Dm Ic Spring

Tutorial: 2D Adiabatic Compression (Remeshing and Spring

Smoothing)

Introduction

This tutorial illustrates the setup and solution of a basic deforming mesh in FLUENT 6.2using the remeshing and spring-based smoothing approaches.

In this tutorial you will learn how to:

Set up a problem for a dynamic mesh Specify dynamic mesh modeling parameters Specify the motion of dynamic zones Preview the dynamic mesh before starting the calculation Perform basic dynamic mesh calculations with residual plotting Examine the temperature and density fields using graphics

The dynamic mesh model in FLUENT can be used to model flows where the shape of thedomain changes with time due to motion on the domain boundaries. The motion can beeither a prescribed motion (e.g., you can specify the linear and angular velocities about thecenter of gravity of a solid body with time), or an unprescribed motion where the subsequentmotion is determined by a user-defined function (UDF). The update of the volume meshis handled automatically by FLUENT at each time step based on the new positions of theboundaries. To use the dynamic mesh model, you need to provide a starting volume meshand the description of the motion of any moving zone in the model.

In this tutorial, you will use the spring-based smoothing and remeshing mesh motion meth-ods to update the volume mesh in the deforming region. For zones with a triangular ortetrahedral mesh, spring-based smoothing can be used to adjust the interior node locationsbased on known displacements at the boundary nodes. The spring-based smoothing methodupdates the volume mesh without changing the mesh connectivity.

When the boundary displacement is large compared to the local cell sizes, the cell qualitymay deteriorate or the cells may become degenerate. This leads to convergence problemswhen the solution is updated to the next time step. To circumvent this problem, FLU-ENT agglomerates poor-quality cells (cells that are too large, too small, or are excessivelystretched) and locally remeshes the agglomeration.

c Fluent Inc. June 15, 2006 1

2D Adiabatic Compression (Remeshing and Spring Smoothing)

Prerequisites

This tutorial assumes that you are familiar with the FLUENT interface and that you havea good understanding of the basic setup and solution procedures. In this tutorial, you willuse the dynamic mesh model, so you should have some experience with it.

If you have not used this model before, please refer to Section 11.7 of the FLUENT 6.3 UsersGuide.

Problem Description

The problem to be considered is shown schematically in Figure 1. A simplified 2D geom-etry consisting of a box is used. The bottom wall of the box represents the piston whichmoves upward from the bottom dead center position (BDC), slowly compressing the fluidadiabatically. After reaching the top dead center (TDC), the piston moves back downwardto the initial position, to complete a cycle.

Figure 1: Schematic of the Problem

Preparation

1. Copy the file, box2d remesh.msh to your working directory.

2. Start FLUENT 2D.

2 c Fluent Inc. June 15, 2006


Setup and Solution

Step 1: Grid

1. Read the mesh file (box2d remesh.msh.gz).

File Read Case...As the mesh file is read in, messages appear in the console window reporting theprogress of the reading.

2. Check the grid.

Grid CheckFLUENT performs various checks on the mesh and reports the progress in the consolewindow. Pay attention to the reported minimum volume and make sure this is apositive number.

3. Scale the grid using cm as the unit of length.

Grid Scale...

(a) Select cm in the Grid Was Created In drop-down list and click Scale.

(b) Click Change Length Units to set the length unit to centimeter.

(c) Close the panel.

4. Display the grid (Figure 2).

Display Grid...



(a) Under Surfaces, select all the surface zones.

(b) Click Display and close the panel.

GridFLUENT 6.3 (2d, pbns, lam)

Figure 2: Grid Display

Use the right mouse button to check the zone number corresponding to eachboundary. When you click the right mouse button on one of the boundaries in thegraphics window, its zone number, name, and type are printed in the FLUENTconsole window. This feature is especially useful when you have several zones ofthe same type and you want to distinguish between them quickly.



Step 2: Models

1. Enable a time-dependent calculation.

Define Models Solver...

(a) Under Time, select Unsteady.

(b) Retain the default Unsteady Formulation of 1st-Order Implicit.

