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Page 1: FLUENT 6.1 Tutorial Guide

FLUENT 6.1 Tutorial Guide

February 2003

Page 2: FLUENT 6.1 Tutorial Guide

Licensee acknowledges that use of Fluent Inc.’s products can only provide an impreciseestimation of possible future performance and that additional testing and analysis, inde-pendent of the Licensor’s products, must be conducted before any product can be finallydeveloped or commercially introduced. As a result, Licensee agrees that it will not relyupon the results of any usage of Fluent Inc.’s products in determining the final design,composition or structure of any product.

Copyright c© 2003 by Fluent Inc.All rights reserved. No part of this document may be reproduced or otherwise used in

any form without express written permission from Fluent Inc.

Airpak, FIDAP, FLUENT, GAMBIT, Icepak, MixSim, and POLYFLOW are registeredtrademarks 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

Page 3: FLUENT 6.1 Tutorial Guide

Volume 1

1 Introduction to Using Fluent2 Modeling Periodic Flow and Heat Transfer3 Modeling External Compressible Flow4 Modeling Unsteady Compressible Flow5 Modeling Radiation and Natural Convection6 Using a Non-Conformal Mesh7 Using a Single Rotating Reference Frame8 Using Multiple Rotating Reference Frames9 Using the Mixing Plane Model10 Using Sliding Meshes11 Using Dynamic Meshes

Volume 2

12 Modeling Species Transport and Gaseous Combustion13 Using the Non-Premixed Combustion Model14 Modeling Surface Chemistry15 Modeling Evaporating Liquid Spray16 Using the VOF Model17 Modeling Cavitation18 Using the Mixture and Eulerian Multiphase Models19 Using the Eulerian Multiphase Model for Granular Flow20 Modeling Solidification21 Using the Eulerian Granular Multiphase Model with Heat Transfer22 Postprocessing23 Turbo Postprocessing24 Parallel Processing

Page 4: FLUENT 6.1 Tutorial Guide
Page 5: FLUENT 6.1 Tutorial Guide

Using This Manual

What’s In This Manual

The FLUENT Tutorial Guide contains a number of tutorials that teach you how to useFLUENT to solve different types of problems. In each tutorial, features related to problemsetup and postprocessing are demonstrated.

Tutorial 1 is a detailed tutorial designed to introduce the beginner to FLUENT. Thistutorial provides explicit instructions for all steps in the problem setup, solution, andpostprocessing. The remaining tutorials assume that you have read or solved Tutorial 1,or that you are already familiar with FLUENT and its interface. In these tutorials, somesteps will not be shown explicitly.

All of the tutorials include some postprocessing instructions, but Tutorial 22 is devotedentirely to standard postprocessing, and Tutorial 23 is devoted to turbomachinery-specificpostprocessing.

Where to Find the Files Used in the Tutorials

Each of the tutorials uses an existing mesh file. (Tutorials for mesh generation areprovided with the mesh generator documentation.) You will find the appropriate meshfile (and any other relevant files used in the tutorial) on the FLUENT documentation CD.The “Preparation” step of each tutorial will tell you where to find the necessary files.(Note that Tutorials 22, 23, and 24 use existing case and data files.)

Some of the more complex tutorials may require a significant amount of computationaltime. If you want to look at the results immediately, without waiting for the calcula-tion to finish, you can find the case and data files associated with the tutorial on thedocumentation CD (in the same directory where you found the mesh file).

How To Use This Manual

Depending on your familiarity with computational fluid dynamics and Fluent Inc. soft-ware, you can use this tutorial guide in a variety of ways.

For the Beginner

If you are a beginning user of FLUENT you should first read and solve Tutorial 1, in orderto familiarize yourself with the interface and with basic setup and solution procedures.

c© Fluent Inc. January 28, 2003 i

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Using This Manual

You may then want to try a tutorial that demonstrates features that you are going touse in your application. For example, if you are planning to solve a problem using thenon-premixed combustion model, you should look at Tutorial 13.

You may want to refer to other tutorials for instructions on using specific features, suchas custom field functions, grid scaling, and so on, even if the problem solved in thetutorial is not of particular interest to you. To learn about postprocessing, you can lookat Tutorial 22, which is devoted entirely to postprocessing (although the other tutorialsall contain some postprocessing as well). For turbomachinery-specific postprocessing, seeTutorial 23.

For the Experienced User

If you are an experienced FLUENT user, you can read and/or solve the tutorial(s) thatdemonstrate features that you are going to use in your application. For example, if youare planning to solve a problem using the non-premixed combustion model, you shouldlook at Tutorial 13.

You may want to refer to other tutorials for instructions on using specific features, suchas custom field functions, grid scaling, and so on, even if the problem solved in thetutorial is not of particular interest to you. To learn about postprocessing, you can lookat Tutorial 22, which is devoted entirely to postprocessing (although the other tutorialsall contain some postprocessing as well). For turbomachinery-specific postprocessing, seeTutorial 23.

Typographical Conventions Used In This Manual

Several typographical conventions are used in the text of the tutorials to facilitate yourlearning process.

• An exclamation point (!) to the left of a paragraph marks an important note orwarning.

• Different type styles are used to indicate graphical user interface menu items andtext interface menu items (e.g., Zone Surface panel, surface/zone-surface com-mand).

• The text interface type style is also used when illustrating exactly what appears onthe screen or exactly what you must type in the text window or in a panel.

• Instructions for performing each step in a tutorial will appear in standard type.Additional information about a step in a tutorial appears in italicized type.

• A mini flow chart is used to indicate the menu selections that lead you to a specificcommand or panel. For example,

ii c© Fluent Inc. January 28, 2003

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Using This Manual

Define −→Boundary Conditions...

indicates that the Boundary Conditions... menu item can be selected from the Definepull-down menu.

The words surrounded by boxes invoke menus (or submenus) and the arrows pointfrom a specific menu toward the item you should select from that menu.

c© Fluent Inc. January 28, 2003 iii

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Using This Manual

iv c© Fluent Inc. January 28, 2003

Page 9: FLUENT 6.1 Tutorial Guide

Contents

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

11 Using Dynamic Meshes 11-1

12 Modeling Species Transport and Gaseous Combustion 12-1

13 Using the Non-Premixed Combustion Model 13-1

14 Modeling Surface Chemistry 14-1

15 Modeling Evaporating Liquid Spray 15-1

16 Using the VOF Model 16-1

c© Fluent Inc. January 28, 2003 i

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CONTENTS

17 Modeling Cavitation 17-1

18 Using the Mixture and Eulerian Multiphase Models 18-1

19 Using the Eulerian Multiphase Model for Granular Flow 19-1

20 Modeling Solidification 20-1

21 Using the Eulerian Granular Multiphase Model with Heat Transfer 21-1

22 Postprocessing 22-1

23 Turbo Postprocessing 23-1

24 Parallel Processing 24-1

ii c© Fluent Inc. January 28, 2003

Page 11: FLUENT 6.1 Tutorial Guide

Tutorial 1. Introduction to Using FLUENT

Introduction: This tutorial illustrates the setup and solution of the two-dimensionalturbulent fluid flow and heat transfer in a mixing junction. The mixing elbowconfiguration is encountered in piping systems in power plants and process indus-tries. It is often important to predict the flow field and temperature field in theneighborhood of the mixing region in order to properly design the location of inletpipes.

In this tutorial you will learn how to:

• Read an existing grid file into FLUENT

• Use mixed units to define the geometry and fluid properties

• Set material properties and boundary conditions for a turbulent forced con-vection problem

• Initiate the calculation with residual plotting

• Calculate a solution using the segregated solver

• Examine the flow and temperature fields using graphics

• Enable the second-order discretization scheme for improved prediction of tem-perature

• Adapt the grid based on the temperature gradient to further improve theprediction of temperature

Prerequisites: This tutorial assumes that you have little experience with FLUENT, butthat you are generally familiar with the interface. If you are not, please review thesample session in Chapter 1 of the User’s Guide.

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Problem Description: The problem to be considered is shown schematically in Fig-ure 1.1. A cold fluid at 26C enters through the large pipe and mixes with a warmerfluid at 40C in the elbow. The pipe dimensions are in inches, and the fluid prop-erties and boundary conditions are given in SI units. The Reynolds number at themain inlet is 2.03 × 105, so that a turbulent model will be necessary.

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

39.93°39.93 °

Viscosity: µ = 8 x 10 -4 Pa-s

pSpecific Heat: C = 4216 J/kg-K

Figure 1.1: Problem Specification

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Preparation

1. Copy the file elbow/elbow.msh from the FLUENT documentation CD to your work-ing directory.

For UNIX systems, you can find the file by inserting the CD into your CD-ROMdrive and going to the following directory:

/cdrom/fluent6.1/help/tutfiles/

where cdrom must be replaced by the name of your CD-ROM drive.

For Windows systems, you can find the file by inserting the CD into your CD-ROMdrive and going to the following directory:

cdrom:\fluent6.1\help\tutfiles\

where cdrom must be replaced by the name of your CD-ROM drive (e.g., E).

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read the grid file elbow.msh.

File −→ Read −→Case...

(a) Select the file elbow.msh by clicking on it under Files and then clicking on OK.

Note: As this grid is read by FLUENT, messages will appear in the console windowreporting the progress of the conversion. After reading the grid file, FLUENTwill report that 918 triangular fluid cells have been read, along with a numberof boundary faces with different zone identifiers.

2. Check the grid.

Grid −→Check

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Grid Check

Domain Extents:x-coordinate: min (m) = 0.000000e+00, max (m) = 6.400001e+01y-coordinate: min (m) = -4.538534e+00, max (m) = 6.400000e+01

Volume statistics:minimum volume (m3): 2.782193e-01maximum volume (m3): 3.926232e+00

total volume (m3): 1.682930e+03Face area statistics:minimum face area (m2): 8.015718e-01maximum face area (m2): 4.118252e+00

Checking number of nodes per cell.Checking number of faces per cell.Checking thread pointers.Checking number of cells per face.Checking face cells.Checking bridge faces.Checking right-handed cells.Checking face handedness.Checking element type consistency.Checking boundary types:Checking face pairs.Checking periodic boundaries.Checking node count.Checking nosolve cell count.Checking nosolve face count.Checking face children.Checking cell children.Checking storage.Done.

Note: The grid check lists the minimum and maximum x and y values from thegrid, in the default SI units of meters, and reports on a number of other gridfeatures that are checked. Any errors in the grid would be reported at this time.In particular, you should always make sure that the minimum volume is notnegative, since FLUENT cannot begin a calculation if this is the case. To scalethe grid to the correct units of inches, the Scale Grid panel will be used.

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3. Smooth (and swap) the grid.

Grid −→ Smooth/Swap...

To ensure the best possible grid quality for the calculation, it is good practice tosmooth a triangular or tetrahedral grid after you read it into FLUENT.

(a) Click the Smooth button and then click Swap repeatedly until FLUENT reportsthat zero faces were swapped.

If FLUENT cannot improve the grid by swapping, no faces will be swapped.

(b) Close the panel.

4. Scale the grid.

Grid −→Scale...

(a) Under Units Conversion, select in from the drop-down list to complete thephrase Grid Was Created In in (inches).

(b) Click Scale to scale the grid.

The reported values of the Domain Extents will be reported in the default SIunits of meters.

(c) Click Change Length Units to set inches as the working units for length.

Confirm that the maximum x and y values are 64 inches (see Figure 1.1).

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(d) The grid is now sized correctly, and the working units for length have beenset to inches. Close the panel.

Note: Because the default SI units will be used for everything but the length, therewill be no need to change any other units in this problem. The choice of inchesfor the unit of length has been made by the actions you have just taken. If youwant to change the working units for length to something other than inches,say, mm, you would have to visit the Set Units panel in the Define pull-downmenu.

5. Display the grid (Figure 1.2).

Display −→Grid...

(a) Make sure that all of the surfaces are selected and click Display.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 13, 2002

Figure 1.2: The Triangular Grid for the Mixing Elbow

Extra: You can use the right mouse button to check which zone number corresponds toeach boundary. If you click the right mouse button on one of the boundaries in thegraphics window, its zone number, name, and type will be printed in the FLUENTconsole window. This feature is especially useful when you have several zones ofthe same type and you want to distinguish between them quickly.

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Step 2: Models

1. Keep the default solver settings.

Define −→ Models −→Solver...

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

Define −→ Models −→Viscous...

(a) Select k-epsilon in the Model list.

The original Viscous Model panel will expand when you do so.

(b) Accept the default Standard model by clicking OK.

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3. Enable heat transfer by activating the energy equation.

Define −→ Models −→Energy...

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Step 3: Materials

1. Create a new material called water.

Define −→Materials...

(a) Type the name water in the Name text-entry box.

(b) Enter the values shown in the table below under Properties:

Property Valuedensity 1000 kg/m3

cp 4216 J/kg-Kthermal conductivity 0.677 W/m-Kviscosity 8 ×10−4 kg/m-s

(c) Click Change/Create.

(d) Click No when FLUENT asks if you want to overwrite air.

The material water will be added to the list of materials which originally con-tained only air. You can confirm that there are now two materials defined byexamining the drop-down list under Fluid Materials.

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Extra: You could have copied the material water from the materials database(accessed by clicking on the Database... button). If the properties in thedatabase are different from those you wish to use, you can still edit thevalues under Properties and click the Change/Create button to update yourlocal copy. (The database will not be affected.)

(e) Close the Materials panel.

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Step 4: Boundary Conditions

Define −→Boundary Conditions...

1. Set the conditions for the fluid.

(a) Select fluid-9 under Zone.

The Type will be reported as fluid.

(b) Click Set... to open the Fluid panel.

(c) Specify water as the fluid material by selecting water in the Material Namedrop-down list. Click on OK.

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2. Set the boundary conditions at the main inlet.

(a) Select velocity-inlet-5 under Zone and click Set....

Hint: If you are unsure of which inlet zone corresponds to the main inlet,you can probe the grid display with the right mouse button and the zoneID will be displayed in the FLUENT console window. In the BoundaryConditions panel, the zone that you probed will automatically be selectedin the Zone list. In 2D simulations, it may be helpful to return to the GridDisplay panel and deselect the display of the fluid and interior zones (inthis case, fluid-9 and internal-3) before probing with the mouse button forzone names.

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(b) Choose Components as the Velocity Specification Method.

(c) Set an X-Velocity of 0.2 m/s.

(d) Set a Temperature of 293 K.

(e) Select Intensity and Hydraulic Diameter as the Turbulence Specification Method.

(f) Enter a Turbulence Intensity of 5%, and a Hydraulic Diameter of 32 in.

3. Repeat this operation for velocity-inlet-6, using the values in the following table:

velocity specification method componentsy velocity 1.0 m/stemperature 313 Kturbulence specification method intensity & hydraulic diameterturbulence intensity 5%hydraulic diameter 8 in

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4. Set the boundary conditions for pressure-outlet-7, as shown in the panel below.

These values will be used in the event that flow enters the domain through thisboundary.

5. For wall-4, keep the default settings for a Heat Flux of 0.

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6. For wall-8, you will also keep the default settings.

Note: If you probe your display of the grid (without the interior cells) you will seethat wall-8 is the wall on the outside of the bend just after the junction. Thisseparate wall zone has been created for the purpose of doing certain postpro-cessing tasks, to be discussed later in this tutorial.

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Step 5: Solution

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

Solve −→ Initialize −→Initialize...

(a) Choose velocity-inlet-5 from the Compute From list.

(b) Add a Y Velocity value of 0.2 m/sec throughout the domain.

Note: While an initial X Velocity is an appropriate guess for the horizontalsection, the addition of a Y Velocity will give rise to a better initial guessthroughout the entire elbow.

(c) Click Init and Close the panel.

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2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

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

Note: By default, all variables will be monitored and checked for determining theconvergence of the solution.

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3. Save the case file (elbow1.cas).

File −→ Write −→Case...

Keep the Write Binary Files (default) option on so that a binary file will be written.

4. Start the calculation by requesting 100 iterations.

Solve −→Iterate...

(a) Input 100 for the Number of Iterations and click Iterate.

The solution reaches convergence after approximately 60 iterations. The resid-ual plot is shown in Figure 1.3. Note that since the residual values are differentfor different computers, the plot that appears on your screen may not be exactlythe same as the one shown here.

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Scaled ResidualsFLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

Iterations

6050403020100

1e+03

1e+02

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

epsilonkenergyy-velocityx-velocitycontinuityResiduals

Figure 1.3: Residuals for the First 60 Iterations

5. Check for convergence.

There are no universal metrics for judging convergence. Residual definitions thatare useful for one class of problem are sometimes misleading for other classes ofproblems. Therefore it is a good idea to judge convergence not only by examiningresidual levels, but also by monitoring relevant integrated quantities and checkingfor mass and energy balances.

The three methods to check for convergence are:

• Monitoring the residuals.

Convergence will occur when the Convergence Criterion for each variable hasbeen reached. The default criterion is that each residual will be reduced toa value of less than 10−3, except the energy residual, for which the defaultcriterion is 10−6.

• Solution no longer changes with more iterations.

Sometimes the residuals may not fall below the convergence criterion set inthe case setup. However, monitoring the representative flow variables throughiterations may show that the residuals have stagnated and do not change withfurther iterations. This could also be considered as convergence.

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• Overall mass, momentum, energy and scalar balances are obtained.

Check the overall mass, momentum, energy and scalar balances in the FluxReports panel. The net imbalance should be less than 0.1% of the net fluxthrough the domain.

Report −→Fluxes

6. Save the data file (elbow1.dat).

Use the same prefix (elbow1) that you used when you saved the case file earlier.Note that additional case and data files will be written later in this session.

File −→ Write −→Data...

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Step 6: Displaying the Preliminary Solution

1. Display filled contours of velocity magnitude (Figure 1.4).

Display −→ Contours...

(a) Select Velocity... and then Velocity Magnitude from the drop-down lists underContours Of.

(b) Select Filled under Options.

(c) Click Display.

Note: Right-clicking on a point in the domain will cause the value of the corre-sponding contour to be displayed in the console window.

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Contours of Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

1.24e+001.18e+001.12e+001.05e+009.93e-019.31e-018.69e-018.07e-017.45e-016.82e-016.20e-015.58e-014.96e-014.34e-013.72e-013.10e-012.48e-011.86e-011.24e-016.20e-020.00e+00

Figure 1.4: Predicted Velocity Distribution After the Initial Calculation

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2. Display filled contours of temperature (Figure 1.5).

(a) Select Temperature... and Static Temperature in the drop-down lists underContours Of.

(b) Click Display.

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Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

3.13e+023.12e+023.11e+023.10e+023.09e+023.08e+023.07e+023.06e+023.05e+023.04e+023.03e+023.02e+023.01e+023.00e+022.99e+022.98e+022.97e+022.96e+022.95e+022.94e+022.93e+02

Figure 1.5: Predicted Temperature Distribution After the Initial Calculation

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3. Display velocity vectors (Figure 1.6).

Display −→ Vectors...

(a) Click Display to plot the velocity vectors.

Note: The Auto Scale button is on by default under Options. This scalingsometimes creates vectors that are too small or too large in the majorityof the domain.

(b) Resize the vectors by increasing the Scale factor to 3.

(c) Display the vectors once again.

(d) Use the middle mouse button to zoom the view. To do this, hold down thebutton and drag your mouse to the right and either up or down to constructa rectangle on the screen. The rectangle should be a frame around the regionthat you wish to enlarge. Let go of the mouse button and the image will beredisplayed (Figure 1.7).

(e) Un-zoom the view by holding down the middle mouse button and dragging itto the left to create a rectangle. When you let go, the image will be redrawn.If the resulting image is not centered, you can use the left mouse button totranslate it on your screen.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

1.40e+001.33e+001.27e+001.20e+001.13e+001.06e+009.96e-019.28e-018.61e-017.93e-017.26e-016.59e-015.91e-015.24e-014.56e-013.89e-013.21e-012.54e-011.86e-011.19e-015.16e-02

Figure 1.6: Resized Velocity Vectors

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, ske)

Nov 13, 2002

1.40e+001.33e+001.27e+001.20e+001.13e+001.06e+009.96e-019.28e-018.61e-017.93e-017.26e-016.59e-015.91e-015.24e-014.56e-013.89e-013.21e-012.54e-011.86e-011.19e-015.16e-02

Figure 1.7: Magnified View of Velocity Vectors

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4. Create an XY plot of temperature across the exit (Figure 1.8).

Plot −→ XY Plot...

(a) Select Temperature... and Static Temperature in the drop-down lists under theY Axis Function.

(b) Select pressure-outlet-7 from the Surfaces list.

(c) Click Plot.

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Static TemperatureFLUENT 6.1 (2d, segregated, ske)

Nov 13, 2002

Position (in)

(k)Temperature

Static

646260585654525048

3.10e+02

3.08e+02

3.06e+02

3.04e+02

3.02e+02

3.00e+02

2.98e+02

2.96e+02

pressure-outlet-7

Figure 1.8: Temperature Distribution at the Outlet

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5. Make an XY plot of the static pressure on the outer wall of the large pipe, wall-8(Figure 1.9).

(a) Choose Pressure... and Static Pressure from the Y Axis Function drop-downlists.

(b) Deselect pressure-outlet-7 and select wall-8 from the Surfaces list.

(c) Change the Plot Direction for X to 0, and the Plot Direction for Y to 1.

With a Plot Direction vector of (0,1), FLUENT will plot static pressure at thecells of wall-8 as a function of y.

(d) Click Plot.

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Static PressureFLUENT 6.1 (2d, segregated, ske)

Nov 13, 2002

Position (in)

(pascal)Pressure

Static

70605040302010

1.00e+02

0.00e+00

-1.00e+02

-2.00e+02

-3.00e+02

-4.00e+02

-5.00e+02

-6.00e+02

wall-8

Figure 1.9: Pressure Distribution along the Outside Wall of the Bend

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6. Define a custom field function for the dynamic head formula (ρ|V |2/2).

Define −→ Custom Field Functions...

(a) In the Field Functions drop-down list, select Density and click the Select button.

(b) Click the multiplication button, X.

(c) In the Field Functions drop-down list, select Velocity and Velocity Magnitudeand click Select.

(d) Click y^x to raise the last entry to a power, and click 2 for the power.

(e) Click the divide button, /, and then click 2.

(f) Enter the name dynam-head in the New Function Name text entry box.

(g) Click Define, and then Close the panel.

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7. Display filled contours of the custom field function (Figure 1.10).

Display −→ Contours...

(a) Select Custom Field Functions... in the drop-down list under Contours Of.

The function you created, dynam-head, will be shown in the lower drop-downlist.

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

Note: You may need to un-zoom your view after the last vector display, if you havenot already done so.

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Contours of dynam-headFLUENT 6.1 (2d, segregated, ske)

Nov 13, 2002

7.69e+027.30e+026.92e+026.53e+026.15e+025.76e+025.38e+025.00e+024.61e+024.23e+023.84e+023.46e+023.07e+022.69e+022.31e+021.92e+021.54e+021.15e+027.69e+013.84e+010.00e+00

Figure 1.10: Contours of the Custom Field Function, Dynamic Head

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Step 7: Enabling Second-Order Discretization

The elbow solution computed in the first part of this tutorial uses first-order discretiza-tion. The resulting solution is very diffusive; mixing is overpredicted, as can be seenin the contour plots of temperature and velocity distribution. You will now change tosecond-order discretization for the energy equation in order to improve the accuracy ofthe solution. With the second-order discretization, you will need to use a less aggressive(lower) value for the energy under-relaxation to ensure convergence.

1. Enable the second-order scheme for the calculation of energy and decrease theenergy under-relaxation factor.

Solve −→ Controls −→ Solution...

(a) Under Discretization, select Second Order Upwind for Energy.

(b) Under Under-Relaxation Factors, set the Energy under-relaxation factor to 0.8.

Note: You will have to scroll down both the Discretization and Under-RelaxationFactors lists to see the Energy options.

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2. Continue the calculation by requesting 100 more iterations.

Solve −→ Iterate...

The solution converges in approximately 35 additional iterations.

Scaled ResidualsFLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

Iterations

9080706050403020100

1e+03

1e+02

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

epsilonkenergyy-velocityx-velocitycontinuityResiduals

Figure 1.11: Residuals for the Second-Order Energy Calculation

Note: Whenever you change the solution control parameters, it is natural to seethe residuals jump.

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3. Write the case and data files for the second-order solution (elbow2.cas and elbow2.dat).

File −→ Write −→ Case & Data...

(a) Enter the name elbow2 in the Case/Data File box.

(b) Click OK.

The files elbow2.cas and elbow2.dat will be created in your directory.

4. Examine the revised temperature distribution (Figure 1.12).

Display −→ Contours...

The thermal spreading after the elbow has been reduced from the earlier prediction(Figure 1.5).

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Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

3.13e+023.12e+023.11e+023.10e+023.09e+023.08e+023.07e+023.06e+023.04e+023.03e+023.02e+023.01e+023.00e+022.99e+022.98e+022.97e+022.96e+022.95e+022.94e+022.93e+022.92e+02

Figure 1.12: Temperature Contours for the Second-Order Solution

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Step 8: Adapting the Grid

The elbow solution can be improved further by refining the grid to better resolve the flowdetails. In this step, you will adapt the grid based on the temperature gradients in thecurrent solution. Before adapting the grid, you will first determine an acceptable rangeof temperature gradients over which to adapt. Once the grid has been refined, you willcontinue the calculation.

1. Plot filled contours of temperature on a cell-by-cell basis (Figure 1.13).

Display −→ Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-downlists.

(b) Deselect Node Values under Options and click Display.

Note: When the contours are displayed you will see the cell values of temper-ature instead of the smooth-looking node values. Node values are obtainedby averaging the values at all of the cells that share the node. Cell val-ues are the values that are stored at each cell center and are displayedthroughout the cell. Examining the cell-by-cell values is helpful when youare preparing to do an adaption of the grid because it indicates the re-gion(s) where the adaption will take place.

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2. Plot the temperature gradients that will be used for adaption (Figure 1.14).

(a) Select Adaption... and Adaption Function in the Contours Of drop-down lists.

(b) Click Display to see the gradients of temperature, displayed on a cell-by-cellbasis.

Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

3.13e+023.12e+023.11e+023.10e+023.08e+023.07e+023.06e+023.05e+023.04e+023.03e+023.02e+023.01e+022.99e+022.98e+022.97e+022.96e+022.95e+022.94e+022.93e+022.91e+022.90e+02

Figure 1.13: Temperature Contours for the Second-Order Solution: Cell Values

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Contours of Adaption FunctionFLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

1.30e-011.23e-011.17e-011.10e-011.04e-019.74e-029.09e-028.44e-027.79e-027.14e-026.49e-025.84e-025.20e-024.55e-023.90e-023.25e-022.60e-021.95e-021.30e-026.49e-031.42e-14

Figure 1.14: Contours of Adaption Function: Temperature Gradient

Note: The quantity Adaption Function defaults to the gradient of the variablewhose Max and Min were most recently computed in the Contours panel.In this example, the static temperature is the most recent variable to haveits Max and Min computed, since this occurs when the Display button ispushed. Note that for other applications, gradients of another variablemight be more appropriate for performing the adaption.

3. Plot temperature gradients over a limited range in order to mark cells for adaption(Figure 1.15).

(a) Under Options, deselect Auto Range so that you can change the minimumtemperature gradient value to be plotted.

The Min temperature gradient is 0 K/m, as shown in the Contours panel.

(b) Enter a new Min value of 0.02.

(c) Click Display.

The colored cells in the figure are in the “high gradient” range, so they will bethe ones targeted for adaption.

4. Adapt the grid in the regions of high temperature gradient.

Adapt −→ Gradient...

(a) Select Temperature... and Static Temperature in the Gradients Of drop-downlists.

(b) Deselect Coarsen under Options, so that only a refinement of the grid will beperformed.

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Contours of Adaption FunctionFLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

1.30e-011.24e-011.19e-011.13e-011.08e-011.02e-019.69e-029.14e-028.59e-028.04e-027.49e-026.94e-026.40e-025.85e-025.30e-024.75e-024.20e-023.65e-023.10e-022.55e-022.00e-02

Figure 1.15: Contours of Temperature Gradient Over a Limited Range

(c) Click Compute.

FLUENT will update the Min and Max values.

(d) Enter the value of 0.02 for the Refine Threshold.

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(e) Click Mark.

FLUENT will report the number of cells marked for adaption in the consolewindow.

(f) Click Manage... to display the marked cells.

This will open the Manage Adaption Registers panel.

(g) Click Display.

FLUENT will display the cells marked for adaption (Figure 1.16).

(h) Click Adapt. Click Yes when you are asked for confirmation.

Note: There are two different ways to adapt. You can click on Adapt in theManage Adaption Registers panel as was just done, or Close this panel anddo the adaption in the Gradient Adaption panel. If you use the Adaptbutton in the Gradient Adaption panel, FLUENT will recreate an adaptionregister. Therefore, once you have the Manage Adaption Registers panelopen, it saves time to use the Adapt button there.

(i) Close the Manage Adaption Registers and Gradient Adaption panels.

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Adaption Markings (gradient-r0)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

Figure 1.16: Cells Marked for Adaption

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5. Display the adapted grid (Figure 1.17).

Display −→ Grid...

GridFLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

Figure 1.17: The Adapted Grid

6. Request an additional 100 iterations.

Solve −→ Iterate...

The solution converges after approximately 40 additional iterations.

