressure will be in balance with the gravitational acceleration terms.For example, in a VOF analysis, the pressure contours for a parallel uniform flow with gravity will consist ofparallel lines with a gradient balancing gravity, whereas they remain constant for other FLOTRAN analyses.

In a VOF analysis, an outlet can have specified pressures or it can have natural conditions. When outletpressures are specified, the values will differ from those in other FLOTRAN analyses by the offsets of thestatic pressure (or elevation head). For natural boundary conditions the outlet pressures will adjust automat-ically. In that case, if a steady state solution exists, the outlet pressures will converge to the correct values.

6.2.2. VFRC Tolerances

Ideally, a VFRC value of one signifies a full or fluid element and a value of zero signifies an empty or voidelement. In reality, however, exact values of one and zero are difficult to maintain in the VOF advection al-gorithm due to various types of error accumulations. Hence, FLOTRAN introduces small cutoff values to de-termine the full and empty elements. An element is considered full if its VFRC value is greater than or equalto 1 - VOFU, where VOFU is the upper tolerance for the VOF advection algorithm. An element is consideredempty if its VFRC value is less than or equal to VOFL, where VOFL is the lower tolerance for the VOF advection

algorithm. By default, VOFL and VOFU are both set to 10-5.

In the FLOTRAN solution routines, a nearly empty element adjacent to a nearly full element may introducean abrupt change in the locally rescaled meshes. This can make the stiffness matrix more ill-conditionedand can adversely affect the quality of the desired solution. To avoid this, FLOTRAN introduces another tol-erance to not assemble the finite element equations for those elements with VFRC values less than or equalto LAML for laminar flows and TRBL for turbulent flows, where LAML and TRBL are the lower tolerances forlaminar and turbulent flows, respectively. Similarly, elements with VFRC values greater than or equal to 1 -LAMU for laminar flows and 1 - TRBU for turbulent flows are considered full when assembling the finite

element equations. You can set any of these tolerance values. By default, LAML and LAMU are set to 10-2

and TRBL and TRBU are set to 10-1.

To set any of the tolerance values, use one of the following:

Command(s): FLDATA35,VFTOL,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> VOF Environment> VFRC Tolerance

Main Menu> Solution> FLOTRAN Setup> VOF Environment> VFRC Tolerance



6.2.3. VOF Time Steps

Because the CLEAR-VOF is explicit in time, it must use a time step for the VOF advection algorithm thatcorresponds to a CFL number less than one. On the other hand, selecting the time step based on the VOFconstraint may be too restrictive sometimes because the FLOTRAN transient solution algorithm is implicitin time, and there is no stability restriction on the time step size. Accordingly, FLOTRAN allows multiple VOFadvection steps per solution step. The VOF advection time step is set equal to the solution time step dividedby a factor that you specify. If the VOF advection time step is still too large, FLOTRAN will automatically reducethe VOF time step by half. This automatic reduction in the VOF time step continues until the local imbalanceof the VFRC field during the VOF advection computations is less than the VOFL tolerance. A good inputparameter guess makes the calculation more efficient by removing some checks on the time step.

To set the number of VOF advection time steps per solution time step, use one of the following:

Command(s): FLDATA4,TIME,NTVF,ValueGUI: Main Menu> Preprocessor> FLOTRAN Setup> VOF Environment> Time Stepping

Main Menu> Solution> FLOTRAN Setup> VOF Environment> Time Stepping

For a VOF analysis, the density is constant. Therefore, mass conservation is equivalent to the conservationof the total fluid volume (or area in two dimensions). Ideally, the difference between the volume cominginto the problem domain and going out of the domain should be equal to the increase or decrease of thetotal volume inside the domain. In an actual finite element analysis, however, continuity satisfaction is ex-pressed in a Galerkin weak form. Therefore, in general, each element has a small mass imbalance. The localmass imbalance is usually of the order of the discretization error, and this error is a major source of theglobal VFRC imbalance introduced in a VOF analysis. Even though this imbalance may be very small comparedto the total volume, it can accumulate exponentially as the number of time steps increases. Hence, FLOTRANperforms a global adjustment of the VFRC field at each VOF time step. It proportionally increases or decreasesthe VFRC values of the partial elements to guarantee the global VFRC balance. It prints the final VFRC imbal-ance in the Jobname.PFL file.

6.3. Postprocessing

The volume fraction is stored as a non-summable miscellaneous record in the element data section of theresults file. If you want to view the volume fraction, issue the command:

Command(s):

PLESOL,NMISC,1

Since the volume fraction is essentially an element based quantity, it is discontinuous across elements. Ifyou wish to see a smooth and continuous volume fraction, you should first store the results in an elementtable, using one of the following:

Command(s): ETABLE,VFRC,NMISC,1GUI: Main Menu> General Postproc> Element Table> Define Table

You can then plot the results with an averaging operation, using one of the following:

Command(s): PLETAB,VFRC,1GUI: Main Menu> General Postproc> Element Table> Plot Elem Table

However, instead of using the foregoing commands, you can use one of the following:

Command(s): PLVFRC,CONTGUI: Main Menu> General Postproc> Plot Results> Contour Plot> Element Solu



6.3. Postprocessing

The PLVFRC macro issues the ETABLE and PLETAB commands. When CONT = 0, PLVFRC uses contourlevels of 0.5 and 1.0 to indicate the free surface and fluid regions. When CONT = 1, it uses the current contoursettings.

You can also animate your results. To obtain an animation over a time sequence by interpolation betweentime steps, use the PLVFRC command macro along with one of the following:

Command(s): PLVFRC,CONT ANTIME,NFRAM, DELAY, NCYCL, AUTOCNTRKY, RSLTDAT, MIN, MAXGUI: Utility Menu> PlotCtrls> Animate> Over Time

To produce an animation based on the time steps without interpolation, use the PLVFRC command macroalong with one of the following:

Command(s): PLVFRC,CONT ANDATA,DELAY,NCYCL, RSCLDAT, MIN, MAX, INCR, FRCLST,AUTOCNTRKYGUI: Utility Menu> PlotCtrls> Animate> Over Results

Note that if CONT = 0, the animation is based on two contour levels of 0.5 and 1.0. If CONT = 1, the animationis based on AUTOCNTRKY setting.

6.4. VOF Analysis of a Dam

6.4.1. The Problem Described

In this example, two vertical walls confine a rectangular column of stationary water. When the right wall isremoved, the water flows out onto a rigid horizontal plane. The ICE command sets the initial volume fractionfield.

6.4.2. Building and Solving the Model (Command Method)

The following command stream shows all the relevant parameters and solution strategy. All text prefacedwith an exclamation point (!) is a comment.

/BATCH,LIST/title, broken dam problem by the VOF solution./com/com ------------------------------------------------------------------/com ** Reference: "Part IV: An Experimental Study of the Collapse of/com ** Liquid Columns on a Rigid Horizontal Plane" /com ** By Martin and Moyce, Phil. Trans. Roy. Soc. /com ** (London,A244, pp. 312-324, 1952./com ** "Volume of Fluid (VOF) Method for the Dynamics of/com ** Free Boundaries" By C.W. Hirt and B.D. Nichols,/com ** J. Comput. Physics, Vol. 39, pp. 201-225, 1981./com **/prep7 !!!!! Define some dimensions and gravity LX = 5.0 ! X lengthLY = 2.5 ! Y lengthDELX = 0.2 ! X spacingDELY = 0.05 ! Y spacinggrav = 9.81 ! Gravityet,1,141!!!! meshingrect,0,LX,0,LYlsel,s,,,2,4,2lesize,all,DELYlsel,s,,,1,3,2lesize,all,DELXamesh,all



nsel,s,loc,y,0.0 ! Wall boundary conditions nsel,a,loc,x,0.0d,all,vx,0.0d,all,vy,0.0

nsel,s,loc,x,0.0,1.0 ! Setup initial VFRCnsel,r,loc,y,0.0,2.0esln,s,1ice,all,vfrc,1.0

alls ! Initial conditions for vx & vyic,all,vx,0ic,all,vy,0savefini

/solu!!!! FLOTRAN inputacel,0.0,grav,0FLDA,NOMI,DENS,1.0e3FLDA,NOMI,VISC,1.0d-3FLDA,SOLU,FLOW,TFLDA,SOLU,TRAN,TFLDA,SOLU,turb,Fflda,solu,vof,tflda,time,glob,5flda,time,numb,70flda,time,step,0.01flda,time,appe,0.1flda,advm,mome,supgflda,relx,vx,0.5flda,relx,vy,0.5flda,relx,pres,1.0solve finiexit,nosa

6.5. VOF Analysis of Open Channel with an Obstruction


In this example, water flows in an open channel with a semicircular obstruction on the bottom. The compu-tation uses the standard k-ε turbulence model since the turbulence model is not very important for theprediction of the free-surface shape. The solution domain extends five cylinder diameters upstream and fivediameters downstream of the obstruction. The fluid starts to fill the domain at the beginning of the simulation.The SFE and SFL commands set a wetting boundary on the left inlet.



/BATCH,LIST/title, initial development of flow over a bump./com/com ------------------------------------------------------------------/com ** Initial development of flow over a semicircular bump /com ** Reference: "Critical Free-Surface Flow Over a Semi-Circular/com ** Obstruction" By L.K. Forbes, J. Eng. Math., /com ** vol. 22, pp. 3-13, 1998./com ** "Computation of free-surface flows using the /com ** finite-volume method and moving grids", /com ** By S. Muzaferija and M. Peric, Numerical Heat/com ** Transfer, Part B, 32:369-384, 1997./com ------------------------------------------------------------------!




!! Property and parameter inputrho = 1.0e0 ! Densitygrav = 9.81 ! Gravity mu = 1.0e-6 ! Viscosity!R = 0.03 ! Bump radiusL = 2*RH = 0.075 ! Inlet heightH0 = R ! Height above the Inletoutlen = 5.0*R ! Outlet lengthinlen = 5.0*R ! Inlet lengthny1 = 8 ! Number of elements in line 1ny2 = 2 ! Number of elements in line 2ny3 = 4 ! Number of elements in line 3ry2 = 1.0 ! Ratio of element size in line 2ry3 = 1.0 ! Ratio of element size in line 3nx1 = 15 ! Number of elements in line 13nx2 = 15 ! Number of elements in line 21nx3 = 20 ! Number of elements in line 17rx1 = 0.5 ! Ratio of element size in line 13rx2 = 1.0 ! Ratio of element size in line 25rx3 = 1.5 ! Ratio of element size in line 17nr1 = 10 ! Number of elements in radial direction near bump!!/prep7et,1,141k,1,-inlen,0.0 ! KP 1 - 4 are at the inletk,2,-inlen,Lk,3,-inlen,Hk,4,-inlen,H+H0!l,1,2 ! Lines 1-3 are the inlet linel,2,3l,3,4!k,5,-L,0.0 ! KP 5 - 8 are before the bump k,6,-L,Lk,7,-L,Hk,8,-L,H+H0!l,5,6 ! Lines 4-6 before the bumpl,6,7l,7,8!k,9,L,0.0 ! KP 9 - 12 are after the bumpk,10,L,Lk,11,L,Hk,12,L,H+H0!l,9,10 ! Lines 7-9 after the bumpl,10,11l,11,12!k,13,outlen,0.0 ! KP 13 - 16 are at the outletk,14,outlen,Lk,15,outlen,Hk,16,outlen,H+H0!l,13,14 ! Lines 10-12 at the outletl,14,15l,15,16!l,1,5 ! Lines 13-16 are horizontal lines near inlet

l,2,6 l,3,7l,4,8!l,9,13 ! Lines 17-20 are horizontal lines near outlet l,10,14l,11,15



l,12,16!l,6,10 ! Lines 21-23 are horizontal lines near the bump l,7,11l,8,12! k,17,R,0.0 ! KP 17 to 23 are for the semicircular bumpk,18,0.0,0.0circle,18,R,,17,180,4lcomb,25,26,0!l,19,9 ! Lines 26, 28-30 in radial direction near bumpl,20,10l,22,6l,23,5!

! Select lines and establish line divisions! lsel,s,,,1,4,3lesize,all,,,ny1! lsel,s,,,2,11,3lesize,all,,,ny2,ry2! lsel,s,,,3,12,3lesize,all,,,ny3,ry3! lsel,s,,,13,16lesize,all,,,nx1,rx1! lsel,s,,,21,23lesize,all,,,nx2,1.0/rx2lsel,s,,,25lesize,all,,,nx2,rx2! lsel,s,,,17,20lesize,all,,,nx3,rx3! lsel,s,,,27lesize,all,,,ny1!lsel,s,,,26lsel,a,,,28,30lesize,all,,,nr1!! define the y-direction meshlsel,s,,,24lsel,a,,,7lsel,a,,,10lesize,all,,,nx2,1.5!alls! Create areas....a,1,5,6,2 ! Inleta,2,6,7,3a,3,7,8,4a,9,13,14,10 ! Outleta,10,14,15,11a,11,15,16,12 a,6,10,11,7 ! Bumpa,7,11,12,8a,19,9,10,20a,20,10,6,22a,5,23,22,6allsamesh,all!! Inlet boundary conditionlsel,s,,,1,2nsll,,1d,all,vx,0.32




d,all,vy,0.0!nsel,s,loc,x,-inlennsel,r,loc,y,0.0d,all,vx,0.001!! boundary volume fraction (SFL and SFE commands)sfl,1,vfrc,1,,1sfl,2,vfrc,1,,1!!!!!! The wallslsel,s,,,13lsel,a,,,17lsel,a,,,24,25lsel,a,,,27lsel,a,,,26lsel,a,,,30nsll,,1d,all,vx,0d,all,vy,0alls/solu!!!! FLOTRAN Input acel,0.0,grav,0.0 FLDA,SOLU,VOF,ON FLDA,SOLU,FLOW,ONFLDA,SOLU,TRAN,ONFLDA,SOLU,TURB,ONFLDA,TIME,GLOB,3FLDA,TIME,NUMB,50FLDA,TIME,STEP,1e-2FLDA,TIME,APPE,0.1FLDA,TIME,PRES,1.0E-6FLDA,ADVM,MOME,SUPGflda,relx,vx,0.5flda,relx,vy,0.5flda,relx,pres,1.0flda,prot,dens,constant ! Constant density flda,prot,visc,constant ! Constant viscosityflda,nomi,dens,rho ! Density set earlier flda,nomi,visc,mu ! Viscosity set earliersolvefiniexit,nosa

6.6. VOF Analysis of an Oscillating Droplet


This example examines the interesting phenomenon of a liquid droplet oscillating in an dynamically inactivegas. For small amplitudes, the angular frequency, ω, is given by the following formula from A. Prosperetti,("Free Oscillations of Drops and Bubbles: The Initial-Value Problem," Journal of Fluid Mechanics, Vol. 100, p.333, 1980):

ω σρ

2 2

F3

= [8 - 5 / Re ]R

( )

where ρ is the density, σ is the surface tension coefficient, and RF is the radius of the drop at its equilibrium

state. Here, Re is the Reynolds number given by:

Re =ρσ

µ

RF



where µ is the dynamic viscosity of the liquid.

When the oscillation is fully damped by the viscosity, the droplet takes a spherical shape and the dropletpressure is given by:

P =2

RFtheory

σ

The droplet analyzed here is initially elliptical with major and minor semiaxes of 24.69 mm and 18 mm, re-

spectively. This corresponds to a final radius of RF of 20 mm. The time increment, ∆t, is set to 2 x 10-4 ms.

The material properties of the droplet are:

• ρ = 10−9 mg/(µm)3

• µ = 10−6 mg/(µm)(ms)

• σ = 0.073 mg/(ms)2

The Prosperetti formula gives an oscillation frequency of 43.0 kHz.

6.6.2. Results

Figure 6.1 (p. 76) and Figure 6.2 (p. 76) show the instantaneous pressure distributions at 0.001 ms and 0.012ms, respectively. Rather than a pressure jump across the interface, the pressure is observed to vary smoothlyin a thin transition region near the interface. Initially, the maximum pressure occurs at the top and bottomportion of the droplet due to a high local curvature. The resulting pressure gradient forces the fluid inwardand redirects it to the sides. As the droplet moves, the pressure starts to rise at the sides due to the increasinglocal curvature. This slows down the movement of the droplet and eventually forces the fluid back inwardfrom the sides. The pressure distribution controls the droplet oscillation by balancing the kinetic energy andthe potential energy due to the surface tension. The simulation produces a free surface profile every 5 timesteps. The frequency is 42.6 kHz (two cycles occur in 0.047 ms). This agrees quite well with the 43.0 kHzpredicted by the Prosperetti formula. The oscillation amplitude decreases with time and damps out at 0.2ms due to viscosity. Averaging the pressure values on interior nodes attached to only full elements givesthe numerical droplet pressure. The difference between the numerical and the analytical pressure is approx-imately 1%. There are some noises in the velocity field near the interface due to the so-called parasitic currentsinherent in the CSF formulation.



6.6.2. Results

Figure 6.1 Instantaneous Pressure Distributions at 0.001 ms

Figure 6.2 Instantaneous Pressure Distributions at 0.012 ms



/title, oscillating axisymmetric drop problem by the VOF/CSF solution./noprLX = 30 ! x length in micrometer (um)LY = 30 ! y length in micrometer (um)RadF = 20 ! radius of the final sphere in micrometer (um)aRad = 18 ! x radius in micrometer (um)bRad = RadF**3/aRad**2 ! y radius in micrometer (um)DELX = 0.1*RadF ! x spacing in micrometer (um)DELY = 0.1*RadF ! y spacing in micrometer (um)



DELT = 2.0e-4 ! time increment in millisecond (ms)APPT = DELT*5 ! append time in millisecond (ms)NDT = 1000 ! total number of time stepsSigm = 0.073 ! SFTS coefficient in unit of (mg)/(ms)^2rho = 1.0e-9 ! density in unit of (mg)/(um)^3mu = 1.0e-6 ! viscosity in unit of (mg)/(um)(ms)pexact=2*Sigm/RadF ! theoretical pressure in equilibrium/prep7 et,1,141,,,1 ! RY geometryrect,0,LX,-LY,LYlsel,s,,,2,4,2lesize,all,DELYlsel,s,,,1,3,2lesize,all,DELXamesh,all

nsel,s,loc,x,0 ! symmetry conditiond,all,vx,0.0

allsicvf,elpt,0.0,0.0,aRad,bRad ! initial VFRCic,all,vx,0 ! initial velocityic,all,vy,0savefini

/soluflda,solu,tran,tflda,solu,vof,tflda,solu,sfts,tflda,nomi,sfts,sigmflda,nomi,dens,rhoflda,nomi,visc,muflda,time,glob,10flda,time,numb,NDTflda,time,step,DELTflda,advm,mome,supgflda,mir,mome,1.0flda,relx,pres,1.0flda,time,appe,APPTsolve fini/post1set,lastPLVFRC,0ANDATA,0.1, ,2,1,51,1,0.0,1

set,last*GET,VFAdvU,FLDA,VFTO,VOFUVFAdvU=1.0-VFAdvU

alls*get,elmmax,elem,0,count ! Get the number of elements*get,elmi,elem,0,num,min ! Get the lowest elem number in the set*get,vfval,elem,elmi,nmis,1 ! Get the VFRC for the element*IF,vfval,LE,VFAdvU,thenesel,u,,,elmi ! Remove elmi from the active set*ENDIF

*do,ilop,2,elmmax ! Loop over selected elements *get,elmn,elem,elmi,nxth ! Get the next higher elem number in the set *get,vfval,elem,elmn,nmis,1 ! Get the VFRC for the element *IF,vfval,LE,VFAdvU,then esel,u,,,elmn ! Remove elmn from the active set *ELSE elmi=elmn *ENDIF*enddo

nsle,s,all ! select all node attached to elementsnsel,u,ext ! unselect ext. nodes of prev. selected nodes




pavg=0.0prms=0.0*get,nodmax,node,0,count ! Get the number of selected nodes*do,ilop,1,nodmax ! Loop over the number of nodes*get,nodi,node,0,num,min ! Get the lowest node number in the set*get,pval,node,nodi,pres ! Get the ypavg=pavg+pval ! pressure sumprms=prms+(pval-pexact)**2 ! pressure rmsnsel,u,,,nodi ! Remove node from the active set*enddopavg=pavg/nodmaxprms=sqrt(prms/nodmax)/pexact

/go*vwrite(9x,'DelX/Rad ', 3x, 'PRES / Pexact ',3x,'Prms ')*vwrite,DELX/RadF,pavg/pexact,prms(3(4x,1pe12.5))finiexit,nosa

6.6.4. Where to Find Other Examples

For more examples on the VOF analysis of free surface problems with surface tension, refer to G. Wang,(“Finite Element Simulations of Gas-Liquid Flows with Surface Tension,” International Mechanical EngineeringCongress & Exposition, November 5-10, 2000, Orlando, Florida).



Chapter 7: Arbitrary Lagrangian-Eulerian (ALE) Formulation for

Moving Domains

Fluid flow problems often involve moving interfaces. The interfaces can be moving internal walls (for example,a solid moving through a fluid), external walls, or free surfaces. In such problems, the fluid domain changeswith time and the finite element mesh must move to satisfy the boundary conditions at the moving interfaces.You can use the Arbitrary Lagrangian-Eulerian (ALE) formulation to solve problems of this type.

Figure 7.1 (p. 79) illustrates a typical fluid flow problem requiring the ALE formulation. It involves a micro-electromechanical system (MEMS) device with a viscous fluid between two rigid plates. Initially, the platesare parallel and the fluid is at rest.

Figure 7.1 Torsional Mirror at t = 0 Seconds

The top plate begins to oscillate about its centerline setting the fluid in motion. The ALE formulation allowsthe fluid domain to change with time and the finite element mesh to move to satisfy the boundary conditionsat the moving plate. Figure 7.2 (p. 80) and Figure 7.3 (p. 80) show the finite element mesh at later times.



Figure 7.2 Torsional Mirror at t = 2.5 Seconds

Figure 7.3 Torsional Mirror at t = 7.5 Seconds

To perform a transient analysis employing the ALE formulation, you must activate the ALE formulation andthe transient solution algorithm. To activate the ALE formulation, you use one of the following:

Command(s): FLDATA1,SOLU,ALE,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Setup> Solution Options


To activate the transient algorithm, you use one of the following:

Command(s): FLDATA1,SOLU,TRAN,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options


For more information on transient analyses and the transient algorithm, see FLOTRAN Transient Analyses (p. 59).

To do an ALE analysis, you need to use one of the following elements:


Chapter 7: Arbitrary Lagrangian-Eulerian (ALE) Formulation for Moving Domains

FLUID141, KEYOPT(3) = 0 (Cartesian coordinates), 1 (axisymmetric about Y-axis), or 2 (axisymmetic about X-axis).

FLUID142, KEYOPT(3) = 0 (Cartesian coordinates). You cannot use a cylindrical coordinate system (KEYOPT(3)= 3) with ALE.

You will need to activate KEYOPT(4) to specify boundary motions (displacement DOFs). To define the elementtype, use one of the following:

Command(s): ET,ITYPE,Ename,KOP1,KOP2,KOP3,KOP4,KOP5,KOP6 KEYOPT,ITYPE,KNUM,VALUEGUI: Main Menu> Preprocessor> Element Type> Add/Edit/Delete

Real constants 18 (BDTOL) and 19 (MMFAC) are also used in an ALE analysis.

Currently, free surfaces are not a part of the ALE formulation. However, you can use the Volume of Fluid(VOF) method in conjunction with the ALE formulation to simulate flows involving free surfaces and movingwalls. (Refer to Volume of Fluid (VOF) Analyses (p. 65).)

The following ALE topics are available:7.1. Boundary Conditions7.2. Mesh Updating7.3. Remeshing7.4. Postprocessing7.5. ALE Analysis of a Simplified Torsional Mirror7.6. ALE/VOF Analysis of a Vessel with a Moving Wall7.7. ALE Analysis of a Moving Cylinder

7.1. Boundary Conditions

Generally, either slip or stick boundary conditions apply for moving internal or external walls (See Figure

7.4 (p. 81).)

Figure 7.4 Boundary Conditions for Moving Walls

Slip or stick boundary conditions for displace-ments and velocities

Fluid

n

n

τ

τ

Moving solid




Table 7.1: Interface Boundary Conditions (p. 82) shows the required displacement and velocity specificationsfor slip and stick boundary conditions.

Table 7.1 Interface Boundary Conditions

Stick[1]Slip[1]Boundary Con-

dition

Specify all displacement components forfluid nodes.

Specify normal com-ponent of displace-

Displacement

That is, specify the following:ment for fluidnodes.

That is, specify thefollowing:

3-D2-D

D = d nn ⋅D = d nn ⋅

D = d nn ⋅D = dτ τ

1 1⋅D = dτ τ⋅

or Dx; Dy D = dτ τ2 2⋅

or Dx; Dy; Dz

Viscous FlowInviscid FlowVelocity

Specify all velocity components for fluidnodes.

Specify normal com-ponent of velocityfor fluid nodes.

That is, specify the following:That is, specify thefollowing:

3-D2-D

V = nn υ ⋅V = nn υ ⋅V = nn υ ⋅

V =1 1τ υ τ⋅V =τ υ τ⋅

or Vx; Vy V =2 2τ υ τ⋅

or Vx; Vy; Vz

1. The time derivative of the normal displacement must be equal to the normal velocity, dDn/dt = Vn.

Slip or stick boundary conditions can apply for displacement. For velocity, slip boundary conditions applyfor inviscid flow and stick boundary conditions apply for viscous flow. In all cases, the time derivative of thenormal displacement must be equal to the normal velocity. In FLOTRAN, only stick boundary conditions arecurrently valid.

To set displacement or velocity boundary conditions at nodes, you can use either of the following:

Command(s): D

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement (orVelocity)> On Nodes



Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Displacement (or Velocity)> On

Nodes

To set boundary conditions on the solid model, you can use any of the following:

Command(s): DL and DA

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement (orVelocity)> On Lines


Lines

Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement (or Velo-city)> On Areas


Areas

If a node is part of a distributed resistance or a fan model or part of a solid region composed of FLUID141or FLUID142 elements, homogenous displacement boundary conditions are automatically applied (that is,D,ALL,UX,0.0 and D,ALL,UY,0.0 for 2-D and D,ALL,UX,0.0, D,ALL,UY,0.0, and D,ALL,UZ,0.0 for 3-D).

You can specify partial displacement boundary conditions to make external nodes move along a global axis.For example, D,ALL,UX,0.0 will make a set of nodes slide along the y-axis in a 2-D model. Currently, normaland tangential components of displacement can not be specified for an external boundary.

You can also specify generalized symmetry boundary conditions. If the ALE formulation is activated, velocitycomponents are then set equal to the mesh velocity. To do so, use one of the following commands or theGUI equivalent:

D,NODE,ENDS,-1DL,LINE,AREA,ENDS,-1,Value2DA,AREA,ENDS,-1,Value2

7.2. Mesh Updating

The ALE formulation uses the displacement boundary conditions applied by the D, DL, and DA commandsto update the finite element mesh. It determines the displacement at the beginning of each time step relativeto the previous time step. For each time step, an elasticity based morphing algorithm updates the mesh.The algorithm ensures that boundary layers are retained (that is, nodes in a fine mesh area move less thannodes in a coarse mesh area).

A transient analysis cannot proceed if morphing fails. If morphing is independent of the fluid flow solution,you can step through the morphing algorithm before doing a fluid flow analysis to determine whethermorphing will fail. To do so, issue the following command sequence:

/solu...fldata,solu,turb,ffldata,solu,temp,ffldata,solu,spec,ffldata,solu,ale,tfldata,solu,flow,fsolve

You cannot check for morphing failure in advance if the time step size depends on the fluid flow variablesor the problem involves a free surface.



7.2. Mesh Updating

Mesh morphing is currently available for the following element shapes:

• Pure quadrilaterals, pure triangles, or a combination for FLUID141

• Pure hexahedrals, pure tetrahedrals, pure pyramids, pure wedges, or any combination for FLUID142

Sometimes mesh morphing produces poor quality elements (for example, when a fluid domain is extremelysqueezed by a moving wall). The birth and death feature can then be useful. To implement this feature, youassign a birth/death tolerance to the candidate elements using the real constant BDTOL. A node is automat-ically deactivated if the distance from it to the center of any element face on the wall becomes less thanthe assigned BDTOL. A element is deactivated if all of its nodes are deactivated. Conversely, a node is react-ivated if the distance from it to the center of the closest element face on the wall becomes greater than orequal to the assigned BDTOL. A element is reactivated if all of its nodes are reactivated.

Setting the MMFAC (mesh morphing multiplier) real constant on the FLUID141 or FLUID142 elements canaffect mesh morphing. If the real constant set number defaults to zero in a third-party mesher, the defaultvalue for the multiplier is set to 0.0. In this case, you will need to either set the real constant set number orthe MMFAC real constant explicitly if you are not satisfied with the 0.0 default value.

7.3. Remeshing

Large fluid domain changes can produce poor quality elements and mesh morphing failure. To avoid elementfailure, you must remesh.

To accomplish remeshing, issue one of the following:

Command(s): FLDATA39,REMESHGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Remesh Ctrl

FLDATA39,REMESH will automatically remesh the fluid elements and linearly interpolate the nodal solutionfrom the old mesh to the new mesh. Use it to specify one of the following three ways of remeshing:

• Remesh all defined fluid elements if the quality of the worst defined element falls below any specifiedquality requirement listed in Table 7.2: Element Qualities (p. 84).

Whole domain remeshing is suitable when the moving boundary affects all of the fluid elements (allthe fluid elements may become distorted during solution).

• Remesh defined fluid elements that have a quality below any specified quality requirement.

Partial domain remeshing is suitable when the distorted elements are locally distributed and the locationof the distorted elements is not known before solution or it changes during solution.

• Remesh all grouped fluid elements with a specified component name if the quality of the worst selectedelement falls below any specified quality requirement.

Selected component remeshing is suitable when the distorted elements are locally distributed, but thelocation of the distorted elements is known before solution and it does not change during solution.

There are three maximum allowable element qualities that you need to specify for remeshing: aspect ratio,change of element size, and change of element aspect ratio.

Table 7.2 Element Qualities

TetrahedronsTrianglesElement Quality

AR = ((lavg)3 / V) / 8.48AR = ((lavg)2 / A) / 2.3Generalized Aspect Ratio (AR)



TetrahedronsTrianglesElement Quality

VOCH = exp | log (V(t) / V(0)) |VOCH = exp | log (A(t) / A(0)) |Change of Element Size (VOCH)

ARCH = exp | log (AR(t) / AR(0)) |Change of Aspect Ratio (ARCH)

where:

lavg = average length of the element edges

A = element areaV = element volumeA(t) and V(t) = element area and volume at time tA(0) and V(0) = element area and volume at time 0

You may also specify the following remeshing inputs:

• Elements Excluded

You can exclude all elements connected to boundary nodes from remeshing. For a fluid-structure inter-action analysis, you can exclude the elements connected to fluid-solid interfaces.

• Element Size

The element remeshing size defaults to 0. The element size at the nearest boundary is then used forremeshing.

• Area Expansion or Contraction

You can size internal elements so that they are approximately the size of the boundary elements timesan expansion or contraction factor.

• Checkpoints

You can specify element quality checkpoints in three ways: every time step, every Nth time step, or ata single time point. The fluid elements will automatically remesh if any quality requirement is not metat a checkpoint.

After each remesh, new databases and results files are written with the extensions .rfl0 n and .db n, wheren is the remesh file number (Jobname.rfl01 , Jobname.rfl02 , ... and Jobname.db01 , Job-name.db02 ,...). Use the ANMRES command to create an animation across the results files.

Note

The original database file is Jobname.db0 . The Jobname.db01 , Jobname.db02 , ... files haveelements that are detached from the solid model.

You can use the FLOTRAN remeshing capability in a pure fluid flow analysis or a fluid-solid interaction ana-lysis. For information on fluid-solid interaction analyses, see "Load Transfer Coupled Physics Analysis" and"The ANSYS Multi-field (TM) Solver - MFS Single-Code Coupling" in the Coupled-Field Analysis Guide.



7.3. Remeshing

Some important remeshing limitations are listed in the following table.

