fluent 6_0 tuturial guide_volume 2

FLUENT 6.0 Tutorial Guide

Volume 2

December 2001

Licensee acknowledges that use of Fluent Inc.’s products can only pro-vide an imprecise estimation of possible future performance and thatadditional testing and analysis, independent of the Licensor’s products,must be conducted before any product can be finally developed or com-mercially introduced. As a result, Licensee agrees that it will not relyupon the results of any usage of Fluent Inc.’s products in determiningthe final design, composition or structure of any product.

Copyright c© 2001 by Fluent Inc.All rights reserved. No part of this document may be reproduced orotherwise used in any form without express written permission from

Fluent Inc.

Airpak, FIDAP , FLUENT, GAMBIT , Icepak, MixSim , and POLYFLOWare registered trademarks of Fluent Inc. All other products or name

brands are trademarks of their respective holders.

Fluent Inc.Centerra Resource Park

10 Cavendish CourtLebanon, NH 03766

Contents

Volume 1

1 Introduction to Using FLUENT 1-1

2 Modeling Periodic Flow and Heat Transfer 2-1

3 Modeling External Compressible Flow 3-1

4 Modeling Unsteady Compressible Flow 4-1

5 Modeling Radiation and Natural Convection 5-1

6 Using a Non-Conformal Mesh 6-1

7 Using a Single Rotating Reference Frame 7-1

8 Using Multiple Rotating Reference Frames 8-1

9 Using the Mixing Plane Model 9-1

10 Using Sliding Meshes 10-1

Volume 2⇒

11 Modeling Species Transport and Gaseous Combustion 11-1

12 Using the Non-Premixed Combustion Model 12-1

c© Fluent Inc. November 27, 2001 i

CONTENTS

13 Modeling Surface Chemistry 13-1

14 Modeling Evaporating Liquid Spray 14-1

15 Using the VOF Model 15-1

16 Modeling Cavitation 16-1

17 Using the Mixture and Eulerian Multiphase Models 17-1

18 Using the Eulerian Multiphase Model for Granular Flow 18-1

19 Modeling Solidification 19-1

20 Postprocessing 20-1

21 Turbo Postprocessing 21-1

22 Parallel Processing 22-1

ii c© Fluent Inc. November 27, 2001

Tutorial 11. Modeling Species

Transport and Gaseous Combustion

Introduction: This tutorial examines chemical species mixing andcombustion of a gaseous fuel. A cylindrical combustor burningmethane (CH4) in air is studied using the finite-rate chemistrymodel in FLUENT.

In this tutorial you will learn how to:

• Enable physical models, select material properties, and defineboundary conditions for a turbulent flow with chemical speciesmixing and reaction

• Initiate and solve the combustion simulation using the segre-gated solver

• Compare the results computed with constant and variablespecific heat

• Examine the reacting flow results using graphics

• Predict thermal and prompt NOx production

• Use custom field functions to compute NO parts per million

Prerequisites: This tutorial assumes that you have performed Tutorial1 and are familiar with the FLUENT interface. It also assumes thatyou have developed a basic familiarity with the solution of turbu-lent flows using FLUENT. You may find it helpful to read aboutchemical reaction modeling in the User’s Guide. Otherwise, no pre-vious experience with chemical reaction or combustion modeling isassumed.

Problem Description: The cylindrical combustor considered in thistutorial is shown in Figure 11.1. The flame considered is a turbu-lent diffusion flame. A small nozzle in the center of the combustor

c© Fluent Inc. November 27, 2001 11-1

Modeling Species Transport and Gaseous Combustion

introduces methane at 80 m/s. Ambient air enters the combustorcoaxially at 0.5 m/s. The overall equivalence ratio is approximately0.76 (about 28% excess air). The high-speed methane jet initiallyexpands with little interference from the outer wall, and entrainsand mixes with the low-speed air. The Reynolds number based onthe methane jet diameter is approximately 5.7 × 103.

Methane, 80 m/s, 300K

Air, 0.5 m/s, 300K Wall: 300K

1.8 m

0.22

5 m

0.00

5m

CL

Figure 11.1: Combustion of Methane Gas in a Turbulent Diffusion FlameFurnace

Background: In this tutorial, you will use the generalized finite-ratechemistry model to analyze the methane-air combustion system.The combustion will be modeled using a global one-step reactionmechanism, assuming complete conversion of the fuel to CO2 andH2O. The reaction equation is

CH4 + 2O2 → CO2 + 2H2O (11.1)

This reaction will be defined in terms of stoichiometric coefficients,formation enthalpies, and parameters that control the reactionrate. The reaction rate will be determined assuming that turbulentmixing is the rate-limiting process, with the turbulence-chemistryinteraction modeled using the eddy-dissipation model.

11-2 c© Fluent Inc. November 27, 2001


Preparation

1. Copy the file gascomb/gascomb.msh from the FLUENT documen-tation CD to your working directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

Step 1: Grid

1. Read the grid file gascomb.msh.

File −→ Read −→Case...

After reading the grid file, FLUENT will report that 1615 quadri-lateral fluid cells have been read, along with a number of boundaryfaces with different zone identifiers.

2. Check the grid.

Grid −→Check

The grid check lists the minimum and maximum x and y valuesfrom the grid, and reports on a number of other grid features thatare checked. Any errors in the grid would be reported at this time.For instance, the cell volumes must never be negative. Note thatthe domain extents are reported in units of meters, the default unitof length in FLUENT. Since this grid was created in units of mil-limeters, the Scale Grid panel will be used to scale the grid intometers.

3. Scale the grid.

Grid −→Scale...

(a) Under Units Conversion, select mm from the drop-down list tocomplete the phrase Grid Was Created In mm.

(b) Click on Scale and confirm that the maximum x and y valuesare 1.8 and 0.225 meters, respectively, as indicated in Fig-ure 11.1.



Note: Because the default SI units will be used in this tutorial,there is no need to change any units in this problem.

4. Display the grid.

Display −→Grid...

GridFLUENT 6.0 (2d, segregated, lam)

Feb 05, 2001

Figure 11.2: The Quadrilateral Grid for the Combustor Model

Extra: You can use the right mouse button to check which zone numbercorresponds to each boundary. If you click the right mouse buttonon one of the boundaries in the graphics window, its zone number,name, and type will be printed in the FLUENTconsole window. Thisfeature is especially useful when you have several zones of the sametype and you want to distinguish between them quickly.



Step 2: Models

1. Define the domain as axisymmetric, and keep the default (segre-gated) solver.

Define −→ Models −→Solver...



2. Enable the k-ε turbulence model.

Define −→ Models −→Viscous...

The panel will expand to provide further options. Click OK to ac-cept the default Standard model and parameters.



3. Enable heat transfer by activating the energy equation.

Define −→ Models −→Energy...



4. Enable chemical species transport and reaction.

Define −→ Models −→Species...

(a) Select Species Transport under Model.

(b) Select Volumetric under Reactions.

(c) Choose methane-air in the Mixture Material drop-down list.

The Mixture Material list contains the set of chemical mixturesthat exist in the FLUENT database. By selecting one of thepre-defined mixtures, you are accessing a complete descrip-tion of the reacting system. The chemical species in the sys-tem and their physical and thermodynamic properties are de-fined by your selection of the mixture material. You can alterthe mixture material selection or modify the mixture materialproperties using the Materials panel (see Step 3: Materials).



(d) Select Eddy-Dissipation under Turbulence-Chemistry Interaction.

The eddy-dissipation model computes the rate of reaction un-der the assumption that chemical kinetics are fast compared tothe rate at which reactants are mixed by turbulent fluctuations(eddies).

(e) Click OK.

After you click OK in the Species Model panel, a warningabout the symmetry zone will appear in the console window:

Warning: It appears that symmetry zone 5 should actually be an axis(it has faces with zero area projections).Unless you change the zone type from symmetry to axis,you may not be able to continue the solution withoutencountering floating point errors.

In this axisymmetric model, the centerline should be treatedusing the axis boundary condition instead of symmetry. Youwill change the symmetry zone to an axis boundary in Step 4:Boundary Conditions.

The console window will also list the properties that are re-quired for the models you have enabled. You will see an In-formation dialog box, reminding you to confirm the propertyvalues that have been extracted from the database.

(f) Click OK to continue.



Step 3: Materials

Define −→Materials...

The Materials panel shows the mixture material, methane-air, that wasenabled in the Species Model panel. The properties for this mixture ma-terial have been copied from the FLUENT database and can be modifiedby you.

Here, you will modify the default setting for the mixture by enabling thegas law. By default, the mixture material uses constant properties: youwill retain this constant property assumption for now, allowing only themixture density to vary with temperature and composition. The influence



of variable property inputs on the combustion prediction will be examinedin a later part of this tutorial.

1. Retain incompressible-ideal-gas in the Density drop-down list.

2. Click the Edit... button to the right of Mixture Species.

This opens the Species panel.

You can add or remove species from the mixture material using thispanel. Here, the species that make up the methane-air mixture arepredefined and require no modification.

3. Click Cancel to close the panel without making any changes.

4. In the Materials panel, click the Edit... button to the right of theReaction drop-down list.

This will open the Reactions panel.



The eddy-dissipation reaction model ignores chemical kinetics (theArrhenius rate) and uses only the Mixing Rate parameters in theReactions panel. The Arrhenius Rate section of the panel is there-fore inactive. (The Rate Exponent and Arrhenius Rate entries areincluded in the database and are employed when the alternate finite-



rate/eddy-dissipation model is used.) See the User’s Guide for de-tails.

5. Accept the default settings for the Mixing Rate constants by clickingthe OK button.

6. Use the scroll bar to review the remaining properties. Click on theChange/Create button to accept the material property settings andthen Close the panel.

As noted above, the initial calculation will be performed assuming that allproperties except density are constant. Using constant transport proper-



ties (viscosity, thermal conductivity, and mass diffusion coefficients) isacceptable here because the flow is fully turbulent. The molecular trans-port properties will play a minor role compared to turbulent transport.The assumption of constant specific heat, in contrast, has a strong effecton the combustion solution, and you will change this property definitionin Step 6: Solution Using Non-Constant Heat Capacity.



Step 4: Boundary Conditions

1. Convert the symmetry zone to the axis type.

The symmetry zone must be converted to an axis to prevent nu-merical difficulties where the radius goes to zero.

Define −→Boundary Conditions...

(a) Select symmetry-5 in the Zone list and then select axis in theType list.



You will be prompted to accept the change of boundary type:

(b) Click Yes to confirm the change.

(c) In the resulting Axis panel, click OK to accept the default axiszone name.

2. Set the boundary conditions for the air inlet, velocity-inlet-8.

Hint: Redisplay the grid without the fluid zone. This will showthe boundaries. Use the right mouse button to probe the airinlet. The console window and the Boundary Conditions panelwill show that the air inlet is labeled velocity-inlet-8.



(a) Rename the boundary air-inlet in the Zone Name text entrybox.

(b) Set the boundary conditions at the air inlet as shown in thepanel.



3. Set the fuel inlet boundary conditions for velocity-inlet-6.

(a) Rename this zone fuel-inlet and assign inlet conditions asshown in the panel.



4. Set the following conditions for the exit boundary, pressure-outlet-9:

Note: The Backflow values in this panel are utilized only whenbackflow occurs at the pressure outlet. Reasonable values shouldalways be assigned, since backflow may occur during interme-diate iterations and could affect the solution stability.



5. Set the boundary conditions for the outer wall, wall-7.

Hint: Use the mouse-probe method described above for the air inletto determine which zone corresponds to the outer wall. Theouter wall zone will be selected in the Boundary Conditionspanel once the outer wall boundary is probed.



(a) Rename this boundary outer-wall in the Zone Name textentry box.

(b) Set the thermal condition to Temperature and keep the defaulttemperature of 300 K.

(c) Retain the default settings in the Momentum and Species sec-tions of the panel.



6. Set the boundary conditions for wall-2, which represents the smallfuel inlet nozzle.

(a) Rename this boundary nozzle in the Zone Name text entrybox.

(b) Accept the default thermal condition of Heat Flux with a valueof zero (adiabatic wall).

(c) Retain the default settings in the Momentum and Species sec-tions of the panel.



Step 5: Initial Solution Using Constant Heat Ca-pacity

1. Initialize the field variables.

Solve −→ Initialize −→Initialize...

(a) Select all-zones in the Compute From drop-down list.

(b) Adjust the Initial Values for Temperature to 2000 and ch4 MassFraction to 0.2.

(c) Click Init to initialize the variables, and then close the panel.

Initializing the flow using a high temperature and non-zero fuelcontent will allow the combustion reaction to begin. The initialcondition acts as a numerical “spark” to ignite the methane-air mixture. This initialization is especially critical when youinclude finite-rate kinetics in the overall reaction rate.



2. Set the under-relaxation factors.

The default under-relaxation parameters in FLUENT are set to highvalues. For a combustion model it may be necessary to reduce theunder-relaxation to stabilize the solution. Some experimentation istypically necessary to establish the optimal under-relaxation. Forthis tutorial it is sufficient to reduce the species under-relaxationto 0.9.

Solve −→ Controls −→Solution...

(a) Use the slider bar next to the Under-Relaxation Factors list tolocate each species and set its under-relaxation factor to 0.9.



3. Turn on residual plotting during the calculation.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click OK.



4. Save the case file (gascomb1.cas).

File −→ Write −→Case...

(a) Keep the Write Binary Files button on to produce a smaller,unformatted binary file.

(b) Enter the file name gascomb1.cas in the Case File text entrybox.

(c) Click OK to proceed with the file writing.

5. Start the calculation by requesting 500 iterations.

Solve −→Iterate...

The solution converges in about 300 iterations.

6. Save the case and data files (gascomb1.cas and gascomb1.dat).

File −→ Write −→Case & Data...

Note: FLUENT will ask you to confirm that the previous case fileis to be overwritten.



7. Review the current state of the solution by viewing contours oftemperature (Figure 11.3).

Display −→Contours...

(a) Select Temperature... and Static Temperature in the ContoursOf drop-down list.

(b) Click Display.

The temperature contours are shown in Figure 11.3. The peak tem-perature, predicted using a constant heat capacity of 1000 J/kg-K,is over 2900 K. This overprediction of the flame temperature canbe remedied by a more realistic model for the temperature and com-position dependence of the heat capacity, as illustrated in the nextstep of the tutorial.



Contours of Static Temperature (k)FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

2.94e+03

2.67e+03

2.41e+03

2.14e+03

1.88e+03

1.62e+03

1.35e+03

1.09e+03

8.27e+02

5.64e+02

3.00e+02

Figure 11.3: Temperature Contours: Constant cp



Step 6: Solution Using Non-Constant Heat Ca-pacity

As noted above, the strong temperature and composition dependence ofthe specific heat will have a significant impact on the predicted flametemperature. In this step you will use the temperature-varying propertyinformation in the FLUENT database to recompute the solution.

1. Enable composition dependence of the specific heat.




(a) In the drop-down list next to Cp, select mixing-law as thespecific heat method.

(b) Click on the Change/Create button to render the mixture spe-cific heat based on a local mass-fraction-weighted average ofall the species.

2. Enable temperature dependence of the specific heat for each species.



(a) In the Material Type drop-down list, select fluid.

The fluid material type gives you access to each species in themixture.

(b) Select carbon-dioxide (co2) under Fluid Materials.

(c) In the drop-down list for Cp, select piecewise-polynomial.

This will open the Piecewise Polynomial Profile panel.

i. Click OK to accept the default coefficients describing thetemperature variation of cp for carbon dioxide.

The default coefficients describe the polynomial cp(T ) andare extracted from the FLUENT property database.

ii. Click on Change/Create in the Materials panel to acceptthe change in properties for CO2.

(d) Repeat steps (b) and (c) above for the remaining species(CH4, N2, O2, and H2O). Remember to click on Change/Create to accept the change for each species.



3. Request 500 more iterations.


Note: The residuals will jump significantly as the solution adjuststo the new specific heat representation. The solution convergesafter about 250 additional iterations.

4. Save the new case and data files (gascomb2.cas and gascomb2.dat).




Step 7: Postprocessing

Review the solution by examining graphical displays of the results andperforming surface integrations at the combustor exit.

1. View contours of temperature (Figure 11.4).



(b) Click Display.

The temperature contours are shown in Figure 11.4. The peak tem-perature has dropped to about 2200 K as a result of the temperature-and composition-dependent specific heat.

Contours of Static Temperature (k)FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

2.23e+03

2.04e+03

1.85e+03

1.65e+03

1.46e+03

1.27e+03

1.07e+03

8.79e+02

6.86e+02

4.93e+02

3.00e+02

Figure 11.4: Temperature Contours: Variable cp



2. Plot contours of specific heat (Figure 11.5).

Contours of the mixture specific heat will show how it varies throughthe domain.


(a) Select Properties... and Specific Heat (Cp) in the Contours Ofdrop-down list.

(b) Click Display.

The contours are shown in Figure 11.5. The mixture specific heatis largest where the CH4 is concentrated, near the fuel inlet, andwhere the temperature and combustion product concentrations arelarge. The increase in heat capacity, relative to the constant valueused before, substantially lowers the peak flame temperature.

Contours of Specific Heat (Cp) (j/kg-k)FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

2.80e+03

2.62e+03

2.44e+03

2.26e+03

2.08e+03

1.90e+03

1.72e+03

1.55e+03

1.37e+03

1.19e+03

1.01e+03

Figure 11.5: Contours of Specific Heat



3. Display velocity vectors (Figure 11.6).

Display −→Vectors...

(a) Click the Vector Options... button.

This opens the Vector Options panel.



(b) Select the Fixed Length option and click Apply.

The fixed length option is useful when the vector magnitudevaries dramatically. With fixed length vectors, the velocitymagnitude is described only by color instead of by both vectorlength and color.

(c) In the Vectors panel, reset the Scale to 0.01 and click Display.

The velocity vectors are shown in Figure 11.6.



Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

8.24e+01

7.42e+01

6.60e+01

5.78e+01

4.96e+01

4.14e+01

3.32e+01

2.50e+01

1.68e+01

8.57e+00

3.66e-01

Figure 11.6: Velocity Vectors: Variable cp



4. Plot contours of stream function (Figure 11.7).


(a) Select Velocity... and Stream Function in the Contours Of drop-down list.

(b) Click Display.

The stream function contours are shown in Figure 11.7. The en-trainment of air into the high-velocity methane jet is clearly visiblein the streamline display.



Contours of Stream Function (kg/s)FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

1.55e-02

1.39e-02

1.24e-02

1.08e-02

9.27e-03

7.73e-03

6.18e-03

4.64e-03

3.09e-03

1.55e-03

0.00e+00

Figure 11.7: Stream Function Contours: Variable cp



5. Plot contours of mass fraction for each species.


(a) Select Species... and Mass fraction of ch4 in the Contours Ofdrop-down list.

(b) Turn on the Filled button under Options.

(c) Click Display.

The CH4 mass fraction contours are shown in Figure 11.8.

(d) Repeat for the remaining species.

The mass fraction contours for O2, CO2, and H2O are shown inFigures 11.9, 11.10, and 11.11.

Contours of Mass fraction of ch4FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

1.00e+00

9.00e-01

8.00e-01

7.00e-01

6.00e-01

5.00e-01

4.00e-01

3.00e-01

2.00e-01

1.00e-01

0.00e+00

Figure 11.8: CH4 Mass Fraction



Contours of Mass fraction of o2FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

2.30e-01

2.07e-01

1.84e-01

1.61e-01

1.38e-01

1.15e-01

9.20e-02

6.90e-02

4.60e-02

2.30e-02

0.00e+00

Figure 11.9: O2 Mass Fraction

Contours of Mass fraction of co2FLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

1.46e-01

1.31e-01

1.17e-01

1.02e-01

8.76e-02

7.30e-02

5.84e-02

4.38e-02

2.92e-02

1.46e-02

0.00e+00

Figure 11.10: CO2 Mass Fraction



Contours of Mass fraction of h2oFLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

1.20e-01

1.08e-01

9.56e-02

8.37e-02

7.17e-02

5.98e-02

4.78e-02

3.59e-02

2.39e-02

1.20e-02

0.00e+00

Figure 11.11: H2O Mass Fraction



6. Determine the average exit temperature and velocity.

Report −→Surface Integrals...

(a) Select Mass-Weighted Average in the Report Type drop-downlist.

(b) Select Temperature... and Static Temperature in the Field Vari-able drop-down list.

The mass-averaged temperature will be computed as

T =∫

Tρ~v · d ~A∫ρ~v · d ~A

(11.2)

(c) Select pressure-outlet-9 as the surface over which to performthe integration.

(d) Click Compute.

The mass-weighted average exit temperature is about 1775 K.



(e) Select Area-Weighted Average as the Report Type and VelocityMagnitude as the Field Variable.

The area-weighted velocity-magnitude average will be computedas

v =1A

∫v dA (11.3)

(f) Click Compute.

The area-averaged exit velocity is about 3.10 m/s.



Step 8: NOx Prediction

In this section you will extend the FLUENT model to include the predic-tion of NOx. You will first calculate the formation of both thermal andprompt NOx, then calculate each separately to determine the contributionof each mechanism.

1. Enable the NOx model.

Define −→ Models −→ Pollutants −→NOx...

(a) Under Models, enable Thermal NO and Prompt NO.

(b) Select Temperature in the PDF Mode drop-down list underTurbulence Interaction to enable the turbulence-chemistry in-teraction.

If turbulence interaction is not enabled, you will be computingNOx formation without considering the important influence ofturbulent fluctuations on the time-averaged reaction rates.



(c) Select Partial-equilibrium in the [O] Model drop down list underThermal NO Parameters.

The partial-equilibrium model is used to predict the O radicalconcentration required for thermal NOx prediction.

(d) Set the Equivalence Ratio to 0.76 under Prompt NO Parame-ters, and keep the default Fuel Species and Fuel Carbon Num-ber.

The equivalence ratio defines the fuel-air ratio (relative to stoi-chiometric conditions) and is used in the calculation of promptNOx formation. The Fuel Carbon Number is the number ofcarbon atoms per molecule of fuel and is used in the promptNOx prediction. The Fuel Species designation is also used inthe prompt NOx model.

(e) Click OK to accept these changes.



2. Enable the calculation of only the NO species, and set the under-relaxation factor for this equation.


(a) In the Equations list, deselect all variables except the NOspecies.

(b) Increase the NO under-relaxation factor to 1.0.

You will predict NOx formation in a “postprocessing” mode, withthe flow field, temperature, and hydrocarbon combustion speciesconcentrations fixed. Thus, only the NO equation is computed.Prediction of NO in this mode is justified on the grounds that theNO concentrations are very low and have negligible impact on thehydrocarbon combustion prediction.



3. Reduce the convergence criterion for the NO species equation.


(a) Set the Convergence Criterion to 1e-6 and click OK.

4. Request 50 more iterations.



5. Save the new case and data files (gascomb3.cas and gascomb3.dat).



6. Review the solution by displaying contours of NO mass fraction(Figure 11.12).


(a) Select NOx... and Mass fraction of NO in the Contours Ofdrop-down list.

(b) Deselect Filled under Options and click Display.

The NO mass fraction contours are shown in Figure 11.12.The peak concentration of NO is located in a region of hightemperature where oxygen and nitrogen are available.

Contours of Mass fraction of noFLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

3.49e-03

3.14e-03

2.79e-03

2.44e-03

2.09e-03

1.74e-03

1.39e-03

1.05e-03

6.97e-04

3.49e-04

0.00e+00

Figure 11.12: Contours of NO Mass Fraction: Prompt and Thermal NOx



7. Calculate the average exit NO mass fraction.


(a) Select Mass-Weighted Average in the Report Type drop-downlist and NOx... and Mass fraction of NO in the Field Variabledrop-down list.

(b) Select pressure-outlet-9 as the surface over which to performthe integration.

(c) Click Compute.

The mass-weighted average exit NO mass fraction is about0.00309.



8. Disable the prompt NOx mechanism and solve for thermal NOx

only.


(a) Turn off Prompt NO under Models to disable the prompt NOx

mechanism, and click OK.

(b) Request 50 iterations.



(c) Review the thermal NOx solution by viewing contours of NOmass fraction (Figure 11.13).


i. Check that NOx... and Mass fraction of NO are selectedin the Contours Of drop-down list.

ii. Click Display.

The NO mass fraction contours are shown in Figure 11.13.The concentration of NO is slightly lower without theprompt NOx mechanism.

(d) Compute the average exit NO mass fraction with only thermalNOx formation.


Hint: Follow the same procedure you used earlier for the cal-culation with both thermal and prompt NOx formation.

The mass-weighted average exit NO mass fraction, with ther-mal but no prompt NOx formation, is about 0.00305.




Jun 05, 2001

3.46e-03

3.11e-03

2.77e-03

2.42e-03

2.08e-03

1.73e-03

1.38e-03

1.04e-03

6.92e-04

3.46e-04

0.00e+00

Figure 11.13: Contours of NO Mass Fraction: Thermal NOx Formation



9. Solve for prompt NOx production only.


(a) Turn off Thermal NO and turn on Prompt NO under Models,and click OK.

(b) Request 50 iterations.



(c) Review the prompt NOx solution by viewing contours of NOmass fraction (Figure 11.14).


The NO mass fraction contours are shown in Figure 11.14.The prompt NOx mechanism is most significant in fuel-richflames. In this case the flame is lean and prompt NO produc-tion is low.


Jun 05, 2001

6.10e-05

5.49e-05

4.88e-05

4.27e-05

3.66e-05

3.05e-05

2.44e-05

1.83e-05

1.22e-05

6.10e-06

7.08e-29

Figure 11.14: Contours of NO Mass Fraction: Prompt NOx Formation



(d) Compute the average exit NO mass fraction with only promptNOx formation.


Hint: Follow the same procedure you used earlier for the cal-culation with both thermal and prompt NOx formation.

The mass-weighted average exit NO mass fraction, with onlyprompt NOx formation, is about 0.000044.

Note: The individual thermal and prompt NO mass fractionsdo not add up to the levels predicted with the two mod-els combined. This is because reversible reactions are in-volved. NO produced in one reaction can be destroyed inanother reaction.



10. Use a custom field function to compute NO parts per million (ppm).

Define −→Custom Field Functions...

NO ppm is computed from the following equation:

NO ppm =NO mole fraction × 106

1 − H2O mole fraction(11.4)

where

NO mole fraction =NO mass fraction × mixture MW

30(11.5)

and the mixture molecular weight is

mixture MW =1∑

i

mass fractionMW

(11.6)

where MW is the molecular weight of each species.

First you will create a function for Equation 11.6. Then you willsubstitute Equation 11.5 into Equation 11.4 and create a functionfor Equation 11.4.



(a) Create a custom field function for the mixture molecular weight.

i. Click on the 1 calculator button, then on /, and then on(.

ii. Select Species... and Mass fraction of ch4 in the FieldFunctions drop-down list. Click Select to add this variableto the field function Definition.

iii. Click on / and then click on 1 and 6 to enter 16 (themolecular weight of methane).

iv. Continue in this fashion to complete the definition of themixture molecular weight field function.

v. Enter bulk-mw in the New Function Name text entry box.

vi. Click Define to add the new field function to the variablelist.



(b) Create a field function for NO ppm.

i. Select NOx... and Mass fraction of NO in the Field Func-tions drop-down list. Click Select to add this variable tothe field function Definition.

ii. Click the × button to introduce the multiplication sign.

iii. Select Custom Field Functions... and bulk-mw in the FieldFunctions drop-down list. Click Select to add this variableto the field function Definition.

iv. Click on / and then click on 3 and 0 to enter 30 (themolecular weight of NO).

v. Click the × button and then click on 1 and 0 to enter 10.

vi. Click on y^x and then on 6.

vii. Complete the definition of NO ppm as shown in the panelabove.

viii. Enter no-ppm in the New Function Name text entry box.

ix. Click Define to add the new field function to the variablelist.



11. Plot contours of NO ppm (Figure 11.15).


(a) Select Custom Field Functions... and no-ppm in the ContoursOf drop-down list.

(b) Click Display.

The NO ppm contours are shown in Figure 11.15. The con-tours closely resemble the mass fraction contours (Figure 11.14),as expected.

Contours of no-ppmFLUENT 6.0 (axi, segregated, spe5, ske)

Jun 05, 2001

6.80e+01

6.12e+01

5.44e+01

4.76e+01

4.08e+01

3.40e+01

2.72e+01

2.04e+01

1.36e+01

6.80e+00

6.80e-23

Figure 11.15: Contours of NO ppm: Prompt NOx Formation



Summary: In this tutorial you used FLUENT to model the transport,mixing, and reaction of chemical species. The reaction systemwas defined by using and modifying a mixture-material entry inthe FLUENT database. The procedures used here for simulationof hydrocarbon combustion can be applied to other reacting flowsystems.

This exercise illustrated the important role of the mixture heatcapacity in the prediction of flame temperature. The combustionmodeling results are summarized in the following table. (Note thatsome of the values in the table were not explicitly calculated duringthe tutorial.)

Peak Temp. Exit Temp. Exit Velocity(K) (K) (m/s)

Constant cp 2935 2150 3.75Variable cp 2231 1775 3.10

The use of a constant cp results in a significant overprediction ofthe peak temperature. The average exit temperature and velocityare also overpredicted.

While the variable cp solution produces dramatic improvements inthe predicted results, further improvements are possible by con-sidering additional models and features available in FLUENT, asdiscussed below.

The NOx production in this case was dominated by the thermalNO mechanism. This mechanism is very sensitive to temperature.Every effort should be made to ensure that the temperature solu-tion is not overpredicted, since this will lead to unrealistically highpredicted levels of NO.

Further Improvements: Further improvements can be expected byincluding the effects of intermediate species and radiation, both ofwhich will result in lower predicted combustion temperatures.

The single-step reaction process used in this tutorial cannot ac-count for the moderating effects of intermediate reaction products,



such as CO and H2. Multiple-step reactions can be used to ad-dress these species. If a multi-step Magnussen model is used, con-siderably more computational effort is required to solve for theadditional species. Where applicable, the non-premixed combus-tion model can be used to account for intermediate species at areduced computational cost. See the User’s Guide for more detailson the non-premixed combustion model.

Radiation heat transfer tends to make the temperature distributionmore uniform, thereby lowering the peak temperature. In addition,radiation heat transfer to the wall can be very significant (especiallyhere, with the wall temperature set at 300 K). The large influence ofradiation can be anticipated by computing the Boltzmann numberfor the flow:

Bo =(ρUcp)inlet

σT3AF

∼ convectionradiation

where σ is the Boltzmann constant (5.729×10−8 W/m2-K4) andTAF is the adiabatic flame temperature. For a quick estimate,assume ρ = 1 kg/m3, U = 0.5 m/s, and cp = 1000 J/kg-K (themajority of the inflow is air). Assume TAF = 2000 K. The resultingBoltzmann number is Bo = 1.09, which shows that radiation is justabout as important as convection for this problem. See the User’sGuide and Tutorial 5 for details on radiation modeling.


Tutorial 12. Using the Non-Premixed

Combustion Model

Introduction: A pulverized coal combustion simulation involves mod-eling a continuous gas phase flow field and its interaction with a dis-crete phase of coal particles. The coal particles, traveling throughthe gas, will devolatilize and undergo char combustion, creating asource of fuel for reaction in the gas phase. Reaction can be mod-eled using either the species transport model or the non-premixedcombustion model. In this tutorial you will model a simplified coalcombustion furnace using the non-premixed combustion model forthe reaction chemistry.


