Tutorial Solving Transonic Flow Over a Turbine Blade With Turbo-Specic NRBCs Nrbc-turbine-cascade

Tutorial: Solving Transonic Flow over a Turbine Blade with

Turbo-Specific NRBCs

Introduction

The standard pressure boundary conditions for compressible flow fix specific flow variablesat the boundary (e.g., static pressure at an outlet boundary). As a result, pressure wavesincident on the boundary will reflect in an unphysical manner, leading to local errors. Theeffects are more pronounced for internal flow problems where boundaries are usually closeto geometry inside the domain, such as compressor or turbine blade rows.

The turbo-specific non-reflecting boundary conditions (NRBCs) permit waves to “pass”through the boundaries without spurious reflections. The method used in FLUENT is basedon the Fourier transformation of solution variables at the non-reflecting boundary.

This tutorial demonstrates how to do the following:

• Set up and solve the turbine blade flow field using the standard pressure outlet bound-ary treatment.

• Activate the turbo-specific NRBCs and solve the problem again.

• Compare the results for the standard and non-reflecting pressure boundaries.

Prerequisites

This tutorial assumes that you are familiar with the FLUENT interface, and have a goodunderstanding of basic setup and solution procedures. In this tutorial, you will use turbo-specific NRBCs, so you should have some experience with them. This tutorial will not coverthe mechanics of using this feature. Instead, it will focus on the application of turbo-specificNRBCs to a turbine blade flow field.

If you have not used this feature before, Refer section 7.23.1 : Turbo-specific Non-ReflectingBoundary Conditions in the FLUENT 6.3 User’s Guide

c© Fluent Inc. January 25, 2007 1

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Solving Transonic Flow over a Turbine Blade with Turbo-Specific NRBCs

Problem Description

This tutorial considers the transonic flow around a turbine blade cascade with a shortenedexit boundary. This configuration is frequently encountered in stage analyses where thespacing between adjacent blade rows is small, and hence, the exit boundary of the upstreamrow must be placed very close to the trailing edge of the blade. Using the traditionalpressure outlet boundary treatment can lead to spurious pressure distributions on the bladesurface since the exit pressure is typically being assumed to be uniform in the blade-to-bladedirection. NRBCs can eliminate this problem by permitting pressure waves to pass throughthe boundary without reflection, thereby leading to a more accurate solution.

Note: Non-reflecting boundary conditions can only be used with the density-based solver.

Figure 1: 2D Stator Blade

Preparation

1. Copy the mesh file 2d-stator.msh to the working folder.

2. Start the 2D (2d) version of FLUENT.

2 c© Fluent Inc. January 25, 2007


Setup and Solution: Standard Boundary Conditions Case

Step 1: Grid

1. Read in the mesh file (2d-stator.msh).

2. Check and display the grid (Figure 2).

GridFLUENT 6.3 (2d, dbns exp, ske)

Figure 2: 2D Stator Mesh Display

Step 2: Units

1. Define the units for pressure.

Define −→Units...

(a) Select pressure from the Quantities list.

(b) Select atm from the Units list.

(c) Close the Set Units panel.

Step 3: Models

1. Define the solver settings.

Define −→ Models −→Solver...

(a) Select Density Based from the Solver list.

(b) Select Explicit in the Formulation list.

(c) Click OK to close the Solver panel.

2. Enable the standard k-ε turbulence model with standard wall functions.

Define −→ Models −→Viscous...



Step 4: Materials

1. Modify the properties of air.

Define −→Materials...

(a) Select fluid from the Material Type drop-down list.

(b) Select ideal-gas from the Density drop-down list under Properties.

Note: FLUENT will automatically enable solution of the energy equation whenthe ideal gas law is used.

(c) Retain the default values for all other properties.

(d) Click Change/Create and close the Materials panel.

Step 5: Operating Conditions

1. Set the operating conditions.

Define −→Operating Conditions...

Here, you will set the operating pressure is set to zero and the boundary conditioninputs for pressure will be defined in terms of absolute pressures. Boundary conditionsfor pressure should always be relative to the value of operating pressure.

(a) Enter 0 for Operating Pressure.

(b) Click OK to close the Operating Conditions panel.

