chapter 11: using a single rotating reference · pdf filethis tutorial is divided ... the...

Chapter 11: Using a Single Rotating Reference Frame

This tutorial is divided into the following sections:

11.1. Introduction

11.2. Prerequisites

11.3. Problem Description

11.4. Setup and Solution

11.5. Summary

11.6. Further Improvements

11.7. References

11.1. Introduction

This tutorial considers the flow within a 2D, axisymmetric, co-rotating disk cavity system. Understanding the

behavior of such flows is important in the design of secondary air passages for turbine disk cooling.

This tutorial demonstrates how to do the following:

• Set up a 2D axisymmetric model with swirl, using a rotating reference frame.

• Use the standard �

- �

and RNG �

- �

turbulence models with the enhanced near-wall treatment.

• Calculate a solution using the pressure-based solver.

• Display velocity vectors and contours of pressure.

• Set up and display XY plots of radial velocity and wall +�

distribution.

• Restart the solver from an existing solution.

11.2. Prerequisites

This tutorial is written with the assumption that you have completed Introduction to Using ANSYS FLUENT:

Fluid Flow and Heat Transfer in a Mixing Elbow (p. 111), and that you are familiar with the ANSYS FLUENT nav-

igation pane and menu structure. Some steps in the setup and solution procedure will not be shown explicitly.

11.3. Problem Description

The problem to be considered is shown schematically in Figure 11.1 (p. 436). This case is similar to a disk

cavity configuration that was extensively studied by Pincombe [1].

Air enters the cavity between two co-rotating disks. The disks are 88.6 cm in diameter and the air enters at

1.146 m/s through a circular bore 8.86 cm in diameter. The disks, which are 6.2 cm apart, are spinning at

71.08 rpm, and the air enters with no swirl. As the flow is diverted radially, the rotation of the disk has a

significant effect on the viscous flow developing along the surface of the disk.

435Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information

of ANSYS, Inc. and its subsidiaries and affiliates.

Figure 11.1 Problem Specification

As noted by Pincombe [1], there are two nondimensional parameters that characterize this type of disk

cavity flow: the volume flow rate coefficient, ��, and the rotational Reynolds number, φ��

. These parameters

are defined as follows:

(11–1)=��

(11–2)=φ� ��where

� is the volumetric flow rate,� is the rotational speed, � is the kinematic viscosity, and

�� is the

outer radius of the disks. Here, you will consider a case for which �� = 1092 and φ

�� = .

11.4. Setup and Solution

The following sections describe the setup and solution steps for this tutorial:

11.4.1. Preparation

11.4.2. Step 1: Mesh

11.4.3. Step 2: General Settings

11.4.4. Step 3: Models

11.4.5. Step 4: Materials

11.4.6. Step 5: Cell Zone Conditions

11.4.7. Step 6: Boundary Conditions

11.4.8. Step 7: Solution Using the Standard k- ε Model

11.4.9. Step 8: Postprocessing for the Standard k- ε Solution

Release 13.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.436


11.4.10. Step 9: Solution Using the RNG k- ε Model

11.4.11. Step 10: Postprocessing for the RNG k- ε Solution

11.4.1. Preparation

1. Download single_rotating.zip from the ANSYS Customer Portal or the User Services Center to

your working folder (as described in Preparation (p. 4) of Introduction to Using ANSYS FLUENT in ANSYS

Workbench: Fluid Flow and Heat Transfer in a Mixing Elbow (p. 1)).

2. Unzip single_rotating.zip .

The file disk.msh can be found in the single_rotating folder created after unzipping the file.

3. Use FLUENT Launcher to start the 2D version of ANSYS FLUENT.

For more information about FLUENT Launcher, see Starting ANSYS FLUENT Using FLUENT Launcher in the

User's Guide.

Note

The Display Options are enabled by default. Therefore, once you read in the mesh, it will be

displayed in the embedded graphics window.

11.4.2. Step 1: Mesh

1. Read the mesh file (disk.msh ).

File → Read → Mesh...

As ANSYS FLUENT reads the mesh file, it will report its progress in the console.


General

1. Check the mesh.

General → Check

ANSYS FLUENT will perform various checks on the mesh and report the progress in the console. Make sure

that the reported minimum volume is a positive number.

2. Examine the mesh (Figure 11.2 (p. 438)).




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Figure 11.2 Mesh Display for the Disk Cavity

Extra

You can use the right mouse button to check which zone number corresponds to each

boundary. If you click the right mouse button on one of the boundaries in the graphics

window, information will be displayed in the ANSYS FLUENT console about the associated

zone, including the name of the zone. This feature is especially useful when you have sev-

eral zones of the same type and you want to distinguish between them quickly.