7. Write the final case and data files (elbow3.cas and elbow3.dat) using the prefixelbow3.

File −→ Write −→ Case & Data...

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Scaled ResidualsFLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

Iterations

140120100806040200

1e+03

1e+02

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

epsilonkenergyy-velocityx-velocitycontinuityResiduals

Figure 1.18: The Complete Residual History

8. Examine the filled temperature distribution (using node values) on the revised grid(Figure 1.19).

Display −→ Contours...

Summary: Comparison of the filled temperature contours for the first solution (us-ing the original grid and first-order discretization) and the last solution (using anadapted grid and second-order discretization) clearly indicate that the latter is muchless diffusive. While first-order discretization is the default scheme in FLUENT, itis good practice to use your first-order solution as a starting guess for a calculationthat uses a higher-order discretization scheme and, optionally, an adapted grid.

Note that in this problem, the flow field is decoupled from temperature since allproperties are constant. For such cases, it is more efficient to compute the flow-fieldsolution first (i.e., without solving the energy equation) and then solve for energy(i.e., without solving the flow equations). You will use the Solution Controls panelto turn solution of the equations on and off during this procedure.

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Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, ske)

Nov 12, 2002

3.13e+023.12e+023.11e+023.10e+023.09e+023.08e+023.07e+023.06e+023.05e+023.04e+023.02e+023.01e+023.00e+022.99e+022.98e+022.97e+022.96e+022.95e+022.94e+022.93e+022.92e+02

Figure 1.19: Filled Contours of Temperature Using the Adapted Grid

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Tutorial 2. Modeling Periodic Flow andHeat Transfer

Introduction: Many industrial applications, such as steam generation in a boiler or aircooling in the coil of an air conditioner, can be modeled as two-dimensional periodicheat flow. This tutorial illustrates how to set up and solve a periodic heat transferproblem, given a pregenerated mesh.

The system that is modeled is a bank of tubes containing a flowing fluid at onetemperature that is immersed in a second fluid in cross-flow at a different temper-ature. Both fluids are water, and the flow is classified as laminar and steady, witha Reynolds number of approximately 100. The mass flow rate of the cross-flow isknown, and the model is used to predict the flow and temperature fields that resultfrom convective heat transfer.

Due to symmetry of the tube bank, and the periodicity of the flow inherent in thetube bank geometry, only a portion of the geometry will be modeled in FLUENT,with symmetry applied to the outer boundaries. The resulting mesh consists ofa periodic module with symmetry. In the tutorial, the inflow boundary will beredefined as a periodic zone, and the outflow boundary defined as its shadow.

In this tutorial you will learn how to:

• Create periodic zones

• Define a specified periodic mass flow rate

• Model periodic heat transfer with specified temperature boundary conditions

• Calculate a solution using the segregated solver

• Plot temperature profiles on specified isosurfaces

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps will not be shownexplicitly.

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Problem Description: This problem considers a 2D section of a tube bank. A schematicof the problem is shown in Figure 2.1. The bank consists of uniformly spaced tubeswith a diameter of 1 cm, that are staggered in the direction of cross-fluid flow.Their centers are separated by a distance of 2 cm in the x direction, and 1 cm inthe y direction. The bank has a depth of 1 m.

Because of the symmetry of the tube bank geometry, only a portion of the domainneeds to be modeled. The computational domain is shown in outline in Figure 2.1.A mass flow rate of 0.05 kg/s is applied to the inflow boundary of the periodicmodule. The temperature of the tube wall (Twall) is 400 K and the bulk temperatureof the cross-flow water (T∞) is 300 K. The properties of water that are used in themodel are shown in Figure 2.1.

Preparation

1. Copy the file tubebank/tubebank.msh from the FLUENT documentation CD toyour working directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

Step 1: Grid

1. Read in the mesh file tubebank.msh.

File −→ Read −→Case...

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Scale the grid.

Grid −→Scale...

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1 cm

Τ∞ = 300 K

4 cm

0.5 cm

Τwall = 400 Km = 0.05 kg/s⋅

ρ = 998.2 kg/m3

= 0.001003 kg/m-sµ= 4182 J/kg-K

= 0.6 W/m-K

c p

k

Figure 2.1: Schematic of the Problem

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(a) In the Units Conversion drop-down list, select cm to complete the phrase GridWas Created In cm (centimeters).

(b) Click on Scale to scale the grid.

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

4. Display the mesh (Figure 2.2).

Display −→Grid...

In Figure 2.2 you can see that quadrilateral cells are used in the regions surroundingthe tube walls, and triangular cells are used for the rest of the domain, resultingin a “hybrid” mesh. The quadrilateral cells provide better resolution of the vis-cous gradients near the tube walls. The remainder of the computational domain isconveniently filled with triangular cells.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 13, 2002

Figure 2.2: Mesh for the Periodic Tube Bank

Extra: You can use the right mouse button to check which zone number corre-sponds to each boundary. If you click the right mouse button on one of theboundaries in the graphics window, its zone number, name, and type will beprinted in the FLUENT console window. This feature is especially useful whenyou have several zones of the same type and you want to distinguish betweenthem quickly.

5. Create the periodic zone.

wall-9 and wall-12, the inflow and outflow boundaries, respectively, are currentlydefined as wall zones and need to be redefined as periodic. wall-9 will be made intoa translationally periodic zone, and wall-12 will be deleted and redefined as wall-9’speriodic shadow.

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

Hint: You may need to enter press the <Enter> key to get the > prompt.

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grid/modify-zones/make-periodic

Periodic zone [()] 9Shadow zone [()] 12Rotational periodic? (if no, translational) [yes] noCreate periodic zones? [yes] yes

Auto detect translation vector? [yes] yes

computed translation deltas: 0.040000 0.000000all 26 faces matched for zones 9 and 12.

zone 12 deleted

created periodic zones.

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Step 2: Models

1. Keep the default solver settings.

Define −→ Models −→Solver...

2. Enable heat transfer by activating the energy equation.

Define −→ Models −→Energy...

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3. Set the periodic flow conditions.

Define −→Periodic Conditions...

(a) Select Specify Mass Flow under Type.

This will allow you to specify the Mass Flow Rate.

(b) Enter a Mass Flow Rate of 0.05 kg/s.

(c) Click OK.

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Step 3: Materials

You will need to add liquid water to the list of fluid materials by copying it from thematerials database.

1. Copy the properties of liquid water from the database.

Define −→Materials...

(a) Click on the Database... button.

This will open the Database Materials panel.

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(b) Scroll down the Fluid Materials list to the bottom, and select water-liquid(h2o<l>).

This will display the default settings for water-liquid as shown in the panelabove.

(c) Click Copy, and Close the Database Materials panel.

The Materials panel will now display the copied information for water.

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Step 4: Boundary Conditions

Define −→Boundary Conditions...

1. Set the conditions for fluid-16.

(a) Select water-liquid in the Material Name drop-down list.

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2. Set the boundary conditions for wall-21.

wall-21 is the bottom wall of the left tube in the periodic module shown in Figure 2.1.

(a) Change the Zone Name from wall-21 to wall-bottom.

(b) Select Temperature under Thermal Conditions.

(c) Change the Temperature to 400 K.

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3. Set the boundary conditions for wall-3.

wall-3 is the top wall of the right tube in the periodic module shown in Figure 2.1.

(a) Change the Zone Name from wall-3 to wall-top.

(b) Select Temperature under Thermal Conditions.

(c) Change the Temperature to 400 K.

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Step 5: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Change the Under-Relaxation Factor for Energy to 0.9.

Hint: You will need to scroll down the Under-Relaxation Factors list to seeEnergy.

(b) Under Discretization, select Second Order Upwind for Momentum and Energy.

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2. Enable the plotting of residuals.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click the OK button.

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3. Initialize the solution.

Solve −→ Initialize −→Initialize...

(a) Under Initial Values, check that the value for Temperature is set to 300 K.

(b) Click Init, and Close the panel.

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

File −→ Write −→Case...

5. Start the calculation by requesting 350 iterations.

Solve −→Iterate...

(a) Set the Number of Iterations to 350.

(b) Click Iterate.

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The energy residual curve begins to flatten out after about 350 iterations. In orderfor the solution to converge, the relaxation factor for energy will have to be furtherreduced.

6. Change the Under-Relaxation Factor for Energy to 0.6.

Solve −→ Controls −→Solution...

7. Continue the calculation by requesting another 300 iterations.

Solve −→Iterate...

After restarting the calculation, you will see an initial dip in the plot of the energyresidual, resulting from a reduction in the under-relaxation factor. The solutionwill converge in a total of approximately 580 iterations.

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

File −→ Write −→Case & Data...

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Step 6: Postprocessing

1. Display filled contours of static pressure (Figure 2.3).

Display −→Contours...

(a) Select Filled under Options.

(b) Select Pressure... and Static Pressure in the Contours Of drop-down list.

(c) Click Display.

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Contours of Static Pressure (pascal) Dec 17, 2002FLUENT 6.1 (2d, segregated, lam)

8.20e-02

-4.50e-02-3.87e-02-3.23e-02-2.60e-02-1.96e-02-1.33e-02-6.91e-03-5.66e-045.78e-031.21e-021.85e-022.48e-023.12e-023.75e-024.39e-025.02e-025.66e-026.29e-026.93e-027.56e-02

Figure 2.3: Contours of Static Pressure

2. Change the view to mirror the display across the symmetry planes (Figure 2.4).

Display −→Views...

(a) Select all of the symmetry zones by clicking the shaded icon to the right ofMirror Planes.

Note: There are four symmetry zones in the Mirror Planes list because thetop and bottom symmetry planes in the domain are each comprised oftwo symmetry zones, one on each side of the tube. It is also possible togenerate the same display shown in Figure 2.4 by selecting just one of thesymmetry zones on the top symmetry plane, and one on the bottom.

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(b) Click Apply, and Close the panel.

(c) Using the left button of your mouse, translate the view so that it is centeredin the window.

Contours of Static Pressure (pascal) Dec 17, 2002FLUENT 6.1 (2d, segregated, lam)

8.20e-02

-4.50e-02-3.87e-02-3.23e-02-2.60e-02-1.96e-02-1.33e-02-6.91e-03-5.66e-045.78e-031.21e-021.85e-022.48e-023.12e-023.75e-024.39e-025.02e-025.66e-026.29e-026.93e-027.56e-02

Figure 2.4: Contours of Static Pressure with Symmetry

Note: The pressure contours displayed in Figure 2.4 do not include the linearpressure gradient computed by the solver; thus the contours are periodic at theinflow and outflow boundaries.

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3. Display filled contours of static temperature (Figure 2.5).

Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-downlist.

(b) Click Display.

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Contours of Static Temperature (k) Dec 17, 2002FLUENT 6.1 (2d, segregated, lam)

4.00e+02

2.77e+022.83e+022.90e+022.96e+023.02e+023.08e+023.14e+023.20e+023.26e+023.32e+023.39e+023.45e+023.51e+023.57e+023.63e+023.69e+023.75e+023.82e+023.88e+023.94e+02

Figure 2.5: Contours of Static Temperature

The contours reveal the temperature increase in the fluid due to heat transfer fromthe tubes. The hotter fluid is confined to the near-wall and wake regions, while anarrow stream of cooler fluid is convected through the tube bank.

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4. Display the velocity vectors (Figure 2.6).

Display −→Vectors...

(a) Select Velocity... and Velocity Magnitude in the Color By drop-down list.

(b) Change the Scale to 2.

This will enlarge the vectors that are displayed, making it easier to view theflow patterns.

(c) Click Display.

(d) Zoom in on the upper right portion of the left tube using your middle mousebutton, to get the display shown in Figure 2.6.

This zoomed-in view of the velocity vector plot clearly shows the recirculating flowbehind the tube and the boundary layer development along the tube surface.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 13, 2002

1.31e-021.25e-021.18e-021.12e-021.05e-029.85e-039.19e-038.53e-037.88e-037.22e-036.57e-035.91e-035.25e-034.60e-033.94e-033.28e-032.63e-031.97e-031.32e-036.59e-042.53e-06

Figure 2.6: Velocity Vectors

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5. Plot the temperature profiles at three cross-sections of the tube bank.

(a) Create an isosurface on the periodic tube bank at x = 0.01 m (through thefirst tube).

You will first need to create a surface of constant x coordinate for each cross-section: x = 0.01, 0.02, and 0.03 m. These isosurfaces correspond to thevertical cross-sections through the first tube, halfway between the two tubes,and through the second tube.

Surface −→Iso-Surface...

i. In the Surface of Constant drop-down lists, select Grid... and X-Coordinate.

ii. Enter x=0.01m under New Surface Name.

iii. Enter 0.01 for Iso-Values.

iv. Click Create.

(b) Follow the same procedure to create surfaces at:

• x = 0.02 m (halfway between the two tubes)

• x = 0.03 m (through the middle of the second tube)

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(c) Create an XY plot of static temperature on the three isosurfaces.

Plot −→XY Plot...

i. Change the Plot Direction for X to 0, and the Plot Direction for Y to 1.

With a Plot Direction vector of (0,1), FLUENT will plot the selected vari-able as a function of y. Since you are plotting the temperature profileon cross-sections of constant x, the y direction is the one in which thetemperature varies.

ii. Select Temperature... and Static Temperature in the Y-Axis Function drop-down lists.

iii. Scroll down the Surfaces list and select x=0.01m, x=0.02m, and x=0.03m.

iv. Click Curves... to define different styles for the different plot curves.

This will open the Curves - Solution XY Plot panel.

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v. Select + in the Symbol drop-down list.

vi. Click Apply.

This assigns the + symbol to the x = 0.01 m curve.

vii. Increase the Curve # to 1 to define the style for the x = 0.02 m curve.

viii. Select x in the Symbol drop-down list.

ix. Change the Size to 0.5.

x. Click Apply, and Close the panel.

Since you did not change the curve style for the x = 0.03 m curve, thedefault symbol will be used.

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

Summary: In this tutorial, periodic flow and heat transfer in a staggered tube bankwere modeled in FLUENT. The model was set up assuming a known mass flowthrough the tube bank and constant wall temperatures. Due to the periodic natureof the flow and symmetry of the geometry, only a small piece of the full geometrywas modeled. In addition, the tube bank configuration lent itself to the use of ahybrid mesh with quadrilateral cells around the tubes and triangles elsewhere.

The Periodicity Conditions panel makes it easy to run this type of model over a va-riety of operating conditions. For example, different flow rates (and hence differentReynolds numbers) can be studied, or a different inlet bulk temperature can beimposed. The resulting solution can then be examined to extract the pressure dropper tube row and overall Nusselt number for a range of Reynolds numbers.

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Static TemperatureFLUENT 6.1 (2d, segregated, lam)

Nov 13, 2002

Position (m)

(k)Temperature

Static

0.010.0090.0080.0070.0060.0050.0040.0030.0020.0010

4.00e+02

3.80e+02

3.60e+02

3.40e+02

3.20e+02

3.00e+02

2.80e+02

2.60e+02

x=0.03mx=0.02mx=0.01m

Figure 2.7: Static Temperature at x=0.01, 0.02, and 0.03 m

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Tutorial 3. Modeling External CompressibleFlow

Introduction: The purpose of this tutorial is to compute the turbulent flow past atransonic airfoil at a non-zero angle of attack. You will use the Spalart-Allmarasturbulence model.

In this tutorial you will learn how to:

• Model compressible flow (using the ideal gas law for density)

• Set boundary conditions for external aerodynamics

• Use the Spalart-Allmaras turbulence model

• Calculate a solution using the coupled implicit solver

• Use force and surface monitors to check solution convergence

• Check the grid by plotting the distribution of y+

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

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Problem Description: The problem considers the flow around an airfoil at an incidenceangle of α = 4 and a free stream Mach number of 0.8 (M∞ = 0.8). This flow istransonic, and has a fairly strong shock near the mid-chord (x/c = 0.45) on theupper (suction) side. The chord length is 1 m. The geometry of the airfoil is shownin Figure 3.1.

M = 0.8∞

α = 4°

1 m

Figure 3.1: Problem Specification

Preparation

1. Copy the file airfoil/airfoil.msh from the FLUENT documentation CD to yourworking directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read the grid file airfoil.msh.

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid.

Display −→Grid...

(a) Display the grid with the default settings (Figure 3.2).

(b) Use the middle mouse button to zoom in on the image so you can see the meshnear the airfoil (Figure 3.3).

Quadrilateral cells were used for this simple geometry because they can bestretched easily to account for different size gradients in different directions.In the present case, the gradients normal to the airfoil wall are much greaterthan those tangent to the airfoil, except near the leading and trailing edges andin the vicinity of the shock expected on the upper surface. Consequently, thecells nearest the surface have very high aspect ratios. For geometries that are

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 14, 2002

Figure 3.2: The Grid Around the Airfoil

GridFLUENT 6.1 (2d, segregated, lam)

Nov 14, 2002

Figure 3.3: The Grid After Zooming In on the Airfoil

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more difficult to mesh, it may be easier to create a hybrid mesh comprised ofquadrilateral and triangular cells.

A parabola was chosen to represent the far-field boundary because it has nodiscontinuities in slope, enabling the construction of a smooth mesh in theinterior of the domain.

Extra: You can use the right mouse button to check which zone number cor-responds to each boundary. If you click the right mouse button on oneof the boundaries in the graphics window, its zone number, name, andtype will be printed in the FLUENT console window. This feature is espe-cially useful when you have several zones of the same type and you wantto distinguish between them quickly.

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Step 2: Models

1. Select the Coupled, Implicit solver.

Define −→ Models −→Solver...

The coupled solver is recommended when dealing with applications involving high-speed aerodynamics. The implicit solver will generally converge much faster thanthe explicit solver, but will use more memory. For this 2D case, memory is not anissue.

2. Enable heat transfer by turning on the energy equation.

Define −→ Models −→Energy...

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Modeling External Compressible Flow

3. Turn on the Spalart-Allmaras turbulence model.

Define −→ Models −→Viscous...

(a) Select the Spalart-Allmaras model and retain the default options and constants.

The Spalart-Allmaras model is a relatively simple one-equation model that solves a mod-eled transport equation for the kinematic eddy (turbulent) viscosity. This embodies arelatively new class of one-equation models in which it is not necessary to calculate alength scale related to the local shear layer thickness. The Spalart-Allmaras model wasdesigned specifically for aerospace applications involving wall-bounded flows and has beenshown to give good results for boundary layers subjected to adverse pressure gradients.

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Step 3: Materials

The default Fluid Material is air, which is the working fluid in this problem. The defaultsettings need to be modified to account for compressibility and variations of the thermo-physical properties with temperature.

Define −→Materials...

1. Select ideal-gas in the Density drop-down list.

2. Select sutherland in the drop-down list for Viscosity.

This will open the Sutherland Law panel.

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(a) Click OK to accept the default Three Coefficient Method and parameters.

The Sutherland law for viscosity is well suited for high-speed compressible flows.

3. Click Change/Create in the Materials panel to save these settings, and then closethe panel.

Note: While Density and Viscosity have been made temperature-dependent, Cp and Ther-mal Conductivity have been left constant. For high-speed compressible flows, thermaldependency of the physical properties is generally recommended. In this case, how-ever, the temperature gradients are sufficiently small that the model is accurate withCp and Thermal Conductivity constant.

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Step 4: Operating Conditions

Set the operating pressure to 0 Pa.

Define −→Operating Conditions...

For flows with Mach numbers greater than 0.1, an operating pressure of 0 is recommended.For more information on how to set the operating pressure, see the FLUENT User’s Guide.

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Step 5: Boundary Conditions

Set the boundary conditions for pressure-far-field-1 as shown in the panel.

Define −→Boundary Conditions...

For external flows, you should choose a viscosity ratio between 1 and 10.

Note: The X- and Y-Component of Flow Direction are set as above because of the 4 angleof attack: cos 4 ≈ 0.997564 and sin 4 ≈ 0.069756.

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Step 6: Solution

1. Set the solution controls.

Solve −→ Controls −→Solution...

(a) Set the Under-Relaxation Factor for Modified Turbulent Viscosity to 0.9.

Larger (i.e., closer to 1) under-relaxation factors will generally result in fasterconvergence. However, instability can arise that may need to be eliminated bydecreasing the under-relaxation factors.

(b) Under Solver Parameters, set the Courant Number to 5.

(c) Under Discretization, select Second Order Upwind for Modified Turbulent Vis-cosity.

The second-order scheme will resolve the boundary layer and shock more ac-curately than the first-order scheme.

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2. Turn on residual plotting during the calculation.

Solve −→ Monitors −→Residual...

3. Initialize the solution.

Solve −→ Initialize −→Initialize...

(a) Select pressure-far-field-1 in the Compute From drop-down list.

(b) Click Init to initialize the solution.

To monitor the convergence of the solution, you are going to enable the plotting ofthe drag, lift, and moment coefficients. You will need to iterate until all of theseforces have converged in order to be certain that the overall solution has converged.For the first few iterations of the calculation, when the solution is fluctuating, thevalues of these coefficients will behave erratically. This can cause the scale of they axis for the plot to be set too wide, and this will make variations in the value ofthe coefficients less evident. To avoid this problem, you will have FLUENT performa small number of iterations, and then you will set up the monitors.

Since the drag, lift, and moment coefficients are global variables, indicating certainoverall conditions, they may converge while conditions at specific points are stillvarying from one iteration to the next. To monitor this, you will create a pointmonitor at a point where there is likely to be significant variation, just upstreamof the shock wave, and monitor the value of the skin friction coefficient. A smallnumber of iterations will be sufficient to roughly determine the location of the shock.

After setting up the monitors, you will continue the calculation.

4. Request 100 iterations.

Solve −→Iterate...

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Modeling External Compressible Flow

This will be sufficient to see where the shock wave is, and the fluctuations of thesolution will have diminished significantly.

5. Increase the Courant number.

Solve −→ Controls −→Solution...

Under Solver Parameters, set the Courant Number to 20.

The solution will generally converge faster for larger Courant numbers, unless theintegration scheme becomes unstable. Since you have performed some initial iter-ations, and the solution is stable, you can try increasing the Courant number tospeed up convergence. If the residuals increase without bound, or you get a floatingpoint exception, you will need to decrease the Courant number, read in the previousdata file, and try again.

6. Turn on monitors for lift, drag, and moment coefficients.

Solve −→ Monitors −→Force...

(a) In the drop-down list under Coefficient, select Drag.

(b) Select wall-bottom and wall-top in the Wall Zones list.

(c) Under Force Vector, enter 0.9976 for X and 0.06976 for Y.

These magnitudes ensure that the drag and lift coefficients are calculated nor-mal and parallel to the flow, which is 4 off of the global coordinates.

(d) Select Plot under Options to enable plotting of the drag coefficient.

(e) Select Write under Options to save the monitor history to a file, and specifycd-history as the file name.

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

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Modeling External Compressible Flow

(f) Click Apply.

(g) Repeat the above steps for Lift, using values of 0.06976 for X and 0.9976 forY under Force Vector.

(h) Repeat the above steps for Moment, using values of 0.25 m for X and 0 m forY under Moment Center.

7. Set the reference values that are used to compute the lift, drag, and moment coef-ficients.

The reference values are used to non-dimensionalize the forces and moments actingon the airfoil. The dimensionless forces and moments are the lift, drag, and momentcoefficients.

Report −→Reference Values...

(a) In the Compute From drop-down list, select pressure-far-field-1.

FLUENT will update the Reference Values based on the boundary conditions atthe far-field boundary.

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8. Define a monitor for tracking the skin friction coefficient value just upstream of theshock wave.

(a) Display filled contours of pressure overlaid with the grid.

Display −→Contours...

i. Turn on Filled.

ii. Select Draw Grid.

This will open the Grid Display panel.

iii. Close the Grid Display panel, since there are no changes to be made here.

iv. Click Display in the Contours panel.

v. Zoom in on the airfoil (Figure 3.4).

Contours of Static Pressure (pascal)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

1.54e+051.49e+051.44e+051.38e+051.33e+051.28e+051.23e+051.17e+051.12e+051.07e+051.02e+059.63e+049.11e+048.58e+048.05e+047.53e+047.00e+046.47e+045.95e+045.42e+044.89e+04

Figure 3.4: Pressure Contours After 100 Iterations

The shock wave is clearly visible on the upper surface of the airfoil, wherethe pressure first jumps to a higher value.

vi. Zoom in on the shock wave, until individual cells adjacent to the uppersurface (wall-top boundary) are visible (Figure 3.5).

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Modeling External Compressible Flow

Contours of Static Pressure (pascal)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

1.54e+051.49e+051.44e+051.38e+051.33e+051.28e+051.23e+051.17e+051.12e+051.07e+051.02e+059.63e+049.11e+048.58e+048.05e+047.53e+047.00e+046.47e+045.95e+045.42e+044.89e+04

Figure 3.5: Magnified View of Pressure Contours Showing Wall-Adjacent Cells

The zoomed-in region contains cells just upstream of the shock wave that areadjacent to the upper surface of the airfoil. In the following step, you willcreate a point surface inside a wall-adjacent cell, to be used for the skin frictioncoefficient monitor.

(b) Create a point surface just upstream of the shock wave.

Surface −→Point...

i. Under Coordinates, enter 0.53 for x0, and 0.051 for y0.

ii. Click on Create to create the point surface (point-4).

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Contours of Static Pressure (pascal)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

1.54e+051.49e+051.44e+051.38e+051.33e+051.28e+051.23e+051.17e+051.12e+051.07e+051.02e+059.63e+049.11e+048.58e+048.05e+047.53e+047.00e+046.47e+045.95e+045.42e+044.89e+04

Figure 3.6: Pressure Contours With Point Surface

Note: Here, you have entered the exact coordinates of the point surface sothat your convergence history will match the plots and description in thistutorial. In general, however, you will not know the exact coordinates inadvance, so you will need to select the desired location in the graphicswindow as follows:

i. Click Select Point With Mouse.

ii. Move the mouse to a point located anywhere inside one of the cellsadjacent to the upper surface (wall-top boundary), in the vicinity ofthe shock wave. (See Figure 3.6.)

iii. Click the right mouse button.

iv. Click Create to create the point surface.

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Modeling External Compressible Flow

(c) Create a surface monitor for the point surface.

Solve −→ Monitors −→Surface...

i. Increase Surface Monitors to 1.

ii. To the right of monitor-1, turn on the Plot and Write options and clickDefine....

This will open the Define Surface Monitor panel.

iii. Select Wall Fluxes... and Skin Friction Coefficient under Report Of.

iv. Select point-4 in the Surfaces list.

v. In the Report Type drop-down list, select Vertex Average.

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vi. Increase the Plot Window to 4.

vii. Specify monitor-1.out as the File Name, and click OK in the Define Sur-face Monitor panel.

viii. Click OK in the Surface Monitors panel.

9. Save the case file (airfoil.cas).

File −→ Write −→Case...

10. Continue the calculation by requesting 200 iterations.

Solve −→Iterate...

Convergence history of Skin Friction Coefficient on point-4 (in SI units)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Iteration

CoefficientFriction

SkinAverage

Vertex

200190180170160150140130120110100

2.00e-03

1.80e-03

1.60e-03

1.40e-03

1.20e-03

1.00e-03

8.00e-04

6.00e-04

4.00e-04

2.00e-04

Figure 3.7: Skin Friction Convergence History for the Initial Calculation

Note: After about 90 iterations, the residual criteria are satisfied and FLUENTstops iterating. Since the skin friction monitor indicates that the skin frictioncoefficient at point-4 has not converged (Figure 3.7), you will need to decreasethe convergence criterion for the modified turbulent viscosity and continue it-erating.

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11. Reduce the convergence criterion for the modified turbulent viscosity equation.

Solve −→ Monitors −→Residual...

(a) Set the Convergence Criterion for nut to 1e-7 and click OK.

nut stands for νt. This is the residual for the modified turbulent viscosity thatthe Spalart-Allmaras model solves for.

12. Continue the calculation for another 600 iterations.

After 600 additional iterations, the force monitors and the skin friction coefficientmonitor (Figures 3.8–3.11), indicate that the solution has converged.

13. Save the data file (airfoil.dat).

File −→ Write −→Data...

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Convergence history of Skin Friction Coefficient on point-4 (in SI units)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Iteration

CoefficientFriction

SkinAverage

Vertex

800700600500400300200100

2.00e-03

1.80e-03

1.60e-03

1.40e-03

1.20e-03

1.00e-03

8.00e-04

6.00e-04

4.00e-04

2.00e-04

Figure 3.8: Skin Friction Coefficient History

Drag ConvergenceFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Iterations

Cd

800700600500400300200100

8.00e-02

7.50e-02

7.00e-02

6.50e-02

6.00e-02

5.50e-02

5.00e-02

Figure 3.9: Drag Coefficient Convergence History

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Lift ConvergenceFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Iterations

Cl

800700600500400300200100

6.00e-01

5.75e-01

5.50e-01

5.25e-01

5.00e-01

4.75e-01

4.50e-01

4.25e-01

4.00e-01

3.75e-01

3.50e-01

3.25e-01

Figure 3.10: Lift Coefficient Convergence History

Moment ConvergenceFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Iterations

Cm

800700600500400300200100

7.00e-02

6.00e-02

5.00e-02

4.00e-02

3.00e-02

2.00e-02

1.00e-02

0.00e+00

-1.00e-02

-2.00e-02

Figure 3.11: Moment Coefficient Convergence History

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Step 7: Postprocessing

1. Plot the y+ distribution on the airfoil.

Plot −→XY Plot...