Table 7.3 Remeshing Limitations

DescriptionLimitation

Remeshing supports models meshed with triangular or tetrahedralelements. It only works for element groups with one element type andone real constant.

Elements

Remeshing will not work for extreme area or volume changes.Area/VolumeChanges

2-D problems can have multiple domains; 3-D problems require a singledomain. Do not allow two separate domains without distance (e.g.,

Domains

when solving a FSI problem with a beam or shell element, at least oneside elements connected to the beam or shell elements must be ex-cluded from remeshing).

Remeshing can treat nodal loads on the boundary, but it cannot treatbody loads applied to interior nodes. Fluid-solid interaction is the onlyvalid element based load.

Loads

Nodes on the boundary cannot be remeshed. Therefore, remeshingwill not work if morphing failed on surface nodes.

Boundary Nodes

See ALE Analysis of a Moving Cylinder for a problem using remeshing.

7.4. Postprocessing

For postprocessing, you can use the following contour and vector command sequence for the referencedomain or the current deformed domain:

set,load step,substep ! sets the set number for processing/dscal,,1.0 ! sets the scaling for displayplns,pres,,0 ! display pressure contours on deformed domainplve,v,,,,,,,1 ! display velocity vectors on the deformed domain

To view the deformed mesh , issue the following command sequence:

set,load step,substep ! sets the set number for processing/dscal,,1.0 ! sets the scaling for displaypldi,2 ! display the deformed mesh overlayed with undeformed ! edges

To produce an animated sequence of the results, issue the ANTIME macro with the above commands.

Note

The displacements of non-structural elements are mesh (or grid) displacements to avoid meshdistortion but have no physical meaning except at the interface between the fluid and thestructure.



7.5. ALE Analysis of a Simplified Torsional Mirror


This is an Arbitrary Lagrangian-Eulerian (ALE) analysis of a micro-electromechanical system (MEMS) device.The device consists of a viscous fluid between two rigid plates. Initially, the plates are parallel and the fluidis at rest. The top plate begins to oscillate about its centerline setting the fluid in motion. The top plate os-cillates with a very small angular amplitude.

You must determine the torque on the moving plate in order to develop a reduced order model for thisdevice.

Figure 7.5 Torsional Mirror Problem Description

LX

HHo = Yo = H

(Xo, Yo)

Y

X

Fixed plate

Oscillating plate

Initial position ofoscillating plate (at t = 0)

θ = θ(t)

7.5.2. Boundary Conditions

This section derives formulas for the displacement and velocity boundary conditions.

The angle of rotation is: θ = θosinωt

Differentiating, the angular velocity is:ɺθ = ωθocosωt

The position of any point on the plate is given by:

x(t) = xo + Rcosθ

y(t) = yo + Rsinθ

where:

R = xr − xo and xr is the x coordinate on the plate at time equals zero.

Therefore, the displacements of the plate are given by:

UX(t) = x(t) − x(o) = x − xr − R

UY(t) = y(t) − y(o) = y − yo



7.5.2. Boundary Conditions

Substituting the expressions for x and y gives:

UX = R(cosθ − 1)UY = Rsinθ

Note

As θ approaches 0, UX approaches 0 and UY approaches Rθ.

Differentiating displacements gives the following velocity equations:

UX UX R

VY UY R

= = −

= =

ɺ ɺ

ɺ ɺ

sin

cos

θθ

θθ

Note

As θ approaches 0, VX approaches −Rθɺθ ∝ θo

2 and VY approaches R ɺθ ∝ θo. Therefore, VX ap-

proaches 0 faster than VY.

The command listing in Building and Solving the Model (Command Method) (p. 90) uses the above expressionsfor UX, UY, VX, and VY in the boundary condition tables.

7.5.3. Forces and Moments

This section derives formulas for the forces and moments acting on the torsional mirror.

Figure 7.6 Torsional Mirror Problem - Boundary Conditions

L

Y

X

Fixed plateU = V = 0Dx = Dy = 0

θ

p = po p = pohoh = h(x,t)

Oscillating plate U = U(x,t) Dx = Dx (x,t) V = V(x,t) Dy = Dy (x,t)

Assuming the flow is 2-D and neglecting inertia terms, the Navier-Stokes equation reduces to the Reynoldsequation for incompressible flow:

∂∂

∂∂

∂∂x

hp

x= 6

xhU + 12 V3 µ µ( )



where: h = h (x,t) is the gap height and U and V are the velocity components of the moving plate.

Assuming that the angular displacement of the mirror is small gives:

U ≈ 0

V ≈ R ɺθ

R ≈ x

Substituting these values in the Reynolds equation and assuming that U variations with x are small gives:

∂∂

∂∂

xh

p

x= 12 V = 12 x3 µ µ θɺ

Integrating gives:

p dx= +∫ ∫6x

h

C

hdx + C

2

313 2µθɺ

where C1 and C2 are constants to be determined.

Substituting ho for h for small angular displacements and completing the integration gives:

p =

6

h

x

3+

C x

h+ C

o3

31

o3 2

µθɺ

Substituting p = po at x = ± L/2 gives:

po =

2

h

L

2+

C

h

L

2+ C

o3

31

o3 2

µθɺ

po =

-

2

h

L

2-

C

h

L

2+ C

o3

1

o3 2

µθɺ 3

Solving these two equations for C1 and C2 gives:

C2 = po

C1 = −2 µɺθ (L/2)2

Substituting the C1 and C2 values into the pressure equation gives:

p po= +

2

hx -

2

h

L

2x

o3

3

o3

µθ µθɺ ɺ 2



7.5.3. Forces and Moments

( )p - p2

hx -

L

2oo3

=

µθɺx2

2

Thus, the force and moment on the torsional mirror are given by:

F = (p - p ) dx = 0p o

- L/2

L/2

∫

M = p - p xdx = -1

60

L

hp o

- L/2

L/25

o3

( )∫ µθɺ

The flow field at any x coordinate is given by:

U x,y,t =1

2

p

xy y -( ) ( )

µ∂∂

h

Accordingly, the shear stress on the torsional mirror is:

µ µθ∂∂

∂∂

U

y=

p

x=

h3x -

L

2y = ho2

22

h

2

ɺ

Thus, the force and moment due to shearing stresses are:

F =U

ydx = 0s

- L/2

L/2

y = hµ ∂∂∫

M =U

yxdx = 0s

- L/2

L/2

y = hµ ∂∂∫


The following command stream shows all the relevant parameters and solution strategy. All text prefacedwith an exclamation point (!) is a comment. Please refer to Figure 7.5 (p. 87).

/BATCH,LIST/tit,Torque Mirror Problem /noprLX = 1.0 ! Plate Length in X directionNDX = 40 ! Number of X divisionsH = 0.01 ! Gap in Y-direction NDY = 10 ! Number of Y divisionsPOUT = 0.0 ! Outlet relative pressureRHO = 1.0000 ! Fluid density



MU = 1.00 ! Fluid viscositynts = 40 ! number of time stepstime = 10. ! total simulation timedelta = time/nts ! time step sizeappf = delta ! append results every time step*AFUN,RAD ! angles are in radiansAMAX = (2*H/LX)/8 ! adjust angular amplitude << 1OMEGA = 2*3.14159/time ! complete 1 cycle in given timeX0 = LX/2 ! pivot point x-coordY0 = H ! pivot point y-coordH0 = H

! use function builder/tables (refer to "Using the Function Tool" in the Basic Analysis Guide)

! for displacements/velocities of oscillating plate

*DIM,UXTAB,TABLE,6,4,1UXTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX, 0.0, 0.0UXTAB(0,1,1) = 1.0,-1 , 0, 1.0 , 27 , 2 , 17 ! Radius = XR - X0UXTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 ! Angle=amax*sin(omega*t) UXTAB(0,3,1) = 0.0,-3 , 10, 1.0 ,-2 , 3 ,-1 ! Radius*cos(Angle) UXTAB(0,4,1) = 0.0,99 , 0, 1.0 ,-3 , 2 ,-1 ! Radius*cos(Angle)-Radius *DIM,UYTAB,TABLE,6,3,1UYTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX, 0.0, 0.0UYTAB(0,1,1) = 1.0,-1 , 0, 1.0 , 27 , 2 , 17 ! Radius = XR - X0UYTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 ! Angle=amax*sin(omega*t) UYTAB(0,3,1) = 0.0,99 , 9, 1.0 ,-2 , 3 ,-1 ! Radius*sin(Angle) *DIM,VXTAB,TABLE,6,5,1VXTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX,OMEGA*AMAX, 0.0VXTAB(0,1,1) = 1.0,-1 , 0,-1.0 , 27 , 1 , 17 ! -Radius = -(XR-X0)VXTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 ! Angle=amax*sin(omega*t) VXTAB(0,3,1) = 0.0,-3 , 10,OMEGA, 1, 3 , 19 ! Angle speed= ! amax*omega*cos(omega*t)VXTAB(0,4,1) = 0.0,-4 , 9, 1.0 ,-2 , 3 , -1 ! -Radius*sin(angle)VXTAB(0,5,1) = 0.0,99 , 0, 1.0 ,-4 , 3 , -3 !-Radius*sin(angle)*angle speed*DIM,VYTAB,TABLE,6,5,1VYTAB(0,0,1) = 0.0,-999, 1, X0 ,AMAX,OMEGA*AMAX, 0.0VYTAB(0,1,1) = 1.0,-1 , 0, 1.0 , 27 , 2 , 17 !Radius = XR - X0VYTAB(0,2,1) = 0.0,-2 , 9,OMEGA, 1 , 3 , 18 !Angle=amax*sin(omega*t)VYTAB(0,3,1) = 0.0,-3 , 10,OMEGA, 1, 3 , 19 !Angle speed= !amax*omega*cos(omega*t)VYTAB(0,4,1) = 0.0,-4 , 10, 1.0 ,-2 , 3 , -1 !Radius*cos(angle)VYTAB(0,5,1) = 0.0,99 , 0, 1.0 ,-4 , 3 , -3 !Radius*cos(angle)*angle speed

/PREP7 $smrt,off et,1,141 ! 2-D XY systemkeyopt,1,4,1 ! allow disp. DOFsesha,2 ! Quad elementsrect,,LX,,Hlesize,1,,,NDX,lesize,3,,,NDX,lesize,2,,,NDY,-10lesize,4,,,NDY,-10allsamesh,all

lsel,s,,,3 ! Moving top plate nsll,s,1d,all,VX,%VXTAB%d,all,VY,%VYTAB%d,all,enke,-1d,all,ux,%UXTAB%d,all,uy,%UYTAB%

lsel,s,,,2 ! Left & Right Outlets lsel,a,,,4 nsll,s,1d,all,pres,POUT

lsel,s,,,1 ! Stationary bottom plate nsll,s,1




d,all,vx, d,all,vy, d,all,ux,0.0d,all,uy,0.0

allsfini

/SOLUFLDA,NOMI,DENS,RHO ! Nominal densityFLDA,NOMI,VISC,MU ! Nominal viscosityFLDA,OUTP,TAUW,T ! Output wall shear stressflda,quad,momd,2 ! increased quadrature for deformedflda,quad,moma,2 ! elementsflda,quad,moms,2flda,quad,prsd,2flda,quad,pres,2flda,solu,tran,tflda,time,step,deltaflda,time,numb,ntsflda,time,tend,timeflda,time,glob,25flda,time,appe,appfflda,solu,ale,t ! Turn ALE onsaveSOLVEfini

!do the comparison with analytical solution here/post1!moving wall*dim,RES1,,NDX+1,15*do,j,1,nts,1 ! loop over the time stepsrsys,0 csys,0set,1,j ! get the results of step j*get,curtime,active,0,set,time ! get the time of this substeptheta = amax*sin(omega*curtime) ! get the plate anglethetad = amax*omega*cos(omega*curtime) ! get plate angular speednsel,s,loc,y,H ! select moving wall nodes*do,i,1,NDX+1 ! loop over these nodes *get,XMAX,node,,mxloc,x n = node(XMAX,H,0) RES1(i,1) = n ! Node number RES1(i,2) = NX(n) ! X-coordinate RES1(i,3) = NY(n) ! Y-coordinate RES1(i,4) = UX(n) ! UX Rn = NX(n)-X0 RES1(i,10) = Rn*(cos(theta)-1.0) ! UX exact RES1(i,5) = UY(n) ! UY RES1(i,11) = Rn*sin(theta) ! UY exact RES1(i,6) = VX(n) ! VX RES1(i,12) = -Rn*sin(theta)*thetad ! VX exact RES1(i,7) = VY(n) ! VY RES1(i,13) = Rn*cos(theta)*thetad ! VY exact RES1(i,8) = PRES(n) ! Pressure c1 = 2.0*MU*thetad/H0**3 c2 = NX(n) - X0 RES1(i,14) = c1*(c2**3 - c2*(LX/2)**2) ! Exact Pressure *get,RES1(i,9),node,n,TAUW ! Shear stress c0 = NX(n) - X0 c1 = H0 + theta*c0 c2 = 3*c0**2 - (LX/2)**2 RES1(i,15) = ABS(c1*mu*thetad*c2/H0**3) ! Exact shear stress nsel,u,,,n*enddo/com Compare disps/velocities/pressures/shears on moving wall(X,H,0)/com*status,curtime*status,theta *vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'UX (FLOTRAN)',5x,'UX (Exact)')



*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,4),RES1(1,10)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'UY (FLOTRAN)',5x,'UY (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,5),RES1(1,11)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'VX (FLOTRAN)',5x,'VX (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,6),RES1(1,12)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'VY (FLOTRAN)',5x,'VY (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,7),RES1(1,13)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'PRE (FLOTRAN)',5x,'PRE (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,8),RES1(1,14)(3x,f5.0,4(1pe17.5))/com*vwrite(4x,'NODE',7x,'X COOR',12x,'Y COOR',9x,'TAU (FLOTRAN)',5x,'TAU (Exact)')*vwrite,RES1(1,1),RES1(1,2),RES1(1,3),RES1(1,9),RES1(1,15)(3x,f5.0,4(1pe17.5))/comnsel,s,loc,y,H ! select nodes on moving platelocal,11,0,X0,Y0,0 ! setup local coord system for moment calcsrsys,11/com compute pressure force/moments on the wallintsrf,pres*get,forcex,intsrf,0,item,fx*get,forcey,intsrf,0,item,fy*get,forcez,intsrf,0,item,fz*get,momx,intsrf,0,item,mx*get,momy,intsrf,0,item,my*get,momz,intsrf,0,item,mz*status,forcex*status,forcey ! should be zero*status,forcez*status,momx*status,momy*status,momz ! FlotranMoment = -0.0166*mu*thetad*LX**5/H0**3 ! Exact*status,moment/com compute shear force/moments on the wall should be zerointsrf,tauw*get,forcex,intsrf,0,item,fx *get,forcey,intsrf,0,item,fy*get,forcez,intsrf,0,item,fz*get,momx,intsrf,0,item,mx*get,momy,intsrf,0,item,my*get,momz,intsrf,0,item,mz*status,forcex ! should be zero*status,forcey*status,forcez*status,momx*status,momy*status,momz ! should be zero*enddofini/exit,nosa




7.6. ALE/VOF Analysis of a Vessel with a Moving Wall


This problem involves a moving wall and a free surface. A square vessel is half filled with liquid and at t =0 the left wall begins to move to the right. The wall stops moving after a short time and the fluid comes torest gradually. The total analysis time is 2 seconds. The left wall comes to rest at 0.125 * (time) = 0.125*(2seconds) = 0.25 seconds. The left wall displacement and velocity are input as tabular boundary conditions(see Figure 7.8 (p. 95)). The simulation uses the Volume of Fluid (VOF) method in conjunction with the ALEformulation.

Figure 7.7 Square Vessel with a Moving Wall

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H

Free SurfaceFree SurfaceRight

StationaryWall

RightWallStationary

LXt = 0

LeftMovingWall

LeftWallStationary

Liquid = 1.0 = 1.0

LXFt = 0.125 * Time

Liquid

LX

µρ

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Free SurfaceSteadySolution

t = Time

Liquid



Figure 7.8 Left Wall Displacement and Velocity

LX-LXF

Time0.125 * Time t

(LX-LXF)0.125 * Time

Time0.125 * Time t

~ 10-6ε

ε

VX

UX

7.6.2. Results

The initial fluid volume is 1/2 H times LX. Since H and LX are both equal to 1, the initial fluid volume is0.500000000. The calculated final fluid volume is 0.499999673.



/BATCH,LIST/title,ALE-VOF combination - container with moving wall & free surface/noprLX = 1.0 ! Initial width in X directionNDX = 10 ! Number of X divisionsH = 1.0 ! Height of container NDY = 10 ! Number of Y divisionsRHO = 1.0000 ! Fluid densityMU = 1.00 ! Fluid viscosityLXF = 0.750 ! Final X-Length time = 2. ! Total simulation timents = 200 ! Total number of time stepsdelta = time/nts ! Time step sizeappf = delta ! Results append frequencyVEL = (LX-LXF)/(0.125*time) ! left wall moves for 12.5% of ! simulation time with velocity VEL

*dim,timutab,table,3,,,time ! left wall displacement historytimutab(1,0)=0,0.125*time,time timutab(1,1)=0,(LX-LXF),(LX-LXF)*dim,timvtab,table,4,,,time ! left wall fluid velocity historytimvtab(1,0)=0,0.125*time,0.125*time+0.000001,time timvtab(1,1)=VEL,VEL,1.e-12,1.e-12




/PREP7 $smrt,off et,1,141 ! 2-D XY systemkeyopt,1,4,1 ! enable disp DOFsesha,2 ! Quad elementsrect,,LX,,Hlesize,1,,,NDX,-10lesize,3,,,NDX,-10lesize,2,,,NDY,lesize,4,,,NDY,allsamesh,all

lsel,s,,,4 ! Moving left wall nsll,s,1d,all,VX,%timvtab%d,all,VY,d,all,enke,-1d,all,ux,%timutab%d,all,uy,0.0

lsel,s,,,1 ! bottom wallnsll,s,1d,all,vxd,all,vy

lsel,s,,,3 ! top wall nsll,s,1d,all,vxd,all,vy

lsel,s,,,2 ! Stationary right wall nsll,s,1d,all,vx, d,all,vy, d,all,ux,0.0d,all,uy,0.0

alls

nsel,s,loc,y,0,0.5*H ! select lower half elementsesln,s,1ice,all,vfrc,1.0 ! apply vof initial conditionsallsel

fini

/SOLUFLDA,NOMI,DENS,RHO ! Nominal densityFLDA,NOMI,VISC,MU ! Nominal viscosityacel,,9.8 ! Apply gravity loadingflda,step,sumf,1flda,solu,tran,tflda,time,step,deltaflda,time,numb,nts flda,time,tend,timeflda,time,glob,25flda,time,appe,appf flda,solu,ale,t ! Ale onflda,solu,vof,t ! Vof onsaveSOLVEfini

!do the comparison here for final fluid volume/post1set,lastfvol = 0. ! initialize volume to zero*do,i,1,NDX*NDY ! loop over elements n1 = nelem(i,1) ! 4 nodes of this element n2 = nelem(i,2) n3 = nelem(i,3) n4 = nelem(i,4)



x1 = nx(n1)+ux(n1) ! current coords of the 4 nodes y1 = ny(n1)+uy(n1) x2 = nx(n2)+ux(n2) y2 = ny(n2)+uy(n2) x3 = nx(n3)+ux(n3) y3 = ny(n3)+uy(n3) x4 = nx(n4)+ux(n4) y4 = ny(n4)+uy(n4) evol1 = x1*y2+y1*x3+y3*x2 ! compute volume of triangle 123 evol1 = evol1-y2*x3-y1*x2-x1*y3 evol1 = abs(0.5*evol1) ! first triangle volume evol2 = x1*y4+y1*x3+y3*x4 ! compute volume of triangle 143 evol2 = evol2-y4*x3-y1*x4-x1*y3 evol2 = abs(0.5*evol2) ! second triangle volume *get,frac,elem,i,nmisc,1 ! get VOF of this quad fvol = fvol + (evol1+evol2)*frac!increment the total fluid volume*enddo*status,fvol ! print the final fluid volumetarget = 0.5*H*LX*status,target ! print the expected fluid volume/comfini/exit,nosa

7.7. ALE Analysis of a Moving Cylinder


This problem involves a cylinder passing through a channel with a constant velocity VX = 1.0. FLUID141 tri-angle elements model the fluid. The simulation uses the ALE formulation and remeshing.FLDATA39,REMESH,Label,Value specifies the quality requirements shown in the following table.

Table 7.4 Quality Requirements

FLDATA39,REMESH,Label,Value CommandElement Quality

FLDATA39,REMESH,ARMA,5.0Aspect Ratio (AR)

FLDATA39,REMESH,VOCH,3.0Change of Element Size (VOCH)

FLDATA39,REMESH,ARCH,3.0Change of Aspect Ratio (ARCH)

FLDATA39,REMESH,ELEM,ALL sets the remeshing to all defined fluid elements if the quality of the worstdefined element falls below any quality requirement. The total analysis time is 44 seconds.

Figure 7.9 Moving Cylinder

5

5

5

12.5 47.5

UX = 0, UY = 0, VY = 0

UX = 0UY = 0

P = 0

UX = 0UY = 0VX = 0VY = 0

y

x UX = 0, UY = 0, VY = 0

VX = 1.0UX = t

ρ = 1.0µ = 1.0



7.7.1.The Problem Described

7.7.2. Results

The ten results files are file.rfl01 through file.rfl10. They were created when one of the remeshing criteriawere met. The following figures display the remeshed elements at 0, 22, and 44 seconds.

Figure 7.10 Elements at 0 Seconds





/batch,list/verify,dv-1101c/title, dv-1101c, Flotran Remeshing: Cylinder pass through a channel/COM,****************************************************/COM,* Cylinder pass through a channel (pure fluid flow)/COM,* Verify partial domain re-meshing/COM,****************************************************r1 = 2.5l1 = 5.0l2= 20.0l3=60.0h = 10.0



rx0= l1+(l2-l1)/2.0ry0 = h/2.0nl1 = 5nl3 = 10nr=8nc=8/PREP7

*DEL,_FNCNAME *DEL,_FNCMTID *DEL,_FNC_C1*SET,_FNCNAME,'DIS'*DIM,_FNC_C1,,1 *SET,_FNC_C1(1),1.0! /INPUT,force.func *DIM,%_FNCNAME%,TABLE,6,3,1 ! ! Begin of equation: a*TIME *SET,%_FNCNAME%(0,0,1), 0.0, -999 *SET,%_FNCNAME%(2,0,1), 0.0 *SET,%_FNCNAME%(3,0,1), %_FNC_C1(1)%*SET,%_FNCNAME%(4,0,1), 0.0 *SET,%_FNCNAME%(5,0,1), 0.0 *SET,%_FNCNAME%(6,0,1), 0.0 *SET,%_FNCNAME%(0,1,1), 1.0, -1, 0, 1, 17, 3, 1 *SET,%_FNCNAME%(0,2,1), 0.0, 99, 0, 1, -1, 0, 0 *SET,%_FNCNAME%(0,3,1), 0 ! End of equation: a*TIME !-->

RECTNG,0,l1,0,h, RECTNG,l1,l2,0,h, RECTNG,l2,l3,0,h, aglue,all

CYl4,rx0,ry0,0,45,r1,135 CYl4,rx0,ry0,0,135,r1,225 CYl4,rx0,ry0,0,225,r1,315 CYl4,rx0,ry0,0,315,r1,405 asel,s,,,2asel,a,,,3asel,a,,,6asel,a,,,7allsel,below,areaaglue,all allselFLST,3,4,5,ORDE,3 FITEM,3,2 FITEM,3,8 FITEM,3,-10 ASBA, 4,P51Xaplot

et,1,141KEYOPT,1,4,1type,1mat,1asel,s,,,1esize,.5mshape,1,2dmshkey,0amesh,all

et,2,141KEYOPT,2,4,1type,2mat,1asel,s,,,3esize,.5mshape,1,2dmshkey,0




amesh,all

et,3,141KEYOPT,3,4,1type,3mat,1asel,s,,,5esize,2.0mshape,1,2dmshkey,0amesh,allnsel,s,loc,x,0D,ALL,VX,0.0, D,ALL,VY, 0.0D,ALL,UX,0.0, D,ALL,UY, 0.0nsel,s,loc,x,l3D,ALL,pres,0.0D,ALL,UX,0.0, D,ALL,UY, 0.0nsel,s,loc,y,0D,ALL,vy,0.0D,ALL,UX,0.0, D,ALL,UY, 0.0nsel,s,loc,y,hD,ALL,vy,0.0D,ALL,UX,0.0, D,ALL,UY,0.0,lsel,s,,,5lsel,a,,,23lsel,a,,,25lsel,a,,,27nsll,s,1d,all,UX,%DIS%d,all,UY,0.0d,all,VX,1.0d,all,VY,0.0allselcdwrite,db,fluid,cdb,fini! Flotran Setup/soluFLDATA30,QUAD,MOMD,2, FLDATA30,QUAD,MOMS,2, FLDATA30,QUAD,PRSD,2, FLDATA30,QUAD,PRES,2, FLDATA30,QUAD,THRD,0, FLDATA30,QUAD,THRS,0, FLDATA30,QUAD,TRBD,0, FLDATA30,QUAD,TRBS,2, /soluFLDATA4,TIME,NUMB,100000, FLDATA4,TIME,TEND,44.0,

FLDA,SOLU,ALE,T ! ALE solutionFLDATA1,SOLU,FLOW,1FLDATA1,SOLU,TRAN,1!FLDATA1,SOLU,TURB,1FLDATA2,TIME,GLOB,5

FLDATA7,PROT,DENS,CONSTANTFLDATA8,NOMI,DENS,1.0FLDATA7,PROT,VISC,CONSTANTFLDATA8,NOMI,VISC,1.0!FLDA,BULK,BETA,1.0e5FLDA,TIME,STEP, 2.0!!!! Newmark method!FLDATA,OUTP,TAUW,TFLDATA,TIME,METH,NEWMFLDATA,TIME,DELT,0.5



!!! Set ANSYS-STRUCTURE commandsSAVE/COM /COM Re-meshing Commands/COM FLDATA,REMESH,ELEM,ALL ! all defined element re-meshingFLDATA,REMESH,ARMA,10.0 ! maximum aspect ratioFLDATA,REMESH,VOCH,5.0 ! maximum volume changeFLDATA,REMESH,ARCH,5.0 ! maximum aspect ratio changeSOLVESAVEfinish





Chapter 8: FLOTRAN Compressible Analyses

As is true with turbulence, activating the compressible algorithm is at your discretion. You should activateturbulence for virtually all compressible analyses, (although in principle the Reynolds number can be in thelaminar range for high Mach numbers). Differences in results (pressure, density, velocity distributions) betweenthe incompressible and compressible algorithms can exist at Mach numbers as low as 0.3, and are quitepronounced when the Mach number is as high as 0.7.

The speed of sound is a function of the equation of state of the fluid and its absolute temperature. For aconstant density fluid, the speed of sound is infinite. For an ideal gas, regardless of whether the incompressibleor compressible solution algorithm is used, the relationship is:

C RT= γ

In the preceding equation:

• R is the Universal Gas Constant

• γ is the ratio of specific heats (Cp/Cv)

• T is the absolute temperature

For 2-D compressible analyses, meshes using quadrilateral elements are highly recommended. Hexagonalelements are recommended for 3-D cases. For more information, see Structured vs. Unstructured Mesh (p. 105).

The following compressible analysis topics are available:8.1. Property Calculations8.2. Boundary Conditions8.3. Structured vs. Unstructured Mesh8.4. Solution Strategies8.5. Example of a Compressible Flow Analysis8.6. Doing the Example Compressible Flow Analysis (GUI Method)8.7. Doing the Example Compressible Flow Analysis (Command Method)

8.1. Property Calculations

The compressible algorithm takes into account the kinetic energy changes of the fluid as it accelerates. Theformulation is in terms of the total temperature.

In an adiabatic analysis, the total temperature remains constant throughout the problem domain. You specifythe temperature using either of the following methods:

Command(s): FLDATA14,TEMP,TTOT,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


The conservation of energy is then a balance between thermal storage (static temperature) and kinetic energy.



The total (stagnation) temperature is the temperature of the fluid after it has been brought isentropicallyto a zero velocity. Typically, you choose the conditions at the inlet. Knowledge of the static temperatureand the velocity magnitude |V| at the inlet enables you to calculate the total temperature via the followingequation,

T TV

Co static

p

= +2

2

This relationship is sometimes useful when cast in terms of the Mach number (M):

T T Mo = +−

( )11

2

2γ

You must specify the specific heat and the ratio of specific heats γ. (To enter this ratio, use one of the follow-ing:)

Command(s): FLDATA17,GAMM,COMP,GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


The ANSYS program uses the resulting static temperature and the absolute pressure to calculate the densityfrom the equation of state.

Note

Unlike incompressible analyses, where freezing the density calculation for the early global iterationscan be an advantage, compressible analyses automatically involve the variable density option.Another difference between these types of analysis is that for compressible analyses, initialproperties are calculated from the calculated static temperature, not from the nominal temperature.


Typically, you will know the Mach number or the velocity or the mass flow along with the static temperaturefor the inlet. Knowing the velocity or Mach number enables you, using the above equations, to calculate ofthe appropriate total temperature. If you know only the mass flow rate, you can approximate the pressureat the inlet by the reference pressure and use it with the equation of state to approximate the inlet densityand thus the velocity.

For subsonic problems, the boundary condition strategy is similar to that used for incompressible flowproblems, that is, velocity or pressure at the inlet and pressure at the outlet. For supersonic problems,however, the nature of the equations changes and the effects of downstream boundary conditions cannotpropagate upstream. It is common in such cases to apply both pressure and velocity to upstream locations.Leave the downstream boundary unspecified.

Free stream conditions are often applied as far field boundary conditions for external flow problems. Oftenspecification of pressure at these boundaries helps. However, as the solution develops, phenomena such asshock waves propagate to these boundaries. In this case, you should remove the boundary conditions.Failure to do so could adversely affect the resultant mass balance. Also, if the boundary is too close to theregion of interest (e.g. the airfoil the flow is moving past), the velocity solution near the boundary will tend



to be greater than the free stream velocity. In such cases, a better choice for the velocity boundary conditionsis the symmetry condition (only specify the velocity normal to the boundary as zero).

If the problem is thermal, ANSYS takes all of the applied boundary conditions to be total temperature, notstatic temperature. Conversely, if a problem is adiabatic, thermal boundary conditions are ignored.

If you use a thermal incompressible solution as a starting point for a thermal compressible problem, youmust change the boundary conditions so that they are specified in terms of total temperature.

8.3. Structured vs. Unstructured Mesh

As noted at the beginning of this chapter, for 2-D compressible flow problems, quadrilateral mesh is thebest to use. Consider Figure 8.1 (p. 105):

Figure 8.1 Three Types of Meshing

(a) Quadrilateral mesh, (b) Triangular mesh with a random pattern, (c) Triangular mesh witha symmetrical pattern

In 2-D compressible analyses, mesh (a), the quadrilateral mesh, produces the most accurate results. Mesh(b) yields 2-D, not 1-D results, and mesh (c) yields 1-D results.

Similarly, in a 3-D compressible analysis, a hexagonal mesh (the equivalent of quadrilateral mesh in 2-D)produces the best results. A tetrahedral mesh with a random pattern (the 3-D equivalent of mesh (b)) yieldsonly 3-D results, not 1-D. And a tetrahedral symmetric mesh, the 3-D equivalent of mesh (c), gives you 1-Dresults.


You must solve compressible analyses as pseudo-transient or transient problems. This is due to the non-el-liptic nature of supersonic problems. The pseudo-transient approach is quite adequate when the time-historyof the developing transient is not of interest. In that approach, you apply inertial relaxation to the pressureequation (see Inertial Relaxation (p. 106)).

For an ideal gas, the density is always calculated from an equation of state involving the absolute pressureand the absolute temperature. Because of this, you must prevent negative values of absolute pressure andabsolute static temperature from being encountered during the iterative process, as these would lead to anegative density. One way to do this is to use a converged incompressible solution as a starting point. An-other way is to use capping to specify a minimum FLOTRAN (relative) pressure. For example, to keep theabsolute pressure at a minimum of 1 psi, you would cap the relative pressure at -13.7 psi for a referencepressure of 14.7 psi. Capping is not a stability control and by itself it will not control the solution progression.It only helps prevent negative properties.