Dynamic mesh simulations currently work only with first-order time advance-ment.

Step 3: Materials

The only material property you need to modify is density. The default values for all otherproperties are acceptable.

1. Specify that the flow is compressible.

Define Materials...



(a) Select ideal-gas in the drop-down list for Density.

(b) Click Change/Create and close the panel.

FLUENT automatically enables the energy equation when the ideal-gas law isselected, so you need not visit the Energy panel.

Step 4: Boundary Conditions

In this tutorial, you need not visit the Boundary Conditions panel to set any conditions.You will use the default adiabatic thermal conditions for all walls. No inlets or outlets arepresent. Dynamic mesh motion and other related parameters are specified using the itemsin the Define/Dynamic Mesh submenu, not through the Boundary Conditions panel. You willset these conditions in the next step.

Step 5: Mesh Motion Setup

1. Enable dynamic mesh motion and specify the associated parameters.

Define Dynamic Mesh Parameters...(a) Under Models, enable Dynamic Mesh.

The panel expands to show additional inputs.



(b) Under Models, enable In-Cylinder.

Enabling the In-Cylinder option allows input for IC-specific needs, including valveand piston motion.

(c) Under Mesh Methods, enable Smoothing and Remeshing.

Make sure the Layering option is disabled.

(d) Retain the default settings for the smoothing parameters.

(e) Click the Remeshing tab.

The Remeshing parameters are displayed.

i. Under Options, retain the default settings for Size Function and Must ImproveSkewness.

By default, the Size Function option is disabled and the Must Improve Skew-ness option is enabled.



ii. Specify the Minimum Length Scale and the Maximum Length Scale.

If a cell exceeds these limits, the cell is marked for remeshing. Hence, youneed to specify problem-specific values for these remeshing parameters.

A. Click Mesh Scale Info....

The Mesh Scale Info panel opens. The values displayed for minimum andmaximum length scale, and maximum cell skewness are obtained fromthe initial mesh.

B. Set the values for Minimum Length Scale and Maximum Length Scale to0.4 and 1.56 respectively as obtained from the Mesh Scale Info panel.

For a uniform mesh as in this problem, the values obtained from theMesh Scale Info panel are sufficient. For a non-uniform mesh, you canuse these values as an initial approximation and later modify the valuesto improve the mesh quality.

iii. Set the Maximum Cell Skewness to 0.5.

A value of 0.6 to 0.7 is recommended for Maximum Cell Skewness for 2Dproblems. Smaller values of maximum skew result in improved grid qualityat increased computational cost.

(f) Set the In-Cylinder parameters.

i. Click the In-Cylinder tab.

The In-Cylinder parameters are displayed.

ii. Set the Crank Shaft Speed to 1000 rpm.

iii. Set the Starting Crank Angle to 180 degrees.

The piston is currently at the bottom dead center (BDC) position. The BDCposition is defined as 180 degrees crank angle, while the top dead center(TDC) position is defined as 0 degrees crank angle.



iv. Retain the default Crank Period of 720 degrees.

A value of 720 degrees is used for four-stroke engines, while a value of 360degrees is used for two-stroke engines. This governs the periodicity associatedwith valve events and valve lift profiles.

v. Set the Crank Angle Step Size to 0.5 degrees.

This value is used along with the crankshaft speed to determine the timestep.

vi. Set the Piston Stroke to 8 cm.

vii. Set the Connecting Rod Length to 14 cm.

viii. Set both the Piston Stroke Cutoff and Minimum Valve Lift to 0 cm.

These two parameters are not utilized in the current simulation.

ix. Click OK.

(g) Plot the piston motion profile using the text command interface as shown.

You may need to press the key to get the > prompt.

> define/models/dynamic-mesh-controls

/define/models/dynamic-mesh-controls> icp

/define/models/dynamic-mesh-controls/in-cylinder-parameter> ppl#fLift Profile:(1) [()] **piston-full**

Lift Profile:(2) [()] Start: [180] 0End: [720] Increment: [10] 5Plot lift? [yes]

/define/models/dynamic-mesh-controls/in-cylinder-parameter>

The **piston-full** profile (Figure 3) describes piston motion in terms of thePiston Stroke and Connecting Rod Length parameters defined previously.