• Prepare a PDF table for a pulverized coal fuel using theprePDF preprocessor

• Define FLUENT inputs for non-premixed combustion chem-istry modeling

• Define a discrete second phase of coal particles

• Solve a simulation involving reacting discrete phase coal par-ticles

The non-premixed combustion model uses a modeling approachthat solves transport equations for one or two conserved scalars,the mixture fractions. Multiple chemical species, including radicalsand intermediate species, may be included in the problem defini-tion and their concentrations will be derived from the predictedmixture fraction distribution. Property data for the species areaccessed through a chemical database and turbulence-chemistryinteraction is modeled using a Beta or double-delta probabilitydensity function (PDF). See the User’s Guide for more detail onthe non-premixed combustion modeling approach.


Using the Non-Premixed Combustion Model

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT, and that you have solved Tutorial 1or its equivalent. Some steps in the setup and solution procedurewill not be shown explicitly.

Problem Description: The coal combustion system considered in thistutorial is a simple 10 m by 1 m two-dimensional duct depicted inFigure 12.1. Only half of the domain width is modeled becauseof symmetry. The inlet of the 2D duct is split into two streams.A high-speed stream near the center of the duct enters at 50 m/sand spans 0.125 m. The other stream enters at 15 m/s and spans0.375 m. Both streams are air at 1500 K. Coal particles enter thefurnace near the center of the high-speed stream with a mass flowrate of 0.1 kg/s (total flow rate in the furnace is 0.2 kg/s). The ductwall has a constant temperature of 1200 K. The Reynolds numberbased on the inlet dimension and the average inlet velocity is about100,000. Thus, the flow is turbulent.

Details regarding the coal composition and size distribution areincluded in Step 5: Models: Continuous (Gas) Phase and Step 8:Materials: Discrete Phase.



0.5 m

10 m

Symmetry Plane

Air: 50 m/s, 1500 K

Air: 15 m/s, 1500 K

0.125 m

Coal Injection: 0.1 kg/s

T = 1200 Kw

Figure 12.1: 2D Furnace with Pulverized Coal Combustion

Preparation for prePDF

1. Start prePDF.

When you use the non-premixed combustion model, you preparea PDF file with the preprocessor, prePDF. The PDF file containsinformation that relates species concentrations and temperatures tothe mixture fraction values, and is used by FLUENT to obtain thesescalars during the solution procedure.



Step 1: Define the Preliminary Adiabatic Systemin prePDF

1. Define the prePDF model type.

You can define either a single fuel stream, or a fuel stream plus asecondary stream. Enabling a secondary stream allows you to keeptrack of two mixture fractions. For coal combustion, this wouldallow you to track volatile matter (the secondary stream) separatelyfrom the char (fuel stream). In this tutorial, we will not followthis approach. Instead, we will model coal using a single mixturefraction.

Setup −→Case...

(a) Under Heat transfer options, keep the default setting of Adia-batic.

The coal combustor studied in this tutorial is a non-adiabaticsystem, with heat transfer at the combustor wall and heat



transfer to the coal particles from the gas. Therefore, a non-adiabatic combustion system must be considered in prePDF.

Because non-adiabatic calculations are more time-consumingthan those for adiabatic systems, you will start the prePDFsetup by considering the results of an adiabatic system. Bycomputing the PDF/equilibrium chemistry results for the adi-abatic system, you will determine appropriate system param-eters that will make the non-adiabatic calculation more ef-ficient. Specifically, the adiabatic calculation will provide in-formation on the peak (adiabatic) flame temperature, the stoi-chiometric mixture fraction, and the importance of individualcomponents to the chemical system. This process of begin-ning with an adiabatic system calculation should be followedin all PDF calculations that ultimately require a non-adiabaticmodel.

(b) Under Chemistry models, keep the default setting of Equilib-rium Chemistry.

In most PDF-based simulations, the Equilibrium Chemistry op-tion is recommended. The Stoichiometric Reaction (mixed isburned) option requires less computation but is generally lessaccurate. The Laminar Flamelets option offers the ability toinclude aerodynamic strain induced non-equilibrium effects,such as super-equilibrium radical concentration andsub-equilibrium temperatures. This can be important for NOx

prediction, but is excluded here.

(c) Keep the default setting of the PDF models.

The Beta PDF integration is always recommended because itis more accurate than the Delta PDF approach.

(d) Under Empirically Defined Streams, enable the Fuel stream op-tion.

This will allow you to define the fuel stream using the empir-ical input option. The empirical input option allows you todefine the composition in terms of atom fractions of H, C, N,and O, along with the lower heating value and heat capacity



of the fuel. This is a useful option when the ultimate analysisand heating value of the coal are known.

(e) Click Apply and close the panel.



2. Define the chemical species in the system.

The choice of which species to include depends on the fuel type andcombustion system. Guidelines on this selection are provided in theFLUENT User’s Guide. Here, you will assume that the equilibriumsystem consists of 13 species: C, C(s), CH4, CO, CO2, H, H2,H2O, N, N2, O, O2, and OH.

C, H, O, and N are included because the fuel stream will be de-fined in terms of these atom fractions, using the “empirical” inputmethod.

! You should include both C and C(S) in the system when theempirical input option is used.

Setup −→ Species −→Define...

(a) Set the Maximum # of Species to 13. Use the up and downarrows to set the maximum number of species, or enter thenumber in the text field followed by <ENTER>.

(b) Select the top species in the Defined Species list (initially la-beled UNDEFINED).



(c) In the Database Species drop-down list, use the slider bar toscroll the list, and select C. The Defined Species list now showsC as the first entry.

(d) Select the next species in the Defined Species list (or incrementthe Species # counter to 2).

(e) In the Database Species drop-down list, use the slider bar toscroll the list, and select the next species (C(S)).

(f) Repeat steps (d) and (e) until all 13 species are defined.

(g) Click Apply and then close the panel.

Note: In other combustion systems, you might want to include ad-ditional chemical species, but you should not add slow chemi-cal species like NOx.

3. Determine the fuel composition inputs.

The fuel considered here is known, from proximate analysis, toconsist of 28% volatiles, 64% char, and 8% ash. You will use thisinformation, along with the ultimate analysis given below, to definethe coal composition in prePDF. The fuel stream composition (charand volatiles) is derived as follows.

Begin by converting the proximate data to a dry-ash-free basis:

Proximate Analysis Wt % Wt %(dry) (DAF)

Volatiles 28 30.4Char (C(s)) 64 69.6Ash 8 -

The ultimate analysis, for the dry-ash-free coal, is known to be:

Element Wt % (DAF)C 89.3H 5.0O 3.4N 1.5S 0.8



For modeling simplicity, the sulfur content of the coal can be com-bined into the nitrogen mass fraction, to yield:

Element Wt % (DAF)C 89.3H 5.0O 3.4N 2.3S -

We can combine the proximate and ultimate analysis data to yieldthe following elemental composition of the volatile stream:

Element Wt % Moles Mole FractionC 89.3 7.44 0.581H 5.0 5 0.390O 3.4 0.21 0.016N 2.3 0.16 0.013Total 12.81

You will enter the mole fractions in the final column, above, inorder to define the fuel composition. prePDF will use this informa-tion, along with the coal heating value, to define the species presentin the fuel.

The lower heating value of coal (DAF) is known to be:

• LCVcoal,DAF = 35.3 MJ/kg

The specific heat and density of the coal are known to be 1000 J/kg-K and 1 kg/m3 respectively.



4. Enter the fuel and oxidizer compositions.

Setup −→ Species −→Composition...

(a) Enable the input of the oxidizer stream composition.

The oxidizer (air) consists of 21% O2 and 79% N2 by volume.

i. Under Stream, select Oxidiser.

ii. Under Specify Composition In, retain the default selectionof Mole Fractions.

iii. Select O2 in the Defined Species list and enter 0.21 in theSpecies Fraction field.



iv. Select N2 in the Defined Species list and enter 0.79 in theSpecies Fraction field.

(b) Enable the input of the fuel stream composition.

Note: Because the empirical input option is enabled for thefuel stream, you will be prompted to enter atom mole frac-tions for C, H, O, and N, along with the heating value andheat capacity of the coal.

i. Under Stream, select Fuel.

ii. Under Specify Composition In, retain the default selectionof Mole Fractions.



iii. Select C in the Defined Species list and enter 0.581 in theAtom Fraction field.

iv. Select H in the Defined Species list and enter 0.390 in theAtom Fraction field.

v. Select N in the Defined Species list and enter 0.016 in theAtom Fraction field.

vi. Select O in the Defined Species list and enter 0.013 in theAtom Fraction field.

vii. Enter 3.53e7 J/kg for the Lower Caloric Value and 1000J/kg-K for the Specific Heat.

viii. Click Apply and close the panel.

5. Define the density of the solid carbon.

Here, a value of 1300 kg/m3 is assumed.

Setup −→ Species −→Density...

(a) Select C(S) in the Defined Species list.

(b) Set the Density to 1300.

(c) Click Apply and close the panel.



Note: prePDF will use this information during computation of themixture density for the fuel. You should enter the density ofsolid char. This input will differ from the coal density de-fined in FLUENT, which is the apparent density of the ash-containing coal particles.

6. Define the system operating conditions.

The system pressure and inlet stream temperatures are required forthe equilibrium chemistry calculation. The fuel stream inlet temper-ature for coal combustion should be the temperature at the onset ofdevolatilization. The oxidizer inlet temperature should correspondto the air inlet temperature. In this tutorial, the coal devolatiliza-tion temperature will be set to 400 K and the air inlet temperatureis 1500 K. The system pressure is one atmosphere.

Setup −→Operating Conditions...



(a) Enter 400 K and 1500 K as the Fuel and Oxidiser inlet tem-peratures.

(b) Click Apply and close the panel.



Step 2: Compute and Review the Adiabatic Sys-tem prePDF Look-Up Tables

1. Accept the default PDF solution parameters.

Setup −→Solution Parameters...

The look-up table calculation performed by prePDF will result in atable of values for species mole fractions and temperature at a setof discrete mixture fraction values. You control the number anddistribution of these discrete points using the Solution Parameterspanel. You can also set the Fuel Rich Flamability Limit in this panel.

The Fuel Rich Flamability Limit allows you to perform a “partialequilibrium” calculation, suspending equilibrium calculations whenthe mixture fraction exceeds the specified rich limit. This increasesthe efficiency of the PDF calculation, allowing you to bypass thecomplex equilibrium calculations in the fuel-rich region, and is morephysically realistic than the assumption of full equilibrium. Forempirically defined streams, the rich limit is always 1.0 and cannotbe altered.



(a) Keep the default setting for Automatic Distribution.

This feature allows you to improve the prePDF prediction byoptimizing the distribution of the discrete mixture fraction val-ues, clustering them around the peak temperature value. If youchoose not to use the Automatic Distribution, you should setthe distribution center point on the rich side of the stoichio-metric scale mixture fraction.


2. Save your inputs (coal ad.inp).

File −→ Write −→Input...

3. Calculate the adiabatic system chemistry.

Calculate −→PDF Table

During the calculation, prePDF first retrieves thermodynamic datafrom the database. Then the time-averaged values of temperature,composition, and density at the discrete mixture-fraction/mixture-fraction-variance points (21 points as defined in the Solution Pa-rameters panel) are calculated. The result will be a set of tablescontaining time-averaged values of species mole fractions, density,and temperature at each discrete value of these two parameters.prePDF reports the progress of the look-up table construction in theconsole window.

When the calculations are complete, prePDF will warn you thatequilibrium calculations have been performed for the fuel inlet. Youcan simply acknowledge this warning, as the equilibrium conditionspredicted do not impact your modeling inputs unless the fuel streamis representing a gaseous fuel inlet.



4. Save the adiabatic PDF file (coal ad.pdf).

File −→ Write −→PDF...

(a) Under File Type, select Write Formatted File.

When you write a PDF file, prePDF will save a binary fileby default. If you are planning to use the PDF file on thesame machine, you can save the file using the default WriteBinary File option. However, if you are planning to use thePDF file on a different machine, you should save an ASCII(formatted) file from prePDF. Note that ASCII files take upmore disk space than binary files.

(b) Under Solver, select FLUENT 6.

(c) Enter coal ad.pdf as the Pdf File name.

(d) Click OK to write the file.

5. Examine the temperature/mixture-fraction relationship in the adi-abatic system.

The results of the adiabatic calculation provide insight into the sys-tem description that will be used for the non-adiabatic calculation.

Display −→PDF Table...

(a) Select TEMPERATURE from the Plot Variable list and thenclick Display to generate the table (Figure 12.2).



The temperature display shows how the time-averaged sys-tem temperature varies with the mean mixture fraction andits variance.

The temperature/mixture-fraction relationship shows that thepeak flame temperature is about 2750 K at fuel stoichiomet-ric mixture fractions of approximately 0.1. The relatively highflame temperature is a result of the high pre-heat in the com-bustion air.

Note: The adiabatic flame temperature predicted by the adi-abatic system calculation will be used to select the maxi-mum temperature in the non-adiabatic system calculation.

2.50E-01

2.00E-01

1.50E-01

1.00E-01

5.00E-02

0.00E+00

SCALED-F-VARIANCE

1.00E+00 8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E+00

TEMPERATURE K

prePDF V4.00

2.8E+03

2.4E+03

2.0E+03

1.6E+03

1.2E+03

7.6E+02

Fluent Inc.

F-MEAN

MEAN FLAME TEMPERATURE

PDF TABLE - CHEMICAL EQUILIBRIUM

Figure 12.2: Time-Averaged Temperature: Adiabatic prePDF Calcula-tion



Step 3: Create and Compute the Non-AdiabaticprePDF System

Creating a non-adiabatic PDF system description requires that you dothe following:

• Redefine the system as non-adiabatic.

• Set the peak system temperature (based on the adiabatic result of2750 K).

After these modifications, you will recompute the system chemistry andsave a non-adiabatic PDF file for use in FLUENT.



1. Define the prePDF model type as non-adiabatic.

Setup −→Case...

(a) Select Non-Adiabatic under Heat transfer options and click Ap-ply.



2. Set the system temperature limits.

Minimum and maximum temperatures in the system are requiredwhen the PDF calculation is non-adiabatic.

The minimum temperature should be a few degrees lower than thelowest boundary condition temperature (e.g., the inlet temperatureor wall temperature). In coal combustion systems, the minimumsystem temperature should also be set below the temperature atwhich the volatiles begin to evolve from the coal. Here, the va-porization temperature at which devolatilization begins will be setto 400 K. Thus, the minimum system temperature is set to 298 K(the default).

The maximum temperature should be at least 100 K higher thanthe peak flame temperature found in the preliminary adiabatic cal-culation. Here, the maximum temperature will be taken as 3000 K,well above the peak adiabatic system temperature of 2750 K.

Setup −→Operating Conditions...



(a) Enter 298 for Min. Temperature and 3000 for Max. Tempera-ture.


3. Save the non-adiabatic system inputs (coal.inp).

File −→ Write −→Input...

4. Compute the non-adiabatic PDF look-up tables.

Calculate −→PDF Table

The non-adiabatic prePDF calculation requires much more compu-tation than the adiabatic calculation. prePDF begins by accessingthe thermodynamic data from the database. Next, the enthalpy



field is initialized and the enthalpy grid adjusted to account forinlet conditions and solution parameters. Time-averaged valuesof temperature, composition, and density at the discrete mixture-fraction/mixture-fraction-variance/enthalpy points (21 points, asdefined in the Solution Parameters panel) are then calculated. Theresult will be a set of tables containing time-averaged values ofspecies mole fractions, density, and temperature at each discretevalue of these three parameters.

When the calculations are complete, prePDF will warn you thatequilibrium calculations have been performed for the fuel inlet. Asnoted above, you can simply acknowledge this warning, which hasno impact on your inputs when you are modeling coal or liquidfuels.

5. Write the PDF output file (coal.pdf).

File −→ Write −→PDF...

(a) Under File Type, select Write Formatted File.

(b) Select FLUENT 6 under Solver.

(c) Enter coal.pdf as the Pdf File name.

(d) Click OK to write the file.



6. Review one slice of the 3D look-up table prepared by prePDF.

Display −→Nonadiabatic Table...

(a) Select TEMPERATURE from the Plot Variable drop-down listand click Display (Figure 12.3).

Note: Review of the 3D look-up tables is accomplished on a slice-by-slice basis. By default, the slice selected is that correspond-ing to the adiabatic enthalpy values. This display should lookvery similar to the look-up table created during the adiabaticcalculation. You can select other slices of constant enthalpyfor display, as well.



2.50E-01

2.00E-01

1.50E-01

1.00E-01

5.00E-02

0.00E+00

SCALED-F-VARIANCE

1.00E+00 8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E+00

TEMPERATURE K

prePDF V4.00

2.8E+03

2.4E+03

2.0E+03

1.6E+03

1.2E+03

7.6E+02

Fluent Inc.

F-MEAN

MEAN FLAME TEMPERATURE FROM 3D-PDF-TABLE

MEAN ENTHALPY SLICE NUMBER 23

Figure 12.3: Non-Adiabatic Temperature Look-Up Table on the SliceCorresponding to Adiabatic Enthalpy



7. Examine the species/mixture-fraction relationship in the non-adiabaticsystem.

Display −→Nonadiabatic Table...

(a) Select SPECIES from the Plot Variable drop-down list.

The Species Selection panel will open automatically.

(b) In the Species Selection panel, select C(S) in the Species drop-down list and click OK.

(c) Click Display in the Nonadiabatic-Table panel to generate thetable (Figure 12.4).

8. Follow the steps above to plot the instantaneous mole fractions forCO (Figure 12.5).



2.50E-01

2.00E-01

1.50E-01

1.00E-01

5.00E-02

0.00E+00

SCALED-F-VARIANCE

1.00E+00 8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E+00

MOLE FRACTION

prePDF V4.00

7.6E-01

6.1E-01

4.6E-01

3.1E-01

1.5E-01

0.0E+00

Fluent Inc.

F-MEAN

SPECIES C(S) FROM 3D-PDF-TABLE


Figure 12.4: Time-Averaged C(S) Mole Fractions: Non-AdiabaticprePDF Calculation

2.50E-01

2.00E-01

1.50E-01

1.00E-01

5.00E-02

0.00E+00

SCALED-F-VARIANCE

1.00E+00 8.00E-01 6.00E-01 4.00E-01 2.00E-01 0.00E+00

MOLE FRACTION

prePDF V4.00

3.1E-01

2.4E-01

1.8E-01

1.2E-01

6.1E-02

0.0E+00

Fluent Inc.

F-MEAN

SPECIES CO FROM 3D-PDF-TABLE


Figure 12.5: Time-Averaged CO Mole Fractions: Non-Adiabatic prePDFCalculation



9. Exit from prePDF.

File −→Exit

Preparation for FLUENT Calculation

With the PDF file creation completed, you are ready to use the non-premixed combustion model in FLUENT to predict the combusting flowin the coal furnace.

1. Copy the file coal/coal.msh from the FLUENT documentation CDto your working directory (as described in Tutorial 1).

The mesh file coal.msh is a quadrilateral mesh describing the sys-tem geometry shown in Figure 12.1.




Step 4: Grid

1. Read the 2D mesh file, coal.msh.


The FLUENT console window reports that the mesh contains 1357quadrilateral cells.

2. Check the grid.

Grid −→Check

The grid check should not report any errors or negative volumes.

3. Display the grid (Figure 12.6).


Due to the grid resolution and the size of the domain, you may findit more useful to display just the outline, or to zoom in on variousportions of the grid display.

Note: You can use the mouse probe button (right button, by de-fault) to find out the boundary zone labels. As annotated inFigure 12.7, the upstream boundary contains two velocity in-lets (for the low-speed and high-speed air streams), the down-stream boundary is a pressure outlet, the top boundary is awall, and the bottom boundary is a symmetry plane.




Aug 28, 2001

Figure 12.6: 2D Coal Furnace Mesh Outline Display

wall-7

symmetry-5

velocity-inlet-8

velocity-inlet-2


Aug 28, 2001

Figure 12.7: Mesh Display with Annotated Boundary Types



Step 5: Models: Continuous (Gas) Phase

1. Accept the default segregated solver.

The non-premixed combustion model is available only with the seg-regated solver.




2. Turn on the standard k-ε turbulence model.


Note: As indicated in the problem description, the Reynolds num-ber of the flow is about 105. Thus, the flow is turbulent andthe high-Re k-ε model is suitable.



3. Turn on the non-premixed combustion model.


(a) Select Non-Premixed Combustion under Model.

The panel will expand to show the related inputs.

When you click OK, FLUENT will open the Select File dialogbox, requesting input of the PDF file to be used in the simu-lation.

(b) In the Select File dialog box, select and read the non-adiabaticPDF file (coal.pdf).

FLUENT reports in the console window that it is reading thenonadiabatic PDF file containing 13 species. It also reportsthat a new material, called pdf-mixture, has been created. Thismixture contains the 13 species that you defined in prePDF andtheir thermodynamic properties.

FLUENT will present an Information dialog box telling you thatavailable material properties have changed. You will be settingproperties later, so you can simply click OK in the dialog boxto acknowledge this information.

Note: FLUENT will automatically activate solution of the en-ergy equation when it reads the non-adiabatic PDF file, soyou do not need to visit the Energy panel to enable heattransfer.



4. Turn on radiation by selecting the P1 radiation model.

Define −→ Models −→Radiation...

The P-1 model is one of the radiation models that can account forthe exchange of radiation between gas and particulates.

After you click OK, FLUENT will present an Information dialog boxtelling you that available material properties have changed. Youwill be setting properties later, so you can simply click OK in thedialog box to acknowledge this information.



Step 6: Models: Discrete Phase

The flow of pulverized coal particles will be modeled by FLUENT using thediscrete phase model. This model predicts the trajectories of individualcoal particles, each representing a continuous stream (or mass flow) ofcoal. Heat, momentum, and mass transfer between the coal and the gaswill be included by alternately computing the discrete phase trajectoriesand the gas phase continuum equations.

1. Enable the discrete phase coupling to the continuous phase flowprediction.

Define −→ Models −→Discrete Phase...

(a) Under Interaction, turn on the Interaction with Continuous Phaseoption.

This option enables coupling, in which the discrete phase tra-jectories (along with heat and mass transfer to the particles)are allowed to impact the gas phase equations. If you leavethis option turned off, you can track particles but they willhave no impact on the continuous phase flow.



(b) Set the coupling parameter, the Number of Continuous PhaseIterations per DPM Iteration, to 20.

You should use higher values of this parameter in problemsthat include a high particle mass loading or a larger grid size.Less frequent trajectory updates can be beneficial in such prob-lems, in order to converge the gas phase equations more com-



pletely prior to repeating the trajectory calculation.

(c) Under Tracking Parameters, set the Max. Number of Steps to10000.

The limit on the number of trajectory time steps is used toabort trajectories of particles that are trapped in the domain(e.g., in a recirculation).

(d) Retain the default Length Scale of 0.01 m.

The Length Scale controls the time step size used for integra-tion of the discrete phase trajectories. The value of 0.01 mused here implies that roughly 1000 time steps will be used tocompute trajectories along the 10 m length of the domain.

(e) Under Options, turn on Particle Radiation Interaction.



2. Create the discrete phase coal injections.

The flow of the pulverized coal is defined by the initial conditionsthat describe the coal as it enters the gas. FLUENT will use theseinitial conditions as the starting point for its time integration ofthe particle equations of motion (the trajectory calculations).

Here, the total mass flow rate of coal (in the half-width of the duct)is 0.1 kg/s (per unit meter depth). The particles will be assumed toobey a Rosin-Rammler size distribution between 70 and 200 microndiameter. Other initial conditions (velocity, temperature, position)are detailed below along with the appropriate input procedures.

Define −→ Injections...

(a) Click the Create button in the Injections panel.

This will open the Set Injection Properties panel where you willdefine the initial conditions defining the flow of coal particles.



In the Set Injection Properties panel you will define the initialconditions of the flow of coal particles. The particle streamwill be defined as a group of 10 distinct initial conditions,all identical except for diameter, which will obey the Rosin-Rammler size distribution law.

(b) Select group in the Injection Type drop-down list.



(c) Set the Number of Particle Streams to 10.

These inputs tell FLUENT to represent the range of specifiedinitial conditions by 10 discrete particle streams, each with itsown set of discrete initial conditions. Here, this will result in10 discrete particle diameters, as the diameter will be variedwithin the injection group.

(d) Select Combusting under Particle Type.

By selecting Combusting you are activating the submodels forcoal devolatilization and char burnout. Similarly, selectingDroplet would enable the submodels for droplet evaporationand boiling.

(e) Select coal-mv in the Material drop-down list.

The Material list contains the combusting particle materialsin the FLUENT database. You can select an appropriate coalfrom this list and then review or modify its properties in theMaterials panel (see Step 8: Materials: Discrete Phase).

(f) Select rosin-rammler in the Diameter Distribution drop-downlist.

The coal particles have a nonuniform size distribution withdiameters ranging from 70 µm to 200 µm. The size distribu-tion fits the Rosin-Rammler equation, with a mean diameterof 134 µm and a spread parameter of 4.52.

(g) Select o2 (the default) in the Oxidizing Species drop-down list.



(h) Specify the range of initial conditions under Point Propertiesstarting with the following inputs for First Point:

• X-Position: 0.001 m

• Y-Position: 0.03124 m

• X-Velocity: 10 m/s

• Y-Velocity: 5 m/s

• Temperature = 300 K

• Total Flow Rate: 0.1 kg/s

• Min. Diameter: 70e-6 m

• Max. Diameter: 200e-6 m

• Mean Diameter: 134e-6 m

• Spread Parameter: 4.52

(i) Under Last Point, specify identical inputs for position, veloc-ity, and temperature.

(j) Define the turbulent dispersion.

i. Click on Turbulent Dispersion.

The panel will change to show the related inputs.



ii. Under Stochastic Tracking, turn on Stochastic Model.

Stochastic tracks model the effect of turbulence in the gasphase on the particle trajectories. Including stochastictracking is important in coal combustion simulations, tosimulate realistic particle dispersion.

iii. Set the Number of Tries to 10.



Note: The new injection (named injection-0, by default) nowappears in the Injections panel.

This panel can be used to copy and delete injection defini-tions. You can also select an existing injection and list theinitial conditions of particle streams defined by that injectionin the console window. The listing for the injection-0 groupwill show 10 particle streams, each with a unique diameterbetween the specified minimum and maximum value, obtainedfrom the Rosin-Rammler distribution, and a unique mass flowrate.



Step 7: Materials: Continuous Phase

All thermodynamic data including density, specific heat, and formationenthalpies are extracted from the prePDF chemical database when thenon-premixed combustion model is used. These properties are transferredto FLUENT as the pdf-mixture material, for which only transport prop-erties, such as viscosity and thermal conductivity, need to be defined.




1. Set Thermal Conductivity to 0.025 (constant).

2. Set Viscosity to 2e-5 (constant).

3. Select wsggm-cell-based in the drop-down list for the AbsorptionCoefficient.

This specifies a composition-dependent absorption coefficient, usingthe weighted-sum-of-gray-gases model. See the User’s Guide fordetails.

4. Click the Change/Create button.

Note: You can click on the View... button next to Mixture Species toview the species included in the pdf-mixture material. These are thespecies included during the system chemistry setup in prePDF. Notethat the Density and Cp laws cannot be altered: these properties arestored in the non-premixed combustion look-up tables. prePDF usesthe gas law to compute the mixture density and a mass-weightedmixing law to compute the mixture cp. Although it is possible foryou to alter the properties of the individual species, you should notdo so when the non-premixed combustion model is used. This wouldcreate an inconsistency with the look-up table created in prePDF.



Step 8: Materials: Discrete Phase


1. Select combusting-particle from the Material Type list.

The combusting-particle material type appears because you have ac-tivated combusting particles using the Set Injection Properties panel.Other discrete phase material types (droplets, inert particles) willappear in this list if you have created injections of those types.

2. Keep the current selection (coal-mv) in the Combusting Particle Ma-terials list.



This is the combusting particle material type that you selected fromthe list of database options in the Set Injection Properties panel.Additional combusting particle materials can be copied from theproperty database, if desired. You can click the Database... buttonin order to view the combusting-particle materials that are available.Here, you will simply modify the property settings for the selectedmaterial, coal-mv.

3. Set the following constant property values for the coal-mv material:

Density 1300 kg/m3

Cp 1000 J/kg-KThermal Conductivity 0.0454 w/m-kLatent Heat 0Vaporization Temperature 400 KVolatile Component Fraction (%) 28Binary Diffusivity 5e-4 m2/sParticle Emissivity 0.9Particle Scattering Factor 0.6Swelling Coefficient 2Burnout Stoichiometric Ratio 2.67Combustible Fraction (%) 64

FLUENT uses these inputs as follows:

• Density impacts the particle inertia and body forces (when thegravitational acceleration is non-zero).

• Cp determines the heat required to change the particle temper-ature.

• Latent Heat is the heat required to vaporize the volatiles. Thiscan usually be set to zero when the non-premixed combustionmodel is used for coal combustion. If the volatile compositionhas been selected in order to preserve the heating value of thefuel, the latent heat has been effectively included. (You would,however, use a non-zero latent heat if water content had beenincluded in the volatile definition as vapor phase H2O.)



• Vaporization Temperature is the temperature at which the coaldevolatilization begins. It should be set equal to the fuel inlettemperature used in prePDF.

• Volatile Component Fraction determines the mass of each coalparticle that is devolatilized.

• Binary Diffusivity is the diffusivity of oxidant to the particlesurface and is used in the diffusion-limited char burnout rate.

• Particle Emissivity is the emissivity of the particles. It is usedto compute radiation heat transfer to the particles.

• Particle Scattering Factor is the scattering factor due to parti-cles.

• Swelling Coefficient determines the change in diameter duringcoal devolatilization. A swelling coefficient of 2 implies thatthe particle size will double as the volatile fraction is released.

• Burnout Stoichiometric Ratio is used in the calculation of thediffusion-controlled burnout rate. Otherwise, this parameterhas no impact when the non-premixed combustion model isused. When finite-rate chemistry is used instead, the stoichio-metric ratio defines the mass of oxidant required per mass ofchar. The default value represents oxidation of C(s) to CO2.

• Combustible Fraction is the mass fraction of char in the coalparticle. It determines the mass of each coal particle that isconsumed by the char burnout submodel.

! The settings for the Vaporization Temperature, Combustible Frac-tion, and Volatile Component Fraction inputs should all beconsistent with your prePDF inputs. (See Step 1: Define thePreliminary Adiabatic System in prePDF.)



4. Select the Single Rate Devolatilization Model for DevolatilizationModel.

(a) Select the single-rate option in the Devolatilization Model drop-down list.

This opens the Single Rate Devolatilization Model panel.

(b) Accept the default devolatilization model parameters.

5. Select kinetics/diffusion-limited for the Combustion Model.

(a) Select the kinetic/diffusion-limited option in the CombustionModel drop-down list.

This opens the Kinetics/Diffusion Limited Combustion Modelpanel.

(b) Accept the default values.

6. Click Change/Create and then close the Materials panel.





Hint: You can click your mouse probe button (the right button, by de-fault) on the desired boundary zone in the graphics display window.FLUENT will then select that zone in the Boundary Conditions panel.

1. Set the following conditions for the velocity-inlet-2 zone (the low-speed inlet boundary).

Note: Turbulence parameters are defined here based on intensityand hydraulic diameter. The relatively large turbulence in-tensity of 10% may be typical for combustion air flows. Thehydraulic diameter has been set to twice the height of the 2Dinlet stream.