(a) Under Y Axis Function, select Turbulence... and Wall Yplus.

(b) In the Surfaces list, select wall-bottom and wall-top.

(c) Deselect Node Values and click Plot.

Wall Yplus is available only for cell values.

The values of y+ are dependent on the resolution of the grid and the Reynoldsnumber of the flow, and are meaningful only in boundary layers. The value of y+

in the wall-adjacent cells dictates how wall shear stress is calculated. When youuse the Spalart-Allmaras model, you should check that y+ of the wall-adjacent cellsis either very small (on the order of y+ = 1), or approximately 30 or greater.Otherwise, you will need to modify your grid.

The equation for y+ is

y+ =y

µ

√ρτw

where y is the distance from the wall to the cell center, µ is the molecular viscosity,ρ is the density of the air, and τw is the wall shear stress.

Figure 3.12 indicates that, except for a few small regions (notably at the shock andthe trailing edge), y+ > 30 and for much of these regions it does not drop signifi-cantly below 30. Therefore, you can conclude that the grid resolution is acceptable.

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Wall YplusFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Position (m)

YplusWall

10.90.80.70.60.50.40.30.20.10

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

wall-topwall-bottom

Figure 3.12: XY Plot of y+ Distribution

2. Display filled contours of Mach number (Figure 3.13).

Display −→Contours...

(a) Select Velocity... and Mach Number under Contours Of.

(b) Turn off the Draw Grid option.

(c) Click Display.

Note the discontinuity, in this case a shock, on the upper surface at aboutx/c ≈ 0.45.

3. Plot the pressure distribution on the airfoil (Figure 3.14).

Plot −→XY Plot...

(a) Under Y Axis Function, choose Pressure... and Pressure Coefficient from thedrop-down lists.

(b) Click Plot.

Notice the effect of the shock wave on the upper surface.

4. Plot the x component of wall shear stress on the airfoil surface (Figure 3.15).

Plot −→XY Plot...

(a) Under Y Axis Function, choose Wall Fluxes... and X-Wall Shear Stress from thedrop-down lists.

(b) Click Plot.

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Contours of Mach NumberFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

1.44e+001.37e+001.30e+001.22e+001.15e+001.08e+001.01e+009.39e-018.68e-017.96e-017.25e-016.53e-015.82e-015.10e-014.39e-013.67e-012.96e-012.25e-011.53e-018.17e-021.02e-02

Figure 3.13: Contour Plot of Mach Number

Pressure CoefficientFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Position (m)

CoefficientPressure

10.90.80.70.60.50.40.30.20.10

1.25e+00

1.00e+00

7.50e-01

5.00e-01

2.50e-01

0.00e+00

-2.50e-01

-5.00e-01

-7.50e-01

-1.00e+00

-1.25e+00

wall-topwall-bottom

Figure 3.14: XY Plot of Pressure

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X-Wall Shear StressFLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

Position (m)

(pascal)StressShear

X-Wall

10.90.80.70.60.50.40.30.20.10

2.25e+02

2.00e+02

1.75e+02

1.50e+02

1.25e+02

1.00e+02

7.50e+01

5.00e+01

2.50e+01

0.00e+00

-2.50e+01

wall-topwall-bottom

Figure 3.15: XY Plot of x Wall Shear Stress

The large, adverse pressure gradient induced by the shock causes the boundary layerto separate. The point of separation is where the wall shear stress vanishes. Flowreversal is indicated here by negative values of the x component of the wall shearstress.

5. Display filled contours of the x component of velocity (Figure 3.16).

Display −→Contours...

(a) Select Velocity... and X Velocity under Contours Of.

(b) Click Display.

Note the flow reversal behind the shock.

6. Plot velocity vectors (Figure 3.17).

Display −→Vectors...

(a) Increase Scale to 15, and click Display.

Zooming in on the upper surface, behind the shock, will produce a displaysimilar to Figure 3.17. Flow reversal is clearly visible.

Summary: This tutorial demonstrated how to set up and solve an external aerody-namics problem using the Spalart-Allmaras turbulence model. It showed how tomonitor convergence using residual, force, and surface monitors, and demonstratedthe use of several postprocessing tools to examine the flow phenomena associatedwith a shock wave.

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Contours of X Velocity (m/s)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

4.46e+02

4.20e+02

3.94e+02

3.68e+02

3.42e+02

3.16e+02

2.90e+02

2.64e+02

2.38e+02

2.12e+02

1.86e+02

1.60e+02

1.34e+02

1.08e+02

8.17e+01

5.56e+01

2.96e+01

3.60e+00

-2.24e+01

-4.85e+01

-7.45e+01

Figure 3.16: Contour Plot of x Component of Velocity

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, coupled imp, S-A)

Nov 14, 2002

4.48e+02

4.25e+02

4.03e+02

3.81e+02

3.58e+02

3.36e+02

3.14e+02

2.91e+02

2.69e+02

2.47e+02

2.24e+02

2.02e+02

1.80e+02

1.57e+02

1.35e+02

1.13e+02

9.05e+01

6.82e+01

4.58e+01

2.35e+01

1.21e+00

Figure 3.17: Plot of Velocity Vectors Near Upper Wall, Behind Shock

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Tutorial 4. Modeling UnsteadyCompressible Flow

Introduction: In this tutorial, FLUENT’s coupled implicit solver is used to predict thetime-dependent flow through a two-dimensional nozzle. As an initial condition forthe transient problem, a steady-state solution is generated to provide the initialvalues for the mass flow rate at the nozzle exit.

In this tutorial you will learn how to:

• Calculate a steady-state solution (using the coupled implicit solver) as aninitial condition for a transient flow prediction

• Define an unsteady boundary condition using a user-defined function (UDF)

• Use dynamic mesh adaption for both steady-state and transient flows

• Calculate a transient solution using the second-order implicit unsteady formu-lation and the coupled implicit solver

• Create an animation of the unsteady flow using FLUENT’s unsteady solutionanimation feature

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: The geometry to be considered in this tutorial is shown in Fig-ure 4.1. Flow through a simple nozzle is simulated as a 2D planar model. Thenozzle has an inlet height of 0.2 m, and the nozzle contours have a sinusoidal shapethat produces a 10% reduction in flow area. Due to symmetry, only half of thenozzle is modeled.

Preparation

1. Copy the files nozzle/nozzle.msh and nozzle/pexit.c from the FLUENT docu-mentation CD to your working directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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p = 0.9 atminlet p = 0.7369 atm

exit

0.2 m

plane of symmetry

p (t )exit

Figure 4.1: Problem Specification

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Step 1: Grid

1. Read in the mesh file nozzle.msh.

File −→ Read −→Case...

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid.

Display −→Grid...

To make the view more realistic, you will need to mirror it across the centerline.

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4. Mirror the view across the centerline.

Display −→Views...

(a) Select symmetry under Mirror Planes.

(b) Click Apply.

The grid for the nozzle is shown in Figure 4.2.

GridFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Figure 4.2: 2D Nozzle Mesh Display

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Step 2: Units

1. For convenience, define new units for pressure.

The pressure for this problem is specified in atm, which is not the default unit. Youwill need to redefine the pressure unit as atm.

Define −→Units...

(a) Select pressure under Quantities, and atm under Units.

Hint: Use the scroll bar to access pressure, which is not initially visible in thelist.

(b) Close the panel.

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Step 3: Models

1. Select the coupled implicit solver.

The coupled implicit solver is the solver of choice for compressible, transonic flows.

Define −→ Models −→Solver...

Note: Initially, you will solve for the steady flow through the nozzle. Later, afterobtaining the steady flow as a starting point, you will revisit this panel toenable an unsteady calculation.

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2. Enable the Spalart-Allmaras turbulence model.

Define −→ Models −→Viscous...

The Spalart-Allmaras model is a relatively simple one-equation model that solvesa modeled transport equation for the kinematic eddy (turbulent) viscosity. Thisembodies a class of one-equation models in which it is not necessary to calculate alength scale related to the local shear layer thickness. The Spalart-Allmaras modelwas designed specifically for aerospace applications involving wall-bounded flows andhas been shown to give good results for boundary layers subjected to adverse pressuregradients.

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Step 4: Materials

1. Set the properties for air, the default fluid material.

Define −→Materials...

(a) Select the ideal-gas law to compute Density.

Note: FLUENT will automatically enable solution of the energy equation whenthe ideal gas law is used. You do not need to visit the Energy panel to turnit on.

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

! Don’t forget to click the Change/Create button to save your change.

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Step 5: Operating Conditions

1. Set the operating pressure to 0 atm.

Define −→Operating Conditions...

Here, the operating pressure is set to zero and boundary condition inputs for pressurewill be defined in terms of absolute pressures. Boundary condition inputs shouldalways be relative to the value used for operating pressure.

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Step 6: Boundary Conditions

Define −→Boundary Conditions...

1. Set the conditions for the nozzle inlet (inlet).

(a) Set the Gauge Total Pressure to 0.9 atm.

(b) Set the Supersonic/Initial Gauge Pressure to 0.7369 atm.

The inlet static pressure estimate is the mean pressure at the nozzle exit. Thisvalue will be used during the solution initialization phase to provide a guessfor the nozzle velocity.

(c) In the Turbulence Specification Method drop-down list, select Turbulent ViscosityRatio.

(d) Set the Turbulent Viscosity Ratio to 1.

For low to moderate inlet turbulence, a viscosity ratio of 1 is recommended.

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2. Set the conditions for the nozzle exit (outlet).

(a) Set the Gauge Pressure to 0.7369 atm.

(b) In the Turbulence Specification Method drop-down list, select Turbulent ViscosityRatio.

(c) Accept the default value of 10 for Backflow Turbulent Viscosity Ratio.

If substantial backflow occurs at the outlet, you may need to adjust the backflowvalues to levels close to the actual exit conditions.

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Step 7: Solution: Steady Flow

1. Initialize the solution.

Solve −→ Initialize −→Initialize...

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

(b) Click Init, and Close the panel.

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2. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Under Discretization, select Second Order Upwind for Modified Turbulent Vis-cosity.

Second-order discretization provides optimum accuracy.

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3. Perform gradient adaption to refine the mesh.

Adapt −→Gradient

(a) Under Method, select Gradient.

The mesh adaption criterion can either be the gradient or the curvature (secondgradient). Because strong shocks occur inside the nozzle, the gradient is usedas the adaption criterion.

(b) Under Gradients Of, make sure that Pressure... and Static Pressure are selected.

(c) Under Normalization, select Scale.

Mesh adaption can be controlled by the raw (or standard) value of the gradient,the scaled value (by its average in the domain), or the normalized value (by itsmaximum in the domain). For dynamic mesh adaption, it is recommended touse either the scaled or normalized value because the raw values will probablychange strongly during the computation, which would necessitate a readjust-ment of the coarsen and refine thresholds. In this case, the scaled gradient isused.

(d) Set the Coarsen Threshold to 0.3.

(e) Set Refine Threshold to 0.7.

As the refined regions of the mesh get larger, the coarsen and refine thresholdsshould get smaller. A coarsen threshold of 0.3 and a refine threshold of 0.7result in a “medium” to “strong” mesh refinement in combination with thescaled gradient.

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(f) Turn on the Dynamic option under Dynamic and set the Interval to 100.

For steady-state flows, it is sufficient to only seldomly adapt the mesh—inthis case an interval of 100 iterations is chosen. For time-dependent flows, aconsiderably smaller interval must be used.

(g) Click Compute and then click Mark to store the information.

(h) Click on Controls... to modify the adaption controls.

i. In the Grid Adaption Controls panel, turn on the Dynamic option underDynamic and set the Interval to 100.

For steady-state flows, it is sufficient to only seldomly adapt the mesh—in this case an interval of 100 iterations is chosen. For time-dependentflows, a considerably smaller interval must be used.

ii. Make sure that fluid is selected under Zones.

iii. Set the Max # of Cells to 20000.

To restrict the mesh adaption, the maximum number of cells can be lim-ited. If this limit is violated during the adaption, the corsen and refinethresholds are adjusted to respect the maximum number of cells. Addi-tional restrictions can be placed on the minimum cell volume, minimumnumber of cells, and maximum level of refinement.

iv. Click OK.

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4. Enable the plotting of residuals.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click OK.

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

Solve −→ Monitors −→Surface...

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

(b) Turn on the Plot and Write options for monitor-1.

Note: When the Write option is selected in the Surface Monitors panel, themass flow rate history will be written to a file. If you do not select thewrite option, the history information will be lost when you exit FLUENT.

(c) Click on Define... to specify the surface monitor parameters in the DefineSurface Monitor panel.

i. Select Mass Flow Rate in the Report Type drop-down list.

ii. Select outlet in the Surfaces list.

iii. In the File Name field, enter the name noz ss.out.

iv. Click on OK to define the monitor.

(d) Click on OK in the Surface Monitors panel to enable the monitor.

6. Save the case file (noz ss.cas).

File −→ Write −→Case...

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7. Start the calculation by requesting 2000 iterations.

Solve −→Iterate...

The solution will converge after about 1800 iterations. The mass flow rate historyis shown in Figure 4.3.

Convergence history of Mass Flow Rate on outletFLUENT 6.1 (2d, coupled imp, S-A)

Nov 27, 2002

Iteration

(kg/s)RateFlow

Mass

180016001400120010008006004002000

-14.0000

-14.5000

-15.0000

-15.5000

-16.0000

-16.5000

-17.0000

Figure 4.3: Mass Flow Rate History

8. Save the data file (noz ss.dat).

File −→ Write −→Data...

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9. Check the mass flux balance.

Report −→Fluxes...

! Although the mass flow rate history indicates that the solution is converged,you should also check the mass fluxes through the domain to ensure that massis being conserved.

(a) Keep the default Mass Flow Rate option.

(b) Select inlet and outlet in the Boundaries list.

(c) Click Compute.

! The net mass imbalance should be a small fraction (say, 0.5%) of the total fluxthrough the system. If a significant imbalance occurs, you should decrease yourresidual tolerances by at least an order of magnitude and continue iterating.

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10. Display the steady-flow velocity vectors (Figure 4.4).

Display −→Vectors...

(a) Change the Scale to 10.

(b) In the Surfaces list, select all of the surfaces.

(c) Click Display.

The steady flow prediction shows the expected form, with peak velocity of about 335m/s through the nozzle.

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Velocity Vectors Colored By Velocity Magnitude (m/s) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A)

3.35e+02

9.40e-011.77e+013.44e+015.11e+016.78e+018.46e+011.01e+021.18e+021.35e+021.51e+021.68e+021.85e+022.02e+022.18e+022.35e+022.52e+022.69e+022.85e+023.02e+023.19e+02

Figure 4.4: Velocity Vectors (Steady Flow)

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11. Display the steady flow contours of static pressure (Figure 4.5).

Display −→Contours...

(a) Under Options, select Filled.

(b) In the Surfaces list, select all of the surfaces.

(c) Click Display.

The steady flow prediction shows the expected pressure distribution, with low pres-sure near the nozzle throat.

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Contours of Static Pressure (atm) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A)

7.85e-01

4.26e-014.44e-014.62e-014.80e-014.98e-015.16e-015.34e-015.52e-015.70e-015.88e-016.06e-016.23e-016.41e-016.59e-016.77e-016.95e-017.13e-017.31e-017.49e-017.67e-01

Figure 4.5: Contours of Static Pressure (Steady Flow)

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Modeling Unsteady Compressible Flow

Step 8: Enable Time Dependence and Set UnsteadyConditions

In this step you will define a transient flow by specifying an unsteady pressure conditionfor the nozzle.

1. Enable a time-dependent flow calculation.

Define −→ Models −→Solver...

(a) Under Time, select Unsteady.

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

Implicit (dual) time-stepping allows you to set the physical time step used for thetransient flow prediction (while FLUENT continues to determine the time step usedfor inner iterations based on a Courant condition). Here, second-order implicittime-stepping is enabled: this provides higher accuracy in time than the first-orderoption.

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2. Define the unsteady condition for the nozzle exit (outlet).

The pressure at the outlet is defined as a wave-shaped profile, and is described bythe following equation:

pexit(t) = 0.12 sin(ωt) + pexit (4.1)

where

ω = circular frequency of unsteady pressure (rad/s)pexit = mean exit pressure (atm)

In this case, ω = 2200 rad/s, and pexit = 0.7369 atm.

A user-defined function (pexit.c) has been written to define the equation (Equa-tion 4.1) required for the pressure profile.

Note: To input the value of Equation 4.1 in the correct units, the function pexit.c

has been multiplied by a factor of 101325 to convert from the chosen pressureunit (atm) to the SI unit required by FLUENT (Pa). This will not affect thedisplayed results. See the separate UDF Manual for details about user-definedfunctions.

(a) Read in the user-defined function.

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

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

ii. Click Interpret.

The user-defined function has already been defined, but it needs to be com-piled within FLUENT before it can be used in the solver.

iii. Close the Interpreted UDFs panel.

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(b) Set the unsteady boundary conditions at the exit.

i. Select udf unsteady pressure (the user-defined function) in the Gauge Pres-sure drop-down list.

3. Update the gradient adaption parameters for the transient case.

Adapt −→Gradient

(a) Reset the Coarsen Threshold to 0.3.

(b) Reset the Refine Threshold to 0.7.

The refine and coarsen thresholds have been changed during the steady-statecomputation to meet the limit of 20000 cells. Therefore, you need to resetthese parameters to their original values.

(c) Under Dynamic, set the Interval to 1.

For the transient case, the mesh adaption will be done every time step.

(d) Click Compute and then Mark to store the values.

The console window will print statistics on the cells that are to be refined andcoarsened.

(e) Click on Controls... to modify the adaption controls.

i. In the Grid Adaption Controls panel, set the Min # of Cells to 8000.

ii. Set the Max # of Cells to 30000.

The maximum number of cells is increased to try to avoid readjustmentof the coarsen and refine thresholds. Additionally, the minimum numberof cells has been limited to 8000 because it is not desired to have a coarsemesh during the computation (the current mesh has about 10000 cells).

iii. Click OK.

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Modeling Unsteady Compressible Flow

Step 9: Solution: Unsteady Flow

1. Set the time step parameters.

The selection of the time step is critical for accurate time-dependent flow predic-tions. Using a time step of 2.85596× 10−5 seconds, 100 time steps are required forone pressure cycle. The pressure cycle begins and ends with the initial pressure atthe nozzle exit.

Solve −→Iterate...

(a) Set the Time Step Size to 2.85596e-5 s.

(b) Set the Number of Time Steps to 600.

(c) Set the Max Iterations per Time Step to 30.

(d) Click Apply.

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2. Modify the plotting of the mass flow rate at the nozzle exit.

Because each time step requires 30 iterations, a smoother plot will be generated byplotting at every time step.

Solve −→ Monitors −→Surface...

(a) For monitor-1, select Time Step in the drop-down list under Every.

(b) Click Define... to modify the surface monitor parameters.

i. In the Define Surface Monitor panel, change the File Name to noz uns.out.

ii. In the X Axis drop-down list, select Time Step.

iii. Click OK.

(c) Click OK in the Surface Monitors panel.

3. Save the transient solution case file (noz uns.cas).

File −→ Write −→Case...

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4. Start the transient calculation.

Solve −→Iterate...

! Calculation of 600 time steps will require significant CPU resources. Insteadof calculating, you can read the data file saved after the iterations have beencompleted:

noz uns.dat

(The data file is available in the same directory where you found the mesh andUDF files.)

By requesting 600 time steps, you are asking FLUENT to compute six pressurecycles. The mass flow rate history is shown in Figure 4.6.

Convergence history of Mass Flow Rate on outlet (in SI units) (Time=1.7136e-02)FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

Dec 09, 2002

Time Step

RateFlow

MassRateFlow

Mass

6005004003002001000

-4.00e+00

-6.00e+00

-8.00e+00

-1.00e+01

-1.20e+01

-1.40e+01

-1.60e+01

-1.80e+01

-2.00e+01

Figure 4.6: Mass Flow Rate History (Unsteady Flow)

5. Save the transient solution data file (noz uns.dat).

File −→ Write −→Data...

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Step 10: Saving and Postprocessing Time-DependentData Sets

The solution has reached a time-periodic state. To study how the flow changes within asingle pressure cycle, you will now continue the solution for 100 more time steps. Youwill use FLUENT’s solution animation feature to save contour plots of pressure and Machnumber at each time step, and the autosave feature to save case and data files every 10time steps. After the calculation is complete, you will use the solution animation playbackfeature to view the animated pressure and Mach number plots over time.

1. Request saving of case and data files every 10 time steps.

File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 10.

(b) In the Filename field, enter noz anim.

(c) Click OK.

When FLUENT saves a file, it will append the time step value to the filename prefix (noz anim). The standard extensions (.cas and .dat) will alsobe appended. This will yield file names of the form noz anim0640.cas andnoz anim0640.dat, where 0640 is the time step number.

Optionally, you can add the extension .gz to the end of the file name (e.g.,noz anim.gz), which will instruct FLUENT to save the case and data files incompressed format, yielding file names of the form noz anim0640.cas.gz.

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2. Create animation sequences for the nozzle pressure and Mach number contour plots.

Solve −→ Animate −→Define...

(a) Increase the number of Animation Sequences to 2.

(b) Under Name, enter pressure for the first sequence and mach-number for thesecond sequence.

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

With the default value of 1 for Every, this instructs FLUENT to update theanimation sequence at every time step.

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3. Define the animation sequence for pressure.

(a) Click Define... on the line for pressure to set the parameters for the pressuresequence.

The Animation Sequence panel will open.

(b) Under Storage Type, select In Memory.

The Memory option is acceptable for a small 2D case such as this. For larger2D or 3D cases, saving animation files with either the Metafile or PPM Imageoption is preferable to avoid using too much of your machine’s memory.

(c) Increase the Window number to 2 and click Set.

Graphics window number 2 will open.

(d) Under Display Type, select Contours.

The Contours panel will open.

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i. In the Contours panel, keep the default selections of Pressure... and StaticPressure.

ii. Make sure that Filled is selected under Options, and deselect Auto Range.

iii. Enter 0.25 under Min and 1.25 under Max.

This will set a fixed range for the contour plot and subsequent animation.

iv. In the Surfaces list, select all of the surfaces.

v. Click Display.

Figure 4.7 shows the contours of static pressure in the nozzle after 600 timesteps.

(e) Click OK in the Animation Sequence panel.

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Contours of Static Pressure (atm) (Time=1.7136e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

1.25e+00

2.50e-013.00e-013.50e-014.00e-014.50e-015.00e-015.50e-016.00e-016.50e-017.00e-017.50e-018.00e-018.50e-019.00e-019.50e-011.00e+001.05e+001.10e+001.15e+001.20e+00

Figure 4.7: Pressure Contours at t = 0.01714 s

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4. Define the animation sequence for Mach number.

(a) In the Solution Animation panel, click Define... on the line for mach-number toset the parameters for the Mach number sequence.

(b) Under Storage Type in the Animation Sequence panel, select In Memory.

(c) Increase the Window number to 3 and click Set.

Graphics window number 3 will open.

(d) Under Display Type, select Contours.

i. In the Contours panel, select Velocity... and Mach Number.

ii. Make sure that Filled is selected under Options, and deselect Auto Range.

iii. Enter 0.00 under Min and 1.30 under Max.

iv. In the Surfaces list, make sure that all of the surfaces are selected.

v. Click Display.

Figure 4.8 shows the Mach number contours in the nozzle after 600 time steps.

Contours of Mach Number (Time=1.7136e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

1.30e+00

0.00e+006.50e-021.30e-011.95e-012.60e-013.25e-013.90e-014.55e-015.20e-015.85e-016.50e-017.15e-017.80e-018.45e-019.10e-019.75e-011.04e+001.11e+001.17e+001.23e+00

Figure 4.8: Mach Number Contours at t = 0.01714 s

(e) Click OK in the Animation Sequence panel.

(f) Click OK in the Solution Animation panel.

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5. Continue the calculation by requesting 100 time steps.

Requesting 100 time steps will march the solution through an additional 0.0028seconds, or roughly one pressure cycle. With the autosave and animation featuresactive (as defined above), the case and data files will be saved approximately every0.00028 seconds; animation files will be saved every 0.000028 seconds.

Solve −→Iterate...

When the calculation finishes, you will have ten pairs of case and data files andthere will be 100 pairs of contour plots stored in memory. In the next few steps,you will play back the animation sequences and examine the results at several timesteps after reading in pairs of newly-saved case and data files.

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6. Change the display options to include double buffering.

Double buffering will allow for a smoother transition between the frames of theanimations.

Display −→Options...

(a) Under Rendering Options, select Double Buffering.

(b) Click Apply.

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7. Play back the animation of the pressure contours.

Solve −→ Animate −→Playback...

(a) Under Sequences, select pressure.

The playback control buttons now become active.

(b) Keep the default settings in the rest of the panel and click the play button(the second from the right in the group of buttons under Playback).

Examples of pressure contours at t = 0.01799 s (630th time step) and t = 0.0191 s(670th time step) are shown in Figures 4.9 and 4.10.

8. Repeat steps 6 and 7, selecting the appropriate active window and sequence namefor the Mach number contours.

Examples of Mach number contours at t = 0.01799 s and t = 0.0191 s are shownin Figures 4.11 and 4.12.

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Contours of Static Pressure (atm) (Time=1.7993e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

1.25e+00

2.50e-013.00e-013.50e-014.00e-014.50e-015.00e-015.50e-016.00e-016.50e-017.00e-017.50e-018.00e-018.50e-019.00e-019.50e-011.00e+001.05e+001.10e+001.15e+001.20e+00

Figure 4.9: Pressure Contours at t = 0.01799 s

Contours of Static Pressure (atm) (Time=1.9135e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

1.25e+00

2.50e-013.00e-013.50e-014.00e-014.50e-015.00e-015.50e-016.00e-016.50e-017.00e-017.50e-018.00e-018.50e-019.00e-019.50e-011.00e+001.05e+001.10e+001.15e+001.20e+00

Figure 4.10: Pressure Contours at t = 0.0191 s

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Contours of Mach Number (Time=1.7993e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

1.30e+00

0.00e+006.50e-021.30e-011.95e-012.60e-013.25e-013.90e-014.55e-015.20e-015.85e-016.50e-017.15e-017.80e-018.45e-019.10e-019.75e-011.04e+001.11e+001.17e+001.23e+00

Figure 4.11: Mach Number Contours at t = 0.01799 s

Contours of Mach Number (Time=1.9135e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

1.30e+00

0.00e+006.50e-021.30e-011.95e-012.60e-013.25e-013.90e-014.55e-015.20e-015.85e-016.50e-017.15e-017.80e-018.45e-019.10e-019.75e-011.04e+001.11e+001.17e+001.23e+00

Figure 4.12: Mach Number Contours at t = 0.0191 s

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Extra: FLUENT gives you the option of exporting an animation as an MPEG fileor as a series of files in any of the hardcopy formats available in the GraphicsHardcopy panel (including TIFF and PostScript).

To save an MPEG file, select MPEG from the Write/Record Format drop-downlist in the Playback panel and then click the Write button. The MPEG file willbe saved in your working directory. You can view the MPEG movie using anMPEG player (e.g., Windows Media Player or another MPEG movie player).

To save a series of TIFF, PostScript, or other hardcopy files, select HardcopyFrames in the Write/Record Format drop-down list in the Playback panel. Clickon the Hardcopy Options... button to open the Graphics Hardcopy panel and setthe appropriate parameters for saving the hardcopy files. Click Apply in theGraphics Hardcopy panel to save your modified settings. In the Playback panel,click the Write button. FLUENT will replay the animation, saving each frameto a separate file in your working directory.

If you want to view the solution animation in a later FLUENT session, youcan select Animation Frames as the Write/Record Format and click Write.

! Since the solution animation was stored in memory, it will be lost if you exitFLUENT without saving it to one of the formats described above. Note thatonly the animation-frame format can be read back into the Playback panel fordisplay in a later FLUENT session.

9. Display velocity vectors after 60 time steps (Figure 4.13).

(a) Read case and data files for the 660th time step (noz anim0660.cas andnoz anim0660.dat) into FLUENT.

File −→ Read −→Case & Data...

(b) Plot vectors at t = 0.01885 s.

Display −→Vectors...

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i. Change the Scale to 10.

ii. Click Display.

The unsteady flow prediction shows the expected form, with peak velocity ofabout 241 m/s through the nozzle at t = 0.01885 seconds.

10. Repeat step 9 using case and data files saved for other time steps of interest.

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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=1.8849e-02) Dec 17, 2002FLUENT 6.1 (2d, coupled imp, S-A, unsteady)

2.41e+02

3.92e+001.58e+012.76e+013.95e+015.13e+016.32e+017.50e+018.69e+019.87e+011.11e+021.22e+021.34e+021.46e+021.58e+021.70e+021.82e+021.93e+022.05e+022.17e+022.29e+02

Figure 4.13: Velocity Vectors at t = 0.01885 s

Summary: In this tutorial, you modeled the transient flow of air through a nozzle.You learned how to generate a steady-state solution as an initial condition for theunsteady case, and how to set solution parameters for implicit time-stepping.

You also learned how to manage the file saving and graphical postprocessing fortime-dependent flows, using file autosaving to automatically save solution informa-tion as the transient calculation proceeds.

Finally, you learned how to use FLUENT’s solution animation tool to create an-imations of transient data, and how to view the animations using the playbackfeature.