Artificial viscosity helps to prevent negative temperatures. You set it at the beginning of the analysis, andmust reduce it slowly for subsequent continuations of the analysis. You will probably encounter divergenceif you increase the viscosity between runs. The magnitude of the artificial viscosity required can vary greatly.The smaller the starting value, the fewer the global iterations required. But if it is not large enough, you mayencounter negative static temperatures. You can use the laminar and effective viscosities to gauge a goodstarting value. It is typically a couple orders of magnitude higher than the effective viscosity, which in turnis initialized as a multiple of the laminar value. Generally, a value 3 or 4 orders of magnitude higher thanthe laminar viscosity is a good approximate starting point.

In a compressible problem, the final answer would be a function of the artificial viscosity if it were not re-moved. Therefore, after stability has been achieved, gradually remove the artificial viscosity during repeatedanalysis continuations.

8.4.1. Inertial Relaxation

Inertial relaxation helps to stabilize a solution by increasing the magnitude of the main diagonal of thematrix equation along with a corresponding increase in the forcing function. Values used are generally

between 1.0 x 10-3 (less relaxation) and 1.0 x 10-6 (more relaxation) for pressure. The smaller values providemore diagonal dominance and thus equation stability. The cost of this is slower convergence since it de-emphasizes the influence of the cross-coupling terms present in the equations.

Unlike artificial viscosity, the inertial relaxation does not affect the answer if the problem is converged and

thus does not have to be removed. It is best to reduce the magnitude to the range of 1 x 10-4 later in theanalysis. You can measure the effectiveness of the relaxation by observing the performance of the parameterRTR in the Jobname.DBG file.

All the techniques discussed so far involve the steady state algorithm. It is common for supersonic problems,even if they are posed as steady state to be solved with the transient algorithm. An initial velocity field canbe imposed as a first guess. The inertial relaxation acts similarly to the transient algorithm and its use isconsidered redundant in transient analyses. Do note that problems involving moving shocks may lead toinaccurate solutions when using the transient algorithm. With the current set of governing partial differentialequations and the discretization techniques used, the transient algorithm has demonstrated solutions thatare qualitatively correct but may yield quantitatively inaccurate results.

8.5. Example of a Compressible Flow Analysis

8.5.1. The Example Described

This example evaluates compressible flow in a converging-diverging nozzle. The nozzle is axisymmetric withinlet, throat, and outlet radii of 2.432 cm, 0.5 cm and 0.80 cm, respectively. The nozzle inlet pressure is given

as 6.13769e+6 dynes/cm2.

8.5.1.1. Fluid Properties

The analysis uses density, viscosity, thermal conductivity, and specific heat properties for air in units of cm-g-sec.

8.5.1.2. Approach and Assumptions

The compressible flow analysis is a turbulent analysis that uses the FLUID141 2-D Fluid-Thermal element.



The analysis assumes atmospheric pressure conditions at the outlet. It assumes a stagnation temperatureof 550 K.

Inlet and outlet pressure boundary conditions are set to 6.13769e+6 dynes/cm2 and 0, respectively. The VYvelocity component is set to 0 along the axis of symmetry and the VX and VY velocity components are setto 0 along the outer surface.

The analysis starts with 20 iterations at an artificial viscosity of 10. It then continues for 20 iterations at arti-ficial viscosity values of 1, .1, .01, .001, .0001, and .00001 to give a total of 140 iterations. The analysis thencontinues for another 160 iterations at an artificial viscosity of 0. After 300 iterations of slowly reducing theviscosity to 0, the analysis continues for 100 iterations with increased momentum and pressure inertial relax-ation factors. Finally, the analysis converges to a final solution with the momentum and pressure inertialrelaxation factors increased to higher values for 400 iterations.

8.6. Doing the Example Compressible Flow Analysis (GUI Method)

You perform the following steps to analyze the converging diverging nozzle using the GUI Method.

Step 1: Establish an Analysis Title and Preferences

1. Choose Utility Menu> File> Change Title. The Change Title dialog box appears.

2. Enter the text "Compressible Flow in a Converging Diverging Nozzle."

3. Click on OK.

4. Choose Main Menu> Preferences. The Preferences for GUI Filtering dialog box appears.

5. Click the button for FLOTRAN CFD to "On."

6. Click on OK.

Step 2: Define Element Types

1. Choose Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Types dialog boxappears.

2. Click on Add. The Library of Element Types dialog box appears.

3. In the two scrollable lists, highlight (click on) "FLOTRAN CFD" and "2D FLOTRAN 141."

4. Click on OK. ANSYS returns you to the Element Types dialog box.

5. Click on Close.

Step 3: Create Keypoints

1. Choose Main Menu> Preprocessor> Modeling> Create> Keypoints> In Active CS. The Create Key-points in Active Coordinate System dialog box appears.

2. In the "Keypoint number (NPT)" field enter 1 and in the "Location in active CS (X and Y)" fields enter0 and 2.432, respectively. Click on Apply.

3. Repeat the previous substep for the following sets of keypoint numbers and (X, Y) locations: 2 (0, 0),3 (1, 2.432), 4 (1, 0), 5 (2, 2.232), 6 (2, 0), 7 (5, 0), 8 (5, 0.7), 9 (6, 0), 10 (6, 0.5), 11 (14, 0), 12 (14, 0.8).After entering each set, click on Apply. After entering the last set, click on OK.

4. Click on SAVE_DB on the ANSYS Toolbar.



Step 3: Create Keypoints

Step 4: Create Lines

1. Choose Utility Menu> PlotCtrls> Numbering. The Plot Numbering Controls dialog box appears.

2. Click the button for "Line Numbers (LINE)" to "On" and click OK.

3. Choose Main Menu> Preprocessor> Modeling> Create> Lines> Lines> In Active Coord. The Linesin Active Coord picking menu appears.

4. Pick the keypoint numbers 2 and 4 and click on Apply.

5. Repeat steps 3 and 4 for the following sets of keypoint numbers: 3 and 4; 1 and 3; 1 and 2; and 5 and8. After entering each set, click on Apply. After entering the last set, click on OK.

6. Choose Main Menu> Preprocessor> Modeling> Create> Lines> Lines> Tan to 2 Lines. The LineTangent to 2 Lines picking menu appears.

7. Pick line number 3 and click on Apply. The Line Tangent to 2 Lines picking menu reappears.

8. Pick keypoint number 3 and click on Apply. The Line Tangent to 2 Lines picking menu reappears.


10. Pick keypoint number 5 and click on OK.


12. Pick the keypoint numbers 10 and 12 and click on OK.

13. Choose Main Menu> Preprocessor> Modeling> Create> Lines> Lines> Tan to 2 Lines. The LineTangent to 2 Lines picking menu appears.


15. Pick keypoint number 8 and click on Apply. The Line Tangent to 2 Lines picking menu reappears.


17. Pick keypoint number 10 and click on OK.


19. Pick the keypoint numbers 4 and 6 and click on Apply.

20. Enter the following sets of keypoint number by repeating steps 18 and 19: 6 and 7; 7 and 9; and 9and 11. After entering each set, click on Apply. After entering the last set, click on OK.

Step 5: Create Areas

1. Choose Main Menu> Preprocessor> Modeling> Create> Areas> Arbitrary> Through KPs. The CreateArea thru KPs picking menu appears.

2. Pick the keypoint numbers (2, 4, 3, 1) and click on Apply.

3. Repeat the previous substep for the following sets of keypoint numbers: (4, 6, 5, 3), (6, 7, 8, 5), (7, 9,10, 8), and (9, 11, 12, 10). After entering each set, click on Apply. After entering the last set, click onOK.

4. Click on SAVE_DB on the ANSYS Toolbar.

Step 6: Define Scalar Parameters

1. Choose Utility Menu> Parameters> Scalar Parameters. The Scalar Parameters dialog box appears.



2. Type in the parameter values shown below. (Press ENTER after entering each value.)

ntran = 24rtran = 10na = 10nb = 10nc = 25nd = 10ne = 100re = -1.5

3. Click on Close to close the dialog box.

Step 7: Mesh the Model

1. Choose Main Menu> Preprocessor> Meshing> Size Cntrls> Lines> Picked Lines. The Element Sizeon Picked Lines picking menu appears.

2. Pick line number 4 and click on Apply. The Element Sizes on Picked Lines dialog box appears.

3. In the "No. of element divisions (NDIV)" field, enter ntran, and in the "Spacing ratio (SPACE)" field enterrtran. Click on Apply.

4. Repeat steps 2 and 3 for line number 2.


6. In the "No. of element divisions (NDIV)" field, enter ntran, and in the "Spacing ratio (SPACE)" field enter1/rtran. Click on Apply.

7. Repeat steps 5 and 6 for line numbers 14, 15, and 16.


9. In the "No. of element divisions (NDIV)" field, enter na, and in the "Spacing ratio (SPACE)" field enter1. Click on Apply.



12. In the "No. of element divisions (NDIV)" field, enter nb, and in the "Spacing ratio (SPACE)" field enter1. Click on Apply.



15. In the "No. of element divisions (NDIV)" field, enter nc, and in the "Spacing ratio (SPACE)" field enter1. Click on Apply.



18. In the "No. of element divisions (NDIV)" field, enter nd, and in the "Spacing ratio (SPACE)" field enter1. Click Apply.



21. In the "No. of element divisions (NDIV)" field, enter ne, and in the "Spacing ratio (SPACE)" field enterre. Click on Apply.

22. Repeat steps 20 and 21 for line number 12 but this time click OK.



Step 7: Mesh the Model

23. Choose Main Menu> Preprocessor> Meshing> Mesh> Areas> Mapped> 3 or 4 sided. A pickingmenu appears.

24. Click on Pick All. The meshed model appears.

Step 8: Compress Numbers

1. Choose Main Menu> Preprocessor> Numbering Ctrls> Compress Numbers. The Compress Numbersdialog box appears.

2. Select Nodes as the "Item to be compressed" and click on Apply.

3. Select Elements as the "Item to be compressed" and click on OK.

Step 9: Apply Boundary Conditions

1. Choose Utility Menu> Select> Entities. The Select Entities dialog box appears.

2. Choose "Lines" and "By Num/Pick," then click on OK. A Select Lines picking menu appears.

3. Choose Utility Menu> Plot>Lines.

4. Pick lines 1, 9, 10, 11, and 12 and click on OK.


6. Choose "Nodes" and "Attached to," click on Lines, all, and then click on OK.

7. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Velocity> On Nodes.The Apply V on Nodes picking menu appears.

8. Click on Pick All. The Velocity Constraints on Nodes dialog box appears.

9. In the "Velocity component (VY)" field, enter 0, and click on OK.


11. Choose "Lines" and "By Num/Pick," then click on the Sele All button. Click on OK. The Select Linespicking menu appears.

12. Pick line number 4 and click on OK.



15. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Pressure DOF> On

Nodes. The Apply PRES on Nodes picking menu appears.

16. Click on Pick All. The Pressure Constraint on Nodes dialog box appears.

17. In the "Pressure value (PRES)" field, enter 6.13769e+6, and click on OK.

18. Choose Utility Menu> Select> Entities.

19. Choose "Lines" and "By Num/Pick," then click on the Sele All button. Click on OK. The Select Linespicking menu appears.

20. Pick line numbers 3, 5, 6, 7, and 8 and click on OK.

21. Choose Utility Menu> Select> Entities.


23. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Velocity> On Nodes.The Apply V on Nodes picking menu appears.

24. Click on Pick All. The Velocity Constraints on Nodes dialog box appears.



25. In the "Velocity component (VX)" field and in the "Velocity component (VY)" enter 0, and click on OK.


27. Choose "Lines" and "By Num/Pick," click on the Sele All button, and then click on OK. The Select Linespicking menu appears.

28. Pick line number 16 and click on OK.



31. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Pressure DOF> On

Nodes. The Apply PRES on Nodes picking menu appears.

32. Click on Pick All. The Pressure Constraint on Nodes dialog box appears.

33. In the "Pressure value (PRES)" field, enter 0, and click on OK.

Step 10: Set Fluid Properties

1. Choose Utility Menu> Select> Everything.

2. Choose Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties. The Fluid Properties dialogbox appears.

3. Set the "Density (DENS)," "Viscosity (VISC)," "Conductivity (COND)," and "Specific heat (SPHT)" fields toAIR-CM.

4. Set the "Allow density variations?" field to yes.

5. Click on Apply. The CFD Flow Properties dialog box appears.

6. Read the information about how coefficients will be calculated, and click on OK.

Step 11: Set Flow Environment Parameters

1. Choose Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions. TheReference Conditions dialog box appears.

2. Set the "Reference pressure (REFE)" field to 1.01325e+6 and the "Nominal temperature (NOMI)" and"Stagnation (total) temperature (TTOT)" fields to 550, and then click on OK.

Step 12: Set Solution Options and CFD Solver Controls

1. Choose Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options. The FLOTRAN SolutionOptions dialog box appears.

2. Set the "Laminar or turbulent (TURB)" field to Turbulent and the "Incompress or compress (COMP)"field to Compressible. Click OK.

3. Choose Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Contr> PRES Solver CFD. ThePRES Solver CFD dialog box appears.

4. Choose Precond conj res.

5. Click on OK. The Semi Direct Solver Options for Pressure dialog box appears.

6. In the "Convergence criterion" field, enter 1.e-12, and click on OK.



Step 12: Set Solution Options and CFD Solver Controls

Step 13: Solve

1. Choose Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation. The PropertyRelaxation dialog box appears.

2. Set the "Density relaxation" field to 1.0 and click on OK.

3. Choose Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization. The ModifiedInertial Relaxation (MIR) dialog box appears.

4. Set the MIR values for the momentum and turbulence equations to 0.2

5. Choose Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms. The StabilityParameters dialog box appears.

6. Set the "Momentum inertia" field to 1.0, the "Pressure inertia" field to 1.e-4, and the "Artificial viscosity"field to 10, and then click on OK.

7. Choose Main Menu> Solution> FLOTRAN Set Up> Execution Ctrl. The Steady State Control Settingsdialog box appears.

8. Set the "Global iterations (EXEC) field to 20 and click on OK.

9. Choose Main Menu> Solution> Run FLOTRAN.

10. After 20 iterations finish, the Solution is done message appears. Close it. Choose Main Menu> Solution>

FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms. The Stability Parameters dialog box appears.

11. Set the "Artificial viscosity" field to 1 and click on OK.


13. Repeat the previous 3 substeps and continue to reduce the "Artificial viscosity" to .1, .01, .001, .0001,and .00001.

14. After 140 total iterations finish, the Solution is done message appears. Close it. Choose Main Menu>

Solution> FLOTRAN Set Up> Relax/Stab/Cap> Stability Parms. The Stability Parameters dialog boxappears.

15. Set the "Artificial viscosity" field to 0 and click on OK.






20. Set the "Momentum inertia" field to 10, the "Pressure inertia" field to 1.e-2, and then click on OK.






25. Set the "Momentum inertia" field to 1e+15, the "Pressure inertia" field to 1.e+15, and then click on OK.





28. Choose Main Menu> Solution> Run FLOTRAN. When the Solution is done message appears, closeit.

29. Click QUIT on the ANSYS Toolbar. Choose an exit option and click OK.

8.7. Doing the Example Compressible Flow Analysis (Command Method)

You issue the following ANSYS commands to perform a compressible flow analysis of the converging divergingnozzle. Text preceded by an exclamation point (!) is a comment.

/title, Compressible Flow in a Converging Diverging Nozzle/prep7!! Assign Element Type!et,1,141!! Create the Model Geometry!/pnum,line,1k,1,0,2.432k,2,0,0k,3,1,2.432k,4,1,0k,5,2,2.232k,6,2,0k,7,5,0k,8,5,.7k,9,6,0k,10,6,.5k,11,14,0k,12,14,.8l,2,4l,3,4l,1,3l,1,2l,5,8l2tan,3,5l,10,12l2tan,5,7l,4,6l,6,7l,7,9l,9,11a,2,4,3,1a,4,6,5,3a,6,7,8,5a,7,9,10,8a,9,11,12,10!! !Mesh the Model and Compress Numbers!ntran=24rtran=10na=10nb=10nc=25nd=10ne=100re=-1.5lesize,4,,,ntran,rtranlesize,2,,,ntran,rtranlesize,13,,,ntran,1/rtranlesize,14,,,ntran,1/rtran




lesize,15,,,ntran,1/rtranlesize,16,,,ntran,1/rtranlesize,1,,,nalesize,3,,,nalesize,6,,,nblesize,9,,,nblesize,5,,,nclesize,10,,,nclesize,8,,,ndlesize,11,,,ndlesize,7,,,ne,relesize,12,,,ne,reamesh,allnumcmp,nodenumcmp,elem!! Apply Boundary Conditions!lsel,s,,,1lsel,a,,,9,12,1nsll,,1d,all,vy,0lsel,alllsel,s,,,4nsll,,1d,all,pres,6.13769e+6lsel,alllsel,s,,,3lsel,a,,,5,8,1nsll,,1d,all,vx,0d,all,vy,0lsel,alllsel,s,,,16nsll,,1d,all,pres,0!! Set Fluid Properties!alls/soluflda,prot,dens,air-cmflda,prot,visc,air-cmflda,prot,cond,air-cmflda,prot,spht,air-cmflda,vary,dens,t!! Set Flow Environment Parameters!flda,pres,refe,1.01325e+6flda,temp,ttot,550flda,temp,nomi,550!! Set Solution Options and CFD Solver Controls!flda,solu,turb,tflda,solu,comp,tflda,meth,pres,3flda,conv,pres,1e-12!! Solve!flda,relx,dens,1flda,mir,mome,0.2flda,mir,turb,0.2flda,stab,mome,1flda,stab,pres,1e-4flda,stab,visc,10flda,iter,exec,20solveflda,stab,visc,1solve



flda,stab,visc,.1solveflda,stab,visc,.01solveflda,stab,visc,.001solveflda,stab,visc,.0001solveflda,stab,visc,.00001solveflda,stab,visc,0flda,iter,exec,160solveflda,stab,mome,10flda,stab,pres,1e-2flda,iter,exec,100solveflda,stab,mome,1e+15flda,stab,pres,1e+15flda,iter,exec,400solve





Chapter 9: Specifying Fluid Properties for FLOTRAN

Every flow analysis requires the fluid properties density and viscosity. Thermal analyses, in addition, requirethe fluid's thermal conductivity as well as specific heat. Volume of Fluid (VOF) analyses, in addition, mightrequire the fluid properties surface tension coefficient and wall static contact angle. You specify fluid prop-erties using one of the following:

Command(s): FLDATA7,PROT,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties

Main Menu> Solution> FLOTRAN Set Up> Fluid Properties

The command shown above simply sets the fluid property type. After choosing the property type, you mayhave to set values.

To specify non-fluid properties (density, specific heat, and thermal conductivity), use one of the following:

Command(s): MP

GUI: Main Menu> Preprocessor> Loads> Other> Change Mat Props> Polynomial

Main Menu> Preprocessor> Material Props> Material Models> Thermal> Density

Main Menu> Preprocessor> Material Props> Material Models> Thermal> Specific Heat

Main Menu> Preprocessor> Material Props> Material Models> Thermal> Conductivity> Isotropic

Main Menu> Solution> Other> Change Mat Props> Polynomial

Non-fluid thermal conductivities can vary with temperature. Orthotropic variation of non-fluid thermal con-ductivity also is supported. For further information, see the descriptions of the MP and MPDATA commands,and related commands.

ANSYS provides no default values for density or viscosity properties. This prevents default properties fromputting the analysis into an unexpected flow regime.

A value of -1 will appear in the user interface for properties that must be set. If you submit an analysiswithout setting these properties, an error message results and you will be reminded that you must specifyproperties.

The following fluid property topics are available:9.1. Fluid Property Types9.2. Initializing and Varying Properties9.3. Modifying the Fluid Property Database9.4. Using Reference Properties9.5. Using the ANSYS Non-Newtonian Flow Capabilities9.6. Using User-Programmable Subroutines

9.1. Fluid Property Types

A "fluid property type" defines how the particular fluid property will vary with temperature (and pressure,in the case of density for a gas). You choose the fluid property type separately for density, viscosity, thermalconductivity, specific heat, surface tension coefficient, and wall static contact angle.



You must use a consistent set of units for all the data that you enter. All thermal quantities must have thesame energy unit as shown in the following table:

Table 9.1 Units for Thermal Quantities

UnitsThermal Quantity

energy/length-temperature-timeThermal Conductivity

energy/mass-temperatureSpecific Heat

energy/length2-timeHeat Flux

energy/length3-timeVolumetric Heat Source

energy/length2-temperature-timeHeat Transfer Coefficient

Except for incompressible flow analyses including viscous heating, you can use any energy unit as long asyou use the same unit for all thermal quantities. The metric and English property types defined below usejoules and BTUs, respectively, as the energy unit for thermal conductivity and specific heat. For an incom-pressible analysis including viscous heating, you must use the energy unit for the system as shown in thefollowing table:

Table 9.2 Energy Units for Incompressible Analyses with Viscous Heating

Energy Unit[1]System

JouleSI (meter-kg-sec)

ErgCGS (cm-g-sec)

Centi-ergmm-g-sec

lbf-ftU. S. Customary (ft-slug-sec)

lbf-inPSI

1. 1 Joule = 1.0E9 Centi-ergs; 1 BTU = 778.26 lbf-ft.

The following property type topics are available:9.1.1. Property Types for Specific Heat9.1.2. Property Types for Density and Thermal Conductivity9.1.3. Property Types for Viscosity9.1.4. Property Types for Surface Tension Coefficient9.1.5. Property Types for Wall Static Contact Angle9.1.6. General Guidelines for Setting Property Types9.1.7. Density9.1.8.Viscosity9.1.9. Specific Heat9.1.10.Thermal Conductivity9.1.11. Surface Tension Coefficient9.1.12.Wall Static Contact Angle

9.1.1. Property Types for Specific Heat

For specific heat, you can choose among the following property types: CONSTANT, CMIX, TABLE, user-definedthrough a file (floprp.ans ), user-programmable subroutine (USER), and the variations of AIR shown belowin Table 9.3: Units for the AIR Property Type (p. 119).



9.1.2. Property Types for Density and Thermal Conductivity

For density and thermal conductivity, the property types you can choose are CONSTANT, CMIX, TABLE, GAS,LIQUID, user-defined through a file (floprp.ans ), and the variations of AIR shown below. (To learn howto add more, see Modifying the Fluid Property Database (p. 127).) A user-programmable subroutine (USER)also is available. For density only, you have one other property type option: CGAS.

Table 9.3 Units for the AIR Property Type

Viscosity UnitsDensity UnitsPressure UnitsUnitsPROT

kg/m-seckg/m3Pascalsmeter-kg-secAIR

kg/m-seckg/m3Pascalsmeter-kg-secAIR-SI

g/cm-sec (poise)g/cm3dynes/cm2cm-g-secAIR-CM

g/mm-secg/mm3Pascalsmm-g-secAIR-MM

slug/ft-secslugs/ft3lbf/ft2ft-slug-secAIR-FT

lbf-s/in2lbf-sec2/in4psiin-(lbf-s2/in)-secAIR-IN

ANSYS automatically supplies for you, in the property database, the relevant input for the AIR property types.

9.1.3. Property Types for Viscosity

For viscosity, you can choose the property types CMIX, TABLE, CONSTANT, LIQUID, GAS, Power Law (POWL),Bingham (BING), Carreau (CARR), user-defined through a file (floprp.ans ), and a user-programmablesubroutine (USER or USRV). The AIR and GAS property types assume that the fluid is an ideal gas with constantspecific heat. The viscosity and thermal conductivity variations with temperature are assumed to followSutherland's laws for gases, the form of which is shown below. A LIQUID assumes up to a second orderpolynomial for the variation of density with temperature, a constant value for specific heat, and Sutherland'slaws for a liquid for viscosity and thermal conductivity.

Viscosity as a function of the velocity gradient is represented by the non-Newtonian viscosity types: PowerLaw, Bingham, and Carreau. Refer to Using the ANSYS Non-Newtonian Flow Capabilities (p. 130) for more in-formation.

9.1.4. Property Types for Surface Tension Coefficient

For surface tension coefficient, you can choose among the following property types: CONSTANT, LIQUID,and user-programmable subroutine (USER).

9.1.5. Property Types for Wall Static Contact Angle

For wall static contact angle, CONSTANT is the only valid property type.

9.1.6. General Guidelines for Setting Property Types

You must use a consistent set of units (the gravitational constant gc must be unity.) Of course, the proper

length unit must be assumed when building the finite element model. Additional choices are available forair as per the table shown below. Units for density are simply mass/volume; the table omits them.

Set the property type using the following:

Command(s): FLDATA7,PROT,Label,Value




GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


For Label, you specify one of the following: DENS (density), VISC (viscosity), COND (thermal conductivity),SPHT (specific heat), or SFTS (surface tension coefficient).

For Value, you specify any of the property types listed in Table 9.4: Property types for Value (p. 120), or youcan specify a table of fluid properties. To specify a table, enclose the table name in percent signs (%) (forexample, FLDATA7,PROT,DENS,%Table%).

9.1.6.1. Using a Fluid Property Table

If working interactively, you define a new table prior to using the table to apply loads. You can define atable interactively via the Utility Menu> Parameters> Array Parameters> Define/Edit menu path, or inbatch mode via the *DIM command. If working interactively, you will be asked to define the table througha series of dialog boxes. If working in batch mode, you need to define the table before issuing any of theloading commands.

For more information on defining tables, see the discussion of table array parameters in the ANSYS Parametric

Design Language Guide.

When you define the table, you can define the following primary variables:

• Temperature (TEMP)

• Pressure (PRESSURE)

• Time (TIME)

• X-coordinate (X)

• Y-coordinate (Y)

• Z-coordinate (Z)

• Velocity (VELOCITY)

• Reference X-coordinate (Xr) (ALE formulation only)

• Reference Y-coordinate (Yr) (ALE formulation only)

• Reference Z-coordinate (Zr) (ALE formulation only)

The valid labels used by the *DIM command are shown in parentheses.

If you need to specify a variable other than one of the primary variables listed, you can do so by definingan independent variable. To specify an independent variable, define an additional table for the independentvariable. That table must have the same name as the independent variable and can be a function of eithera primary variable or another independent variable.

9.1.6.2. Specifying Property Types

The following table describes the property types that you can specify.

Table 9.4 Property types for Value

ArgumentProperty Type

CONSTANTConstant properties



ArgumentProperty Type

GASGas properties

LIQUIDLiquid properties

TABLETable of property values and corresponding temperature values (which youenter using the MPDATAand MPTEMP commands)

AIR or AIR-SIAir properties in units of meter-kg-sec

AIR_B or AIR-SI_B

Air properties in units of meter-kg-sec, with pressure set to the referencepressure for the evaluation of density

AIR-CMAir properties in units of cm-g-sec

AIR-CM_BAir properties in units of cm-g-sec, with pressure set to the reference pressurefor the evaluation of density

AIR-MMAir properties in units of mm-g-sec

AIR-MM_BAir properties in units of mm-g-sec, with pressure set to the reference pressurefor the evaluation of density

AIR-FTAir properties in units of fl-slug-sec

AIR-FT_BAir properties in unites of fl-slug-sec, with pressure set to the reference pressurefor the evaluation of density

AIR-INAir properties in units of in-(lbf-s**2/in)-sec (results in units of psi for pressure)

AIR-IN_BAir properties in units of in-(lbf-s**2/in)-sec (results in units of psi for pressure),with pressure set to the reference pressure for the evaluation of density

POWLPower Law non-Newtonian viscosity type

CARRCarreau non-Newtonian viscosity type

BINGBingham non-Newtonian viscosity type

CMIXProperty is mass fraction average of the species component

USERUser-programmable via subroutines:UserVisLaw for viscosityUserSpht for spe-cific heatUserDens for densityUserCond for conductivityUserSfts for surfacetension

CGASA variation of ideal gas law based on species mass fractions. Available fordensity only.

Once you choose property types, you do not need to specify any coefficients for the properties. If the char-acters _B are added to these property types (as in the AIR types listed above), the pressure in the ideal gaslaw calculation is at a constant density corresponding to atmospheric pressure. The length and time unitsof conductivity and specific heat must be consistent with the rest of the properties. The energy units inthese quantities are unrestricted.

If using property types CONSTANT, GAS, or LIQUID, you must specify property coefficients. To do so, eitherissue the commands shown below or choose one of the following menu paths:

Command(s): FLDATA8,NOMI,Label,Value FLDATA9,COF1,Label,Value FLDATA10,COF2,La-bel,Value FLDATA11,COF3,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


If you use the commands, you enter the property in the Label field of each command and enter the valueitself in each command's Value field.




The format of the equations for GAS and LIQUID input is oriented towards calculating constants based onchosen data points. All cases take COF1 to be the absolute temperature at which the chosen property hasthe value set by NOMI. (Using Reference Properties (p. 129) discusses the use of relative temperatures and anoffset temperature to calculate absolute temperatures.) This is not used in the COF1 specification; COF1should always be an absolute temperature.

Once values are inserted into the relationships below for NOMI and COF1, the values of COF2 and COF3, ifnecessary, follow from knowledge of one or two additional data points, respectively. When calculating COF2and COF3 for GAS and LIQUID property types, you must use absolute temperatures and pressures in theserelationships. If COF1 is set to zero, the property will become constant at the value set by NOMI. For GASand LIQUID property types, the specific heat is constant and therefore the parameters COF1, COF2 and COF3are not needed. For viscosity types Power Law, Bingham, and Carreau, NOMI, COF1, COF2, and COF3 havedifferent interpretations. This is discussed in the Theory Reference for the Mechanical APDL and Mechanical

Applications and in Viscosity (p. 123).

9.1.7. Density

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the density to 1.205 via:

Command(s):

FLDATA8,NOMI,DENS,1.205

If the property type is GAS, the ideal gas law is used for the density. You specify density for this choice as:

Density = NOMI * (P/COF2) / (T/COF1)

If the choice is LIQUID, then a second order polynomial as a function of temperature is used for density.

Density = NOMI + COF2*(T - COF1) + COF3*(T - COF1)2

If the property type is CMIX, then:

Density ==∑ Yi ii

Nρ

1

In the equation shown above, N is the defined number of species, Yi is the mass fraction of the ith species,

and ρi is the density of the ith species.

If the property is CGAS, then:

Density =∑

P

RT Y Mi ii

N( / )

In the CGAS equation shown above, N is the defined number of species, Yi is the mass fraction of the ith

species, Mi is the molecular weight of the ith species, R is the universal gas constant, and P is the absolute

pressure.

If the property type is TABLE, the density is interpolated linearly between the data points provided via theMPTEMP or MPDATA commands (or their GUI equivalents).



If the choice is USER, the density is computed in the user-programmable subroutine UserDens. The fourcoefficients NOMI, COF1, COF2, and COF3 are available in this routine.

9.1.8. Viscosity

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the viscosity to 1.205 via:

Command(s):

FLDATA8,NOMI,VISC,1.205

If the choice is GAS, Sutherland's law for gases is used for viscosity. You can enter the parameters NOMI,COF1, and COF2.

The ideal gas constant R is defined as (COF2/NOMI*COF1)

Viscosity ("Property"):

Property/NOMI = (T/COF1)1.5 * (COF1 + COF2)/(T + COF2)

As an example of using this relationship, suppose that there are two data points available for the calculationof viscosity as a function of temperature:

Viscosity = 4.18 x 10-5 at T = 760

Viscosity = 5.76 x 10-5 at T = 1010

Consider the first data point as the nominal value. This means that NOMI = 4.18 x 10-5 and COF1 = 760. Usingthese in the Sutherland relationship yields:

Property/4.18 x 10-5 = (T/760)1.5 (760 + COF2)/(T + COF2)

Use the remaining data point to calculate COF2 by setting "Property" to 5.76 x 10-5 and T = 1010. Thus, theconstants are calculated from the data points.

If the choice is LIQUID, then Sutherland's liquid law is used for the viscosity.