For the non-premixed combustion calculation, you need to de-fine the inlet Mean Mixture Fraction and Mixture Fraction Vari-ance. For coal combustion, all fuel comes from the discretephase and thus the gas phase inlets have zero mixture frac-tion. Therefore, you can accept the zero default settings.



2. Set the following conditions for the velocity-inlet-8 zone (the high-speed inlet boundary).



3. Set the following conditions for the pressure-outlet-6 zone (the exitboundary).

The exit gauge pressure of zero simply defines the system pressureat the exit to be the operating pressure. The backflow conditionsfor scalars (temperature, mixture fraction, turbulence parameters)will be used only if flow is entrained into the domain through theexit. It is a good idea to use reasonable values in case flow reversaloccurs at the exit at some point during the solution process.



4. Set conditions for the wall-7 zone (the furnace wall).

The furnace wall will be treated as an isothermal boundary with atemperature of 1200 K.

(a) Under Thermal Conditions, select Temperature.

(b) Enter 1200 in the Temperature field.

Note: The default boundary condition for particles that hit thewall is reflect, as shown under DPM. Alternate treatmentscan be selected, using the BC Type list, for particles that hitthe wall.



Step 10: Solution

1. Set the P1 under-relaxation factor to 1.


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


(a) Select velocity-inlet-2 in the Compute From list.

(b) Click the Init button to initialize the flow field, and then closethe panel.

! The Apply button does not initialize the flow field data. Youmust use the Init button. (Apply simply allows you to storeyour initialization parameters for later use.)

Note: Here, with very high pre-heat of the oxidizer stream, youcan start the combustion calculation from the inlet-based ini-tialization. In general, you may need to start your coal com-bustion calculations by patching a high-temperature region and



performing a discrete phase trajectory calculation. This pro-vides the initial volatile and char release required to initiatecombustion. The Solve/Initialize/Patch... menu item and thesolve/dpm-update text command can be used to perform thisinitialization.

3. Enable the display of residuals during the solution process.


4. Save the case file (coal.cas).


5. Begin the calculation by requesting 400 iterations.


Note: The default convergence criteria will be met in about 170iterations.

6. Save the converged flow data (coal.dat).

File −→ Write −→Data...




1. Display the predicted temperature field (Figure 12.8).


The peak temperature in the system is about 2260 K.

Hint: Use the Views panel (Display/Views...) to mirror the displayabout the symmetry plane.



Contours of Static Temperature (k)FLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

2.26e+03

2.16e+03

2.05e+03

1.94e+03

1.84e+03

1.73e+03

1.63e+03

1.52e+03

1.41e+03

1.31e+03

1.20e+03

Figure 12.8: Temperature Contours



2. Display the Mean Mixture Fraction distribution (Figure 12.9).


The mixture-fraction distribution shows where the char and volatilesreleased from the coal exist in the gas phase.



Contours of Mean Mixture FractionFLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

3.72e-02

3.35e-02

2.98e-02

2.61e-02

2.23e-02

1.86e-02

1.49e-02

1.12e-02

7.45e-03

3.72e-03

0.00e+00

Figure 12.9: Mixture-Fraction Distribution



3. Display the devolatilization rate (Figure 12.10).


(a) Select Discrete Phase Model... and DPM Evaporation/Devola-tilization in the drop-down lists under Contours Of.

4. Display the char burnout rate (Figure 12.11) by selecting DPMBurnout from the lower drop-down list.

Note: The display of devolatilization rate shows that volatiles arereleased after the coal travels about one eighth of the fur-nace length. (The onset of devolatilization occurs when thecoal temperature reaches the specified value of 400 K.) Thechar burnout occurs following complete devolatilization. Fig-ure 12.11 shows that burnout is complete at about three-quartersof the furnace.



Contours of DPM Evaporation/Devolatilization (kg/s)FLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

2.95e-03

2.66e-03

2.36e-03

2.07e-03

1.77e-03

1.48e-03

1.18e-03

8.86e-04

5.90e-04

2.95e-04

0.00e+00

Figure 12.10: Devolatilization Rate

Contours of DPM Burnout (kg/s)FLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

4.42e-04

3.97e-04

3.53e-04

3.09e-04

2.65e-04

2.21e-04

1.77e-04

1.32e-04

8.83e-05

4.42e-05

0.00e+00

Figure 12.11: Char Burnout Rate



5. Display the particle trajectory of one particle stream (Figure 12.12).

Display −→Particle Tracks...

(a) Select injection-0 in the Release From Injections list.

(b) Select Particle Residence Time in the Color By drop-down list.

(c) Turn on Track Single Particle Stream and set the Stream ID to5.

(d) Click Display.



Particle Traces Colored by Particle Residence Time (s)FLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

3.63e-01

3.27e-01

2.90e-01

2.54e-01

2.18e-01

1.81e-01

1.45e-01

1.09e-01

7.26e-02

3.63e-02

0.00e+00

Figure 12.12: Trajectories of Particle Stream 5 Colored by Particle Res-idence Time



6. Display the oxygen distribution (Figure 12.13).


Note: Although transport equations are solved only for the mixturefraction and its variance, you can still display the predictedchemical species concentrations. These are predicted by thePDF equilibrium chemistry model.

7. Select other species and display their mass fraction distributions(e.g., Figures 12.14–12.16).



Contours of Mass fraction of o2FLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

2.33e-01

2.22e-01

2.11e-01

2.00e-01

1.89e-01

1.78e-01

1.67e-01

1.56e-01

1.45e-01

1.34e-01

1.23e-01

Figure 12.13: O2 Distribution

Contours of Mass fraction of co2FLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

1.19e-01

1.07e-01

9.54e-02

8.35e-02

7.15e-02

5.96e-02

4.77e-02

3.58e-02

2.38e-02

1.19e-02

0.00e+00

Figure 12.14: CO2 Distribution



Contours of Mass fraction of h2oFLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

1.60e-02

1.44e-02

1.28e-02

1.12e-02

9.62e-03

8.02e-03

6.42e-03

4.81e-03

3.21e-03

1.60e-03

0.00e+00

Figure 12.15: H2O Distribution

Contours of Mass fraction of coFLUENT 6.0 (2d, segregated, pdf13, ske)

Sep 10, 2001

6.99e-03

6.29e-03

5.59e-03

4.89e-03

4.19e-03

3.49e-03

2.79e-03

2.10e-03

1.40e-03

6.99e-04

0.00e+00

Figure 12.16: CO Distribution



Step 12: Energy Balances and Particle Report-ing

FLUENT can provide many useful reports, including overall energy ac-counting and detailed information regarding heat and mass transfer fromthe discrete phase. Here, you will examine these reports.

1. Compute the fluxes of heat through the domain boundaries.

Report −→Fluxes...

(a) Select Total Heat Transfer Rate under Options.

(b) Under Boundaries, select the pressure-outlet-6, velocity-inlet-2,velocity-inlet-8, and wall-7 zones.

(c) Click Compute.

Note: Positive flux reports indicate heat addition to the domain.Negative values indicate heat leaving the domain. In reactingflows, the heat report uses total enthalpy (sensible heat plus



heat of formation of the chemical species). Here, the net “im-balance” of total enthalpy (about 14 KW) represents the totalenthalpy addition from the discrete phase.

2. Compute the volume sources of heat transferred between the gasand discrete particle phase.

Report −→Volume Integrals...

(a) Select Sum under Options.

(b) Select Discrete Phase Model... and DPM Enthalpy Source inthe drop-down lists under Field Variable.

(c) Select fluid-1 under Cell Zones.

(d) Click Compute.

The total enthalpy transfer to the discrete phase from the gas isabout -13.2 KW, as expected based on the boundary flux reportabove. This represents the total enthalpy addition from the discretephase to the gas during the devolatilization and char combustionprocesses.



3. Obtain a summary report on the particle trajectories.

The discrete phase model summary report provides detailed infor-mation about the particle residence time, heat and mass transferbetween the continuous and discrete phases, and (for combustingparticles) char conversion and volatile yield.


(a) Select Summary under Report Type.

(b) Select injection-0.

(c) Click Track.

FLUENT will report the summary in the console window. (Youcan write the report to a file by selecting File under Report to.

(d) Review the summary printed in the console window:



DPM Iteration ....

number tracked = 100, escaped = 0, aborted = 0, trapped = 0, evaporated = 0, incomp

Fate Number Elapsed Time (s) Inj

Min Max Avg Std Dev

---- ------ ---------- ---------- ---------- ---------- -------

Incomplete 100 2.398e-01 4.653e-01 3.096e-01 4.818e-02 inj

(*)- Mass Transfer Summary -(*)

Fate Mass Flow (kg/s)

Initial Final Change

---- ---------- ---------- ----------

Incomplete 1.000e-01 8.005e-03 -9.200e-02

(*)- Energy Transfer Summary -(*)

Fate Heat Content (W)

Initial Final Change

---- ---------- ---------- ----------

Incomplete -3.712e+03 9.532e+03 1.324e+04

(*)- Combusting Particles -(*)

Fate Volatile Content (kg/s) Char Content (kg/s)

Initial Final %Conv Initial Final %Con

---- ---------- ---------- ------- ---------- ---------- ------

Incomplete 2.800e-02 0.000e+00 100.00 6.400e-02 5.351e-06 99.9

Done.

The report shows that the average residence time of the coal parti-cles is about 0.33 seconds. Volatiles are completely released withinthe domain and the char conversion is 100% .

Extra: You can obtain a detailed report of the particle position, velocity,diameter, and temperature along the trajectories of individual par-ticles. This type of detailed track reporting can be useful if you aretrying to understand unusual or important details in the discretemodel behavior. To generate the report, visit the Particle Trackspanel. Select Step By Step under Report Type, and File under Re-port to. Enable the Track Single Particle Stream option, and set theStream ID to the desired particle stream. Clicking Track will bring



up the Select File dialog box, where you will enter the name of thefile to be written. This file can then be viewed with a text editor.

Summary: Coal combustion modeling involves the prediction of volatileevolution and char burnout from the pulverized coal along withsimulation of the combustion chemistry occuring in the gas phase.In this tutorial you learned how to use the non-premixed combus-tion model to represent the gas phase combustion chemistry. Inthis approach the fuel composition was defined in prePDF and thefuel was assumed to react according to the equilibrium system data.This equilibrium chemistry model can be applied to other turbu-lent, diffusion-reaction systems. Note that you can also model coalcombustion using the finite-rate chemistry model.

You also learned how to set up and solve a problem involving adiscrete phase of combusting particles. You created discrete phaseinjections, activated coupling to the gas phase, and defined thediscrete phase material properties. These procedures can be usedto set up other simulations involving reacting or inert particles.


Tutorial 13. Modeling Surface

Chemistry

Introduction: In chemically reacting laminar flows, such as those en-countered in chemical vapor deposition (CVD) applications, accu-rate modeling of time-dependent hydrodynamics, heat and masstransfer, and chemical reactions (including wall surface reactions)is important. Tutorials 11 and 12 deal with reacting flows withapplications in gaseous fuel and coal combustion. In this tutorial,surface reactions are considered.

In this tutorial, you will learn how to:

• Enable physical models, select material properties, and defineboundary conditions for a chemically reacting laminar flowinvolving wall surface reactions.

• Read a user-defined function into FLUENT and use the file todefine a parabolic velocity profile

• Set temperature-dependent thermal conductivity in solids

• Calculate the deposition solution using the segregated solver

• Examine the flow results using graphics

• Compare results for a single-step surface deposition reactionand a three-reaction mechanism

Prerequisites: This tutorial assumes that you are familiar with theFLUENT user interface, and that you have solved Tutorial 1. Somesteps in the setup and solution procedure will not be shown explic-itly.

Before beginning, you should read Sections 13.1 and 13.2 in theUser’s Guide. Section 13.1 deals with species transport and chem-ically reacting flows. In particular, you should be familiar with


Modeling Surface Chemistry

the Arrhenius rate equation as this equation is used for both thegas phase and surface reactions modeled in this tutorial. Section13.2 describes wall surface reaction modeling and chemical vapordeposition (CVD).

Problem Description: The laminar horizontal CVD reactor shown inFigure 13.1 will be modeled.

2

.5

3.5

.5

INLET OUTLET

QuartzSusceptor

Top wall – cooled

Quartz

15105

(All dimensions in centimeters.)

2

Figure 13.1: An Outline of the Reactor Configuration

The inlet gas is a mixture of silane SiH4(g) and hydrogen H2(g)at a temperature of 300 K. It enters the reactor through the inletat the left end and flows for 5 cm between quartz walls that areseparated by 2 cm. The gas mixture then flows over the heatedsubstrate and silicon Si(s) is deposited on the heated susceptor asgoverned by the following gas phase and surface reactions:

Reaction 1 (gas): SiH4(g) → SiH2(g) + H2(g)Reaction 2 (surface): SiH4(g) → Si(s) + 2H2(g)Reaction 3 (surface): SiH2(g) → Si(s) + H2(g)

As mentioned earlier, the inlet gas is a mixture of silane and hy-drogen. In the inlet mixture the mass fraction of SiH4 is 0.0157and the remainder is H2. The inlet velocity is parabolic with zerovelocity at the wall and an average velocity of 17.5 cm/sec, andthe Reynolds number is approximately 60. The top wall is cooledto 300 K, and the susceptor is heated to a uniform temperature of1300 K.



This tutorial has been divided into two parts. In the first case tobe analyzed, a single-step surface deposition reaction is simulatedand deposition of silicon from silane is examined. This involvesdeposition on a heated substrate, and only Reaction 2 is modeled.The deposition reaction is diffusion controlled: any silane that dif-fuses to solid surfaces will react and deposit silicon. The lowerquartz walls are treated as thermally conducting walls. The ex-terior edges of the quartz walls are modeled as insulated (that is,zero-heat-flux) walls. Heat will be transferred into these quartzwalls from the edges in contact with the heated susceptor, and theheat conducted from the susceptor is eventually transferred to thegas mixture through the interior faces of the lower quartz walls.

The second part deals with the complete three-reaction mechanism.The mass diffusivity of SiH2 is determined from kinetic theory.



Preparation

1. Copy the files cvd/cvd.msh and cvd/inlet.c from the FLUENTdocumentation CD to your working directory (as described in Tu-torial 1).

A user-defined function will be used to define the parabolic inletvelocity. This function has already been written (inlet.c). Youwill only need to compile it within FLUENT.


Step 1: Grid

1. Read in the mesh file cvd.msh.


As FLUENT reads the grid file, it will report that several wall zonesare being separated. In the original grid, a single wall zone wasused as the external boundary of the quartz regions and the internalboundary between the quartz and the fluid. FLUENT splits up theinitial wall zone, placing the internal and external boundaries inseparate zones.

Note: If a wall zone has a fluid or solid region on each side, it iscalled a “two-sided wall”. When you read a grid with this typeof wall zone into FLUENT a “shadow” zone is automaticallycreated so that each side of the wall is a distinct wall zone. Inthis tutorial, FLUENT gives a message in the console windowto inform you that it is creating a shadow wall (wall-24:005-shadow). This is coupled to wall-24:005.



2. Check the grid.

Grid −→Check

Note: The grid check lists the minimum and maximum x and yvalues from the grid, and reports on a number of other gridfeatures that are checked. Any errors in the grid would bereported at this time. For instance, the cell volumes mustnever be negative. Note that the domain extents are reportedin units of meters, the default unit of length in FLUENT. Sincethis grid was created in units of centimeters, the Scale Gridpanel will be used to scale the grid into meters.

3. Scale the grid.

Grid −→Scale...

(a) In the Units Conversion drop-down list, select cm to completethe phrase Grid Was Created In cm (centimeters).

(b) Click on Scale to scale the grid.

The final Domain Extents should appear as in the panel above.

Note: Because the default SI units will be used in this tutorial,there is no need to change any units.





Extra: You can use the right mouse button to check which zonenumber corresponds to each boundary. If you click the rightmouse button on one of the boundaries in the graphics window,its name and type will be printed in the FLUENT console win-dow. This feature is especially useful when you have severalzones of the same type and you want to distinguish betweenthem quickly.




Jun 06, 2001

Figure 13.2: Grid Display



Step 2: Models

In this problem, the energy equation and the species conservation equa-tions will be solved, along with the momentum and continuity equations.

1. Keep the default solver settings.








(a) Under Model, select Species Transport.

This will expand the Species Model panel.

(b) Under Reactions, select Volumetric.

The panel will expand further.

(c) Under Reactions, select Wall Surface.

The panel will expand again.



(d) Under Wall Surface Reaction Options, select Heat of SurfaceReactions and Mass Deposition Source.

Turning on the Heat of Surface Reactions option enables mod-eling of heat release due to surface reactions. Mass DepositionSource is selected because there is a certain loss of mass dueto the surface deposition reaction, i.e., Si(s) is being depositedout. If you were to do an overall mass balance without takingthis fact into account, you would end up with a slight imbal-ance.

(e) Keep the Diffusion Energy Source option turned on.

Note: This includes the effect of enthalpy transport due tospecies diffusion in the energy equation, which contributesto the energy balance, especially for the case of Lewisnumbers far from unity.

(f) In the Mixture Material drop-down list, select silane-hydrogen(near the bottom).

FLUENT will report the Number of Volumetric Species to be 2,and the Number of Surface Species to be 1.

Note: In the first part of this tutorial, a one-step reaction isconsidered. Later, a three-step reaction will be considered.

(g) Click OK.

The console window will list the properties that are required forthe models that you have enabled. You will see an Informationdialog box, reminding you to confirm the property values thathave been extracted from the database.



(h) Click OK in the Information dialog box to continue.

Step 3: Materials


The Materials panel shows the mixture material, silane-hydrogen, thatwas enabled in the Species Model panel. The properties for this mixturematerial are stored in the FLUENT database and can be modified by you.



Here, you will modify the default settings for the mixture by selecting themixing-law model for cp.

Density will be computed using the incompressible ideal-gas law, assum-ing an operating pressure of one atmosphere (1.0132 × 105 Pa, the de-fault). Viscosity and thermal conductivity are predefined as polynomialfunctions of temperature, given by the following equations:

µ = 3.17 × 10−6 + 2.04 × 10−8T − 3.52 × 10−12T 2 (13.1)

k = 3.8× 10−2 + 5.41× 10−4T − 2.51× 10−7T 2 + 8.57× 10−11T 3 (13.2)

These properties are those of pure H2 and can be used here because ofthe low concentration of SiH4.

1. Define the material properties for the silane-hydrogen mixture.

(a) Under Properties, click the Edit... button to the right of Mix-ture Species.

This will open the Species panel.



In general, you can add or remove species from the mixturematerial. Here, the species that make up the silane-hydrogenmixture are predefined and require no modification.

(b) Click Cancel to close the panel without making any changes.

(c) In the Materials panel, select mixing-law in the Cp drop-downlist.

This instructs FLUENT to compute the mixture’s specific heatcapacity as a mass fraction average of the pure species heatcapacities. (The properties of these individual species will bereviewed in a later step.)

(d) Click Change/Create.

This will accept the material property settings for the mixture.

(e) Under Properties, click the Edit... button to the right of Re-action.

This will open the Reactions panel.



The panel shows that the Total Number of Reactions is 1, theNumber of Reactants is 1, and the Number of Products is 2.The stoichiometric coefficients for the reaction are also shown,along with the values of Pre-exponential Factor Ak, ActivationEnergy Ek and Temperature Exponent βk used in the ArrheniusRate equation.

(f) Click Cancel to close the panel without making any changes.



2. Review the properties of the constituent species in the mixture.

(a) In the Materials panel, select fluid in the Material Type drop-down list.

(b) In the Fluid Materials drop-down list, select silane (sih4) orhydrogen (h2) to view its individual properties.



3. Define the material properties for the quartz wall.

The lower quartz wall is a conducting wall, with its thermal con-ductivity defined as a second-order polynomial given by

k = 1.692 − 0.00193T + 3.196 × 10−6T 2 (13.3)

(a) In the Material Type drop-down list, select solid.

(b) Enter quartz in the Name text entry box.

(c) Delete the name al in the Chemical Formula text entry box.



(d) Under Properties, select polynomial in the Thermal Conductivitydrop-down list.

This will open the Polynomial Profile panel.

(e) Increase the number of Coefficients to 3.

This will activate the coefficient text entry fields.

(f) Input the values for Coefficients 1, 2, 3, as shown in the panelabove.

(g) Click OK.

(h) Answer No when FLUENT asks if it is OK to overwrite alu-minum.

FLUENT will create the new material, quartz, leaving alu-minum unchanged.

Note: The values of Density and Cp for quartz are left as thedefault values, since these values will not be used in anycalculations.

(i) In the Materials panel, click Change/Create and Close the panel.

This will accept the material property settings for the solidmaterial.





1. Keep the default settings for fluid-1.

The material for the fluid zone was set to silane-hydrogen whensilane-hydrogen was selected as the mixture material in the SpeciesModel panel. You cannot change the material in the Fluid panelwhen you are modeling species transport or reactions.

2. Set the conditions for solid-2.

(a) In the Material Name drop-down list, select quartz.



3. Set the boundary conditions for the top wall of the domain (wall-10).

(a) Change the Zone Name from wall-10 to top-wall.

(b) Under Thermal Conditions, select Temperature and keep thedefault setting of 300 K.



4. Set the boundary conditions for the top of the susceptor (wall-20).

(a) Change the Zone Name from wall-20 to susceptor.

(b) Under Thermal Conditions, select Temperature.

(c) Set the Temperature to 1300 K.

(d) Click the Species tab to view the conditions for species trans-port and reactions.



(e) Turn on the Surface Reactions option.



5. Set the boundary conditions for the side of the susceptor (wall-24:003).

(a) Change the Zone Name from wall-24:003 to susceptor-side.

(b) Under Thermal Conditions, select Temperature.

(c) Set the Temperature to 1300 K.

(d) In the Species section of the panel, turn on the Surface Reac-tions option.

6. Set the boundary conditions for the outer wall of the quartz region(wall-24).

(a) Change the Zone Name from wall-24 to outer-quartz-wall.

(b) Keep the default setting of 0 for Heat Flux.

(c) In the Material Name drop-down list, select quartz.



7. Set the conditions for the boundary between the quartz and fluidregions (wall-24:005).

(a) Change the Zone Name from wall-24:005 to quartz-fluid-boundary.

(b) Under Thermal Conditions, keep the default setting of Coupled.

(c) In the Material Name drop-down list, select quartz.

8. Set the boundary conditions for wall-24:005-shadow.

The boundary conditions are already set for wall-24:005-shadow,because it is coupled to wall-24:005 (renamed quartz-fluid-boundary).



It just needs to be given a more meaningful name.

(a) Change the Zone Name from wall-24:005-shadow toquartz-fluid-boundary-shadow.

9. Define the conditions for the flow inlet (velocity-inlet-4).

The u velocity at the inlet is defined as a parabolic profile in the ydirection. The fully developed parabolic velocity profile for a two-dimensional parallel plate duct is described by the following equa-tion:

u

Um=

32

(1 −

(y

a

)2)

(13.4)

whereu = local velocity in the x direction (m/s)Um = mean velocity (m/s)y = y coordinate measured from the center of the duct (m)a = half-height of the duct (m)

In this case, Um is given as 0.175 m/s and a is 0.01 m.

To use the polynomial fit for the u velocity, it is necessary to trans-form the y coordinate to the FLUENT global coordinate system, andto substitute the actual values of a and Um in Equation 13.4. Sincethe centerline of the duct is located at yFL = 0.03, the following re-lationship exists:

y = yFL − 0.03 (13.5)

Substituting these values of y, a, and Um into the definition of afully developed velocity profile, the polynomial equation required forFLUENT is obtained:

u = −2.1 + 157.5yFL − 2625y2FL (13.6)

A user-defined function (inlet.c) has been written to define thepolynomial equation (Equation 13.6) required for the parabolic ve-locity profile.



Note: See the separate UDF Manual for details about user-definedfunctions.

(a) Read in the user-defined function.

Define −→ User-Defined −→ Functions −→Interpreted...

i. Enter inlet.c as the Source File Name.

ii. Click Compile.

The user-defined function has already been defined, but itneeds to be compiled within FLUENT before it can be usedin the solver.

iii. Close the Interpreted UDFs panel.



(b) Set the boundary conditions for velocity-inlet-4.

i. In the Velocity Specification Method drop-down list, selectComponents.

ii. Select udf inlet uv parabolic (the user-defined function) inthe X-Velocity drop-down list.

iii. Keep the default temperature of 300 K.

iv. Under Species Mass Fractions, enter 0.0157 for sih4.



10. For the flow outlet (pressure-outlet-11), keep the default value ofzero for the Species Mass Fraction.



Step 5: Solution for Single-Reaction Case

1. Initialize the flow field using the boundary conditions set at velocity-inlet-4.


(a) Select velocity-inlet-4 in the Compute From drop-down list.

(b) Click Init, and Close the panel.





(a) Select Plot under Options, and click OK.

3. Save the case file (cvd.cas).







During the first few iterations, the console window will report re-versed flow on pressure-outlet 11. This is normal, and is related tothe iterative process and the value of the pressure field during thatiteration. Eventually, you will have all the flow leaving the domain.

5. Save the case and data files (cvd1.cas and cvd1.dat).




Step 6: Postprocessing for Single-Reaction Case



(a) Click Display.



Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, spe2, lam)

Jun 06, 2001

6.33e-01

5.70e-01

5.07e-01

4.44e-01

3.81e-01

3.18e-01

2.55e-01

1.93e-01

1.30e-01

6.67e-02

3.72e-03

Figure 13.3: Velocity Vectors for the One-Reaction Case

The magnitude of the velocity increases as the gas flows over theheated substrate. Since the density of the gas decreases with in-creasing temperature, the velocity increases so as to conserve themass flow rate. A small recirculation zone is also seen downstreamof the susceptor.



2. Display contours of temperature (Figure 13.4).



(b) Click Display.



Contours of Static Temperature (k)FLUENT 6.0 (2d, segregated, spe2, lam)

Jun 06, 2001

1.30e+03

1.20e+03

1.10e+03

1.00e+03

9.00e+02

8.00e+02

7.00e+02

6.00e+02

5.00e+02

4.00e+02

3.00e+02

Figure 13.4: Temperature Contours for the One-Reaction Case

The temperature contours show that the heat conduction into thequartz wall heats the gas mixture upstream of the susceptor.



3. Display contours of silane mass fraction (Figure 13.5).


(a) Select Species... and Mass fraction of sih4 in the Contours Ofdrop-down list.

(b) Click Display.

Contours of Mass fraction of sih4FLUENT 6.0 (2d, segregated, spe2, lam)

Jun 06, 2001

1.57e-02

1.41e-02

1.26e-02

1.10e-02

9.43e-03

7.86e-03

6.29e-03

4.72e-03

3.16e-03

1.59e-03

2.07e-05

Figure 13.5: Contours of SiH4 Mass Fraction for the One-Reaction Case

Figure 13.5 shows that the mass fraction gradient is large wherethe deposition reaction begins. The mass fraction of SiH4 near thesusceptor is very small since the reaction is very fast and diffusion-controlled. The mass fraction gradient of SiH4 above the susceptordrives the diffusion of SiH4 from above the susceptor to the surfacewhere the reaction occurs.



4. Plot the surface deposition rate of Si on the susceptor (Figure 13.6).

Plot −→XY Plot...

(a) Select Species... and Surface Deposition Rate of si<s> in theY Axis Function drop-down list.

(b) Under Options, deselect Node Values.

The source/sink terms due to the surface reaction are de-posited in the cell adjacent to the wall cells, so it is necessaryto plot the cell values and not the node values.

(c) In the Surfaces list, select susceptor.

(d) Click Plot.



Surface Deposition Rate of si<s>FLUENT 6.0 (2d, segregated, spe2, lam)

Jun 06, 2001

Position (m)

si<s>of

RateDeposition

Surface

0.150.140.130.120.110.10.090.080.070.060.05

4.50e-05

4.00e-05

3.50e-05

3.00e-05

2.50e-05

2.00e-05

1.50e-05

1.00e-05

susceptor

Figure 13.6: Surface Deposition Rate of Si

The peak of the surface deposition rate occurs at the beginningof the susceptor (where the concentration of SiH4 is highest).

The increase in deposition rate at the right-hand side of thesusceptor is related to the backward-facing step in this prob-lem.



(e) Write the deposition rate data to a file.

You can read this file into FLUENT at a later time to recreatethis plot. You will do this later in the tutorial to compare thedeposition rates for the one-reaction and three-reaction cases.

i. In the Solution XY Plot panel, select Write to File underOptions.

The Plot button will become the Write... button.

ii. Click on the Write... button.

This will open the Select File dialog box.

iii. In the XY File text entry box, enter one reac.xy andclick OK.



Step 7: Solution for Three-Step Reaction Case

The single-step surface reaction will now be replaced by the followingthree-step reaction mechanism:

SiH4(g) → SiH2(g) + H2(g)SiH4(g) → Si(s) + 2H2(g)SiH2(g) → Si(s) + H2(g)

The first reaction is a gas phase reaction which breaks SiH4 into SiH2.The surface deposition of Si(s) takes place in the two separate surfacereactions listed above. The reaction rates (as defined in Jasinski andChilds [1]) are as follows:

Reaction (k) Phase Ak Ek ν′j′ ,k βk

1 g 2.115×1015 2.590 ×108 1.0 0.02 s 3.340×10−1 7.815 ×107 1.0 0.53 s 1.000×1015 1.000 ×102 1.0 0.0

Since the current model has SiH2 added to the gas mixture, the massdiffusivity of SiH2 in hydrogen needs to be determined. Kinetic theorywill be used to model this process.

1. Copy the material for the three-reaction mechanism from the ma-terials database, and modify its properties.


(a) Click on Database... to open the Database Materials panel.



(b) In the Mixture Materials list, select silane-hydrogen-3-step.

The properties of this mixture will be displayed.

(c) Click the View... button to the right of Mixture Species toview the selected species.

(d) Click the View... button to the right of Reaction to view thedefined reactions.

The different reactions can be viewed by changing the ReactionID in the top left corner of the Reactions panel.

(e) In the Database Materials panel, click Copy and then Close thepanel.



The properties will be down-loaded from the database into yourFLUENT case. Your own copy of the mixture’s properties willnow be displayed in the Materials panel, where you can modifythem.

(f) In the Materials panel, select mixing-law in the Cp drop-downlist.

(g) In the Mass Diffusivity drop-down list, select kinetic-theory .

Hint: You will need to scroll down to see Mass Diffusivity.

(h) Click Change/Create, and Close the Materials panel.



2. Select the three-step reaction for the species transport calculation.


(a) In the Mixture Material drop-down list, select silane-hydrogen-3-step.

(b) Under Wall Surface Reaction Options, turn off the Heat of Sur-face Reactions and Mass Deposition Source.

Turning off these effects temporarily makes the solution pro-cess more stable at the start of the calculation.

(c) Click OK to accept the updated model.



! When you changed the mixture material by addingspecies, the order of the species changed. When this oc-curs, all boundary conditions, solver parameters, and so-lution data for species will be reset to the default values.You must redefine species boundary conditions and solu-tion parameters for the newly defined problem.

3. Review the boundary conditions for the flow inlet (velocity-inlet-4).


Check to see that these are the same as those set in Step 4:Boundary Conditions, Part 9.

4. Re-initialize the flow field.


! Since the order of the species has been changed, the originaldata file now has incorrect data for the species. It is thereforerecommended that you re-initialize the flow field by reselectingthe conditions at velocity-inlet-4 as the initial conditions.