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Tutorial 5. Modeling Radiation and NaturalConvection

Introduction: In this tutorial, combined radiation and natural convection are solved ina two-dimensional square box on a mesh consisting of quadrilateral elements.

In this tutorial you will learn how to:

• Use the radiation models in FLUENT (Rosseland, P-1, DTRM, discrete or-dinates (DO), and surface-to-surface (S2S)) and understand their ranges ofapplication

• Use the Boussinesq model for density

• Set the boundary conditions for a heat transfer problem involving naturalconvection and radiation

• Separate a single wall zone into multiple wall zones

• Change the properties of an existing fluid material

• Calculate a solution using the segregated solver

• Display velocity vectors and contours of stream function and temperature forflow visualization

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT, and that you have solved Tutorial 1. Some steps in the setup and solutionprocedure will not be shown explicitly.

Problem Description: The problem to be considered is shown schematically in Fig-ure 5.1. A square box of side L has a hot right wall at T = 2000 K, a cold left wallat T = 1000 K, and adiabatic top and bottom walls. Gravity points downwards. Abuoyant flow develops because of thermally-induced density gradients. The mediumcontained in the box is assumed to be absorbing and emitting, so that the radiantexchange between the walls is attenuated by absorption and augmented by emis-sion in the medium. All walls are black. The objective is to compute the flow andtemperature patterns in the box, as well as the wall heat flux, using the radiationmodels available in FLUENT, and to compare their performance for different valuesof the optical thickness aL.

The working fluid has a Prandtl number of approximately 0.71, and the Rayleighnumber based on L is 5 × 105. This means the flow is inherently laminar. The

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Boussinesq assumption is used to model buoyancy. The Planck number k/(4σLT 30 )

is 0.02, and measures the relative importance of conduction to radiation; hereT0 = (Th + Tc)/2. Three values for the optical thickness are considered: aL = 0,aL = 0.2, and aL = 5.

Note that the values of physical properties and operating conditions (e.g., gravita-tional acceleration) have been adjusted to yield the desired Prandtl, Rayleigh, andPlanck numbers.

ρ = 1000 kg/m3

k = 15.309 W/mK

µ = 10-3

β = 10-5

g = -6.96 x 10-5 2

c = 1.1030x10p4

a = 0, 0.2, 5 1/mL = 1 m

5Ra = 5 x 10

Pl = 0.02Pr = 0.71

τ = 0.2, 5

Adiabatic

L

x

y

g

T=

2000K

h

T=

1000

Kc

J/kgK

kg/ms1/K

m/s

Figure 5.1: Schematic of the Problem

Preparation

1. Copy the file rad/rad.msh from the FLUENT documentation CD to your workingdirectory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read the mesh file rad.msh.

File −→ Read −→Case...

As the mesh is read in, messages will appear in the console window reporting theprogress of the reading. The mesh size will be reported as 2500 cells.

2. Check the grid.

Grid −→Check

FLUENT performs various checks on the mesh and reports the progress in the consolewindow. Pay particular attention to the minimum volume. Make sure this is apositive number.

3. Display the grid (Figure 5.2).

Display −→ Grid...

Note: All the walls are currently contained in a single wall zone, wall-4. You willneed to separate them out into four different walls so that you can specifydifferent boundary conditions for each wall.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Figure 5.2: Graphics Display of Grid

4. Separate the single wall zone into four wall zones.

Grid −→ Separate −→Faces...

(a) Select the Angle separation method (the default) under Options.

(b) Select wall-4 in the Zones list.

(c) Specify 89 as the significant Angle.

(d) Click on the Separate button.

Faces with normal vectors that differ by more than 89 will be placed in separatezones. Since the four wall zones are perpendicular (angle = 90), wall-4 will beseparated into four zones.

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5. Display the grid again.

(a) Select all Surfaces and click on Display.

Notice that you now have four different wall zones instead of only one.

Extra: You can use the right mouse button to check which wall zone numbercorresponds to each wall 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 FLUENT console window. This feature isespecially useful when you have several zones of the same type and youwant to distinguish between them quickly. In some cases, you may wantto disable the display of the interior grid so as to more accurately selectthe boundaries for identification.

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Step 2: Models

As discussed earlier, in this tutorial you will enable each radiation model in turn, obtaina solution, and postprocess the results. You will start with the Rosseland model, then usethe P-1 model, the discrete transfer radiation model (DTRM), and the discrete ordinates(DO) model. At the end of the tutorial, you will use the surface-to-surface (S2S) model.

1. Keep the default solver settings.

Define −→ Models −→Solver...

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2. Turn on the Rosseland radiation model.

Define −→ Models −→Radiation...

When you click OK in the Radiation Model panel, FLUENT will present an Infor-mation dialog box telling you that new material properties have been added for theradiation model. You will be setting properties later, so you can simply click OK inthe dialog box to acknowledge this information.

Note: FLUENT will automatically enable the energy calculation when you enablea radiation model, so you need not visit the Energy panel.

3. Add the effect of gravity on the model.

Define −→Operating Conditions...

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(a) Turn on Gravity.

The panel will expand to show additional inputs.

(b) Set the Gravitational Acceleration in the Y direction to -6.94e-5 m/s2.

As mentioned earlier, the gravitational acceleration has been adjusted to yieldthe correct dimensionless quantities (Prandtl, Rayleigh, and Planck numbers).See Figure 5.1 and the associated comments.

(c) Set the Operating Temperature to 1000 K.

The operating temperature will be used by the Boussinesq model, which youwill enable in the next step.

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Step 3: Materials

The default fluid material is air, which is the working fluid in this problem. However,since you are working with a fictitious fluid whose properties have been adjusted to givethe desired values of the dimensionless parameters, you must change the default propertiesfor air. You will use an optical thickness aL of 0.2 for this calculation. (Since L = 1, theabsorption coefficient a will be set to 0.2.) Later in the tutorial, results for an opticallythick medium with aL = 5 and non-participating medium with aL = 0 are computed toshow how the different radiation models behave for different optical thicknesses.

Define −→Materials...

1. Select boussinesq in the drop-down list next to Density, and then set the Density to1000 kg/m3.

For details about the Boussinesq model, see the User’s Guide.

2. Set the specific heat, Cp, to 1.103e4 J/kg-K.

3. Set the Thermal Conductivity to 15.309 W/m-K.

4. Set the Viscosity to 0.001 kg/m-s.

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5. Set the Absorption Coefficient to 0.2 m−1.

Hint: Use the scroll bar to access the properties that are not initially visible in thepanel.

6. Keep the default settings for the Scattering Coefficient and the Scattering PhaseFunction, since there is no scattering in this problem.

7. Set the Thermal Expansion Coefficient (used by the Boussinesq model) to 1e-5 K−1.

8. Click on Change/Create and close the Materials panel.

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Step 4: Boundary Conditions

Define −→Boundary Conditions...

1. Set the boundary conditions for the bottom wall (wall-4.006).

Note: The bottom wall should be called wall-4.006, but to be sure that you have thecorrect wall, use your right mouse button to click on the bottom wall in thegraphics window. When you do this, the corresponding zone will be selectedautomatically in the Zone list in the Boundary Conditions panel. You can dothis when you set boundary conditions for the other walls as well, to be surethat you are defining the correct conditions.

(a) Change the Zone Name to bottom.

(b) Retain the default thermal conditions (heat flux of 0) to specify an adiabaticwall.

Note: The Rosseland model does not require you to set a wall emissivity. Later inthe tutorial, you will need to define the wall emissivity for the other radiationmodels.

2. Set the boundary conditions for the left wall, wall-4.

(a) Change the Zone Name to left.

(b) Select Temperature under Thermal Conditions and set the Temperature to1000 K.

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3. Set the boundary conditions for the right wall, wall-4:007.

(a) Change the Zone Name to right.

(b) Select Temperature under Thermal Conditions and set the Temperature to2000 K.

4. Set the boundary conditions for the top wall, wall-4:005.

(a) Change the Zone Name to top.

(b) Retain the default thermal conditions (heat flux of 0) to specify an adiabaticwall.

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Step 5: Solution for the Rosseland Model

1. Set the parameters that control the solution.

Solve −→ Controls −→Solution...

(a) Retain the default selected Equations (all of them) and Under-Relaxation Fac-tors.

(b) Under Discretization, select PRESTO! for Pressure, and Second Order Upwindfor Momentum and Energy.

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2. Initialize the flow field.

Solve −→ Initialize −→Initialize...

(a) Set the Temperature to 1500 K and click on Init.

3. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

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(a) Under Options, select Plot.

(b) Click OK.

Note: There is no extra residual for the radiation heat transfer because the Rosse-land model does not solve extra transport equations for radiation; instead, itaugments the thermal conductivity in the energy equation. When you use theP-1 and DO radiation models, which both solve additional transport equations,you will see additional residuals for radiation.

4. Save the case file (rad ross.cas).

File −→ Write −→Case...

5. Start the calculation by requesting 200 iterations.

Solve −→Iterate...

The solution will converge in about 180 iterations.

6. Save the data file (rad ross.dat).

File −→ Write −→Data...

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Step 6: Postprocessing for the Rosseland Model

1. Display velocity vectors (Figure 5.3).

Display −→Vectors...

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.11e-042.00e-041.90e-041.79e-041.69e-041.58e-041.48e-041.37e-041.27e-041.16e-041.05e-049.49e-058.44e-057.38e-056.33e-055.27e-054.22e-053.16e-052.11e-051.05e-052.61e-09

Figure 5.3: Velocity Vectors for the Rosseland Model

2. Display contours of stream function (Figure 5.4).

Display −→Contours...

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The recirculatory patterns observed are due to the natural convection in the box.At a low optical thickness (0.2), radiation should not have a large influence on theflow. The flow pattern is expected to be similar to that obtained with no radiation(Figure 5.5). However, the Rosseland model predicts a flow pattern that is verysymmetric (Figure 5.4), and quite different from the pure natural convection case.This discrepancy occurs because the Rosseland model is not appropriate for smalloptical thickness.

Contours of Stream Function (kg/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

6.96e-026.62e-026.27e-025.92e-025.57e-025.22e-024.88e-024.53e-024.18e-023.83e-023.48e-023.13e-022.79e-022.44e-022.09e-021.74e-021.39e-021.04e-026.96e-033.48e-030.00e+00

Figure 5.4: Contours of Stream Function for the Rosseland Model

Extra: If you want to compute the results without radiation yourself, turn off allthe radiation models in the Radiation Model panel, set the under-relaxationfactor for energy to 0.8, and calculate until convergence. (Remember to resetthe under-relaxation factor to 1 before continuing with the tutorial).

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Contours of Stream Function (kg/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

1.97e-021.87e-021.77e-021.67e-021.58e-021.48e-021.38e-021.28e-021.18e-021.08e-029.84e-038.86e-037.88e-036.89e-035.91e-034.92e-033.94e-032.95e-031.97e-039.84e-040.00e+00

Figure 5.5: Contours of Stream Function with No Radiation

3. Display filled contours of temperature (Figure 5.6).

Display −→Contours...

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Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.00e+031.95e+031.90e+031.85e+031.80e+031.75e+031.70e+031.65e+031.60e+031.55e+031.50e+031.45e+031.40e+031.35e+031.30e+031.25e+031.20e+031.15e+031.10e+031.05e+031.00e+03

Figure 5.6: Contours of Temperature for the Rosseland Model

The Rosseland model predicts a temperature field (Figure 5.6) very different fromthat obtained without radiation (Figure 5.7). For the low optical thickness in thisproblem, the temperature field predicted by the Rosseland model is not physical.

4. Plot the y velocity along the horizontal centerline of the box.

(a) Create an isosurface at y = 0.5, the horizontal line through the center of thebox.

Surface −→Iso-Surface...

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Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.00e+031.95e+031.90e+031.85e+031.80e+031.75e+031.70e+031.65e+031.60e+031.55e+031.50e+031.45e+031.40e+031.35e+031.30e+031.25e+031.20e+031.15e+031.10e+031.05e+031.00e+03

Figure 5.7: Contours of Temperature with No Radiation

i. Select Grid... in the Surface of Constant drop-down list and select Y-Coordinate from the list below.

ii. Click on Compute to see the extents of the domain.

iii. Set a value of 0.5 in the Iso-Values field, and change the New SurfaceName to y=0.5.

iv. Click on Create to create a surface at y = 0.5.

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(b) Create an XY plot of y velocity on the isosurface.

Plot −→XY Plot...

i. Make sure that Node Values is turned on under Options.

By default, the Node Values option is turned on, and the values that havebeen interpolated to the nodes are displayed. If you prefer to display the cellvalues, turn the Node Values option off. Note that you will need to ensurethat the selected option for Node Values is used throughout the tutorial fordisplaying and saving XY plots. This will enable you to correctly comparethe XY plots for different radiation models in a later step, as they will useidentical options.

ii. Check that the Plot Direction for X is 1, and the Plot Direction for Y is 0.

With a Plot Direction vector of (1,0), FLUENT will plot the selected vari-able as a function of x. Since you are plotting the velocity profile on across-section of constant y, the x direction is the one in which the velocityvaries.

iii. Select Velocity... and Y Velocity under Y Axis Function.

iv. Select y=0.5 in the Surfaces list.

v. Click on Plot.

The velocity profile reflects the rising plume at the hot right wall, and thefalling plume at the cold left wall. Compared to the case with no radiation,

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Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

6.78e-21

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.8: XY Plot of Centerline y Velocity for the Rosseland Model

the profile predicted by the Rosseland model exhibits thicker wall layers.As discussed before, the expected profile for aL = 0.2 is similar to the casewith no radiation.

(c) Save the plot data to a file.

i. Select the Write to File option, and click the Write... push button.

ii. In the resulting Select File dialog box, specify rad ross.xy in the XY Filetext entry box and click OK.

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5. Compute the total wall heat flux on each lateral wall.

Report −→Fluxes...

(a) Select Total Heat Transfer Rate under Options.

(b) Select right and left under Boundaries.

(c) Click the Compute button.

The total wall heat transfer rate is reported for the hot and cold walls as ap-proximately 7.43× 105 W. The sum of the heat fluxes on the lateral walls is anegligible imbalance.

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

File −→ Write −→Case & Data...

Thus far in this tutorial, you have learned how to set up a natural convection problemusing the Rosseland model to compute radiation. You have also learned to postprocess theresults. You will now turn on the P-1 model and compare the results so computed withthose of the Rosseland model.

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Step 7: P-1 Model Definition, Solution, and Postpro-cessing

You will now repeat the above calculation using the P-1 radiation model. The main stepsare identical to the procedure described above for the Rosseland model.

1. Enable the P-1 model.

Define −→ Models −→Radiation...

2. Confirm that the wall emissivity is 1 for all walls.

Define −→Boundary Conditions...

For each wall boundary, there will be a new entry, Internal Emissivity, in the Thermalsection of the Wall panel. Retain the default value of 1.

3. Modify the under-relaxation parameters.

Solve −→ Controls −→Solution...

(a) Under Under-Relaxation Factors, set the factor for P1 to 1.0, and retain thedefault factors for Pressure, Momentum, and Energy (0.3, 0.7, and 1.0).

Note that an additional equation, P1, appears because the P-1 model solvesan additional radiation transport equation. This problem is relatively easyto converge for the P-1 model since there is not much coupling between theradiation and temperature equations at low optical thicknesses. Consequentlya high under-relaxation factor can be used for P-1.

4. Save the case file (rad p1.cas).

File −→ Write −→Case...

5. Continue the calculation by requesting another 200 iterations.

Solve −→Iterate...

The P-1 model reaches convergence after about 115 additional iterations.

6. Save the data file (rad p1.dat).

File −→ Write −→Data...

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7. Examine the results of the P-1 model calculation.

Note: The steps below do not include detailed instructions because the procedureis the same one that you followed for the Rosseland model postprocessing.See Step 6: Postprocessing for the Rosseland Model if you need moredetailed instructions.

(a) Display velocity vectors (Figure 5.9).

Display −→Vectors...

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.87e-042.72e-042.58e-042.44e-042.29e-042.15e-042.01e-041.86e-041.72e-041.58e-041.43e-041.29e-041.15e-041.00e-048.61e-057.18e-055.75e-054.32e-052.89e-051.46e-052.63e-07

Figure 5.9: Velocity Vectors for the P-1 Model

(b) Plot the y velocity along the horizontal centerline (Figure 5.10), and save theplot data to a file called rad p1.xy.

Plot −→XY Plot...

! You will need to reselect Y Velocity under Y Axis Function. Also, remem-ber to turn off the Write to File option so that you can access the Plotbutton to generate the plot.

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

The total heat transfer rate reported on the right wall is 8.47 × 105 W. Theheat imbalance at the lateral walls is negligibly small. You will see later thatthe Rosseland and P-1 wall heat transfer rates are substantially different fromthose obtained by the DTRM and the DO model.

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Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

-1.36e-20

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

-3.00e-04

y=0.5

Figure 5.10: XY Plot of Centerline y Velocity for the P-1 Model

Notice how different the velocity vectors and y-velocity profile are from those obtainedusing the Rosseland model. The P-1 velocity profiles show a clear momentum boundarylayer along the hot and cold walls. These profiles are much closer to those obtained fromthe non-radiating case (Figures 5.11 and 5.12). Though the P-1 model is not appropriatefor this optically thin limit, it yields the correct velocity profiles since the radiation sourcein the energy equation, which is proportional to the absorption coefficient, is small. TheRosseland model uses an effective conductivity to account for radiation, and yields thewrong temperature field, which in turn results in an erroneous velocity field.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.16e-042.05e-041.94e-041.83e-041.73e-041.62e-041.51e-041.40e-041.29e-041.19e-041.08e-049.71e-058.63e-057.55e-056.47e-055.39e-054.31e-053.24e-052.16e-051.08e-059.22e-09

Figure 5.11: Velocity Vectors with No Radiation

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

6.78e-21

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.12: XY Plot of Centerline y Velocity with No Radiation

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Step 8: DTRM Definition, Solution, and Postprocess-ing

1. Turn on the discrete transfer radiation model (DTRM) and define the ray tracing.

Define −→ Models −→Radiation...

(a) Select Discrete Transfer under Model.

The panel will expand to show additional inputs.

(b) Accept the defaults by clicking OK.

The Ray Tracing panel will open automatically.

(c) Accept the default settings for Clustering and Angular Discretization by clickingOK.

When you click OK, FLUENT will open a Select File dialog box so you canspecify a name for the ray file used by the DTRM. A detailed description of theray tracing procedure can be found in the User’s Guide. In brief, the number ofCells Per Volume Cluster and Faces Per Surface Cluster control the total numberof radiating surfaces and absorbing cells. For a small 2D problem, the default

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number of 1 is acceptable. For a large problem, however, you will want toincrease these numbers to reduce the ray tracing expense. The Theta Divisionsand Phi Divisions control the number of rays being created from each surfacecluster. For most practical problems, the default settings will suffice.

(d) In the Ray File text entry box in the Select File dialog box, enter rad dtrm.ray

for the name of the ray file. Then click OK.

FLUENT will print an informational message describing the progress of the raytracing procedure.

2. Retain the current under-relaxation factors for pressure, momentum, and energy(0.3, 0.7, and 1.0).

Solve −→ Controls −→Solution...

3. Save the case file (rad dtrm.cas).

File −→ Write −→Case...

4. Continue the calculation by requesting another 100 iterations.

Solve −→Iterate...

The solution will converge after about 80 additional iterations.

5. Save the data file (rad dtrm.dat).

File −→ Write −→Data...

6. Examine the results of the DTRM calculation.

Note: The steps below do not include detailed instructions because the procedureis the same one that you followed for the Rosseland model postprocessing.See Step 6: Postprocessing for the Rosseland Model if you need moredetailed instructions.

(a) Display velocity vectors (Figure 5.13).

Display −→Vectors...

(b) Plot the y velocity along the horizontal centerline (Figure 5.14), and save theplot data to a file called rad dtrm.xy.

Plot −→XY Plot...

! You will need to reselect Y Velocity under Y Axis Function. Also, remem-ber to turn off the Write to File option so that you can access the Plotbutton to generate the plot.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.88e-042.73e-042.59e-042.45e-042.30e-042.16e-042.02e-041.87e-041.73e-041.58e-041.44e-041.30e-041.15e-041.01e-048.65e-057.21e-055.77e-054.33e-052.90e-051.46e-052.08e-07

Figure 5.13: Velocity Vectors for the DTRM

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

-1.36e-20

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

-3.00e-04

y=0.5

Figure 5.14: XY Plot of Centerline y Velocity for the DTRM

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(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

The total heat transfer rate reported on the right wall is 6.06 × 105 W. Notethat this is substantially lower than the values predicted by the Rosseland andP-1 models.

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Step 9: DO Model Definition, Solution, and Postpro-cessing

1. Turn on the discrete ordinates (DO) radiation model and define the angular dis-cretization.

Define −→ Models −→Radiation...

(a) Select Discrete Ordinates under Model.

The panel will expand to show additional inputs for the DO model.

(b) Set the number of Flow Iterations Per Radiation Iteration to 1.

This is a relatively simple flow problem, and will converge easily. Consequentlyit is useful to do the DO calculation every iteration of the flow solution. Forproblems that are difficult to converge, it is sometimes useful to allow the flowsolution to establish itself between radiation calculations. In such cases, it maybe useful to set Flow Iterations Per Radiation Iteration to a higher value, suchas 10.

(c) Retain the default settings for Angular Discretization and Non-Gray Model.

For details about the angular discretization used by the DO model, see theUser’s Guide. The Number of Bands for the Non-Gray Model is zero becauseonly gray radiation is being modeled in this tutorial.

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Note: When you click OK in the Radiation Model panel, FLUENT will presentan Information dialog box telling you that new material properties havebeen added for the radiation model. The property that is new for the DOmodel is the refractive index, which is relevant only when you are model-ing semi-transparent media. Since you are not modeling semi-transparentmedia here, you can simply click OK in the dialog box to acknowledge thisinformation.

2. Retain the current under-relaxation factors for pressure, momentum, and energy(0.3, 0.7, and 1.0), as well as the default under-relaxation of 1 for the discreteordinates transport equation.

Solve −→ Controls −→Solution...

3. Save the case file (rad do.cas).

File −→ Write −→Case...

4. Continue the calculation by requesting another 100 iterations.

Solve −→Iterate...

The solution will converge after about 25 additional iterations.

5. Save the data file (rad do.dat).

File −→ Write −→Data...

6. Examine the results of the DO calculation.

Note: The steps below do not include detailed instructions because the procedureis the same one that you followed for the Rosseland model postprocessing.See Step 6: Postprocessing for the Rosseland Model if you need moredetailed instructions.

(a) Display velocity vectors (Figure 5.15).

Display −→Vectors...

(b) Plot the y velocity along the horizontal centerline (Figure 5.16), and save theplot data to a file called rad do.xy.

Plot −→XY Plot...

! You will need to reselect Y Velocity under Y Axis Function. Also, remem-ber to turn off the Write to File option so that you can access the Plotbutton to generate the plot.

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.90e-042.75e-042.61e-042.46e-042.32e-042.17e-042.03e-041.88e-041.74e-041.59e-041.45e-041.30e-041.16e-041.02e-048.70e-057.26e-055.81e-054.36e-052.91e-051.47e-051.90e-07

Figure 5.15: Velocity Vectors for the DO Model

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

3.00e-04

2.00e-04

1.00e-04

-1.36e-20

-1.00e-04

-2.00e-04

-3.00e-04

y=0.5

Figure 5.16: XY Plot of Centerline y Velocity for the DO Model

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Modeling Radiation and Natural Convection

The total heat transfer rate reported on the right wall is 6.12 × 105 W. Notethat this is about 1.5% higher than that predicted by the DTRM. The DOand DTRM values are comparable to each other, while the Rosseland and P-1values are both substantially different. The DTRM and DO models are validacross the range of optical thickness, and the heat transfer rates computedusing them are expected to be closer to the correct heat transfer rate.

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Step 10: Comparison of y-Velocity Plots

In this step, you will read the plot files you saved for all the solutions and compare themin a single plot.

Plot −→File...

1. Read in all the XY plot files.

(a) Click on the Add... button.

(b) In the resulting Select File dialog box, select rad do.xy, rad dtrm.xy, rad p1.xy,and rad ross.xy in the Files list.

They will be added to the XY File(s) list. If you accidentally add an incorrectfile, you can select it in this list and click Remove.

(c) Click OK to load the 4 files.

2. Click on Plot.

Extra: You can click Curves... in the File XY Plot panel to open the Curves panel,where you can define different styles for different plot curves. In Figure 5.17,different symbols have been selected for each curve.

3. Resize and move the legend box so that you can read the information inside it.

(a) To resize the box, press any mouse button on a corner and drag the mouse tothe desired position.

(b) To move the legend box, press any mouse button anywhere else on the boxand drag it to the desired location.

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Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position

VelocityY

10.90.80.70.60.50.40.30.20.10

3.00e-04

2.00e-04

1.00e-04

-1.36e-20

-1.00e-04

-2.00e-04

-3.00e-04

Y Velocity (rad_ross.xy)Y Velocity (rad_p1.xy)Y Velocity (rad_dtrm.xy)Y Velocity

Y Velocity

Figure 5.17: Comparison of Computed y Velocities for aL = 0.2

Notice in Figure 5.17 that the velocity profiles for the P-1 model, DTRM, and DO modelare nearly identical even though the reported wall heat transfer rates are different. Thisis because in an optically thin problem, the velocity field is essentially independent of theradiation field, and all three models give a flow solution very close to the non-radiatingcase. The Rosseland model gives substantially erroneous solutions for an optically thincase.

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Step 11: Comparison of Radiation Models for an Op-tically Thick Medium

In the previous steps, you compared the results of four radiation models for an opticallythin (aL = 0.2) medium. It was found that, as a result of the low optical thickness,the velocity fields predicted by the P-1, DTRM, and DO models were very similar andclose to that obtained in the non-radiating case. The wall heat transfer rates for DOand DTRM were very close to each other, and substantially different from those obtainedwith the Rosseland and P-1 models. In this step, you will recalculate a solution (usingeach radiation model) for an optically thick (aL = 5) medium. This is accomplished byincreasing the value of the absorption coefficient from 0.2 to 5. You will repeat the processoutlined below for each set of case and data files that you saved earlier in the tutorial.

1. For each radiation model, calculate a new solution for aL = 5.

(a) Read in the case and data file saved earlier (e.g., rad ross.cas andrad ross.dat).

File −→ Read −→Case & Data...

(b) Set the absorption coefficient to 5.

This will result in an optical thickness aL of 5, since L = 1.

Define −→Materials...

(c) Calculate until the new solution converges.

Solve −→Iterate...

! For the DTRM calculation, you may need to click the Iterate buttonrepeatedly until the radiation field is updated. Since the number of FlowIterations Per Radiation Iteration in the Radiation Model panel is 10, itis possible that the radiation field will not be updated for as many as 9iterations, although FLUENT will report that the solution is converged. Ifthis happens, keep clicking the Iterate button until the radiation field isupdated and the solution proceeds for multiple iterations.

(d) Save the new case and data files using a different file name (e.g., rad ros5.cas

andrad ros5.dat).

File −→ Write −→Case & Data...

(e) Compute the total wall heat transfer rate.

Report −→Fluxes...

(f) Plot the y velocity along the horizontal centerline, and save the plot data toa file (e.g., rad ros5.xy).

Plot −→XY Plot...

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2. Compare the computed heat transfer rates for the four models.

The wall heat transfer rates predicted by the four radiation models range from 3.50×105 to 3.97× 105 W.

3. Compare the y-velocity profiles in a single plot (Figure 5.18).

Plot −→File...

Note: Use the Delete button in the File XY Plot panel to remove the old XY plotdata files.

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position

VelocityY

10.90.80.70.60.50.40.30.20.10

5.00e-04

4.00e-04

3.00e-04

2.00e-04

1.00e-04

1.36e-20

-1.00e-04

-2.00e-04

-3.00e-04

-4.00e-04

-5.00e-04

Y Velocity (rad_ros5.xy)Y Velocity (rad_p15.xy)Y Velocity (rad_dtr5.xy)Y Velocity

Y Velocity

Figure 5.18: Comparison of Computed y Velocities for aL = 5

The XY plots of y velocity are nearly identical for the P-1 model, DO model, andDTRM. The Rosseland model gives somewhat different velocities, but is still within10% of the other results. The Rosseland and P-1 models are suitable for the opti-cally thick limit; the DTRM and DO models are valid across the range of opticalthicknesses. Consequently, they yield similar answers at aL = 5. For many ap-plications with large optical thicknesses, the Rosseland and P-1 models provide asimple low-cost alternative.

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Step 12: S2S Model Definition, Solution and Postpro-cessing for a Non-Participating Medium

In the previous steps, you compared the results of four radiation models for optically thin(aL = 0.2) and optically thick (aL = 5) media.

The surface-to-surface (S2S) radiation model can be used to account for the radiation ex-change in an enclosure of gray-diffuse surfaces. The energy exchange between two surfacesdepends in part on their size, separation distance, and orientation. These parameters areaccounted for by a geometric function called a “view factor”.

The S2S model assumes that all surfaces are gray and diffuse. Thus, according to thegray-body model, if a certain amount of radiation is incident on a surface, a fraction isreflected, a fraction is absorbed, and a fraction is transmitted. The main assumption ofthe S2S model is that any absorption, emission, or scattering of radiation can be ignored;therefore, only “surface-to-surface” radiation need be considered for analysis.