Viscosity ("Property"):

Property/NOMI = EXPCOF2*(1/T - 1/COF1) + COF3(1/T - 1/COF1)2

If the choice is POWL, then the non-Newtonian Power Law model is used for the viscosity:

Viscosity =NOMI*COF2*D ,D>COF1

NOMI*COF2*COF1

(COF3-1)

(COF3-1),,D COF1≤

If the choice is BING, then the non-Newtonian Bingham model is used for the viscosity:



9.1.8.Viscosity

Viscosity =

NOMI+COF1

D,D

COF1

COF2 NOMI

COF2 ,D<COF1

COV2-NOMI

≥−

If the choice is CARR, the non-Newtonian Carreau model is used for the viscosity:

Viscosity =COF1+(NOMI-COF1)*(1+(COF2*D) )2

COF3-1

2


Viscosity ==∑ Yi ii

Nµ

1


and µi is the viscosity of the ith species.


If the choice is USRV or USER, then the viscosity is computed in the user programmable subroutine UserVisLaw.The four coefficients NOMI, COF1, COF2, and COF3 are available in this routine.

9.1.9. Specific Heat

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the specific heat to 1.205 via:

Command(s):

FLDATA8,NOMI,SPHT,1.205

If the choice is USER, specify specific heat via user-programmable subroutine UserSpht. For specific heat,NOMI, COF1, COF2, and COF3 are available in the user-programmable subroutine UserSpht.


Specific Heat ==∑ Y Ci pi

N

i1


and Cp

i is the specific heat of the ith species.

If the property type is TABLE, the specific heat is interpolated linearly between the data points provided viathe MPTEMP or MPDATA commands (or their GUI equivalents).



9.1.10. Thermal Conductivity

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the thermal conductivity to 1.205 via:

Command(s):

FLDATA8,NOMI,COND,1.205

If the choice is GAS, Sutherland's law for gases is used for conductivity. You can enter the parameters NOMI,COF1, and COF2.

The ideal gas constant R is defined as (COF2/NOMI*COF1)

Thermal Conductivity ("Property"):

Property/NOMI = (T/COF1)1.5 * (COF1 + COF2)/(T + COF2)

If the choice is LIQUID, then Sutherland's liquid law is used for conductivity.

Thermal Conductivity ("Property"):

Property/NOMI = EXPCOF2*(1/T - 1/COF1) + COF3(1/T - 1/COF1)2


Conductivity ==∑ Y Ki ii

N

1


and Ki is the conductivity of the ith species.


If the choice is USER, then the thermal conductivity is computed in the user programmable subroutineUserCond. The four coefficients NOMI, COF1, COF2, and COF3 are available in this routine.

9.1.11. Surface Tension Coefficient

If the property type choice is CONSTANT, then set the constant value of the property using the FLDATA8,NOMIcommand or the equivalent menu path. For example, you set the surface tension coefficient to 73.0 via:

Command(s):

FLDATA8,NOMI,SFTS,73.0

If the choice is LIQUID, then a second order polynomial as a function of temperature is used for surfacetension coefficient.

Surface tension coefficient = NOMI + COF2*(T - COF1) + COF3*(T - COF1)2

If the choice is USER, the surface tension coefficient is computed in the user-programmable subroutineUserSfts. The four coefficients NOMI, COF1, COF2, and COF3 are available in this routine.



9.1.11. Surface Tension Coefficient

9.1.12. Wall Static Contact Angle

To set the constant value use the FLDATA8,NOMI command or the equivalent menu path. For example, setthe wall static contact angle to 120.0 degrees via:

Command(s):

FLDATA8,NOMI,WSCA,120.0

The wall static contact angle defaults to 90 degrees. Angles less than 90 degrees describe an adhesive wallcondition and angles between 90 and 180 degrees describe a nonadhesive wall condition. In reality, theangle is not only a material property of the fluid, but also depends on the local fluid and wall conditions.FLOTRAN treats it as a single input constant for simplicity.

9.2. Initializing and Varying Properties

When an analysis begins, ANSYS calculates properties based on the specified property type and the appro-priate constants. To set the initial temperature, choose one of the following:

Command(s): FLDATA14,TEMP,NOMI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


You can choose to treat this temperature as an absolute or a relative temperature. If it is a relative temper-ature, the difference between the relative and the absolute temperature is the offset from absolute zero setby one of the following:

Command(s): TOFFST,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


Either way, FLOTRAN initializes the absolute nominal temperature as the sum of the values set by theFLDATA,TEMP,NOMI and TOFFST commands or their equivalent menu paths.

Unless otherwise specified through boundary or initial condition commands, the initial relative pressure iszero. In the absence of gravity and rotation the absolute pressure is the sum of the reference and relativepressures. Therefore, the initial absolute pressure is the reference pressure.

For specific heat, density, surface tension coefficient, and thermal conductivity, the ANSYS program usesinitial values of absolute nominal temperature and absolute pressure to calculate the initial properties.However, for non-Newtonian viscosity, you specify initial properties using either the commandFLDATA12,PROP,IVISC,Value (Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties). If youspecify a value less than or equal to zero, the NOMI coefficient described in the previous section is used toinitialize the viscosity.

9.2.1. Activating Variable Properties

Once the analysis begins, the properties will vary only between global iterations as the temperature andpressure change if the property variations are activated. This is accomplished with theFLDATA13,VARY,Label,Value command with the labels SPHT, DENS, VISC, SFTS, and COND. AllowableValues are TRUE and FALSE (T or F). The VARY setting has no effect if the property type are set to CONSTANTor COF1 is zero for a GAS or LIQUID.



9.3. Modifying the Fluid Property Database

Choices other than CGAS, CMIX, TABLE, USER, GAS, LIQUID, CONSTANT or AIR for density, thermal conduct-ivity, viscosity, and specific heat imply that all the properties will be obtained from the information in thefloprp.ans file (a text file), where the data for AIR resides. This file is provided with ANSYS, and youshould make a local copy if you plan additions to it. You can make the copy at the system level with a texteditor. The procedure for making additions requires you to:

1. Choose a property name.

2. Specify functional form and constants.

id Integer equation identifier (two digit number)n Number of coefficientsCi Equation coefficients

You can access the following forms through the property database by specifying the appropriate ID. Thevariable "y" refers to the value of the property of interest, T is the absolute temperature, and P is the absolutepressure.

Polynomial ID: 01

y = C1 + C2T + C3T2 + ... + CnTn-1

Inverse Polynomial ID: 02

y CC

T

C

T

C

T

nn

= + + + +−1

2 32 1

…⋯ ⋯

Exponential Polynomial ID: 03

In(y) = C1 + C2T + C3T2 + ... + CnTn-1

Exponential Inverse Polynomial ID: 04

In y CC

T

C

T

C

T

nn

( ) = + + + +−1

2 32 1

…⋯ ⋯

Power Law ID: 05

y = C1TC2

Ideal Gas Law ID: 11

yP

C T=

1

⋯

Sutherland's Formula ID: 12



9.3. Modifying the Fluid Property Database

yC T

T C=

+1

2

3

2

Pressure based variation ID: 15

yC C P

C C P

C

C=

+

+1 2

3

4 56

Non-Newtonian Power Law ID: 16 (applies to viscosity only)

y C C D D C

y C C C D C

C

C

= >

= ≤

−

−

1 31

2

1 3 21

2

4

4

( )

( )

,

,

where D I= 2 , I2 is the second invariant of the strain rate tensor.

Non-Newtonian Bingham Model ID: 17 (applies to viscosity only)

y CC

DD

C

C C

y C DC

C C

= + ≥−

= <−

12 2

3 1

32

3 1

,

,

Carreau Model ID: 18 (applies to viscosity only)

y C C C C D

C

= + − +−

2 1 2 321

4 1

2( ) * ( ( ) )

User-programmable subroutine: 19

y = y (C1, C2, C3, C4)

Because you can use the subroutine to describe property variations, you can use the four coefficients in anyway within the subroutine.

The format of the property database file floprp.ans is provided in the table below:

Table 9.5 Property Database Format

DescriptionLine

Fluid Name [A8] and optional comments1

nLines [I6]2

Proplab, tProp, nPropnLines

(PropCF(i)=1,nProp)



DescriptionLine

[A4, 1x, 2I6, 5E12.5/6E 12.5]

Fluid Name=Fluid property type

nLines=Number of properties to be read

Proplab=Property label (one of the following):

SPHT - Specific heatDENS - DensityVISC - ViscosityCOND - ConductivityGAMM - GammatProp - Equation identifier for propertynProp - Number of coefficients for propertyPropCF - Coefficients for property calculation

9.4. Using Reference Properties

The following properties are part of the flow environment:

• The ratio of specific heats, Cp/Cv, known as gamma, is a reference property that applies only to com-

pressible problems. Currently it is a constant. Specify this property using one of these methods:

Command(s): FLDATA17,GAMM,COMP,VALUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions

File:

Edit the file floprp.ans and set the value of GAMM.

• The pressures FLOTRAN calculates are relative pressures. A reference pressure is added to the relativepressure to calculate the absolute pressure. Rotational and gravitational terms also are added as needed.For more information, see FLOTRAN Special Features (p. 133).

To specify the reference pressure, use one of the following:

Command(s): FLDATA15,PRES,REFE,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


• You can use a relative temperature (for example, degrees Fahrenheit rather than degrees Rankine). Inthis case, an offset temperature is set so that property calculations include absolute temperatures. Thisis necessary, for instance, for calculating densities from the ideal gas law. ANSYS automatically adds theoffset temperature to all of the boundary condition temperatures applied.

To set the offset temperature, use one of the following

Command(s): TOFFST,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


• The nominal temperature is that at which the properties initialize. It may be a relative temperature ifyou use the TOFFST command or an equivalent menu path. If the viscosity is not stored in the resultsfile (the default condition) and is now allowed to vary, ANSYS recalculates it when the analysis continuesat the nominal temperature.



9.4. Using Reference Properties

To specify the nominal temperature, use one of the following:

Command(s): FLDATA14,TEMP,NOMI,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Ref Conditions


• You can specify gravitational accelerations using one of the following:

Command(s): ACEL,ACELX,ACELY,ACELZGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Gravity

Main Menu> Solution> FLOTRAN Set Up> Flow Environment> Gravity

The sign convention of the gravitational acceleration denotes as positive the direction of the reaction force.

9.5. Using the ANSYS Non-Newtonian Flow Capabilities

The ANSYS program enables you to specify viscosity for non-Newtonian fluid flows. (You can use this capab-ility only with FLUID141 and FLUID142 elements.) You can choose among four types of models:

• The Power Law model, useful for modeling polymers, blood, rubber solutions, etc.

• The Carreau model, which removes some of the deficiencies associated with the Power Law model. Usethis model when fluid has intermediate values of shear rate but remains bounded for zero/infinite shearrates.

• The Bingham model, useful for modeling slurries and pastes.

• A user-programmable subroutine UserVisLaw, which gives you greater flexibility in choosing viscositymodels.

Typically, you select one of these models after you have built and meshed the model for your problem andafter you have applied the boundary conditions.

9.5.1. Activating the Power Law Model

To activate the Power Law viscosity model, issue the command or use one of the menu paths shown below:

Command(s): FLDATA7,PROT,VISC,POWLGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


Choosing any of the above automatically issues other commands which set output and storage controlsand the property variation flag. For details, see the descriptions of the FLDATA commands in the Command

Reference.

To specify the four coefficients associated with the Power Law model, choose either of the menu pathsshown above (and specify the appropriate coefficients), or issue the following commands:

Command(s):

FLDATA8,NOMI,VISC,Value (specifies nominal viscosity)FLDATA9,COF1,VISC,Value (specifies the cutoff shear rate)FLDATA10,COF2,VISC,Value (specifies the consistency coefficient)FLDATA11,COF3,VISC,Value (specifies the power)

The Theory Reference for the Mechanical APDL and Mechanical Applications describes these coefficients.



Once you have specified the coefficients, you can issue the SOLVE command or choose menu path Main

Menu> Solution> Run FLOTRAN.

9.5.2. Activating the Carreau Model

To activate the Carreau viscosity model, issue the command or use one of the menu paths shown below:

Command(s): FLDATA7,PROT,VISC,CARRGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


Choosing one of the above automatically issues commands which set output and storage controls and theproperty variation flag. For more information about the FLDATA commands, see the Command Reference.

You need to specify the four coefficients associated with the Carreau model, using either of the menu pathsshown above or the following commands:

Command(s):

FLDATA8,NOMI,VISC,Value (specifies the zero shear viscosity)FLDATA9,COF1,VISC,Value (specifies the infinite shear viscosity)FLDATA10,COF2,VISC,Value (specifies the time constant)FLDATA11,COF3,VISC,Value (specifies the power)

The Theory Reference for the Mechanical APDL and Mechanical Applications describes these coefficients. Onceyou have specified them, you can issue the SOLVE command or choose menu path Main Menu> Solution>

Run FLOTRAN.

9.5.3. Activating the Bingham Model

To activate the Bingham viscosity model, issue the command or choose one of the menu paths shown below:

Command(s): FLDATA7,PROT,VISC,BINGGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


Choosing one of the items shown above automatically issues commands that set output and storage controlsand the property variation flag.

To set the coefficients associated with the Bingham model, either use one of the menu paths shown aboveor issue the following commands:

FLDATA8,NOMI,VISC,Value (specifies the plastic viscosity)FLDATA9,COF1,VISC,Value (specifies the plastic/yield stress)FLDATA10,COF2,VISC,Value (specifies the Newtonian viscosity)

The Theory Reference for the Mechanical APDL and Mechanical Applications describes these coefficients.

You can also specify an initial viscosity to accelerate convergence. Typically, you can set this to be theNewtonian viscosity (that is, COF2) via one of the following:

Command(s): FLDATA12,PROP,VISC,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties




9.5.3. Activating the Bingham Model

9.6. Using User-Programmable Subroutines

User-programmable subroutines are available for specific heat, density, viscosity, surface tension coefficient,and thermal conductivity of fluid regions. Since the procedures are quite similar, only one property will bedescribed in depth here.

If you wish to use the user-programmable viscosity subroutine, UserVisLaw, you will need to customize itfor the particular model you are analyzing. You compile the subroutine, link it with the ANSYS libraries, andmake an executable copy available. Then, you can resume the model to be analyzed and activate the viscositymodel you have defined. To do so, use one of the following:

Command(s): FLDATA7,PROT,VISC,USRV (or USER)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


At this point, you may want to specify that properties are updated every iteration and that you want viscosityoutput to go to the results file. To do so, issue the following commands or use the following menu paths:

Command(s): FLDATA12,PROP,UFRQ,1 and FLDATA5,OUTP,VISC,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


Next, you need to specify the four coefficients associated with the user-defined viscosity model. To do so,use either of the menu paths shown above or issue the following commands:

Command(s):

FLDATA7,NOMI,VISC,Value (specifies coefficient 1)FLDATA6,COF1,VISC,Value (specifies coefficient 2)FLDATA9,COF2,VISC,Value (specifies coefficient 3)FLDATA10,COF3,VISC,Value (specifies coefficient 4)

These coefficients are available within the UserVisLaw subroutine. By default, this subroutine produces aPower Law viscosity model using the coefficients you define. To see a copy of the subroutine, see the Guide

to ANSYS User Programmable Features.

You can also specify an initial viscosity to accelerate convergence, via one of the following:

Command(s): FLDATA12,PROP,IVISC,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties

Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties

Once you have specified the coefficients, and, optionally, an initial viscosity, you can solve your model byissuing the SOLVE command or choosing Main Menu> Solution> Run FLOTRAN.



Chapter 10: FLOTRAN Special Features

The following FLOTRAN special features are available:10.1. Coordinate Systems10.2. Rotating Frames of Reference10.3. Swirl10.4. Distributed Resistance/Source

10.1. Coordinate Systems

You set the coordinate system via one of the following:

Command(s): KEYOPT

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> FLOTRAN Coor Sys

Main Menu> Solution> FLOTRAN Set Up> Flow Environment> FLOTRAN Coor Sys

The table below shows you how to select various coordinate systems and describes the velocities representedby DOFs VX, VY, and VZ in these systems. The default value of the KEYOPT is zero, which selects Cartesiancoordinates.



Figure 10.1 Direction of Positive Swirl Velocity VZ for Axisymmetric Models

X

Y

Z

X

Y

Z

+VZ

+VZ

(a) Y-axis axisymmetric (VZ positive "into the page")

(b) X-axis axisymmetric (VZ positive "out of page")

Table 10.1 Coordinate System Specification

VZVYVXKEYOPT(3)Coordinate System

ZYX0Cartesian

swirlaxialradial12-D - Axisymmetric about Y axis

swirlradialaxial22-D - Axisymmetric about X axis

N/Athetaradial32-D - Polar Coordinates

axialthetaradial33-D - Cylindrical Coordinates

For axisymmetric problems, the sign convention for the swirl (VZ) component conforms to positive rotationabout the axis of symmetry, as defined by the right hand rule. Thus, for a model that is axisymmetric aboutthe Y axis, a nonnegative swirl velocity VZ is considered to be pointing "into the page." Similarly, for amodel that is axisymmetric about the X axis, a nonnegative swirl velocity VZ is considered to be pointing"out of the page." This should be accounted for when you apply boundary conditions in rotating coordinates.

Note

Based on the definition of directions for the cylindrical coordinate system, gravity is only appro-priate for the Z direction when KEYOPT(3) is set to 3.



10.2. Rotating Frames of Reference

You can choose to solve your problem in a rotating reference frame. In this case, the velocities are calculatedand specified with respect to a coordinate system which is rotating at constant angular velocity. Such anapproach is useful for pump blade passage analysis. Figure 10.2 (p. 135) shows a schematic of a rotatingproblem which requires moving coordinate systems. Figure 10.3 (p. 136) shows the problem schematic in therotating coordinate system.

The pressures specified by boundary conditions are in terms of the static pressure observable by the stationaryanalyst, not in terms of the rotating coordinate system. The transformations necessary to solve the equationsin the rotating coordinate frame are done internally.

You can set rotational speeds using any of the following:

Command(s): CGOMGA

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Rotating Coords

Main Menu> Solution> FLOTRAN Set Up> Flow Environment> Rotating Coords

For all but 3-D Cartesian coordinate systems, you must specify the axis of rotation as being about the Z axis.For 2-D axisymmetric systems, the ANSYS program automatically interprets the specified Z-axis rotation asactually acting about the correct axis of symmetry (that is, about either the X or Y axis). For 3-D Cartesiangeometries, the rotational axis need not be in the same direction as one of the principal axes of the globalcoordinate system, and may be offset from the origin of the global coordinate system.

To specify offsets for the axis of rotation, use one of the following:

Command(s): CGLOC

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Flow Environment> Rotating Coords

Main Menu> Solution> FLOTRAN Set Up> Flow Environment> Rotating Coords

Figure 10.2 Rotating Flow Problem

Rotating shaft withangular speed ω



10.2. Rotating Frames of Reference

Figure 10.3 Problem Schematic with Rotating Coordinate

System rotates at ω

v = 0

v = ωR

10.3. Swirl

Swirl applies only to axisymmetric problems and refers to motion perpendicular to the X-Y plane. To activateswirl, choose one of the following:

Command(s): FLDATA1,SOLU,SWIRL,TRUEGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options


Either a moving wall (for instance, a rotating shaft) or a component of swirl at an inlet can cause the motionin the swirl direction (with velocity component VZ).

In a swirl problem, there are no changes in the "theta" direction since it is axisymmetric.

The swirl component is calculated through solution of the momentum equation in the swirl direction. Withno pressure gradient in the swirl direction, nothing contributes to the swirl velocity directly from the velocityupdate step in the segregated solution algorithm. It is thus sometimes useful to accelerate the convergenceof swirl problems by solving the momentum in the swirl direction equation with a relaxation factor of 1.0for a few global iterations.

10.4. Distributed Resistance/Source

Distributed resistances are macroscopic representations of geometric features not directly concerned withthe region of interest and considered too detailed for exact representation. A typical example is pipe flowwhich encounters a screen.

You apply distributed resistance on an element basis through the use of real constants. See the Element

Reference for the formulation and the list and meaning of the real constants.

Since the distributed resistance parameters will describe the known behavior of the flow in the region, theuse of the turbulence model is redundant. You should deactivate it in the distributed resistance region bysetting ENKE to 0.0 and ENDS to 1.0.

To do so, choose one of the following:



Command(s): D

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Turbulence> On Nodes

Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Turbulence> On Nodes

The distributed resistances referred to above are used to describe losses to the system. You can model mo-mentum sources in similar fashion. Such sources can be used to represent fans or pumps in a system. Typ-ical characterization of these components is a "Head-Capacity Curve," representing the pressure rise as afunction of flow for a constant speed pump. The fan or pump model is not intended to describe the detailsof the flow in the pump region, but rather to approximate its effects on the rest of the system. You can useany coordinate system or FLOTRAN element shape, but Cartesian coordinate systems with hex shaped elementsin three dimensions and quadrilateral elements in two dimensions tend to give more stable results.

The fan model input takes the form of element real constants, and is described in detail in the Element Ref-

erence.

The ANSYS program supports two types of fan model. A "Type Four" fan model acts only along a specificcoordinate direction, while a "Type Five" model enables the user to align the fan or pump in an arbitrarydirection. Coefficients are assigned for each coordinate direction.

The equation for the fan model is in terms of a pressure gradient applied in the direction of flow. Youtherefore must know over what length the fan model is to be applied in order to achieve the correct totalpressure rise. The relationship defining the momentum source for an arbitrary direction "s" is as follows:

dP

dsC C V C V= + +1 2 3

2

In the above equation, V is the velocity through the fan. If the given data is in terms of volumetric flow, youmust know the area of the actual pump. The actual velocity at the outlet of the pump as well as the volu-metric flow rate should be preserved. Consistent units must be used, that is, the gravitational conversionconstant must be 1.0. If, for example, the pressure drop is in psi, the velocity units are in/sec.

Generally, you determine the fan or pump coefficients by taking three pairs of pressure-velocity points onthe "fan curve" and solving for the coefficients. If the flow is to be in the negative direction, the signs of allthe coefficients change.

The type 5 model is used for pumps not aligned with one of the coordinate directions. Given V as the velocityin the S arbitrary direction and the pump constants C1, C2, and C3; the directional coefficients can be calcu-

lated.

If θx is the angle between the arbitrary direction S and the x coordinate direction, the directional constants

are:

C C

C C

CC

x x

x

xx

1 1

2 2

33

==

=

cos

cos

θ

θ

Similarly, if θy and θz are defined as the angles between the fan direction and the y and z coordinate direction

respectively:



10.4. Distributed Resistance/Source

C C

C C

CC

C C

C C

CC

y y

y

yy

z z

z

zz

1 1

2 2

33

1 1

2 2

33

=

=

=

==

=

cos

cos

cos

cos

θ

θ

θ

θ



Chapter 11: FLOTRAN CFD Solvers and the Matrix Equation

In the sequential solution algorithm, you have three options for solving equations sets for degrees of freedom:

1. A fast, approximate solver

This solver, the Tri-Diagonal Matrix Algorithm (TDMA), performs a user-specified number of iterationsthrough the problem domain.

2. "Exact" solvers

The "exact" methods are semi-direct conjugate direction methods that iterate to a specified convergencecriterion.

These methods are:

• The Conjugate Residual (CR), Preconditioned Conjugate Residual (PCCR), Preconditioned GeneralizedMinimum Residual (PGMR), and Preconditioned BiCGStab (PBCGM) methods for non-symmetricmatrix equations.

• The preconditioned conjugate gradient method for the incompressible pressure equation.

3. Sparse Direct solver

This solver uses Gaussian elimination to factorize the matrix and then uses backward/forward substitutionto solve for the unknowns.

You choose the method for each DOF via one of the following:

Command(s): FLDATA18,METH,Label,Value (Label = DOF)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> PRES Solver CFD

Main Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> PRES Solver CFD

Valid choices are: 1 (TDMA), 2 (conjugate residual), 3 (preconditioned conjugate residual or gradient), 4(preconditioned generalized minimum residual), 5 (sparse direct), or 6 (preconditioned BiCGStab). A choiceof 0 indicates that the equation set is not to be solved. The preconditioned conjugate gradient methodautomatically applies to the incompressible pressure equation for choices 2 or 3.

The default solver (TDMA) for the velocities and the turbulence equations is adequate for virtually everyproblem encountered. The number of sweeps (iterations) for the velocity is 1. Do not change this value. Ex-perience has shown that the default number of 10 sweeps for the turbulence equations is most efficientalthough you can increase this number to see if better convergence is attained for a particular application.

In general, the solution of the pressure equation must be accurate and conjugate direction methods areused. However, the TDMA method can be successful for natural convection flows. The sections for the varioustypes of analyses discuss where to use solvers other than the default choices.

The following FLOTRAN CFD solver topics are available:11.1.Tri-Diagonal Matrix Algorithm11.2. Semi-Direct Solvers11.3. Sparse Direct Method



11.1. Tri-Diagonal Matrix Algorithm

You set the number of sweeps for the TDMA solver using one of the following:

Command(s): FLDATA19,TDMA,Label,Value (Label = DOF)GUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

In the GUI, you do not have access to this command unless the TDMA method has been requested for thatDOF. It is not available in the GUI at all for velocities.

11.2. Semi-Direct Solvers

You can gauge the performance of the semi-direct solvers by the behavior during the solution process ofthe inner product of the residuals, referred to as RTR (or ZTR for the incompressible pressure equation.) RTR

should be reduced during the global iteration to a fraction, typically 1.0 x 10-7 of its initial value.

The fraction is the convergence criterion for the semi-direct methods, set with one of the following:

Command(s): FLDATA21,CONV,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

To set the maximum number of iterations allowed during a global iteration, choose one of the following:

Command(s): FLDATA22,MAXI,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

Data concerning how the semi-direct solvers are performing appears in the text file Jobname.DBG for everyDOF for which they are used, generally PRES, TEMP, or both.

The semi-direct algorithms may conclude in three different ways: convergence is achieved, the maximumnumber of iterations has been reached without convergence, or the solution has stalled.

If the maximum number has been reached without convergence, more iterations may be required (for example,in a large or ill-conditioned problem). If so, increase the maximum number of iterations. The maximumnumber also may be reached if the convergence criterion has been set to a very small value (for example,

less than 1.0 x 10-15), in which case the convergence criterion should be eased. It may also, however, mean

that the solution is diverging. If so, large values of RTR or ZTR (perhaps above 1.0 x 1020) will appear in thedebug file; but increasing the number of iterations will not help.

Stall occurs when the new iteration makes no progress towards the solution but the convergence criterionhas not been achieved. If the rate of change is small enough the solution process stops.

Note

You specify the rate of change which leads to termination of the solver by using one of the fol-lowing:

Command(s): FLDATA23,DELT,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver



Main Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

The label refers to the DOF being solved. Stall can occur in the solution of the compressible pressure equationor in the solution of the temperature equation of some conjugate heat transfer problems. The value of RTRdoes not decrease significantly and at the last iteration the value of DelMax is less than the value you specified.This means that the solution is essentially not changing, and further computational effort is wasted.

You can resolve a stall situation by increasing the number of search directions or using inertial relaxation.To increase search directions, either use one of the menu paths described above (with the FLDATA23,DELTcommand), or issue the following command:

Command(s):

FLDATA20,SRCH,Label,Value

The default value is 2, appropriate for well conditioned problems. The number of search directions requiredmay vary widely among problems. Values of 20 may be required, but be aware that each search directionspecified requires N compute storage locations in memory. (N is the number of finite element nodes in theproblem). The computer storage required for large values of SRCH could exceed the computational resourcesavailable, in which case inertial relaxation should be used.

Figure 11.1 (p. 141) shows typical debug files.

Figure 11.1 Typical Debug Files

11.2.1. Preconditioned Generalized Minimum Residual (PGMR) Solver

The PGMR method uses fill-in when constructing the L and U decomposition matrices. The PGMR methodis a version of the generalized minimum residual method that uses an LU preconditioning to transform thesystem of equations into a set easier to solve. As with the PCCR method, the coefficient matrix is decomposedinto an approximate LU product. In the PCCR method, the sparsity pattern of the original matrix is preservedin the L and U matrices.

Accordingly, when you are using the Preconditioned Generalized Minimum Residual (PGMR) solver, you needto specify the amount of fill-in. You must also specify the number of search vectors.

The fill-in value represents the number of extra elements allowed in each row of the L and U decompositionmatrices. An extra element is defined as being in addition to the number of nonzero elements in the rowof the original matrix.

There are two PGMR algorithms available for FLOTRAN. The choice is automatically made by the program.The difference lies in the "fill-in". It is only required and only available for the PRES and TEMP degrees offreedom.



11.2.1. Preconditioned Generalized Minimum Residual (PGMR) Solver

To specify the amount of fill-in, use either of these methods:

Command(s): FLDATA20A,PGMR,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

The allowable range for fill-in is 1 to 10. The default value is 6. A single fill-in value is input for all applicableDOF.

For some problems, it is unnecessary to obtain an exact solution to the energy equation every global iteration.To save some time, you can then employ the foregoing command with a Label of MODP. You use it tospecify a number of global iterations performed using the TDMA method between global iterations performedusing the PGMR method for the temperature DOF.

The number of search directions required may vary widely among problems. If large values of SRCH resultin the required computer storage exceeding the computational resources, inertial relaxation should be used.To specify the number of search vectors, use either of these methods:

Command(s): FLDATA20,SRCH,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

For the PGMR solver, the allowable range of search vectors is 12 to 20. The default value is 12.

The PGMR method is not recommended for velocity DOF.

The output associated with the solver is recorded in the Jobname.OUT file for non-FLOTRAN analyses. TheFLOTRAN iterative solver output is recorded in the jobname.dbg file.

The fact that the PGMR solver is being used is indicated in the Jobname.DBG file. The file shows if conver-gence is reached, the maximum number of iterations is reached without convergence, or the solution isstalled.

The PGMR method output is in the same form as that provided in the jobname.out file for non-FLOTRANanalyses. The NORM referred to in the Jobname.OUT file is the square root of the convergence criterionspecified in the FLOTRAN input. For example, a EQSLV command solver tolerance value of 1.E-5 correspondsto the FLOTRAN default convergence criterion value of 1.E-10.

The PGMR method can fail for the following reasons:

• The problem is ill-conditioned.

• The problem is improperly formulated.

• The specified convergence criterion is too tight.

• An insufficient number of iterations is specified.

If the PGMR method stalls, it may be because the problem is ill-conditioned or improperly formulated. If theproblem is ill-conditioned, you can control several parameters to enhance performance. You can increasethe amount of fill-in or the number of search vectors. You can also use inertial relaxation. If the problem isimproperly formulated, there may be an input error or the boundary conditions may be applied incorrectly.You need to check the input parameters and boundary conditions to ensure that they are accurate.

FLOTRAN does not allow a convergence criterion less restrictive than the default value. You can enter ahigher value, but FLOTRAN issues a warning message and changes it to the default value.



If the maximum number of iterations has been reached without convergence, it may mean more iterationsare required. This could be the case if you see that the Norm has been lowered, but it is not quite to thetarget. If so, you can try increasing the maximum number of iterations.

If the PGMR method converges and the results are questionable, reduce the convergence criterion belowthe default value of 1.E-10. A convergence criterion as low as 1.E-20 may be necessary for some problems.

11.2.2. Preconditioned BiCGStab (PBCGM) Solver

The PBCGM method is a version of the generalized bi-conjugate gradient method that uses two sets ofvectors constructed from both the coefficient matrix and its real transpose matrix by making them orthogonalto each other. At each iteration, a new vector is first generated orthogonal to some user-specified numberof previous vectors (search directions) from the basis of the real transpose matrix. A minimization procedureis then used to stabilize the numerical procedure. Similar to PGMR, the PBCGM method uses fill-in whenconstructing the L and U decomposition matrices. This preconditioning procedure transforms the system ofequations into a set easier to solve by decomposing the coefficient into an approximate LU product.

Accordingly, when you are using the Preconditioned BiCGStab (PBCGM) solver, you need to specify theamount of fill-in. You must also specify the number of search vectors.

The fill-in value represents the number of extra elements allowed in each row of the L and U decompositionmatrices. An extra element is defined as being in addition to the number of nonzero elements in the rowof the original matrix.