3. Define new units for angular velocity and length.

General → Units...

In the problem description, angular velocity and length are specified in rpm and cm, respectively, which is

more convenient in this case. These are not the default units for these quantities.



a. Select angular-velocity from the Quantities list, and rpm in the Units list.

b. Select length from the Quantities list, and cm in the Units list.

c. Close the Set Units dialog box.

4. Specify the solver formulation to be used for the model calculation and enable the modeling of

axisymmetric swirl.

General

a. Retain the default selection of Pressure-Based in the Type list.

b. Retain the default selection of Absolute in the Velocity Formulation list.

For a rotating reference frame, the absolute velocity formulation has some numerical advantages.

c. Select Axisymmetric Swirl in the 2D Space list.




11.4.4. Step 3: Models

Models

1. Enable the standard �

- �

turbulence model with the enhanced near-wall treatment.

Models → Viscous → Edit...

a. Select k-epsilon in the Model list.

The Viscous Model dialog box will expand.

b. Retain the default selection of Standard in the k-epsilon Model list.

c. Select Enhanced Wall Treatment in the Near-Wall Treatment list.

d. Click OK to close the Viscous Model dialog box.

The ability to calculate a swirl velocity permits the use of a 2D mesh, so the calculation is simpler and

more economical to run. This is especially important for problems where the enhanced wall treatment

is used. The near-wall flow field is resolved through the viscous sublayer and buffer zones (that is, the

first mesh point away from the wall is placed at a +

of the order of 1).



For details, see Enhanced Wall Treatment ε-Equation (EWT-ε) of the Theory Guide.

11.4.5. Step 4: Materials

Materials

For the present analysis, you will model air as an incompressible fluid with a density of 1.225 kg/

� and a dynamic

viscosity of 1.7894 × −� kg/m-s. Since these are the default values, no change is required in the Create/Edit

Materials dialog box.

1. Retain the default properties for air.

Materials → air → Create/Edit...

Extra

You can modify the fluid properties for air at any time or copy another material from the

database.

2. Click Close to close the Create/Edit Materials dialog box.

For details, see "Physical Properties" in the User's Guide.


Cell Zone Conditions




Set up the present problem using a rotating reference frame for the fluid. Then define the disk walls to rotate with

the moving frame.

1. Define the rotating reference frame for the fluid zone (fluid-7).

Cell Zone Conditions → fluid-7 → Edit...



a. Enable Frame Motion.

b. Click Reference Frame tab.

c. Enter 71.08 rpm for Speed in the Rotational Velocity group box.

d. Click OK to close the Fluid dialog box.


Boundary Conditions




1. Set the following conditions at the flow inlet (velocity-inlet-2).

Boundary Conditions → velocity-inlet-2 → Edit...



a. Select Components from the Velocity Specification Method drop-down list.

b. Enter 1.146 m/s for Axial-Velocity.

c. Select Intensity and Viscosity Ratio from the Specification Method drop-down list in the Tur-bulence group box.

d. Enter 5 % for Turbulent Intensity.

e. Enter 5 cm for Turbulent Viscosity Ratio.

f. Click OK to close the Velocity Inlet dialog box.

2. Set the following conditions at the flow outlet (pressure-outlet-3).

Boundary Conditions → pressure-outlet-3 → Edit...




a. Select From Neighboring Cell from the Backflow Direction Specification Method drop-down

list.

b. Select Intensity and Viscosity Ratio from the Specification Method drop-down list in the Tur-bulence group box.

c. Enter 5% for Backflow Turbulent Intensity.

d. Retain the default value of 10 for Backflow Turbulent Viscosity Ratio.

e. Click OK to close the Pressure Outlet dialog box.

Note

ANSYS FLUENT will use the backflow conditions only if the fluid is flowing into the

computational domain through the outlet. Since backflow might occur at some point

during the solution procedure, you should set reasonable backflow conditions to prevent

convergence from being adversely affected.

3. Accept the default settings for the disk walls (wall-6).

Boundary Conditions → wall-6 → Edit...



a. Click OK to close the Wall dialog box.

Note

For a rotating reference frame, ANSYS FLUENT assumes by default that all walls rotate at

the speed of the moving reference frame, and hence are moving with respect to the station-

ary (absolute) reference frame. To specify a non-rotating wall, you must specify a rotational

speed of 0 in the absolute frame.