(b) Click Init, and then Close the panel.

5. Save the case file (cvd2.cas).


6. Request 20 iterations.


7. Add the effects of surface reactions and the deposition source inthe continuity equation.


(a) Under Wall Surface Reaction Options, turn on the Heat of Sur-face Reactions and Mass Deposition Source options.

8. Request another 20 iterations.


The solution converges in a total of about 30 iterations.



9. Save the case and data files (cvd3.cas and cvd3.dat).


Step 8: Postprocessing for Three-Step ReactionCase



The flow pattern looks very similar to that observed in Figure 13.3,for the single-step reaction.

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (2d, segregated, spe3, lam)

Jun 06, 2001

6.33e-01

5.70e-01

5.07e-01

4.44e-01

3.81e-01

3.18e-01

2.55e-01

1.92e-01

1.30e-01

6.67e-02

3.78e-03

Figure 13.7: Velocity Vectors for the Three-Step Reaction



2. Display contours of temperature (Figure 13.8).


The temperature contours look very similar to those shown in Fig-ure 13.4, for the single-step reaction.

Contours of Static Temperature (k)FLUENT 6.0 (2d, segregated, spe3, lam)

Jun 06, 2001

1.30e+03

1.20e+03

1.10e+03

1.00e+03

9.00e+02

8.00e+02

7.00e+02

6.00e+02

5.00e+02

4.00e+02

3.00e+02

Figure 13.8: Temperature Contours for the Three-Step Reaction

3. Display contours of SiH4 mass fraction (Figure 13.9) and SiH2 massfraction (Figure 13.10).


The primary effect of changing the reaction mechanism is the dis-tribution of species mass fraction.




Jun 06, 2001

1.57e-02

1.41e-02

1.26e-02

1.10e-02

9.42e-03

7.85e-03

6.28e-03

4.71e-03

3.14e-03

1.57e-03

2.64e-11

Figure 13.9: Contours of SiH4 Mass Fraction for the Three-Step Reaction


Jun 06, 2001

4.63e-03

4.17e-03

3.70e-03

3.24e-03

2.78e-03

2.31e-03

1.85e-03

1.39e-03

9.26e-04

4.63e-04

0.00e+00

Figure 13.10: Contours of SiH2 Mass Fraction for the Three-Step Reac-tion



4. Plot the surface deposition rate of Si on the susceptor for the three-reaction case and compare the results for the two reaction mecha-nisms.


(a) Plot the surface mass flux of Si on the susceptor for the three-reaction case (Figure 13.11).

i. In the Solution XY Plot panel, select Species... and SurfaceDeposition Rate of si<s> in the Y Axis Function drop-downlists.

ii. Check that Node Values is turned off and susceptor is se-lected in the Surfaces list.

iii. Click on the Curves... button.

This will open the Curves - Solution XY Plot panel.

iv. In the Curves - Solution XY Plot panel, select x in theSymbol drop-down list.

v. Change the Size of the Marker Style to 0.5.

vi. Click Apply, and Close the panel.



vii. In the Solution XY Plot panel under Options, deselectWrite to File.

The Write... button will become the Plot button again.

viii. Click Plot.


Jun 06, 2001

Position (m)

si<s>of

RateDeposition

Surface

0.150.140.130.120.110.10.090.080.070.060.05

4.00e-05

3.50e-05

3.00e-05

2.50e-05

2.00e-05

1.50e-05

1.00e-05

susceptor

Figure 13.11: Surface Deposition Rate of Si for the Three-Step Reaction



(b) Compare the results for the two reaction mechanisms, usinga single XY plot of Si surface deposition rate.

i. In the Solution XY Plot panel, click the Load File... button.


ii. In the Select File dialog box, select one reac.xy (the XYplot created for the one-step reaction) in the Files list.

iii. Click OK.

iv. In the Solution XY Plot panel, click Plot.

The surface deposition rates for the one-reaction and thethree-reaction cases can now be easily compared in Fig-ure 13.12.


Jun 06, 2001

Position (m)

si<s>of

RateDeposition

Surface

0.150.140.130.120.110.10.090.080.070.060.05

4.50e-05

4.00e-05

3.50e-05

3.00e-05

2.50e-05

2.00e-05

1.50e-05

1.00e-05

susceptorsusceptor

Figure 13.12: Composite Plot of Surface Deposition Rate of Si



Summary: In chemically reacting laminar flows, accurate modeling oftime-dependent hydrodynamics, heat and mass transfer, and chem-ical reactions (including wall surface reactions) is important. Inthis tutorial, you first simulated a single-step surface depositionreaction and examined the deposition of silicon from silane ontoa susceptor. The lower quartz walls were modeled as thermallyconducting walls using a second-order polynomial distribution todefine the thermal conductivity. The velocity profile at the inletwas defined as parabolic, using a user-defined function.

The single-step surface reaction was then replaced with a three-step reaction, and kinetic theory was used to determine the massdiffusivity of SiH2 in hydrogen. The surface deposition rate wascompared for the one-step reaction and three-step reaction cases.

References:

1. Jasinski, T.J. and Childs, E.P., “Numerical Modeling Toolsfor Chemical Vapor Deposition”, NASA Report CR-4480, TM-1504, Creare Inc., December 1992.


Tutorial 14. Modeling Evaporating

Liquid Spray

Introduction: In this tutorial, FLUENT’s air-blast atomizer model isused to predict the droplet behavior of an evaporating methanolspray. The air flow is modeled first as a steady-state problem with-out droplets. To predict the behavior of individual droplets in theatomizer, several other discrete-phase models, including collisionand breakup, are used in an unsteady calculation.


• Create periodic zones

• Define a discrete-phase spray injection for an air-blast atom-izer

• Calculate a transient solution using the second-order implicitunsteady formulation

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT and that you have solved or read Tu-torial 1. Some steps in the setup and solution procedure will notbe shown explicitly.

Problem Description: The geometry to be considered in this tutorialis shown in Figure 14.1. Methanol is cooled to −10C before beingintroduced into an air-blast atomizer. The atomizer contains aninner air stream surrounded by a swirling annular stream. (Thespecies include the components of air as well as water vapor, sothe model can be expanded to include combustion, if desired.) Tomake use of the periodicity of the problem, only a 30-degree sectionof the atomizer will be modeled.


Modeling Evaporating Liquid Spray

ZY

X

inner air stream

swirling annular stream

Figure 14.1: Problem Specification

Preparation

1. Copy the file spray/sector.msh from the FLUENT documentationCD to your working directory (as described in Tutorial 1).




Step 1: Grid

1. Read in the mesh file sector.msh.


2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will reportthe progress in the console window. Pay particular attention to thereported minimum volume. Make sure this is a positive number.



(a) Under Options, select Faces.

(b) Under Surfaces, select only atomizer-wall, central air, and swirling air.

(c) Click the Colors... button.



(d) In the Grid Colors panel, select Color By ID.

This will assign a different color to each zone in the domain,rather than to each type of zone.

(e) In the Grid Display panel, click Display.

The graphics display will be updated to show the grid. Youwill now change the display again to zoom in on an isometricview of the atomizer section.

4. Change the display to an isometric view.

Display −→Views...



(a) Select isometric in the Views list and click Restore.

(b) Zoom in with your mouse to obtain the view shown in Fig-ure 14.2.


Apr 19, 2001

ZY

X

Figure 14.2: Air-Blast Atomizer Mesh Display



5. Using the text interface, change zones periodic-a and periodic-bfrom wall zones to periodic zones.

(a) In the console window, type the commands shown in boxesin the dialog below.

> grid

/grid> modify-zones

/grid/modify-zones> list-zonesid name type material kind

---- ---------------- ----------------- ------------------ ----1 fluid fluid air cell2 atomizer-wall wall aluminum face3 central_air mass-flow-inlet face4 co-flow-air velocity-inlet face5 outlet pressure-outlet face6 swirling_air velocity-inlet face7 periodic-a wall aluminum face8 periodic-b wall aluminum face9 outer-wall wall aluminum face11 default-interior interior face

/grid/modify-zones> make-periodic

Periodic zone [()] 7

Shadow zone [()] 8Rotational periodic? (if no, translational) [yes] yes

Create periodic zones? [yes] yes

all 1923 faces matched for zones 7 and 8.

zone 8 deleted

created periodic zones.



6. Reorder the grid.

To speed up the solution procedure, the mesh should be reordered,which will substantially reduce the bandwidth.

Grid −→ Reorder −→Domain

FLUENT will report its progress in the console window:

>> Reordering domain using Reverse Cuthill-McKee method:zones, cells, faces, done.

Bandwidth reduction = 3286/102 = 32.22Done.



Step 2: Models

1. Keep the default solver settings.






3. Enable the realizable k-ε turbulence model.


The realizable k-ε model gives a more accurate prediction of thespreading rate of both planar and round jets than the standard k-εmodel.





(a) Select Species Transport under Model.

(b) Choose methyl-alcohol-air in the Mixture Material drop-downlist.

The Mixture Material list contains the set of chemical mix-tures that exist in the FLUENT database. By selecting oneof the pre-defined mixtures, you are accessing a complete de-scription of the reacting system. The chemical species in thesystem and their physical and thermodynamic properties aredefined by your selection of the mixture material. You can al-ter the mixture material selection or modify the mixture mate-rial properties using the Materials panel (see Step 6: Solution:Unsteady Flow).



! When you click OK, the console window will list the prop-erties that are required for the models you have enabled.You will see an Information dialog box, reminding you toconfirm the property values that have been extracted fromthe database.

(c) Click OK in the Information dialog box to continue.





1. Set the following conditions for the inner air stream (central air).



2. Set the following conditions for the air stream surrounding theatomizer (co-flow-air).



3. Set the following conditions for the exit boundary (outlet).



4. Set the following conditions for the swirling annular stream(swirling air).



5. Set the following conditions for the outer wall of the atomizer(outer-wall).



Step 4: Initial Solution Without Droplets

The airflow will first be solved and analyzed without droplets.

1. Initialize the flow field.


(a) Select co-flow-air in the Compute From drop-down list.

(b) Click Init to initialize the variables, and then close the panel.



2. Keep the default under-relaxation factors.







(b) Click OK.



4. Save the case file (spray1.cas).




The solution will converge after about 175 iterations.

6. Save the case and data files (spray1.cas and spray1.dat).


Note: FLUENT will ask you to confirm that the previous case fileis to be overwritten.

7. Create a clip plane to examine the flow field at the midpoint of theatomizer section.

Surface −→Iso-Surface...



(a) Select Grid... and Angular Coordinate in the Surface of Constantlists.

(b) Click on Compute to update the minimum and maximum val-ues.

(c) Enter 15 in the Iso-Values field.

(d) Enter angle=15 for the New Surface Name.

(e) Click on Create to create the isosurface.

8. Review the current state of the solution by examining contours ofvelocity magnitude (Figure 14.3).




(a) Select Velocity... and Velocity Magnitude in the Contours Ofdrop-down list.

(b) Under Options, select Filled and Draw Grid.

This will open the Grid Display panel.

(c) Keep the current grid display settings and close the Grid Dis-play panel.

(d) In the Contours panel, select angle=15 in the Surfaces list.

(e) Click Display.

(f) Use your mouse to obtain the view shown in Figure 14.3.



Contours of Velocity Magnitude (m/s)FLUENT 6.0 (3d, segregated, spe5, rke)

Jul 03, 2001

8.53e+01

7.68e+01

6.82e+01

5.97e+01

5.12e+01

4.27e+01

3.41e+01

2.56e+01

1.71e+01

8.53e+00

0.00e+00

ZY

X

Figure 14.3: Velocity Magnitude at Mid-Point of Atomizer Section



9. Display path lines of the air in the swirling annular stream (Fig-ure 14.4).

Display −→Path Lines...

(a) In the Release From Surfaces list, select swirling air.

You will need to scroll down to access this item.

(b) Increase the Skip value to 5.

(c) Under Options, select Draw Grid.


(d) Keep the current grid display settings and close the Grid Dis-play panel.

(e) Click Display in the Path Lines panel.




Path Lines Colored by Particle IdFLUENT 6.0 (3d, segregated, spe5, rke)

Jul 03, 2001

3.00e+01

2.70e+01

2.40e+01

2.10e+01

1.80e+01

1.50e+01

1.20e+01

9.00e+00

6.00e+00

3.00e+00

0.00e+00

ZY

X

Figure 14.4: Path Lines of Air in the Swirling Annular Stream



Step 5: Enable Time Dependence and Create aSpray Injection

In this step you will define a transient flow and create a discrete phasespray injection.

1. Enable a time-dependent flow calculation.


(a) Under Time, select Unsteady.

(b) Under Unsteady Formulation, select 2nd-Order Implicit.



2. Define the discrete phase modeling parameters.

Define −→ Models −→Discrete Phase...



(a) Define the interphase interaction.

i. Under Interaction, turn on Interaction with Continuous Phase.

This will include the effects of the discrete phase trajec-tories on the continuous phase.

ii. Under Number of Continuous Phase Iterations per DPMIteration, enter a value of 1000.

This option controls the iterative solution of the discretephase within each gas-phase time step. Higher values aremore desirable for sprays.

(b) Specify the Tracking Parameters.

i. Deselect the Specify Length Scale option.

ii. Keep the default value of Step Length Factor.

(c) Set the Unsteady Options.

i. Under Spray Models, select Droplet Collision and DropletBreakup.

ii. Under Breakup Model, keep the default selection of TAB.

iii. Under Constants, enter a value of 0.05 for y0.

This parameter is the dimensionless droplet distortion att = 0.

(d) Under Drag Parameters, select dynamic-drag in the Drag Lawdrop-down list.

The dynamic-drag law is available only when the Droplet Breakupmodel is used.



3. Create the spray injection.

In this step, you will define the characteristics of the atomizer.

Define −→Injections...

(a) Click the Create button at the top of the panel.

This will open the Set Injection Properties panel.



(b) In the Injection Type drop-down list, select air-blast-atomizer.

(c) Increase the Number Of Particle Streams to 60.

This option controls how many parcels of droplets are intro-duced into the domain at every time step.

(d) Under Particle Type, select Droplet.

(e) In the Material drop-down list, select methyl-alcohol-liquid.

(f) Set the point properties for the injection.



i. Set the X-Position, Y-Position, and Z-Position of the injec-tion to 0, 0, and 0.0015.

ii. Set the X-Axis, Y-Axis, and Z-Axis of the injection to 0, 0,and 1.

iii. Set the Temperature to 263 K.

iv. Set the Flow Rate to 1.7e-4 kg/s.

This is the methanol flow rate for a 30-degree section ofthe atomizer. The actual atomizer flow rate is 12 timesthis value.

v. Keep the default Start Time of 0 s and set the Stop Timeto 100 s.

For this problem, the injection should begin at t = 0 andnot stop until long after the time period of interest. Alarge value for the stop time (e.g., 100 s) will ensure thatthe injection will essentially never stop.

vi. Set the Injector Inner Diam. to 0.0035 m, and the InjectorOuter Diam. to 0.0045 m.

vii. Set the Spray Half Angle to -45 deg.

The spray angle is the angle between the liquid sheet tra-jectory and the injector centerline. In this case, the valueis negative because the sheet is initially converging towardthe centerline.

viii. Set the Relative Velocity to 82.6 m/s.

The relative velocity is the expected relative velocity be-tween the atomizing air and the liquid sheet.

ix. Keep the default Azimuthal Start Angle of 0 deg and setthe Azimuthal Stop Angle to 30 deg.

This will restrict the injection to the 30-degree section ofthe atomizer that is being modeled.



(g) Define the turbulent dispersion.

i. Click the Turbulent Dispersion tab.

The lower half of the panel will change to show optionsfor the turbulent dispersion model.

ii. Under Stochastic Tracking, turn on the Stochastic Modeland Random Eddy Lifetime options.

These models will account for the turbulent dispersion ofthe droplets.

4. Set the droplet material properties.

Because the secondary atomization models (breakup and coales-cence) are used, the droplet properties must be set.




(a) In the Material Type drop-down list, select droplet-particle.

(b) Under Properties, enter a value of 0.0056 kg/m-s for Viscosity.

(c) Under Properties, scroll down and enter a value of 0.0222N/m for Droplet Surface Tension.

(d) Click Change/Create to accept the change in properties for themethanol droplet material.



Step 6: Solution: Unsteady Flow

1. Set the initial condition for the discrete phase.

Resetting the discrete phase model sources will make sure that theinterphase coupling is initialized.

Solve −→ Initialize −→Reset DPM Sources

2. Set the time step parameters.

The selection of the time step is critical for accurate time-dependentflow predictions.




(a) Set the Time Step Size to 5e-05 s.

(b) Click Apply.

3. Save the transient solution case file (spray2.cas).


4. Calculate a solution for one time step.


It is a good idea to do one time step initially so you can checkthe position of the atomizer droplets before they are significantlydispersed.

(a) Set the Number of Time Steps to 1.

(b) Click Iterate.

! You will notice that FLUENT will perform 20 iterations for thefirst time step. Since this is the specified Max Iterations perTime Step, the solution is not yet completely converged. Fora real problem, it is important that you allow the solution toconverge at each time step, so you may need to increase theMax Iterations per Time Step. The default of 20 is used in thistutorial to speed up the calculation.

5. Save the new case and data files (spray2.cas and spray2.dat).


6. Display the trajectories of the droplets in the spray injection (Fig-ure 14.5).

This will allow you to review the location of the atomizer dropletsafter just one time step. They should therefore still be near theirinitial injection positions.




(a) In the Style drop-down list, select point.

(b) Click the Style Attributes... button.

This will open the Path Style Attributes panel.



(c) Set the Marker Size to 0.25 and click OK.

(d) In the Particle Tracks panel, select Draw Grid under Options.




(e) Keep the current display settings and close the panel.

(f) In the Particle Tracks panel, select Particle Variables... andParticle Diameter in the Color By drop-down list.

This will display the location of the droplets colored by theirdiameters.

(g) In the Release From Injections list, select injection-0.

(h) Click Display.

(i) Use your mouse to obtain the view shown in Figure 14.4.

Particle Traces Colored by Particle Diameter (m) (Time=5.0000e-05)FLUENT 6.0 (3d, segregated, spe5, rke, unsteady)

Jul 11, 2001

1.35e-04

1.22e-04

1.10e-04

9.79e-05

8.57e-05

7.35e-05

6.13e-05

4.91e-05

3.69e-05

2.46e-05

1.24e-05

ZY

X

Figure 14.5: Particle Tracks for the Spray Injection After 1 Time Step

The air-blast atomizer model assumes that a cylindrical liquidsheet exits the atomizer, which then disintegrates into liga-ments and droplets. Appropriately, the model determines thatthe droplets should be input into the domain in a ring. The ra-dius of this disk is determined from the inner and outer radiiof the injector.

Note that the maximum diameter of the droplets is about10−4 m, or 0.1 mm. This is slightly smaller than the filmheight, which makes sense. Recall that the inner diameter



and outer diameter of the injector are 3.5 mm and 4.5 mm,respectively. The film height is then 1

2(4.5 − 3.5) = 0.5 mm.The range in the droplet sizes is due to the fact that the air-blast atomizer automatically uses a droplet distribution.

Also note that the droplets are placed a slight distance awayfrom the injector. Once the droplets are injected into the do-main, they can collide/coalesce with other droplets as deter-mined by the secondary models (breakup and collision). How-ever, once a droplet has been introduced into the domain, theair-blast atomizer model no longer affects the droplet.

7. Request 10 more time steps.


8. Save the new case and data files (spray3.cas and spray3.dat).




1. Display the particle trajectories again, to see how the droplets havedispersed.


(a) Click Display in the Particle Tracks panel.

(b) Use your mouse to obtain the view shown in Figure 14.6.

Particle Traces Colored by Particle Diameter (m) (Time=5.5000e-04)FLUENT 6.0 (3d, segregated, spe5, rke, unsteady)

Jul 11, 2001

2.78e-04

2.52e-04

2.25e-04

1.98e-04

1.72e-04

1.45e-04

1.18e-04

9.18e-05

6.52e-05

3.85e-05

1.19e-05

ZY

X

Figure 14.6: Particle Tracks for the Spray Injection After 11 Time Steps



2. Create an isosurface of the methanol mass fraction.


(a) Select Species... and Mass fraction of ch3oh in the Surface ofConstant lists.

(b) Click on Compute to update the minimum and maximum val-ues.

(c) Enter 0.001339 in the Iso-Values field.

(d) Enter methanol-mf=0.001339 for the New Surface Name.

(e) Click on Create to create the isosurface.



3. Display the isosurface you just created (methanol-mf=0.001339).


(a) Select methanol-mf=0.001339 in the Surfaces list.

(b) Click the Colors... button.



(c) In the Grid Colors panel, select Color By Type.

(d) Scroll down and select surface in the Types list and dark redin the Colors list.

This will ensure that the isosurface is displayed in red, whichcontrasts better with the rest of the grid.

(e) In the Grid Display panel, click Display.

The graphics display will be updated to show the isosurface.



4. Modify the view to include the entire atomizer.


(a) Increase the number of Periodic Repeats to 11.

(b) Click Apply in the Views panel.

(c) In the Grid Display panel, click Display.

The graphics display will be updated to show the entire atom-izer.

(d) Use your mouse to obtain the view shown in Figure 14.7.



ZY

X

Grid (Time=5.5000e-04)FLUENT 6.0 (3d, segregated, spe5, rke, unsteady)

Jul 16, 2001

Figure 14.7: Full Atomizer Display with Surface of Constant MethanolMass Fraction

Summary: In this tutorial, you defined a discrete-phase spray injectionfor an air-blast atomizer and calculated a transient solution usingthe second-order implicit unsteady formulation. You viewed thelocation of methanol droplet particles after they had exited theatomizer and examined an isosurface of the methanol mass fraction.


Tutorial 15. Using the VOF Model

Introduction: This tutorial illustrates the setup and solution of thetwo-dimensional turbulent fluid flow in a partially filled spinningbowl.


• Set up and solve a transient free-surface problem using thesegregated solver

• Model the effect of gravity

• Copy a material from the property database

• Patch initial conditions in a subset of the domain

• Define a custom field function

• Mirror and rotate the view in the graphics window

• Examine the fluid flow and the free-surface shape using veloc-ity vectors and volume fraction contours

Prerequisites: This tutorial requires a basic familiarity with FLUENT.You may also find it helpful to read about VOF multiphase flowmodeling in the FLUENT User’s Guide. Otherwise, no previousexperience with multiphase modeling is required.

Problem Description: The information relevant to this problem isshown in Figure 15.1. A large bowl, 1 m in radius, is one-thirdfilled with water and is open to the atmosphere. The bowl spinswith an angular velocity of 3 rad/sec. Based on the rotating wa-ter, the Reynolds number is about 106, so the flow is modeled asturbulent.


Using the VOF Model

2 m

1 m

=Bowl: Ω 3 rad/s 3

-5

-3

Air: ρ = 1.225 kg/m

µ = 1.7894 x 10 kg/m-sWater: ρ = 998.2 kg/m 3

µ = 1 x 10 kg/m-s

Figure 15.1: Water and Air in a Spinning Bowl

Preparation

1. Copy the file vof/bowl.msh from the FLUENT documentation CDto your working directory (as described in Tutorial 1).

The mesh file bowl.msh is a quadrilateral mesh describing the sys-tem geometry shown in Figure 15.1.



Using the VOF Model

Step 1: Grid

1. Read the 2D grid file, bowl.msh.




As shown in Figure 15.2, half of the bowl is modeled, with a sym-metry boundary at the centerline. The bowl is shown lying on itsside, with the region to be modeled extending from the centerline tothe outer wall. When you begin to display data graphically, you willneed to rotate the view and mirror it across the centerline to obtaina more realistic view of the model. This step will be performed laterin the tutorial.


Using the VOF Model


Jun 12, 2001



Using the VOF Model

Step 2: Models

1. Specify a transient model with axisymmetric swirl.


(a) Retain the default Segregated solver.

The segregated solver must be used for multiphase calculations.

(b) Under Space, select Axisymmetric Swirl.

(c) Under Time, select Unsteady.


Using the VOF Model

2. Turn on the VOF model.

Define −→ Models −→Multiphase...

(a) Select Volume of Fluid as the Model.

The panel will expand to show inputs for the VOF model.

(b) Under VOF Parameters, select Geo-Reconstruct (the default)as the VOF Scheme.

This is the most accurate interface-tracking scheme, and isrecommended for most transient VOF calculations.

When you click OK, FLUENT will report that one of the zonetypes will need to be changed before proceeding with the calcu-


Using the VOF Model

lation. You will take care of this step when you input boundaryconditions for the problem.

3. Turn on the standard k-ε turbulence model.


(a) Select k-epsilon as the Model, and retain the default setting ofStandard under k-epsilon Model.


Using the VOF Model

Step 3: Materials

1. Copy water from the materials database so that it can be used forthe secondary phase.


(a) Click on the Database... button to open the Database Materialspanel.


Using the VOF Model

(b) In the Fluid Materials list (near the bottom), select water-liquid.

(c) Click on Copy and close the Database Materials and Materialspanels.

Step 4: Phases

Here, water is defined as the secondary phase mainly for convenience insetting up the problem. When you define the initial solution, you will bepatching an initial swirl velocity in the bottom third of the bowl, wherethe water is. It is more convenient to patch a water volume fraction of 1there than to patch an air volume fraction of 1 in the rest of the domain.Also, the default volume fraction at the pressure inlet is 0, which is thecorrect value if water is the secondary phase.

In general, you can specify the primary and secondary phases whicheverway you prefer. It is a good idea, especially in more complicated problems,to consider how your choice will affect the ease of problem setup.

1. Define the air and water phases within the bowl.

Define −→Phases...


Using the VOF Model

(a) Specify air as the primary phase.

i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter air for the Name.

iii. Keep the default selection of air for the Phase Material.

(b) Specify water as the secondary phase.


ii. In the Secondary Phase panel, enter water for the Name.

iii. Select water-liquid from the Phase Material drop-down list.


Using the VOF Model

Step 5: Operating Conditions

1. Set the gravitational acceleration.

Define −→Operating Conditions...

(a) Turn on Gravity.

The panel will expand to show additional inputs.

(b) Set the Gravitational Acceleration in the X direction to 9.81m/s2.

Since the centerline of the bowl is the x axis, gravity points inthe positive x direction.

2. Set the operating density.

(a) Under Variable-Density Parameters, turn on the Specified Op-erating Density option and accept the Operating Density of1.225.

It is a good idea to set the operating density to be the densityof the lighter phase. This excludes the buildup of hydrostaticpressure within the lighter phase, improving the round-off ac-curacy for the momentum balance.


Using the VOF Model

Note: The Reference Pressure Location (0,0) is situated in a re-gion where the fluid will always be 100% of one of the phases(air), a condition that is essential for smooth and rapid con-vergence. If it were not, you would need to change it to amore appropriate location.



1. Change the bowl centerline from a symmetry boundary to an axisboundary.

For axisymmetric models, the axis of symmetry must be an axiszone.

(a) Select symmetry-2 in the Zone list in the Boundary Conditionspanel.

(b) In the Type list, choose axis.

You will have to scroll to the top of the list.

(c) Click Yes in the Question dialog box that appears.

(d) Click OK in the Axis panel to accept the default Zone Name.


Using the VOF Model

2. Set the conditions at the top of the bowl (the pressure inlet).

For the VOF model, you will specify conditions for the mixture(i.e., conditions that apply to all phases) and also conditions thatare specific to the secondary phase. There are no conditions to bespecified for the primary phase.

(a) Set the conditions for the mixture.

i. In the Boundary Conditions panel, keep the default se-lection of mixture in the Phase drop-down list and clickSet....

ii. Set the Turb. Kinetic Energy to 2.25e-2 and the Turb.Dissipation Rate to 7.92e-3.

Since there is initially no flow passing through the pres-sure inlet, you need to specify k and ε explicitly ratherthan using one of the other turbulence specification meth-ods. All of the other methods require you to specify theturbulence intensity, which is 0 in this case.

The values for k and ε are computed as follows:


Using the VOF Model

k = (Iwwall)2

ε =0.093/4k3/2

`

where the turbulence intensity I is 0.05 (close to zero),wwall is 3 m/s, and ` is 0.07 (obtained by multiplying0.07 by the maximum radius of the bowl, which is 1).See the User’s Guide for details about the specification ofturbulence boundary conditions at flow inlets and exits.

(b) Check the volume fraction of the secondary phase.

i. In the Boundary Conditions panel, select water from thePhase drop-down list and click Set....

ii. Retain the default Volume Fraction of 0.

A water volume fraction of 0 indicates that only air ispresent at the pressure inlet.


Using the VOF Model

3. Set the conditions for the spinning bowl (the wall boundary).

For a wall boundary, all conditions are specified for the mixture.There are no conditions to be specified for the individual phases.

(a) In the Boundary Conditions panel, select mixture in the Phasedrop-down list and click Set....


Using the VOF Model

(b) Select Moving Wall under Wall Motion.

The panel will expand to show inputs for the wall motion.

(c) Under Motion, choose Rotational and then set the rotationalSpeed (Ω) to 3 rad/s.


Using the VOF Model

Step 7: Solution

In simple flows, the under-relaxation factors can usually be increased atthe start of the calculation. This is particularly true when the VOF modelis used, where high under-relaxation on all variables can greatly improvethe performance of the solver.

1. Set the solution parameters.


(a) Set all Under-Relaxation factors to 1.

! Be sure to use the scroll bar to access the under-relaxationfactors that are initially out of view.


Using the VOF Model

(b) Under Discretization, choose the Body Force Weighted schemein the drop-down list next to Pressure.

The body-force-weighted pressure discretization scheme is rec-ommended when you solve a VOF problem involving gravity.

(c) Also under Discretization, select PISO as the Pressure-VelocityCoupling method.

PISO is recommended for transient flow calculations.

2. Enable the display of residuals during the solution process.



(b) Click the OK button.


Using the VOF Model

3. Enable the plotting of the axial velocity of water near the outeredge of the bowl during the calculation.

For transient calculations, it is often useful to monitor the valueof a particular variable to see how it changes over time. Here youwill first specify the point at which you want to track the velocity,and then define the monitoring parameters.

(a) Define a point surface near the outer edge of the bowl.

Surface −→Point...

i. Set the x0 and y0 coordinates to 0.75 and 0.65.

ii. Enter point for the New Surface Name.

iii. Click Create.


Using the VOF Model

(b) Define the monitoring parameters.

Solve −→ Monitors −→Surface...

i. Increase the Surface Monitors value to 1.

ii. Turn on the Plot and Write options for monitor-1.

Note: When the Write option is selected in the SurfaceMonitors panel, the velocity history will be written to afile. If you do not select the Write option, the historyinformation will be lost when you exit FLUENT.

iii. In the drop-down list under Every, choose Time Step.

iv. Click on Define... to specify the surface monitor parame-ters in the Define Surface Monitor panel.


Using the VOF Model

v. Select Vertex Average from the Report Type drop-downlist.

This is the recommended choice when you are monitoringthe value at a single point using a point surface.

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

vii. Select Velocity... and Axial Velocity in the Report Of drop-down lists.

viii. Select point in the Surfaces list.

ix. Enter axial-velocity.out for the File Name.

x. Click OK in the Define Surface Monitor panel and then inthe Surface Monitors panel.


Using the VOF Model

4. Initialize the solution.


(a) Select pressure-inlet-4 in the Compute From drop-down list.

All initial values will be set to zero, except for the turbulencequantities.

(b) Click Init and close the panel.