There are two PBCGM algorithms available for FLOTRAN. The difference lies in the fill-in value. When it isspecified to be zero, the algorithm is parallelized except the LU preconditioning part. For other fill-in values,the algorithm is not parallelized at all.

To specify the amount of fill-in, use the following command or menu path:

Command(s): FLDATA20B,PBCGM,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

The allowable range for fill-in is 0 to 10. The default value is 6. A single fill-in value is input for all applicableDOF.

The number of search directions required may vary widely among problems. If large values of SRCH resultin the required computer storage exceeding the computational resources, use inertial relaxation. In practice,you should usually use a value of 1 or 2 in order to save the memory storage. To specify the number ofsearch vectors, use the following command or menu path:

Command(s): FLDATA20,SRCH,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> CFD Solver Controls> desired DOF solverMain Menu> Solution> FLOTRAN Set Up> CFD Solver Controls> desired DOF solver

For the PBCGM solver, the allowable range of search vectors is 1 to 8. The default value is 2.

11.3. Sparse Direct Method

The Sparse Direct method is memory intensive and you should only use it if all other methods have failed.This method produces intermediate files during matrix factorization and it is difficult to predict the memoryrequired. Ensure enough hard disk space exists for intermediate files.



11.3. Sparse Direct Method

If you choose the Sparse Direct method for the VX, VY, or VZ DOFs, FLOTRAN will reset the method to Pre-conditioned Conjugate Residual (PCCR). The Sparse Direct method is not suitable for the velocity degreesof freedom.



Chapter 12: Coupling Algorithms

FLOTRAN CFD Solvers and the Matrix Equation (p. 139) describes the linear solvers available to solve each indi-vidual equation. To obtain a final solution, you must usually account for the coupling between the individualequations. In FLOTRAN, this nonlinear coupling is handled in a segregated or decoupled manner. Thecoupling algorithms belong to a general class referred to as the Semi-Implicit Method for Pressure LinkedEquations (SIMPLE). For more information on this general class of algorithms, see S.V. Patankar, D.B. Spalding,("A calculation procedure for heat, mass and momentum transfer in 3-D parabolic flows," InternationalJournal of Heat and Mass Transfer, Vol 15, pp. 1787-1806, 1972).

To handle the coupling between the pressure and momentum equations, there are two segregated solutionalgorithms: SIMPLEF and SIMPLEN. For many years, SIMPLEF was the sole pressure-velocity coupling algorithm.It was developed by R.J. Schnipke and J.G. Rice ("Application of a new finite element method to convectionheat transfer," Fourth International Conference on Numerical Methods in Thermal Problems, Swansea, U.K.,July 1985). The SIMPLEF algorithm has been improved by utilizing some ideas from the SIMPLEC algorithmdeveloped by J.P. Van Doormaal and G.D. Raithby ("Enhancements of the SIMPLE method for predicting in-compressible fluid flows," Numerical Heat Transfer, Vol. 7, pp. 147-163, 1984). To improve the rate of conver-gence, the SIMPLEN algorithm has been added to FLOTRAN. It was developed by G. Wang ("A fast and robustvariant of the SIMPLE algorithm for finite-element simulations of incompressible flows," Computational Fluidand Solid Mechanics, Vol. 2, pp. 1014-1016, Elsevier, 2001).

SIMPLEF is the default algorithm. To activate the SIMPLEN algorithm, use one of the following:

Command(s): FLDATA37

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Algorithm Control

Main Menu> Solution> FLOTRAN Set Up> Algorithm Control

The following coupling algorithm topics are available:12.1. Algorithm Settings12.2. Performance

12.1. Algorithm Settings

In general, FLOTRAN automatically set defaults suited for the two segregated algorithms. However, for someproblems, you may need to reset the advection scheme, solver choice, or relaxation factors.

12.1.1. Advection Scheme

You can discretize the advection term using three approaches: Monotone Streamline Upwind (MSU),Streamline Upwind/Petrov-Galerkin (SUPG), or Collocated Galerkin (COLG). Refer to Advection Discretization

Options (p. 161) for information on how to select a proper advection scheme.



Refer to the following table for a list of the defaults.

Table 12.1 Advection Scheme Defaults

SIMPLEN AlgorithmSIMPLEF AlgorithmTransport Equation

SUPGSUPGMomentum

MSUSUPGTurbulence

MSUMSUPressure

SUPGSUPGEnergy

SUPGSUPGSpecies

12.1.2. Solver

For the SIMPLEF algorithm, the TDMA solver is the default for the momentum and turbulence equations.None of the other solvers will improve the overall rate of convergence. Even when exact solutions are obtainedon those individual equations, the overall rate of convergence will not improve. This is due to weak couplingbetween the pressure and momentum equations.

For the SIMPLEN algorithm, the overall rate of convergence can be improved considerably when more exactsolutions are obtained for each individual equation. Therefore, when SIMPLEN is activated, FLOTRAN auto-matically resets the solver option to the preconditioned BiCGStab method (PBCGM) for the momentum,turbulence and energy equations. Furthermore, it will reset the fill-in parameter for PBCGM to zero forcomputational efficiency.

12.1.3. Relaxation Factors

Due to the nonlinear coupling between equations, in order to stabilize the overall solution procedure, relax-ation is usually necessary to moderate changes from one global iteration to the next. Experience indicatesthat relaxation factors greater than 0.5 for the velocity and pressure degrees of freedom will generally causeinstability and divergence for the SIMPLEF algorithm. On the other hand, the SIMPLEN algorithm providesmore consistent coupling between the pressure and velocity degrees of freedom. For incompressible flowproblems, SIMPLEN removes the need for relaxation for the pressure equation and allows a relaxation factorclose to 1.0 for the momentum equations. For compressible flow problems, relaxation is usually needed forthe pressure equation in order to obtain a convergent solution. The default for SIMPLEF is 0.5 for the pressureand velocity degrees of freedom. When SIMPLEN is activated, FLOTRAN automatically resets the relaxationfactor to 1.0 for the incompressible pressure equation, 0.5 for the compressible pressure equation, and 0.8for the momentum equations.

12.2. Performance

Table 12.2: SIMPLEF and SIMPLEN Performance Results (p. 146) presents results for laminar flow in a 2-D squarecavity. The Reynolds number is 100 based on the length of the cavity side and the velocity at the top. The

uniform grid consists of 322 = 1024 elements.

Table 12.2 SIMPLEF and SIMPLEN Performance Results

SIMPLENSIMPLEF

0.990.980.950.90.80.5RELX

1761146681153325Iter. No.

8.95.73.34.07.212.9CPU (sec)



For the SIMPLEN algorithm , the total number of global iterations and the computational time decrease asthe relaxation factor (RELX) increases from 0.8 to 0.95. As RELX increases above 0.95, the iteration numberand computational time increase. The optimal RELX value is 0.95. At this value, the SIMPLEN convergencerate is about 4 times faster than SIMPLEF. The SIMPLEN computational time is about 1/4 of the SIMPLEFcomputational time.

Results for a finer mesh of 1282 = 16,384 elements show an even better SIMPLEN performance. At an optimalRELX value of 0.99, the SIMPLEN computational time is about 1/40 of the SIMPLEF computational time.

SIMPLEN significantly improves the rate of convergence if pressure-velocity coupling dominates the conver-gence. If other factors affect the overall rate of convergence, SIMPLEN will not increase the rate of convergenceas significantly. However, for those problems, SIMPLEN will generally be more robust than SIMPLEF, and itwill usually give a better convergence behavior. For more comparisons, see Wang G., "A fast and robustvariant of the SIMPLE algorithm for finite-element simulations of incompressible flows," Computational Fluidand Solid Mechanics, vol. 2, pp. 1014-1016, Elsevier, 2001.

Below is the command input listing used to perform this analysis. All text preceded by an exclamation point(!) is a comment.

/title, Lid driven cavity flow analysis using SIMPLEF/SIMPLEN algorithmsNDL = 32 ! Number of line divisionsMU = 0.010 ! Fluid viscosityRHO = 1.0L = 1.0sL = 1.0e-8Vel = 1.000niter = 10000

/PREP7et,1,141 ! 2-D XY systemesha,2 ! Quad elementsrect,,L,,Llesi,all,,,NDLamesh,1alls! Apply Boundary Conditionsnsel,s,ext ! Wall boundary conditionsd,all,vxd,all,vynsel,r,loc,y,L-sL,L+sL !topd,all,vx,veld,all,vyd,all,enke,-1allsd,1,PRESfinisave

/SOLU ! SIMPLEF algorithmflda,iter,exec,niter ! No. of global iterationsflda,nomi,visc,MUflda,nomi,dens,RHOflda,term,pres,1.e-6solvefini/delete,,rfl

/SOLU ! SIMPLEN algorithmflda,algr,segr,simplensolvefini/delete,,rfl

/SOLUflda,relx,vx,0.9flda,relx,vy,0.9



12.2. Performance

solvefini/delete,,rfl

/SOLUflda,relx,vx,0.95flda,relx,vy,0.95solvefini/delete,,rfl

/SOLUflda,relx,vx,0.98flda,relx,vy,0.98solvefini/delete,,rfl

/SOLUflda,relx,vx,0.99flda,relx,vy,0.99solvefini



Chapter 13: Multiple Species Transport

The multiple species transport capability enables you to track several different fluids at once, subject to thelimitation that a single momentum equation is solved for the flow field. Transport equations are solved foreach species. The properties used in the momentum equation can be those of a "main" fluid, a "bulk" fluid(dilute mixture analysis), or a combination of component fluids. Momentum effects such as advection anddiffusion cause the fluid transport.

The following restrictions apply to this type of analysis:

• Currently, no reactions are modeled among the species.

• Solid model boundary /initial conditions are not supported for species mass fractions.

• Also, you must postprocess multiple species results by issuing commands instead of via the GUI.

The following multiple species transport topics are available:13.1. Mixture Types13.2. Doing a Multiple Species Analysis13.3. Doing a Heat Exchanger Analysis Using Two Species13.4. Example Analysis Mixing Three Gases

13.1. Mixture Types

In terms of property variations, the strategies for solving multiple species problems parallel those for thermalproblems. The key issue is determining how large a mass fraction of the overall flow field the species to betraced represents. You can choose among three mixture types for analysis: dilute mixture, composite mixture,and composite gas. For each mixture type, the properties may be a function of temperature.

13.1.1. Dilute Mixture Analysis

In a dilute mixture analysis, small mass fractions of species fluids are tracked in a flow field, and the speciesproperties do not significantly influence the flow field. The fluid properties are set and the bulk fluid analysisproceeds as in any other FLOTRAN analysis. You solve the transport equations for species using the bulkdensity and the velocities from the bulk fluid analysis.

If the analysis problem is isothermal or the properties are assumed not to vary with temperature, you canconverge the flow field completely before the species transport option is activated. The number of speciesto be solved is a feature of the element and is controlled via a key option on the element. The appropriateKEYOPT setting must be defined during the PREP7 phase of the analysis. Once the element type and numberof species has been set, the multiple species input commands (e.g., MSSPEC) can be issued from eitherPREP7 or SOLUTION phases. However, the multiple species menus are accessible only from PREP7.

To activate multiple species transport, use one of the following:

Command(s): FLDATA1,SOLU,SPEC,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options




13.1.2. Composite Mixture Analysis

A composite mixture analysis calculates the properties used in the solution from a linear combination of thespecies, weighted by mass fraction as a function of space. The solution of the momentum equation dependson the species distribution, so the momentum and transport equations are strongly coupled.

You initialize the species mass fractions using either the MSNOMF command (which has no GUI menuequivalent) or (typically for a transient analysis) one of the following:

Command(s): IC,Label,ValueGUI: Main Menu> Preprocessor> Loads> Analysis Type> Analysis Options

Main Menu> Solution> Define Loads> Apply> Initial Condit'n> Define

The mass fractions specified must add up to 1.0. To activate the composite mixture option for an individualproperty, use one of the following:

Command(s): FLDATA7,PROT,Label,CMIXGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties


13.1.3. Composite Gas Analysis

In a composite gas analysis, at each node the fluid density is calculated as a function of the mass fractionsand molecular weights of the gases:

ρ =

=∑

P

RTY

Mi

ii

N

1

In the equation above:

• R is the Universal Gas constant. You can set it using one of the following:

Command(s): MSDATA

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

• Mi is the molecular weight of the ith species. You set this weight using one of the following:

Command(s): MSSPEC


• N is the total number of species defined.

• P is pressure degree of freedom (PRES).

• T is the absolute temperature (TEMP).

To invoke the composite gas option for the bulk fluid, use one of the following:

Command(s): FLDATA7,PROT,DENS,CGASGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Fluid Properties




13.2. Doing a Multiple Species Analysis

The procedure for a multiple species analysis has six steps:

1. Establish the number of species to model and assign species names.

2. Designate an algebraic species.

3. Adjust output format if desired.

4. Set properties.

5. Specify boundary conditions and nominal mass fractions.

6. Set relaxation and solution parameters for the solution of the transport equations (if necessary).

13.2.1. Establish the Species

To set the number of species, use one of these methods:

Command(s): KEYOPT,1,1,n (n = number of species (at least 2, but no more than 6))GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

To name each species, use the menu paths shown above or the following command:

Command(s):

MSSPEC

FLOTRAN uses these names for assigning boundary conditions and in postprocessing listings and plots. Thedefault names for species are SP01, SP02, and so on.

13.2.2. Choose an Algebraic Species

The transport equations solve for the mass fractions of each species. You must choose one as the algebraic

species, using the value set by the ALGEB argument or one of the following:

Command(s): MSDATA


The transport equation for the algebraic species is not solved, but its concentration as a function of spaceis calculated by ensuring that the mass fractions of all the species add up to 1.0 everywhere.

Note

The MSDATA command also sets the universal gas constant. Every issuance of the command setsboth numbers.

13.2.3. Adjust Output Format

You can set the format of the convergence monitors on the file Jobname.PFL to list columns of values forall the degrees of freedom for a single iteration. (This also affects the ANSYS output file.) To adjust output,use one of the following:

Command(s): FLDATA6

GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Additional Out> Print Controls

Main Menu> Solution> FLOTRAN Set Up> Additional Out> Print Controls



13.2.3. Adjust Output Format

13.2.4. Set Properties

For a dilute mixture analysis, set the bulk property type as appropriate (CONSTANT, Liquid, etc.).

If the bulk properties are to be a linear combination of the species properties, set the bulk property type toCMIX. For example, you would use the following command:

Command(s):

FLDATA7,PROT,Label,Type

In the preceding command, Label can be DENS, VISC, COND, or SPHT, and Type is CMIX. If Label = DENSE,Type may be CGAS. Using CGAS requires you to enter a molecular weight for the gas via the MSSPEC

command or its equivalent GUI path.

You handle individual species property variations the same way, and with the same options as, the bulkfluid. The CONSTANT, LIQUID, and GAS fluid types are available. Specify them, along with coefficients, usingone of the following:

Command(s): MSPROP


For all analyses, you must enter the mass diffusion coefficient data for each species. For a dilute mixture,the density is the only other relevant property because the bulk or main fluid properties govern the solutionof the momentum equation. For the CMIX and CGAS options, you need to specify density and viscosity usingMSPROP or an equivalent menu path. Also specify conductivity if the energy equation is to be solved.

The form of the diffusion term is:

∇⋅ ∇( )ρD Ymi i

The value Dmi is the diffusion coefficient, and Yi is the mass fraction being solved.

Sometimes, the available data is expressed as a Schmidt number. The following equality enables expressionof the diffusion portion of transport in terms of laminar viscosity µ, the density ρ, and the Schmidt number:

ρµ

D YSC

Ymi ii

i∇ = ∇

Note

The input must be in terms of the mass diffusion coefficient, not the Schmidt number. The Schmidtnumber relating the diffusion coefficient to the density and viscosity differs from the turbulentSchmidt number discussed below.

In addition, the flow field may be turbulent. Another representation of the diffusion term, this time includingthe effect of the turbulent viscosity µ, is:

∇⋅ +

∇

µ µSC SC

Yi

t

Tii

The quantity SCTi is the turbulent Schmidt number, which you specify via one of the following:



Command(s): MSSPEC


The normal default value of 1.0 is sufficient unless you want to regulate explicitly the effect of turbulenceon the transport.

13.2.5. Specify Boundary Conditions

The default boundary condition is zero gradient of the mass fraction at the boundaries. You can specify themass fraction at a boundary, such as the inlet, by entering the species name in the LAB field of one of thefollowing:

Command(s): D

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid/CFD> Displacement> On

Nodes

Main Menu> Solution> Define Loads> Apply> Fluid/CFD> Displacement> On Nodes

Initialize the mass fractions for every species, including the algebraic species. The fractions must sum to 1.0.

13.2.6. Set Relaxation and Solution Parameters

Relaxation factors for the property calculations and the mass fraction update default to 0.5. To change thefactors, use one of the following:

Command(s): MSRELAX


You can set modified inertial relaxation factors for multiple species. To do so, use one of the following:

Command(s): MSMIR,SPNUM,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

A larger modified inertial relaxation factor gives a more robust scheme, but it may yield a slower convergence.The recommended range is 0.1 to 1.0.

You can change parameters for the algebraic solvers for the transport equation and choose a solver by usingone of the following commands or menu paths:

Command(s): MSSOLU, MSMETH


Activating mass fraction capping is recommended to prevent intermediate calculations from producing un-realistic results. Use either of the following for each species:

Command(s): MSCAP


Finally, you activate the multiple species option using one of the following:

Command(s): FLDATA1,SOLU,Spec,TGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options

Main Menu> Preprocessor> FLOTRAN Set Up> Solution Options



13.2.6. Set Relaxation and Solution Parameters

13.3. Doing a Heat Exchanger Analysis Using Two Species

Although FLOTRAN permits only one fluid region to correspond to material number 1 (using the commandMAT,1 or an equivalent GUI path), you can simulate multiple fluids within this restriction. To do so, you setall fluid property types to CMIX, then set the appropriate species mass fraction to 1.0 in a particular region.These settings enable all properties in that region to correspond to that of species with mass fraction 1.0.For such multiple fluid simulations, the mass fractions must remain constant throughout the analysis; thatis, the analysis should not turn on the species solution.

A typical heat exchanger analysis consists of two fluids flowing in opposite directions, separated by a wallas shown in Figure 13.1 (p. 154):

Figure 13.1 Environment for a Typical Heat Exchanger Analysis

LX

LY3

LY2

LY1

X

Y

Solid region (MAT,2)

Pressureandtemperaturespecified oninlet

Pressurespecifiedon outlet

Symmetry surface

YOFFSET

Pressurespecifiedon outlet

Pressureandtemperaturespecified oninlet

Fluid region 2 (MAT,1)(Mass fraction: species 1 = 0.0, species 2 = 1.0)

Fluid region 1 (MAT,1)(Mass fraction: species 1 = 1.0, species 2 = 0.0)

Vy = 0, ∂y

∂T = 0

The sample command stream that follows shows you how to set up the model shown in Figure 13.1 (p. 154),apply boundary conditions, set up appropriate properties, etc. It is important to note that, although twospecies are defined, the species transport has not been activated. In addition, all fluid properties must bedeclared variable so that the initial value (the same in regions 1 and 2) is reset based on the mass fraction.

/BATCH,LIST/tit,heat exchanger problem !two different fluids separated by a solid wall!cartesian geometry, pressure-driven flow!solve by 2 speciesLX = 10 ! Length in X directionNDX = 10 ! Number of X divisionsLY1 = 2 ! fluid 1 widthLY2 = 0.1 ! solid widthLY3 = 1.0 ! fluid 2 widthNDY1 = 10NDY2 = 3 NDY3 = 10 YOFFSET = 0 !offset from X-axis /prep7 $smrt,offet,1,141 ! 2-D XY system!specieskeyopt,1,1,2 ! 2 species!axisymm!keyopt,1,3,2 !use for axisymm RY system only



esha,2 !Quad elementsrect,,LX,YOFFSET,YOFFSET+LY1 !fluid 1 arearect,,LX,YOFFSET+LY1,YOFFSET+LY1+LY2 !solid arearect,,LX,YOFFSET+LY1+LY2,YOFFSET+LY1+LY2+LY3` !fluid 2 areanummrg,allnumcmp,alllsel,s,,,3,9,3lsel,a,,,1lesi,all,,,NDX,

lsel,s,,,2,4,2lesi,all,,,NDY1,-5.0 lsel,s,,,5,7,2lesi,all,,,NDY2,-5.0 lsel,s,,,8,10,2lesi,all,,,NDY3,-5.0 allselmat,1 !for fluids material must be 1amesh,1 !mesh fluid 1 regionamesh,3 !mesh fluid 2 regionmat,2 !for solid set material to 2amesh,2 !mesh solid region!inner region 1!bc inletlsel,s,,,4nsll,s,1d,all,pres,10 !inlet pressure & temp specified for fluid 1d,all,temp,100!bc outletlsel,s,,,2nsll,s,1d,all,pres,0. !outlet pressure specified for fluid 1!symmlsel,s,,,1nsll,s,1d,all,vy,0 !symmetry surface for fluid 1 only!region 2!bc inletlsel,s,,,8nsll,s,1d,all,pres,10. !inlet pressure & temp specified for fluid 2d,all,temp,400!bc outletlsel,s,,,10nsll,s,1d,all,pres,0. !outlet pressure specified for fluid 2!top walllsel,s,,,9 nsll,s,1d,all,vx,0 !wall boundary conditions d,all,vy,0 allsel!solid propertiesmp,dens,2,5. !specify solid region 3 propertiesmp,kxx,2,100mp,c,2,13/SOLU!ic for speciesnsel,s,loc,x,,lx !select nodes for fluid 1nsel,s,loc,y,o,ly1ic,all,sp01,1.0 !set mass fraction for fluid 1ic,all,sp02,0.0nsel,s,loc,x,,lxnsel,s,loc,y,ly1+ly2,ly1+ly2+ly3 !select nodes for fluid 2ic,all,sp01,0.0 !set mass fraction for fluid 2ic,all,sp02,1.0allselFLDA,ITER,EXEC,200 FLDA,PROT,DENS,CMIX ! Fluid densityFLDA,PROT,VISC,CMIX ! Fluid viscosity FLDA,PROT,COND,CMIX ! Fluid conductivityFLDA,PROT,SPHT,CMIX ! Fluid specific heat



13.3. Doing a Heat Exchanger Analysis Using Two Species

flda,vary,dens,t !all properties MUST be variableflda,vary,visc,tflda,vary,cond,tflda,vary,spht,tFLDA,NOMI,DENS,1.0 ! initial density for all fluid regionFLDA,NOMI,VISC,2.0 ! initial viscosity for all fluid regionFLDA,NOMI,COND,3.0 ! initial conductivity for all fluid regionFLDA,NOMI,SPHT,4.0 ! initial specific heat for all fluid regionmsprop,1,spht,constant,1 !sp heat for fluid 1msprop,2,spht,constant,2 !sp heat for fluid 2msprop,1,dens,constant,1 !density for fluid 1msprop,2,dens,constant,2 !density for fluid 2msprop,1,visc,constant,1.0 !viscosity for fluid 1msprop,2,visc,constant,2.0 !viscosity for fluid 2msprop,1,cond,constant,.1 !conductivity for fluid 1msprop,2,cond,constant,.2 !conductivity for fluid 2FLDA,CONV,PRES,1.0E-10 ! PCCR convergence criterionFLDA,TERM,PRES,1.E-09FLDA,OUTP,SP01,TFLDA,OUTP,SP02,TsaveSOLVE !solve for flow onlyFLDA,SOLU,ENRG,TFLDA,SOLU,FLOW,FFLDA,METH,ENRG,3 FLDA,ITER,EXEC,50FLDA,RELX,TEMP,1.SOLVE !solve for temperature onlyfini/exit,nosa

13.4. Example Analysis Mixing Three Gases

The following example analysis mixes three gases: oxygen (O2), nitrogen (N2), and hydrogen (H2). The mass

fractions of the gases are set at each inlet along with the velocity. For the three inlets:

Bottom:Left:Top:

VX = 0VX = 0.1VX = 0

VY = 0.1VY = 0VY = -0.1

TEMP = 300TEMP = 400TEMP = 300

O2 = 0.0O2 = 0.0O2 = 1.0

N2 =0.0N2 = 1.0N2 = 0.0

H2 = 1.0H2 = 0.0H2 = 0.0

The command stream for the example (shown below) shows all the relevant properties and the solutionstrategy.

/batch,list/filename,spec/com ** Analysis Types Laminar and Turbulent, Incompressible/com 2-D - quadrilateral and triangular elements/com ** Features Thermal, Multiple Species Transport/com ** Options Dilute mixtures, composite property types (CGAS, CMIX)/com ** Variable laminar properties/com ** Turbulence/com ** Construction of geometry/prep7!!!!!!! Define some dimensions - SI units are usedlenin=.3



half=lenin/2.width=.1hfwid=width/2.outlen=1.2!!!!!!! Define inlet and outlet rectanglesrect,-lenin,0,-hfwid,hfwidrect,.2,.3,.25,.25+leninrect,.2,.3,-.25,-.25-leninrect,.4,.4+outlen,-.15,.15!!!!!!! Lines that border the mixing areal2tan,-3,-8l2tan,-6,-15l2tan,-13,-10l2tan,-12,-1!!!!!!! Parameters defined for meshingnlcurv=16rlcurv=1nscurv=9rscurv=1nispan=8rispan=-1.5nospan=13rospan=-2nilen=10rilen=-2nolen=24rolen=4!!!!!!!!flst,2,2,4,orde,2!fitem,2,17!fitem,2,20lsel,s,,,17,20,3lesize,all,,,nlcurv,rlcurvlsel,s,,,18,19!fitem,2,18!fitem,2,-19lesize,19,,,nscurv,rscurv!flst,2,3,4,orde,3!fitem,2,2!fitem,2,5!fitem,2,11lsel,s,,,2,5,3lsel,a,,,11lesize,all,,,nispan,1!flst,2,3,4,orde,3!fitem,2,4!fitem,2,7!fitem,2,9lsel,s,,,4,7,3lsel,a,,,9lesize,all,,,nispan,rispan!flst,2,6,4,orde,6!fitem,2,1!fitem,2,3!fitem,2,6!fitem,2,8!fitem,2,10!fitem,2,12lsel,s,,,1,3,2lsel,a,,,6,12,2lesize,all,,,nilen,rilenlsel,s,,,13,16lesize,13,,,nolen,rolenlesize,15,,,nolen,1./rolenlesize,16,,,nospan,rospanlesize,14,,,nospan,rospanalls!!!!!!! Define the mixing area...!flst,2,8,3!fitem,2,2!fitem,2,12!fitem,2,11




!fitem,2,13!fitem,2,16!fitem,2,6!fitem,2,5!fitem,2,3a,2,12,11,13,16,6,5,3alls/com ** CONSTRUCTION OF THE MESH!!!!!!! Put triangles in the mixing area (5)asel,s,,,5et,1,141mshape,1,2damesh,5!!!!!!! Put a mapped mesh in the rectangles (quads)asel,s,,,1,4mshape,0,2dmshkey,1amesh,all/com ** BOUNDARY CONDITIONS!!!!!!! Wall boundary conditionslsel,s,,,1,3,2lsel,a,,,6,12,2lsel,a,,,13,17,2lsel,a,,,18,20nsll,,1d,all,vx,0d,all,vy,0!!!!!!! Define velocities, temperature at top, bottom, leftvtop=.1vbot=.1vlef=.1lsel,s,,,7nslld,all,vx,0d,all,vy,-vtopnsll,,1d,all,temp,300lsel,s,,,4nslld,all,vx,vlefd,all,vy,0nsll,,1d,all,temp,400lsel,s,,,9nslld,all,vx,0d,all,vy,vbotnsll,,1d,all,temp,300lsel,s,,,14nsll,,1d,all,pres,0flda,conv,iter,5savefinishalls/solu/com ** FLOTRAN INPUTflda,iter,exec,40flda,temp,nomi,300 ! Initial temperature field is 300Kflda,prot,dens,air-si ! Initial solution will be for AIRflda,vary,dens,trueflda,prot,visc,air-siflda,vary,visc,trueflda,prot,cond,air-siflda,vary,cond,trueflda,prot,spht,air-sisavesolve ! Solve 40 iterations with air at 300Kfinish ! Prepare for species transport .../prep7flda,prot,dens,cmix ! Composite mixture for density



flda,prot,visc,cmix ! Composite mixture for viscositykeyopt,1,1,3 ! Specify that there are 3 species

flda,solu,spec,t ! Turn on solution for multiple species transportmsdata,2 ! Specify species 2 (N2) as the algebraic species!!!!!!!! Species Property Inputmsspec,1,o2,31.999msprop,1,DENS,GAS,1.2998,300,1.01325E+5msvary,1,dens,tmsnomf,1,.3msprop,1,VISC,CONSTANT,1.2067E-5msprop,1,mdif,CONSTANT,2.149E-5msprop,1,cond,CONSTANT,.02674mscap,1,1!msspec,2,n2,28.018msprop,2,DENS,GAS,1.1381,300,1.01325E+5msvary,2,dens,tmsnomf,2,.3msprop,2,VISC,CONSTANT,1.786E-5msprop,2,mdif,CONSTANT,1.601E-5msprop,2,cond,CONSTANT,.02598mscap,2,1!msspec,3,h2,2.016msprop,3,DENS,GAS,0.0819,300,1.01325E+5msvary,3,dens,tmsnomf,3,.4msprop,3,VISC,CONSTANT,8.94E-6msprop,3,mdif,CONSTANT,4.964E-5msprop,3,cond,CONSTANT,.1815mscap,3,1!msrelx,1,1.0msrelx,3,1.0msmeth,1,3mssolu,1,,,2,1.e-8msmeth,3,3mssolu,3,,,2,1.e-8alls!!!!!!! Species boundary conditionslsel,s,,,7nsll,,1d,all,o2,1.0d,all,n2,0.0d,all,h2,0.0lsel,s,,,4nsll,,1d,all,o2,0.0d,all,n2,1.0d,all,h2,0.0lsel,s,,,9nsll,,1d,all,o2,0.0d,all,n2,0.0d,all,h2,1.0alls!!!!!!! End of species boundary conditionsflda,iter,exec,20 ! Ask for 20 global iterationsflda,conv,outp,land ! Adjust convergence monitor output stylesavefinish/solusolve ! 20 iterations with species activated!!Prepare for energy solutionflda,solu,temp,t ! Achieve a constant flow temperature solutionflda,solu,flow,f ! Freeze the flow fieldflda,meth,temp,3 ! Activate PCCR solverflda,conv,temp,1.e-10 ! Convergence criterion for PCCRflda,iter,exec,5 ! Need only a few iterations for solution...




flda,relx,temp,1.0 ! no relaxation on temperaturesavesolve!! Prepare for coupled solution

flda,iter,exec,35 ! Achieve a flow and thermal solutionflda,solu,flow,tsolveflda,iter,exec,50 ! Run 50 more iterations to refine solutionsavesolve



Chapter 14: Advection Discretization Options

When momentum, energy, species transport, turbulence or the compressible pressure equations are solved,the advection term plays a significant role in the solution. When the advection term dominates over otherterms in the governing equations, it can lead to numerical instabilities. Accordingly, you must be carefulwith the discretization of this particular term.

You can discretize the advection term using three approaches: monotone streamline upwind (MSU),streamline upwind/Petrov-Galerkin (SUPG), or collocated Galerkin (COLG). For the momentum, energy, tur-bulence or compressible pressure equations, you specify the approach using one of the following:

Command(s): FLDATA33,ADVM,Label,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Advection

Main Menu> Solution> FLOTRAN Set Up> Advection

For the species transport equation, you specify the approach using one of the following:

Command(s): MSADV,SPNUM,MTHAGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Multiple Species

Main Menu> Solution> FLOTRAN Set Up> Multiple Species

MSU tends to be first order accurate while SUPG and COLG are second order accurate. MSU produces diag-onally dominant matrices and is generally quite robust. SUPG and COLG provide less diagonal dominance,but are generally more accurate. COLG provides an exact energy balance for incompressible flows, evenwith a coarse mesh. Special techniques may be required to achieve convergence using SUPG or COLG.