Step 6: Boundary Conditions

1. Set the conditions for the inlet (pressure-inlet).

Define −→Boundary Conditions...

(a) Enter 1.5 atm for the Gauge Total Pressure.

(b) Enter 1.0 atm for the Supersonic/Initial Gauge Pressure.

(c) Enter 1.0 for the X-Component of Flow Direction.

(d) Enter 0 for the Y-Component of Flow Direction.

Note: You must use the Direction Vector specification method for the pressureinlet in order to use the NRBCs.

(e) Select Intensity and Viscosity Ratio from the Specification Method drop-down listunder Turbulence.

(f) Enter 1% for the Turbulent Intensity.

(g) Enter 1.0 for the Turbulent Viscosity Ratio.

(h) Click the Thermal tab and enter 300 K for Total Temperature.

(i) Click OK to close the Pressure Inlet panel.



2. Set the conditions for the outlet (pressure-outlet).

(a) Enter 0.8 atm for the Gauge Pressure.

(b) Select Intensity and Viscosity Ratio from the Specification Method drop-down list.

(c) Enter 1% for the Backflow Turbulent Intensity.

(d) Enter 1.0 for the Backflow Turbulent Viscosity Ratio.

(e) Click the Thermal tab and enter 300 K for the Backflow Total Temperature.

(f) Click OK to close the Pressure Outlet panel.

3. Close the Boundary Conditions panel.

Step 7: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Enter 0.8 for the Turbulent Kinetic Energy and Turbulent Dissipation Rate in theUnder-Relaxation Factors group box.

(b) Select First Order Upwind for all the discretizations under Discretization.

(c) Enter 0.5 for the Courant Number under the Solver Parameters.

(d) Set the Multigrid Levels to 4.

(e) Click OK to close the Solution Controls panel.

2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

(a) Enable Plot in the Options list.

(b) Enter 0.0001 for Absolute Criteria for continuity.

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

3. Enable monitors for lift and drag coefficients.

Solve −→ Monitors −→Force...

(a) Select Drag from the Coefficient drop-down list.

(b) Select stator-blade from the Wall Zones list.

(c) Enable Plot and Write in the Options list.

(d) Enter cd-history for the File Name.

If you do not select the Write option, the history information will be lost whenyou exit FLUENT.

(e) Click Apply.



(f) Similarly define the parameters for Lift and enter cl-history as the File Name.

(g) Close the Force Monitors panel.

4. Initialize the solution.

Solve −→ Initialize −→Initialize...

(a) Select inlet from the Compute From drop-down list.

(b) Click Init and close the Solution Initialization panel.

5. Save the case file (nrbc-1.cas.gz).

File −→ Write −→Case...

6. Iterate the solution.

(a) Enter 2000 for Number of Iterations.

(b) Click Iterate.

Scaled ResidualsFLUENT 6.3 (2d, dbns exp, ske)

Iterations1400120010008006004002000

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

epsilonkenergyy-velocityx-velocitycontinuity

Residuals

Figure 3: Scaled Residuals

(c) Close the Iterate panel.

7. Save the data file (nrbc-1.dat.gz).

File −→ Write −→Data...



Drag Convergence HistoryFLUENT 6.3 (2d, dbns exp, ske)

Iterations

Cd

1400120010008006004002000

27500.0000

25000.0000

22500.0000

20000.0000

17500.0000

15000.0000

12500.0000

10000.0000

7500.0000

5000.0000

2500.0000

Figure 4: Drag Coefficient Convergence History

Lift Convergence HistoryFLUENT 6.3 (2d, dbns exp, ske)

Iterations

Cl

1400120010008006004002000

16000.0000

14000.0000

12000.0000

10000.0000

8000.0000

6000.0000

4000.0000

2000.0000

Figure 5: Lift Coefficient Convergence History



Step 8: Postprocessing

1. Display filled contours of static pressure (Figure 6).

Display −→Contours...

(a) Enable Filled in the Options list.

(b) Select Pressure... and Static Pressure in the Contours of drop-down lists.

(c) Click Display.