For most applications the surfaces in question are opaque to thermal radiation (in theinfrared spectrum), so the surfaces can be considered opaque. The transmissivity, there-fore, can be neglected. Effectively, for the S2S model the absorption coefficient can beconsidered to be zero.

When the S2S model is used, you also have the option to define a “partial enclosure”;i.e., you can disable view factor calculations for walls that are not participating in theradiative heat transfer calculation. In this step, you will calculate a solution for aL = 0using the S2S radiation model without partial enclosure. In the next step, you will usethe DTRM and DO models for aL = 0, and compare the results of the three models. TheRosseland and P-1 models are not considered here as they have been shown (earlier inthe tutorial) to be inappropriate for optically thin media. Later in the tutorial, you willcalculate a solution for S2S model with partial enclosure and compare the results with thesolution for S2S model for a non-participating medium calculated here.

1. Turn on the surface-to-surface (S2S) radiation model and define the view factorand cluster parameters.

Define −→ Models −→Radiation...

(a) Select Surface to Surface under Model.

The panel will expand to show additional inputs for the S2S model.

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(b) Set the view factor and cluster parameters.

i. Click Set... under Parameters.

The View Factor and Cluster Parameters panel will open automatically.

ii. Click OK to accept the default settings.

The S2S radiation model is computationally very expensive when there area large number of radiating surfaces. The number of radiating surfaces is

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Modeling Radiation and Natural Convection

reduced by clustering surfaces into surface “clusters”. The surface clustersare made by starting from a face and adding its neighbors and their neigh-bors until a specified number of faces per surface cluster is collected. Fora small 2D problem, the default value of 1 for Faces Per Surface Cluster isacceptable. For a large problem, you can increase this number to reducethe memory requirement for the view factor file that is saved in a laterstep. This may also lead to some reduction in the computational expense.However, this is at the cost of some accuracy.

Using the Blocking option ensures that any additional surface that is block-ing the view between two opposite surfaces is considered in the view factorcalculation. In this case, there is no obstructing surface between the oppo-site walls, so selecting either the Blocking or the Nonblocking option willproduce the same result. The default setting for Smoothing is None, whichis appropriate for small problems. The Least Square option is more accu-rate, but also more computationally expensive. See the User’s Guide fordetails about view factors and clusters for the S2S model.

(c) Compute the view factors for the S2S model.

This step is required only if the problem is being solved for the first time. Forsubsequent calculations, you can read the view factor and cluster informationfrom an existing file (by clicking Read... instead of Compute/Write...).

i. Click Compute/Write... under Methods in the Radiation Model panel.

FLUENT will open a Select File dialog box so you can specify a name forthe file where the cluster and view factor parameters are stored.

ii. In the S2S File text entry box in the Select File dialog box, enter rad s2s.s2s

for the name of the S2S file. Then click OK.

FLUENT will print an informational message describing the progress ofthe view factor calculation.

2. Retain the current under-relaxation factors for pressure, momentum, and energy(0.3, 0.7, and 1.0).

Solve −→ Controls −→Solution...

3. Save the case file (rad s2s.cas).

File −→ Write −→Case...

4. Continue the calculation by requesting another 100 iterations.

Solve −→Iterate...

The solution will converge after about 80 additional iterations.

5. Save the data file (rad s2s.dat).

File −→ Write −→Data...

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6. Examine the results of the S2S calculation.

Note: The steps below do not include detailed instructions because the procedureis the same one that you followed for the Rosseland model postprocessing.See Step 6: Postprocessing for the Rosseland Model if you need moredetailed instructions.

(a) Display velocity vectors (Figure 5.19).

Display −→Vectors...

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.47e-042.35e-042.22e-042.10e-041.98e-041.85e-041.73e-041.61e-041.48e-041.36e-041.24e-041.11e-049.90e-058.66e-057.43e-056.19e-054.96e-053.72e-052.49e-051.25e-051.92e-07

Figure 5.19: Velocity Vectors for the S2S Model

(b) Plot the y velocity along the horizontal centerline (Figure 5.20), and save theplot data to a file called rad s2s.xy.

Plot −→XY Plot...

! You will have to reselect Y Velocity under Y Axis Function. Also, remem-ber to turn off the Write to File option to access the Plot button to generatethe plot.

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

The total heat transfer rate on the right wall is 6.77× 105 W.

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Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

6.78e-21

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.20: XY Plot of Centerline y Velocity for the S2S Model

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Step 13: Comparison of Radiation Models for a Non-Participating Medium

In this step, you will calculate a solution for the aL = 0 case, using the DTRM and DOmodels, and then compare the results with the S2S results.

1. For the DTRM and DO models, calculate a new solution for aL = 0.

(a) Read in the case and data files saved earlier (e.g., rad dtrm.cas andrad dtrm.dat).

File −→ Read −→Case & Data...

(b) Set the absorption coefficient to 0.

This will result in an optical thickness aL of 0.

Define −→Materials...

(c) Calculate until the new solution converges.

Solve −→Iterate...

! For the DTRM calculation, you may need to click the Iterate buttonrepeatedly until the radiation field is updated. Since the number of FlowIterations Per Radiation Iteration in the Radiation Model panel is 10, itis possible that the radiation field will not be updated for as many as 9iterations, although FLUENT will report that the solution is converged. Ifthis happens, keep clicking the Iterate button until the radiation field isupdated and the solution proceeds for multiple iterations.

(d) Save the new case and data files using a different file name (e.g., rad dtr0.cas

and rad dtr0.dat).

File −→ Write −→Case & Data...

(e) Compute the total wall heat transfer rate.

Report −→Fluxes...

(f) Plot the y velocity along the horizontal centerline, and save the plot data toa file (e.g., rad dtr0.xy)

Plot −→XY Plot...

2. Compare the computed heat transfer rates for the three models.

For the S2S model, the total heat transfer rate on the right wall was 6.77× 105 W.This is about 5% higher than that predicted by the DTRM and 1.5% higher than DO.Although the S2S, DO, and DTRM values are comparable to each other, this probleminvolves enclosure radiative transfer without participating media. Therefore, theS2S model provides the most accurate solution.

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3. Compare the y-velocity profiles in a single plot (Figure 5.21)

Plot −→File...

(a) Use the Delete button in the File XY Plot panel to remove the old XY plotdata files.

(b) Read in all the XY plot files you saved for the S2S, DTRM, and DO models.

(c) Click on Plot.

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position

VelocityY

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

6.78e-21

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

Y Velocity (rad_s2s.xy)

Y Velocity (rad_dtr0.xy)

Y Velocity

Y Velocity

Figure 5.21: Comparison of Computed y Velocities for aL = 0

In Figure 5.21, the velocity profiles for the DTRM, DO, and S2S models are almostidentical even though the wall heat transfer rates are different.

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Step 14: S2S Model Definition, Solution and Postpro-cessing with Partial Enclosure

As mentioned earlier, when the S2S model is used, you also have the option to define a“partial enclosure”; i.e., you can disable view factor calculations for walls that are notparticipating in the radiative heat transfer calculation. This feature allows you to savetime computing the view factors and also reduce the memory required to store the viewfactor file during the FLUENT calculation.

For this problem, you will specify the left wall boundary as the non-participating wall inS2S radiation. Consequently, you will need to specify the partial enclosure temperaturefor the wall boundary that is not participating in S2S radiation. Note that if multiple wallboundaries are not participating in S2S radiation and each has a different temperature,then the partial enclosure option may not yield accurate results, as the same partialenclosure temperature is specified for each of the non-participating walls.

1. Read in the case and data files for the S2S model (rad s2s.cas and rad s2s.dat).

2. In the Radiation Model panel, retain Surface to Surface (S2S) as the radiation model.

Define −→ Models −→Radiation...

3. Under Partial Enclosure, set the Temperature to 1000 k.

In previous radiation model setups for this problem, the left wall temperature wasspecified as 1000 k. Therefore, you will set the partial enclosure temperature to thistemperature.

4. Click OK to close the Radiation Model panel.

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5. Set the boundary conditions for the left wall.

Define −→Boundary Conditions

(a) Turn off the Participates in S2S Radiation option.

You will now revisit the Radiation Model panel to recompute the view factors.

6. Compute the view factors for the S2S model.

Define −→ Models −→Radiation...

The view factor file will store the view factors for the radiating surfaces only. Thismay help you to control the size of the view factor file as well as the memoryrequired to store view factors in FLUENT. Furthermore, the time required to computethe view factors will reduce as only the view factors for radiating surfaces will becalculated.

! You should compute the view factors only when you have specified the bound-aries that will participate in the radiation model using the Boundary Conditionspanel. If you first compute the view factors and then make a change to theboundary conditions, FLUENT will use the view factor file stored earlier forcalculating a solution, in which case, the changes that you made to the modelwill not be used for the calculation. Therefore, you should recompute the viewfactors and save the case file whenever you modify the number of objects thatwill participate in radiation.

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(a) Click Compute/Write... under Methods in the Radiation Model panel.

FLUENT will open a Select File dialog box so you can specify a name for thefile where the cluster and view factor parameters are stored.

(b) In the S2S File text entry box in the Select File dialog box, enter rad s2sp.s2s

for the name of the S2S file. Then click OK.

FLUENT will print an informational message describing the progress of theview factor calculation.

7. Retain the current under-relaxation factors for pressure, momentum, and energy(0.3, 0.7, and 1.0).

Solve −→ Controls −→Solution...

8. Save the case file (rad s2sp.cas).

File −→ Write −→Case...

9. Continue the calculation by requesting another 100 iterations.

Solve −→Iterate...

The solution will converge after about 80 additional iterations.

10. Save the data file (rad s2sp.dat).

File −→ Write −→Data...

11. Examine the results of the S2S calculation.

Note: The steps below do not include detailed instructions because the procedureis the same one that you followed for the Rosseland model postprocessing.See Step 6: Postprocessing for the Rosseland Model if you need moredetailed instructions.

(a) Display velocity vectors (Figure 5.22).

Display −→Vectors...

(b) Plot the y velocity along the horizontal centerline (Figure 5.20), and save theplot data to a file called rad s2s.xy.

Plot −→XY Plot...

! You will have to reselect Y Velocity under Y Axis Function. Also, remem-ber to turn off the Write to File option to access the Plot button to generatethe plot.

(c) Compute the total wall heat transfer rate.

Report −→Fluxes ...

The total heat transfer rate on the right wall is 6.77 × 105 W. Note that thetotal heat transfer rate on left wall is zero as it is not participating in S2Sradiation.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

2.47e-042.35e-042.22e-042.10e-041.98e-041.85e-041.73e-041.61e-041.48e-041.36e-041.24e-041.11e-049.89e-058.65e-057.42e-056.19e-054.95e-053.72e-052.49e-051.25e-051.92e-07

Figure 5.22: Velocity Vectors for the S2S Model with Partial Enclosure

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position (m)

(m/s)Velocity

Y

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

6.78e-21

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

y=0.5

Figure 5.23: XY Plot of Centerline y Velocity for the S2S Model with Partial Enclosure

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Step 15: Comparison of S2S Models with and withoutPartial Enclosure

1. Compare the computed heat transfer rates for the two S2S models.

2. Compare the y-velocity profiles in a single plot (Figure 5.24)

Plot −→File...

(a) Use the Delete button in the File XY Plot panel to remove the old XY plotdata files.

(b) Read in all the XY plot files you saved for the S2S models.

(c) Click on Plot.

Y VelocityFLUENT 6.1 (2d, segregated, lam)

Nov 27, 2002

Position

VelocityY

10.90.80.70.60.50.40.30.20.10

2.50e-04

2.00e-04

1.50e-04

1.00e-04

5.00e-05

6.78e-21

-5.00e-05

-1.00e-04

-1.50e-04

-2.00e-04

-2.50e-04

Y Velocity (rad_s2sp.xy)

Y Velocity

Y Velocity

Figure 5.24: Comparison of Computed y Velocities for S2S models

In Figure 5.24, the velocity profiles for the S2S model without partial enclosure and theS2S model with partial enclosure are almost identical.

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Summary: In this tutorial, you studied combined natural convection and radiation ina square box and compared the performance of four radiation models in FLUENTfor optically thin and optically thick cases, and the performance of three radiationmodels for a non-participating medium.

• For the optically thin case, the Rosseland and P-1 models are not appropriate;the DTRM and the DO model are applicable, and yield similar results.

• In the optically thick limit, all four models are appropriate and yield similarresults. In this limit, the less computationally-expensive Rosseland and P-1models may be adequate for many engineering applications.

• The S2S radiation model is appropriate for modeling the enclosure radiativetransfer without participating media, where the methods for participatingradiation may not always be efficient.

For more information about the applicability of the different radiation models, seethe User’s Guide.

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Tutorial 6. Using a Non-Conformal Mesh

Introduction: Film cooling is a process that is used to protect turbine vanes in a gasturbine engine from exposure to hot combustion gases. This tutorial illustrateshow to set up and solve a film cooling problem using a non-conformal mesh. Thesystem that is modeled consists of three parts: a duct, a hole array, and a plenum.The duct is modeled with a hexahedral mesh, and the plenum and hole regions aremodeled using a tetrahedral mesh. These two meshes are merged together to forma “hybrid” mesh, with a non-conformal interface boundary between them.

Due to symmetry of the hole array, only a portion of the geometry is modeled inFLUENT, with symmetry applied to the outer boundaries. The duct contains ahigh-velocity, hot fluid in streamwise flow (Figure 6.1). An array of holes intersectsthe duct at an inclined angle, and a cooler fluid is injected into the holes from aplenum. The coolant that moves through the holes acts to cool the surface of theduct, downstream of the injection. Both fluids are air, and the flow is classified asturbulent. The velocity and temperature of the streamwise and cross-flow fluidsare known, and FLUENT is used to predict the flow and temperature fields thatresult from convective heat transfer.

In this tutorial you will learn how to:

• Merge hexahedral and tetrahedral meshes to form a hybrid mesh

• Create a non-conformal grid interface

• Model heat transfer across a non-conformal interface with specified tempera-ture and velocity boundary conditions

• Calculate a solution using the segregated solver

• Plot temperature profiles on specified isosurfaces

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps will not be shownexplicitly.

Problem Description: This problem considers a model of a 3D section of a film coolingtest rig. A schematic is shown in Figures 6.1 and 6.2. The problem consists of aduct, 24.5 in long, with cross-sectional dimensions of 0.75 in × 5 in. An arrayof uniformly spaced holes is located at the bottom of the duct. Each hole has adiameter of 0.5 inches, is inclined at 35 degrees, and is spaced 1.5 inches apart

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laterally. Cooler injected air enters the system through the plenum, with cross-sectional dimensions of 3.3 in × 1.25 in.

Because of the symmetry of the geometry, only a portion of the domain needs to bemodeled. The computational domain is shown in outline in Figure 6.2. The bulktemperature of the streamwise air (T∞) is 273 K, and the velocity of the air streamis 20 m/s. The bottom wall of the duct that intersects the hole array is assumedto be a completely insulated (adiabatic) wall. The secondary (injected) air entersthe plenum at a uniform velocity of 0.4559 m/s. The temperature of the injectedair (Tinject) is 136.6 K. The properties of air that are used in the model are shownin Figure 6.2.

35°x

y

Plenum

Hole

Duct

9.5 in 0.5 in 14.5 in

1.25 in

3.3 in

1.25 in

5 in

v = 20 m/s

v = 0.4559 m/sT = 136.6 K

inject

Τ∞ = 273 K

Figure 6.1: Schematic of the Problem, Front View

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0.75 in

z

x

0.25 in

Τ∞ = 273 K

= 0.000017894 kg/m-sµ= 1006.43 J/kg-Kc p

Figure 6.2: Schematic of the Problem, Top View

Preparation

1. Copy the files filmcool/film_hex.msh and filmcool/film_tet.msh from theFLUENT documentation CD to your working directory (as described in Tutorial 1).

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Step 1: Merging the Mesh Files

1. Start the 3D version of tmerge by typing utility tmerge -3d at the systemprompt.

2. Provide the mesh file names film tet.msh and film hex.msh as prompted. Pro-vide scaling of 1 and translations and rotations of zero for each mesh file. Save thenew merged mesh file as filmcool.msh.

Append 3D grid files.tmerge3D Fluent Inc, Version 2.1.8

Enter name of grid file (ENTER to continue) : film_tet.msh

x,y,z scaling factor, eg. 1 1 1 : 1 1 1

x,y,z translation, eg. 0 1 0 : 0 0 0

rot axis (0,1,2), angle (deg), eg. 1 45 : 0 0

Enter name of grid file (ENTER to continue) : film_hex.msh

x,y,z scaling factor, eg. 1 1 1 : 1 1 1

x,y,z translation, eg. 0 1 0 : 0 0 0

rot axis (0,1,2), angle (deg), eg. 1 45 : 0 0

Enter name of grid file (ENTER to continue) : <ENTER>

Enter name of output file : filmcool.msh

! The mesh files must be read into tmerge in this order for the tutorial to runas written. Otherwise, zone names and numbers will be assigned differentlywhen the files are merged together. In general, however, you can specify filesto be read into tmerge in any order.

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Step 2: Grid

1. Start the 3D version of FLUENT.

2. Read in the mesh file filmcool.msh.

File −→ Read −→Case...

3. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

4. Scale the grid and change the unit of length to inches.

Grid −→Scale...

(a) In the Units Conversion drop-down list, select in to complete the phrase GridWas Created In in (inches).

(b) Click Scale to scale the grid.

(c) Click Change Length Units to set inches as the working units for length.

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

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5. Display an outline of the 3D grid (Figure 6.3).

Display −→Grid...

(a) In the Surfaces list, deselect symmetry-3, symmetry-5 and symmetry-tet.

(b) Click Display.

Z

Y

X

GridFLUENT 6.1 (3d, segregated, lam)

Nov 13, 2002

Figure 6.3: Hybrid Mesh for Film Cooling Problem

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Using a Non-Conformal Mesh

(c) Zoom in using your middle mouse button to get the view displayed in Fig-ure 6.4.

GridFLUENT 6.1 (3d, segregated, lam)

Nov 13, 2002

Z

Y

X

Figure 6.4: Hybrid Mesh (Zoomed-In View)

In Figure 6.4 you can see the quadrilateral faces of the hexahedral cells that areused to model the duct region, and the triangular faces of the tetrahedral cells thatare used to model the plenum and hole regions, resulting in a hybrid mesh.

Extra: You can use the right mouse button to check which zone number corre-sponds to each boundary. If you click the right mouse button on one of theboundaries in the graphics window, its zone number, name, and type will beprinted in the FLUENT console window. This feature is especially useful whenyou have several zones of the same type and you want to distinguish betweenthem quickly.

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Step 3: Models

1. Keep the default solver settings.

Define −→ Models −→Solver...

2. Enable heat transfer by activating the energy equation.

Define −→ Models −→Energy...

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3. Enable the standard k-ε turbulence model.

Define −→ Models −→Viscous...

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Step 4: Materials

Define −→Materials...

1. Select air (the default material) as the fluid material, and use the incompressible-ideal-gas law to compute density. Retain the default values for all other properties.

! Don’t forget to click the Change/Create button after selecting incompressible-ideal-gas in the drop-down list for Density.

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Step 5: Operating Conditions

1. Keep the default operating conditions.

Define −→Operating Conditions...

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Using a Non-Conformal Mesh

Step 6: Boundary Conditions

Define −→Boundary Conditions...

1. Set the boundary conditions for the streamwise flow inlet (velocity-inlet-1).

(a) Change the Zone Name from velocity-inlet-1 to velocity-inlet-duct.

(b) Set the Velocity Magnitude to 20 m/s.

(c) Set the Temperature to 273 K.

(d) In the Turbulence Specification Method drop-down list, select Intensity and Hy-draulic Diameter.

(e) Set the Turbulence Intensity to 1% and the Hydraulic Diameter to 5 in.

The Intensity and Hydraulic Diameter specification method is convenient in this casesince the hydraulic diameter of the duct at the inlet is known.

2. Set the boundary conditions for the injected stream inlet (velocity-inlet-14).

(a) Change the Zone Name from velocity-inlet-14 to velocity-inlet-plenum.

(b) Set the Velocity Magnitude to 0.4559 m/s.

(c) Set the Temperature to 136.6 K.

(d) In the Turbulence Specification Method drop-down list, select Intensity and Vis-cosity Ratio.

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(e) Set the Turbulence Intensity to 1% and keep the Turbulent Viscosity Ratio defaultof 10.

In the absence of any identifiable length scale for turbulence, the Intensity and Vis-cosity Ratio method should be used. See the User’s Guide for more information onhow to set the boundary conditions for turbulence.

3. Set the boundary conditions for the flow exit (pressure-outlet-1).

(a) Change the Zone Name from pressure-outlet-1 to pressure-outlet-duct.

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(b) Keep the default setting of 0 Pa for Gauge Pressure.

(c) Set the Backflow Total Temperature to 273 K.

(d) In the Turbulence Specification Method drop-down list, select Intensity and Vis-cosity Ratio.

(e) Set the Backflow Turbulence Intensity to 1% and keep the Backflow TurbulentViscosity Ratio default of 10.

4. Set the conditions for the fluid in the duct (fluid-9).

(a) Change the Zone Name from fluid-9 to fluid-duct.

(b) Keep the default selection of air as the Material Name.

5. Set the conditions for the fluid in the plenum and hole (fluid-17).

(a) Change the Zone Name from fluid-17 to fluid-plenum.

(b) Keep the default selection of air as the Material Name.

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6. Keep the default boundary conditions for the plenum and hole wall (wall-15).

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7. Define the zones on the non-conformal boundary as interface zones.

The non-conformal grid interface contains two boundary zones: wall-1 and wall-12.wall-1 is the bottom surface of the duct, and wall-12 represents the hole throughwhich the cool air is injected from the plenum (Figure 6.5). These boundaries weredefined as walls in the original mesh files, film hex.msh and film tet.msh, andmust be redefined as interface boundary types.

GridFLUENT 6.1 (3d, segregated, lam)

Aug 02, 2002

Z

YX

Figure 6.5: Grid for the wall-1 and wall-12 Boundaries

(a) Select wall-1 in the Zone list and choose interface as the new Type.

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Using a Non-Conformal Mesh

(b) Confirm that it is OK to change the boundary type.

(c) Change the Zone Name to interface-duct.

(d) Repeat this procedure to convert wall-12 to an interface boundary zone namedinterface-hole.

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Step 7: Grid Interfaces

In this step, you will create a non-conformal grid interface between the hexahedral andtetrahedral meshes.

Define −→Grid Interfaces...

1. Select interface-hole in the Interface Zone 1 list.

! When one interface zone is smaller than the other, it is recommended thatyou choose the smaller zone as Interface Zone 1.

2. Select interface-duct in the Interface Zone 2 list.

3. Enter the name junction under Grid Interface.

4. Click Create.

Note: In the process of creating the grid interface, FLUENT creates two new wallboundary zones: wall-11 and wall-18. You will not be able to display thesewalls.

wall-11 is the non-overlapping region of the interface-hole zone that results fromthe intersection of the interface-hole and interface-duct boundary zones, and islisted under Boundary Zone 1 in the Grid Interfaces panel. wall-11 is empty,since interface-hole is completely contained within the interface-duct boundary.

wall-18 is the non-overlapping region of the interface-duct zone that results fromthe intersection of the two interface zones, and is listed under Boundary Zone2 in the Grid Interfaces panel.

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! In general, you will need to set boundary conditions for wall-18 (since it isnot empty). In this case, default settings are used.

Step 8: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Under Discretization, select Second Order Upwind for Momentum and TurbulenceKinetic Energy.

(b) Scroll down the list and select Second Order Upwind for Turbulence DissipationRate and Energy.

2. Enable the plotting of residuals.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click the OK button.

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3. Initialize the solution.

Solve −→ Initialize −→Initialize...

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

(b) Click Init, and Close the panel.

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Using a Non-Conformal Mesh

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

File −→ Write −→Case...

5. Start the calculation by requesting 250 iterations.

Solve −→Iterate...

(a) Set the Number of Iterations to 250.

(b) Click Iterate.

Note: During the first few iterations, the console window will report that turbu-lent viscosity is limited in a couple of cells. This message should go away asthe solution converges and the turbulent viscosity approaches more reasonablelevels.

The solution will converge after about 190 iterations.

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

File −→ Write −→Case & Data...

Note: If you choose a file name that already exists in the current directory, FLU-ENT will prompt you for confirmation to overwrite the file.

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Step 9: Postprocessing

1. Display filled contours of static pressure (Figure 6.6).

Display −→Contours...

(a) Select Filled under Options.

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

(c) In the Surfaces list, select interface-duct and interface-hole.

(d) Scroll down the Surfaces list and select symmetry-1, symmetry-tet, and wall-15.

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(e) Reset the view to the default view.

Display −→Views...

i. Click Default under Actions.

ii. Close the panel.

(f) In the Contours panel, click Display.

(g) Zoom in on the view to get the display shown in Figure 6.6.

Contours of Static Pressure (pascal)FLUENT 6.1 (3d, segregated, ske)

Nov 13, 2002

3.43e+023.17e+022.91e+022.65e+022.39e+022.14e+021.88e+021.62e+021.36e+021.10e+028.45e+015.87e+013.28e+017.03e+00-1.88e+01-4.46e+01-7.04e+01-9.62e+01-1.22e+02-1.48e+02-1.74e+02

Z

Y

X

Figure 6.6: Contours of Static Pressure

Note the high/low pressure zones on the upstream/downstream sides of thecoolant hole, where the jet first penetrates the primary flow in the duct.

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2. Display filled contours of static temperature (Figures 6.7 and 6.8).

Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-downlists.

(b) Under Options, deselect Auto Range so that you can change the maximum andminimum temperature gradient values to be plotted.

(c) Keep the default Min value of 0.

(d) Enter a new Max value of 273.096.

(e) Under Options, deselect Clip to Range.

(f) Reset the view to the default view.

Display −→Views...

(g) In the Contours panel, click Display.

(h) Zoom in on the view to get the display shown in Figure 6.8.

Figures 6.7 and 6.8 clearly show how the coolant flow insulates the bottom ofthe duct from the higher-temperature primary flow.

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Contours of Static Temperature (k)FLUENT 6.1 (3d, segregated, ske)

Nov 13, 2002

2.73e+022.59e+022.46e+022.32e+022.18e+022.05e+021.91e+021.78e+021.64e+021.50e+021.37e+021.23e+021.09e+029.56e+018.19e+016.83e+015.46e+014.10e+012.73e+011.37e+010.00e+00

Z

Y

X

Figure 6.7: Contours of Static Temperature

Contours of Static Temperature (k)FLUENT 6.1 (3d, segregated, ske)

Nov 13, 2002

2.73e+022.59e+022.46e+022.32e+022.18e+022.05e+021.91e+021.78e+021.64e+021.50e+021.37e+021.23e+021.09e+029.56e+018.19e+016.83e+015.46e+014.10e+012.73e+011.37e+010.00e+00

Z

Y

X

Figure 6.8: Contours of Static Temperature (Zoomed-In View)

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3. Display the velocity vectors (Figure 6.9).

Display −→Vectors...

(a) Select Velocity... and Velocity Magnitude in the Color By drop-down lists.

(b) Change the Scale to 2.

This will enlarge the vectors that are displayed, making it easier to view theflow patterns.

(c) In the Surfaces list, select interface-duct and interface-hole.

(d) Scroll down the Surfaces list and select symmetry-1, symmetry-tet, and wall-15.

(e) Reset the view to the default view.

Display −→Views...

(f) In the Vectors panel, click Display.

(g) Zoom in on the view to get the display shown in Figure 6.9.

The flow pattern in the vicinity of the coolant hole shows the level of penetrationof the coolant jet into the main flow. Notice that the velocity field varies smoothlyacross the non-conformal interface.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (3d, segregated, ske)

Nov 13, 2002

2.13e+012.02e+011.92e+011.81e+011.71e+011.60e+011.49e+011.39e+011.28e+011.17e+011.07e+019.60e+008.53e+007.47e+006.40e+005.34e+004.27e+003.21e+002.14e+001.08e+001.50e-02

Z

Y

X

Figure 6.9: Velocity Vectors

4. Plot the temperature profile along a horizontal cross-section of the duct, 0.1 inchesabove the bottom.

(a) Create an isosurface on the duct surface at y = 0.1 in.

Surface −→Iso-Surface...

i. Select Grid... and Y-Coordinate in the Surface of Constant drop-down lists.

ii. Enter y=0.1in under New Surface Name.

iii. Enter 0.1 for Iso-Values.

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iv. Click Create.

(b) Create an XY plot of static temperature on the isosurface.

Plot −→XY Plot...

i. Keep the default Plot Direction.

ii. Select Temperature... and Static Temperature in the Y-Axis Function drop-down lists.

iii. Scroll down the Surfaces list and select y=0.1in.

iv. Click Plot.

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Z

Y

X

Static TemperatureFLUENT 6.1 (3d, segregated, ske)

Nov 13, 2002

Position (in)

(k)Temperature

Static

17.51512.5107.552.50-2.5-5-7.5-10

2.80e+02

2.60e+02

2.40e+02

2.20e+02

2.00e+02

1.80e+02

1.60e+02

1.40e+02

1.20e+02

y=0.1in

Figure 6.10: Static Temperature at y=0.1 in

In this plot you can see how the temperature of the fluid changes as the coolair from the injection hole mixes with the primary flow. As expected, the tem-perature is coolest just downstream of the hole. Note that you could also makea similar plot on the lower wall itself, to examine the wall surface temperature.