For more information on the approaches, consult the Theory Reference for the Mechanical APDL and Mechan-

ical Applications.

The following advection topics are available:14.1. Using SUPG and COLG14.2. Strategies for Difficult Solutions

14.1. Using SUPG and COLG

For simple geometries and simple flows, the SUPG or COLG approach provides a convergent solution in astraight forward fashion.

For laminar flow past obstacles, which generally produce regions of recirculation in the wake, you may needto turn on modified inertial relaxation in the momentum equation using one of the following:

Command(s): FLDATA34,MIR,MOME,ValueGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> MIR Stabilization


For turbulent problems, FLOTRAN will sometimes display a message stating that the coefficient matrix hasa negative diagonal and the solution is probably divergent. You should then try turning on modified inertialrelaxation in the momentum equation or turbulence equation.



Command(s):

FLDATA34,MIR,MOME,Value or FLDATA34,MIR,TURB,Value

The modified inertial relaxation Value should be between 0.1 and 1.0. A larger Value leads to more relax-ation. To achieve a faster convergence rate, use the smallest Value possible.

For complex geometries with turbulence and complex flow fields, you can employ the following techniquesto achieve a convergent solution with SUPG or COLG.

• Set the turbulence ratio to a high value of 1 x 106 and the effective viscosity relaxation factor to a lowvalue of 0.1 using the following commands. These conditions provide the necessary diagonal dominanceuntil the solution enters the radius of convergence.

Command(s): FLDATA24,TURB,RATI,1.0E6GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Model

Main Menu> Preprocessor> FLOTRAN Set Up> Turbulence> Turbulence Param

Main Menu> Solution> FLOTRAN Set Up> Turbulence Model

Main Menu> Solution> FLOTRAN Set Up> Turbulence Param

Command(s): FLDATA25,RELX,EVIS,0.1GUI: Main Menu> Preprocessor> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation

Main Menu> Solution> FLOTRAN Set Up> Relax/Stab/Cap> Prop Relaxation

• Achieve a convergent solution using MSU on all variables. Then, using the following command, performa restart employing SUPG or COLG on the momentum variables only. After achieving a convergentsolution, you can perform a restart again employing SUPG or COLG on the turbulence, pressure, tem-perature and species variables.

Command(s): FLDATA33,ADVM,MOME,SUPG FLDATA33,ADVM,MOME,COLGGUI: Main Menu> Preprocessor> FLOTRAN Set Up> Advection

Main Menu> Solution> FLOTRAN Set Up> Advection

• Although the foregoing techniques might work on a coarse mesh, both may fail on a fine mesh. In thiscase, you may have to resort to a transient algorithm which has the necessary diagonal dominance dueto the inertia term.

14.2. Strategies for Difficult Solutions

Although SUPG and COLG are more accurate than MSU, they may lead to spurious oscillations in the solution.This may lead to nonphysical solutions or convergence difficulties. You may encounter negative temperaturesin the energy equation solution. In this case, you should refine the mesh in that region. You may also en-counter negative turbulence values. Internally, FLOTRAN tries to reset these values to some realistic numbers,but this may lead to a situation where the solution stalls. In this situation, you should try using MSU onturbulence variables while retaining SUPG or COLG on momentum variables. The solution to the speciestransport equation must be bounded between 0 and 1.0, and oscillations in the SUPG or COLG solution maymake this difficult to achieve even though capping has been turned on. If convergence is not achieved, youshould then refine the mesh.

A poor mesh, recirculating regions, or a strong swirl might cause the SUPG technique to have strong oscil-lations in an axisymmetric analysis. Temperatures (or species concentrations) could be higher or lower thanany applied boundary conditions. The mesh should be refined or another advection discretization methodshould be used.


Chapter 14: Advection Discretization Options

Acoustics

Chapter 1: Acoustics

Acoustics is the study of the generation, propagation, absorption, and reflection of sound pressure wavesin a fluid medium. Applications for acoustics include the following:

• Sonar - the acoustic counterpart of radar

• Design of concert halls, where an even distribution of sound pressure is desired

• Noise minimization in machine shops

• Noise cancellation in automobiles

• Underwater acoustics

• Design of speakers, speaker housings, acoustic filters, mufflers, and many other similar devices.

• Geophysical exploration

Types of Acoustic Analysis

An acoustic analysis, available in the ANSYS Multiphysics and ANSYS Mechanical programs only, usually in-volves modeling the fluid medium and the surrounding structure. Typical quantities of interest are thepressure distribution in the fluid at different frequencies, pressure gradient, particle velocity, the soundpressure level, as well as, scattering, diffraction, transmission, radiation, attenuation, and dispersion ofacoustic waves. A coupled acoustic analysis takes the fluid-structure interaction into account. An uncoupled

acoustic analysis models only the fluid and ignores any fluid-structure interaction.

The ANSYS program assumes that the fluid is compressible, but allows only relatively small pressure changeswith respect to the mean pressure. Also, the fluid is assumed to be non-flowing and inviscid (that is, viscositycauses no dissipative effects). Uniform mean density and mean pressure are assumed, with the pressuresolution being the deviation from the mean pressure, not the absolute pressure.

The following acoustics topics are available:1.1. Solving Acoustics Problems1.2. Building the Model1.3. Meshing the Model1.4. Applying Loads and Obtaining the Solution1.5. Reviewing Results1.6. Fluid-Structure Interaction1.7. Sample Applications

1.1. Solving Acoustics Problems

You can solve many acoustics problems by performing a harmonic response analysis. The analysis calculatesthe pressure distribution in the fluid due to a harmonic (sinusoidally varying) load at the fluid-structure in-terface. By specifying a frequency range for the load, you can observe the pressure distribution at variousfrequencies. You can also perform modal and transient acoustic analyses. (See the Structural Analysis Guide

for more information on these types of analyses.)

The procedure for a harmonic acoustic analysis consists of three main steps:



• Build the model.

• Apply boundary conditions and loads and obtain the solution.

• Review the results.

1.2. Building the Model

In this step, you specify the jobname and analysis title and then use the PREP7 preprocessor to define theelement types, element real constants, material properties, and the model geometry. These tasks, commonto most analyses, are described in the Basic Analysis Guide.

1.2.1. Harmonic Acoustic Analysis Guidelines

For a harmonic acoustic analysis, consider the following points:

Element Types - Four ANSYS element types are specifically designed for acoustic analyses: FLUID29, FLUID30,FLUID220, and FLUID221. FLUID29 is used to model the fluid portion of 2-D model. FLUID30, FLUID220, andFLUID221 are used to model the fluid portion of 3-D model. FLUID30 is 3-D 8-Node element. FLUID220 isthe higher order 20 node hexahedral element, and FLUID221 is the higher order 10 node tetrahedral element.

FLUID129 and FLUID130, companion elements to FLUID29 and FLUID30, are used to model an infinite envelopearound the FLUID29 and FLUID30 elements. Use these element types to model the fluid portion, and thenuse a corresponding structural element (PLANE182, SOLID185, etc.) for the solid. Only FLUID29 and FLUID30elements can be in contact with structural elements (either on the inside or outside of the structure); FLUID129and FLUID130 can contact only the FLUID29 and FLUID30 elements, and not the structural elements directly.

1.2.1.1. FLUID29, FLUID30, FLUID220, and FLUID221

For acoustic elements that are in contact with the solid, be sure to use KEYOPT(2) = 0, the default settingthat allows for fluid-structure interaction. This results in unsymmetric element matrices with UX, UY, UZ, andPRES as the degrees of freedom. For all other acoustic elements, set KEYOPT(2) = 1, which results in symmetricelement matrices with the PRES degree of freedom. (See Figure 1.1 (p. 167).) Symmetric matrices require muchless storage and computer time, so use them wherever possible. For more information on fluid-structureinteraction, see Acoustics Fluid-Structure Coupling in the Theory Reference for the Mechanical APDL and

Mechanical Applications.

In FLUID220 and FLUID221, KEYOPT(4) is used to specify the existence of perfectly matched layers (PML) toabsorb the outgoing sound waves. Refer to Perfectly Matched Layers (PML) in the Mechanical APDL High-

Frequency Electromagnetic Analysis Guide for more information about using PML.



Figure 1.1 Example of a 2-D Acoustic Model (Fluid Within a Structure)

Structural elements

Acoustic elements (FLUID29, FLUID30),KEYOPT(2) = 0

Acoustic elements (FLUID29, FLUID30),KEYOPT(2) = 1

1.2.1.2. FLUID129 and FLUID130

These infinite acoustic elements absorb the pressure waves, simulating the outgoing effects of a domainthat extends to infinity beyond the FLUID29 and FLUID30 elements. FLUID129 and FLUID130 provide asecond-order absorbing boundary condition so that an outgoing pressure wave reaching the boundary ofthe model is absorbed with minimal reflections back into the fluid domain.

FLUID129 is used to model the boundary of 2-D fluid regions and as such is a line element. FLUID130 is usedto model the boundary of 3-D fluid regions and as such is a plane surface element.

Material Properties - The acoustic elements require density (DENS) and speed of sound (SONC) as materialproperties (FLUID129 and FLUID130 require only SONC). If sound absorption at the fluid-structure interfaceexists, use the label MU to specify boundary admittance β (absorption coefficient). Values of β are usuallydetermined from experimental measurements. For the structural elements, specify the Young's modulus(EX), density (DENS), and Poisson's ratio (PRXY or NUXY).

Real Constants - When using FLUID129 and FLUID130, the boundary of the underlying finite element meshmust be circular (2-D and axisymmetric) or spherical (3-D), and the radius of the circular or sphericalboundary of the finite domain must be specified as real constant RAD. (See Figure 1.2 (p. 168).) The centerof the circle or sphere is also specified using real constants:

R,3,RAD,X0,Y0!REAL set 3 for FLUID129R,3,RAD,X0,Y0,Z0!REAL set 3 for FLUID130

If the coordinates (X0, Y0) for the 2-D and axisymmetric cases or (X0, Y0, Z0) for the 3-D case of the centerof the circle or sphere are not specified via real constants, ANSYS assumes the center to be the origin of theglobal coordinate system.



1.2.1. Harmonic Acoustic Analysis Guidelines

Figure 1.2 Example of Absorption Element Application

r

x

y

SOLID42(vibrating beam)

FLUID29(surrounding air)

FLUID129(absorption surface tosimulate infinite extent of air)

REAL set for FLUID129; R,3,RAD,0,0

Figure 1.3 Submerged Cylindrical Shell

rsy

x

ts

vacuumcylindrical shell

water

( ( (( ( (

( ( (

1.3. Meshing the Model

A typical meshing procedure using the 2-D infinite acoustic elements follows. The procedure is the samewith 3-D elements. If you have a structural component as well, the structural elements must lie next to theFLUID29 elements, and cannot lie next to the infinite fluid elements (FLUID129).

This process automatically adds the FLUID129 elements on the boundary of the finite domain. Here an an-nular structural ring is meshed with PLANE182 structural elements. The layer of fluid elements in touch withPLANE182 elements is modeled using FLUID29 with UX and UY DOFs and with the fluid-structure interfaceturned on. The outer layers of fluid are modeled using FLUID29 without the UX and UY DOFs. The radius



for placing FLUID129 is 0.31242 (see Step 2: Generate the Infinite Acoustic Elements (p. 169)) with X0 = Y0 = 0.You define the FLUID129 elements using:

Command(s): ESURF

GUI: Main Menu> Preprocessor> Modeling> Create> Elements> Inf Acoustic

1.3.1. Step 1: Mesh the Interior Fluid Domain

Mesh the interior fluid domain that is bounded by a circular or spherical boundary (PLANE182) with FLUID29elements.

Figure 1.4 Mesh the Fluid Domain

FLUID29

PLANE42(structuralcomponent)

circular boundary

x

y

1.3.2. Step 2: Generate the Infinite Acoustic Elements

Follow these steps:

1. Select the nodes on the circular or spherical boundary.

Command(s): NSEL

GUI: Utility Menu> Select> Entities

2. Specify FLUID129 as the infinite fluid element type associated with the FLUID29 element.

Command(s): TYPE, REAL

GUI: Main Menu> Preprocessor> Meshing> Mesh Attributes> Default Attribs

Main Menu> Preprocessor> Real Constants> Add/Edit/Delete

The infinite elements perform well for low as well as high frequency excitations. Numerical experimentshave determined that the placement of the absorbing elements at a distance of approximately 0.2 λbeyond the region occupied by the structure or source of vibration can produce accurate solutions.Here λ = c/f is the dominant wavelength of the pressure waves. c is the speed of sound (SONC) in thefluid and f is the dominant frequency of the pressure wave. For example, in the case of a submergedcircular or spherical shell of diameter D, the radius of the enclosing boundary, RAD, should be at least



1.3.2. Step 2: Generate the Infinite Acoustic Elements

(D/2) + 0.2 λ. Also, for acoustic analysis in general, the mesh must be fine enough to resolve thesmallest dominant frequency.

3. Generate the absorption elements (FLUID129) on the boundary.

Command(s): ESURF

GUI: Main Menu> Preprocessor> Modeling> Create> Elements> Inf Acoustic

Figure 1.5 Add the Absorption Element on the Boundary

rb

y

x

Select nodes on thecircular boundaryCSYS,2

NSEL,s,loc,x,rb

ESURF

1.3.3. Step 3: Specify the Fluid-Structure Interface

Specify the fluid-structure interface:

1. Select all nodes on the interface.

Command(s): NSEL

GUI: Utility Menu> Select Entities

2. Select the fluid elements attached to this set of nodes.

Command(s): ESEL

GUI: Utility Menu> Select> Entities

3. Specify the selected nodes as fluid-structure interface nodes.

Command(s): SF

GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Fluid-Struct Intr> On Nodes

Note

Be sure to reselect all nodes before solving your analysis.



Figure 1.6 Specify Fluid-Structure Interface

FLUID29(type-2)

SOLID42(type-1)

Fluid-structure interfaceNSEL,s,x,loc,x,(rst ts)ESLN,s,0ESEL,r,type,,2SF,all,FSI

rst tsx

y

1.4. Applying Loads and Obtaining the Solution

In this step, you define the analysis type and options, apply loads, specify load step options, and initiate thefinite element solution. The next few sections explain how to do these tasks.

1.4.1. Step 1: Enter the SOLUTION Processor

Enter the SOLUTION processor by choosing GUI path Main Menu> Solution or by executing the /SOLU

command.

1.4.2. Step 2: Define the Analysis Type

Using either the GUI or a set of commands, define the analysis type and analysis options.

To define the analysis type, use one of the following:

Command(s): ANTYPE,HARMICGUI: Main Menu> Solution> Analysis Type> New Analysis

You must choose New Analysis because restarts are not valid in a harmonic response analysis. If you needto apply additional harmonic loads, do a new analysis each time (or use the "partial solution" proceduredescribed in the Basic Analysis Guide).

1.4.3. Step 3: Define Analysis Options

To specify the solution method, use one of the following:

Command(s): HROPT

GUI: Main Menu> Solution> Analysis Options

Although full, reduced, or mode superposition methods are options, choose the full method because it alonecan handle unsymmetric matrices.



1.4.3. Step 3: Define Analysis Options

To define the solution listing format, use one of the following:

Command(s): HROUT


This option determines how ANSYS lists the harmonic degree-of-freedom solution in the printed output(Jobname.OUT ).

To specify the equation solver to be used, use one of the following:

Command(s): EQSLV


You can choose the sparse direct solver (default), the Jacobi Conjugate Gradient (JCG) solver, or the IncompleteCholesky Conjugate Gradient (ICCG) solver. The JCG solver is recommended for most models.

1.4.4. Step 4: Apply Loads on the Model

A harmonic analysis, by definition, assumes that any applied load varies harmonically (sinusoidally) withtime. To completely specify a harmonic load in an acoustic analysis, two pieces of information are usuallyrequired: the amplitude and the forcing frequency. The amplitude is the maximum value of the load, whichyou specify using the commands shown in Table 1.2: Commands for Applying Loads in Acoustic Analysis (p. 173).The forcing frequency is the frequency of the harmonic load (in cycles/time). You specify it later as a loadstep option with the HARFRQ command (Main Menu> Solution> Time/Frequenc> Freq & Substeps). Step

5: Specify Load Step Options (p. 175) describes this task.

Table 1.1: Loads Applicable in an Acoustic Analysis (p. 172) shows all possible loads for a harmonic acousticanalysis and the commands to define, list, and delete them. Notice that except for inertia loads, you candefine loads either on the solid model (keypoints, lines, and areas) or on the finite element model (nodesand elements). For a general discussion of solid-model loads versus finite-element loads, see "Loading" and"Solution" in the Basic Analysis Guide.

Table 1.1 Loads Applicable in an Acoustic Analysis

GUI PathCmd FamilyCategoryLoad Type

DConstraintsDisplacement(UX,UY,UZ),

Main Menu> Preprocessor> Define

Loads> Apply> Structural> Displace-

ment or PotentialPressure (PRES) Main Menu> Solution> Define Loads>

Apply> Structural> Displacement

FForcesForce (FX,FX,FZ), Main Menu> Preprocessor> Define

Loads> Apply> Force/MomentMoment (MX,MY,MZ), Main Menu> Solution> Define Loads>

Apply> Force/MomentFlow loading

SFSurfaceLoads

Pressure (PRES)

Impedance boundaryflag (IMPD)

Main Menu> Preprocessor> Define

Loads> Apply> load typeMain Menu> Solution> Define Loads>

Apply> load type

Fluid-structure interac-tion flag (FSI)



GUI PathCmd FamilyCategoryLoad Type

ACEL,OMEGA,

Inertia LoadsGravity, Spinning, etc. Main Menu> Preprocessor> Define

Loads> Apply> load typeDOMEGA, Main Menu> Solution> Define Loads>

Apply> load typeCGLOC,CGOMGA,DCGOMG,IRLF

In an analysis, you can apply, remove, operate on, or list loads.

1.4.4.1. Applying Loads Using the GUI

You access all loading operations except List (see below) through a series of cascading menus. From theSolution menu, you choose the operation (apply, etc.), then the load type (displacement, force, etc.), andthen the object (keypoint, etc.) to which you are applying the load.

For example, to apply a displacement load to a line, follow this GUI path: Main Menu> Solution> Define

Loads> Apply> Displacement> On Lines

To list loads, use this GUI path: Utility Menu> List> Loads> load type

1.4.4.2. Applying Loads Using Commands

Table 1.2: Commands for Applying Loads in Acoustic Analysis (p. 173) lists all the commands you can use toapply loads in an acoustic analysis.

Table 1.2 Commands for Applying Loads in Acoustic Analysis

Apply

Settings

OperateListDeleteApplyEntitySolid

Mod-

el or

FE

Load Type

-DTRANDKLISTDKDELEDKKeypo-ints

SolidModel

Displacement,Pressure

-DTRANDLLISTDLDELEDLLinesSolidModel

-DTRANDALISTDADELEDAAreasSolidModel

DCUMDSCALEDLISTDDELEDNodesFiniteElem

-FTRANFKLISTFKDELEFKKeypo-ints

SolidModel

Force, Moment

FCUMFSCALEFLISTFDELEFNodesFiniteElem

SFGRADSFTRANSFLLISTSFLDELESFLLinesSolidModel

Pressure, Im-pedanceboundary flag, SFGRADSFTRANSFALISTSFADELESFAAreasSolid

ModelFluid-Structure



1.4.4. Step 4: Apply Loads on the Model

Apply

Settings

OperateListDeleteApplyEntitySolid

Mod-

el or

FE

Load Type

InteractionFlag

SFCUM ,SFGRAD

SFSCALESFLISTSFDELESFNodesFiniteElem

SFBEAM,SFCUM,

SFSCALESFELISTSFEDELESFEEle-ments

FiniteElem

SFFUN,SFGRAD

----ACEL, CG-

LOC,--Inertia

CGOMGA,DCGOMG,OMEGA,DOMEGA,IRLF

1.4.4.3. Load Types

Displacements (UX, UY, UZ) and pressures (PRES)

These are DOF (degree-of-freedom) constraints. For example, you specify zero displacements at a rigid fluid-structure interface. You may also specify nonzero displacements, but remember that they are assumed tobe harmonic. You usually specify zero pressures at free fluid boundaries (where the fluid is not enclosed,such as at an opening).

Forces (FX, FY, FZ) and moments (MX, MY, MZ)

Usually, you specify these loads on the solid portion of the model to "excite" the fluid.

Flow Load

This is a mass flow rate per unit time (for example, kg/sec/sec in SI units). It represents a pulsating massflow rate at a node. Specify it using the FLOW force label:

Command(s): F,,FLOWGUI: Main Menu> Solution> Define Loads> Apply> Structural> Force/Moment> On Nodes

Pressure (PRES)

You can specify surface loads on the solid portion instead of forces and moments.

Impedance boundary flag(IMPD)

These are not really loads but indicate surfaces that absorb sound. Specify the degree of sound absorptionas the material property MU (boundary admittance or absorption coefficient).

Fluid-structure interaction flag (FSI)

This denotes an interface surface between the fluid and structure part of the model.



For problems with fluid-structure interaction on both sides of a structure (e.g., a submerged plate), meshthe structure with solid elements to provide two distinct fluid-interaction surfaces. For problems with fluid-structure interaction on only one side of a structure, mesh the structure with shell or solid elements.

1.4.5. Step 5: Specify Load Step Options

You have the following options for a harmonic acoustic analysis:

Table 1.3 Load Step Options for a Harmonic Acoustic Analysis

GUI PathCom-

mand

Option

Dynamics Options

Main Menu> Solution> Load Step Opts> Time/Fre-

quenc> Freq & Substeps

HAR-

FRQ

Forcing frequencyrange

General Options



NSUBSTNumber of harmonicsolutions



KBCStepped or rampedloads

Output Controls

Main Menu> Solution> Output Ctrls> Solu PrintoutOUT-

PR

Control of printedoutput

Main Menu> Solution> Output Ctrls> DB/Results FileOUTRESDatabase and resultsfile output

Main Menu> Solution> Output Ctrls> Integration PtERESXExtrapolation of res-ults

1.4.5.1. Dynamics Options

The only valid option in this category is the forcing frequency range, which must be defined (in cycles/time)for a harmonic analysis. Within this range, you then specify the number of solutions to be calculated. (See"General Options.")

1.4.5.2. General Options

You can request any number of harmonic solutions (via the NSUBST command or its equivalent GUI path)to be calculated. The solutions (or substeps) will be evenly spaced within the previously specified frequencyrange. For example, if you specify 10 solutions in the range 30 to 40 Hz, the program will calculate the re-sponse at 31, 32, 33, ..., 39, and 40 Hz. No response is calculated at the lower end of the frequency range.

The loads may be stepped or ramped (via KBC or its GUI counterpart). By default, they are ramped; that is,the load value increases gradually with each substep. By stepping the loads, you maintain the same loadvalue for all substeps in the frequency range.

1.4.5.3. Output Controls

Use OUTPR or its GUI equivalent if you want to include any results data on the printed output file (Job-name.OUT). OUTRES and its GUI counterpart control the data on the results file (Jobname.RST ). ERESX



1.4.5. Step 5: Specify Load Step Options

and its GUI path allow you to review element integration point results by copying them to the nodes insteadof extrapolating them (default).

Note

By default, the program writes only the last substep of each load step to the results file. If youwant all substeps (the solution at all frequencies) on the results file, be sure to set the FREQ fieldon OUTRES to ALL (or 1).

1.4.6. Step 6: Back Up Your Database

Save a backup copy of the database on a named file using Utility Menu> File> Save as or the SAVE com-mand. Doing so enables you to retrieve your model should your computer abort during the solution. (Toretrieve a model, reenter ANSYS and then issue the RESUME command or choose Utility Menu> File> Re-

sume.)

1.4.7. Step 7: Apply Additional Load Steps (Optional)

If you wish to apply additional load steps, repeat steps 5 and 6.

1.4.8. Step 8: Finish the Solution

Solve the analysis and then finish.

Command(s): SOLVE

GUI: Main Menu> Solution> Solve> Current LS

Command(s): FINISH

GUI: Main Menu> Finish

1.5. Reviewing Results

The ANSYS program writes results from a harmonic acoustic analysis to the structural results file, Job-name.RST. Results consist of the following data, all of which vary harmonically at each forcing frequencyfor which the solution was calculated:

• Primary data

– Nodal pressures

– Nodal displacements

• Derived data

– Nodal and element pressure gradients

– Nodal and element stresses

– Element forces

– Nodal reaction forces

You can review this information using POST1 or POST26.



1.6. Fluid-Structure Interaction

The interaction of the fluid and the structure at a mesh interface causes the acoustic pressure to exert aforce applied to the structure and the structural motions produce an effective "fluid load." The governingfinite element matrix equations then become:

[ ] [ ] [ ]

[ ] [ ] [ ]

M U K U F R P

M P K P F R

s s s

f f f oT

ɺɺ

ɺɺ

+ = +

+ = −ρ ɺɺU

[R] is a "coupling" matrix that represents the effective surface area associated with each node on the fluid-structure interface (FSI). The coupling matrix [R] also takes into account the direction of the normal vectordefined for each pair of coincident fluid and structural element faces that comprises the interface surface.The positive direction of the normal vector, as the ANSYS program uses it, is defined to be outward fromthe fluid mesh and in towards the structure. Both the structural and fluid load quantities that are producedat the fluid-structure interface are functions of unknown nodal degrees of freedom. Placing these unknown"load" quantities on the left hand side of the equations and combining the two equations into a singleequation produces the following:

M O

R M

U

P

K R

O K

U

P

F

F

s

oT

f

s

f

s

fρ

+−

=

ɺɺ

ɺɺ

The foregoing equation implies that nodes on a fluid-structure interface have both displacement and pressuredegrees of freedom.

1.7. Sample Applications

The three example problems presented here illustrate the application of the acoustic elements. The firstexample shows the use of the acoustic absorption elements in modeling far-field problems. The second ex-ample is a near-field problem showing the use of standing wave prediction in an enclosed space. The thirdexample is a problem with radiation from two waveguides, where perfectly matched layers (PML) are usedto simulate absorption.

1.7.1. Example 1: Fluid-Structure Coupled Acoustic Analysis (Command

Method)

In this problem you will determine the first flexural mode (egg mode) frequency of an annular ring submergedin water which extends to infinity. You will perform a harmonic analysis using a frequency sweep between34 and 38 Hz. The distance from the center of the ring to the infinite elements will at least be equal to (D/2)+ 0.2λ where D is the outer diameter of the ring and λ = c/f is the dominant wavelength of the pressurewaves. Using 0.26035 for the outer radius of the ring, 1460 for the speed of sound (c), and 36 for the estimateddominant frequency (f ), gives (D/2) + 0.2λ = 0.26035 + (0.2)(1460)/36 = 8.37146. However, this is muchgreater than the distance required when using the acoustic infinite element and a distance of 2 times theouter radius of the ring will be used ( 2 x .26035 = .5207), as shown in the command listing.

/BATCH,LIST/VERIFY,EV129-1S/PREP7/TITLE,AMA,EV129-1S,FLUID129,HARMONIC ANALYSISET,1,PLANE182 ! structural elementET,2,FLUID29 ! acoustic fluid element with ux & uyet,3,129 ! acoustic infinite line elementr,3,0.5207,0,0



1.7.1. Example 1: Fluid-Structure Coupled Acoustic Analysis (Command Method)

ET,4,FLUID29,,1,0 ! acoustic fluid element without ux & uy! material propertiesMP,EX,1,2.068e11MP,DENS,1,7929MP,NUXY,1,0MP,DENS,2,1030MP,SONC,2,1460! create inner and outer quarter circlesCYL4,0,0,0.254,0,0.26035,90 CYL4,0,0,0.26035,0,0.5207,90! select, assign attribute to and mesh area 1ASEL,S,AREA,,1AATT,1,1,1,0LESIZE,1,,,16,1LESIZE,3,,,16,1LESIZE,2,,,1,1LESIZE,4,,,1,1MSHKEY,1MSHAPE,0,2D ! mapped quad meshAMESH,1! select, assign attribute to and mesh area 2ASEL,S,AREA,,2AATT,2,1,2,0LESIZE,5,,,16,1LESIZE,7,,,16,1LESIZE,6,,,5LESIZE,8,,,5MSHKEY,0MSHAPE,0,2D ! mapped quad meshAMESH,2! reflect quarter circle into semicircle about x-axisnsym,x,1000,all ! offset node number by 1000esym,,1000,all! reflect semicircle into full circle about y-axisnsym,y,2000,all ! offset node number by 2000esym,,2000,allNUMMRG,ALL ! merge all quantities! modify outer 2 layers of el29 into type 4esel,s,type,,1nsle,sesln,s,0nsle,sesel,invensle,semodif,all,type,4esel,allnsel,all! define el129 line elementcsys,1nsel,s,loc,x,0.5207type,3real,3mat,2esurfesel,allnsel,all! flag interface as fluid-structure interfacensel,s,loc,x,0.26035esel,s,type,,2sf,all,fsi,1nsel,allesel,allFINISH! enter solution module/SOLUANTYPE,harmic ! select harmonic analysishropt,fullf,19,fx,1000.f,1019,fx,-1000.harfrq,34.,38.nsubst,100kbc,1



SOLVEFINISH! postprocess/post26plcplx,0nsol,2,1,u,x,d1uxstoreconjug,3,2prod,4,2,3sqrt,5,4*get,uxmx,vari,5,extrem,tmax/COM -------------------------------------------------------------/COM Expected Result:/COM/COM The following "uxmx" should equal 34.52 Hz./COM -------------------------------------------------------------*status,uxmxfinish

1.7.2. Example 2: Room Acoustic Analysis (Command Method)

This sample problem demonstrates the use of FLUID30 to predict the acoustic standing wave pattern of atypical enclosure representing a room. A sound-absorption material is located at the bottom surface of theenclosure and a vibrating structure with a cylindrical surface is located at the top right hand corner of theenclosure. This problem will determine the acoustic pressure wave pattern when the structure vibrates atan excitation frequency of 80 HZ.

