Assessment of Turbulence Modeling for Compressible Flow

Around Stationary and Oscillating Cylinders

by Alejandra Uranga

Supervisors: Drs Nedjib Djilali and Afzal Suleman Dept. of Mechanical Engineering - University of Victoria

August 21, 2006

A p p l i e d V e h i c l e

Technologies

Outline

  Introduction

  Simulation Methodology

  Stationary Cylinder

  Oscillating Cylinder

  Conclusions

Introduction

Periodic pattern of counter-rotating vortices caused by unsteady separation from a bluff body

Kármán Vortex Street

Introduction Methodology Stationary Oscillating Conclusions

Introduction

Periodic pattern of counter-rotating vortices caused by unsteady separation from a bluff body

Kármán Vortex Street

Introduction Methodology Stationary Oscillating Conclusions

NASA satellite image 1999

Introduction

  Interaction between 3 shear layers -  Boundary layer -  Free shear layer -  Wake

Flow Around a Circular Cylinder

Introduction Methodology Stationary Oscillating Conclusions

Introduction

  Interaction between 3 shear layers -  Boundary layer -  Free shear layer -  Wake

Flow Around a Circular Cylinder

Introduction Methodology Stationary Oscillating Conclusions

  Transition to turbulence in -  Wake ReD 200 → 400 -  Free Shear layer ReD 400 → 150x103 -  Boundary layer ReD 150x103 → 8x106

Introduction

  Simulation of turbulent flow around circular cylinders - Stationary ReD = 3900 - Oscillating ReD = 3600

  Compare accuracy of turbulence models using same numerical procedure with respect to experiments

and other simulations

Scope

Introduction Methodology Stationary Oscillating Conclusions

Methodology

Numerical Simulation of Turbulent Flows

Methodology

Example: Incompressible Momentum Equation

Applying an average or filter operator (overbar) to the momentum equation yields

The terms , , are solved for

The cross terms are unknown closure problem

Introduction Methodology Stationary Oscillating Conclusions

The Need for Turbulence Models

Methodology

Introduction Methodology Stationary Oscillating Conclusions

Simulation of Turbulence

DNS Direct Numerical

Simulation

Solve all Scales

very thin grid required €

ui

URANS Unsteady

Reynolds Averaged Navier-Stokes

(One-point closure)

mean fluctuating

Solve mean quantities

Model Reynolds stresses

€

u i

LES Large Eddy Simulation

large scale Subgrid-Scale

Solve large scale eddies

Model subgrid-scale stress €

u i

Methodology

  URANS - One equation Spalart-Allmaras - K-tau Speziale et al.

  Large Eddy Simulation (LES) - Smagorinsky-Lilly

  Very Large Eddy Simulation (VLES) - Adaptive k-tau Magagnato & Gabi (uses a URANS type subgrid-scale model)

Introduction Methodology Stationary Oscillating Conclusions

Turbulence Models Considered

Methodology

  SPARC Structured PArallel Research Code

  Finite Volume, Cell Centered, Block-Structured, Multigrid

  Simulations are 3D Unsteady Compressible Viscous

Introduction Methodology Stationary Oscillating Conclusions

Computational Code

Stationary Cylinder

Stationary Circular Cylinder in a Uniform Flow

Stationary Cylinder

  Cylinder diameter D = 1m   Flow velocity U0 = 68.63m/s   Mach number Mach 0.2   Reynolds number ReD = 3900

Problem Setup

Introduction Methodology Stationary Oscillating Conclusions

Stationary Cylinder

2D figures: x-y plane at span center

Computational Domain

Introduction Methodology Stationary Oscillating Conclusions

Stationary Cylinder URANS : Average Fields

Introduction Methodology Stationary Oscillating Conclusions

SA Sp

u/U0

ωzD/U0

Stationary Cylinder URANS : Average Streamlines

Introduction Methodology Stationary Oscillating Conclusions

SA Sp

Stationary Cylinder URANS : Average Profiles

Introduction Methodology Stationary Oscillating Conclusions

u/U0 at x/D = 1.54

cp around cylinder

cf around cylinder

Stationary Cylinder LES-VLES : Streamlines

Introduction Methodology Stationary Oscillating Conclusions

LES VLES

Stationary Cylinder LES-VLES : Average Fields

Introduction Methodology Stationary Oscillating Conclusions

LES VLES

u/U0

ωzD/U0

Stationary Cylinder LES-VLES : Average Profiles

Introduction Methodology Stationary Oscillating Conclusions

u/U0 at x/D=1.54

cp around cylinder

cf around cylinder

Stationary Cylinder 3-Dimensionality

Streamwise velocity iso-surfaces

Introduction Methodology Stationary Oscillating Conclusions

URANS Sp LES

Stationary Cylinder Comparison

Introduction Methodology Stationary Oscillating Conclusions

Oscillating Cylinder

Circular Cylinder in Cross-Flow Oscillations

Oscillating Cylinder

  Vertical sinusoidal motion

  2D URANS k-tau Speziale

  Reynolds number 3600

  Lock-in: vortex shedding frequency matches cylinder motion frequency

Motion and Cases

Introduction Methodology Stationary Oscillating Conclusions

Oscillating Cylinder URANS Sp Fields

Introduction Methodology Stationary Oscillating Conclusions

ωzD/U0 u/U0

Case IV fc / f0 = 0.800

Oscillating Cylinder Lock-in

Introduction Methodology Stationary Oscillating Conclusions

46%

40% 2%

1%

63%

32%

motion frequency fc/f0

sheddi

ng f

requ

ency

fS/f

0

Conclusions

Summary and Further Work

Conclusions

  comparison of results from different turbulence models with same numerical procedure

  Spalart-Allmaras model -  error in separation point flow remains attached too long small recirculation zone low back pressure large drag

-  Accurate Strouhal number

Introduction Methodology Stationary Oscillating Conclusions

Conclusions

  K-tau Speziale model -  Good mean global quantities Strouhal number, drag, back pressure, separation point velocity profiles along the wake

  LES and VLES -  reveal secondary eddies -  LES resolves dynamics in boundary layer

  Oscillating Cylinder

-  No other numerical results in same regime

-  Lock-in over large range of motion frequencies

-  Further investigation required

Introduction Methodology Stationary Oscillating Conclusions

Conclusions

  Better averages on LES and VLES

  LES with Dynamic and Dynamic Mixed subgrid-scale models

  LES of oscillating cylinder

Further Work

Introduction Methodology Stationary Oscillating Conclusions

Questions