Summary: This tutorial demonstrates how FLUENT’s non-conformal grid interface ca-pability can be used to handle hybrid meshes for complex geometries, such as thefilm cooling hole configuration examined here. One of the principal advantages ofthis approach is that it allows you to merge existing component meshes togetherto create a larger, more complex mesh system, without requiring that the differentcomponents have the same node locations on their shared boundaries. Thus, youcan perform parametric studies by merging the desired meshes, creating the non-conformal interface(s), and solving the model. For example, in the present case,you can

• Use a different hole/plenum mesh

• Reposition the existing hole/plenum mesh

• Add additional hole/plenum meshes to create aligned or staggered multiplehole arrays

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Tutorial 7. Using a Single RotatingReference Frame

Introduction: This tutorial considers the flow within a 2D, axisymmetric, co-rotatingdisk cavity system. Understanding the behavior of such flows is important in thedesign of secondary air passages for turbine disk cooling.

In this tutorial you will learn how to:

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

• Use the standard k-ε and RNG k-ε turbulence models with the enhanced near-wall treatment

• Calculate a solution using the segregated solver

• Display velocity vectors and contours of pressure

• Set up and display XY plots of radial velocity

• Restart the solver from an existing solution

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: The problem to be considered is shown schematically in Fig-ure 7.1. This case is similar to a disk cavity configuration that was extensivelystudied by Pincombe [1].

Air enters the cavity between two co-rotating disks. The disks are 88.6 cm indiameter and the air enters at 1.146 m/s through a circular bore 8.86 cm in diam-eter. The disks, which are 6.2 cm apart, are spinning at 71.08 rpm, and the airenters with no swirl. As the flow is diverted radially, the rotation of the disk has asignificant effect on the viscous flow developing along the surface of the disk.

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RotatingDisk

RotatingDisk

Outflow

Inflow71.08 rpm

6.2 cm

44.3 cm

4.43 cm

Figure 7.1: Problem Specification

As noted by Pincombe [1], there are two nondimensional parameters that charac-terize this type of disk cavity flow: the volume flow rate coefficient, Cw, and therotational Reynolds number, Reφ. These parameters are defined as follows:

Cw =Q

ν rout

(7.1)

Reφ =Ωr2

out

ν(7.2)

where Q is the volumetric flow rate, Ω is the rotational speed, ν is the kinematicviscosity, and rout is the outer radius of the disks. Here, you will consider a casefor which Cw = 1092 and Reφ = 105.

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Preparation

1. Copy the file disk/disk.msh from the FLUENT documentation CD to your workingdirectory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

Step 1: Grid

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

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid (Figure 7.2).

Display −→Grid...

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Grid Aug 02, 2002FLUENT 6.1 (axi, swirl, segregated, ske)

Figure 7.2: Grid Display for the Disk Cavity

Extra: You can use the right mouse button to check which zone number corresponds toeach boundary. If you click the right mouse button on one of the boundaries in thegraphics window, its zone number, name, and type will be printed in the FLUENTconsole window. This feature is especially useful when you have several zones ofthe same type and you want to distinguish between them quickly.

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Step 2: Units

1. For convenience, define new units for angular velocity and length.

In the problem description, angular velocity and length are specified in rpm and cm,respectively. These are not the default units for these quantities.

Define −→Units...

(a) Select angular-velocity under Quantities, and rpm under Units.

(b) Select length under Quantities, and cm under Units.

(c) Close the panel.

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Step 3: Models

1. Specify the solver formulation to be used for the model calculation, and enable themodeling of axisymmetric swirl.

Define −→ Models −→Solver...

(a) Retain the default Segregated solver.

(b) Select Axisymmetric Swirl under Space.

(c) Retain the default selection of Absolute under Velocity Formulation.

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

(d) Retain the default selection of Cell-Based under Gradient Option.

(e) Retain the default selection of Superficial Velocity under Porous Formulation.

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2. Turn on the standard k-ε turbulence model with the enhanced near-wall treatment.

Define −→ Models −→Viscous...

(a) Under Model, select k-epsilon.

The panel will expand.

(b) Keep the Standard setting under k-epsilon Model.

(c) Under Near-Wall Treatment, select Enhanced Wall Treatment and keep the de-fault settings.

The ability to calculate a swirl velocity permits the use of a 2D mesh, so thecalculation is simpler and more economical to run. This is especially importantfor problems where the enhanced wall treatment is used, and the near-wall flowfield is resolved through the viscous sublayer and buffer zones (that is, the firstgrid point away from the wall is placed at a y+ on the order of 1). See theUser’s Guide for details.

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Step 4: Materials

1. Accept the default properties for air.

Define −→Materials...

For the present analysis, you will model air as an incompressible fluid with a densityof 1.225 kg/m3 and a dynamic viscosity of 1.7894×10−5 kg/m-s. Since these arethe default values, no change is required in the Materials panel.

Extra: You can modify the fluid properties for air at any time or copy anothermaterial from the database. See the “Physical Properties” chapter of the User’sGuide for details.

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Step 5: Boundary Conditions

You will set up the present problem using a rotating reference frame for the fluid. Thedisk walls will then be defined to rotate with the moving frame.

Define −→Boundary Conditions...

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

(a) Select Moving Reference Frame in the Motion Type drop-down list.

(b) Scroll down below Motion Type and set the Speed (under Rotational Velocity)to 71.08 rpm.

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

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

Note: FLUENT will use the backflow conditions only if the fluid is flowing intothe computational domain through the outlet. Since backflow might occur atsome point during the solution procedure, you should set reasonable backflowconditions to prevent convergence from being adversely affected.

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

Note: For a rotating reference frame, FLUENT assumes by default that all wallsrotate at the speed of the moving reference frame, and hence are moving withrespect to the stationary (absolute) reference frame. To specify a non-rotatingwall, you must specify a rotational speed of 0 in the absolute frame.

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Step 6: Solution Using the Standard k-ε Model

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Under Discretization, select PRESTO! from the drop-down list to the right ofPressure.

The PRESTO! scheme is well suited for steep pressure gradients involved inrotating flows. It provides improved pressure interpolation in situations wherelarge body forces or strong pressure variations are present as in swirling flows.

(b) Select Second Order Upwind from the adjacent drop-down list for Momentum,Swirl Velocity, Turbulence Kinetic Energy, and Turbulence Dissipation Rate.

! Use the scroll bar to access the turbulence discretization schemes.

(c) Retain the default Under-Relaxation Factors.

Note: For this problem, the default under-relaxation factors are satisfactory.However, if the solution diverges or the residuals display large oscillations,you may need to reduce the under-relaxation factors from their defaultvalues. See the User’s Guide for tips on how to adjust the under-relaxationparameters for different situations.

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2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click the OK button.

Note: For this calculation, the convergence tolerance on the continuity equationis kept at 0.001. You can reduce this value if necessary, depending on thebehavior of the solution.

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

Solve −→ Monitors −→Surface...

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

(b) Turn on the Plot and Write options for monitor-1.

Note: When the Write option is selected in the Surface Monitors panel, themass flow rate history will be written to a file. If you do not select theWrite option, the history information will be lost when you exit FLUENT.

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(c) Click Define... to specify the surface monitor parameters.

This will open the Define Surface Monitor panel.

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

ii. Select pressure-outlet-3 in the Surfaces list.

iii. Click OK to define the monitor.

(d) Click OK in the Surface Monitors panel to enable the monitor.

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

Solve −→ Initialize −→Initialize...

(a) Choose velocity-inlet-2 from the Compute From list.

(b) Click Init and close the panel.

5. Save the case file (disk ke.cas).

File −→ Write −→Case...

6. Start the calculation by requesting 500 iterations.

Solve −→Iterate...

Throughout the calculation, FLUENT will report reversed flow at the exit. This isreasonable for the current case.

The solution should be sufficiently converged after about 230 iterations. The massflow rate history is shown in Figure 7.3.

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Convergence history of Mass Flow Rate on pressure-outlet-3 FLUENT 6.1 (axi, swirl, segregated, ske)

Aug 02, 2002

Iteration

RateFlow

Mass

2502252001751501251007550250

0.0300

0.0200

0.0100

0.0000

-0.0100

-0.0200

-0.0300

Figure 7.3: Mass Flow Rate History (k-ε Turbulence Model)

7. Check the mass flux balance.

Report −→Fluxes...

! Although the mass flow rate history indicates that the solution is converged,you should also check the net mass fluxes through the domain to ensure thatmass is being conserved.

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(a) Select velocity-inlet-2 and pressure-outlet-3 under Boundaries.

(b) Keep the default Mass Flow Rate option.

(c) Click Compute.

! The net mass imbalance should be a small fraction (say, 0.5%) of the total fluxthrough the system. If a significant imbalance occurs, you should decrease yourresidual tolerances by at least an order of magnitude and continue iterating.

8. Save the data file (disk ke.dat).

File −→ Write −→Data...

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Step 7: Postprocessing for the Standard k-ε Solution

1. Display the velocity vectors.

Display −→Vectors...

(a) Increase the Scale value to 50.

(b) Increase the Skip value to 1.

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(c) Click Vector Options... to open the Vector Options panel.

i. Turn off the Z Component.

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

ii. Click Apply and close the panel.

(d) Click Display in the Vectors panel to plot the velocity vectors.

A magnified view of the velocity field displaying a counter-clockwise circulationof the flow is shown in Figure 7.4.

Velocity Vectors Colored By Velocity Magnitude (m/s) Aug 02, 2002FLUENT 6.1 (axi, swirl, segregated, ske)

3.27e+00

1.64e-021.79e-013.41e-015.04e-016.66e-018.29e-019.91e-011.15e+001.32e+001.48e+001.64e+001.80e+001.97e+002.13e+002.29e+002.45e+002.62e+002.78e+002.94e+003.10e+00

Figure 7.4: Magnified View of Velocity Vectors within the Disk Cavity

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2. Display filled contours of static pressure.

Display −→Contours...

(a) Select Pressure... and Static Pressure in the Contours Of drop-down list.

(b) Turn on the Filled option.

(c) Click Display.

The pressure contours are displayed in Figure 7.5. Notice the high pressure thatoccurs on the right disk near the hub due to the stagnation of the flow entering fromthe bore.

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Contours of Static Pressure (pascal) Aug 02, 2002FLUENT 6.1 (axi, swirl, segregated, ske)

6.56e-01

-6.35e-01-5.70e-01-5.06e-01-4.41e-01-3.77e-01-3.12e-01-2.48e-01-1.83e-01-1.18e-01-5.39e-021.07e-027.53e-021.40e-012.04e-012.69e-013.34e-013.98e-014.63e-015.27e-015.92e-01

Figure 7.5: Contours of Static Pressure for Entire Disk Cavity

3. Create a constant y-coordinate line for postprocessing.

Surface −→Iso-Surface...

(a) Select Grid... and Y-Coordinate in the Surface of Constant drop-down lists.

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

(c) Enter 37 in the Iso-Values field.

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

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

(e) Click Create to create the isosurface.

Note: The name you use for an iso-surface can be any continuous string ofcharacters (without spaces).

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

Plot −→XY Plot...

(a) Enable Node Values under Options.

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

(c) Select the y-coordinate line y=37cm under Surfaces.

(d) Click Plot.

Figure 7.6 shows a plot of the radial velocity distribution along y = 37 cm.

(e) Save the radial velocity profile.

i. Select Write to File under Options.

ii. Click the Write... button.

iii. In the resulting Select File dialog box, specify ke-data.xy in the XY Filetext entry box and click OK.

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Radial VelocityFLUENT 6.1 (axi, swirl, segregated, ske)

Aug 02, 2002

Position (cm)

(m/s)Velocity

Radial

76543210

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00

-5.00e-02

y=37cm

Figure 7.6: Radial Velocity Distribution: Standard k-ε Solution

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Step 8: Solution Using the RNG k-ε Model

You will now recalculate the solution using the RNG k-ε turbulence model.

1. Turn on the RNG k-ε turbulence model with the enhanced near-wall treatment.

Define −→ Models −→Viscous...

(a) Select RNG under k-epsilon Model.

(b) Enable the Differential Viscosity Model and Swirl Dominated Flow under RNGOptions.

The differential viscosity model and swirl modification can provide better accu-racy for swirling flows such as the disk cavity. See the User’s Guide for moreinformation.

(c) Keep the Enhanced Wall Treatment as the Near-Wall Treatment.

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2. Continue the calculation by requesting 200 iterations.

Solve −→Iterate...

The solution should converge after about 160 additional iterations.

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

File −→ Write −→Case & Data...

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Step 9: Postprocessing for the RNG k-ε Solution

1. Plot the radial velocity distribution for the RNG solution and compare it with thedistribution for the standard k-ε solution.

Plot −→XY Plot...

(a) Load the k-ε data.

i. Click the Load File... button.

This will open the Select File dialog box.

ii. In the Select File dialog box, select the file ke-data.xy in the Files list.

iii. Click OK.

(b) In the Solution XY Plot panel, select Velocity... and Radial Velocity in the YAxis Function drop-down lists.

(c) In the Surfaces list, select y=37cm.

(d) Turn off the Write to File option.

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(e) Click the Curves... button to define a different curve symbol for the RNG k-εdata.

This will open the Curves - Solution XY Plot panel.

i. Set the Curve # to 0.

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

iii. Click Apply and Close the panel.

(f) Click Plot in the Solution XY Plot panel.

Radial VelocityFLUENT 6.1 (axi, swirl, segregated, rngke)

Aug 02, 2002

Position (cm)

(m/s)Velocity

Radial

76543210

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00

-5.00e-02

-1.00e-01

y=37cmy=37cm

Figure 7.7: Radial Velocity Distribution: RNG and Standard k-ε Solutions

The plot should be similar to the one shown in Figure 7.7. The peak velocitypredicted by the RNG solution is higher than that predicted by the k-ε solution.This is due to the less diffusive character of the RNG k-ε model.

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(g) Adjust the range of the x axis to magnify the region of the peaks.

i. In the Solution XY Plot panel, click the Axes... button to specify the x-axisrange.

This will open the Axes - Solution XY panel.

ii. Deselect Auto Range under Options.

iii. Under Range, enter 0 for the Minimum and 1 for the Maximum.

iv. Click Apply and Close the panel.

v. Click Plot in the Solution XY Plot panel.

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

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Radial VelocityFLUENT 6.1 (axi, swirl, segregated, rngke)

Aug 02, 2002

Position (cm)

(m/s)Velocity

Radial

10.90.80.70.60.50.40.30.20.10

4.00e-01

3.50e-01

3.00e-01

2.50e-01

2.00e-01

1.50e-01

1.00e-01

5.00e-02

0.00e+00

y=37cmy=37cm

Figure 7.8: Radial Velocity Distribution: RNG and Standard k-ε Solutions (x = 0 cm tox = 1 cm)

Summary: This tutorial has demonstrated how to set up an axisymmetric disk cavityproblem in FLUENT. The ability to calculate a swirl velocity permits the use ofa 2D mesh, so the calculation is simpler and more economical to run. This isespecially important for problems where the enhanced wall treatment is used, andthe near-wall flow field is resolved through the viscous sublayer and buffer zones(that is, the first grid point away from the wall is placed at a y+ on the order of 1).See the User’s Guide for more information about grid considerations for turbulencemodeling.

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Further Improvements: The case modeled in this tutorial lends itself to parametricstudy due to its relatively small size. Here are some things you may wish to try:

• Separate wall-6 into two walls.

Grid −→ Separate −→Faces...

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

• Use adaption to see if resolving the high velocity and pressure-gradient regionof the flow has a significant effect on the solution.

• Introduce a non-zero swirl at the inlet or use a velocity profile for fully-developed pipe flow. This is probably more realistic than the constant axialvelocity used here, since the flow at the inlet is typically being supplied by apipe.

• Model compressible flow (using the ideal gas law for density) rather thanassuming incompressible flow.

References: 1. Pincombe, J.R., “Velocity Measurements in the Mk II - RotatingCavity Rig with a Radial Outflow”, Thermo-Fluid Mechanics Research Centre,University of Sussex, Brighton, UK, 1981.

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Tutorial 8. Using Multiple RotatingReference Frames

Introduction: Many engineering problems involve rotating flow domains. One exampleis the centrifugal blower unit that is typically used in automotive climate controlsystems. For problems where all the moving parts (fan blades, hub and shaftsurfaces, etc.) are rotating at a prescribed angular velocity, and the stationarywalls (e.g., shrouds, duct walls) are surfaces of revolution with respect to the axisof rotation, the entire domain can be referred to as a single rotating frame ofreference. However, when each of several parts is rotating about a different axisof rotation, or about the same axis at different speeds, or when the stationarywalls are not surfaces of revolution (such as the volute around a centrifugal blowerwheel), a single rotating coordinate system is not sufficient to “immobilize” thecomputational domain so as to predict a steady-state flow field.

In FLUENT, the flow features associated with multiple rotating parts can be ana-lyzed using the multiple reference frame (MRF) capability. This model is powerfulin that multiple rotating reference frames can be included in a single domain. Theresulting flow field is representative of a snapshot of the transient flow field in whichthe rotating parts are moving. However, in many cases the interface can be chosenin such a way that the flow field at this location is independent of the orientationof the moving parts. In other words, if an interface can be drawn on which thereis little or no angular dependence, the model can be a reliable tool for simulatingtime-averaged flow fields. It is therefore very useful in complicated situations whereone or more rotating parts are present.

This tutorial illustrates the procedure for setting up and solving a problem usingthe MRF capability. As an example, the flow field on a 2D section of a centrifugalblower will be calculated. The example will be limited to a single rotating referenceframe.

The following FLUENT features will be demonstrated in this tutorial:

• Specifying different frames of reference for different fluid zones.

• Setting the relative velocity of each wall.

• Calculating a solution using the segregated solver

Prerequisites: This tutorial assumes that you are familiar with the menu structurein FLUENT and that you have solved or read Tutorial 1. Some steps will not beshown explicitly. In general, to solve problems using the MRF feature, you shouldbe familiar with the concept of creating multiple fluid zones in your grid generator.

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Problem Description: This problem considers a 2D section of a generic centrifugalblower. A schematic of the problem is shown in Figure 8.1. The blower consists of 32blades, each with a chord length of 13.5 mm. The blades are located approximately56.5 mm (measured from the leading edge) from the center of rotation. The radiusof the outer wall varies logarithmically from 80 mm to 146.5 mm. The total pressureat the inlet is defined to be 200 Pa and the flow discharges to ambient conditions(static pressure = 0 Pa). The blades are rotating with an angular velocity of261 rad/s. The flow is assumed to be turbulent.

145 mm

261 rad/s35 mm

56.5 mm

Pressure-inlet-5

blower blades(13.5 mm chord length)

Pressure-Outlet-9

Figure 8.1: Schematic of the Problem

Preparation

1. Copy the file blower/blower.msh from the FLUENT documentation CD to yourworking directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read in the mesh file (blower.msh).

File −→ Read −→Case...

2. Check the grid.

Grid −→Check

Note: FLUENT will perform various checks on the mesh and will report the progressin the console window. Pay particular attention to the reported minimumvolume. Make sure this is a positive number.

3. Smooth and swap the grid.

Grid −→Smooth/Swap...

Node smoothing and face swapping will improve the mesh quality. This step isrecommended for triangular and tetrahedral meshes.

(a) Retain the default smoothing parameters and click Smooth.

(b) Click Swap repeatedly until the Number Swapped under Swap Info is zero.

4. Display the mesh (Figure 8.2).

Display −→Grid...

The mesh consists of three fluid zones, fluid-13, fluid-14, and fluid-18. These arereported in the console window when the grid is read. In the Grid Display panel, thefluid zones are reported as interior zones interior-61, interior-62 and interior-66. Ina later step, you will learn how to associate a fluid zone with an interior zone. Thefluid zone containing the blades will be solved in a rotational reference frame.

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Grid Jul 09, 2002FLUENT 6.1 (2d, segregated, ske)

Figure 8.2: Mesh of the 2D Centrifugal Blower

The fluid zones are separated by wall boundaries. These boundaries were used inthe grid generator to separate the fluid zones, and will be converted to interior zoneswhen the boundary conditions are set later in this tutorial. Each of these wall zonesalso has an associated “shadow wall” which was created by FLUENT when it readthe grid. Shadow walls are created whenever a wall has fluid zones on both sides.

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Step 2: Models

1. Keep the default solver settings.

Define −→ Models −→Solver...

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

Define −→ Models −→Viscous...

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Step 3: Materials

You will use the default material, air, with its predefined properties, for all fluid zones.No action is required in the panel.

Define −→Materials...

Extra: If needed, you could modify the fluid properties for air or copy another materialfrom the database. See Chapter 7 of the User’s Guide for details.

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Step 4: Boundary Conditions

Define −→Boundary Conditions...

1. Change wall-2 and wall-3 to type interior.

The zones wall-2 and wall-3 are the interfaces between the three fluid zones. Theyneed to be changed to type interior, as discussed earlier. The resulting interior facesare those that have fluid cells on both sides but do not require any boundary condi-tions to be set.

(a) Select wall-2 in the Zone list and then select interior in the Type list.

FLUENT will prompt for confirmation before changing the zone type.

(b) Click Yes and FLUENT will fuse wall-2 and wall-shadow-2 together to forminterior-2.

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(c) Click OK to keep the default Zone Name.

(d) Repeat the previous steps to change wall-3 to an interior zone named interior-3.

2. Identify the rotating fluid zone (i.e., the zone containing the blades) by displayingthe mesh for each zone.

Display −→Grid...

It is unclear when you read the grid which fluid zone corresponds to which interiorzone. While the interior zones can be selected individually in the Grid Display panel,the fluid zones cannot. Commands in the text interface, however, can be used tomake this association.

(a) Deselect all surfaces by clicking on the unshaded icon to the right of Surfaces.

(b) Click the Outline button at the bottom of the panel to select only the outlinesurfaces of the domain.

(c) Click Display.

Only the domain boundaries and interior walls will be displayed.

(d) In the console window, type the commands shown in boxes in the dialog below.

Hint: You may need to press the <Enter> key to get the > prompt.

> display

/display> zone-grid()zone id/name(1) [()] 13zone id/name(2) [()] <Enter>

The resulting display (Figure 8.3) shows that zone fluid-13 corresponds to the ro-tating region.

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Thread Grid: (13) Jul 09, 2002FLUENT 6.1 (2d, segregated, ske)

Figure 8.3: Mesh in fluid-13

3. Define a rotational reference frame for fluid-13.

Define −→Boundary Conditions...

(a) Keep the Rotation-Axis Origin default setting of (0,0).

This is the center of curvature for the circular boundaries of the rotating zone.

(b) Select Moving Reference Frame from the Motion Type drop-down list.

Hint: Use the scroll bar to access the Motion Type list.

(c) Scroll down further, and set the Speed under Rotational Velocity to 261 rad/s.

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Note: Since the other fluid zones are stationary, you do not need to set any bound-ary conditions for them. If one of the remaining fluid zones was also rotating,you would need to set the appropriate rotational speed for it.

4. Set the following conditions (see Figure 8.1) for the flow inlet (pressure-inlet-5).

Note: All pressures that you specify in FLUENT are gauge pressures, relative tothe operating pressure specified in the Operating Conditions panel. By default,the operating pressure is 101325 Pa. See the User’s Guide for details.

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5. Set the backflow turbulence parameters for the flow outlet (pressure-outlet-9) to thesame values used for pressure-inlet-5.

Note: The backflow values are used only if reversed flow occurs at the outlet, but itis a good idea to use reasonable values, even if you do not expect any backflowto occur.

6. Define the velocity of the wall zone representing the blades (wall-7) relative to themoving fluid zone.

With fluid-13 set to a rotating reference frame, wall-7 becomes a moving wall.

(a) In the Momentum section of the Wall panel, enable the Moving Wall option.

The panel will expand to show the wall motion parameters.

(b) Under Motion, select Relative to Adjacent Cell Zone and Rotational.

(c) Set the (relative) Speed to 0 rad/s.

The Rotation-Axis Origin should be located at x = 0 m and y = 0 m. Withthese settings, the blades will move at the same speed as the surrounding fluid.

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Step 5: Solution

1. Choose the second-order discretization scheme for the governing equations.

Solve −→ Controls −→Solution...

(a) In the drop-down lists next to Momentum, Turbulence Kinetic Energy, andTurbulence Dissipation Rate, select Second Order Upwind.

The second-order scheme will provide a more accurate solution.

(b) Keep the default parameters for all other solution controls.

2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

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

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3. Initialize the solution using the boundary conditions set at pressure-inlet-5.

Solve −→ Initialize −→Initialize...

(a) Select pressure-inlet-5 in the Compute From drop-down list.

(b) Select Absolute under Reference Frame.

(c) Click Init to initialize the solution.

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Note: In this tutorial, you chose an Absolute reference frame for initializing thesolution. In certain cases, Relative to Cell Zone may help the solution convergefaster. See the User’s Guide for guidelines.

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

File −→ Write −→Case...

5. Start the calculation by requesting 400 iterations.

Solve −→Iterate...

During the calculation, FLUENT will report that there is reversed flow occurring atthe exit. This is due to the sudden expansion, which results in a recirculating flownear the exit.

The solution will converge in around 160 iterations (when all residuals have droppedbelow 0.001).

6. Save the case and data files (blower2.cas and blower2.dat).

File −→ Write −→Case & Data...

Note: It is good practice to save the case file whenever you are saving the data.This will ensure that the relevant parameters corresponding to the currentsolution data are saved accordingly.

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Step 6: Postprocessing

1. Display filled contours of total pressure (Figure 8.4).

Display −→Contours...

(a) Select Pressure... and Total Pressure in the Contours Of drop-down lists.

(b) Select Filled under Options.

(c) Click Display.

Total pressure contours show the expected pressure jump across the blower blades.

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Contours of Total Pressure (pascal) Jul 09, 2002FLUENT 6.1 (2d, segregated, ske)

1.13e+03

-8.97e+02-7.96e+02-6.94e+02-5.93e+02-4.92e+02-3.91e+02-2.89e+02-1.88e+02-8.66e+011.47e+011.16e+022.17e+023.19e+024.20e+025.21e+026.23e+027.24e+028.25e+029.26e+021.03e+03

Figure 8.4: Contours of Total Pressure

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2. Display velocity vectors (Figure 8.5).

Display −→Vectors...

(a) Set the Scale factor to 5.

(b) Click Display to view the vectors.

By default, Auto Scale is chosen. This will automatically scale the length of velocityvectors relative to the size of the smallest cell in the mesh. To increase the lengthof the “scaled” vectors, set the Scale factor to a value greater than 1.

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Velocity Vectors Colored By Velocity Magnitude (m/s) Jul 09, 2002FLUENT 6.1 (2d, segregated, ske)

6.99e+01

4.30e-023.54e+007.03e+001.05e+011.40e+011.75e+012.10e+012.45e+012.80e+013.15e+013.50e+013.85e+014.19e+014.54e+014.89e+015.24e+015.59e+015.94e+016.29e+016.64e+01

Figure 8.5: Velocity Vectors

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3. Report the mass flux at pressure-inlet-5 and pressure-outlet-9.

Report −→Fluxes...

(a) Keep the Mass Flow Rate setting under Options.

(b) Select pressure-inlet-5 and pressure-outlet-9 in the Boundaries list.

(c) Click Compute.

The net mass imbalance should be no more than a small fraction (say, 0.5%) of thetotal flux through the system. If a significant imbalance occurs, you should decreaseyour residual tolerances by at least an order of magnitude and continue iterating.

The flux report will compute fluxes only for boundary zones. To report fluxes onsurfaces or planes, use the Surface Integrals... option in the Report menu.

Summary: This tutorial illustrates the procedure for setting up and solving problemswith multiple reference frames using FLUENT. Although this tutorial considers onlyone rotating fluid zone, extension to multiple rotating fluid zones is straightforwardas long as you delineate each fluid zone.

Note that this tutorial was solved using the default absolute velocity formulation.For some problems involving rotating reference frames, you may wish to use therelative velocity formulation. See the User’s Guide for details.

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Tutorial 9. Using the Mixing Plane Model

Introduction: This tutorial considers the flow in an axial fan with a rotor in front andstators (vanes) in the rear. This configuration is typical of a single-stage axial flowturbomachine. By considering the rotor and stator together in a single calculation,you can determine the interaction between these components.

In this tutorial you will learn how to:

• Use the standard k-ε model with standard wall functions

• Use a mixing plane to model the rotor-stator interface

• Calculate a solution using the segregated solver

• Compute and display circumferential averages of total pressure on a surface

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: The problem to be considered is shown schematically in Fig-ure 9.1. The rotor and stator consist of 9 and 12 blades, respectively. A steady-statesolution for this configuration using only one rotor blade and one stator blade isdesired. Since the periodic angles for the rotor and stator are different, a mixingplane must be used at the interface.

The mixing plane is defined at the rotor outlet/stator inlet. The grid is set up withperiodic boundaries on either side of the rotor and stator blades. A pressure inlet isused at the upstream boundary and a pressure outlet at the downstream boundary.Ambient air is drawn into the fan (at 0 Pa gauge total pressure) and is exhaustedback out to the ambient environment (0 Pa static pressure). The hub and blade ofthe rotor are assumed to be rotating at 1800 rpm.