/batch,list/com, Harmonic Analysis - Room Acoustics

/PREP7/TITLE,Room Acoustic AnalysisANTYPE,HARMET,1,30 ! Acoustic elements in contact with walls and vibrating surfaceET,2,30,,1 ! Acoustic elements in interior (not in contact with walls)

! Set parameters for mesh generation

XDIV=29 ! Number of divisions along x-axisYDIV=19 ! Number of divisions along y-axisZDIV=1 ! Number of divisions along z-axisCDIV=2 ! Number of divisions along radius

! Dimensions of the room

LEN=27HGT=20RAD=0.9

! Mesh generation

K,1K,2,LENK,3,LEN,HGTK,4,,HGTK,5,,,-1K,6,LEN,,-1K,7,LEN,HGT,-1K,8,,HGT,-1L,1,5,1L,2,6,1L,3,7,1L,4,8,1CIRC,3,RAD,7,2,90,2ADRAG,5,6,,,,, 3PIO4=ATAN(1)LENC=COS(PIO4)LENC=LENC*RADHGTC=HGT-LENC



1.7.2. Example 2: Room Acoustic Analysis (Command Method)

LENC=LEN-LENCK,15,,HGTCK,16,,HGTC,-1K,17,LENCK,18,LENC,,-1L,1 ,17,XDIVL,10,15,XDIVL,11,4 ,XDIVL,17,10,YDIVL,15, 1,YDIVL,2 ,9 ,YDIVL,5 ,18,XDIVL,13,16,XDIVL,14,8 ,XDIVL,18,13,YDIVL,16,5 ,YDIVL,6 ,12,YDIVESIZE,,CDIVV,1 ,17,10,15, 5,18,13,16V,15,10,11,4 ,16,13,14,8V,17,2 ,9 ,10,18,6 ,12,13VMESH,ALL

! Material properties

MP,DENS,1,2.35E-3 ! (Rho) density of air (lb/ft**3)MP,SONC,1,1100.0 ! (C) speed of sound in air (ft/sec)MP,MU,1,0.04 ! (Beta) absorption coefficient of the walls ! ('Beta' should be between 0 - 1)MP,DENS,2,2.35E-3MP,SONC,2,1100.0MP,MU,2,0.70 ! (Beta) absorption coefficient of ! the absorbing material on the floor ! ('Beta' should be between 0 -1)MP,DENS,3,2.35E-3MP,SONC,3,1100.0MP,MU,3,0.0 ! (Beta) zero absorption coefficient for interior elementsNSEL,S,LOC,Y,0.0NSEL,R,LOC,X,12,15ESLNMAT,2EMODIF,ALL ! Elements which have the absorbing material on the floor

! Boundary conditions

ALLSNSEL,S,LOC,X,0.0NSEL,A,LOC,Y,0.0NSEL,A,LOC,X,LENNSEL,A,LOC,Y,HGTD,ALL,UX,,,,,UY,UZ! Constrain all displacements to zero at the wallsLOCAL,11,1,27,20NSEL,A,LOC,X,RADESLNESEL,INVETYPE,2MAT,3EMODIF,ALL ! Interior elements are specified as Type=2 & material=3ALLS

! Fluid-Structure Interface (FSI)

NSEL,S,LOC,X,RAD ! Select interface (FSI) surface nodesESLN ! Select elements attached to interface surfaceSF,ALL,FSI ! Specify vibrating surface as Fluid-structure interfaceNROTAT,ALLD,ALL,UX,.01 ! Radial vibration amplitude of Vibrating surfaceD,ALL,UY,,,,,UZ

! Impedance Surface (IMPD)

CSYS,0



ALLSNSEL,S,LOC,X,0.0NSEL,A,LOC,X,LENNSEL,A,LOC,Y,0.0NSEL,A,LOC,Y,HGTSF,ALL,IMPD,1 ! Specify the walls as Impedance Surface flag ! to activate absorptionALLSFINISH/SOLU

! Excitation Frequency for Harmonic Analysis

HARF,80,80 ! Frequency of excitation = 80 HzSOLVEFINISH

! Plot the Standing Wave Pattern (f = 80 Hz)

/POST1/SHOW,ENCL1,GRPH,1SET,1,1 ! plot the real part of pressure responseEPLOT/EDGE,1/TITLE,-ROOM ACOUSTICS- * REAL PART OF PRESSUREPLNS,PRESSET,1,1,,1 ! plot the imag. part of pressure response/TITLE,-ROOM ACOUSTICS- * IMAG. PART OF PRESSUREPLNS,PRESFINISH

1.7.3. Example 2: Radiation From Two Waveguides

This sample problem demonstrates the use of FLUID220 to predict the acoustic standing wave pattern. Asound-absorption material is located at the surfaces of the enclosure, which is modeled by using PML. Referto Perfectly Matched Layers (PML) in the Mechanical APDL High-Frequency Electromagnetic Analysis Guide formore information about using PML

/batch/prep7! structure dimensionspi=3.1415926535k=8*pic0=340freq=k*c0/(2*pi)! define elements and materialet,11,200,7et,1,220,,1 ! acousticet,2,220,,1,,1 ! pmlmp,dens,1,1.mp,sonc,1,c0d=0.1l=1.s=0.5a=2dpml=0.25h=d/2rect,-l,0,s/2,s/2+drect,-l,0,-s/2,-s/2-drect,0,a,-a/2,a/2rect,0,a+dpml,-a/2-dpml,a/2+dpmlasba,4,3,,delete,keepaglue,allesize,htype,11amesh,allmshape,0mshkey,0asel,allasel,u,,,5



1.7.3. Example 2: Radiation From Two Waveguides

eslatype,1mat,1esize,,1vext,all,,,0,0,d,asel,s,,,5type,2,mat,1esize,,1vext,all,,,0,0,d,

asel,s,loc,z,0aclear,allallsnummrg,all! define boundary conditionnsel,s,loc,x,a+dpmlnsel,a,loc,y,-a/2-dpmlnsel,a,loc,y,a/2+dpmld,all,pres,0.! hard excitation sourcensel,s,loc,x,-ld,all,pres,1allsfini

! perform solution/solueqslv,sparseantype,harmicharfrq,freqsolvefini

/post26/outprcplx,0nsel,s,loc,x,0nsel,r,loc,y,s/2+d*get,A1,node,0,num,maxnsel,s,loc,x,0nsel,r,loc,y,s/2*get,A2,node,0,num,maxnsel,s,loc,x,0nsel,r,loc,y,-s/2-d*get,B1,node,0,num,maxnsel,s,loc,x,0nsel,r,loc,y,-s/2*get,B2,node,0,num,maxnsel,s,loc,x,ansel,r,loc,y,a/2*get,C1,node,0,num,maxnsel,s,loc,x,ansel,r,loc,y,-a/2*get,C2,node,0,num,maxallselnsol,2,A1,pres,,Input_A1nsol,3,A2,pres,,Input_A2

nsol,4,B1,pres,,Input_B1nsol,5,B2,pres,,Input_B2nsol,6,C1,pres,,Output_C1nsol,7,C2,pres,,Output_C2/com ***************Results****************************prvar,2,4,prvar,3,5,prvar,6,7/com *******************************************************fini



Thin Film

Chapter 1: Thin Film Analysis

A thin film is a small gap of fluid between moving surfaces. This thin layer of fluid can alter the structuralresponse of the structure by adding stiffness and/or damping to the system. Movement normal to the gapproduces a squeeze film effect. Movement tangential to the gap produces a slide film effect.

Thin film effects are important in macrostructures, but they are particularly critical in microstructures wherethe damping and stiffening effects of thin layers of air can significantly affect the behavior of devices usedin micro-electromechanical systems (MEMS). Squeeze film effects are important in devices such as accelero-meters and micromirrors. Slide film effects are important in devices such as comb drives.

One method for assessing the effect of thin films is to use thin film fluid elements based on the Reynoldsnumber (which is known from lubrication technology and rarified gas physics) to calculate the stiffeningand damping effects. These effects can then be added to the overall system model. Separate element typesare used to assess squeeze and slide film effects.

The governing Reynolds equation limits the application of thin film analyses to structures with lateral dimen-sions much greater than the gap separation. In addition, the pressure change across the gap must be muchsmaller than the ambient (i.e., surrounding) pressure, and any viscous heating effects must be ignored. Ifthese three conditions are not satisfied, then the effects of the thin film cannot be assessed using thin filmelements. For those situations, the Navier Stokes equations must be solved using FLOTRAN to assess theeffect of the fluid.

The following thin film topics are available:1.1. Elements for Modeling Thin Films1.2. Squeeze Film Analysis1.3. Modal Projection Method for Squeeze Film Analysis1.4. Slide Film Damping

1.1. Elements for Modeling Thin Films

The ANSYS program has three elements for modeling thin film effects. FLUID136 and FLUID138 are used tomodel squeeze film effects. FLUID139 is used to model slide film effects.

Table 1.1 Thin Film Fluid Elements

DOFShape or CharacteristicDimens.Element

PRESQuadrilateral, 4 or 8-node3-DFLUID136

PRESLine, 2-node3-DFLUID138

UX or UY orUZ

Line, 2-node1-DFLUID139

1.2. Squeeze Film Analysis

Squeeze film analysis simulates the effects of fluid in small gaps between fixed surfaces and structuresmoving perpendicular to the surfaces. Depending on the operating frequencies, the fluid can add stiffening



and/or damping to the system. At low frequencies, the fluid can escape before it compresses. Therefore, thefluid only adds damping to the system. At high frequencies, the fluid compresses before it can escape.Therefore, the fluid adds both stiffening and damping to the system.

A static analysis is used to determine the damping effects at low frequencies. A harmonic analysis is usedto determine the stiffening and damping effects at high frequencies.

The FLUID136 element is used to model the fluid domain between a fixed surface and a structure movingnormally to that surface. The fluid domain is modeled by overlaying FLUID136 elements on the movingsurface of the structure (i.e., lower surface of the structure adjacent to the fixed wall).

Figure 1.1 Moving Plate above a Fixed Wall

The FLUID138 element is used to model the pressure drop through holes in a moving structure. Microstructuresare commonly perforated to reduce the damping effects of the fluid layer. FLUID138 elements are used inconjunction with FLUID136 elements to obtain a consistent pressure distribution, including the effects ofholes.

Figure 1.2 Perforated Plate Structure

A squeeze film analysis can be performed on structures with known velocities or unknown velocities. If thevelocity profile is known, you can apply it directly to the fluid elements. If the velocity profile is not known(or is too complicated), it can be determined from the mode-frequency response of the structure (modelprojection method). This section deals with directly applying the velocities. Modal Projection Method for

Squeeze Film Analysis (p. 201) covers the modal projection method.

The following squeeze film analysis topics are available:1.2.1. Static Analysis Overview1.2.2. Harmonic Response Analysis Overview1.2.3.Transient Response Analysis Overview1.2.4. Flow Regime Considerations1.2.5. Modeling and Meshing Considerations1.2.6. Analysis Settings and Options1.2.7. Loads and Solution1.2.8. Review Results1.2.9. Sample Harmonic Analysis


Chapter 1:Thin Film Analysis

1.2.10. Simplified Transient Analysis1.2.11. Complex Transient Analysis

1.2.1. Static Analysis Overview

Use a static analysis to calculate the pressure distribution for low operating frequencies, where the compres-sion of the fluid (and thus the stiffening effect) is negligible. The resulting pressure distribution can then beused to extract a damping coefficient that reflects the damping effect of the fluid.

CF

vz

=

F is the total pressure force at the fluid structure interface and vz is the normal velocity component of the

moving structure. A typical pressure distribution on a rectangular plate is shown in Figure 1.3 (p. 187).

Figure 1.3 Pressure Distribution on a Plate at a Low Driving Frequency

1.2.2. Harmonic Response Analysis Overview

Use a harmonic analysis to calculate the complex pressure distribution for high operating frequencies. Thecomplex pressure distribution can be used to extract a damping coefficient and a stiffness coefficient. Thephase shift between the pressure and the velocity is caused by compression of the fluid. The real pressurecomponent contributes to the damping of the system. The imaginary pressure component contributes tothe stiffening of the system.

CF

vK

F

vz z

= =Re Imω

FRe is the real component of the pressure force. FIm is the imaginary component of the pressure force. Omega(ω) is the frequency (rad/sec). The damping and stiffness coefficients are frequency-dependent. Figure

1.4 (p. 187) illustrates the frequency dependency for a typical microsystem application.

Figure 1.4 Damping and Squeeze Stiffness Coefficients vs. Frequency



1.2.2. Harmonic Response Analysis Overview

The DMPEXT command is used to extract frequency-dependent damping parameters for use with theMDAMP, DMPRAT, ALPHAD, and BETAD command inputs.

1.2.3. Transient Response Analysis Overview

A transient analysis is often necessary (for example, in problems where a moving structure closes the gap).When there is contact, it is prudent to use a nonlinear analysis to model the contact more accurately. A lineartransient analysis can be performed when the gap between a moving structure and a fixed surface remainsrelatively large. For information on the linear and nonlinear Reynolds equatons, refer to Flow Between FlatSurfaces in the Theory Reference for the Mechanical APDL and Mechanical Applications.

For transient analysis example problems, see Simplified Transient Analysis (p. 194) and Complex Transient

Analysis (p. 196).

1.2.4. Flow Regime Considerations

The Reynolds squeeze film approach assumes a continuous fluid flow regime. To ensure a continuous flowregime, the characteristic length (i.e., gap thickness) must be more than one hundred times larger than themean free path of the fluid particles.

L pL P

pm( )0

0 0

0

=

Lm(po) is the mean free path of the fluid at the operating pressure P0, and L0 is the mean path at reference

pressure P0. If the fluid is air at atmospheric pressure (1.01325*105), then by definition L0 is approximately

64*10-9 meters (64 µm). So, for continuum theory to be directly applicable (without modification) to air at

atmospheric pressure, the gap should be greater than 6.4 µm (64*10-9 meters * 100).

The applicability of the continuum theory is generally assessed using the Knudsen number, which is equalto the mean free fluid path divided by the gap. For continuum theory to be valid, the Knudsen numbershould be less than 0.01.

KnL

d

L P

p dm= = 0 0

0

For high Knudsen numbers, the continuum theory is not valid. However, the dynamic viscosity can be adjustedto simulate the high Knudsen number flow regime. The default flow regime for FLUID136 and FLUID138 iscontinuum theory (KEYOPT(1) = 0). Set KEYOPT (1) = 1 to specify the high Knudsen number flow regime.For FLUID136, set KEYOPT(1) = 2 to specify the high Knudsen number flow regime with surface accommod-ation factors.

The type of reflection of the gas molecules at the wall interface is specified using accommodation factors.Squeeze film models assume diffuse reflection of the gas molecules at the wall interface (accommodationfactor = 1). This assumption is valid for most metals, but is less accurate for micromachined surfaces, partic-ularly those fabricated from silicon. Materials such as silicon cause specular reflection. Typical accommodationfactors for silicon are between 0.80 and 0.90. For more information on accommodation factors, see FlowBetween Flat Surfaces in the Theory Reference for the Mechanical APDL and Mechanical Applications.



1.2.5. Modeling and Meshing Considerations

The methods used to model and mesh the fluid domain depend on the squeeze film analysis method. If thevelocities are directly applied to the fluid elements, the fluid elements can be independent of the structure.If the velocities are determined from the mode-frequency response of the structure (modal projectionmethod), the fluid elements cannot be independent of the structure.

In the modal projection method, the FLUID136 elements must lie on the surface of the structural mesh. Usethe ESURF command to overlay FLUID136 elements on the surface of an existing structural mesh. FLUID136supports 4-node and 8-node options, along with degenerative triangles.

The FLUID138 element is used to model the pressure drop in the channels (holes) in a structure as shownin Figure 1.2 (p. 186). The element supports a circular hole configuration and a rectangular hole configuration(KEYOPT(3)). The element works in conjunction with FLUID136 to correctly compute the pressure distributionon the structure's surface and through the channels. To correctly model the FLUID138 element:

1. Use a single FLUID138 element for each hole.

2. Align the FLUID138 element at the center of the hole. The element should extend through the depthof the hole and have a length equal to the depth of the hole.

3. Assume the pressure at the center of the hole (flush with the plate surface in the thin film region) isat the same pressure as the nodes modeled at the periphery of the hole. Couple the nodes of theFLUID136 element at the whole periphery with the node of the FLUID138 element as shown in Figure

1.5 (p. 189).

Figure 1.5 Coupling of Nodes at the Hole Periphery with the Center Node of a FLUID138

Element

FLUID138 element

Coupled nodes of hole periphery with the first node of the FLUID138 element

Structural mesh shown. FLUID136elements lie underneath the structure on the thin film surface.

1.2.6. Analysis Settings and Options

A thin film analysis using FLUID136 and FLUID138 can be a linear or nonlinear solution for both a static anda transient analysis. No special analysis options or load step options are required. See the Basic Analysis Guide

for general guidelines on defining the analysis type and analysis options.

Harmonic response analysis is a linear analysis. For a harmonic response analysis, you must use the fullmethod.



1.2.6. Analysis Settings and Options

1.2.7. Loads and Solution

The fluid elements support pressure loads at the nodal PRES degrees of freedom and velocity body loads(FLUE) at the node or element as shown in Table 1.2: Load Options for Thin Film Fluid Elements (p. 190). Pressureloads are applied using the D family of commands. The velocity load is applied using the BF family ofcommands. For the velocity load, a positive velocity load will cause a positive pressure. For a harmonic re-sponse analysis, a positive velocity load will cause a positive in-phase pressure load. See Applying BodyLoads for details on applying body loads.

Note

Velocity body loads (FLUE) are the velocities of the moving wall in a direction normal to the wall.They are not in-plane velocities of the fluid.

Table 1.2 Load Options for Thin Film Fluid Elements

ANSYS LabelTypeLoad

PRESNodal DOFPressure

FLUEBody LoadNormal Velocity

The recommended equation solvers for the fluid elements are the Sparse Direct Solver (SPARSE), the JacobiConjugate Gradient Solver (JCG) and the Incomplete Cholesky Conjugate Gradient Solver (ICCG).

1.2.8. Review Results

Results from a thin film fluid analysis are stored on the Jobname.RST file. The primary result from the fluidanalysis is the nodal pressures. For a harmonic response analysis, the pressures are stored as complex values(Real and Imaginary components). "The General Postprocessor (POST1)" discusses reading results into thedatabase and viewing the nodal degree of freedom (pressure) results.

Each fluid element computes and stores results for the mid-plane fluid velocity (PG) and effective viscosity.Use the element table to retrieve and view these results.

To compute the damping and squeeze stiffness coefficients from the resulting pressure distribution on thesurface of a structure, use the element table tools to compute the force on a per-element basis, then sumover all elements to compute the coefficients. The following command sequence demonstrates how to dothis task. This example assumes parameters “omega” and “velo” exist (frequency and normal velocity (FLUEloading), respectively).

set,1,1 ! store Real solutionetable,presR,temp ! extract "Real" pressureetable,earea,volu ! extract element areasmult,forR,presR,earea ! compute "Real" forcessum ! sum over all elements*get,Fre,ssum,,item,forR ! get the total "real" forceset,1,1,,1 ! store Imaginary solutionetable,presI,temp ! extract "Imaginary" pressuresmult,forI,presI,earea ! compute "Imaginary" forcessum ! sum over all elements *get,Fim,ssum,,item,forI ! get the total "imaginary" force

K=abs(Fim*omega/velo) ! Compute squeeze stiffness coefficientC=abs(Fre/velo) ! Compute damping coefficient

/com, ** Equivalent squeeze stiffness coefficient ** *stat,K



/com, ** Equivalent damping coefficient ** *stat,C

1.2.9. Sample Harmonic Analysis

Problem Description

A rectangular beam with perforated holes under transverse motion is modeled to compute the effectivedamping and squeeze stiffness coefficients. The thin film surface of the structure is modeled with FLUID136elements. FLUID138 elements are used to model the hole regions. By altering the boundary condition ofthe free FLUID138 node, we can simulate different pressure boundary conditions of the hole region. Thepurpose of the analysis is to compute the equivalent squeeze stiffness and damping coefficient for an assumeduniform plate velocity. A harmonic response analysis is performed at 150 kHz. A previous modal analysisindicated that the pertinent eigenfrequency was 150 kHz. Since the analysis is linear, the magnitude of thevelocity can be arbitrary for computing the coefficients.

Three cases were considered:

1. Holes modeled with no resistance (pressure = 0 at hole location, no FLUID138 elements ).

2. Holes modeled with finite resistance (FLUID138 elements modeled, pressure set to zero on fluid nodeat top of plate).

3. Holes modeled with infinite resistance (no pressure specification at hole location, no FLUID138 elements).

Case 1 is typical for large diameter holes compared to the hole depth. Case 3 is typical for very high flowresistance, which happens in the case of narrow and long holes. Case 2 is the most accurate case where thefluid pressure drop is taken into account by the FLUID138 elements.

Results

Table 1.3: Beam Model Results Considering Perforated Holes (p. 191) lists the damping and squeeze coefficientresults. Figure 1.6 (p. 192) and Figure 1.7 (p. 192) illustrate the real and imaginary pressure distribution. Theinput file for case 2 is listed.

Table 1.3 Beam Model Results Considering Perforated Holes

Squeeze stiffness coefficientDamping Coeffi-

cient

Hole optionFrequency

(kHz.)

1.2012.016e-5Infinite resist-ance

150

.54651.325e-5Finite resistance150

.46071.165e-5No resistance150



Results

Figure 1.6 Pressure Distribution (Real Component)

Figure 1.7 Pressure Distribution (Imaginary Component)

Command Listing

The input file for this example is shown below for the finite-resistance Case 2

/batch,list/PREP7/title, Damping and Squeeze film stiffness calculations for a rigid /com, plate with holes/com uMKS units

ET, 1,136,1 ! 4-node option, High Knudsen NumberET, 2,138,1 ! Circular hole option, Hugh Knudsen Number

s_l=100 ! Half Plate length (um)s_l1=60 ! Plate hole locations_w=20 ! Plate widths_t=1 ! Plate thicknessc_r=3 ! Hole radiusd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)velo=2000 ! arbitrary velocity (um/s)freq=150000 ! Frequency (Hz.)pi=3.14159omega=2*pi*freq ! Frequency (rad/sec)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,visc,1,visc ! Dynamic viscosity gapmp,visc,2,visc ! Dynamic viscosity holes



r,1,d_el,,,pamb ! Real constants - gaprmore,pref,mfp

r,2,c_r,,,pamb ! Real constants - holermore,pref,mfp

! Build the model

rectng,-s_l,s_l,-s_w,s_w ! Plate domainpcirc,c_r ! Hole domainagen,3,2,,,-s_l1/3agen,3,2,,,s_l1/3ASBA, 1, all

TYPE, 1MAT, 1smrtsize,4AMESH, all ! Mesh plate domain

! Begin Hole generation*do,i,1,5 nsel,all *GET, numb, node, , num, max ! Create nodes for link elements N, numb+1,-s_l1+i*s_l1/3,, N, numb+2,-s_l1+i*s_l1/3,, s_t TYPE,2 MAT, 2 REAL,2 NSEL, all E, numb+1, numb+2 ! Define 2-D link element ESEL, s, type,,1 NSLE,s,1 local,11,1,-s_l1+i*s_l1/3 csys,11 NSEL,r, loc, x, c_r ! Select all nodes on the hole circumference NSEL,a, node, ,numb+1 *GET, next, node, , num, min CP, i, pres, numb+1, next nsel,u,node, ,numb+1 nsel,u,node, ,next CP, i, pres,all !Coupled DOF set for constant pressure csys,0*enddo ! End hole generation

nsel,s,loc,x,-s_lnsel,a,loc,x,s_lnsel,a,loc,y,-s_wnsel,a,loc,y,s_wnsel,r,loc,z,-1e-9,1e-9d,all,pres ! Fix pressure at outer plate boundarynsel,all

esel,s,type,,2nsle,s,1nsel,r,loc,z,s_td,all,pres,0 ! P=0 at top of plate dlist,all

allsel

bfe,all,flue,,velo ! Apply arbitrary velocity fini

finish/soluantyp,harm ! Full Harmonic analysisharfrq,freqsolvefinish



Command Listing

/post1esel,s,type,,1set,1,1etable,presR,pres ! extract "Real" pressureetable,earea,volusmult,forR,presR,earea ! compute "Real" forcessum*get,Fre,ssum,,item,forRset,1,1,,1etable,presI,pres ! extract "Imaginary" pressuresmult,forI,presI,earea ! compute "Imaginary" pressuressum*get,Fim,ssum,,item,forI

K=abs(Fim*omega/velo) ! Compute equivalent stiffnessC=abs(Fre/velo) ! Compute equivalent damping

/com, ******* Equivalent stiffness *************************stat,K/com, ******* Equivalent damping ***************************stat,Cfinish

1.2.10. Simplified Transient Analysis

Problem Description

A simplified transient analysis is performed for a rectangular plate fixed at two ends with a hole in the center.A stepped pressure load is applied to the top surface of the plate. SOLID185 elements model the structure.FLUID136 elements model the thin film surface and a FLUID138 element models the hole region. Displacementand pressure time history results are determined at the bottom of the plate on the circumference of thehole.

Command Listing

The input file for this example is shown below.

/PREP7/title, Simplified Transient Analysis/com uMKS units

ET, 1,136,1 ! 4-node option, High Knudsen Numberkeyop,1,3,2 ! PRES + UZ + UY + UZ DOFs, implicit treatmentet,2,138,1 ! HoleET,3,185,,3 ! Structural element

s_l=20 ! Half Plate length (um)s_w=20 ! Plate widths_t=10 ! Plate thicknessc_r=6 ! Hole radiusd_el=2 ! Gappamb=.1 ! Ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! Mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,visc,1,visc ! Dynamic viscosity gapmp,visc,2,visc ! Dynamic viscosity holemp,ex,3,79e3 ! Goldmp,dens,3,19300e-18mp,nuxy,3,.1

r,1,d_el,,,pamb ! Real constants - FLUID136rmore,pref,mfp



r,2,c_r,,,pamb ! Real constants - FLUID138rmore,pref,mfp

block,-s_l,s_l,-s_w,s_w,0,s_tcyl4,0,0,c_r,,c_r,,s_tvsbv,1,2numcmp,alltype,3mat,3real,3mshape,1,3desize,,3vmesh,1 ! SOLID185 mesh

nsel,s,loc,z,0esln,sTYPE, 1MAT, 1real,1esurf ! FLUID136 meshallsel

!make the nodes/elem for 138*get,numb,node,,num,maxn,numb+1,0,0,0n,numb+2,0,0,s_ttype,2mat,2real,2e,numb+1,numb+2 ! FLUID138 mesh

!couple hole pres eqesel,s,type,,1nsle,s,1local,11,1,0,0,0csys,11nsel,r,loc,x,c_rnsel,a,node,,numb+1cp,1,pres,allcsys,0allsel

nsel,s,loc,x,-s_lnsel,a,loc,x,s_lnsel,a,loc,y,-s_wnsel,a,loc,y,s_wnsel,r,loc,z,-1e-9,1e-9nsel,a,node,,numb+2d,all,pres ! Fix pressure at outer plate boundarynsel,alldlist

!esel,s,type,,1!nsle,s,1!nsel,u,cp,,1!cm,FLUN,node!allsel

nsel,s,loc,x,-s_l ! Fix two ends of SOLID185 elementsnsel,a,loc,x,s_ld,all,uxd,all,uyd,all,uzallsel

nsel,s,loc,z,s_t ! Apply pressure loading on SOLID185 top surfacesf,all,pres,1.e+1allsel

fini

/solu



Command Listing

antype,transkbc,1 ! Specify a stepped loadingnropt,fulltime,180e-6!time,6e-6deltim,2e-6 ! Specify time step sizeoutres,all,noneoutres,nsol,alloutres,esol,all cnvtol,pres,,1.e-6 ! Specify convergence valuescnvtol,u ,,1.e-6savesolvefini

/post26nl=node(c_r,0,0)nsol,2,nl,uznsol,3,nl,pres ! Print time history resultsprvar,2,3fini/post1set,last ! Retrieve results at last substepesel,s,type,,1 ! FLUID136etable,_gap,nmisc,2pretab,_gap ! Print GAP valuefini

1.2.11. Complex Transient Analysis

Problem Description

A complex transient analysis is performed for a rectangular top plate fixed at two ends with a hole in thecenter. A voltage is applied to the bottom surface of the top plate. After the top plate makes contact withthe bottom plate the voltage is set to a release value. SOLID185 elements model the top plate. TRANS126transducer elements are created between the plates. FLUID136 elements model the thin film surface and aFLUID138 element models the hole region. The applied voltage is shown in Figure 1.8 (p. 197). Displacementand pressure results at the bottom of the top plate on the circumference of the hole are shown in Figure

1.9 (p. 197) and Figure 1.10 (p. 198).



Results

Figure 1.8 Applied Voltage

Figure 1.9 Displacement Time History



Results

Figure 1.10 Pressure Time History

Command Listing


/batch,list/title, Complex Transient Analysis!/nerr,,,-1

/PREP7/title, Complex Transient Analysis/com uMKS units

ET, 1,136,1 ! 4-node option, High Knudsen Numberkeyop,1,3,2 !implicitkeyop,1,4,0 !compressiblekeyop,1,5,2 !fluid gap optionkeyop,1,6,1 !mech gap optionet,2,185ET,3,185 ! Structural element

s_l=100 ! Half Plate length (um)s_w=20 ! Plate widths_t=1 ! Plate thicknessd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen numbermingapf=1e-2 ! Minimum gap for real constanst on element 136mech_mingapf=1e-2 ! Mechanical minumum gap for real constant on element 136app_volt=23.281 ! Applied voltageapp_pres=0 ! Applied pressure at boundaries

mp,visc,1,visc ! Dynamic viscosity gapmp,ex,3,79e+3 ! Goldmp,dens,3,19300e-18mp,nuxy,3,.1

r,1,d_el,,,pamb ! Real constants - gaprmore,pref,mfp,0,0,1,mech_mingapfrmore,mingapf,1.e+18,0.e-2,-4.e+0,-0.e-2,1.e-0! mingapf,penpar,deadpres,deadspr,deaddam,deadeps



!top plateblock,-s_l,s_l,-s_w,s_w,0,s_t !INSTALL TOP PLATElsel,s,line,,4,5,1 !Set element depthlsel,a,line,,2,7,5 lesize,all,,,19,-.1 lsel,s,line,,1,8,7 lsel,a,line,,3,6,3 lesize,all,,,11,-.1lsel,s,line,,9,12,1lesize,all,,,2type,3 !Mesh top plate with Gold materialmat,3real,3!mshape,1,3dmshape,1,3dcyl4,0,0,s_w/50,,,,s_t+1 !Create a hole in top plate vsbv,1,2numcmp,voluvmesh,1

!holen,10000,0,0,0 !Specify nodes for hole element (138)n,10001,0,0,s_tet,6,138,1,,0 !Define hole shaper,10,s_w/200,,,pamb, !Define hole diameter and pressuresrmore,pref,mfptype,6real,10mat,1e,10000,10001lsel,s,line,,13,16nsll,s,1 !Tie top plate hole edge to hole element.nsel,a,node,,10000cp,next,pres,alld,10001,pres,0allsel

!else emtgen computes INCORRECT areas nsel,s,loc,z,0cm,trun,nodeallselemtgen,'TRUN',,,'uz',-d_el,mingapf*d_el,1.e-18!Create transducer elements 126 using emtgen!apply gap information!fluidnsel,s,loc,z,0 !Define Fluid regionesln,sTYPE, 1MAT, 1real,1esurf !Surface the solid top plate with 136 squeeze film elements

nsel,s,loc,x,-s_lnsel,a,loc,x,s_lnsel,a,loc,y,-s_wnsel,a,loc,y,s_wnsel,r,loc,z,-1e-9,1e-9d,all,pres !Fix pressure at outer plate boundarynsel,all

nsel,s,loc,x,-s_lnsel,a,loc,x,s_ld,all,uxd,all,uyd,all,uzallsel

nsel,s,loc,z,s_t !Apply pressure at boundarysf,all,pres,app_presallsel



Command Listing

!fix bottom node voltage/dispnsel,s,loc,z,-d_el !Set voltage/displacement at bottom plated,all,ux !V(bottom)=0Vd,all,uy !displacement(bottom)=(0,0,0)d,all,uzd,all,voltallsel

!fix top node voltagecmsel,s,trun !Set voltage on top side to applied voltage valued,all,volt,app_volt !for pulldownallsel

fini

/soluantype,trans !Pulldown stagekbc,1time,11.e-5!autots,on !enforce regular timestepsdeltim,1.e-5,nsubst,10,1000,2outres,all,noneoutres,nsol,2outres,rsol,2outres,esol,2cnvtol,pres,,5.e-6 cnvtol,u ,,5.e-6 nropt,fullneqit,500savesolvetime,20e-5 !Contact time.nropt,full !Reduce number of equilibrium iterations to save time.neqit,100outres,all,noneoutres,nsol,2outres,rsol,2outres,esol,2cnvtol,pres,,5.e-6 cnvtol,u ,,5.e-6 solvecmsel,s,trun !Setup release timed,all,volt,1.5 !Set release voltage acrossallseltime,20.4e-5 !only limited time hereoutres,all,noneoutres,nsol,20 !Long grinding period here, reduce result steps so we don't gooutres,rsol,20 !over 1000 results.outres,esol,20cnvtol,pres,,5.e-6 cnvtol,u ,,5.e-6 cnvtol,pres,,1.e-4 cnvtol,u ,,1.e-4 autots,on !Let Autotimestep run heredeltim,.005e-5,0.001e-5,1e-5 !to better capture the overshoot movement on releasesolvetime,30e-5 !After initial snapback, autots,on !increase timestep as overshoot decays.deltim,.5e-5,0.02e-5,1e-5solvefini

/POST1 allsel GG=node(0,-0.4,0)SET,LIST,999SET,,, ,,, ,30 !* !* PLESOL, NMISC,13, 0,1.0 presol,nmisc,13



/out,fini!*list,closes,lis1!*list,closes,lis2/post26NUMVAR,200 SOLU,191,NCMIT STORE,MERGE FILLDATA,191,,,,1,1 REALVAR,191,191 NSOL,2,GG,U,Z,UZ_2NSOL,3,GG,PRES,,PRES_3NSOL,4,GG,VOLT,,VOLT_4plvar,2plvar,3plvar,4

fini

1.3. Modal Projection Method for Squeeze Film Analysis

Modal projection techniques provide an efficient method for computing damping parameters for flexiblebodies. The Modal Projection Technique is the process of calculating the squeeze stiffness and dampingcoefficients of the fluid using the eigenvectors of the structure. In the modal projection method, the velocityprofiles are determined from the mode-frequency response of the structure.