Contours of Static Pressure (atm)FLUENT 6.3 (2d, dbns exp, ske)

1.50e+001.44e+001.39e+001.34e+001.28e+001.23e+001.17e+001.12e+001.07e+001.01e+009.58e-019.04e-018.50e-017.96e-017.42e-016.88e-016.34e-015.80e-015.26e-014.72e-014.18e-01

Figure 6: Contours of Static Pressure

2. Display filled contours of Mach number (Figure 7).

(a) In the Contours panel, select Velocity... and Mach Number in the Contours Ofdrop-down lists.

(b) Make sure that Filled is selected under Options.

(c) Click Display.



Contours of Mach NumberFLUENT 6.3 (2d, dbns exp, ske)

1.40e+001.34e+001.27e+001.20e+001.13e+001.06e+009.89e-019.20e-018.51e-017.82e-017.13e-016.44e-015.74e-015.05e-014.36e-013.67e-012.98e-012.29e-011.59e-019.02e-022.11e-02

Figure 7: Contours of Mach Number

3. Close the Contours panel.

4. Create an XY plot of the static pressure distribution on the blade surface.

Plot −→XY Plot...

(a) Select Pressure... and Static Pressure in the Y Axis Function drop-down lists.

(b) Select stator-blade, in the Surfaces list.

(c) Retain the default Plot Direction of X.

This will plot temperature vs. the x coordinate along the selected surface (stator-blade).

(d) Click Plot (Figure 8).



Static PressureFLUENT 6.3 (2d, dbns exp, ske)

Position (m)

(atm)Pressure

Static

0.060.050.040.030.020.010

1.60e+00

1.40e+00

1.20e+00

1.00e+00

8.00e-01

6.00e-01

4.00e-01

stator-blade

Figure 8: XY Plot of Static Pressure Distribution on Stator Blade

(e) Save the plot data to a file.

i. Select the Write to File option and click the Write... button to open the SelectFile dialog box.

ii. Enter pdata-std-bc.xy in the XY File text entry box and click OK to closethe Select File dialog box.

(f) Close the Solution XY Plot panel.



Setup and Solution: Non-Reflecting Boundary Conditions Case

Step 1: Turbo-Specific Non-Reflecting Boundary Conditions

1. Enable the turbo-specific NRBC using the commands shown in boxes:

> /define/boundary-conditions/non-reflecting-bc>turbo-specific-nrbc

/define/boundary-conditions/non-reflecting-bc>turbo-specific-nrbc> enable

enable non-reflecting b.c.’s [no] yes

Step 2: Solution

1. Set the turbo-specific NRBC under-relaxation factor to 0.5 using the commands inboxes:

(a) In the FLUENT console window, type the following command:

/define/boundary-conditions/non-reflecting-bc/turbo-specific-nrbc/set> under

non-reflecting b.c. under-relaxation factor [0.75] 0.5

2. Perform turbo-specific NRBC initialization using the initialize TUI command:

/define/boundary-conditions/non-reflecting-bc/turbo-specific-nrbc> initialize

FLUENT will display the following summary in the console window.

2D Initialize_Non_Reflecting_Boundariespressure-inlet-2: l = 0, kmax = 1x extents : -1.29761e-01 -> -1.29761e-01r extents : -3.81080e-02 -> 3.81283e-02q extents : 0.00000e+00 -> 0.00000e+00pressure-outlet-4: l = 1, kmax = 1x extents : 6.38378e-02 -> 6.38378e-02r extents : -9.90170e-02 -> -2.27807e-02q extents : 0.00000e+00 -> 0.00000e+00pressure-inlet-2:Pitch = 7.62364e-02 (m)pressure-outlet-4:Pitch = 7.62363e-02 (m)



3. Save the case file (nrbc-2.cas.gz).

File −→ Write −→Case...

4. Iterate the solution.

(a) Enter 1000 for Number of Iterations.

(b) Click Iterate.

(c) Close the Iterate panel.

Scaled ResidualsFLUENT 6.3 (2d, dbns exp, ske)

Iterations25002250200017501500125010007505002500

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

epsilonkenergyy-velocityx-velocitycontinuity

Residuals

Figure 9: Scaled Residuals

5. Save the data file (nrbc-2.dat.gz).

File −→ Write −→Data...