Using the VOF Model

5. Patch the initial distribution of water (i.e., water volume fractionof 1.0) and a swirl velocity of 3 rad/s in the bottom third of thebowl (where the water is).

In order to patch a value in just a portion of the domain, you willneed to define a cell “register” for that region. You will use thesame tool that is used to mark a region of cells for adaption. Also,you will need to define a custom function for the swirl velocity.

(a) Define a register for the bottom third of the domain.

Adapt −→Region...

i. Set the (Xminimum,Yminimum) coordinate to (0.66,0),and the (Xmaximum,Ymaximum) coordinate to (1,1).

ii. Click the Mark button.

This creates a register containing the cells in this region.


Using the VOF Model

(b) Check the register to be sure it is correct.

Adapt −→Manage...

i. Select the register (hexahedron-r0) in the Registers list andclick Display.

The graphics display will show the bottom third of the bowlin red.


Using the VOF Model

(c) Define a custom field function for the swirl velocity w = 3r.


i. Click the 3 button on the calculator pad.

The 3 will appear in the Definition field. If you make amistake, click the DEL button to delete the last item youadded to the function definition.

ii. Click the X button on the calculator pad.

iii. In the Field Functions drop-down list, select Grid... andRadial Coordinate.

iv. Click the Select button.

radial-coordinate will appear in the Definition.

v. Enter a New Function Name of swirl-init.

vi. Click Define.

Note: If you wish to check the function definition, clickon the Manage... button and select swirl-init.


Using the VOF Model

(d) Patch the water volume fraction in the bottom third of thebowl.

Solve −→ Initialize −→Patch...

i. Choose water Volume Fraction in the Variable list.

ii. Select hexahedron-r0 in the Registers To Patch list.

iii. Set the Value to 1.

iv. Click Patch.

This sets the water volume fraction to 1 in the lower third ofthe bowl. That is, you have defined the lower third of the bowlto be filled with water.


Using the VOF Model

(e) Patch the swirl velocity in the bottom third of the bowl.

i. Choose Swirl Velocity in the Variable list.

ii. Enable the Use Field Function option and select swirl-initin the Field Function list.

iii. Click Patch.

It’s a good idea to check your patch by displaying contours ofthe patched fields.


Using the VOF Model

(f) Display contours of swirl velocity.


i. Select Velocity... and Swirl Velocity in the Contours Oflists.

ii. Enable the Filled option and turn off the Node Valuesoption.

Since the values you patched are cell values, you shouldview the cell values, rather than the node values, to checkthat the patch has been performed correctly. (FLUENTcomputes the node values by averaging the cell values.)

iii. Click Display.

To make the view more realistic, you will need to rotate thedisplay and mirror it across the centerline.


Using the VOF Model

(g) Rotate the view and mirror it across the centerline.


i. Select axis-2 in the Mirror Planes list and click Apply.

ii. Use your middle and left mouse buttons to zoom andtranslate the view so that the entire bowl is visible in thegraphics display.

iii. Click on the Camera... button to open the Camera Param-eters panel.


Using the VOF Model

iv. Using your left mouse button, rotate the dial clockwiseuntil the bowl appears upright in the graphics window(90).

v. Close the Camera Parameters panel.

vi. In the Views panel, click on the Save button under Actionsto save the mirrored, upright view, and then close thepanel.

When you do this, view-0 will be added to the list of Views.

The upright view of the bowl in Figure 15.3 correctly showsthat w = 3r in the region of the bowl that is filled with water.

Contours of Swirl Velocity (m/s) (Time=0.0000e+00)FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

Jun 12, 2001

2.35e+00

2.12e+00

1.88e+00

1.65e+00

1.41e+00

1.18e+00

9.41e-01

7.06e-01

4.70e-01

2.35e-01

0.00e+00

Figure 15.3: Contours of Initial Swirl Velocity


Using the VOF Model

(h) Display contours of water volume fraction.

i. Select Phases... and Volume fraction of water in the Con-tours Of lists.

ii. Set the number of contour Levels to 2 and click Display.

There are only two possible values for the volume fractionat this point: 0 or 1.

Figure 15.4 correctly shows that the bottom third of the bowlcontains water.


Using the VOF Model

Contours of Volume fraction of water (Time=0.0000e+00) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.4: Contours of Initial Water Volume Fraction


Using the VOF Model

6. Set the time-step parameters for the calculation.


(a) Set the Time Step Size to 0.002 seconds.

(b) Click Apply.

This will save the time step size to the case file (the next timea case file is saved).

7. Request saving of data files every 100 time steps.

File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency to 0 and the AutosaveData File Frequency to 100.

(b) Enter the Filename bowl and then click OK.

FLUENT will append the time step value to the file name prefix(bowl). The standard .dat extension will also be appended.This will yield file names of the form bowl100.dat, where 100is the time step number.

8. Save the initial case and data files (bowl.cas and bowl.dat).


9. Request 1000 time steps.



Using the VOF Model

Since the time step is 0.002 seconds, you will be calculating up tot= 2 seconds. FLUENT will automatically save a data file afterevery 0.2 seconds, so you will have 10 data files for postprocessing.

Figure 15.5 shows the time history for the axial velocity. The veloc-ity is clearly oscillating, and the oscillations appear to be decayingover time (as the peaks become smaller). This periodic oscillationhas a cycle of 1 second. The switch from a positive to a negativeaxial velocity indicates that the water is sloshing up and down thesides of the bowl in an attempt to reach an equilibrium position.The fact that the amplitude is decaying suggests that equilibriumwill be reached at some point. The periodic behavior in evidencewill therefore be present only during the initial startup phase of thebowl rotation.

Convergence history of Axial Velocity on point (Time=2.0000e+00)FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

Jun 13, 2001

Flow Time

(m/s)ValuesVertex

Surfaceof

Average

2.00001.80001.60001.40001.20001.00000.80000.60000.40000.20000.0000

0.3000

0.2000

0.1000

0.0000

-0.1000

-0.2000

-0.3000

Figure 15.5: Time History of Axial Velocity


Using the VOF Model


As indicated by changes in axial velocity in Figure 15.5, the flow field isoscillating periodically. In this step, you will examine the flow field atseveral different times. (Recall that FLUENT saved 10 data files for youduring the calculation.)

1. Read in the data file of interest.

File −→ Read −→Data...

2. Display filled contours of water volume fraction.


Hint: Follow the instructions in substep 5h of Step 7: Solution(on page 15-31), but turn Node Values back on.

Figures 15.6–15.9 show that the water level decreases from t = 0.4to t = 0.6, then increases from t = 0.6 to t = 1. At t = 1, thewater level in the center of the bowl has risen above the initiallevel, so you can expect the cycle to repeat as the water level beginsto decrease again in an attempt to return to equilibrium. (You canread in the data files between t = 1 and t = 2 to confirm that thisis in fact what happens.

Since the time history of axial velocity (Figure 15.5) shows thatthe velocity oscillation is decaying over time, you can expect that ifyou were to continue the calculation, the water level would eventu-ally reach some point where the gravitational and centrifugal forcesbalance and the water level reaches a new equilibrium point.

Extra: Try continuing the calculation to determine how long ittakes for the axial velocity oscillations in Figure 15.5 to dis-appear.


Using the VOF Model

Contours of Volume fraction of water (Time=4.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.00e+00

0.00e+00

Figure 15.6: Shape of the Free Surface at t = 0.4


1.00e+00

0.00e+00



Using the VOF Model


1.00e+00

0.00e+00



1.00e+00

0.00e+00

Figure 15.9: Shape of the Free Surface at t = 1


Using the VOF Model

3. Plot contours of stream function.

(a) Select Stream Function (in the Velocity... category) in the Con-tours Of drop-down list.

(b) Turn off the Filled option and increase the number of contourLevels to 30.

(c) Click on Display.

In Figures 15.10–15.13, you can see a recirculation region that fallsand rises as the water level changes. To get a better sense of theserecirculating patterns, you will next look at velocity vectors.


Using the VOF Model

Contours of Stream Function (kg/s) (Time=4.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

2.58e+01

0.00e+00

1.72e+00

3.44e+00

5.16e+00

6.88e+00

8.60e+00

1.03e+01

1.20e+01

1.38e+01

1.55e+01

1.72e+01

1.89e+01

2.06e+01

2.24e+01

2.41e+01

Figure 15.10: Contours of Stream Function at t = 0.4


2.65e+01

0.00e+00

1.76e+00

3.53e+00

5.29e+00

7.06e+00

8.82e+00

1.06e+01

1.24e+01

1.41e+01

1.59e+01

1.76e+01

1.94e+01

2.12e+01

2.29e+01

2.47e+01



Using the VOF Model


4.73e+01

0.00e+00

3.15e+00

6.31e+00

9.46e+00

1.26e+01

1.58e+01

1.89e+01

2.21e+01

2.52e+01

2.84e+01

3.15e+01

3.47e+01

3.78e+01

4.10e+01

4.41e+01



8.84e+00

0.00e+00

5.89e-01

1.18e+00

1.77e+00

2.36e+00

2.95e+00

3.54e+00

4.13e+00

4.71e+00

5.30e+00

5.89e+00

6.48e+00

7.07e+00

7.66e+00

8.25e+00

Figure 15.13: Contours of Stream Function at t = 1


Using the VOF Model

4. Plot velocity vectors in the bowl.


(a) In the Style drop-down list, select arrow.

This will make the velocity direction easier to see.

(b) Increase the Scale factor to 6 and increase the Skip value to1.

(c) Click on Vector Options... to open the Vector Options panel.


Using the VOF Model

i. Turn off the Z Component.

This allows you to examine the non-swirling componentsonly.

ii. Click Apply and close the panel.

(d) Click on Display.

Figures 15.14–15.17 show the changes in water and air flow pat-terns between t = 0.4 and t = 1. In Figure 15.14, you can see thatthe flow in the middle of the bowl is being pulled down by gravi-tational forces, and pushed out and up along the sides of the bowlby centrifugal forces. This causes the water level to decrease in thecenter of the bowl, as shown in the volume fraction contour plots,and also results in the formation of a recirculation region in theair above the water surface.

In Figure 15.15, the flow has reversed direction, and is slowly risingup in the middle of the bowl and being pulled down along the sidesof the bowl. This reversal occurs because the earlier flow patterncaused the water to overshoot the equilibrium position. The gravityand centrifugal forces now act to compensate for this overshoot.


Using the VOF Model

Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=4.0000e-01) Jun 12, 2001FLUENT 6.0 (axi, swirl, segregated, vof, ske, unsteady)

1.92e+00

8.63e-03

1.36e-01

2.63e-01

3.91e-01

5.18e-01

6.46e-01

7.73e-01

9.00e-01

1.03e+00

1.16e+00

1.28e+00

1.41e+00

1.54e+00

1.66e+00

1.79e+00

Figure 15.14: Velocity Vectors for the Air and Water at t = 0.4


1.94e+00

4.88e-04

1.30e-01

2.59e-01

3.89e-01

5.18e-01

6.48e-01

7.77e-01

9.07e-01

1.04e+00

1.17e+00

1.30e+00

1.42e+00

1.55e+00

1.68e+00

1.81e+00



Using the VOF Model


2.13e+00

5.04e-03

1.47e-01

2.89e-01

4.31e-01

5.73e-01

7.15e-01

8.56e-01

9.98e-01

1.14e+00

1.28e+00

1.42e+00

1.57e+00

1.71e+00

1.85e+00

1.99e+00



2.12e+00

3.06e-03

1.44e-01

2.85e-01

4.27e-01

5.68e-01

7.09e-01

8.50e-01

9.91e-01

1.13e+00

1.27e+00

1.41e+00

1.56e+00

1.70e+00

1.84e+00

1.98e+00

Figure 15.17: Velocity Vectors for the Air and Water at t = 1


Using the VOF Model

In Figure 15.16 you can see that the flow is rising up more quicklyin the middle of the bowl, and in Figure 15.17 you can see that theflow is still moving upward, but more slowly. These patterns cor-respond to the volume fraction plots at these times. As the upwardmotion in the center of the bowl decreases, you can expect the flowto reverse as the water again seeks to reach a state of equilibrium.

Summary: In this tutorial, you have learned how to use the VOF freesurface model to solve a problem involving a spinning bowl of wa-ter. The time-dependent VOF formulation is used in this problemto track the shape of the free surface and the flow field inside thespinning bowl.

You observed the changing pattern of the water and air in the bowlby displaying volume fraction contours, stream function contours,and velocity vectors at t = 0.4, t = 0.6, t = 0.8, and t = 1 second.


Tutorial 16. Modeling Cavitation

Introduction: This tutorial examines the flow of water around a tor-pedo. Cavitation occurs in many applications as a result of flowacceleration over a body surface. Vapor production is localized atthe wall where the pressure is below the vaporization pressure pv,so grid refinement and the use of non-equilibrium wall functionsimprove the accuracy of the simulation. The case is taken from apaper by Kunz et al. [1]. Using FLUENT’s multiphase modelingcapability, you will be able to predict the inception of cavitationnear the nose of the torpedo.


• Set boundary conditions for external flow

• Use the mixture model with cavitation effects

• Calculate a solution using the segregated solver

• Use a pressure coefficient monitor to check solution conver-gence


Problem Description: The problem considers the cavitation causedby the flow of water around a torpedo at an incidence angle of zeroand a free-stream velocity of 1 m/s (U∞ = 1 m/s). The torpedodiameter is 0.136 m. The geometry of the torpedo is shown inFigure 16.1.


Modeling Cavitation

U = 1 m/s

D = 0.136 m


Preparation

1. Copy the file cav/cav.msh from the FLUENT documentation CDto your working directory (as described in Tutorial 1).



Modeling Cavitation

Step 1: Grid

1. Read the grid file (cav.msh).


As FLUENT reads the grid file, it will report its progress in theconsole window.

2. Check the grid.

Grid −→Check





Modeling Cavitation

(a) Display the grid using the default settings (Figure 16.2).

As shown in Figure 16.2, half of the torpedo is modeled, withan axis boundary at the centerline. Especially when you beginto display data graphically, you may want to mirror the viewacross the centerline to obtain a more realistic view of themodel. This step will be performed later in the tutorial.

(b) Use the middle mouse button to zoom in on the image so youcan see the mesh near the torpedo (Figures 16.3 and 16.4).

GridFLUENT 6.0 (axi, segregated, mixture, ske)

Jun 18, 2001

Figure 16.2: The Grid Around the Torpedo

This mesh is quadrilateral. The gradients normal to the tor-pedo wall are much greater than those tangent to the torpedo,except near the tip and at the transition between the nose andthe main body. Consequently, the cells nearest the surfacehave very high aspect ratios.


Modeling Cavitation


Jun 18, 2001

Figure 16.3: The Grid After Zooming In on the Torpedo


Jun 18, 2001

Figure 16.4: The Grid After Zooming In Further on the Torpedo


Modeling Cavitation

Step 2: Models

1. Specify a steady-state axisymmetric model.



(a) Under Space, select Axisymmetric.

(b) Keep the default settings for everything else.

Note: A computationally-intensive unsteady calculation is neces-sary to accurately simulate the irregular cyclic process of bub-ble formation, growth, filling by water jet re-entry, and breakoff.In this tutorial, you will perform a steady-state calculation tosimulate just the formation of the first bubble near the noseof the torpedo.


Modeling Cavitation

2. Enable the multiphase mixture model with cavitation effects.


(a) Select Mixture as the Model.

The panel will expand.

(b) Under Mixture Parameters, turn off Slip Velocity.

Since there is no significant difference in velocities for thedifferent phases, there is no need to solve for the slip velocityequation.

(c) Select Cavitation under Interphase Mass Transfer.

The panel will expand again to show the cavitation inputs.


Modeling Cavitation

(d) Enter 101175 for the Vaporization Pressure.

The vaporization pressure depends on the operating pressure,the free-stream velocity, the density of the liquid, and a non-dimensional parameter known as the cavitation number. Thevalue above is taken from the literature.

(e) Set the Bubble Number Density to 9e6.

The Bubble Number Density is the number of bubbles of vaporper unit volume, and is assumed constant. The value of 9×106

is taken from the literature.

3. Turn on the standard k-ε turbulence model with non-equilibriumwall functions.


(a) Select k-epsilon as the Model.


Modeling Cavitation

(b) Keep the default selection of Standard under k-epsilon Model.

The standard k-ε model has been found to be quite effective inaccurately resolving the near-wall region when non-equilibriumwall functions are used.

(c) Select Non-Equilibrium Wall Functions under Near-Wall Treat-ment.


Modeling Cavitation

Step 3: Materials

1. Copy liquid water and water vapor from the materials database sothat they can be used for the primary and secondary phases.


(a) Click the Database... button in the Materials panel.

The Database Materials panel will open.


Modeling Cavitation

(b) In the list of Fluid Materials, select water-liquid (h2o<l>).

(c) Click Copy to copy the information for liquid water to yourmodel.

(d) In the list of Fluid Materials, select water-vapor (h2o).

(e) Click Copy to copy the information for water vapor to yourmodel.

(f) Close the Database Materials panel and the Materials panel.


Modeling Cavitation

Step 4: Phases

1. Define the liquid water and water vapor phases that flow aroundthe torpedo.


(a) Specify liquid water as the primary phase.


ii. In the Primary Phase panel, enter water for the Name.



Modeling Cavitation

(b) Specify water vapor as the secondary phase.


ii. In the Secondary Phase panel, enter water-vapor for theName.

iii. Select water-vapor from the Phase Material drop-down list.


Modeling Cavitation


For this problem, you need to set the boundary conditions for two bound-aries: the velocity inlet and the pressure outlet. The velocity inlet com-prises the circular arc grid boundary, and the pressure outlet is the down-stream boundary, opposite the velocity inlet.

1. Set the conditions for the velocity inlet (velocity-inlet-5).

For the multiphase mixture model, you will specify conditions forthe mixture (i.e., conditions that apply to all phases) and also con-ditions that are specific to the primary and secondary phases. Inthis tutorial, boundary conditions are needed for the mixture andsecondary phase only.




ii. In the Velocity Specification Method drop-down list, selectComponents.

iii. In the Reference Frame drop-down list, keep the defaultselection of Absolute.

iv. Under Axial-Velocity (m/s), input 1.

v. In the Turbulence Specification Method drop-down list, se-lect Intensity and Viscosity Ratio.

vi. Set Turbulence Intensity to 0.5% and Turbulence ViscosityRatio to 5.

For external flows, you should choose a viscosity ratiobetween 1 and 10.


Modeling Cavitation


i. In the Boundary Conditions panel, select water-vapor fromthe Phase drop-down list and click Set....



Modeling Cavitation

2. Set the boundary conditions for the pressure outlet (pressure-outlet-4).

The turbulence conditions you input at the pressure outlet will beused only if flow enters the domain through this boundary. You canset them equal to the inlet values, as no flow reversal is expectedat the pressure outlet. In general, however, it is important to setreasonable values for these downstream scalar values, in case flowreversal occurs at some point during the calculation.


i. In the Boundary Conditions panel, select mixture in thePhase drop-down list and click Set....

ii. Select Intensity and Viscosity Ratio for the Turbulence Spec-ification Method.

iii. Set the Turbulence Intensity to 0.5%.

iv. Set the Turbulent Viscosity Ratio to 5.


i. In the Boundary Conditions panel, select water-vapor fromthe Phase drop-down list and click Set....



Modeling Cavitation

Step 6: Solution



(a) Under Under-Relaxation Factors, set the under-relaxation fac-tor for Momentum to 0.1.

(b) Scroll down and set the Vaporization Mass under-relaxationfactor to 0.001.

The source term created by “evaporation” greatly affects thenumerics of the pressure correction. In order to prevent di-vergence, you need to use a small under-relaxation factor forthis source term.


Modeling Cavitation

(c) Set the under-relaxation factor for Volume Fraction to 0.1.

(d) Under Discretization, select PRESTO! in the Pressure drop-down list and Second Order Upwind in the Momentum drop-down list.

2. Enable the plotting of residuals during the calculation.


(a) Change the convergence criterion for continuity to 1e-5 forimproved accuracy.

(b) Select Plot under Options, and click on OK.


Modeling Cavitation




(b) Click Init to initialize the solution.

4. Set the reference values for the torpedo.

To monitor the convergence of the calculation, you will enable theplotting of the area-weighted average of the pressure coefficient onthe outer boundary of the torpedo. Reference values must be setcorrectly in order for the pressure coefficient calculated by FLUENTto be realistic. FLUENT uses the reference density to calculate thepressure coefficient. For the first few iterations, when the solutionis fluctuating, the pressure coefficient will behave erratically. Thiscan cause the scale of the y axis for the plot to be set too wide,making variations in the value of the coefficient less evident. Toavoid this problem, you will have FLUENT perform a small num-ber of iterations, and then you will adjust the pressure coefficientmonitor scale.


Modeling Cavitation

Report −→Reference Values...

(a) In the Compute From drop-down list, select velocity-inlet-5.

The panel will update to reflect the new values.


Modeling Cavitation

5. Set up a monitor for the pressure coefficient.


Plotting the pressure coefficient will help you monitor the conver-gence of the solution.

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

(b) Enable the Plot and Write options for monitor-1.

(c) Click on Define... to the right of monitor-1.

This will open the Define Surface Monitor panel.


Modeling Cavitation

(d) In the Report Of drop-down lists, select Pressure... and Pres-sure Coefficient.

(e) In the Report Type drop-down list, select Area-Weighted Aver-age.

(f) Set the Plot Window to 1.

(g) In the Surfaces list, select wall-1.

(h) Click OK in the Define Surface Monitor panel and then in theSurface Monitors panel.


Modeling Cavitation

6. Save the case file (cav.cas).




8. Change the plot scale for the pressure coefficient.


(a) Click on Define... to the right of monitor-1.

This will open the Define Surface Monitor panel.

i. Click the Axes... button.

The Axes - Surface Monitor Plot panel will open.


Modeling Cavitation

ii. In the Axes - Surface Monitor Plot panel, select Y as theAxis.

iii. Under Number Format, set Precision to 4.

iv. Deselect Auto Range.

v. Enter a new Range of -0.04 to 0.

vi. Click Apply and close the Axes - Surface Monitor Plotpanel.

(b) Continue the calculation by requesting 1100 additional itera-tions.


FLUENT will ask you to confirm that it is OK to append datato the pressure coefficient monitor file.

(c) Click Yes to continue.

The pressure coefficient has not converged yet, as shown inFigure 16.5, but an inspection of the pressure contours and


Modeling Cavitation

the pressure coefficient values on the surface of the torpedo inthe next step show good correlation with existing experimentaldata [1].

Convergence history of Pressure Coefficient on wall-1FLUENT 6.0 (axi, segregated, mixture, ske)

Jun 19, 2001

Iteration

AverageWeighted

Area

120010008006004002000

0.0000

-0.0050

-0.0100

-0.0150

-0.0200

-0.0250

-0.0300

-0.0350

-0.0400

Figure 16.5: Pressure Coefficient History

(d) Save the data file (cav.dat).



Modeling Cavitation


1. Plot the pressure around the torpedo.


(a) Select Pressure... and Static Pressure in the drop-down listsunder Contours Of.

(b) Select Filled under Options.

(c) Click Display.

Note the low-pressure region near the nose of the torpedo inFigure 16.6. This is where cavitation is expected to occur.

To make the view more realistic, you will need to mirror itacross the centerline.


Modeling Cavitation

Contours of Static Pressure (pascal) Jun 19, 2001FLUENT 6.0 (axi, segregated, mixture, ske)

5.33e+02

-2.14e+02

-1.39e+02

-6.46e+01

1.02e+01

8.49e+01

1.60e+02

2.34e+02

3.09e+02

3.84e+02

4.59e+02

Figure 16.6: Contours of Static Pressure

2. Mirror the display across the centerline.



Modeling Cavitation

(a) Select axis-2 in the Mirror Planes list and click Apply.

(b) Use your middle and left mouse buttons to zoom and translatethe view so that the entire torpedo is visible in the graphicsdisplay (Figure 16.7).

Contours of Static Pressure (pascal) Jun 28, 2001FLUENT 6.0 (axi, segregated, mixture, ske)

5.33e+02

-2.14e+02

-1.39e+02

-6.46e+01

1.02e+01

8.49e+01

1.60e+02

2.34e+02

3.09e+02

3.84e+02

4.59e+02

Figure 16.7: Mirrored View of Contours of Static Pressure

3. Plot the volume fraction of water vapor.


(a) Select Phases... and Volume fraction of water-vapor in the drop-down lists under Contours Of.

(b) Click Display.

Note that the low-pressure region near the nose of the torpedo (Fig-ure 16.7) coincides with the highest volume fraction of water vaporin Figure 16.8.


Modeling Cavitation

Contours of Volume fraction of water-vapor Jun 28, 2001FLUENT 6.0 (axi, segregated, mixture, ske)

7.33e-01

0.00e+00

7.33e-02

1.47e-01

2.20e-01

2.93e-01

3.66e-01

4.40e-01

5.13e-01

5.86e-01

6.59e-01

Figure 16.8: Contours of Water Vapor Volume Fraction


Modeling Cavitation

4. Plot the variation of the pressure coefficient on the surface of thetorpedo.

You used the area-weighted average of the pressure coefficient onwall-1 to monitor the solution convergence. Now you will plot thepressure coefficient distribution on wall-1 at the last iteration per-formed.


(a) Under Y Axis Function, select Pressure... and Pressure Coeffi-cient.

(b) Under Surfaces, select wall-1.

(c) Click Plot.


Modeling Cavitation

Pressure CoefficientFLUENT 6.0 (axi, segregated, mixture, ske)

Jun 19, 2001

Position (m)

CoefficientPressure

0.70.60.50.40.30.20.10-0.1

1.20e+00

1.00e+00

8.00e-01

6.00e-01

4.00e-01

2.00e-01

0.00e+00

-2.00e-01

-4.00e-01

-6.00e-01

wall-1

Figure 16.9: Pressure Coefficient Distribution on the Torpedo


Modeling Cavitation

Summary: This tutorial demonstrated how to set up a cavitating flowaround a torpedo, using FLUENT’s multiphase mixture model withcavitation effects. You learned how to set the boundary conditionsfor an external flow, check grid validity by plotting y+, and howto use surface monitors to monitor the solution convergence. Asteady-state solution was calculated to simulate the formation ofa vapor bubble close to the nose of the torpedo. Even within thisfirst approximation, good correlation is found between the calcu-lated pressure coefficient distribution on the surface of the torpedoand that shown in published data [1]. A more computationally-intensive unsteady calculation is necessary to accurately simulatethe irregular cyclic process of bubble formation, growth, filling bywater jet re-entry, and breakoff.

References:

1. Kunz, R.F., Boger, B.A., Chyczewski, T.S., Stineberg, D.R.,Gibeling, H.J., and Govindan T.R.,“Multiphase CFD of Natu-ral Ventilated Cavitation about Submerged Bodies”, in ASMEpaper FEDSM99-7364, Proceedings of 3rd ASME/JSME JointFluids Engineering Conference, 1999.


Tutorial 17. Using the Mixture and

Eulerian Multiphase Models

Introduction: This tutorial examines the flow of water and air in a teejunction. First you will solve the problem using the less computa-tionally-intensive mixture model, and then you will turn to themore accurate Eulerian model. Finally, you will compare the re-sults obtained with the two approaches.


• Use the mixture model with slip velocities

• Set boundary conditions for internal flow


• Use the Eulerian model

• Compare the results obtained with the two approaches


Problem Description: This problem considers an air-water mixtureflowing upwards in a duct and then splitting in a tee-junction.The ducts are 25 mm in width, the inlet section of the duct is125 mm long, and the top and the side ducts are 250 mm long.The geometry and data for the problem are shown in Figure 17.1.


Using the Mixture and Eulerian Multiphase Models

velocity inletwater: air:

ρ=1000 kg/m ρ=1.2 kg/mµ=9e-4 kg/m-s µ=2e-5 kg/m-sv=1.53 m/s v=1.6 m/s

vol frac=0.02bubble diam=1 mm

3 3

velocity inletwater: v = - 0.31 m/sair: v = - 0.45 m/s

pressure outlet




Preparation

1. Copy the file tee/tee.msh from the FLUENT documentation CDto your working directory (as described in Tutorial 1).




Step 1: Grid

1. Read the grid file (tee.msh).



2. Check the grid.

Grid −→Check








Jul 24, 2001

Figure 17.2: The Grid in the Tee Junction

Extra: You can use the right mouse button to check whichzone number corresponds to each boundary. If you clickthe right mouse button on one of the boundaries in thegraphics window, its zone number, name, and type will beprinted in the FLUENT console window. This feature isespecially useful when you have several zones of the sametype and you want to distinguish between them quickly.



Step 2: Models

1. Keep the default settings for the 2D segregated steady-state solver.



2. Enable the multiphase mixture model with slip velocities.


(a) Select Mixture as the Model.

The panel will expand to show the inputs for the mixturemodel.

(b) Under Mixture Parameters, keep the Slip Velocity turned on.

Since there will be significant difference in velocities for thedifferent phases, you need to solve the slip velocity equation.



(c) Under Body Force Formulation, select Implicit Body Force.

This treatment improves solution convergence by accountingfor the partial equilibrium of the pressure gradient and bodyforces in the momentum equations. It is used when bodyforces are large in comparison to viscous and convective forces,namely in VOF and mixture problems.



3. Turn on the standard k-ε turbulence model with standard wallfunctions.


(a) Select k-epsilon as the Model.

(b) Under k-epsilon Model, keep the default selection of Standard.

The standard k-ε model has been found to be quite effectivein accurately resolving mixture problems when standard wallfunctions are used.

(c) Keep the default selection of Standard Wall Functions underNear-Wall Treatment.

This problem does not require a particularly fine grid, andstandard wall functions will be used.







(b) Set the Gravitational Acceleration in the Y direction to -9.81m/s2.



Step 3: Materials

1. Copy liquid water from the materials database so that it can beused for the primary phase.






(b) In the list of Fluid Materials, select water-liquid (h2o<l>).


(d) Close the Database Materials panel and the Materials panel.



Step 4: Phases

1. Define the liquid water and air phases that flow in the tee junction.


(a) Specify liquid water as the primary phase.






(b) Specify air as the secondary phase.


ii. In the Secondary Phase panel, enter air for the Name.

iii. Select air from the Phase Material drop-down list.

iv. Set the Diameter to 0.001 m.



2. Check the slip velocity formulation to be used.

(a) Click the Interaction... button in the Phases panel.

(b) In the Phase Interaction panel, keep the default selection ofmanninen-et-al in the Slip Velocity drop-down list.




For this problem, you need to set the boundary conditions for three bound-aries: the upper and lower velocity inlets and the pressure outlet.


1. Set the conditions for the lower velocity inlet (velocity-inlet-4).

For the multiphase mixture model, you will specify conditions ata velocity inlet for the mixture (i.e., conditions that apply to allphases) and also conditions that are specific to the primary andsecondary phases.

(a) Set the conditions at velocity-inlet-4 for the mixture.


ii. In the Turbulence Specification Method drop-down list, se-lect Intensity and Length Scale.

iii. Set Turbulence Intensity to 10% and Turbulence LengthScale to 0.025 m.



(b) Set the conditions for the primary phase.


ii. Keep the default Velocity Specification Method and Refer-ence Frame.

iii. Set the Velocity Magnitude to 1.53.



(c) Set the conditions for the secondary phase.

i. In the Boundary Conditions panel, select air from the Phasedrop-down list and click Set....


iii. Set the Velocity Magnitude to 1.6.

iv. Set the Volume Fraction to 0.02.