The following modal projection method topics are available:1.3.1. Modal Projection Method Overview1.3.2. Steps in Computing the Damping Parameter Using the Modal Projection Technique1.3.3. Example Problem Using the Modal Projection Method1.3.4. Damping Extraction for Large Signal Cases

1.3.1. Modal Projection Method Overview

For a structure undergoing flexible body dynamics, the displacement and velocity vary along the structure.For a thin-film fluid adjacent to the structure, there is a true dependency between the structural velocityand the fluid pressure. A modal analysis of a structure provides information on the fundamental eigenfre-quencies and mode shapes (eigenvectors). For each mode, i, we can impress the distributed eigenvectorvalues as velocity loads and compute the resulting pressure distribution and hence the fluid force acting onmode j. Therefore, we can compute a matrix of modal squeeze stiffness coefficients, Kij, and modal damping

coefficients, Cij. The diagonal terms of these matrices are the coefficients of each mode, the off-diagonal

terms represent the "cross-talk" coefficients between modes. Figure 1.11 (p. 202) illustrates the modal projectiontechnique.



1.3.1. Modal Projection Method Overview

Figure 1.11 Modal Projection Technique for Damping Characterization

From the modal squeeze and stiffness coefficients for the main diagonal terms (source mode = target mode),other useful damping parameters can be calculated. For example, the modal damping ratio, ξ , and themodal squeeze to stiffness ratio, kri, can be computed by:

ξ ω ωi ii i i i ii iC m kr K= =/( ) /2 2

Where mi is the modal mass and ωi the eigenfrequency. The damping ratio can be used to compute ALPHAD

and BETAD parameters for Rayleigh damping (see ABEXTRACT command), or to specify constant andmodal damping by means of the DMPRAT or MDAMP commands.

The squeeze to stiffness ratio represents the relative stiffening of the mechanical system due to fluid com-pression and resonance shift. If the squeeze-to-stiffness ratio is small (e.g., <.02), then the squeeze stiffnessaffects the structural stiffness by less than 2%, which may be negligible. At higher frequencies, the ratio canbe much larger, indicating a significant stiffening of the structure.

The stiffness and damping coefficients may be strongly frequency-dependent. Figure 1.12 (p. 202) shows atypical frequency dependency of the squeeze and damping forces on a flat plate, and the resulting stiffnessand damping constant. The frequency where the forces intersect is known as the cut-off frequency. Belowthis frequency, structures may be accurately characterized by a constant damping coefficient, and stiffnesseffects can be ignored. Structures which operate far above the cut-off can be described by a constant stiffnesscoefficient, and damping effects can be ignored.

Figure 1.12 Damping and Squeeze Stiffness Parameters for a Rectangular Plate

1.3.2. Steps in Computing the Damping Parameter Using the Modal Projection

Technique

The basic steps in performing the analysis are as follows:

1. Build a structural and thin-film fluid model and mesh.



2. Perform a modal analysis on the structure.

3. Extract the desired mode eigenvectors.

4. Select the desired modes for damping parameter calculations.

5. Perform a harmonic analysis on the thin-film elements.

6. Compute the modal squeeze stiffness and damping parameters.

7. Compute modal damping ratio and squeeze stiffness coefficient.

8. Display the results.

Steps 4-7 have been automated using the DMPEXT command macro. Step 8 is available through the MDPLOT

command macro.

1.3.2.1. Modeling and Meshing

Model preparation for the modal projection method for damping parameter extraction follows very closelyto the method outlined in Modeling and Meshing Considerations (p. 189). Both the structural model and thethin-film fluid model need to be defined simultaneously. Group the fluid nodes on the structure surface intoa node component named "FLUN". This component should only include nodes attached to FLUID136 elements.This component defines the nodes for which the eigenvector values will be extracted from the mode-frequencyanalysis.

1.3.2.2. Perform Modal Analysis

A modal analysis of the structure is required to obtain the eigenvectors of the desired modes. The modalanalysis should be set up with the following options:

1. Use the Block Lanczos, Supernode, or PCG Lanczos (if applicable) method (MODOPT command).

2. Extract the eigenmodes of interest (MODOPT command).

3. Expand the eigenmodes of interest (MXPAND command).

The expanded eigenmodes will compute the necessary eigenvectors required for the modal projectiontechnique. Note: The thin-film fluid elements may be left active in the model when performing the modalanalysis. These elements will not contribute to the modal solution.

1.3.2.3. Extracting Eigenvectors

The eigenvectors from the modal analysis must be retrieved and stored in a format appropriate for use bythe thin-film fluid elements for a subsequent harmonic fluid analysis. Use the RMFLVEC command in POST1to retrieve the eigenvectors. The data is stored in the file Jobname.EFL .

1.3.2.4. Performing a Harmonic Response Analysis and Extracting Damping Parameters

The command macro DMPEXT performs a harmonic response analysis with the thin-film fluid elements usingthe eigenvector information for the desired mode(s). The macro also extracts damping parameter informationfor use in subsequent dynamic structural analysis. Damping parameters extracted include the modaldamping coefficient, modal squeeze stiffness coefficient, damping ratio, and the squeeze-to-stiffness ratio.

DMPEXT requires a "source" mode number and a "target" mode number. The source mode is the mode forwhich the eigenvectors are used to impart a velocity field on the fluid elements. The target mode is themode which is acted on by the pressure solution (fluid forces). For transverse oscillations and a uniform gap,there is little mode interaction and hence only diagonal terms are required (source mode (i) = target mode



1.3.2. Steps in Computing the Damping Parameter Using the Modal Projection Technique

(j)). For transverse motion with nonuniform gaps, or asymmetric plate motion, mode interaction effects(cross-talk) can be significant and should be computed (source mode .ne. target mode). Typical cross-talkscenarios are shown in Figure 1.13 (p. 204).

Figure 1.13 Fluidic Cross-Talk between Transverse and Rotational Motion

Damping parameter extraction can be selected over a desired frequency range or at the eigenfrequenciesof the structure. Damping results are computed and stored in an array parameter.

Computed damping ratios may be used in subsequent dynamic structural analyses. A constant dampingratio can be applied using DMPRAT for a subsequent harmonic or mode-superposition transient analysis.Mode damping ratios may be applied using the MDAMP command for use in mode-superposition harmonicand transient analyses. Note: Subsequent structural analysis using these damping parameters do not requirethe thin-film fluid elements in the model.

The command macro ABEXTRACT (like DMPEXT) extracts alpha and beta damping parameters for use inthe ALPHAD and BETAD commands. These commands define Rayleigh damping and can be used in time-transient structural analysis to model damping effects. The damping parameters are computed from twomodes defined by the user.

The command macro MDPLOT may be used to display the frequency-dependent damping parameters.

1.3.3. Example Problem Using the Modal Projection Method

A rectangular beam with perforated holes is modeled to compute the effective damping coefficient, stiffnesscoefficient, and damping ratio. The surface of the structure is modeled with FLUID136 elements to representthe thin film. The structure is modeled with SOLID185 elements. This example computes the Rayleighdamping coefficients (α and β) and modal damping ratios ξi for use in a transient dynamic analysis.

The problem is defined as an extension to the earlier squeeze film example. After modeling the fluid domain,the structure of the beam is modeled and meshed with SOLID185 elements. A modal analysis is performedon the structure and the first two eigenvalues and eigenvectors are computed. RMFLVEC is used to extractthe eigenvectors for use in the modal projection method to compute the thin-film damping parameters.The command macro ABEXTRACT is used to compute the Rayleigh parameters from the lowest two eigen-modes . Modal damping ratios are also provided by the ABEXTRACT macro for the two eigenmodes.



Table 1.4: Modal Damping Parameters for First Two Eigenfrequencies (p. 205) lists the results from the dampingparameter extraction. Computed Rayleigh parameters are: ALPHAD=65212, BETAD=1.829e-8. The input filefor this example is shown below.

Table 1.4 Modal Damping Parameters for First Two Eigenfrequencies

Stiffness

Ratio

Damping

Ratio

Modal Squeeze Stiffness

Coefficient

Modal Damping

Coefficient

Frequency

(Hz.)

.2285e-2.9703e-1.2758e96741955294

.3644e-2.4200e-1.3568e1083123157497


/batch,list/PREP7/title, Damping Ratio and Rayleigh Damping Calculations for a Perforated Plate/com uMKS units

ET, 1,136,1 ! 4-node option, High Knudsen NumberET, 2,138,1 ! Circular hole option, Hugh Knudsen Number ET,3,185,,3 ! Structural element

s_l=100 ! Half Plate length (um)s_l1=60 ! Plate hole locations_w=20 ! Plate widths_t=1 ! Plate thicknessc_r=3 ! Hole radiusd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,visc,1,visc ! Dynamic viscosity gapmp,visc,2,visc ! Dynamic viscosity holesmp,ex,3,79e3 ! Goldmp,dens,3,19300e-18mp,nuxy,3,.1

r,1,d_el,,,pamb ! Real constants - gaprmore,pref,mfp

r,2,c_r,,,pamb ! Real constants - holermore,pref,mfp

! Build the model



! Begin Hole generation*do,i,1,5 nsel,all *GET, numb, node, , num, max ! Create nodes for link elements N, numb+1,-s_l1+i*s_l1/3,, N, numb+2,-s_l1+i*s_l1/3,, s_t




TYPE,2 MAT, 2 REAL,2 NSEL, all E, numb+1, numb+2 ! Define 2-D link element ESEL, s, type,,1 NSLE,s,1 local,11,1,-s_l1+i*s_l1/3 csys,11 NSEL,r, loc, x, c_r ! Select all nodes on the hole circumference NSEL,a, node, ,numb+1 *GET, next, node, , num, min CP, i, pres, numb+1, next nsel,u,node, ,numb+1 nsel,u,node, ,next CP, i, pres,all !Coupled DOF set for constant pressure csys,0 *enddo ! End hole generation

esize,,2type,3mat,3real,3vext,all,,,,,s_t ! Extrude structural domain

nsel,s,loc,x,-s_lnsel,a,loc,x,s_lnsel,a,loc,y,-s_wnsel,a,loc,y,s_wnsel,r,loc,z,-1e-9,1e-9d,all,pres ! Fix pressure at outer plate boundarynsel,all

esel,s,type,,2nsle,s,1nsel,r,loc,z,s_td,all,pres,0 ! P=0 at top of plate dlist,all

esel,s,type,,1nsle,s,1nsel,u,cp,,1,5cm,FLUN,nodeallsel

nsel,s,loc,x,-s_lnsel,a,loc,x,s_ld,all,uxd,all,uyd,all,uz

allsel

fini

/soluantype,modal ! Modal analysismodopt,lanb,2 ! Extract lowest two eigenmodeseqslv,sparsemxpand,2 ! Expand lowest two eigenmodessolvefini

/post1RMFLVEC ! Extract eigenvectorsfini

/solu



abextract,1,2 ! Extract damping ratios and Rayleigh constantsfinish

A transient dynamic analysis on the switch can be performed using the extracted damping parameters. Thefollowing input illustrates a coupled electrostatic-structural time-transient solution. The electrostatic field isassumed to be normal to the plate in the gap, and fringing effects are ignored. TRANS126 elements are usedto model the coupled electrostatic-structural interaction with the switch. The EMTGEN command is used togenerate the transducer elements. A step voltage pulse is applied over a short duration (65 micro-seconds)then released. Rayleigh damping parameters, when used, are applied to the global mass (ALPHAD parameter)and stiffness (BETAD parameter) matrices. We want to apply these only to the mass and stiffness matrix ofthe SOLID185 elements, and not the TRANS126 elements, because doing so may overdamp the system. TheTRANS126 elements produce a damping matrix and a stiffness matrix only. Hence, we can use the ALPHADparameter for the global mass matrix since there is no contribution from the TRANS126 elements. To isolatethe SOLID185 elements for beta damping, we can apply the beta damping via a material damping option(MP,DAMP). Figure 1.14 (p. 208) illustrates the displacement of a node near the center of the plate over time.The maximum amplitude of displacement (0.11 microns) is small enough to ignore large deflection dampingeffects.

/batch,list/PREP7/title, Damped Transient Dynamic Response of an RF MEMS switch/com uMKS units/com, Small deflection assumption

et,1,200,6ET,3,185,,3 ! Structural element

s_l=100 ! Plate length (um)s_l1=60 ! Plate hole locations_w=20 ! Plate widths_t=1 ! Plate thicknessc_r=3 ! Hole radiusd_el=2 ! Gappamb=.1 ! ambient pressure (MPa)visc=18.3e-12 ! viscosity kg/(um)(s)pref=.1 ! Reference pressure (MPa)mfp=64e-3 ! mean free path (um)Knud=mfp/d_el ! Knudsen number

mp,ex,3,79e3 ! Goldmp,dens,3,19300e-18mp,nuxy,3,.1mp,damp,1,1.829e-8 ! Material damping (from squeeze film results)! Build the model



esize,,2type,3mat,3real,3vext,all,,,,,s_t ! Extrude structural domain

nsel,s,loc,x,-s_lnsel,a,loc,x,s_ld,all,uxd,all,uyd,all,uz




allselaclear,allsave

nsel,s,loc,zcm,base,nodesemtgen,'base',,,'uz',-d_el ! generate Transducer elementsallsel,allnsel,s,loc,z,-d_eld,all,uz,0d,all,volt,0cmsel,s,base d,all,volt,10allsel,allfini/soluantyp,transalphad,65211 ! alpha damping computed from Squeeze-film theorykbc,1time,.000065deltime,2.0e-6outres,all,noneoutres,nsol,allsolvetime,.0002cmsel,s,based,all,volt,0allsel,allsolvefinin1=node(0,2,0)/post26nsol,2,n1,uzprvar,2plvar,2finish

Figure 1.14 Time-Transient Response from Voltage Pulse

1.3.4. Damping Extraction for Large Signal Cases

If a structure does not undergo significant deformation, the gap between the structure and the fixed wallmay be assumed to be constant (small signal case). If the structural deformation in the gap is significant,the change in the gap may effect the damping of the structure (large signal case). The gap is defined as areal constant in the thin-film fluid elements. Use SETFGAP to automatically define and/or update the gapreal constants for the thin-film FLUID136 elements. The command can be used to:

• Create real constant table entries for every selected FLUID136 element (large signal case).



• Update an existing real constant table according to structural displacements for every FLUID136 element(large signal case).

This option allows you to check the dependence of the damping parameters over the deflection range ofthe structure.

1.4. Slide Film Damping

Slide film damping occurs if two surfaces separated by a thin fluid film move tangentially with respect toeach other, because energy is dissipated due to viscous flow. Typical applications are damping between thefingers of comb drives and horizontally-moving seismic masses.

FLUID139 is used to model slide film damping. FLUID139 can model Couette and Stokes flow (Figure

1.15 (p. 210)). Couette flow assumes a constant velocity gradient across the fluid gap. Tangentially movingsurfaces at low frequencies produce a nearly constant velocity gradient in the fluid, so Couette flow is ap-plicable to low frequencies.

Stokes flow assumes that the velocity gradient is not constant across the fluid gap. Tangentially movingsurfaces at high frequencies do not produce a constant velocity gradient, so the Stokes flow is applicableto high frequencies. The transition from Couette to Stokes flow occurs near the cut-off frequency.

fd

c =η

πρ2 2

where ρ is the fluid density, η the dynamic viscosity and d the gap separation.

Couette flow does not occur at high frequencies, because inertial effects are important and viscous frictionis only able to accelerate a thin fluid layer near the moving surface. The penetration depth is given by

δηρ

=2

Ω



1.4. Slide Film Damping

Figure 1.15 Slide Film Damping at Low and High Frequencies

Low frequencies:

Moving Wall

Couette flow:

Stokes flow:

High frequencies:

Moving Wall

FD =η A

νpd

d

Plate velocity

Plate velocity

2 2

2 2

F A

d d

d dD

sinh sin

cosh cos

ΩΩ=

+

-

ηρ δ δ

δ δ

2

νρ

( ) ( )( ) ( )

FLUID139 models the effect of viscous flow in the thin film with a series of mass-damper elements, as shownin Figure 1.16 (p. 211). Couette flow is modeled using a two-node option. Stokes flow is modeled using a 32-node option. In the 32-node option, the end nodes (node 1 and 32) are connected to the structural portionof the model with structural degrees of freedom, and the series of mass-damper elements are containedwithin "auxiliary" nodes (nodes 2-31).

The gap separation distance (GAP) and the overlap area of the surfaces (AREA) are specified as real constantsfor FLUID139. If the overlap area changes during the analysis, the area change rate (DADU) must also bespecified as a real constant. A changing overlap area is typical in lateral comb drives.

A AdA

duu unew initial n i= + −( )

AREA is the initial overlap area, DADU is the change in the overlap area with respect to the surface displace-ment, and un and ui are the location of the interface nodes (1 and 32). Note: For a constant surface area,

DADU is the width of the overlap surface.

FLUID139 may be used for a prestress static analysis in conjunction with a prestress harmonic analysis, aswell as a full transient analysis. Prestress analysis is required if the plate area changes due to the structuraldisplacement. A typical command sequence for a prestress harmonic analysis would include the following:

/solu antyp,static pstress,on . .



solve fini /solu antyp,harmonic pstress,on . . solve finish

KEYOPT(3) specifies the continuous flow options. For a no-slip assumption at the wall, use the continuumtheory (KEYOPT(3) = 0). For slip flow where the Knudsen number is much less or much greater than 1.0, usethe first order slip flow condition (KEYOPT(3) = 1). For slip flow with a Knudsen number of approximately1.0, use the extended slip flow option (KEYOPT(3) = 2).

Figure 1.16 Viscous Slide Film Element FLUID139

KEYOPT(2)=0 and KEYOPT(3)=0

First wall

First wall

First wall



Node I

Node I

Node I

Node J

Node J

Node J

Second wall

Second wall

I

I

I

J

I+1 I+2 I+3 I+29 I+30 I+31 I+32

Lm

Second wall

I+32 = J

I+1 I+2 I+3 I+29 I+30 I+31 I+32

TK

TK

TK

1.4.1. Slide Film Damping Example

Comb drive resonators are a common application for slide film damping. Figure 1.17 (p. 212) illustrates atypical comb drive assembly consisting of fixed and moving comb drives, springs, and a central mass.




Figure 1.17 Comb Drive Resonator

Details on the comb drive geometry are given in the input file listed below. The electrostatic behavior ofthe moving comb drives are represented by two TRANS126 transducer elements with prescribed Stroke vs.Capacitance data obtained from finite element runs. The structural behavior of the crab legs is modeled bya spring element. The inertial effects of the central mass are modeled with a mass element. Damping occursbetween the comb teeth (lateral dimension), and between the comb teeth and the substrate (vertical dimen-sion). Four FLUID139 elements are used to model the lateral and vertical damping (two per comb drive).The cut-off frequency is well below the frequency range for the analysis; therefore, Couette flow is assumed.Since the comb drive effective surface area changes with displacement, the DADU real constant is used(equal to the width of the plate area).

A static prestress analysis is run using a DC bias voltage on the input and output fixed comb drives. A har-monic analysis sweep is then performed using a small AC voltage. The displacement (magnitude and phaseangle) of the central mass is shown in Figure 1.18 (p. 212). Figure 1.19 (p. 213) shows the current.

Figure 1.18 Displacement of Central Mass



Figure 1.19 Real and Imaginary Current

/prep7/title Comb drive resonator with FLUID139 Couette damping

! DRIVE COMB! |! | ! CRAB LEG SPRING --- CENTRAL MASS --- CRAB LEG SPRING! |! |! PICK-UP COMB

! Reference:! "Microelectromechanical Filters for Signal Processing",! Lin, L., Howe, R.T., J. Microelectromechanical Systems,! VOL 7, No. 3, Sept 1998

! beam parameters (uMKS units)E = 190e3 !Young modulusd = 2.33e-15 ! densityhb = 2 ! beam thicknesswb = 2 ! beam width Lb = 100 ! beam lengthk = 5.699 ! mechanical stiffness

! comb parametern= 9 ! number of fingernp=n*2 ! number of finger pairsx0= 10 ! initial finger overlapL0= 26 ! finger length (stator comb)L=20 ! finger length (moving comb)gi= L0-x0 ! initial gapw= 4 ! finger widthh= hb ! finger thicknessgp=3 ! finger gap (lateral)g= 3 ! comb gap (vertical)Mr = 1.96563e-11 ! mass

! Lateral gap areaareal=np*h*x0! Vertical gap areaareav=n*w*x0

! Stroke vs. Capacitance data

x1 = 14cx1 = 0.97857e-2x2 = 15cx2 = 0.96669e-2x3 = 16cx3 = 0.95445e-2x4 = 17




cx4 = 0.94185e-2x5 = 18cx5 = 0.93384e-2

! Voltage conditions

Vi = 40 ! input dc biasVo = 60 ! output dc biasVac = 10 ! input ac bias

! Damping parmeters

nu=18.3e-12 ! dynamic viscositypo=0.1 ! reference pressuredens=1.17e-18 ! densityfc=nu/(2*3.14159*dens*(g**2)) ! cutoff frequency daduv=w*n ! change in plate area - verticaldadul=h*np ! change in plate area - lateral

! Model

n,1,0n,2,0n,3,0n,4,0

et,1,126,,0,1 !Trans126, UX-Volt DOFr,1,,,gi,,rmore,x1,cx1,x2,cx2,x3,cx3rmore,x4,cx4,x5,cx5

e,1,2e,2,3

et,2,21,,,4 ! Mass elementr,2,Mrtype,2real,2e,2

et,3,14,,1 ! linear spring, UX DOFr,3,ktype,3real,3e,2,4

! Lateral damperset,4,139 ! Slide-film damper, Couette flow, Continuum theorymp,visc,4,nump,dens,4,densr,4,g,areal,-dadul,potype,4mat,4real,4e,1,2e,2,3

! Vertical dampersr,5,g,areav,-daduv,poreal,5e,1,2e,2,3

d,1,ux,0d,3,ux,0d,4,ux,0d,2,uy,0d,2,volt,0

! Prestress static analysis



/solud,1,volt,Vid,3,volt,Vopstres,onsolvefini

! Harmonic Frequency Sweep

fr0=60000fr1=120000/soluantyp,harmd,1,volt,Vac ! AC voltage component on capacitord,3,volt,0pstres,on ! prestressharfrq,fr0,fr1nsubs,60outres,all,allkbc,1solve

/post26nsol,2,2,u,x,ux2esol,3,2,,nmisc,24,iresol,4,2,,nmisc,25,ii

/axlab,x,Frequency (Hz) ! label of x axisplcplx,0/axlab,y, Displacement (um)plvar,2 ! plot displacement versus time (frequency)plcplx,1/axlab,y, Phase angleplvar,2plcplx,2/axlab,y, Current (pA)plvar,3,4fini





Index

Aacceleration, 129ACEL command, 43, 129acoustic analysis, 165

load step options, 175loads for, 172reviewing results from, 176

acoustics, 165absolute pressure, 165absorbing boundary condition, 167amplitude, 172applications of, 165axisymmetric cases, 167boundary admittance, 167circular or spherical boundary (RAD), 167compressible fluid, 165coupled acoustic analysis, 165coupling matrix, 177definition of, 165density, 167far-field problems, 177fluid load, 177fluid-structure interaction, 165, 177fluid-structure interface, 170forcing frequency, 172harmonic acoustic analysis, 166infinite acoustic elements, 167inviscid fluid, 165mean pressure, 165meshing the model, 168modal analysis, 165outgoing pressure wave, 167particle velocity, 165pressure changes, 165pressure gradient, 165sample fluid-structure acoustic analysis (batch), 177sample room acoustic analysis, 179solving acoustics problems, 165sound-absorption material, 179speed of sound (SONC), 167standing wave pattern, 179transient acoustic analysis, 165uncoupled acoustic analysis, 165unsymmetric matrices, 171wavelength, 169

adiabatic boundaries, 40advection limit, 60advection term, 161ambient radiation, 40

amplitude, 172analysis options

acoustics, 171analysis type

acoustics, 165Arbitrary Lagrangian-Eulerian analysis, 79

boundary conditions, 81mesh updating, 83remeshing, 84

arbitrary Lagrangian-Eulerian analysisexample problems, 87

artificial viscosity, 105axis of rotation, 135

Bbackward time integration method, 59Bingham viscosity model, 119, 123, 131boundary conditions, 104

FLOTRAN analysis, 11laminar and turbulent flow, 33thermal analysis, 40transient analysis, 62

bulk temperature, 42buoyancy, 43

CCarreau viscosity model, 119, 123, 131CGLOC command, 135CGOMEGA command, 135collocated Galerkin approach, 46, 161compressible flow analysis, 4, 23, 103compressible fluid, 165conduction limit, 60conductivity matrix algorithm, 44conjugate heat transfer, 4, 44convergence, 60, 140coordinate systems, 133Couette flow, 209coupled acoustic analysis, 165coupling algorithms, 145cross-talk, 203

DD command, 33, 81, 136, 153DA command, 33, 81database

backing up, 176density, 39, 119displacements, 174distributed resistance, 136divergence, 105



DL command, 33, 81drag, 38

Eeffective viscosity, 24elements

FLOTRAN, 7example problems

arbitrary Lagrangian-Eulerian analysis, 87compressible flow, 106incompressible flow, 38modal projection method, 204multiple species, 154slide film, 211squeeze film, 191thermal analysis, 47volume of fluid analysis, 70

Ffiles

Jobname.RST, 176FLDATA1 command, 25, 39, 59FLDATA10 command, 120FLDATA11 command, 120FLDATA12 command, 126, 131FLDATA13 command, 43, 126FLDATA14 command, 42, 103, 126FLDATA15 command, 129FLDATA17 command, 103, 129FLDATA18 command, 44, 139FLDATA19 command, 140FLDATA20 command, 140–141FLDATA21 command, 140FLDATA22 command, 140FLDATA23 command, 140FLDATA24 command, 25, 33, 36, 161FLDATA25 command, 43, 161FLDATA31 command, 36FLDATA33 command, 161FLDATA34 command, 36, 161FLDATA35 command, 68FLDATA36 command, 67FLDATA37 command, 44, 145FLDATA38 command, 59FLDATA4 command, 61, 69FLDATA4A command, 59–60FLDATA7 command, 117, 119, 130, 150FLDATA8 command, 120FLDATA9 command, 120FLOCHECK command, 62FLOTRAN analysis

applications, 3

artificial viscosity, 16boundary conditions, 11characterizing flow, 25compressible flow, 4, 103compressible flow analysis, 10convergence, 13, 17convergence and stability tools, 15coordinate systems, 7divergence, 20DOF capping, 16domain file, 14element characteristics, 7element limitations, 8evaluating, 20examining results, 12files, 12flow regime, 10fluid properties, 117free surface, 4global iterations, 17graphical solution tracking, 17incompressible flow, 4inertial relaxation, 15laminar flow, 4meshing, 11modified inertial relaxation, 15multiple species transport, 4nodal residuals file file, 13non-Newtonian fluid flow, 4overview, 10overwrite frequency option, 12print file, 13problem domain, 10quadrature order, 16relaxation factors, 15residuals, 13restart file, 13restarting, 14results file, 12setting parameters, 11solvers, 139solving, 11special features, 133stopping, 19thermal analysis, 4, 39transient analysis, 59turbulence model, 10, 17turbulent flow, 4types, 3verifying results, 20

flow regimethin film, 188


Index

fluid analysesacoustics, 165 (see acoustics)slide film, 209squeeze film, 185thin film, 185

fluid propertiesinitializing and varying, 126specifying, 117tables, 120user-defined file, 118, 127user-programmable subroutines, 118, 132

fluid property types, 117fluid-structure interaction, 165, 174, 177fluid-structure interface, 170forced convection, 4, 43forces, 174forcing frequency, 172free convection, 43free surface analysis, 4

Ggeneralized symmetry boundary conditions, 33, 81global iterations, 60, 140gravitational acceleration, 129

Hharmonic acoustic analysis, 166harmonic acoustic analysis guidelines, 166heat balance, 46–47heat fluxes, 40heat transfer (film) coefficients, 40hydraulic diameter, 24

IIC command, 150ICE command, 66ICVFRC command, 66impedance, 174incompressible flow analysis, 4, 23

boundary conditions, 33difficult problems, 36example problem, 38meshing requirements, 32

inertial relaxation, 106infinite acoustic elements, 167inlet parameters, 25inlet values, 33intersections, 33INTSRF command, 38

KKEYOPT command, 133, 151Knudsen number, 188

Llaminar flow, 4, 23, 25large signal cases, 208lift, 38load step options

acoustics, 175loads, 40, 171

Mmass imbalances, 33mass types, 59material model interface, 4meshing, 32, 39

FLOTRAN analysis, 11mixture types, 149modal projection method, 201modified inertial relaxation, 153moments, 174monotone Streamline Upwind approach, 46monotone streamline upwind approach, 161moving wall, 33MP command, 39, 117MSADV command, 161MSCAP command, 153MSDATA command, 150–151MSMETH command, 153MSNOMF command, 150MSPROP command, 152MSRELAX command, 153MSSOLU command, 153MSSPEC command, 149–150, 152multiple species transport, 4, 149

Nnatural convection, 4Newmark time integration method, 59non-fluid properties, 39, 117non-Newtonian fluid flow analysis, 4, 130non-Newtonian viscosity models, 119, 123

Pparticle velocity, 165PERI command, 33periodic boundaries, 33/PICE command, 66PLVFRC command, 69power law viscosity model, 119, 123, 130



Index

preconditioned bicgstab solver, 143preconditioned generalized minimum residual solver,141pressure gradient, 165pressure surface loads, 174pressure wave limit, 60property calculations, 103property types, 117, 120

Rradiosity solver method, 47ratio of specific heats, 103, 129reference pressure, 129reference properties, 129relaxation factors, 43, 153reviewing results

acoustics, 176Reynolds number, 24rotating reference frames, 135rotational speeds, 135

Ssample acoustic analysis

batch method, 177search directions, 140semi-direct solvers, 140SFE command, 67SFL command, 67SIMPLEF algorithm, 145SIMPLEN algorithm, 145slide film, 185, 209solution, 171Solvers, 139, 171sparse direct solver, 143, 171species mass fractions, 150specific heat, 39, 103, 118, 124specified flow, 33specified pressure, 33squeeze film, 185squeeze film analysis

harmonic analysis, 187static analysis, 187transient analysis, 188

squeeze stiffness effect, 185stationary wall, 33stepped or ramped loads, 175Stokes flow, 209streamline upwind/Petrov-Galerkin approach, 46, 161surface tension coefficient, 65, 117, 119, 125surface-to-surface radiation, 40, 47Sutherland's law, 123swirl, 136

symmetry boundary, 33

Ttemperature equation, 39temperature field algorithm, 44temperature load, 40temperature offset, 126thermal analysis, 4

example problems, 47loads and boundary conditions, 40property specifications, 39

thermal boundary conditions, 40thermal conductivity, 39, 119, 125thin film analysis, 185

Couette vs. Stokes flow, 209cross-talk, 203flow regime, 188large signal cases, 208modal projection method, 201slide film, 209squeeze film, 185

time steps, 60TOFFST command, 126, 129total temperature, 103transient analysis, 59

boundary conditions, 62settings, 60terminating, 61

tri-diagonal matrix algorithm, 140turbulence model, 24–25turbulence ratio, 25, 36turbulent flow, 4, 23turbulent kinetic energy, 25, 33

Uuncoupled acoustic analysis, 165units, 117unspecified boundary, 33

Vvariable density option, 43velocity capping, 36viscosity, 39

Bingham model, 119, 123, 131Carreau model, 119, 123, 131effective, 24power law model, 119, 123, 130

viscous heating, 43volume of fluid analysis, 65

boundary conditions, 67example problems, 70


Index

input settings, 67loads, 66postprocessing, 69

Wwall roughness, 33wall static contact angle, 117, 119, 126



Index


Documents

ANSYS FLUIDS