2. Specify the motion of the piston and the deforming wall.

Define Dynamic Mesh Zones...(a) Specify the motion of the piston.



Valve Lifts (Time=0.0000e+00)FLUENT 6.2 (2d, segregated, dynamesh, lam, unsteady)

Crank Angle (deg)8007006005004003002001000

8.00e+00

7.00e+00

6.00e+00

5.00e+00

4.00e+00

3.00e+00

2.00e+00

1.00e+00

0.00e+00

Figure 3: The **piston-full** Profile

i. In the Zone Names drop-down list, select moving wall.

ii. Under Type, retain the default selection of Rigid Body.

iii. Under the Motion Attributes tab, set the following:

A. In the Motion UDF/Profile drop-down list, select **piston-full**.

B. Set the Valve/Piston Axis to (0, 1).

iv. Click the Meshing Options tab and set the following:

A. Set the Cell Height to 1 cm.

B. Click Create.



(b) Specify the motion of the deforming wall (side walls).

The declaration of the deforming boundary zones is necessary only for boundaryzones adjacent to the cell zones that are remeshed.

i. In the Zone Names drop-down list, select side walls.

ii. Under Type, select Deforming.

iii. Click the Geometry Definition tab and set the following:

A. Select cylinder in the Definition drop-down list.

B. Enter a Cylinder Radius of 4 cm.

C. Set the Cylinder Origin to (4, 0).

D. Set the Cylinder Axis to (0, 1).

iv. Click the Meshing Options tab and set the following:



To determine the Minimum Length Scale and the Maximum Length Scale, youneed to know the approximate average length scale. The average length scalecan be calculated using the length scale values in the Zone Scale Info panel.Click Zone Scale Info... to open the Zone Scale Info panel. For this case, theaverage length scale is 0.65.

A. Specify the Minimum Length Scale as 0.26.

The Minimum Length Scale is recommended to be (0.40.65) where 0.65is the average length scale.

B. Specify the Maximum Length Scale as 0.91.

The Maximum Length Scale is recommended to be (1.40.65) where 0.65is the average length scale.

C. Click Create.

v. Close the Dynamic Mesh Zones panel.

3. Preview the zone motion.

The zone motion preview utility is useful for quickly checking the rigid body motion set-tings. The mesh coordinates are not actually modified during this procedure. Instead,dynamic zones with rigid body motion settings are simply translated in the displaywindow to emulate the actual grid motion. User errors such as an improperly scaledmesh or valve lift profile, incorrect valve/piston axis definition, etc., can be quicklyidentified using this procedure. Only the motion of zones with rigid body motion isrepresented, remeshing on deforming zones is not depicted.



(a) Display the grid outline.

Display Grid...i. Deselect all surfaces.

ii. Click the Outline button to select the outline surfaces.

iii. Click Display to display the grid outline.

iv. Close the Grid Display panel.

(b) Initiate the zone motion.

Display Zone Motion...

i. Retain the settings for Motion History Integration and click Integrate.

This allows FLUENT to create a table of surface positions in time.

The Preview Controls are highlighted.

ii. Retain the default settings for Preview Controls and click Preview.

If the case is set up properly, you should see the piston move through twocomplete cycles.

iii. Close the Zone Motion panel.

Step 6: Mesh Preview

1. Save the case file (box2d remesh.cas.gz).

Since the mesh changes during the preview, ensure that you save the case before meshpreview.



2. Display the grid.

Display Grid...(a) Select all the surfaces.

(b) Click Display.

(c) Close the Grid Display panel.

3. Set up the mesh preview.

Solve Mesh Motion...

The Time Step Size displayed in the read-only text field (8.3333e-05) corresponds to12 degree crank angle and is based on the crankshaft speed and crank angle incrementparameters defined earlier.

(a) Specify the Number of Time Steps as 720.

This corresponds to one full revolution of the crankshaft.