1. Set the solution parameters.

Solution Methods




a. Retain the default selection of Least Squares Cell Based from the Gradient list in the SpatialDiscretization group box.

b. Select PRESTO! from the Pressure drop-down list in the Spatial Discretization group box.

The PRESTO! scheme is well suited for steep pressure gradients involved in rotating flows. It provides

improved pressure interpolation in situations where large body forces or strong pressure variations

are present as in swirling flows.

c. Select Second Order Upwind from the Momentum, Swirl Velocity, Turbulent Kinetic Energy,

and Turbulent Dissipation Rate drop-down lists.

Use the scroll bar to access the discretization schemes that are not initially visible in the task page.

2. Set the solution controls.

Solution Controls



a. Retain the default values in the Under-Relaxation Factors group box.

Note

For this problem, the default under-relaxation factors are satisfactory. However, if the

solution diverges or the residuals display large oscillations, you may need to reduce

the under-relaxation factors from their default values.

For tips on how to adjust the under-relaxation parameters for different situations, see Setting

Under-Relaxation Factors in the User’s Guide.

3. Enable the plotting of residuals during the calculation.

Monitors → Residuals → Edit...




a. Ensure that Plot is enabled in the Options group box.

b. Click OK to close the Residual Monitors dialog box.

Note

For this calculation, the convergence tolerance on the continuity equation is kept at 0.001.

Depending on the behavior of the solution, you can reduce this value if necessary.

4. Enable the plotting of mass flow rate at the flow exit.

Monitors (Surface Monitors) → Create...



a. Enable the Plot and Write options for surf-mon-1 .

Note

When the Write option is selected in the Surface Monitor dialog box, the mass flow

rate history will be written to a file. If you do not enable the Write option, the history

information will be lost when you exit ANSYS FLUENT.

b. Select Mass Flow Rate from the Report Type drop-down list.

c. Select pressure-outlet-3 from the Surfaces selection list.

d. Click OK in the Surface Monitor dialog box to enable the monitor.

5. Initialize the flow field using the boundary conditions set at velocity-inlet-2.

Solution Initialization




a. Select Hybrid Initialization from the Initialization Methods group box.

b. Click Initialize.

Note

For flows in complex topologies, hybrid initialization will provide better initial velocity

and pressure fields than standard initialization. This in general will help in improving

the convergence behavior of the solver.

6. Save the case file (disk-ke.cas.gz ).

File → Write → Case...

7. Start the calculation by requesting 500 iterations.

Run Calculation

a. Enter 500 for the Number of Iterations.

b. Click Calculate.

Throughout the calculation, ANSYS FLUENT will report reversed flow at the exit. This is reasonable for

the current case. The solution should be sufficiently converged after approximately 270 iterations. The

mass flow rate history is shown in Figure 11.3 (p. 453).



Figure 11.3 Mass Flow Rate History (k- ε Turbulence Model)

8. Check the mass flux balance.

Reports → Fluxes → Set Up...

Warning

Although the mass flow rate history indicates that the solution is converged, you should

also check the net mass fluxes through the domain to ensure that mass is being conserved.




a. Select velocity-inlet-2 and pressure-outlet-3 from the Boundaries selection list.

b. Retain the default Mass Flow Rate option.

c. Click Compute and close the Flux Reports dialog box.

Warning

The net mass imbalance should be a small fraction (say, 0.5%) of the total flux through the

system. If a significant imbalance occurs, you should decrease the residual tolerances by

at least an order of magnitude and continue iterating.

9. Save the data file (disk-ke.dat.gz ).

File → Write → Data...

Note

If you choose a file name that already exists in the current folder, ANSYS FLUENT will prompt you

for confirmation to overwrite the file.


1. Display the velocity vectors.

Graphics and Animations → Vectors → Set Up...



a. Enter 50 for Scale

b. Set Skip to 1.

c. Click the Vector Options... button to open the Vector Options dialog box.

i. Disable Z Component.

This allows you to examine only the non-swirling components.

ii. Click Apply and close the Vector Options dialog box.

d. Click Display in the Vectors dialog box to plot the velocity vectors.

A magnified view of the velocity field displaying a counter-clockwise circulation of the flow is shown

in Figure 11.4 (p. 456).




Figure 11.4 Magnified View of Velocity Vectors within the Disk Cavity

e. Close the Vectors dialog box.