Preparation

1. Copy the file mstage/fanstage.msh from the FLUENT documentation CD to yourworking directory (as described in Tutorial 1).

2. Start the 3D version of FLUENT.

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inlet

outletrotor

stator

ω = 1800 rpmxz

y

Figure 9.1: Problem Specification

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Step 1: Grid

1. Read the grid file (fanstage.msh).

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the grid and will report the progress in theconsole window. Pay particular attention to the minimum volume. Make sure thatthis is a positive number.

3. Display the grid (Figure 9.2).

Display −→Grid...

(a) Select rotor-blade, rotor-hub, rotor-inlet-hub, stator-blade, and stator-hub in theSurfaces list.

(b) Click Display.

(c) Rotate the view to get the display shown in Figure 9.2.

Extra: You can use the right mouse button to check which zone number corresponds toeach boundary. If you click the right mouse button on one of the boundaries in thegraphics window, its zone number, name, and type will be printed in the FLUENTconsole window. This feature is especially useful when you have several zones ofthe same type and you want to distinguish between them quickly.

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GridFLUENT 6.1 (3d, segregated, ske)

Nov 29, 2002

Z

Y

X

Figure 9.2: Grid Display for the Multistage Fan

Step 2: Units

1. For convenience, define new units for angular velocity.

The angular velocity for this problem is known in rpm, which is not the default unitfor angular velocity. You will need to redefine the angular velocity units as rpm.

Define −→Units...

(a) Select angular-velocity under Quantities, and rpm under Units.

(b) Close the panel.

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Step 3: Models

1. Keep the default solver settings.

Define −→ Models −→Solver...

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

Define −→ Models −→Viscous...

(a) Under Model, select k-epsilon.

The panel will expand.

(b) Under k-epsilon Model, keep the default Standard option.

(c) Under Near-Wall Treatment, keep the default Standard Wall Functions option.

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Step 4: Mixing Plane

In this step, you will create the mixing plane between the pressure outlet of the rotor andthe pressure inlet of the stator.

Define −→Mixing Planes...

1. Select pressure-outlet-rotor in the Upstream Zone list.

2. Select pressure-inlet-stator in the Downstream Zone list.

3. Click Create.

FLUENT will name the mixing plane by combining the names of the zones selectedas the Upstream Zone and Downstream Zone. This new name will be displayed inthe Mixing Plane list.

The essential idea behind the mixing plane concept is that each fluid zone (statorand rotor) is solved as a steady-state problem. At some prescribed iteration inter-val, the flow data at the mixing plane interface are averaged in the circumferentialdirection on both the rotor outlet and the stator inlet boundaries. FLUENT usesthese circumferential averages to define “profiles” of flow properties. These profilesare then used to update boundary conditions along the two zones of the mixing planeinterface.

In this example, profiles of averaged total pressure (p0), static pressure (ps), direc-tion cosines of the local flow angles in the radial, tangential, and axial directions(αr, αt, αz), total temperature (T0), turbulence kinetic energy (k), and turbulencedissipation rate (ε) are computed at the rotor exit and used to update boundaryconditions at the stator inlet. Likewise, the same profiles, except for that of totalpressure are computed at the stator inlet and used as a boundary condition on the

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rotor exit. You can view the profiles computed at the rotor exit and stator inlet inthe Boundary Profiles panel.

Define −→Profiles...

You will also see that these profiles appear in the boundary conditions panels for therotor exit and stator inlet. See the User’s Guide for more information on mixingplanes.

Step 5: Materials

1. Accept the default properties for air.

Define −→Materials...

For the present analysis, you will model air as an incompressible fluid with a densityof 1.225 kg/m3 and a dynamic viscosity of 1.7894× 10−5 kg/m-s. Since these arethe default values, no change is required in the materials panel.

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Step 6: Boundary Conditions

Define −→Boundary Conditions...

1. Set the conditions for the rotor fluid (fluid-rotor).

(a) Under Rotation-Axis Direction, enter -1 next to Z .

According to the right-hand rule and Figure 9.1, the axis of rotation is the −Zaxis. You specify this by entering the vector (0, 0,−1) for the Rotation-AxisDirection.

(b) Select Moving Reference Frame in the Motion Type drop-down list.

Hint: Use the scroll bar to access Motion Type.

(c) Set the Speed (under Rotational Velocity) to 1800 rpm.

Hint: Use the scroll bar to access Rotational Velocity.

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2. Set the conditions for the stator fluid (fluid-stator).

(a) Under Rotation-Axis Direction, enter -1 next to Z.

3. Specify rotational periodicity for the periodic boundary of the rotor (periodic-11).

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4. Specify rotational periodicity for the periodic boundary of the stator (periodic-22).

5. Set the following conditions for the pressure inlet of the rotor (pressure-inlet-rotor).

To model ambient conditions, you use P0 = 0 gauge. The turbulence level is as-sumed to be low (1% ) and the hydraulic diameter is used as the length scale.

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6. Examine the conditions for the pressure inlet of the stator (pressure-inlet-stator).

The profiles computed at the rotor outlet are used to update the boundary conditionsat the stator inlet. These profiles were set for you automatically when the mixingplane was created. Therefore, you do not need to set any parameters in this panel.

7. Examine the conditions for the pressure outlet of the rotor (pressure-outlet-rotor).

The Backflow Direction Specification Method was set to Direction Vector when youcreated the mixing plane, and the Coordinate System to Cylindrical (like for the statorinlet ). The values for the direction cosines are taken from the profiles at the stator.

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8. Set the conditions for the pressure outlet of the stator (pressure-outlet-stator).

(a) Select Radial Equilibrium Pressure Distribution.

Radial equilibrium is used to simulate the pressure distribution which existsdue to rotation according to

∂p

∂r=ρv2

θ

r

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where vθ is the tangential velocity. This is a good approximation for axial flowconfigurations with 0 straight flow paths (i.e., little change in radius from inletto exit).

(b) Retain the default Backflow Direction Specification Method.

In problems where a backflow exists at the pressure outlet boundary (e.g.,torque-converter), you can use this option to specify the direction of the back-flow.

(c) Select Intensity and Viscosity Ratio for the Turbulence Specification Method.

(d) Set the Backflow Turbulence Intensity to 1%.

(e) Set the Backflow Turbulent Viscosity Ratio to 1.

9. Set the conditions for the inlet hub of the rotor (rotor-inlet-hub).

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(a) Select Moving Wall.

The panel will expand to show the wall motion inputs.

(b) Select Absolute and Rotational under Motion.

(c) Set the Rotation-Axis Direction by entering -1 next to Z.

These conditions set the rotor-inlet-hub to be a stationary wall in the absolute frame.

10. Set the conditions for the shroud of the rotor inlet (rotor-inlet-shroud).

(a) Select Moving Wall.

(b) Select Absolute and Rotational under Motion.

(c) Set the Rotation-Axis Direction by entering -1 next to Z.

These conditions set the rotor-inlet-shroud to be a stationary wall in the absoluteframe.

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11. Set the following conditions for the rotor shroud (rotor-shroud).

(a) Select Moving Wall.

(b) Select Absolute and Rotational under Motion.

(c) Set the Rotation-Axis Direction by entering -1 next to Z.

These conditions set the rotor-shroud to be a stationary wall in the absolute frame.

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12. Accept the default conditions for the rotor-hub.

For a rotating reference frame, FLUENT assumes by default that walls rotate withthe grid, and hence are moving with respect to the stationary (absolute) referenceframe. Since the rotor-hub is rotating, you should keep the default settings.

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Step 7: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Under Discretization, select Second Order Upwind for Momentum.

(b) Select Power Law for Turbulence Kinetic Energy and Turbulence Dissipation Rate.

(c) Set the Under-Relaxation Factors for Pressure to 0.2, Momentum to 0.5, Tur-bulence Kinetic Energy to 0.5, and Turbulence Dissipation Rate to 0.5.

Note: For this problem, it was found that these under-relaxation factors workedwell. See the User’s Guide for tips on how to adjust the under-relaxationparameters for different situations.

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2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click OK.

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

Solve −→ Monitors −→Surface...

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(a) Increase the Surface Monitors value to 1.

(b) Turn on the Plot and Write options for monitor-1.

Note: When the Write option is selected in the Surface Monitors panel, themass flow rate history will be written to a file. If you do not select thewrite option, the history information will be lost when you exit FLUENT.

(c) Click on Define... to specify the surface monitor parameters in the DefineSurface Monitor panel.

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

ii. Select pressure-outlet-stator in the Surfaces list.

iii. Click on OK to define the monitor.

(d) Click on OK in the Surface Monitors panel to enable the monitor.

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4. Initialize the flow field.

Solve −→ Initialize −→Initialize...

(a) Select Absolute under Reference Frame.

For rotor-stator problems, the absolute velocity formulation is superior to therelative velocity formulation, since, at the inlet/outlet boundaries, the absolutevelocity and total pressure are uniform, whereas the corresponding relativeconditions are non-uniform.

(b) Set the initial value for Z Velocity to -1.

(c) Click on Init and close the panel.

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

File −→ Write −→Case...

6. Start the calculation by requesting 800 iterations.

Solve −→Iterate...

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! Calculating until the mass flow rate converges will require significant CPU re-sources. Instead of calculating the solution, you can read the data file (fanstage.dat)with the pre-calculated solution, and proceed to the postprocessing section ofthe tutorial (Step 8). This data file can be found in the directory where youfound the mesh file.

The solution will converge after about 640 iterations. However, the residual historyplot is only one indication of solution convergence. Notice that the mass flow ratehas not reached a constant value. To remedy this, you will reduce the convergencecriterion for the continuity equation and iterate until the mass flow rate reaches aconstant value.

7. Reduce the convergence criterion for the continuity equation.

Solve −→ Monitors −→Residual...

(a) Set the Convergence Criterion for continuity to 1e-05.

(b) Click OK.

Note: In this case, the reason for continuing the calculation is to obtain bet-ter global mass conservation; thus, only the convergence tolerance for thecontinuity equation is adjusted. In general, the convergence behavior ofthe continuity equation is a good indicator of the overall convergence ofthe solution.

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8. Request 2000 more iterations.

Solve −→Iterate...

After about 1400 iterations, the mass flow rate has leveled off and the solution hasconverged. The mass flow rate history is shown in Figure 9.3.

Z

Y

X

Convergence history of Mass Flow Rate on pressure-outlet-statorFLUENT 6.1 (3d, segregated, ske)

Nov 29, 2002

Iteration

(kg/s)RateFlow

Mass

2000180016001400120010008006004002000

-0.0020

-0.0040

-0.0060

-0.0080

-0.0100

-0.0120

-0.0140

-0.0160

-0.0180

-0.0200

-0.0220

Figure 9.3: Mass Flow Rate History

9. Save the data file (fanstage.dat).

File −→ Write −→Data...

10. Check the mass flux balance.

Report −→Fluxes...

! Although the mass flow rate history indicates that the solution is converged,you should also check the mass fluxes through the domain to ensure that massis being conserved.

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(a) Select pressure-outlet-stator, pressure-inlet-stator, pressure-inlet-rotor, and pressure-outlet-rotor under Boundaries.

(b) Keep the default Mass Flow Rate option and click on Compute.

! The net mass imbalance should be a small fraction (say, 0.5%) of the total fluxthrough the system. If a significant imbalance occurs, you should decrease yourresidual tolerances by at least an order of magnitude and continue iterating.

Note: The fluxes for the portions of the rotor and stator that have been modeled aredifferent. However, the flux for the whole rotor and the whole stator are verynearly equal: approximately 0.23274 kg/s (0.02586 × 9 rotor blades), versusapproximately 0.23328 kg/s (0.01944 × 12 stator blades).

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Step 8: Postprocessing

1. Create two surfaces for postprocessing, one at y = 0.12 m and one at z = −0.1 m.

Surface −→Iso-Surface...

The surface y = 0.12 m is a midspan slice through the grid. This view is goodfor looking at the blade-to-blade flow field. The surface z = −0.1 m is an axialplane downstream of the stator. This will be used to plot circumferentially-averagedprofiles.

(a) Select Grid... and Y-Coordinate in the Surface of Constant lists.

(b) Click on Compute to update the minimum and maximum values.

(c) Enter 0.12 in the Iso-Values field.

(d) Enter y=0.12 for the New Surface Name.

(e) Click on Create to create the isosurface.

(f) Select Grid... and Z-Coordinate in the Surface of Constant lists.

(g) Click on Compute to update the minimum and maximum values.

(h) Enter -0.1 in the Iso-Values field.

(i) Enter z=-0.1 for the New Surface Name.

Note: The default name that FLUENT gave the surface, z-coordinate-17, in-dicates that this is surface number 17. This fact will be used later in thetutorial when you plot circumferential averages.

(j) Click on Create to create the isosurface.

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2. Display velocity vectors on the midspan surface y = 0.12.

Display −→Vectors...

(a) Select y=0.12 in the Surfaces list.

(b) Increase the Scale value to 10.

(c) Increase the Skip value to 2.

(d) Select arrow from the Style drop-down list.

(e) Click on Display to plot the velocity vectors.

(f) Rotate and zoom the view to get the display shown in Figure 9.4.

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Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (3d, segregated, ske)

Nov 29, 2002

2.77e+012.63e+012.49e+012.35e+012.22e+012.08e+011.94e+011.80e+011.66e+011.53e+011.39e+011.25e+011.11e+019.73e+008.35e+006.97e+005.58e+004.20e+002.82e+001.44e+005.67e-02

Z

Y X

Figure 9.4: Velocity Vectors on y = 0.12 Near the Stator Blade

Plotting the velocity field in this manner gives a good indication of the midspanflow over the stator. For the rotor, it is instructive to similarly plot the relativevelocity field.

3. Plot a circumferential average of the total pressure on the plane z = −0.1.

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

Note: Surface 17 is the surface z = −0.1 you created earlier. For increased reso-lution, 15 bands are used instead of the default 5.

> plot

/plot> circum-avg-radial

averages of> total-pressure

on surface [] 17number of bands [5] 15

The radial variation in the total pressure can be seen to be very non-uniform in thisplot (Figure 9.5). This implies that losses are largest near the hub.

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Z

Y X

Circumferential AveragesFLUENT 6.1 (3d, segregated, ske)

Nov 29, 2002

Radius

(kg/s)Pressure

Total

0.140.1350.130.1250.120.1150.110.1050.1

3.75e+01

3.50e+01

3.25e+01

3.00e+01

2.75e+01

2.50e+01

2.25e+01

2.00e+01

1.75e+01

1.50e+01

Figure 9.5: Plot of Circumferential Average of the Total Pressure on the Plane z = −0.1.

4. Display filled contours of total pressure.

Display −→Contours...

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(a) Select rotor-blade and rotor-hub in the Surfaces list.

(b) Select Pressure... and Total Pressure in the Contours Of drop-down lists.

(c) Turn on the Filled option.

(d) Click Display.

The pressure contours are displayed in Figure 9.6. Notice the high pressure thatoccurs on the leading edge of the rotor blade due to the motion of the blade.

Contours of Total Pressure (pascal)FLUENT 6.1 (3d, segregated, ske)

Nov 29, 2002

5.38e+024.98e+024.59e+024.20e+023.81e+023.41e+023.02e+022.63e+022.24e+021.84e+021.45e+021.06e+026.65e+012.73e+01-1.20e+01-5.12e+01-9.05e+01-1.30e+02-1.69e+02-2.08e+02-2.48e+02Z

Y

X

Figure 9.6: Contours of Total Pressure for the Rotor Blade and Hub

Summary: This tutorial has demonstrated the use of the mixing plane model for atypical axial flow turbomachine configuration. The mixing plane model is usefulfor predicting steady-state flow in a turbomachine stage, where local interactioneffects (such as wake and shock waves) are secondary. If local effects are important,then an unsteady, sliding mesh calculation is required.

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Tutorial 10. Using Sliding Meshes

Introduction: In this tutorial, the sliding mesh capability of FLUENT is used to predictthe time-dependent flow through a two-dimensional rotor-stator blade row. Thetime-varying rotor-stator interaction is modeled by allowing the mesh associatedwith the moving rotor to translate (slide) relative to the stationary mesh associatedwith the stator blade.

In this tutorial you will learn how to:

• Merge two meshes into a single mesh, using tmerge

• Define boundary conditions and create grid-interface planes for sliding meshsimulations

• Calculate a steady-state solution (using the coupled explicit solver) as aninitial guess for a transient flow prediction

• Calculate a transient solution using the second-order implicit unsteady formu-lation and the coupled explicit solver

• Monitor solution history for time-dependent parameters

• Postprocess and store transient data sets, using the automatic proceduresavailable in FLUENT

Prerequisites: This tutorial assumes that you are familiar with the basic menu structureand solution procedure used by FLUENT and that you have solved Tutorial 1.

Problem Description: The rotor-stator geometry considered in this tutorial is shownin Figure 10.1. The geometry consists of a planar slice through the rotor and statorblades, extracted by unrolling a plane of constant radius (R = 0.686 m) in an axialflow turbomachine. The speed of rotation, 410 RPM, yields a linear velocity of therotor, RΩ, equal to 29.4 m/s, as indicated in the figure. The fluid, assumed to beair, enters the stator row at the specified total pressure and temperature and exitsthe rotor at the specified exit static pressure. The inlet Mach number is 0.07 andthe flow will be treated as compressible.

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Stator Vanes Rotor Blades(stationary) (moving)

direction ofmotion

(V = 29.445 m/s)

blade pitch = 0.1959 m

sliding interface

= 300 KT01

M = 0.07

= 101325 PaP01

= 97576 PaP2

Cx= 0.1524 m

Figure 10.1: Rotor-Stator Problem Description

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Preparation

1. Copy the files slide/rotor.msh and slide/stator.msh from the FLUENT docu-mentation CD to your working directory (as described in Tutorial 1).

Note: The geometries of the rotor and stator flow domains have been meshed separately.This is the usual procedure when the sliding mesh capability is used: separate meshfiles are created for the sliding and stationary mesh regions. This ensures that thesliding interface between the two regions is defined by two separate boundary zoneswhich share no common nodes. The two separate mesh files must be merged priorto reading them into FLUENT, as detailed in Step 1, below.

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Step 1: Merging the Mesh Files

1. Start tmerge by typing utility tmerge -2d at the system prompt.

2. Provide the mesh file names, rotor.msh and stator.msh, as prompted. Providescaling factors of 1 and translations and rotations of zero for each mesh file. Savethe new merged mesh file as slide.msh.

Append 2D grid files.tmerge2D Fluent Inc, Version 2.1.8

Enter name of grid file (ENTER to continue) : rotor.msh

x,y scaling factor, eg. 1 1 : 1 1

x,y translation, eg. 0 1 : 0 0

rotation angle (deg), eg. 45 : 0

Enter name of grid file (ENTER to continue) : stator.msh

x,y scaling factor, eg. 1 1 : 1 1

x,y translation, eg. 0 1 : 0 0

rotation angle (deg), eg. 45 : 0

Enter name of grid file (ENTER to continue) : <ENTER>

Enter name of output file : slide.msh

! The mesh files must be read into tmerge in this order for the tutorial to runas written. Otherwise, zone names and numbers will be assigned differentlywhen the files are merged together. In general, however, you can specify filesto be read into tmerge in any order.

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Step 2: Grid

1. Start the 2D version of FLUENT.

2. Read in the mesh file slide.msh.

File −→ Read −→Case...

3. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

4. Scale the grid.

Grid −→Scale...

(a) Select in in the Units Conversion drop-down list to complete the phrase GridWas Created In in (inches).

(b) Click on Scale to scale the grid.

The final domain extents should appear as in the panel above.

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5. Display the grid (Figure 10.2).

Display −→Grid...

Note: You can use the mouse probe button (right button, by default) to find out theboundary zone labels. As annotated in Figure 10.3, the upstream boundary is apressure inlet, the downstream boundary is a pressure outlet, and the lateral topand bottom boundaries are periodic. The stator blade and stator-side fluid areidentified as wall-7 and fluid-9. The rotor blade and rotor-side fluid are wall-16and fluid-18. (Your mouse probe will report the fluid regions as interior-8 andinterior-17 zones, for the stator and rotor sides, respectively. These are theface zones associated with the fluid regions.)

To determine which fluid zone is the stator-side fluid, you can create the fluid-9 and fluid-18 display surfaces using the Zone Surface panel. Then, display thezones (one at a time) using the Grid Display panel.

If you wish to annotate your own graphics display, you can use the Annotatepanel.

Display −→Annotate...

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 15, 2002

Figure 10.2: Rotor-Stator Mesh Display

fluid-18periodic-15

pressure-outlet-14

wall-16wall-7

pressure-inlet-3

periodic-8

RotorStator

GridFLUENT 6.1 (2d, segregated, lam)

Nov 15, 2002

Figure 10.3: Annotated Mesh

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Step 3: Models

1. Select the coupled explicit solver.

Define −→ Models −→Solver...

Note: Initially, you will solve for the steady flow through the blade passage. Later,after obtaining the steady flow as the starting point for the transient calcula-tion, you will revisit this panel to turn on time-dependent flow.

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2. Enable the standard k-ε turbulence model.

Define −→ Models −→Viscous...

Note: The Reynolds number of the flow is about 105, and the flow will be treatedas fully turbulent.

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Step 4: Materials

1. Select air (the default material) as the fluid material, and use the ideal-gas law tocompute density. Retain the default values for all other properties.

Define −→Materials...

! Don’t forget to click the Change/Create button after selecting ideal-gas in thedrop-down list for Density.

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Step 5: Operating Conditions

1. Set the operating pressure to 0 Pa.

Define −→Operating Conditions...

Here, the operating pressure is set to zero and boundary condition inputs for pressurewill be defined in terms of absolute pressures. Boundary condition inputs shouldalways be relative to the value used for operating pressure.

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Step 6: Boundary Conditions

Define −→Boundary Conditions...

1. Set the conditions for the upstream boundary (pressure-inlet-3).

(a) Change the Zone Name from pressure-inlet-3 to pressure-inlet.

(b) Set the Gauge Total Pressure to 101325 Pa.

(c) Set the Supersonic/Initial Gauge Pressure to 100978.2 Pa.

The inlet static pressure estimate is computed from the assumed inlet totalpressure and Mach number (see Figure 10.1).

(d) Set the Total Temperature to 300 K.

(e) In the Direction Specification Method drop-down list, select Direction Vector.

(f) In the Turbulence Specification Method drop-down list, select Intensity and Hy-draulic Diameter.

(g) Set the Turbulence Intensity to 5%, and the Hydraulic Diameter to 0.1959 m.

The inlet turbulence length scale will be computed using the blade pitch as anequivalent “hydraulic diameter”.

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2. Set the conditions for the exit plane boundary (pressure-outlet-14).

(a) Change the Zone Name from pressure-outlet-14 to pressure-outlet.

(b) Set the Gauge Pressure to 97576 Pa.

(c) Set the Backflow Total Temperature to 300 K.

(d) In the Turbulence Specification Method drop-down list, select Intensity and Hy-draulic Diameter.

(e) Set the Turbulence Intensity to 5%, and the Hydraulic Diameter to 0.1959 m.

Note: The temperature and turbulence conditions you input at the pressure outletwill be used only if flow enters the domain through this boundary. You can setthem equal to the inlet values, as no flow reversal is expected at the domain exitin this problem. In general, however, it is important to set reasonable valuesfor these downstream scalar values, in case flow reversal occurs at some pointduring the calculation.

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3. Keep the default Momentum boundary conditions for the stator blades (wall-7) andthe rotor blades (wall-16).

The velocity of a “non-moving” wall is assumed to match that of the adjacent meshregion, yielding a no-slip condition in the reference frame of the mesh. Thus, FLU-ENT will assume that the stator blade is stationary in the non-moving referenceframe of the stator mesh. Similarly, FLUENT will assume that the rotor blade ismoving at the grid speed in the sliding rotor region. Therefore, you will not modifythe wall velocity of the rotor (wall-16), even though the rotor is moving. The defaultsetting of a non-moving wall is correct and implies zero velocity in the moving ref-erence frame of the sliding region. (The motion of the mesh region will be definedas a boundary condition for the fluid zone, below.)

4. Set the conditions for the stator-side fluid (fluid-9).

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(a) Change the Zone Name from fluid-9 to fluid-stator.

(b) Keep the default selection of air as the Material Name, and the Motion Type asStationary.

Hint: Use the scroll bar to access the Motion Type field.

5. Set the conditions for the rotor-side fluid (fluid-18).

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(a) Change the Zone Name from fluid-18 to fluid-rotor.

(b) Keep the default selection of air as the Material Name, and the Motion Type asStationary.

Later, after solving the steady flow through the non-moving rotor passage, you willreturn to this panel to specify that the rotor zone is sliding, as illustrated in Fig-ure 10.1.

6. Define the zones on the sliding boundary as interface zones.

The sliding grid interface contains two boundary zones: pressure-inlet-12 and pressure-outlet-5. pressure-inlet-12 is the upstream boundary of the rotor-side fluid region,and pressure-outlet-5 is the downstream boundary of the stator-side fluid region.These boundaries were defined as the upstream and downstream boundaries of theoriginal mesh files, rotor.msh and stator.msh, and must be redefined as interfaceboundary types for the merged mesh.

(a) Select pressure-inlet-12 in the Zone list and choose interface as the new Type.

(b) Confirm that it is OK to change the boundary type.

(c) Change the Zone Name to interface-rotor.

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(d) Repeat this procedure to convert pressure-outlet-5 to an interface boundarynamed interface-stator.

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Step 7: Grid Interfaces

In this step, you will create a periodic grid interface between the rotor and stator meshregions.

Define −→Grid Interfaces...

1. Select interface-rotor in the Interface Zone 1 list.

Note: In general, when one interface zone is smaller than the other, it is recom-mended that you choose the smaller zone as Interface Zone 1. In this case,however, since both zones are the same size, the order is not significant.

2. Select interface-stator in the Interface Zone 2 list.

3. Enter the name interface-rotor-stator under Grid Interface.

4. Select Periodic under Interface Type, and click Create.

The interface between the sliding and non-sliding zones will be treated as periodicwhere the two zones are non-overlapping.

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Step 8: Solution: Steady Flow with Non-Moving Ro-tor

1. Initialize the solution for steady flow.

Solve −→ Initialize −→Initialize...

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

(b) Click Init, and Close the panel.

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2. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Set the Courant Number to 2.

Setting the Courant number to 2.0 promotes rapid convergence for the steadyflow simulation. (For more information on the Courant number, see Step 9:Enable Time Dependence and Sliding Rotor Motion).

(b) Change Multigrid Levels to 5.

Five levels of multigrid enable boundary condition information to propagaterapidly across the solution domain.

(c) Under Discretization, select Second Order Upwind for Turbulence Kinetic Energyand Turbulence Dissipation Rate.

Second-order discretization provides optimum accuracy.

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3. Enable the plotting of residuals.

Solve −→ Monitors −→Residual...

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

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4. Enable the monitoring of the lift force on the rotor blade (wall-16).

Note: Monitoring forces on the rotor blade provides a good measure of convergenceduring the initial steady-state flow prediction. Here, you will request dynamicplotting of lift as the solution proceeds. In addition, you will write the liftinformation to a file, cl-hist.ss. You could choose to monitor any othervariable (e.g., mass flow rate), including a custom field function.

Solve −→ Monitors −→Force...

(a) Select Lift in the Coefficient drop-down list.

(b) In the Wall Zones list, select wall-16 (the rotor).

(c) Enable the Plot and Write options.

(d) In the File Name field, enter cl-hist.ss.

(e) Keep the Plot Window set to 1.

(f) Click Apply, and Close the panel.

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5. Set the reference values to be used in the lift coefficient calculation.

Report −→Reference Values...

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

(b) Change the Area to 0.1524 m2.

(c) Change the Length to 0.1524 m (the axial chord length).

6. Save the steady flow case file (slide ss.cas).

File −→ Write −→Case...

7. Start the calculation by requesting 500 iterations.

Solve −→Iterate...

The residual history and lift force history will be displayed as the calculation pro-ceeds. The lift history should be similar to Figure 10.4.

Note: After 500 iterations, the steady flow calculation may not be fully converged.Here, this is not of concern, as the steady-state prediction will be used only asa starting solution for the transient sliding-mesh calculation.

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Lift ConvergenceFLUENT 6.1 (2d, coupled exp, ske)

Nov 15, 2002

Iterations

Cl

500450400350300250200150100500

-2.00e+00

-4.00e+00

-6.00e+00

-8.00e+00

-1.00e+01

-1.20e+01

-1.40e+01

-1.60e+01

Figure 10.4: Lift Coefficient History: Steady Flow, Non-Moving Rotor

8. Save the case and data files (slide ss.cas and slide ss.dat).

File −→ Write −→Case & Data...

Note: If you choose a file name that already exists in the current directory, FLU-ENT will prompt you for confirmation to overwrite the file.

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9. Display the steady flow velocity vectors (Figure 10.5).

Display −→Vectors...

(a) Change the Scale to 10.

(b) Click Display.

The steady flow prediction shows the expected form, with peak velocity of about 140m/s through the passage.

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10. Enable the display of three periodic repeats of the solution domain (Figure 10.5).

Display −→Views...

(a) Set the number of Periodic Repeats to 3.

(b) Under Periodic Repeats, click the Define... button.

This will open the Graphics Periodicity panel.

(c) Click Reset.

This will reset Y Translation to the value shown above.

(d) Click OK in the Graphics Periodicity panel.