(b) Click Preview to preview the mesh motion.

As the mesh is updated by FLUENT, messages appear in the console windowreporting the progress of the update.

Step 7: Solution

1. Read the case file back into FLUENT (box2d remesh.cas.gz).

File Read Case...2. Enable the plotting of volume-averaged temperature in the domain during the calcu-

lation by defining a volume monitor.

Solve Monitors Volume...The Volume Monitors panel is displayed.

(a) Increase the number of Volume Monitors to 1.

(b) Enable Plot, Print, and Write for the first monitor (vol-mon-1).

When the Write option is enabled, the volume-averaged temperature history iswritten to a file. If you do not select the Write option, the history informationwill be lost when you exit FLUENT.



(c) In the When drop-down list, select Time Step.

(d) Click Define... to define the monitor.

The Define Volume Monitor panel opens automatically.

i. Select Volume-Average in the Report Type drop-down list.

ii. Select Flow Time in the X Axis drop-down list.

iii. Select Temperature... and Static Temperature in the Field Variable drop-downlists.

iv. Under Cell Zones, select fluid.

v. In the File Name field, enter vol-monitor-1.out.

vi. Click OK in the Define Volume Monitor panel, and then in the Volume Mon-itors panel.

3. Enable the plotting of residuals during the calculation.

Solve Monitors Residual...



(a) Under Options, enable Plot.

(b) Under Plotting, set Iterations to 100.

To avoid a cluttered residual plot in transient simulations, it is useful to displayonly the most recent iterations.

(c) Set Absolute Criteria for continuity to 0.1.

(d) Click OK to close the Residual Monitors panel.

4. Initialize the solution.

Solve Initialize Initialize...

The solution is initialized at this point in the problem setup so that the contours forsetting up the view for the animation can be displayed.

(a) Retain the default values for all variables, including an initial Temperature valueof 300 K.

(b) Click Apply.

The Apply button does not initialize the flow field data. It only allows you tosave the initialization parameters for later use. You need to use the Init buttonto initialize the solution.

(c) Click Init to initialize the solution.

(d) Click Close.

5. Set up an animation for temperature.

(a) Display filled contours of temperature (Figure 4).

Display Contours ...



i. Select Temperature... and Static Temperature in the Contours of drop-downlists.

ii. Under Options, select only Filled and Node Values.

iii. Enter 300 for Min and 500 for Max.

iv. Click Display.

v. Close the Contours panel.

Contours of Static Temperature (k) (Time=0.0000e+00)FLUENT 6.2 (2d, segregated, dynamesh, lam, unsteady)

5.00e+02

3.00e+023.10e+023.20e+023.30e+023.40e+023.50e+023.60e+023.70e+023.80e+023.90e+024.00e+024.10e+024.20e+024.30e+024.40e+024.50e+024.60e+024.70e+024.80e+024.90e+02

Figure 4: Contours of Static Temperature



(b) Save the current view.

Display Views...

i. Click Save to save the current view as view-0.

ii. Close the Views panel.

(c) Specify the commands for animation.

Solve Execute Commands...

i. Set Defined Commands to 1.

ii. Select the On checkbox for command-1.

iii. Under Every, specify 10.

iv. Select Time Step in the When drop-down list.

v. Under Command, enter the following commands sequentially (in a singleline):

/di/sw 2/di/view/restore-view view-0/di/cont temp 300 570/di/hc temperature%t.tiff



It is possible to specify multiple text commands in a single entry. Make sureto maintain at least a single space between commands. The above commandwill first activate window 2, restore the saved view view-0, display contoursof static temperature and then make a hardcopy of the resulting image. The%t appended to the file name instructs FLUENT to append the timestepindex to the filename.

vi. Click OK.

(d) Set hardcopy settings.

File Hardcopy...The Graphics Hardcopy panel is displayed.

i. Under Format, select TIFF.

ii. Under Coloring, select Color.

iii. Click Apply and close the panel.

6. Request saving of case and data files every 90 time steps.

File Write Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 90.

Since the mesh changes during the simulation, you must save both the case anddata files.