2. Display filled contours of static pressure.

Graphics and Animations → Contours → Set Up...



a. Enable Filled in the Options group box.

b. Retain the selection of Pressure... and Static Pressure from the Contours of drop-down lists.

c. Click Display and close the Contours dialog box.

The pressure contours are displayed in Figure 11.5 (p. 458). Notice the high pressure that occurs on the right

disk near the hub due to the stagnation of the flow entering from the bore.




Figure 11.5 Contours of Static Pressure for the Entire Disk Cavity

3. Create a constant �

-coordinate line for postprocessing.

Surface → Iso-Surface...

a. Select Mesh... and Y-Coordinate from the Surface of Constant drop-down lists.

b. Click Compute to update the minimum and maximum values.

c. Enter 37 in the Iso-Values field.

This is the radial position along which you will plot the radial velocity profile.

d. Enter y=37cm for the New Surface Name.



e. Click Create to create the isosurface.

Note

The name you use for an isosurface can be any continuous string of characters (without

spaces).

f. Close the Iso-Surface dialog box.

4. Plot the radial velocity distribution on the surface y=37cm.

Plots → XY Plot → Set Up...

a. Select Velocity... and Radial Velocity from the Y Axis Function drop-down lists.

b. Select the y-coordinate line y=37cm from the Surfaces selection list.

c. Click Plot.

Figure 11.6 (p. 460) shows a plot of the radial velocity distribution along =� ��.




Figure 11.6 Radial Velocity Distribution—Standard k- ε Solution

d. Enable Write to File in the Options group box to save the radial velocity profile.

e. Click the Write... button to open the Select File dialog box.

i. Enter ke-data.xy in the XY File text entry box and click OK.

5. Plot the wall y+ distribution on the rotating disk wall along the radial direction (Figure 11.7 (p. 462)).




a. Disable Write to File in the Options group box.

b. Select Turbulence... and Wall Yplus from the Y Axis Function drop-down lists.

c. Deselect y=37cm and select wall-6 from the Surfaces selection list.

d. Enter 0 and 1 for X and Y respectively in the Plot Direction group box.

e. Click the Axes... button to open the Axes - Solution XY Plot dialog box.

i. Retain the default selection of X from the Axis group box.

ii. Disable Auto Range in the Options group box.

iii. Retain the default value of 0 for Minimum and enter 43 for Maximum in the Range group

box.




iv. Click Apply and close the Axes - Solution XY Plot dialog box.

f. Click Plot in the Solution XY Plot dialog box.

Figure 11.7 (p. 462)shows a plot of wall y+ distribution along wall-6.

Figure 11.7 Wall Yplus Distribution on wall-6— Standard k- ε Solution

g. Enable Write to File in the Options group box to save the wall y+ profile.

h. Click the Write... button to open the Select File dialog box.

i. Enter ke-yplus.xy in the XY File text entry box and click OK.

Note

Ideally, while using enhanced wall treatment, the wall y+ should be in the order of 1

(at least less than 5) to resolve viscous sublayer. The plot justifies the applicability of

enhanced wall treatment to the given mesh.

i. Close the Solution XY Plot dialog box.


Recalculate the solution using the RNG �

- �

turbulence model.

1. Enable the RNG �

- �

turbulence model with the enhanced near-wall treatment.

Models → Viscous → Edit...



a. Select RNG in the k-epsilon Model list.

b. Enable Differential Viscosity Model and Swirl Dominated Flow in the RNG Options group box.

The differential viscosity model and swirl modification can provide better accuracy for swirling flows

such as the disk cavity.

For more information, see RNG Swirl Modification of the Theory Guide.

c. Retain Enhanced Wall Treatment as the Near-Wall Treatment.

d. Click OK to close the Viscous Model dialog box.

2. Continue the calculation by requesting 200 iterations.

Run Calculation

The solution converges after approximately 170 additional iterations.

3. Save the case and data files (disk-rng.cas.gz and disk-rng.dat.gz ).

File → Write → Case & Data...