2. Set the conditions for the upper velocity inlet (velocity-inlet-5).

(a) Set the conditions at velocity-inlet-5 for the mixture.



iii. Set Turbulence Intensity to 10% and Turbulence LengthScale to 0.025 m.



(b) Set the conditions for the primary phase.



iii. Set the Velocity Magnitude to -0.31.

In this problem, outflow characteristics at the upper veloc-ity inlet are assumed to be known, and therefore imposedas a boundary condition.



(c) Set the conditions for the secondary phase.



iii. Set the Velocity Magnitude to -0.45.

iv. Set the Volume Fraction to 0.02.



3. Set the boundary conditions for the pressure outlet (pressure-outlet-3).

For the multiphase mixture model, you will specify conditions at apressure outlet for the mixture and for the secondary phase. Thereare no conditions to be set for the primary phase.

The turbulence conditions you input at the pressure outlet will beused only if flow enters the domain through this boundary. You canset them equal to the inlet values, as no flow reversal is expectedat the pressure outlet. In general, however, it is important to setreasonable values for these downstream scalar values, in case flowreversal occurs at some point during the calculation.

(a) Set the conditions at pressure-outlet-3 for the mixture.



iii. Set the Backflow Turbulence Intensity to 10%.

iv. Set the Backflow Turbulence Length Scale to 0.025.



(b) Set the conditions for the secondary phase.


ii. Set the Backflow Volume Fraction to 0.02.



Step 6: Solution Using the Mixture Model



(a) Keep all default Under-Relaxation Factors.

(b) Under Discretization, select PRESTO! in the Pressure drop-down list.







4. Save the case file (tee.cas).




The solution will converge in approximately 600 iterations.

6. Save the case and data files (tee.cas and tee.dat).




Step 7: Postprocessing for the Mixture Solution

1. Display the pressure field in the tee.


(a) Select Pressure... and Static Pressure in the Contours Of drop-down lists.

(b) Select Filled under Options.

(c) Click Display.



Contours of Static Pressure (pascal) Aug 17, 2001FLUENT 6.0 (2d, segregated, mixture, ske)

2.34e+03

-1.59e+03

-1.19e+03

-8.01e+02

-4.08e+02

-1.54e+01

3.77e+02

7.70e+02

1.16e+03

1.55e+03

1.95e+03




2. Display contours of velocity magnitude (Figure 17.4).


(a) Select Velocity... and Velocity Magnitude in the Contours Ofdrop-down lists.

(b) Click Display.

Contours of Velocity Magnitude (m/s) Aug 17, 2001FLUENT 6.0 (2d, segregated, mixture, ske)

2.22e+00

0.00e+00

2.22e-01

4.45e-01

6.67e-01

8.89e-01

1.11e+00

1.33e+00

1.56e+00

1.78e+00

2.00e+00

Figure 17.4: Contours of Velocity Magnitude

3. Display the volume fraction of air.


(a) Select Phases... and Volume fraction of air in the Contours Ofdrop-down lists.

(b) Click Display.

In Figure 17.5, note the small bubble of air that separates at thesharp edge of the horizontal arm of the tee junction, and the smalllayer of air that floats in the same area above the water, marchingtowards the pressure outlet.



Contours of Volume fraction of air Aug 17, 2001FLUENT 6.0 (2d, segregated, mixture, ske)

9.34e-01

0.00e+00

9.34e-02

1.87e-01

2.80e-01

3.74e-01

4.67e-01

5.60e-01

6.54e-01

7.47e-01

8.41e-01

Figure 17.5: Contours of Air Volume Fraction



Step 8: Setup and Solution for the Eulerian Model

You will use the solution obtained with the mixture model as an initialcondition for the calculation with the Eulerian model.

1. Turn on the Eulerian model.


(a) Under Models, select Eulerian.



2. Specify the drag law to be used for computing the interphase mo-mentum transfer.


(a) Click the Interaction... button in the Phases panel.

(b) In the Phase Interaction panel, keep the default selection ofschiller-naumann in the Drag Coefficient drop-down list.

Note: For this problem there are no parameters to be set for theindividual phases, other than those that you specified when youset up the phases for the mixture model calculation. If you usethe Eulerian model for a flow involving a granular secondaryphase, there are additional parameters that you need to set.There are also other options in the Phase Interaction panel thatmay be relevant for other applications. See the User’s Guidefor complete details on setting up an Eulerian multiphase cal-culation.



3. Select the multiphase turbulence model.


(a) Under k-epsilon Multiphase Model, keep the default selectionof Mixture.

The mixture turbulence model is applicable when phases sepa-rate, for stratified (or nearly stratified) multiphase flows, andwhen the density ratio between phases is close to 1. In thesecases, using mixture properties and mixture velocities is suffi-cient to capture important features of the turbulent flow. Seesection 20.4.7 of the User’s Guide for more information onturbulence models for the Eulerian multiphase model.



4. Continue the solution by requesting 1000 additional iterations.


The solution will converge after about 300 additional iterations.

5. Save the case and data files (tee2.cas and tee2.dat).




Step 9: Postprocessing for the Eulerian Model

1. Display the pressure field in the tee.


Contours of Static Pressure (pascal) Aug 17, 2001FLUENT 6.0 (2d, segregated, eulerian, ske)

2.54e+03

-1.42e+03

-1.02e+03

-6.29e+02

-2.33e+02

1.63e+02

5.59e+02

9.55e+02

1.35e+03

1.75e+03

2.14e+03


2. Display contours of velocity magnitude for the water (Figure 17.7).


(a) In the Contours Of drop-down lists, select Velocity... and waterVelocity Magnitude.

Because the Eulerian model solves individual momentum equa-tions for each phase, you have the choice of which phase toplot solution data for.

(b) Click Display.

3. Display the volume fraction of air.




Contours of water Velocity Magnitude (m/s) Aug 17, 2001FLUENT 6.0 (2d, segregated, eulerian, ske)

2.25e+00

1.43e-02

2.38e-01

4.62e-01

6.85e-01

9.09e-01

1.13e+00

1.36e+00

1.58e+00

1.80e+00

2.03e+00

Figure 17.7: Contours of Water Velocity Magnitude

Contours of Volume fraction of air Aug 17, 2001FLUENT 6.0 (2d, segregated, eulerian, ske)

9.41e-01

0.00e+00

9.41e-02

1.88e-01

2.82e-01

3.76e-01

4.70e-01

5.64e-01

6.58e-01

7.53e-01

8.47e-01

Figure 17.8: Contours of Air Volume Fraction



Note that the air bubble at the tee junction in Figure 17.8 is slightlydifferent from the one that you observed in the solution obtainedwith the mixture model (Figure 17.5). The Eulerian model gen-erally offers better accuracy than the mixture model, as it solvesseparate sets of equations for each individual phase, rather thanmodeling slip velocity between phases. See Sections 20.3 and 20.4of the User’s Guide for more information about the mixture andEulerian models.

Summary: This tutorial demonstrated how to set up and solve a mul-tiphase problem using the mixture model and the Eulerian model.You learned how to set boundary conditions for the mixture andboth phases. The solution obtained with the mixture model wasused as a starting point for the calculation with the Eulerian model.After completing calculations with both models, you compared theresults obtained with the two approaches.


Tutorial 18. Using the Eulerian

Multiphase Model for Granular Flow

Introduction: Mixing tanks are used to maintain solid particles ordroplets of heavy fluids in suspension. Mixing may be requiredto enhance reaction during chemical processing or to prevent sed-imentation. In this tutorial, you will use the Eulerian multiphasemodel to solve the particle suspension problem. The Eulerian mul-tiphase model solves momentum equations for each of the phases,which are allowed to mix in any proportion.


• Use the granular Eulerian multiphase model

• Specify fixed velocities with a user-defined function (UDF) tosimulate an impeller

• Set boundary conditions for internal flow


• Solve a time-accurate transient problem


Problem Description: The problem involves the transient startup ofan impeller-driven mixing tank. The primary phase is water, whilethe secondary phase consists of sand particles with a 111 microndiameter. The sand is initially settled at the bottom of the tank,to a level just above the impeller. A schematic of the mixing tank


Using the Eulerian Multiphase Model for Granular Flow

and the initial sand position is shown in Figure 18.1. The domainis modeled as 2D axisymmetric.

The fixed-values option will be used to simulate the impeller. Ex-perimental data are used to represent the time-averaged velocityand turbulence values at the impeller location. This approachavoids the need to model the impeller itself. These experimentaldata are provided in a user-defined function.

.4446 m

.4446 m

water

settledsandbed

impeller

.1728 m

.116 m.0864 m

.016 m




Preparation

1. Copy the files mixtank/mixtank.msh and mixtank/fix.c fromthe FLUENT documentation CD to your working directory (as de-scribed in Tutorial 1).


Step 1: Grid

1. Read the grid file (mixtank.msh).



2. Check the grid.

Grid −→Check





Extra: You can use the right mouse button to check whichzone number corresponds to each boundary. If you clickthe right mouse button on one of the boundaries in thegraphics window, its zone number, name, and type will beprinted in the FLUENT console window. This feature isespecially useful when you have several zones of the sametype and you want to distinguish between them quickly.



Z

Y

X

Grid (Time=2.1000e+01)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Jul 30, 2001


4. Manipulate the grid display to show the full tank upright.




(a) Under Mirror Planes , select axis.

(b) Click Apply.

The grid display will be updated to show both sides of the tank.

(c) Click Auto Scale .

This option is used to scale and center the current displaywithout changing its orientation (Figure 18.3).

Z

Y

X


Jul 30, 2001

Figure 18.3: Grid Display with Both Sides of the Tank



(d) Click on Camera... to display the tank in an upright position.

This will open the Camera Parameters panel.

(e) Click with the left mouse button on the indicator of the dialand drag it in the counter-clockwise direction till the uprightview is displayed (Figure 18.4).

(f) Click Applyand close the Camera Parameters and Views panels.

Note: When experimenting with different view manipulation tech-niques, you may accidentally “lose” your geometry in the dis-play. You can easily return to the default (front) view by click-ing on the Default button in the Views panel.




Jul 30, 2001

ZY

X

Figure 18.4: Grid Display of the Upright Tank



Step 2: Models

1. Specify a transient, axisymmetric model.


(a) Retain the default Segregated solver.


(b) Under Space , select Axisymmetric.

(c) Under Time, select Unsteady .



2. Enable the Eulerian multiphase model.


(a) Select Eulerian as the Model .

The panel will expand to show the inputs for the Eulerianmodel.

(b) Keep the default settings for the Eulerian model.



3. Turn on the k-ε turbulence model with standard wall functions.


(a) Select k-epsilon (2 eqn) as the Model .

(b) Keep the default selection of Standard Wall Functions underNear-Wall Treatment.

This problem does not require a particularly fine grid, andstandard wall functions will be used.

(c) Under k-epsilon Multiphase Model , select the Dispersed model.

The dispersed turbulence model is applicable in this case be-cause there is clearly one primary continuous phase and thematerial density ratio of the phases is about 2.5. Furthermore,



the Stokes number is much less than 1. Therefore, the parti-cle’s kinetic energy will not depart significantly from that ofthe liquid.



(a) Turn on Gravity .


(b) Set the Gravitational Acceleration in the X direction to -9.81m/s2.



Step 3: Materials

In this step, you will add liquid water to the list of fluid materials bycopying it from the materials database, and create a new material calledsand.


1. Copy liquid water from the materials database so that it can beused for the primary phase.





(b) In the list of Fluid Materials , select water-liquid (h2o <l>).


(d) Close the Database Materials panel.

2. Create a new material called sand .



(a) Type the name sand in the Name text-entry box.

(b) Under Properties , enter 2500 kg/m3 as the Density .

(c) Remove the entry for Chemical Formula so the field is blank.

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

When you click Change/Create , a question dialog box will ap-pear, asking you if water-liquid should be overwritten. ClickNo to retain water-liquid and add the new material, sand , tothe list. The Materials panel will be updated to show the newmaterial name in the Fluid Materials list.



Step 4: Phases

1. Define the primary (water) and secondary (sand) phases.


(a) Specify water as the primary phase.






(b) Specify sand as the secondary phase.


ii. In the Secondary Phase panel, enter sand for the Name.

iii. Select sand from the Phase Material drop-down list.

iv. Turn on the Granular option.

v. Define the properties of the sand phase.

A. Enter 0.000111 as the Diameter.

B. Select syamlal-obrien from the Granular Viscosity drop-down list.

C. Select lun-et-al from the Granular Bulk Viscosity drop-down list.

D. Enter 0.6 as the Packing Limit .



(c) Specify the drag law to be used for computing the interphasemomentum transfer.

i. Click the Interaction... button in the Phases panel.

ii. In the Phase Interaction panel, select gidaspow in the DragCoefficient drop-down list.




For this problem, there are no conditions to be specified on the outerboundaries. Within the domain, there are three fluid zones, representingthe impeller region, the region where the sand is initially located, and therest of the tank. There are no conditions to be specified in the latter twozones, so you will need to set conditions only in the zone representingthe impeller.

As mentioned earlier, a UDF is used to specify the fixed velocities thatsimulate the impeller. The values of the time-averaged impeller velocitycomponents and turbulence quantities are based on experimental mea-surement. The variation of these values may be expressed as a functionof radius, and imposed as polynomials according to:

variable = A1 + A2r + A3r2 + A4r

3 + ...

The order of polynomial to be used depends on the behavior of the func-tion being fitted. For this tutorial, the polynomial coefficients shown inTable 18.1 are provided in the UDF fix.c.

Table 18.1: Impeller Profile Specifications

Variable A1 A2 A3

u velocity -7.1357e-2 54.304 -3.1345e+3v velocity 3.1131e-2 -10.313 9.5558e+2

kinetic energy 2.2723e-2 6.7989 -424.18dissipation -6.5819e-2 88.845 -5.3731e+3

Variable A4 A5 A6

u velocity 4.5578e+4 -1.9664e+5 –v velocity -2.0051e+4 1.1856e+5 –

kinetic energy 9.4615e+3 -7.7251e+4 1.8410e+5dissipation 1.1643e+5 -9.1202e+5 1.9567e+6

See the separate UDF Manual for details about setting up a UDF usingthe DEFINE PROFILE macro. Note that, while this macro is usually usedto specify a profile condition on a boundary face zone, it is used in fix.c



to specify the condition in a fluid cell zone. The arguments of the macrohave been changed accordingly.

1. Compile the UDF, fix.c, using the Interpreted UDFs panel.

Define −→ User-Defined −→ Functions −→Interpreted...

(a) Enter fix.c under Source File Name .

! Make sure that the C source code for your UDF and yourmesh file reside in your working directory. If your sourcecode is not in your working directory, then when you com-pile the UDF you must enter the file’s complete path inthe Interpreted UDFs panel, instead of just the filename.

(b) Keep the default Stack Size setting of 10000.

(c) Turn on the Display Assembly Listing option.

Turning on the Display Assembly Listing option will cause alisting of the assembly language code to appear in your consolewindow when the function compiles.

(d) Click Compile to compile your UDF.

Note: The name and contents of your UDF will be stored inyour case file when you write the case file.



2. Set the conditions for the fluid zone representing the impeller (fix-zone ).

You will specify the conditions for the water and the sand sepa-rately. There are no conditions to be specified for the mixture (i.e.,conditions that apply to all phases); the default conditions for themixture are acceptable.


(a) Set the conditions on fix-zone for the water.

All of the conditions for the water will come from the UDF.

i. In the Boundary Conditions panel, select water from thePhase drop-down list and click Set... .

ii. Turn on the Fixed Values option.


iii. Select udf fixed u from the drop-down list to the right ofAxial Velocity .

iv. Select udf fixed v for Radial Velocity .



v. Select udf fixed ke for Turbulence Kinetic Energy .

vi. Select udf fixed diss for Turbulence Dissipation Rate .

(b) Set the conditions on fix-zone for the sand.

All of the conditions for the sand will come from the UDF.

i. In the Boundary Conditions panel, select sand from thePhase drop-down list and click Set... .

ii. Turn on the Fixed Values option.


iii. Select udf fixed u for Axial Velocity .

iv. Select udf fixed v for Radial Velocity .



Step 6: Solution



(a) For the Under-Relaxation Factors , set Pressure to 0.5, Momen-tum to 0.2, and Turbulent Viscosity to 0.8.

(b) Under Discretization , keep the default settings.



3. Initialize the solution using the default initial values.




4. Patch the initial sand bed configuration.

(a) In the Variable list, select sand Volume Fraction .

(b) Select initial-sand in the Zones To Patch list.

(c) Set the Value to 0.56.

(d) Click Patch .

5. Set the time stepping parameters.


(a) Set the Time Step Size to 0.005.

(b) Under Iteration , set the Max Iterations per Time Step to 40.

(c) Click Apply.



6. Save the initial case and data files (mixtank.cas and mixtank.dat).


The problem statement is now complete. As a precaution, youshould review the impeller velocity fixes and sand bed patch afterrunning the calculation for a single time step. Since you are usinga UDF for the velocity profiles, you need to perform one time stepin order for the profiles to be calculated and available for viewing.

7. Run the calculation for 0.005 seconds.



(b) Click Iterate.



8. Check the initial velocities and sand volume fraction.

In order to display the initial velocities in the fluid zone where youhave fixed their values (fix-zone) , you will need to create a zonesurface for it.

(a) Create a zone surface for fix-zone .

Surface −→Zone...

i. In the Zone list, select fix-zone .

ii. Under New Surface Name , retain the default name.

The default name is the same as the zone name. FLUENTwill automatically assign the default name to the new sur-face when it is created.

iii. Click on Create and close the panel.

The new surface will be added to the Surfaces list in theZone Surface panel.



(b) Display the initial impeller velocities for water.


i. Select water Velocity in the Vectors Of drop-down list.

ii. Select Velocity... and water Velocity Magnitude in the ColorBy drop-down lists.

iii. In the Surfaces list, select fix-zone .

iv. In the Style drop-down list, select arrow .

v. Click Display.

FLUENT will display the water velocity vector fixes at theimpeller location, as shown in Figure 18.5.



water-velocity Colored By water Velocity Magnitude (m/s) (Time=5.0000e-03)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Nov 19, 2001

8.08e-01

7.27e-01

6.46e-01

5.65e-01

4.85e-01

4.04e-01

3.23e-01

2.42e-01

1.62e-01

8.08e-02

8.41e-06

Figure 18.5: Initial Impeller Velocities for Water



(c) Display the initial impeller velocities for sand.


i. Select sand Velocity in the Vectors Of drop-down list.

ii. Select Velocity... and sand Velocity Magnitude in the ColorBy drop-down lists.

iii. Click Display.

FLUENT will display the sand velocity vector fixes at theimpeller location, as shown in Figure 18.6.

sand-velocity Colored By sand Velocity Magnitude (m/s) (Time=5.0000e-03)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Nov 19, 2001

8.01e-01

7.21e-01

6.41e-01

5.61e-01

4.80e-01

4.00e-01

3.20e-01

2.40e-01

1.60e-01

8.01e-02

0.00e+00

Figure 18.6: Initial Impeller Velocities for Sand



(d) Display contours of sand volume fraction.


i. Select Phases... and Volume fraction of sand in the Con-tours Of drop-down lists.

ii. Select Filled under Options .

iii. Click Display.

FLUENT will display the initial location of the settled sandbed, shown in Figure 18.7.



Contours of Volume fraction of sand (Time=5.0000e-03) Nov 19, 2001FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

5.62e-01

0.00e+00

5.62e-02

1.12e-01

1.69e-01

2.25e-01

2.81e-01

3.37e-01

3.94e-01

4.50e-01

5.06e-01

Figure 18.7: Initial Settled Sand Bed



9. Run the calculation for 1 second.



(b) Click Iterate.

After 200 time steps have been computed (a total of 1 secondof operation), you will review the results before continuing.

10. Save the case and data files (mixtank1.cas and mixtank1.dat).


11. Examine the results of the calculation after 1 second.

(a) Display the velocity vectors in the whole tank for the water.


! Remember to deselect fix-zone in the Surfaces list.

Figure 18.8 shows the water velocity vectors after 1 second ofoperation. The circulation is confined to the region near theimpeller, and has not yet had time to develop in the upperportions of the tank.

(b) Display the velocity vectors for the sand.


Figure 18.9 shows the sand velocity vectors after 1 second ofoperation. The circulation of sand around the impeller is sig-nificant, but note that no sand vectors are plotted in the upperpart of the tank, where the sand is not yet present.



water-velocity Colored By water Velocity Magnitude (m/s) (Time=1.0000e+00)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Nov 19, 2001

8.11e-01

7.30e-01

6.49e-01

5.68e-01

4.87e-01

4.06e-01

3.25e-01

2.44e-01

1.62e-01

8.14e-02

2.31e-04

Figure 18.8: Water Velocity Vectors after 1 Second

sand-velocity Colored By sand Velocity Magnitude (m/s) (Time=1.0000e+00)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Nov 19, 2001

8.17e-01

7.35e-01

6.53e-01

5.72e-01

4.90e-01

4.08e-01

3.27e-01

2.45e-01

1.63e-01

8.17e-02

0.00e+00

Figure 18.9: Sand Velocity Vectors after 1 Second



(c) Display contours of sand volume fraction.


Notice that the action of the impeller draws clear fluid fromabove the originally settled bed and mixes it into the sand. Tocompensate, the sand bed is lifted up slightly. The maximumsand volume fraction has increased as a result of settling un-derneath the impeller and near the outer radius of the tank.

Contours of Volume fraction of sand (Time=1.0000e+00) Nov 19, 2001FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

5.47e-01

0.00e+00

5.47e-02

1.09e-01

1.64e-01

2.19e-01

2.74e-01

3.28e-01

3.83e-01

4.38e-01

4.93e-01

Figure 18.10: Contours of Sand Volume Fraction after 1 Second

12. Continue the calculation for another 19 seconds.


(a) Set the Time Step Size to 0.01.

The initial calculation was performed with a very small timestep size to stabilize the solution. After the initial calcula-tion, you can usually increase the time step to speed up thecalculation.

(b) Set the Number of Time Steps to 1900.

(c) Click Iterate.



The transient calculation will continue to 20 seconds.

13. Save the case and data files (mixtank20.cas and mixtank20.dat).





You will now examine the progress of the sand and water in the mixingtank after a total of 20 seconds.The mixing tank has nearly, but not quite,reached a steady flow solution.

1. Display the velocity vectors for the water.


Figure 18.11 shows the water velocity vectors after 20 seconds ofoperation. The circulation of water is now very strong in the lowerportion of the tank, though modest near the top.

water-velocity Colored By water Velocity Magnitude (m/s) (Time=2.0000e+01)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Nov 19, 2001

8.31e-01

7.48e-01

6.65e-01

5.82e-01

4.99e-01

4.16e-01

3.33e-01

2.50e-01

1.67e-01

8.44e-02

1.41e-03

Figure 18.11: Water Velocity Vectors after 20 Seconds



2. Display the velocity vectors for the sand.


Figure 18.12 shows the sand velocity vectors after 20 seconds ofoperation. The sand has now been suspended much higher withinthe mixing tank, but does not reach the upper region of the tank.The water velocity in that region is not sufficient to overcome thegravity force on the sand particles.

sand-velocity Colored By sand Velocity Magnitude (m/s) (Time=2.0000e+01)FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

Nov 19, 2001

8.34e-01

7.51e-01

6.67e-01

5.84e-01

5.01e-01

4.17e-01

3.34e-01

2.50e-01

1.67e-01

8.34e-02

0.00e+00

Figure 18.12: Sand Velocity Vectors after 20 Seconds



3. Display contours of sand volume fraction.


Figure 18.13 shows the contours of sand volume fraction after 20seconds of operation.

Contours of Volume fraction of sand (Time=2.0000e+01) Nov 19, 2001FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

3.23e-01

0.00e+00

3.23e-02

6.47e-02

9.70e-02

1.29e-01

1.62e-01

1.94e-01

2.26e-01

2.59e-01

2.91e-01

Figure 18.13: Contours of Sand Volume Fraction after 20 Seconds



4. Display filled contours of static pressure in the mixing tank.

(a) Select Pressure... and Relative Static Pressure in the ContoursOf drop-down lists.

(b) Click Display.

Figure 18.14 shows the pressure distribution after 20 secondsof operation. Notice that the pressure field represents the hy-drostatic pressure except for some slight deviations due to theflow of the impeller near the bottom of the tank.

Contours of Static Pressure (pascal) (Time=2.0000e+01) Nov 19, 2001FLUENT 6.0 (axi, segregated, eulerian, ske, unsteady)

1.50e+02

-1.19e+03

-1.06e+03

-9.23e+02

-7.89e+02

-6.55e+02

-5.20e+02

-3.86e+02

-2.52e+02

-1.18e+02

1.63e+01

Figure 18.14: Contours of Pressure after 20 Seconds

Summary: This tutorial demonstrated how to set up and solve a granu-lar multiphase problem using the Eulerian multiphase model. Theproblem involved particle suspension in a mixing tank and post-processing showed the near-steady-state behavior of the sand inthe mixing tank.


Tutorial 19. Modeling Solidification

Introduction: This tutorial illustrates how to set up and solve a prob-lem involving solidification. In this tutorial, you will learn howto:

• Define a solidification problem

• Define pull velocities for simulation of continuous casting

• Define a surface tension gradient for Marangoni convection

• Solve a solidification problem

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT, and that you have solved Tutorial 1.Some steps in the setup and solution procedure will not be shownexplicitly.

Problem Description: This tutorial demonstrates the setup and solu-tion procedure for a fluid flow and heat transfer problem involvingsolidification, namely the Czochralski growth process. The geome-try considered is a 2D axisymmetric bowl (shown in Figure 19.1),containing a liquid metal. The bottom and sides of the bowl areheated above the liquidus temperature, as is the free surface of theliquid. The liquid is solidified by heat loss from the crystal andthe solid is pulled out of the domain at a rate of 0.001 m/s and atemperature of 500 K. There is a steady injection of liquid at thebottom of the bowl with a velocity of 1.01×10−3 and a temperatureof 1300 K. Material properties are listed in Figure 19.1.

Starting with an existing 2D mesh, the details regarding the setupand solution procedure for the solidification problem are presented.The steady conduction solution for this problem is computed as aninitial condition. Then, the fluid flow is turned on to investigate theeffect of natural and Marangoni convection in an unsteady fashion.


Modeling Solidification

Free Surface

h = 100 W/m KT = 1500 K

2

env

T = 1400 K

T = 1300 K

u = 0.00101 m/s

T = 500 K

Mushy Region Crystal

u = 0.001 m/s

Ω = 1 rad/s

0.05 m

0.1 m

0.03 m

0.1 m

g

ρ = 8000 − 0.1*T kg/m3

µ = 5.53 x 10 kg/m-s-3

k = 30 W/m-Kc = 680 J/kg-Kp∂σ/∂T

= −3.6 x 10 N/m-K-4

solidusliquidus

T = 1100 KT = 1200 KL = 1 x 10 J/kg5

mushA = 1 x 10 kg/m -s4 3

T = 1300 K

T = 500 K

Figure 19.1: Solidification in Czochralski model



Preparation

1. Copy the file solid/solid.msh from the FLUENT documentationCD to your working directory (as described in Tutorial 1).


Step 1: Grid

1. Read the mesh file solid.msh.


As this mesh is read by FLUENT, messages appear in the consolewindow reporting the progress of the reading.

2. Check the grid.

Grid −→Check

FLUENT performs various checks on the mesh and reports the progressin the console window. Pay particular attention to the minimumvolume. Make sure this is a positive number.


Display −→ Grid...




Jun 19, 2001

Figure 19.2: Graphics Display of Grid



Step 2: Models

1. Enable the modeling of axisymmetric swirl.


(a) Under Space, select Axisymmetric Swirl.

(b) Keep the default settings for everything else.



2. Define the solidification model.

Define −→ Models −→Solidification & Melting...

(a) Under Model, turn on Solidification/Melting.


(b) Under Parameters, keep the default value for the Mushy ZoneConstant.

The default value of 100000 is acceptable for most cases.

(c) Turn on Include Pull Velocities.

The panel will expand to show an additional input.

Including the pull velocities accounts for the movement of thesolidified material as it is continuously withdrawn from thedomain in the continuous casting process.

Note: It is possible to have FLUENT compute the pull ve-locities during the calculation, but this approach is com-putationally expensive, and is recommended only if thepull velocities are strongly dependent on the location ofthe liquid-solid interface. In this tutorial, you will patchvalues for the pull velocities instead of having FLUENTcompute them. See the User’s Guide for more informa-tion.



Note: When you click OK in the Solidification/Melting panel, FLU-ENT will present an Information dialog box telling you thatavailable material properties have changed for the solidifica-tion model. You will be setting properties later, so you cansimply click OK in the dialog box to acknowledge this infor-mation.

Note: FLUENT will automatically enable the energy calculationwhen you enable the solidification model, so you need not visitthe Energy panel.

3. Add the effect of gravity on the model.




(b) Set the Gravitational Acceleration in the X direction to -9.81m/s2.



Step 3: Materials

In this step, you will create a new material and specify its properties,including the melting heat, solidus temperature, and liquidus temperature.


1. In the Name field, enter liquid-metal.

2. Specify the density as a function of temperature.

As shown in Figure 19.1, the density of the material is defined bya polynomial function: ρ = 8000 − 0.1T .



(a) Select Polynomial in the Density drop-down list.

The Polynomial Profile will open.

(b) Increase the value of Coefficients to 2.

(c) Enter 8000 for coefficient 1 and -0.1 for coefficient 2.

When you click OK in the Polynomial Profile panel, a questiondialog box will appear, asking you if air should be overwritten.Click No to retain air and add the new material, liquid-metal,to the list. The Materials panel will be updated to show thenew material name in the Fluid Materials list. You will needto select liquid-metal in the Fluid Materials drop-down list toset the other material properties.

3. Set the specific heat, Cp, to 680 J/kg-K.

4. Set the Thermal Conductivity to 30 W/m-K.

5. Set the Viscosity to 0.00553 kg/m-s.

6. Set the Melting Heat to 100000 J/kg.

7. Set the Solidus Temperature to 1100 K.

8. Set the Liquidus Temperature to 1200 K.

9. Click on Change/Create and close the Materials panel.





1. Set the boundary conditions for the fluid.

(a) Select liquid-metal in the Material Name drop-down list.

2. Set the boundary conditions for the velocity inlet.



(a) Set the Velocity Magnitude to 0.00101 m/s.

(b) Set the Temperature to 1300 K.

3. Set boundary conditions for the outlet.

Here, the solid is pulled out with a specified velocity, so a velocityinlet is used with the velocities pointing outwards.

(a) In the Velocity Specification Method drop-down list, selectComponents.

The panel will change to show related inputs.

(b) Set the Axial-Velocity to 0.001 m/s.

(c) Set the Swirl Angular Velocity to 1 rad/s.

(d) Set the Temperature to 500 K.



4. Set the boundary conditions for the bottom wall.

(a) Select Temperature under Thermal Conditions.




5. Set the boundary conditions for the free surface.

The specified shear and Marangoni stress boundary conditions areuseful in modeling situations in which the shear stress (rather thanthe motion of the fluid) is known. A free surface condition isan example of such a situation. In this case, the conduction isMarangoni stress driven and the shear stress is dependent on thesurface tension, which is a function of temperature.

(a) Specify the thermal conditions.

i. Select Convection under Thermal Conditions.

The panel will change to show related inputs.

ii. Set the Heat Transfer Coefficient to 100 W/m2-K.

iii. Set the Free Stream Temperature to 1500 K.