(b) In the Filename field, enter box2d remesh and click OK.

When FLUENT saves a file, it appends the time step value to the file name prefix(box2d remesh). The standard extensions (.cas and .dat) are also appended.

7. Set the solution parameters.

Solve Controls Solution...



(a) Set the Under-Relaxation Factors for Pressure and Momentum to 0.6 and 0.9respectively.

(b) Under Discretization, select PRESTO! for Pressure.

(c) Under Pressure-Velocity Coupling, select PISO.

i. Set the Skewness Correction to 0.

ii. Retain the default settings for the other parameters.

(d) Click OK.

8. Start the calculation.

Solve Iterate...



(a) Set the Number of Time Steps to 720.

(b) Set the Max Iterations per Time Step to 10.

(c) Click Iterate.

The plot for volume-averaged temperature is shown in Figure 5. The values may bedifferent for different computers. Hence, the plot that appears on your screen may notbe exactly the same as the one shown here.

Crank Angle=540.00(deg)Convergence history of Static Temperature on fluid (in SI units) (Time=6.0000e-02)

FLUENT 6.3 (2d, pbns, dynamesh, lam, unsteady)

Flow Time

(k)Temperature

StaticAverageVolume-

0.0700.0600.0500.0400.0300.0200.0100.000

600

550

500

450

400

350

300

Figure 5: Convergence History of Static Temperature

Step 8: Postprocessing

1. Inspect the solution at the bottom dead center (final time step).

(a) Display filled contours of static temperature (Figure 6).

Display Contours...i. Select Temperature... and Static Temperature in the Contours of drop-down

lists.


iii. Enter 300 for Min and 500 for Max.

iv. Click Display.



Crank Angle=540.00(deg) FLUENT 6.3 (2d, pbns, dynamesh, lam, unsteady)Contours of Static Temperature (k) (Time=6.0000e-02)

5.70e+02


Figure 6: Contours of Static Temperature at Bottom Dead Center (final time step)

(b) Display filled contours of density (Figure 7).

i. Select Density... and Density in the Contours of drop-down lists,


iii. Enter 1.18 for Min and 5.88 for Max.

iv. Click Display.

The temperature and density at the end of one full cycle closely replicate thoseat the beginning of the simulation.

2. Inspect the solution at the top dead center.

(a) Read in the case and data files corresponding to the TDC position (box2d remesh0360.casand box2d remesh0360.dat).

File Read Case & Data...(b) Display filled contours of static temperature (Figure 8).

i. Under Options, select only Filled and Node Values.

ii. Enter 300 for Min and 500 for Max.

iii. Click Display.

The temperature very closely obeys the analytical result for a reversible, adiabaticcompression:

T2T1

=(21

)1For = 1.4 and a compression ratio of 5:1, the theoretical temperature at thetop dead center is 571 K.



Crank Angle=540.00(deg) FLUENT 6.3 (2d, pbns, dynamesh, lam, unsteady)Contours of Density (kg/m3) (Time=6.0000e-02)

5.88e+00


Figure 7: Contours of Density at Bottom Dead Center (final time step)

Crank Angle=360.00(deg) FLUENT 6.3 (2d, pbns, dynamesh, lam, unsteady)Contours of Static Temperature (k) (Time=3.0000e-02)

5.00e+02


Figure 8: Contours of Static Temperature at Top Dead Center



(c) Display filled contours of density (Figure 9).

i. Under Options, select only Filled and Node Values.

ii. Enter 1.18 for Min and 5.88 for Max.

iii. Click Display.

Crank Angle=360.00(deg) FLUENT 6.3 (2d, pbns, dynamesh, lam, unsteady)Contours of Density (kg/m3) (Time=3.0000e-02)

5.88e+00


Figure 9: Contours of Density at Top Dead Center

Summary

In this tutorial, you learned how to use the dynamic mesh feature in FLUENT. If youhave to set up and solve real-life simulations that involve valve movement as well as pistonmovement, you will need to perform some additional steps that could not be illustratedwith the geometry in this problem.


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Dm Ic Spring