1. Plot the radial velocity distribution for the RNG �

- �

solution and compare it with the distribution for

the standard �

- �

solution.


a. Enter 1 and 0 for X and Y respectively in the Plot Direction group box.

b. Select Velocity... and Radial Velocity from the Y Axis Function drop-down lists.

c. Select y=37cm and deselect wall-6 from the Surfaces selection list.

d. Disable the Write to File option.

e. Click the Load File... button to load the �

- �

data.

i. Select the file ke-data.xy in the Select File dialog box.

ii. Click OK.

f. Click the Axes... button to open the Axes - Solution XY Plot dialog box.

i. Enable Auto Range in the Options group box.

ii. Click Apply and close the Axes - Solution XY Plot dialog box.

g. Click the Curves... button to open the Curves - Solution XY Plot dialog box, where you will

define a different curve symbol for the RNG �

- �

data.



i. Retain 0 for the Curve #.

ii. Select x from the Symbol drop-down list.

iii. Click Apply and close the Curves - Solution XY Plot dialog box.

h. Click Plot in the Solution XY Plot dialog box (Figure 11.8 (p. 465)).

Figure 11.8 Radial Velocity Distribution — RNG k- ε and Standard k- ε Solutions

The peak velocity predicted by the RNG �

- �

solution is higher than that predicted by the standard �

-� solution. This is due to the less diffusive character of the RNG

�- �

model. Adjust the range of the �

axis to magnify the region of the peaks.

i. Click the Axes... button to open the Axes - Solution XY Plot dialog box, where you will specify

the �

-axis range.




i. Disable Auto Range in the Options group box.

ii. Retain the value of 0 for Minimum and enter 1 for Maximum in the Range dialog box.

iii. Click Apply and close the Axes - Solution XY Plot dialog box.

j. Click Plot.

The difference between the peak values calculated by the two models is now more apparent.

Figure 11.9 RNG k- ε and Standard k- ε Solutions (x=0 cm to x=1 cm)



2. Plot the wall y+ distribution on the rotating disk wall along the radial direction Figure 11.10 (p. 468).


a. Select Turbulence... and Wall Yplus from the Y Axis Function drop-down lists.

b. Deselect y=37cm and select wall-6 from the Surfaces selection list.

c. Enter 0 and 1 for X and Y respectively in the Plot Direction group box.

d. Select any existing files that appear in the File Data selection list and click the Free Data button

to remove the file.

e. Click the Load File... button to load the RNG �

- �

data.

i. Select the file ke-yplus.xy in the Select File dialog box.

ii. Click OK.

f. Click the Axes... button to open the Axes - Solution XY Plot dialog box.

i. Retain the default selection of X from the Axis group box.

ii. Retain the default value of 0 for Minimum and enter 43 for Maximum in the Range group

box.

iii. Click Apply and close the Axes - Solution XY Plot dialog box.

g. Click Plot in the Solution XY Plot dialog box.




Figure 11.10 wall-6 — RNG k- ε and Standard k- ε Solutions (x=0 cm to x=43 cm)

11.5. Summary

This tutorial illustrated the setup and solution of a 2D, axisymmetric disk cavity problem in ANSYS FLUENT.

The ability to calculate a swirl velocity permits the use of a 2D mesh, thereby making the calculation simpler

and more economical to run than a 3D model. This can be important for problems where the enhanced wall

treatment is used, and the near-wall flow field is resolved using a fine mesh (the first mesh point away from

the wall being placed at a y+ on the order of 1).

For more information about mesh considerations for turbulence modeling, see Model Hierarchy in the User's

Guide.

11.6. Further Improvements

The case modeled in this tutorial lends itself to parametric study due to its relatively small size. Here are

some things you may wish to try:

• Separate wall-6 into two walls.

Mesh → Separate → Faces...

Specify one wall to be stationary, and rerun the calculation.

• Use adaption to see if resolving the high velocity and pressure-gradient region of the flow has a signi-

ficant effect on the solution.



• Introduce a non-zero swirl at the inlet or use a velocity profile for fully-developed pipe flow. This is

probably more realistic than the constant axial velocity used here, since the flow at the inlet is typically

being supplied by a pipe.

• Model compressible flow (using the ideal gas law for density) rather than assuming incompressible flow

text.

This tutorial guides you through the steps to reach an initial solution. You may be able to obtain a more

accurate solution by using an appropriate higher-order discretization scheme and by adapting the mesh.

Mesh adaption can also ensure that the solution is independent of the mesh. These steps are demonstrated

in Introduction to Using ANSYS FLUENT: Fluid Flow and Heat Transfer in a Mixing Elbow (p. 111).

11.7. References

1. Pincombe, J.R., “Velocity Measurements in the Mk II - Rotating Cavity Rig with a Radial Outflow”, Thermo-

Fluid Mechanics Research Centre, University of Sussex, Brighton, UK, 1981.



11.7. References

chapter 11: using a single rotating reference · pdf filethis tutorial is divided ... the...

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