Drag Convergence HistoryFLUENT 6.3 (2d, dbns exp, ske)

Iterations

Cd

25002250200017501500125010007505002500

27500.0000

25000.0000

22500.0000

20000.0000

17500.0000

15000.0000

12500.0000

10000.0000

7500.0000

5000.0000

2500.0000

Figure 10: Drag Coefficient Convergence History

Lift Convergence HistoryFLUENT 6.3 (2d, dbns exp, ske)

Iterations

Cl

25002250200017501500125010007505002500

16000.0000

14000.0000

12000.0000

10000.0000

8000.0000

6000.0000

4000.0000

2000.0000

Figure 11: Lift Coefficient Convergence History



Step 3: Postprocessing

1. Display filled contours of static pressure (Figure 12).

Display −→Contours...

(a) Enable Filled in the Options list.

(b) Select Pressure... and Static Pressure in the Contours of drop-down lists.

(c) Click Display.

Contours of Static Pressure (atm)FLUENT 6.3 (2d, dbns exp, ske)

1.50e+001.45e+001.40e+001.36e+001.31e+001.26e+001.22e+001.17e+001.12e+001.08e+001.03e+009.83e-019.36e-018.89e-018.43e-017.96e-017.49e-017.02e-016.56e-016.09e-015.62e-01

Figure 12: Contours of Static Pressure

2. Display filled contours of Mach number (Figure 13).

(a) Select Velocity... and Mach Number in the Contours of drop-down lists.

Make sure that Filled is selected under Options.

(b) Click Display.

Contours of Mach NumberFLUENT 6.3 (2d, dbns exp, ske)

1.25e+001.18e+001.12e+001.06e+001.00e+009.40e-018.78e-018.17e-017.56e-016.95e-016.33e-015.72e-015.11e-014.50e-013.88e-013.27e-012.66e-012.05e-011.43e-018.21e-022.08e-02

Figure 13: Contours of Mach Number



3. Create an XY plot of the static pressure distribution on the blade surface.

Plot −→XY Plot...

(a) Select Pressure... and Static Pressure in the Y Axis Function drop-down lists.

(b) Select stator-blade, in the Surfaces list.

(c) Keep the default Plot Direction of X.

This will plot temperature vs. the x coordinate along the selected surface (stator-blade).

(d) Click Plot.

The resulting XY plot for static pressure distribution is displayed in Figure 14.


Position (m)

(atm)Pressure

Static

0.060.050.040.030.020.010

1.50e+00

1.40e+00

1.30e+00

1.20e+00

1.10e+00

1.00e+00

9.00e-01

8.00e-01

7.00e-01

6.00e-01

5.00e-01

stator-blade

Figure 14: XY Plot of Static Pressure Distribution on Stator Blade

(e) Save the plot data to a file.

i. Select the Write to File option and click the Write... button to open the SelectFile dialog box.

ii. Enter pdata-nrbc.xy in the XY File text entry box and click OK to closethe dialog box.

4. Read the plot files you saved for the two solutions and compare them in a single plot(Figure 15).

Notice that the shock wave position for the NRBC case is moved closer to the trailingedge of the vane. This is due to the fact that pressure variations in the vicinity ofthe shock are permitted to pass through the exit boundary without being artificiallyconstrained by assuming a constant (uniform) exit pressure, as is the case when theNRBCs are disabled.




Position (m)

(atm)Pressure

Static

0.060.050.040.030.020.010

1.60e+00

1.40e+00

1.20e+00

1.00e+00

8.00e-01

6.00e-01

4.00e-01

NRBCStandard BC

Figure 15: Comparison of XY Plots

Summary

This tutorial demonstrated the salient points of setting up and solving of a problem withFLUENT’s turbo-specific NRBCs.

It was shown that the location of the shockwave is dramatically different when standardpressure BCs are used. This is not surprising since you are forcing the static pressure at theexit to be uniform. With NRBCs, the pressure waves are not constrained and are permittedto vary along the boundary such that waves are not spuriously reflected.

NRBCs can be used in 2D or 3D and with FLUENT 6.3 can be used with the coupledimplicit solver.


Documents

Tutorial Solving Transonic Flow Over a Turbine Blade With Turbo-Specic NRBCs Nrbc-turbine-cascade