(b) Specify the shear conditions.

i. Click the Momentum tab.

The wall motion and shear condition will be displayed.



ii. Under Shear Condition, select Marangoni Stress.

The Marangoni Stress condition allows you to specify thegradient of the surface tension with respect to temperatureat a wall boundary.

iii. Set the Surface Tension Gradient to -0.00036 N/m-K.

6. Set the boundary conditions for the side wall.

(a) Select Temperature under Thermal Conditions.


7. Set the boundary conditions for the solid wall.

(a) Specify the thermal conditions.

i. Select Temperature under Thermal Conditions.

ii. Set the Temperature to 500 K.

(b) Specify the wall motion.

i. Click the Momentum tab.



ii. Under Wall Motion, select Moving Wall.

The panel will expand to show additional parameters.

iii. Under Motion, select Rotational.

The panel changes to show the rotational speed.

iv. Under Speed, set the rotational velocity to 1.0 rad/s.



Step 5: Solution: Steady Conduction

In this step, you will disable the calculation of the flow and swirl velocityequations, and calculate the conduction only. This steady-state solutionwill be used as the initial condition for the time-dependent fluid flow andheat transfer calculation.


In this step, you will specify the discretization schemes to be used,and temporarily turn off the calculation of the flow and swirl ve-locity equations.




(a) In the Equations list, deselect Flow and Swirl Velocity.

(b) Keep the default values for all Under-Relaxation Factors.

(c) Under Discretization, select PRESTO! for Pressure, SIMPLE forPressure-Velocity Coupling, and First Order Upwind for Momen-tum and Swirl Velocity.



(a) Check that the value for Initial Temperature is set to 300 K.

Since you are solving only the steady conduction problem, theinitial values for the pressure and velocities will not be used.

(b) Click on Init and Close the panel.



3. Define a custom field function for the swirl pull velocity.

You will use this field function to patch a variable value for theswirl pull velocity in the next step. The swirl pull velocity is equalto Ωr, where Ω is the angular velocity and r is the radial coordinate.Since Ω = 1 rad/s, you can simplify the equation to simply r. Inthis example, the value of Ω is included for demonstration purposes.


(a) In the Field Functions drop-down lists, select Grid... and RadialCoordinate.

(b) Click the Select button.

radial-coordinate will appear in the Definition field. If youmake a mistake, click the DEL button on the calculator pad todelete the last item you added to the function definition.

(c) Click the X button on the calculator pad.

(d) Click on 1.

(e) Enter omegar as the New Function Name.



(f) Click Define and close the panel.

If you wish to check the function definition, click on Manage...and select omegar.

4. Patch the pull velocities.

As noted earlier, you will patch values for the pull velocities, ratherthan having FLUENT compute them. Since the radial pull velocityis zero, you will patch just the axial and swirl pull velocities.

Solve −→ Initialize −→Patch...

(a) Specify the value of the axial pull velocity.

i. In the Variable list, select Axial Pull Velocity.

ii. Select fluid in the Zones To Patch list.

iii. Set the Value to 0.001 m/s.

iv. Click Patch.



(b) Specify the value of the swirl pull velocity.

i. In the Variable list, select Swirl Pull Velocity.

ii. Enable the Use Field Function option.

iii. Select omegar in the Field Function list.

iv. Click Patch.






(b) Click OK.

6. Save the initial case and data files (solid0.cas and solid0.dat).






8. Display filled contours of temperature (Figure 19.3).


(a) Under Options, select Filled.

(b) Select Temperature... and Static Temperature in the ContoursOf drop-down lists.

(c) Click Display.



Contours of Static Temperature (k)FLUENT 6.0 (axi, swirl, segregated, lam)

Jun 20, 2001

1.40e+03

1.31e+03

1.22e+03

1.13e+03

1.04e+03

9.50e+02

8.60e+02

7.70e+02

6.80e+02

5.90e+02

5.00e+02

Figure 19.3: Contours of Temperature for Steady Conduction Solution

The thickness of the mushy zone can be determined from the con-tours of temperature. The mushy zone is the region where the tem-perature is between the liquidus temperature and solidus tempera-ture.

9. Save the case and data files for the steady conduction solution(solid.cas and solid.dat).




Step 6: Solution: Unsteady Flow and Heat Trans-fer

In this step, you will turn on time dependence and include the flow andswirl velocity equations in the calculation. You will then solve the un-steady problem using the steady conduction solution as the initial condi-tion.

1. Enable a time-dependent solution.


(a) Under Time, select Unsteady.

(b) Under Unsteady Formulation, retain 1st-Order Implicit.



2. Enable the solution of the flow and swirl velocity equations.


(a) Select Flow and Swirl Velocity in the Equations list and keepthe selection of Energy.

Now all three items in the Equations list will be selected.

(b) Keep the default values for all Under-Relaxation Factors.

(c) Under Discretization, retain the settings for all parameters.

3. Save the initial case and data files (solid01.cas and solid01.dat).


4. Run the calculation for 2 time steps.




(a) Under Time, set the Time Step Size to 0.1 seconds.

(b) Set the Number of Time Steps to 2.

(c) Under Iteration, retain the default value of 20 for Max Itera-tions per Time Step.

(d) Click Iterate.

5. Examine the results of the calculation after 0.2 seconds.

(a) Display filled contours of temperature (Figure 19.4).


i. Select Temperature... and Static Temperature in the Con-tours Of drop-down lists.

ii. Click Display.

Contours of Static Temperature (k) (Time=2.0000e-01)FLUENT 6.0 (axi, swirl, segregated, lam, unsteady)

Jul 06, 2001

1.40e+03

1.31e+03

1.22e+03

1.13e+03

1.04e+03

9.50e+02

8.60e+02

7.70e+02

6.80e+02

5.90e+02

5.00e+02

Figure 19.4: Contours of Temperature at t = 0.2 s

The temperature contours show the gradient in tempera-ture from the hot walls on the left to the cooler zone onthe right.



(b) Display contours of stream function (Figure 19.5).

i. Under Options, deselect Filled.

ii. Select Velocity... and Stream Function in the Contours Ofdrop-down lists.

iii. Click Display.

Contours of Stream Function (kg/s) (Time=2.0000e-01)FLUENT 6.0 (axi, swirl, segregated, lam, unsteady)

Nov 19, 2001

2.12e-02

1.91e-02

1.69e-02

1.48e-02

1.27e-02

1.06e-02

8.47e-03

6.36e-03

4.24e-03

2.12e-03

0.00e+00

Figure 19.5: Contours of Stream Function at t = 0.2 s

As shown in Figure 19.5, the liquid is beginning to cir-culate in a large eddy, driven by natural convection andMarangoni convection on the free surface.

(c) Display contours of liquid fraction (Figure 19.6).

i. Select Solidification/Melting... and Liquid Fraction in theContours Of drop-down lists.

ii. Click Display.

The liquid fraction contours show the current position ofthe melt front. Note that in Figure 19.6, the mushy zonedivides the liquid and solid regions roughly in half.



Contours of Liquid Fraction (Time=2.0000e-01)FLUENT 6.0 (axi, swirl, segregated, lam, unsteady)

Aug 07, 2001

1.00e+00

9.00e-01

8.00e-01

7.00e-01

6.00e-01

5.00e-01

4.00e-01

3.00e-01

2.00e-01

1.00e-01

0.00e+00

Figure 19.6: Contours of Liquid Fraction at t = 0.2 s



6. Continue the calculation for 48 additional time steps.


After a total of 50 time steps have been completed, the elapsed timewill be 5 seconds.

7. Examine the results of the calculation after 5 seconds.

(a) Display filled contours of temperature (Figure 19.7).

Contours of Static Temperature (k) (Time=5.0000e+00)FLUENT 6.0 (axi, swirl, segregated, lam, unsteady)

Aug 07, 2001

1.40e+03

1.31e+03

1.22e+03

1.13e+03

1.04e+03

9.50e+02

8.60e+02

7.70e+02

6.80e+02

5.90e+02

5.00e+02

Figure 19.7: Contours of Temperature at t = 5 s

As shown in Figure 19.7, the temperature contours are fairlyuniform through the melt front and solid material. The dis-tortion of the temperature field due to the recirculating liquidis also clearly evident.

In a continuous casting process, it is important to pull out thesolidified material at the proper time. If the material is pulledout too soon, it will not have solidified; that is, it will still bein a mushy state. If it is pulled out too late, it solidifies in thecasting pool and cannot be pulled out in the required shape.The optimal rate of pull can be determined from the contoursof liquidus temperature and solidus temperature.



(b) Display contours of stream function (Figure 19.8).


Contours of Stream Function (kg/s) (Time=5.0000e+00)FLUENT 6.0 (axi, swirl, segregated, lam, unsteady)

Nov 19, 2001

1.33e-01

1.20e-01

1.07e-01

9.32e-02

7.99e-02

6.66e-02

5.33e-02

4.00e-02

2.66e-02

1.33e-02

0.00e+00

Figure 19.8: Contours of Stream Function at t = 5 s

Note that the flow has developed more fully now, as comparedwith Figure 19.5 after 0.2 seconds. The main eddy, driven bynatural convection and Marangoni stress, dominates the flow.

To examine the position of the melt front and the extent ofthe mushy zone, you will plot the contours of liquid fraction.

(c) Display contours of liquid fraction (Figure 19.9).

The introduction of liquid material at the left of the domainis balanced by the pulling of the solidified material from theright. After 5 seconds, the equilibrium position of the meltfront is beginning to be established.

8. Save the case and data files for the solution at 5 seconds (solid5.casand solid5.dat).




Contours of Liquid Fraction (Time=5.0000e+00)FLUENT 6.0 (axi, swirl, segregated, lam, unsteady)

Nov 19, 2001

1.00e+00

9.00e-01

8.00e-01

7.00e-01

6.00e-01

5.00e-01

4.00e-01

3.00e-01

2.00e-01

1.00e-01

0.00e+00

Figure 19.9: Contours of Liquid Fraction at t = 5 s



Summary: In this tutorial, you studied the setup and solution fora fluid flow problem involving solidification for the Czochralskigrowth process.

The solidification model in FLUENT can be used to model thecontinuous casting process where a solid material is continuouslypulled out from the casting domain. In this tutorial, you patcheda constant value and a custom field function for the pull velocitiesinstead of computing them. For cases where the pull velocity isnot changing over the domain, this approach is used as it is com-putationally less expensive than having FLUENT compute the pullvelocities during the calculation.

For more information about the solidification/melting model, seethe User’s Guide.


Tutorial 20. Postprocessing

Introduction: In this tutorial, the postprocessing capabilities ofFLUENT are demonstrated for a 3D laminar flow involving conju-gate heat transfer. The flow is over a rectangular heat-generatingelectronics chip which is mounted on a flat circuit board. Theheat transfer involves the coupling of conduction in the chip andconduction and convection in the surrounding fluid. The physicsof conjugate heat transfer such as this is common in many engi-neering applications, including the design and cooling of electroniccomponents.

In this example, you will read the case and data files (without doingthe calculation) and perform a number of postprocessing exercises.In the process, you will learn how to:

• Create surfaces for the display of 3D data

• Display velocity vectors

• Display filled contours of temperature on several surfaces

• Mirror a display about a symmetry plane

• Add lights to the display at multiple locations

• Use the Scene Description and Animate panels to animate thegraphics display

• Use the Sweep Surface panel to display results on successiveslices of the domain

• Display pathlines

• Plot quantitative results

• Overlay and “explode” a display

• Annotate your display


Postprocessing

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT, and that you have solved Tutorial 1.

Problem Description: The problem to be considered is shown schemat-ically in Figure 20.1. The configuration consists of a series of side-by-side electronic chips, or modules, mounted on a circuit board.Air flow, confined between the circuit board and an upper wall,cools the modules. To take advantage of the symmetry present inthe problem, the model will extend from the middle of one moduleto the plane of symmetry between it and the next module.

As shown in the figure, each half-module is assumed to generate2.0 Watts and to have a bulk conductivity of 1.0 W/m2-K. Thecircuit board conductivity is assumed to be one order of magnitudelower: 0.1 W/m2-K. The air flow enters the system at 298 K witha velocity of 1 m/s. The Reynolds number of the flow, based onthe module height, is about 600. The flow is therefore treated aslaminar.

Symmetry Planes

Air Flow 1.0 m/s 298 K

Circuit Boardk = 0.1 W/m2-K

Electronic Module (one half)k = 1.0 W/m2-KQ = 2.0 Watts

Top WallExternally Cooled

Bottom WallExternally Cooled



Postprocessing

Preparation

1. Copy the files chip/chip.cas and chip/chip.dat from the FLU-ENT documentation CD to your working directory (as describedin Tutorial 1).


Step 1: Reading the Case and Data Files

1. Read in the case and data files (chip.cas and chip.dat).

File −→ Read −→Case & Data...

Once you select chip.cas, chip.dat will be read automatically.


Postprocessing

Step 2: Grid Display



(a) Under Options, select Edges.

(b) In the Surfaces list, select board-top and chip.

(c) Click Display.

Note: You may want to scroll through the Surfaces list to be surethat no other surfaces are selected. You can also deselect allsurfaces by clicking on the far-right button at the top of theSurfaces list, and then select the desired surfaces for display.


Postprocessing

2. Use your left mouse button to rotate the view, and your middlemouse button to zoom the view until you obtain an enlarged iso-metric display of the circuit board in the region of the chip, asshown in Figure 20.2.


Jul 05, 2001

Z

YX

Figure 20.2: Graphics Display of the Chip and Board Surfaces

Extra: You can use the right mouse button to check which zonenumber corresponds to each boundary. If you click the rightmouse button on one of the boundaries displayed in the graph-ics window, its zone number, name, and type will be printedin the console window. This feature is especially useful whenyou have several zones of the same type and you want to dis-tinguish between them quickly.


Postprocessing

3. Create a filled surface display.

(a) In the Grid Display panel under Options, deselect Edges andselect Faces.

(b) Click Display.

The surfaces run together with no shading to separate the chipfrom the board.

4. Add shading effects by enabling lights.

Display −→Options...

(a) Under Lighting Attributes, enable the Lights On.

(b) Click Apply.

Shading will be added to the surface grid display (Figure 20.3).


Postprocessing

Z

YX


Jul 05, 2001

Figure 20.3: Graphics Display of the Chip and Board Surfaces withDefault Lighting


Postprocessing

(c) In the Display Options panel, click on the Lights... button.

This will open the Lights panel.

Note: When you turn lights on, the default settings are forlight 0 (indicated by the Light ID), corresponding to awhite light at the position (1, 1, 1), as indicated by theunit vectors under Direction.


Postprocessing

(d) Add a light at (-1,1,1).

i. Increase the Light ID to 1 and enable the Light On option.

ii. Set X, Y, and Z to -1, 1, and 1.

iii. Click Apply.

(e) Repeat this procedure to add a second light (Light ID=2) at(-1,1,-1).

The result is a more softly shaded display (Figure 20.4).

Z

YX


Jul 05, 2001

Figure 20.4: Graphics Display of the Chip and Board Surfaces withAdditional Lighting


Postprocessing

Extra: You can use your left mouse button to rotate the ball in the ActiveLights window in the Lights panel, as shown below. By doing so,you can gain a perspective view on the relative locations of the lightsthat are currently active, and see the shading effect on the ball atthe center.

You can also change the color of one or more of the lights by typingthe name of a color in the Color field or moving the Red, Green,and Blue sliders.


Postprocessing

Step 3: Isosurface Creation

To display results in a 3D model, you will need surfaces on which thedata can be displayed. FLUENT creates surfaces for all boundary zonesautomatically. In the case file that you have read, several of these sur-faces have been renamed. Examples are board-sym and board-ends, whichcorrespond to the side and end faces of the circuit board. In general, youmay want to define additional surfaces for the purpose of viewing yourresults, such as a plane in Cartesian space, for example. In this exer-cise, you will create a horizontal plane cutting through the middle of themodule. This surface will have a y value of 0.25 inches, and will be usedin a later step for displaying the temperature and velocity fields.

1. Create a surface of constant y coordinate.



Postprocessing

(a) In the Surface of Constant drop-down lists, select Grid... andY-Coordinate.

(b) Click Compute.

The Min and Max fields will display the y extents of the do-main.

(c) Enter 0.25 under Iso-Values.

(d) Enter y=0.25in under New Surface Name.

(e) Click Create, and Close the panel.


Postprocessing

Step 4: Contours

1. Plot filled contours of temperature on the symmetry plane (Fig-ure 20.5).




(c) In the Surfaces list, select board-sym, chip-sym, and fluid-sym.

(d) Click Display.

The temperature contour will be displayed.

(e) Rotate and zoom the display using the left and middle mousebuttons, respectively, to obtain the view shown in Figure 20.5.


Postprocessing

Contours of Static Temperature (k)FLUENT 6.0 (3d, segregated, lam)

Jun 06, 2001

4.09e+02

3.98e+02

3.87e+02

3.76e+02

3.64e+02

3.53e+02

3.42e+02

3.31e+02

3.20e+02

3.09e+02

2.98e+02Z

Y

X

Figure 20.5: Filled Contours of Temperature on the Symmetry Surfaces

Hint: If the display disappears from the screen at any time, or ifyou are having difficulty manipulating it with the mouse, youcan open the Views panel from the Display pull-down menuand use the Default button to reset the view.

Note the peak temperatures in the chip where the heat is generated,along with the higher temperatures in the wake where the flow isrecirculating.


Postprocessing

2. Plot filled contours of temperature on the horizontal plane aty=0.25 in (Figure 20.6).

(a) In the Contours panel under Surfaces, deselect the symmetryplanes and select y=0.25in.

(b) Click Display.

(c) Zoom the display using your middle mouse button to obtainthe view shown in Figure 20.6.


Jun 06, 2001

4.09e+02

3.98e+02

3.87e+02

3.76e+02

3.64e+02

3.53e+02

3.42e+02

3.31e+02

3.20e+02

3.09e+02

2.98e+02 Z

YX

Figure 20.6: Filled Contours of Temperature on the y = 0.25 in. Surface

In the contour display (Figure 20.6), the high temperatures in thewake of the module are clearly visible. You may want to displayother quantities using the Contours panel, such as velocity magni-tude or pressure).


Postprocessing

Step 5: Velocity Vectors

Velocity vectors provide an excellent visualization of the flow around themodule, depicting details of the wake structure.

1. Display velocity vectors on the symmetry plane through the modulecenterline (Figure 20.7).


(a) In the Surfaces list, select fluid-sym.

(b) Set the Scale Factor to 1.9.

(c) Click Display.


Postprocessing

(d) Rotate and zoom the display to observe the vortex near thestagnation point and in the wake of the module (Figure 20.7).

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.0 (3d, segregated, lam)

Jun 06, 2001

1.41e+00

1.27e+00

1.13e+00

9.89e-01

8.50e-01

7.11e-01

5.72e-01

4.33e-01

2.94e-01

1.54e-01

1.53e-02 Z

YX

Figure 20.7: Velocity Vectors in the Module Symmetry Plane

Note: The vectors in Figure 20.7 are shown without arrowheads.You can modify the arrow style in the Vectors panel by select-ing a different option from the Style drop-down list.

Extra: If you want to decrease the number of vectors displayed,you can increase the Skip factor to a non-zero value.


Postprocessing

2. Plot velocity vectors in the horizontal plane intersecting the module(Figure 20.9).

After plotting the vectors, you will enhance your view by mirroringthe display about the module centerline and by adding the displayof the module surfaces.


(a) Deselect all surfaces by clicking the unshaded icon to the rightof Surfaces.

(b) In the Surfaces list, select y=0.25in.

(c) Set the Scale to 3.8.


Postprocessing

(d) Under Options, select Draw Grid.


(e) Under Options, check that Faces is selected.

(f) In the Surfaces list, select board-top and chip.

(g) Click Colors....

This will open the Grid Colors panel.


Postprocessing

(h) In the Types list, select wall.

(i) In the Colors list, select light blue, and then Close the panel.

(j) In the Grid Display panel, click Display and then Close thepanel.

(k) Use your mouse to obtain the view shown in Figure 20.8.

(l) In the Vectors panel, click Display.

(m) Rotate the display with your mouse to obtain the view shownin Figure 20.9.


Postprocessing


Jun 06, 2001

Z

YX

Figure 20.8: Filled Surface Display for the Chip and Board Top


Jun 06, 2001

1.41e+00

1.27e+00

1.13e+00

9.89e-01

8.50e-01

7.11e-01

5.72e-01

4.33e-01

2.94e-01

1.54e-01

1.53e-02 Z

YX

Figure 20.9: Velocity Vectors and Chip and Board Top Surfaces


Postprocessing

3. Mirror the view about the chip symmetry plane (Figure 20.10).


(a) In the Mirror Planes list, select symmetry-18.

Note: This zone is the centerline plane of the module, and itsselection will create a mirror of the entire display aboutthe centerline plane.

(b) Click Apply.

The display will be updated in your graphics window (Fig-ure 20.10).

Extra: You may want to experiment with different views and/orscale factors for the velocities to examine different regions (up-stream and downstream of the chip, for example).


Postprocessing


Jun 06, 2001

1.41e+00

1.27e+00

1.13e+00

9.89e-01

8.50e-01

7.11e-01

5.72e-01

4.33e-01

2.94e-01

1.54e-01

1.53e-02 Z

YX

Figure 20.10: Velocity Vectors and Chip and Board Top Surfaces afterMirroring


Postprocessing

Step 6: Animation

The surface temperature distribution on the module and on the circuitboard can be displayed by selecting these boundaries for display of tem-perature contours. You can then view the display dynamically, using theanimation feature. While effective animation is best conducted on “high-end” graphics workstations, you can follow the procedures below on anyworkstation. If your graphics display speed is slow, the animation play-back will take some time and will appear choppy, with the redrawingvery obvious. On fast graphics workstations, the animation will appearsmooth and continuous and will provide an excellent visualization of thedisplay from a variety of spatial orientations. On many machines, youcan improve the smoothness of the animation by turning on the DoubleBuffering option in the Display Options panel.

1. Display filled contours of surface temperature on the board-top andchip, excluding the symmetry surfaces (Figure 20.11).



Postprocessing



(c) Deselect all surfaces by clicking the unshaded icon to the rightof Surfaces.

(d) In the Surfaces list, select board-top and chip.

(e) Click Display.

(f) Zoom the display as needed to obtain the view shown in Fig-ure 20.11.

The temperature display (Figure 20.11) shows the high tempera-tures on the downstream portions of the module and the relativelylocalized heating of the circuit board around the module.


Postprocessing


Jun 06, 2001

4.09e+02

3.98e+02

3.87e+02

3.76e+02

3.64e+02

3.53e+02

3.42e+02

3.31e+02

3.20e+02

3.09e+02

2.98e+02 Z

YX

Figure 20.11: Filled Temperature Contours on the Chip and Board TopSurfaces


Postprocessing

2. Animate the surface temperature display by changing the point ofview.

Display −→Animate...

You will use the current display (Figure 20.11) as the starting viewfor the animation (Frame = 1).

(a) Under Key Frames, click Add.

This will store the current display as Key-1.

(b) Zoom the view to focus on the module region.

(c) Under Key Frames, change the Frame number to 10.

(d) Click Add.

This will store the new display as Key-10.


Postprocessing

The zoomed view will be the tenth keyframe of the animation,with intermediate displays (2 through 9) to be filled in duringthe animation.

(e) Rotate the view and un-zoom the display so that the down-stream side of the module is in the foreground, as shown inFigure 20.12.

(f) Change the Frame number to 20.

(g) Click Add.

This will store the new display as Key-20.

3. To animate the view, click on the “play” arrow button (second fromthe right in the row of playback buttons) in the Playback sectionof the Animate panel.

Extra: You can change the Playback mode if you want to “auto repeat”or “auto reverse” the animation. When you are in either of thesePlayback modes, you can click on the “stop” button (square) to stopthe continuous animation.


Postprocessing


Jun 06, 2001

4.09e+02

3.98e+02

3.87e+02

3.76e+02

3.64e+02

3.53e+02

3.42e+02

3.31e+02

3.20e+02

3.09e+02

2.98e+02 Z

Y

X

Figure 20.12: Filled Temperature Contours on the Chip and Board TopSurfaces


Postprocessing

Step 7: Displaying Pathlines

Pathlines are the lines traveled by neutrally buoyant particles in equilib-rium with the fluid motion. Pathlines are an excellent tool for visualiza-tion of complex three-dimensional flows. In this example, you will usepathlines to examine the flow around and in the wake of the module.

1. Create a rake from which the pathlines will emanate.

Surface −→Line/Rake...


Postprocessing

(a) In the Type drop-down list, select Rake.

A rake surface consists of a specified number of points equallyspaced between two specified endpoints. A line surface (theother option in the Type list) is a line that includes the spec-ified endpoints and extends through the domain; data pointson a line surface will not be equally spaced.

(b) Keep the default of 10 for the Number of Points along the rake.

This will generate 10 pathlines.

(c) Under End Points, enter the coordinates of the line, using astarting coordinate of (1.0, 0.105, 0.07) and an ending coor-dinate of (1.0, 0.25, 0.07), as shown in the panel above.

This will define a vertical line in front of the module, abouthalfway between the centerline and edge.

(d) Enter pathline-rake for the New Surface Name.

You will refer to the rake by this name when you plot thepathlines.

(e) Click Create, and Close the panel.


Postprocessing

2. Draw the pathlines (Figure 20.13).

Display −→Path Lines...

(a) In the Release From Surfaces list, select pathline-rake.

(b) Set the Step Size to 0.001 inch and the number of Steps to6000.

Note: A simple rule of thumb to follow when you are settingthese two parameters is that if you want the particles toadvance through a domain of length L, the Step Size timesthe number of Steps should be approximately equal to L.

(c) Under Options, select Draw Grid.


(d) In the Surfaces list, select board-top and chip.

These surfaces should already be selected from the earlier ex-ercise where the grid was displayed with velocity vectors, Step5: Velocity Vectors.


Postprocessing

(e) Under Options, check that Faces is selected, and then Closethe panel.

(f) In the Path Lines panel, click Display.

The pathlines will be drawn on the surface.

(g) Rotate the display so that the flow field in front and in thewake of the chip is visible, as shown in Figure 20.13.

Path Lines Colored by Particle IdFLUENT 6.0 (3d, segregated, lam)

Jun 06, 2001

3.00e+01

2.70e+01

2.40e+01

2.10e+01

1.80e+01

1.50e+01

1.20e+01

9.00e+00

6.00e+00

3.00e+00

0.00e+00 Z

YX

Figure 20.13: Pathlines Shown on a Display of the Chip and BoardSurfaces.


Postprocessing

Step 8: Overlaying Velocity Vectors on the Path-line Display

The overlay capability, provided in the Scene Description panel, allowsyou to display multiple results on a single plot. You can exercise thiscapability by adding a velocity vector display to the pathlines just plotted.

1. Enable the overlays feature.

Display −→Scene...

(a) Under Scene Composition, select Overlays.

(b) Click Apply.


Postprocessing

2. Add a plot of vectors on the chip centerline plane.


(a) Under Options, deselect Draw Grid.

(b) Deselect all surfaces by clicking the unshaded icon to the rightof Surfaces.

(c) In the Surfaces list, select fluid-sym.

(d) Set the Scale to 3.8.

Because the grid surfaces are already displayed and overlayingis active, there is no need to redisplay the grid surfaces.


Postprocessing

(e) Click Display.

(f) Use your mouse to obtain the view that is shown in Fig-ure 20.14.


Jun 06, 2001

1.41e+00

1.27e+00

1.13e+00

9.89e-01

8.50e-01

7.11e-01

5.72e-01

4.33e-01

2.94e-01

1.54e-01

1.53e-02 Z

YX

Figure 20.14: Overlay of Velocity Vectors and Pathlines Display

Note: The final display (Figure 20.14) does not require mirroring aboutthe symmetry plane because the vectors obscure the mirrored image.You may turn off the mirroring option in the Views panel at anystage during this exercise.


Postprocessing

Step 9: Exploded Views

The Scene Description panel stores each display that you request and al-lows you to manipulate the displayed items individually. This capabilitycan be used to generate “exploded” views, in which results are translatedor rotated out of the physical domain for enhanced display. Below, youcan experiment with this capability by displaying “side-by-side” velocityvectors and temperature contours on a streamwise plane in the modulewake.

1. Delete the velocity vectors and pathlines from the current display.


(a) In the Names list, select the velocity vectors and pathlines.

(b) Click Delete Geometry.

(c) Click Apply.

The Scene Description panel should then contain only the twogrid surfaces (board-top and chip).


Postprocessing

2. Create a plotting surface at x=3 inches (named x=3.0in), justdownstream of the trailing edge of the module.


Hint: If you forget how to create an isosurface, see Step 3: Iso-surface Creation.


Postprocessing

3. Add the display of filled temperature contours on the x=3.0in sur-face.



(b) Deselect all surfaces by clicking on the unshaded icon to theright of Surfaces.

(c) In the Surfaces list, select x=3.0in.

(d) Click Display, and Close the panel.

The filled temperature contours will be displayed on the x=3.0 in.surface.


Postprocessing

4. Add the velocity vectors on the x=3.0in plotting surface.



(b) Deselect all surfaces by clicking on the unshaded icon to theright of Surfaces.

(c) In the Surfaces list, select x=3.0in.

(d) Increase the Skip to 2.

(e) Change the Scale to 1.9.

(f) Click Display.


Postprocessing

The display will show the vectors superimposed on the con-tours of temperature at x=3.0 in.

5. Create the exploded view (Figure 20.15) by translating the contourdisplay, placing it above the vectors.


(a) In the Scene Description panel, select contour-6-temperature inthe Names list.

(b) Click Transform....

This will open the Transformations panel.

(c) Under Translate, enter 1 inch for Y.

(d) Click Apply, and Close the Transformations panel.

The exploded view allows you to see the contours and vectorsas distinct displays in the final scene (Figure 20.15).

6. Turn off the Overlays.

(a) In the Scene Description panel, deselect the Overlays option.

(b) Click Apply, and Close the panel.


Postprocessing


Jun 12, 2001

1.41e+00

1.27e+00

1.13e+00

9.89e-01

8.50e-01

7.11e-01

5.72e-01

4.33e-01

2.94e-01

1.54e-01

1.53e-02 Z

YX

Figure 20.15: Exploded Scene Display of Temperature and Velocity


Postprocessing

Step 10: Animating the Display of Results inSuccessive Streamwise Planes

Often, you may want to march through the flow domain, displaying aparticular variable on successive slices of the domain. While this taskcould be accomplished manually, plotting each plane in turn, or usingthe Scene Description and Animate panels, here you will use the SweepSurface panel to facilitate the process. To illustrate the display of re-sults on successive slices of the domain, you will plot contours of velocitymagnitude on planes of constant x coordinate.

1. Delete the vectors and temperature contours from the display.


(a) In the Scene Description panel, select contour-6-temperatureand vv-6-velocity-magnitude in the Names list.

(b) Click Delete Geometry.

(c) Click Apply, and Close the panel.

The panel and display window will be updated to contain onlythe grid surfaces.

2. Use your mouse to un-zoom the view in the graphics window sothat the entire board surface is visible.

3. Generate contours of velocity magnitude and sweep them throughthe domain along the x axis.

Display −→Sweep Surface...


Postprocessing

(a) Keep the default Sweep Axis (the x axis).

(b) Under Animation, set the Initial Value to 0 m and the FinalValue to 0.1651 m.

! The units for the initial and final values are in meters, re-gardless of the length units being used in the model. Here,the initial and final values are set to the Min Value andMax Value, to generate an animation through the entiredomain.

(c) Set the number of Frames to 20.

(d) Select Contours under Display Type.

This will open the Contours panel.


Postprocessing

i. In the Contours panel, select Velocity... and Velocity Mag-nitude in the Contours Of drop-down lists.

ii. In the Contours panel, click OK.

(e) Click on Animate in the Sweep Surface panel.

You will see the velocity contour plot displayed at 20 successivestreamwise planes. FLUENT automatically interpolates the con-toured data on the streamwise planes between the specified endpoints. Especially on high-end graphics workstations, this can bean effective way to study how a flow variable changes throughoutthe domain.


Postprocessing

Step 11: XY Plots

XY plotting can be used to display quantitative results of your CFD sim-ulations. Here, you will complete your review of the module cooling sim-ulation by plotting the temperature distribution along the top centerlineof the module.

1. Define the line along which to plot results.

Surface −→Line/Rake...

(a) In the Type drop-down list, select Line.

(b) Under End Points, enter the coordinates of the line, using astarting coordinate of (2.0, 0.4, 0.01) and an ending coordinateof (2.75, 0.4, 0.01), as shown in the panel above.

These coordinates define the top centerline of the module.

(c) Enter top-center-line as the New Surface Name.


Postprocessing

(d) Click Create.

2. Plot the temperature distribution along the top centerline of themodule (Figure 20.16).


(a) Select Temperature... and Static Temperature in the Y AxisFunction drop-down lists.

(b) In the Surfaces list, select top-center-line.

(c) Keep the default Plot Direction of X.

This will plot temperature vs. the x coordinate along the se-lected line (top-center-line).

(d) Click Axes... to modify the axis range.

This will open the Axes - Solution XY Plot panel .


Postprocessing

(e) Under Axis, select X.

(f) Under Options, deselect Auto Range.

(g) Set the Range using a Minimum of 2.0 and a Maximum of2.75.

(h) Click Apply, and Close the panel.

(i) In the Solution XY Plot panel, click Plot.

The temperature distribution (Figure 20.16) shows the tem-perature increase across the module surface as the thermalboundary layer develops in the cooling air flow.


Postprocessing

Z

Y

X

Static TemperatureFLUENT 6.0 (3d, segregated, lam)

Jun 06, 2001

Position (in)

(k)Temperature

Static

2.82.72.62.52.42.32.22.12

4.02e+02

4.00e+02

3.98e+02

3.96e+02

3.94e+02

3.92e+02

3.90e+02

3.88e+02

top-center-line

Figure 20.16: Temperature Along the Top Centerline of the Module


Postprocessing

Step 12: Annotation

You can annotate your display with the text of your choice.

Display −→Annotate...

1. In the Annotation Text field, enter the text describing your plot(e.g., Temperature Along the Top Centerline).

2. Click Add.

A Working dialog box will appear telling you to select the desiredlocation of the text using the mouse-probe button, which is, by de-fault, the right button.

3. Click your right mouse button in the graphics display windowwhere you want the text to appear, and you will see the text dis-played at the desired location (Figure 20.17).


Postprocessing

Z

Y

X

Static TemperatureFLUENT 6.0 (3d, segregated, lam)

Jun 06, 2001

Position (in)

(k)Temperature

Static

2.82.72.62.52.42.32.22.12

4.02e+02

4.00e+02

3.98e+02

3.96e+02

3.94e+02

3.92e+02

3.90e+02

3.88e+02

Temperature Along the Top Centerlinetop-center-line

Figure 20.17: Temperature Along the Top Centerline of the Module

Extra: If you want to move the text to a new location on thescreen, click Delete Text in the Annotate panel, and click Addonce again, defining a new position with your mouse.

Note: Depending on the size of your graphics window and thehardcopy file format you choose, the font size of the anno-tation text you see on the screen may be different from thefont size in a hardcopy file of that graphics window. The an-notation text font size is absolute, while the rest of the itemsin the graphics window are scaled to the proportions of thehardcopy.


Postprocessing

Step 13: Saving Hardcopy Files

You can save hardcopy files of the graphics display in many differentformats, including PostScript, encapsulated PostScript, TIFF, PICT,and window dumps. Here, the procedure for saving a color PostScriptfile is shown.

File −→Hardcopy...

1. Under Format, select PostScript.

2. Under Coloring, select Color.

3. Click Save....


4. In the Select File dialog box, enter a name for the hardcopy file.

Summary: This tutorial has demonstrated the use of many of the ex-tensive postprocessing features available in FLUENT. For more in-formation on these and related features, see the “Graphics and Vi-sualization” and “Alphanumeric Reporting” chapters in the User’sGuide.


Tutorial 21. Turbo Postprocessing

Introduction: This tutorial demonstrates the turbomachinery postpro-cessing capabilities of FLUENT.

In this example, you will read the case and data files (without doingthe calculation) and perform a number of turbomachinery-specificpostprocessing exercises. In the process, you will learn how to:

• Define the topology of a turbomachinery model

• Create surfaces for the display of 3D data

• Revolve 3D geometry to display a 360-degree image

• Report turbomachinery quantities

• Display averaged contours for turbomachinery

• Display 2D contours for turbomachinery

• Display averaged XY plots for turbomachinery

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT, and that you have solved Tutorial 1.Some steps will not be shown explicitly.

Problem Description: The problem to be considered is shown schemat-ically in Figure 21.1. The flow of air through a centrifugal com-pressor is simulated. The model consists of a single 3D sector ofthe compressor, to take advantage of the circumferential periodic-ity in the problem. FLUENT’s postprocessing capabilities readilyallow you to display realistic full 360-degree images of the solutionobtained.


Turbo Postprocessing

inlet

outlet

hub side

shroud side




Preparation

1. Copy the files turbo/turbo.cas and turbo/turbo.dat from theFLUENT documentation CD to your working directory (as de-scribed in Tutorial 1).


Step 1: Reading the Case and Data Files

1. Read in the case and data files (turbo.cas and turbo.dat).

File −→ Read −→Case & Data...

Once you select turbo.cas, turbo.dat will be read automatically.



Step 2: Grid Display


1. Under Options, select Edges.

2. Under Edge Type, select Outline.

3. Deselect all surfaces, and then click on Outline at the bottom ofthe panel.

4. Click Display.

5. Use your left mouse button to rotate the view, and your middlemouse button to zoom the view until you obtain an isometric dis-play of the compressor duct, as shown in Figure 21.2.



Z

YX

GridFLUENT 6.0 (3d, coupled imp, rke)

Jul 31, 2001

Figure 21.2: Graphics Display of the Edges of the Compressor Mesh

Extra: You can use the right mouse button to check which zone numbercorresponds to each boundary. If you click the right mouse buttonon one of the boundaries displayed in the graphics window, its zonenumber, name, and type will be printed in the console window. Thisfeature is especially useful when you have several zones of the sametype and you want to distinguish between them quickly.



Step 3: Defining the Turbomachinery Topology

In order to establish the turbomachinery-specific coordinate system usedin subsequent postprocessing functions, FLUENT requires you to definethe topology of the flow domain. Specifically, you will select boundaryzones that comprise the hub, shroud, inlet, outlet, and periodics. Notethat boundaries may consist of more than one zone. See Section 25.9.1of the User’s Guide for more information. The topology setup that youdefine will be saved to the case file when you save the current model.Thus, if you read this case back into FLUENT, you do not need to set upthe topology again.

Define −→Turbo Topology...

1. Specify the surfaces representing the hub.

(a) Under Boundaries, keep the default selection of Hub.

(b) In the Surfaces list, select the surfaces that represent the hub(wall-diffuser-hub, wall-hub, and wall-inlet-hub.)



2. Specify the surfaces representing the casing.

(a) Under Boundaries, select Casing.

(b) In the Surfaces list, select wall-diffuser-shroud, wall-inlet-shroud,and wall-shroud.

3. Specify the surfaces representing the periodic boundaries.

(a) Under Boundaries, select Theta Periodic.

(b) In the Surfaces list, select periodic.33, periodic.34, and peri-odic.35.

Note: While Theta Periodic represents periodic boundary zones onthe circumferential boundaries of the flow passage, Theta Minand Theta Max are wall surfaces at the minimum and maxi-mum θ position on a circumferential boundary. There are nosuch wall surfaces in this problem.

4. Specify the surface representing the Inlet (inlet).

5. Specify the surface representing the Outlet (outlet).

6. Specify the surface representing the Blade (wall-blade).

7. Click Apply to set all of the turbomachinery boundaries.

FLUENT will inform you that the turbomachinery postprocessingfunctions have been activated, and the Turbo menu will appear inFLUENT’s menu bar at the top of the console window.

Note: You can display the selected surfaces by clicking on Display at thebottom of the panel. This is useful as a graphical check to ensurethat all relevant surfaces have been selected.



Step 4: Isosurface Creation

To display results in a 3D model, you will need surfaces on which the datacan be displayed. FLUENT creates surfaces for all boundary zones auto-matically. In a general application, you may want to define additionalsurfaces for the purpose of viewing results. FLUENT’s turbo postprocess-ing capabilities allow you to define more complex surfaces, specific to theapplication and the particular topology that you defined. In this step,you will create surfaces of iso-meridional (marching along the stream-wise direction) and spanwise (distance between the hub and the shroud)coordinates in the compressor.


1. Create surfaces of constant meridional coordinate.

(a) In the Surface of Constant drop-down lists, select Grid... andMeridional Coordinate.

(b) Enter 0.2 under Iso-Values.

(c) Enter meridional-0.2 under New Surface Name.



(d) Click Create.

Note: The iso-values you enter for these turbo-specific sur-faces are expressed as a percentage of the entire domain(i.e., you just defined a surface of meridional coordinateequal to 20% of the path along the duct).

(e) Repeat the steps above to define surfaces of meridional coor-dinates equal to 0.4, 0.6, and 0.8.

2. Create surfaces of constant spanwise coordinate.

(a) In the Surface of Constant drop-down lists, select Grid... andSpanwise Coordinate

(b) Enter 0.25 under Iso-Values.

(c) Enter spanwise-0.25 under New Surface Name.

(d) Click Create.

(e) Repeat the steps above to define surfaces of spanwise coordi-nates equal to 0.5 and 0.75.



Step 5: Contours

1. Plot filled contours of pressure on the meridional isosurfaces (Fig-ure 21.3).



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

(c) In the Surfaces list, select inlet, meridional-0.2, meridional-0.4,meridional-0.6, meridional-0.8, and outlet.

(d) Under Options, select Draw Grid, and keep the current settingsin the Grid Display panel.



(e) Click Display in the Contours panel.

(f) Rotate and zoom the display using the left and middle mousebuttons, respectively, to obtain the view shown in Figure 21.3.

Contours of Static Pressure (atm)FLUENT 6.0 (3d, coupled imp, rke)

Jul 27, 2001

1.84e+00

1.73e+00

1.62e+00

1.50e+00

1.39e+00

1.28e+00

1.17e+00

1.06e+00

9.44e-01

8.32e-01

7.20e-01 Z

Y

X

Figure 21.3: Filled Contours of Pressure on the Meridional Isosurfaces

In Figure 21.3, you can observe the buildup of static pressure alongthe duct.



2. Plot filled contours of Mach number (Figure 21.4).

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

(b) Click Display.

Contours of Mach NumberFLUENT 6.0 (3d, coupled imp, rke)

Jul 27, 2001

1.04e+00

9.35e-01

8.35e-01

7.34e-01

6.34e-01

5.33e-01

4.33e-01

3.32e-01

2.32e-01

1.31e-01

3.05e-02 Z

Y

X

Figure 21.4: Filled Contours of Mach Number on the Meridional Isosur-faces

In Figure 21.4, you can observe locations at which the flow becomesslightly supersonic, about halfway through the duct.



3. Plot filled contours of Mach number on the spanwise isosurfaces(Figure 21.5).

(a) In the Surfaces list, deselect all surfaces, and then select spanwise-0.25, spanwise-0.5, and spanwise-0.75.

(b) Click Display.


Jul 27, 2001

1.04e+00

9.35e-01

8.35e-01

7.34e-01

6.34e-01

5.33e-01

4.33e-01

3.32e-01

2.32e-01

1.31e-01

3.05e-02Z

YX

Figure 21.5: Filled Contours of Mach Number on the Spanwise Isosur-faces

The display in Figure 21.5 allows you to further study the variationof the Mach number inside the duct. You may want to explore usingdifferent combinations of surfaces to display the same or additionalvariables.



4. Display a 360-degree image of the Mach number contours on the0.5 spanwise isosurface (Figure 21.6).

(a) Redisplay the contours, just on the 0.5 spanwise isosurface.

i. In the Surfaces list, deselect spanwise-0.25 and spanwise-0.75.

ii. Click Display.

(b) Display the full 360-degree geometry.


i. Set Periodic Repeats to 20.

ii. Click Apply.

The display will be updated to show the entire geometry.

Note: This step demonstrates a typical view-manipulationtask. See Tutorial 20 for further examples of postpro-cessing features.




Jul 27, 2001

1.04e+00

9.35e-01

8.35e-01

7.34e-01

6.34e-01

5.33e-01

4.33e-01

3.32e-01

2.32e-01

1.31e-01

3.05e-02Z

YX

Figure 21.6: Filled Contours of Mach Number on the 0.5 Spanwise IsoSurface



Step 6: Reporting Turbo Quantities

The turbomachinery report gives you some tabulated information specificto the application and the defined topology. See Section 25.9.2 of theUser’s Guide for details.

Turbo −→Report...

1. Under Averages, keep the default of Mass-Weighted.

2. Click Compute.



Step 7: Averaged Contours

Turbo averaged contours are generated as projections of the values of avariable averaged in the circumferential direction and visualized on an r-z plane.

1. Turn off the periodic repeats.


(a) In the Views panel, enter 0 in the Periodic Repeats field.

(b) Click Apply.

2. Display filled contours of averaged static pressure (Figure 21.7).

Turbo −→Averaged Contours...

(a) In the Contours Of drop-down lists, select Pressure... andStatic Pressure.

(b) Click Display.



Averaged Turbo Contour - pressure (atm) (atm)FLUENT 6.0 (3d, coupled imp, rke)

Aug 13, 2001

1.80e+00

1.72e+00

1.63e+00

1.54e+00

1.45e+00

1.36e+00

1.28e+00

1.19e+00

1.10e+00

1.01e+00

9.24e-01Z

Y

X

Figure 21.7: Filled Contours of Averaged Static Pressure



Step 8: 2D Contours

In postprocessing a turbomachinery solution, it is often desirable to dis-play contours on constant pitchwise, spanwise, or meridional coordi-nates, and then project these contours onto a plane. This permits easierevaluation of the contours, especially for surfaces that are highly three-dimensional. FLUENT allows you to display contours in this fashionusing the Turbo 2D Contours panel.

1. Display 2D contours of Mach number.

Turbo −→2D Contours...

(a) Under Surface of Constant, keep the default selection of Pitch-wise Value.

(b) In the Contours Of drop-down lists, select Velocity... and MachNumber.

(c) Under Fractional Distance, enter 0.25.

(d) Under Projection Direction, select Radial.



(e) Click Display.


2D Turbo Contour - mach-numberFLUENT 6.0 (3d, coupled imp, rke)

Jul 27, 2001

8.30e-01

7.63e-01

6.95e-01

6.28e-01

5.61e-01

4.94e-01

4.26e-01

3.59e-01

2.92e-01

2.25e-01

1.57e-01 ZY

X

Figure 21.8: 2D Contours of Mach Number on Surface of Pitchwise Value0.25.



Step 9: Averaged XY Plots

In addition to displaying data on different combinations of complex 3Dand flattened surfaces, FLUENT’s turbo postprocessing capabilities allowyou to display XY plots of averaged variables, relevant to the specifictopology of a turbomachinery problem. In particular, you will be able toplot circumferentially-averaged values of variables as a function of eitherthe spanwise coordinate or the meridional coordinate.

1. Plot temperature as a function of the meridional coordinate.

Turbo −→Averaged XY Plot...

(a) In the Y Axis Function drop-down lists, select Temperature...and Static Temperature.

(b) In the X Axis Function drop-down list, select Meridional Dis-tance.

(c) Under Fractional Distance, enter 0.9.

(d) Click Plot.



Z

Y

X

Averaged XY - temperature (k)FLUENT 6.0 (3d, coupled imp, rke)

Jul 27, 2001

Meridional Distance

(k)temperature

10.90.80.70.60.50.40.30.20.10

3.60e+02

3.50e+02

3.40e+02

3.30e+02

3.20e+02

3.10e+02

3.00e+02

2.90e+02

2.80e+02

Figure 21.9: Averaged XY Plot of Static Temperature on Spanwise Sur-face of 0.9 Isovalue

Summary: This tutorial has demonstrated the use of some of the turbo-machinery-specific postprocessing features of FLUENT. These fea-tures can be accessed once you have defined the topology of theproblem. More extensive general-purpose postprocessing featuresare demonstrated in Tutorial 20. See also the “Graphics and Vi-sualization” and “Alphanumeric Reporting” chapters in the User’sGuide.


Tutorial 22. Parallel Processing

Introduction: This tutorial illustrates the setup and solution of a sim-ple 2D problem using FLUENT’s parallel processing capabilities. Inorder to be run in parallel, the mesh must be divided into smaller,evenly sized partitions. Each FLUENT process, called a computenode, will solve on a single partition, and information will be passedback and forth across all partition interfaces. FLUENT’s solver al-lows parallel processing on a dedicated parallel machine, or a net-work of heterogeneous workstations running UNIX, or a networkof workstations running Windows. The tutorial assumes that bothFLUENT and network communication software have been correctlyinstalled (see the separate installation instructions and related in-formation for details). The case chosen is the mixing elbow problemyou solved in Tutorial 1.


• Start the parallel version of FLUENT

• Partition a grid for parallel processing

• Use a parallel network of workstations

• Check the performance of the parallel solver

Prerequisites: This tutorial assumes that you are familiar with themenu structure in FLUENT, and that you have solved Tutorial 1.

Problem Description: The problem to be considered is shown sche-matically in Figure 22.1. A cold fluid at 26C enters through thelarge pipe and mixes with a warmer fluid at 40C in the elbow.The pipe dimensions are in inches, and the fluid properties andboundary conditions are given in SI units. The Reynolds numberat the main inlet is 2.03 × 105, so that a turbulent model will benecessary.


Parallel Processing

32

12

16

4

″

32 ″

16 ″

″

″″

U = 0.2 m/sT = 26 CI = 5%

U = 1 m/sT = 40 CI = 5%

x

y

°

°

Conductivity: k = 0.677 W/m-K

Density: = 1000 kg/mρ 3

Viscosity: µ = 8 x 10 Pa-s-4

p

39.93°39.93 °

Specific Heat: C = 4216 J/kg-K



Parallel Processing

Preparation

1. Copy the file parallel/elbow3.cas from the FLUENT documen-tation CD to your working directory (as described in Tutorial 1).

You can partition the grid before or after you set up the problem (bydefining models, boundary conditions, etc.). It is best to partitionafter the problem is set up, since partitioning has some model de-pendencies (e.g., sliding-mesh and shell-conduction encapsulation).Because you already set up this problem in Tutorial 1, you can savethe effort of redefining the models and boundary conditions.

Step 1: Starting the Parallel Version of FLUENT

Since the procedure for starting the parallel version of FLUENT is de-pendent upon the type of machine(s) you are using, four versions of thisstep are provided here. Follow the procedure for the machine configura-tion that is appropriate for you.

• Step 1A: Multiprocessor UNIX Machine

• Step 1B: Multiprocessor Windows Machine

• Step 1C: Network of UNIX Workstations

• Step 1D: Network of Windows Workstations


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Step 1A: Multiprocessor UNIX Machine

1. At the command prompt, type fluent.

! Do not specify any argument (e.g., 2d).

2. Specify the 2D parallel version.

File −→Run...

(a) Under Versions, turn on Parallel.

(b) Under Options, specify 2 as the number of Processes.

(c) Under Options, keep the Default selection in the Communicatordrop-down list.

(d) Click Run.


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Note: It is also possible to start the multiprocessor parallel versionof FLUENT from the command line instead of using the SelectSolver panel. See Chapter 28 of the User’s Guide for details.

Step 1B: Multiprocessor Windows Machine

1. At the DOS command prompt, type

fluent 2d -t2

to start the 2D parallel version with two processes.


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Step 1C: Network of UNIX Workstations

1. At the command prompt, type fluent.

! Do not specify any argument (e.g., 2d).

2. Specify the 2D network parallel version.

File −→Run...

(a) Under Versions, turn on Parallel.

(b) Under Options, keep the default value of 1 as the number ofProcesses.

You will spawn processes to other machines in the next step.


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(c) Under Options, select Socket in the Communicator drop-downlist.

(d) Click Run.

Note: It is also possible to start the network parallel version fromthe command line instead of using the Select Solver panel. SeeChapter 28 of the User’s Guide for details.

3. Spawn one additional computational node.

Parallel −→ Network −→Configure...

(a) Specify the machine on which you want to spawn the process.

i. Under Host Entry, specify the machine name in the Host-name field.

ii. Enter your user ID in the Username field.


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iii. Click Add.

The machine will be added to the Available Hosts list.

Note: It is possible to create a list of available machines andadd them to the hosts database, rather than adding ma-chines manually. See Chapter 28 of the User’s Guide fordetails.

(b) Select the newly added host in the Available Hosts list.

Note: If you do not have access to another machine, you canspawn the second node on your own machine by selectingit from the Available Hosts list, although you will incur aperformance penalty on a single processor machine.

(c) Under Spawn Count, keep the default value of 1.

This will give you the desired total number of 2 computationalnodes.

(d) Click Spawn.

FLUENT will inform you in a Working dialog box that it isspawning the new node. When it is done, the new node willappear in the Spawned Compute Nodes list, as shown below.


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Hint: If you accidentally spawn an undesired computationalnode, you can remove it by selecting it from the SpawnedCompute Nodes list and clicking on Kill.

4. Check the network connectivity information.

Although FLUENT displays a message confirming the connection toeach new compute node and summarizing the host and node pro-cesses defined, you may find it useful to review the same informa-tion at some time during your session, especially if more computenodes are spawned to several different machines.

Parallel −→Show Connectivity...


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(a) Specify the number of the Compute Node of interest (0).

For information about all defined compute nodes, you will se-lect node 0, since this is the node from which all other nodesare spawned.

(b) Click Print.

--------------------------------------------------------------------ID Comm. Hostname O.S. PID Mach ID HW ID Name--------------------------------------------------------------------n1 net dori hpux 11681 1 7 Fluent Nodehost net bilbo hpux 12697 0 3 Fluent Hostn0* net bilbo hpux 12698 0 -1 Fluent Node

ID is the sequential denomination of each compute node (thehost process is always host), Hostname is the name of themachine hosting the compute node (or the host process), O.Sis the architecture, PID is the process ID number, Mach ID isthe compute node ID, and HW ID is an identifier specific tothe communicator used.


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Step 1D: Network of Windows Workstations

The procedure below is for using the RSHD communicator software thatis included with FLUENT. You can use a different communicator if oneis available on your system. See the User’s Guide for more information.

1. At the DOS command prompt, type

fluent 2d -pnet -t1

to start the 2D network parallel version with one process.

You will spawn a second compute node in the next step.

2. Spawn an additional compute node, following the procedure de-scribed in Step 1C, substep 3, for a network of UNIX machines.

3. Check the network connectivity, following substep 4 of Step 1C.


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Step 2: Reading and Partitioning the Grid

When you use the parallel solver, you need to subdivide (or partition)the grid into groups of cells that can be solved on separate processors.If you read an unpartitioned grid into the parallel solver, FLUENT willautomatically partition it, using the default partition settings. You canthen check the partitions, to see if you need to modify the settings andrepartition the grid.

1. Inspect the automatic partitioning settings.

Parallel −→Auto Partition...

If the Case File option is turned on (the default setting), and thereexists a valid partition section in the case file (i.e., one where thenumber of partitions in the case file divides evenly into the numberof compute nodes), then that partition information will be usedrather than repartitioning the mesh. You need to turn off the CaseFile option only if you want to change other parameters in the AutoPartition Grid panel.

(a) Keep all defaults in the Auto Partition Grid panel.

When you keep the Case File option turned on, FLUENT willautomatically select a partitioning method for you. This is thepreferred initial approach for most problems. In the next stepyou will inspect the partitions created and be able to changethem, if you so choose.


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2. Read the case file parallel.cas.




GridFLUENT 6.0 (2d, segregated, ske)

Jul 03, 2001

Figure 22.2: Triangular Grid for the Mixing Elbow


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4. Check the partition information.

Parallel −→Partition...

(a) Click Print Active Partitions.

FLUENT will print the active partition statistics to the consolewindow.

Note: FLUENT distinguishes between two cell partition schemeswithin a parallel problem: the active cell partition, andthe stored cell partition. Here, both are set to the cellpartition that was created upon reading the case file. Ifyou re-partition the grid using the Partition Grid panel,the new partition will be referred to as the stored cell par-tition. To make it the active cell partition, you need toclick on the Use Stored Partitions button in the PartitionGrid panel. The active cell partition is used for the cur-rent calculation, while the stored cell partition (the lastpartition performed) is used when you save a case file.This distinction is made mainly to allow you to partitiona case on one machine or network of machines and solve


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it on a different one. See Chapter 28 of the User’s Guidefor more information.

>> 2 Active Partitions:P Cells I-Cells Cell Ratio Faces I-Faces Face Ratio Neigh0 612 10 0.016 985 13 0.0131 612 13 0.021 1010 13 0.013

-----------------------------------------------------------------Collective Partition Statistics: Minimum Maximum Total-----------------------------------------------------------------Cell count 612 612 1224Mean cell count deviation 0.0% 0.0%Partition boundary cell count 10 13 23Partition boundary cell count ratio 1.6% 2.1% 1.9%

Face count 985 1010 1982Mean face count deviation -1.3% 1.3%Partition boundary face count 13 13 13Partition boundary face count ratio 1.3% 1.3% 0.7%

Partition neighbor count 1 1-----------------------------------------------------------------Partition Method Principal AxesOriginal Partition Count 2

Done.

(b) Review the partition statistics.

An optimal partition should produce an equal number of cellsin each partition for load balancing, a minimum number ofpartition interfaces to reduce interpartition communication band-width, and a minimum number of partition neighbors to reducethe startup time for communication. Here, you will be lookingfor relatively small values of mean cell and face count devia-tion and total partition boundary cell and face count ratio.


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5. Examine the partitions graphically.

(a) Initialize the solution.

Even though you are not going to start a solution at this point,you have to perform a solution initialization in order to usethe Contours panel to inspect the partition you just created.


(b) Display the cell partitions (Figure 22.3).


i. In the Contours Of drop-down lists, select Cell Info... andActive Cell Partition.

ii. Under Options, select Filled.

iii. Set the number of Levels to 2, the number of computenodes.


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iv. Click Display.

Contours of Cell Partition Jul 03, 2001FLUENT 6.0 (2d, segregated, ske)

1.00e+00

0.00e+00

Figure 22.3: Cell Partitions

As shown in Figure 22.3, the cell partitions are acceptablefor this problem. The position of the interface reveals thatthe criteria mentioned above will be matched. If you wereunsatisfied with the partitions, you could use the Partition Gridpanel to repartition the grid. See the User’s Guide for detailsabout the procedure and options for manually partitioning agrid. Recall that, if you wish to use the modified partitions fora calculation, you will need to make the Stored Cell Partitionthe Active Cell Partition by either clicking on the Use StoredPartitions button in the Partition Grid panel or saving the casefile and reading it back into FLUENT.

6. Save the case file with the partitioned mesh (elbow4.cas).



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Step 3: Solution

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


(a) Choose velocity-inlet-5 from the Compute From list.

(b) Click on Init and Close the panel.





The solution will converge in approximately 72 iterations.

4. Save the data file (elbow4.dat).



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Step 4: Checking Parallel Performance

Generally, you will use the parallel solver for large, computationally-intensive problems, and you will want to check the parallel performanceto determine if any optimization is required. See Chapter 28 of the User’sGuide for details. Although the example in this tutorial is a simple 2Dcase, here you will check the parallel performance as an exercise.

Parallel −→ Timer −→Usage

Performance Timer for 71 iterations on 2 compute nodesAverage wall-clock time per iteration: 0.021 secGlobal reductions per iteration: 80 opsGlobal reductions time per iteration: 0.000 sec (0.0%)Message count per iteration: 199 messagesData transfer per iteration: 0.009 MBLE solves per iteration: 6 solvesLE wall-clock time per iteration: 0.005 sec (23.7%)LE global solves per iteration: 2 solvesLE global wall-clock time per iteration: 0.000 sec (0.8%)AMG cycles per iteration: 9 cyclesRelaxation sweeps per iteration: 276 sweepsRelaxation exchanges per iteration: 61 exchanges

Total wall-clock time: 1.463 secTotal CPU time: 2.900 sec

The most accurate way to evaluate parallel performance is by runningthe same parallel problem on 1 CPU and on n CPUs, and comparingthe Total wall-clock time (elapsed time for the iterations) in bothcases. Ideally you would want to have the Total wall-clock time withn CPUs be 1/n times the Total wall-clock time with 1 CPU. In prac-tice, this improvement will be reduced by the performance of the commu-nication subsystem of your hardware, and the overhead of the parallelprocess itself. As a rough estimate of parallel performance, you can com-pare the Total wall-clock time with the CPU time. In this case theCPU time was approximately 1.98 times the Total wall-clock time.


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For a parallel process run on two compute nodes, this reveals very goodparallel performance, even though the advantage over a serial calculationis small, as expected for this simple 2D problem.


See Tutorial 1 for complete postprocessing exercises for this example.Here, two plots are generated so that you can confirm that the resultsyou obtained with the parallel solver are the same as those you obtainedwith the serial solver.

1. Display an XY plot of temperature across the exit (Figure 22.4).

Plot −→ XY Plot...

(a) Select Temperature... and Static Temperature in the Y AxisFunction drop-down lists.


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(b) Select pressure-outlet-7 in the Surfaces list.

(c) Click on Plot.

Static TemperatureFLUENT 6.0 (2d, segregated, ske)

Jul 03, 2001

Position (in)

(k)Temperature

Static

646260585654525048

3.15e+02

3.10e+02

3.05e+02

3.00e+02

2.95e+02

2.90e+02

pressure-outle

Figure 22.4: Temperature Distribution at the Outlet


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2. Display filled contours of the custom field function dynam-head(Figure 22.5).

Display −→ Contours...

(a) Select Custom Field Functions... in the drop-down list underContours Of.

The function you created in Tutorial 1, dynam-head, will beshown in the lower drop-down list.

(b) Change the number of Levels back to 20.

(c) Click on Display, and then Close the panel.


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Contours of dynam-head Jul 03, 2001FLUENT 6.0 (2d, segregated, ske)

7.60e+02

0.00e+00

7.60e+01

1.52e+02

2.28e+02

3.04e+02

3.80e+02

4.56e+02

5.32e+02

6.08e+02

6.84e+02

Figure 22.5: Contours of the Custom Field Function, Dynamic Head

Summary: In this tutorial you learned how to solve a simple 2D prob-lem using FLUENT’s parallel solver. Here the automatic grid par-titioning performed by FLUENT when you read the mesh into theparallel version was found to be acceptable. You also learned howto check the performance of the parallel solver to determine if opti-mizations are required. See the User’s Guide for additional detailsabout using the parallel solver.


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