(e) In the Views panel, click Apply.

The grid display will be updated to show three periodic repeats. You may need totranslate the display using your mouse to get the view shown in Figure 10.5.

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Velocity Vectors Colored By Velocity Magnitude (m/s) Dec 17, 2002FLUENT 6.1 (2d, coupled exp, ske)

1.42e+02

7.04e-017.78e+001.48e+012.19e+012.90e+013.61e+014.31e+015.02e+015.73e+016.44e+017.14e+017.85e+018.56e+019.26e+019.97e+011.07e+021.14e+021.21e+021.28e+021.35e+02

Figure 10.5: Velocity Vectors: Steady Flow, Non-Moving Rotor

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11. Display the steady flow contours of static pressure (Figure 10.6).

Display −→Contours...

The steady flow prediction shows the expected pressure distribution through the pas-sage, with low pressure on the suction surfaces and stagnation around the impinge-ment point on the rotor.

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Contours of Static Pressure (pascal) Dec 17, 2002FLUENT 6.1 (2d, coupled exp, ske)

1.02e+05

8.83e+048.90e+048.97e+049.04e+049.11e+049.17e+049.24e+049.31e+049.38e+049.45e+049.51e+049.58e+049.65e+049.72e+049.79e+049.86e+049.92e+049.99e+041.01e+051.01e+05

Figure 10.6: Contours of Static Pressure: Steady Flow, Non-Moving Rotor

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Step 9: Enable Time Dependence and Sliding RotorMotion

In this step you will enable the rotor motion by turning on time dependence and settingthe sliding velocity of the rotor fluid zone.

1. Enable a time-dependent flow calculation.

Define −→ Models −→Solver...

(a) Under Time, select Unsteady.

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

Implicit (dual) time-stepping allows you to set the physical time step used for thetransient flow prediction (while FLUENT continues to determine the time step usedfor inner iterations based on a Courant condition). Here, second-order implicittime-stepping is enabled: this provides higher accuracy in time than the first-orderoption.

In explicit (global) time-stepping, FLUENT uses a single time step for the transientcalculation. This time step is based on the Courant condition:

∆t =CFL∆x

λmax

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where CFL is the Courant number. Explicit time-stepping might be the optimumsolution strategy if you are modeling a traveling shock wave, where the Courantcondition is ideal for determination of the time step value.

2. Define the sliding motion of the rotor-side fluid zone (fluid-rotor).

Define −→Boundary Conditions...

(a) Scroll down and select Moving Mesh in the Motion Type drop-down list.

(b) Change the Translational Velocity in the Y direction to -29.445.

3. Save the case file. (slide un.cas).

File −→ Write −→Case...

The mesh changes during the preview so be sure to save the case before mesh pre-view.

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4. Preview the sliding motion of the rotor-side fluid zone.

Solve −→Mesh Motion...

(a) Under Number of Time Steps, enter 50.

(b) Click Preview.

The graphics display will preview the sliding motion of the rotor-stator gridgeometry.

5. Read the case file back into FLUENT.

As the mesh preview option advances the time step, thereby updating the mesh, itis essential to reread the case file to ensure that the mesh is at the proper positionbefore the calculation is started. If the case file is not read again and the solutionis initialized after the mesh preview, the solution time is initialized to zero but themesh does not go back to its original position.

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Step 10: Solution: Unsteady Flow with Moving Rotor

1. Change the Courant number to 1 for the transient calculation.

Solve −→ Controls −→Solution...

The Courant number controls the time step used by FLUENT during the inner iter-ations performed during each time step. A Courant number of 1 is a conservativesetting that should ensure the stability of the inner iterations.

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2. Reset the lift force monitor.

Solve −→ Monitors −→Force...

(a) In the File Name field, enter cl-hist.td.

(b) Click Apply.

(c) Click Clear.

This will remove the lift coefficient data for the steady-state calculation (i.e.,the contents of the file cl-hist.ss) from memory.

(d) Click Yes when asked to confirm the data discard.

! If you do not clear the old force-monitoring data, FLUENT will plot themwith the new data, corrupting the new lift coefficient plot.

(e) Click on the Axes... button.

This will open the Axes - Force Monitor Plot panel.

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(f) Under Axis, select X (the default).

(g) Under Number Format, check that the Type is float.

(h) Set the Precision to 4.

(i) Click Apply.

(j) Under Axis, select Y.

(k) Under Number Format, check that the Type is float and the Precision is 4.

(l) Close the Axes - Force Monitor Plot and Force Monitors panels.

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Note: Monitoring the lift force is an ideal way to determine when the transient flowprediction becomes time-periodic (independent of the initial condition). In thetime-periodic solution, the lift force variation will repeat identically from onepassing period to the next.

3. Set the time step parameters.

Solve −→Iterate...

(a) Set the Time Step Size to 0.0001 second.

(b) Check that the Max Iterations per Time Step is set to 20.

(c) Click Apply.

Note: The selection of the time step is critical for accurate time-dependent flowpredictions. Here, the time step is chosen to be about 1/70 of the passingperiod, T. The passing period is the time it takes for the rotor blade to passfrom one stator blade row to the next:

T = (0.1959 m)/(29.4 m/s) = 6.7× 10−3 sec

Using a time step of 0.0001 second, 67 time steps will be performed as therotor performs one pass.

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! The maximum number of iterations per time step should be set large enoughso that the inner iterations converge before the solution moves to the nexttime value. The value of 20, selected here, is quite small: it is likely thatthe initial time steps will not fully converge within 20 inner iterations. Whilethis would be unsuitable for prediction of most time-dependent flows, the cur-rent simulation does not require high accuracy during the initial time steps.The rotor-stator flow prediction will be continued in time until a time-periodicflow is obtained. Low accuracy during the initial passing periods is acceptableas long as convergence is achieved during each time step of the final passingperiods.

4. Save the transient sliding mesh case file (slide td.cas).

File −→ Write −→Case...

5. Start the transient calculation by requesting 1000 time steps.

! Calculation of 1000 time steps will require significant CPU resources. Insteadof calculating, you can read the case and data files saved after 0.1 seconds:

slide01.cas and slide01.dat

After reading the files, skip to Step 11: Postprocessing at t=0.1 Second. (Thecase and data files are available in the same directory where you found themesh files.)

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By requesting 1000 time steps, you are asking FLUENT to compute until time isequal to 0.1 second. This will include roughly 15 passing periods (15 × 6.7e-3 sec= 0.10 sec). Experience shows that the flow becomes time-periodic after about 12passing periods. The lift history display allows you to confirm this. Your lift forcehistory should be similar to that shown in Figure 10.7. Notice the periodicity of thelift coefficient after approximately 0.05 seconds.

Lift Convergence (Time=1.0000e-01)FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Nov 16, 2002

Time

Cl

0.110.10.090.080.070.060.050.040.030.020.010

5.00e+01

4.00e+01

3.00e+01

2.00e+01

1.00e+01

0.00e+00

-1.00e+01

-2.00e+01

-3.00e+01

Figure 10.7: Lift Coefficient History: Unsteady Flow, Moving Rotor

6. Reset the lift coefficient history range to focus on the periodicity.

Solve −→ Monitors −→Force...

(a) Click the Axes... button.

This will open the Axes - Force Monitor Plot panel.

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i. Under Axis, select X.

ii. Under Options, deselect Auto Range.

iii. Under Range, set the Minimum to 0.02, and the Maximum to 0.1.

iv. Click Apply.

v. Under Axis, select Y.

vi. Under Options, deselect Auto Range.

vii. Under Range, set the Minimum to -9.2, and the Maximum to -7.6.

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viii. Click Apply and Close the panel.

(b) In the Force Monitors panel, click Plot.

In Figure 10.8, you can see the periodicity more clearly.

Lift Convergence History (Time=1.0000e-01)FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Jul 15, 2002

Time

Cl

0.1100.1000.0900.0800.0700.0600.0500.0400.0300.020

-7.4000

-7.6000

-7.8000

-8.0000

-8.2000

-8.4000

-8.6000

-8.8000

-9.0000

-9.2000

Figure 10.8: Lift Coefficient History: Narrowed Range

7. Save the case and data files at t = 0.1 second (slide01.cas and slide01.dat).

File −→ Write −→Case & Data...

! When the sliding mesh model is used, you must save a case file whenever adata file is saved. This is because the case file contains the grid information,which is changing with time.

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Step 11: Postprocessing at t = 0.1 Second

The solution data saved at t = 0.1 second can be reviewed using any of FLUENT’s post-processing features. Time-dependent data are analyzed just like steady-state results: youread a case and data file for each time value of interest. Note that this means you mustsave case and data files (or graphics files) at all intermediate time values for which resultsare of interest. Automatic saving of results during a transient calculation is used in Step12, Saving and Postprocessing Time-Dependent Data Sets.

! For sliding mesh cases, it is important that you read the associated case file wheneveryou read a data file, because the case file contains the grid information, which ischanging with time.

1. Display the velocity vectors at t = 0.1 second (Figure 10.9).

Display −→Vectors...

Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=1.0000e-01) Dec 17, 2002FLUENT 6.1 (2d, coupled exp, ske, unsteady)

9.19e+01

1.60e+006.11e+001.06e+011.51e+011.97e+012.42e+012.87e+013.32e+013.77e+014.23e+014.68e+015.13e+015.58e+016.03e+016.48e+016.94e+017.39e+017.84e+018.29e+018.74e+01

Figure 10.9: Velocity Vectors at T = 0.1 Second: Unsteady Flow

Note: The velocity vectors in Figure 10.9 are displayed with respect to the absolutereference frame (default). If you want to display the vectors with respect tothe moving reference frame, you can select Relative Velocity in the Vectors Ofdrop-down list and select the rotor fluid zone as the Reference Zone in theReference Values panel.

2. Display contours of static pressure at t = 0.1 second (Figure 10.10).

Display −→Contours...

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Contours of Static Pressure (pascal) (Time=1.0000e-01) Dec 17, 2002FLUENT 6.1 (2d, coupled exp, ske, unsteady)

1.01e+05

9.41e+049.45e+049.48e+049.52e+049.56e+049.59e+049.63e+049.66e+049.70e+049.74e+049.77e+049.81e+049.84e+049.88e+049.92e+049.95e+049.99e+041.00e+051.01e+051.01e+05

Figure 10.10: Contours of Static Pressure at Time = 0.1 Second: Unsteady Flow

Note: Slight discontinuities in the pressure contours along the sliding interface areexpected. This is because the contour plotting uses one-sided interpolation oneither side of the sliding plane. This is purely a display issue.

3. Determine the instantaneous total pressure loss through the system.

Report −→Surface Integrals...

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(a) In the Report Type drop-down list, select Mass-Weighted Average.

(b) Select Pressure... and Total Pressure in the Field Variable drop-down lists.

(c) In the Surfaces list, select pressure-outlet.

(d) Click Compute.

The mass-averaged (instantaneous) total pressure at the exit is about 98100Pa, implying a loss of about 3200 Pa from the inlet total pressure of 101325Pa.

4. Plot the instantaneous pressure coefficient on the rotor blade at t = 0.1 second(Figure 10.11).

Plot −→XY Plot...

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(a) Select Pressure... and Pressure Coefficient in the Y Axis Function drop-downlists.

(b) In the Surfaces list, select wall-16.

(c) Click Plot.

Pressure Coefficient (Time=1.0000e-01)FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Nov 15, 2002

Position (m)

CoefficientPressure

0.40.3750.350.3250.30.2750.250.2250.20.175

-2.00e+00

-4.00e+00

-6.00e+00

-8.00e+00

-1.00e+01

-1.20e+01

-1.40e+01

-1.60e+01

-1.80e+01

-2.00e+01

wall-16

Figure 10.11: Pressure Coefficient on the Moving Rotor at Time = 0.1 Second

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Step 12: Saving and Postprocessing Time-DependentData Sets

After 0.1 second, the sliding mesh flow prediction has achieved a time-periodic state. Inorder to study how the flow changes within a single passing period, you will now continuethe time-marching through the next period and save results every 5 time steps.

1. Request saving of case and data files every 5 time steps.

File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 5.

(b) In the Filename field, enter slid.gz.

(c) Click OK.

FLUENT will append the time step value to the file name prefix (slid). Thestandard extensions (.cas and .dat will also be appended. This will yield filenames of the form slid1005.cas and slid1005.dat, where 1005 is the timestep number.

The extension “.gz”, supplied in the panel above, instructs FLUENT to savethe case and data files in compressed format, yielding file names of the formslid1005.cas.gz and slid1005.dat.gz. If you leave off the “.gz” exten-sion, FLUENT will save the files as slid1005.cas and slid1005.dat, etc.

! When the sliding mesh model is used, you must save a case file whenever adata file is saved. This is because the case file contains the grid information,which is changing with time.

Extra: If you want to generate a solution animation by plotting, for example, pres-sure contours every 5 time steps, you can use the Solution Animation panel toset up the animation before you begin the calculation. Tutorial 4 demonstrateshow to do this.

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2. Reset the lift force monitor.

Supplying a new file name eliminates overwriting of the file stored during the pre-vious time steps.

Solve −→ Monitors −→Force...

(a) In the File Name field, enter cl-hist.cyc.

(b) Click Apply.

(c) Click Clear.

This will remove the lift coefficient data for the previous time steps from mem-ory (i.e., cl-hist.td).

(d) Click Yes when asked to confirm the data discard.

(e) Click on the Axes... button to reset the domain and range.

This will open the Axes - Force Monitor Plot panel.

i. Under Axis, select X.

ii. Under Options, select Auto Range.

This will deactivate the Minimum and Maximum range fields.

iii. Click Apply.

iv. Under Axis, select Y.

v. Under Options, select Auto Range.

This will deactivate the Minimum and Maximum range fields.

vi. Click Apply, and Close the Axes - Force Monitor Plot panel.

(f) Close the Force Monitors panel.

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3. Continue the calculation by requesting 70 time steps.

This performs the time-marching iterations for the next passing period, startingfrom the current solution data at time = 0.1 second.

Solve −→Iterate...

Note: Requesting 70 time steps will march the solution through 0.007 seconds, orroughly one passing period. With the autosave and command monitor featuresactive (as defined above), the case, data, and pressure contour plot files will besaved every 0.0005 seconds. The lift history should appear as in Figure 10.12.

Lift Convergence (Time=1.0000e-01)FLUENT 6.1 (2d, coupled exp, ske, unsteady)

Nov 15, 2002

Time

Cl

0.1080.1070.1060.1050.1040.1030.1020.1010.1

-7.70e+00

-7.80e+00

-7.90e+00

-8.00e+00

-8.10e+00

-8.20e+00

-8.30e+00

Figure 10.12: Lift History During the Final Passing Period

4. Examine the results at different time steps within a single passing period.

(a) Read in the case and data files of interest.

File −→ Read −→Case & Data...

(b) Display contours of static pressure.

The display of pressure contours every five time steps will show the time-varying pressure distribution and the motion of the rotor. Examples of twopressure contour plots at t = 0.1030 and t = 1.070 seconds are shown inFigures 10.13 and 10.14, respectively.

Display −→Contours...

Extra: If you generated a solution animation during the calculation as mentionedearlier in this tutorial, you could play it back inside FLUENT to see the pressurecontour animation over time. See Tutorial 4 for details.

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Contours of Static Pressure (pascal) (Time=1.0300e-01) Dec 17, 2002FLUENT 6.1 (2d, coupled exp, ske, unsteady)

1.02e+05

9.42e+049.46e+049.49e+049.53e+049.57e+049.60e+049.64e+049.68e+049.71e+049.75e+049.79e+049.82e+049.86e+049.90e+049.93e+049.97e+041.00e+051.00e+051.01e+051.01e+05

Figure 10.13: Pressure Contours at Time = 0.103 Seconds

Contours of Static Pressure (pascal) (Time=1.0700e-01) Dec 17, 2002FLUENT 6.1 (2d, coupled exp, ske, unsteady)

1.01e+05

9.39e+049.43e+049.47e+049.51e+049.54e+049.58e+049.62e+049.65e+049.69e+049.73e+049.77e+049.80e+049.84e+049.88e+049.91e+049.95e+049.99e+041.00e+051.01e+051.01e+05

Figure 10.14: Pressure Contours at Time = 0.107 Seconds

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Summary: In this tutorial, you have modeled the time-periodic flow involving rotor-stator interaction. You have learned how to merge the separate rotor and statormeshes using tmerge, and to create the grid-interface zones along the sliding inter-face. Similar procedures can be used to tie together meshes for non-sliding meshanalyses.

You have used FLUENT’s time-dependent flow prediction capability, and you havelearned how to set solution parameters for implicit time-stepping. These time-dependent flow prediction procedures can also be applied to other, non-slidingmesh, analyses. The procedures in this tutorial, however, are applicable to time-periodic calculations, in which the initial condition and initial phase of the transientcalculation are treated without concern for time accuracy.

You have also learned how to manage the file saving and graphical postprocessingfor time-dependent flows, using file autosaving and command monitors to automat-ically save solution information as the transient calculation proceeds.

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Tutorial 11. Using Dynamic Meshes

Introduction: This tutorial provides information for performing basic dynamic meshcalculations. In addition to combining the basic mesh-motion schemes, this tutorialwill introduce rigid-body motion of a cell zone. This is useful for a multitude ofrealistic cases with moving meshes.

In this tutorial you will learn how to:

• Use the dynamic mesh capability of FLUENT to solve a simple flow-driven rigid-body motion problem

• Set boundary conditions for internal flow

• Use a compiled user-defined function (UDF) to specify flow-driven rigid-body mo-tion

• Calculate a solution using the segregated solver.

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT, and that you have solved Tutorial 1. Some steps in the setup and solutionprocedure will not be shown explicitly.

Problem Description: The problem to be considered is shown schematically in Fig-ure 11.1. A 2D axisymmetric valve geometry is used, consisting of a pressurizedcavity on the left, driving the motion of a poppet that toggles the flow to the cir-cumferential pressure outlets. A spring force is also acting on the poppet. In thiscase the transient closure of the valve is studied.

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pressure outlets

massflowinlet

movingpoppet

Figure 11.1: Problem Specification

Preparation

1. Copy the files valve.msh, and valve.c from the FLUENT documentation CD toyour working directory (as described in Tutorial 1).

A user-defined function will be used to define the rigid-body motion of the poppetin the valve geometry. This function has already been written (valve.c). You willonly need to compile it within FLUENT.

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read the grid file valve.msh.

File −→ Read −→Case...

2. Check the grid.

Grid −→Check

Note: You should always make sure that the cell minimum volume is not negative,since FLUENT cannot begin a calculation if this is the case.

3. Scale the grid.

Grid −→Scale...

(a) Under Units Conversion, select in from the drop-down list to complete thephrase Grid Was Created In in (inches).

(b) Click Scale to scale the grid.

(c) Click Change Length Units to set inches as the working units for length, andthen close the panel.

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4. Display the grid (Figure 11.2).

Display −→Grid...

GridFLUENT 6.1 (2d, segregated, lam)

Nov 19, 2002

Figure 11.2: Initial Grid for the Valve

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Step 2: Units

1. For convenience, define new units for pressure and mass flow.

In the problem description, pressure, length, and mass flow are specified in psi, in,and gpm, respectively. While the units for length were switched while scaling thegrid in the previous step, psi and gpm are not the default units for pressure andmass flow.

Define −→Units...

(a) Select pressure under Quantities, and psi under Units.

(b) Select mass-flow under Quantities, and click New...

The Define Unit panel will appear.

i. Enter gpm under Unit.

ii. Enter 0.0536265 under Factor.

iii. Click OK.

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Step 3: Models

1. Enable an axisymmetric time-dependent calculation.

Define −→ Models −→Solver...

(a) Under Space, select Axisymmetric.

(b) Select Unsteady under Time.

(c) Keep the default Unsteady Formulation option of 1st-Order Implicit.

! Dynamic mesh simulations currently work only with first-order time ad-vancement.

(d) Click OK.

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

Define −→ Models −→Viscous...

(a) Select k-epsilon as the Model, and retain the default setting of Standard underk-epsilon Model.

(b) Click OK.

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Step 4: Materials

You will create a new material called oil.

Define −→Materials...

1. In the Name field, enter oil.

2. Specify 850 for the Density.

3. Specify 0.17 for the Viscosity.

4. Click Change/Create.

5. Click No when prompted to overwrite air.

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Step 5: Operating Conditions

Set the operating pressure to 0 psi.

Define −→Operating Conditions...

For this problem, you will work with absolute pressures.

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Step 6: Boundary Conditions

Dynamic mesh motion and all related parameters are specified using the items in theDefine/Dynamic Mesh submenu, not through the Boundary Conditions panel. You will setthese conditions in the next step.

Define −→Boundary Conditions...

1. Set the conditions for the mass flow inlet (inlet) as shown in the following figure.

2. Click OK.

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3. Set the conditions for the exit boundary (outlet) as shown in the following figure.

4. Click OK.

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Step 7: Grid Interfaces

In this step, you will create a non-conformal grid interface between the deforming wallscorresponding to the radial boundary of the pressure outlets, and the deforming wall cor-responding to the radial boundary of the deforming fluid zone next to the poppet.

Define −→Grid Interfaces...

1. Select ext intf in the Interface Zone 1 list.

Note that when one interface zone is smaller than the other, it is recommended thatyou choose the smaller zone as Interface Zone 1.

2. Select int int in the Interface Zone 2 list.

3. Enter the name if under Grid Interface.

4. Click Create.

Note: In the process of creating the grid interface, FLUENT creates two new wallboundary zones: wall-22 and wall-23. You will not be able to display thesewalls.

wall-22 is the non-overlapping region of the ext intf zone that results fromthe intersection of the ext intf and int int boundary zones, and is listed un-der Boundary Zone 1 in the Grid Interfaces panel.

wall-23 is the non-overlapping region of the int int zone that results from theintersection of the two interface zones, and is listed under Boundary Zone 2 inthe Grid Interfaces panel.

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Note that in general, you will need to set boundary conditions for these new wallzones, when they are not empty. In this case, default settings are used.

Step 8: Mesh Motion

1. Read in and compile the user-defined function.

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

(a) Under Source Files, click Add...

A Select File panel will open.

(b) In the Select File panel, select the source code valve.c, and click OK.

(c) In the Compiled UDFs panel, click Build.

The user-defined function has already been defined, but it needs to be compiledwithin FLUENT before it can be used in the solver. Here you will create alibrary with the default name of libudf in your working directory. If youwould like to use a different name, you can enter it in the Library Name field.Note that in this case you need to make sure that you will open the correctlibrary in the next step.

(d) Click OK in the dialog box that will appear.

(e) Click Load to load the user-defined function library you just compiled.

! Note that this UDF will write a file called udf loc velo in your workingdirectory. This file will be written just before the first iteration in every timestep, and will contain the location of the CG and the value of the velocity in

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the X direction for that time step. However, the UDF will first attempt toread information from this file. You will need to make sure that if there is afile of this name in your working directory, it contains the correct information,unless you are continuing the iteration process from the last case and data filesyou used.

2. Activate dynamic mesh motion and specify the associated parameters.

Define −→ Dynamic Mesh −→Parameters...

(a) Under Model, select Dynamic Mesh.

Selection of the In-Cylinder option allows input for IC-specific needs, includingvalve and piston motion.

(b) Under Mesh Methods, select Smoothing and Remeshing.

FLUENT will automatically flag the existing mesh zones for use of the differentdynamic mesh methods where applicable.

(c) Set the parameters under Smoothing as follows:

i. Keep the default specification of 1 for the Spring Constant Factor.

ii. Specify 0.7 for the Boundary Node Relaxation.

iii. Keep the default specification of 0.001 for the Convergence Tolerance.

iv. Specify 50 for the Number of Iterations.

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(d) Set the parameters under Remeshing as follows:

i. Under Options, be sure that the Must Improve Skewness option is selected.

ii. Specify 1.1e-13 m3 for the Minimum Cell Volume.

iii. Specify 1.2e-10 m3 for the Maximum Cell Volume.

iv. Specify 0.7 for the Maximum Cell Skewness.

v. Specify 1 for the Size Remesh Interval.

If a cell exceeds these limits, the cell is marked for remeshing. Therefore, youwill always need to specify problem-specific values under Remeshing Parameters.

(e) Click OK.

3. Specify the motion of the poppet, the adjacent walls, and the fluid region left ofthe poppet.

The poppet motion and the motion of the deforming wall side-wall-3 are specified bymeans of the user-defined function valve.

Define −→ Dynamic Mesh −→Zones...

(a) Specify the motion of the poppet.

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

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

iii. Under Motion Attributes, select valve in the Motion UDF/Profile drop-downlist.

iv. Keep the default values of (0, 0) m for C.G. Location, and 0 for C.G.Orientation.

FLUENT will automatically update the position of the CG based on theinput you gave for the motion.

v. Click the Meshing Options tab.

vi. Specify 0.005 in for Cell Height.

vii. Click Create.

(b) Specify the motion of the deforming axis (def axis).

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i. In the Zone Names drop-down list, select def axis.

ii. Under Type, select Deforming.

The panel will expand to show the inputs for a deforming zone.

iii. Click the Geometry Definition tab.

iv. In the Definition drop-down list, select plane.

The panel will expand again to show the inputs for a planar geometry.

v. Under Point on Plane, enter 0, 0.

vi. Under Plane Normal, enter 0, 1.

vii. Click the Meshing Options tab.

viii. Under Methods, keep the default selections of Smoothing and Remeshing,and set the Height to 0.005 in.

ix. Set the Height Factor to 0.4, and keep the default value of 1 for MaximumSkewness.

x. Click Create.

(c) Specify the motion of the deforming wall corresponding to the radial boundaryof the deforming fluid zone next to the poppet (int int).

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

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ii. Under Type, keep the previous selection of Deforming.

iii. Click the Geometry Definition tab.

iv. In the Definition drop-down list, select plane.

The panel will expand again to show the inputs for a planar geometry.

v. Under Point on Plane, enter 0, 0.22625.

vi. Under Plane Normal, keep the previous setting of 0, 1.

vii. Click the Meshing Options tab.

viii. Under Mesh Methods, be sure that Smoothing and Remeshing are selected,and keep the previous settings for Height (0.005 in), Height Factor (0.4),and Maximum Skewness (1).

ix. Click Create.

In many MDM problems, you may want to preview the mesh motion before proceed-ing any further. In this problem, the mesh motion is driven by the pressure exertedby the fluid on the poppet and acting against the inertia of the poppet and the forceof a preloaded spring attached to it. Hence, for this problem, mesh motion in theabsence of a flow field solution is meaningless, and you will not use this featurehere.

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Step 9: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Keep all default discretization schemes and values for under-relaxation factors.

This problem has been found to converge satisfactorily with these default set-tings. Alternatively, you may want to try PISO discretization for Pressure-Velocity Coupling, in conjunction with higher under-relaxation factors.

(b) Click OK.

2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

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3. Request that case and data files are automatically saved every 10 time steps.

File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency and Autosave Data File Frequency to 10.

(b) In the Filename field, enter valve.

When FLUENT saves a file, it will append the time step value to the file nameprefix (valve). The standard extensions (.cas and .dat) will also be ap-pended.

(c) Click OK.

4. Initialize the solution.

You will initialize the flow field at this point in order to be able to display contoursand vectors that you will use to define animations.

Solve −→ Initialize −→Initialize...

(a) Set Gauge Pressure to 80 psi.

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(b) Set Axial Velocity to 3.097237 m/s.

(c) Set Turbulence Kinetic Energy to 0.1438932.

(d) Set Turbulence Dissipation Rate to 16.8147.

(e) Click Init.

5. Create animation sequences for the static pressure contour plots and velocity vectorsplots in the valve.

You will use FLUENT’s solution animation feature to save contour plots of temper-ature every 5 time steps. After the calculation is complete, you will use the solutionanimation playback feature to view the animated temperature plots over time.

Solve −→ Animate −→Define...

(a) Increase the number of Animation Sequences to 2.

(b) Under Name, enter pressure for the first animation, and vv for the secondone.

(c) Under Every, increase the number to 2 for both sequences.

The default value of 1 instructs FLUENT to update the animation sequence atevery time step. For this case, this would generate a large number of files.

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

(e) Define the animation sequence for pressure.

i. Click Define... on the line for pressure to set the parameters for thesequence.

The Animation Sequence panel will open.

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ii. Under Storage Type, keep the default selection of Metafile.

Note: If you want to store the plots in a directory other than your workingdirectory, enter the directory path in the Storage Directory field. Ifthis field is blank (the default), the files will be saved in your workingdirectory (i.e., the directory where you started FLUENT).

iii. Increase the Window number to 1 and click Set.

Graphics window number 1 will open.

iv. Under Display Type, select Contours.

The Contours panel will open.

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A. Under Options, turn on Filled.

B. In the Contours Of drop-down lists, select Pressure... and Static Pres-sure.

C. Click Display.

Contours of Static Pressure (psi) (Time=0.0000e+00)FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Nov 19, 2002

8.00e+017.67e+017.35e+017.02e+016.69e+016.37e+016.04e+015.71e+015.39e+015.06e+014.74e+014.41e+014.08e+013.76e+013.43e+013.10e+012.78e+012.45e+012.12e+011.80e+011.47e+01

Figure 11.3: Contours of Static Pressure at t = 0 s

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v. Click OK in the Animation Sequence panel.

The Animation Sequence panel will close, and the checkbox in the Activecolumn next to pressure in the Solution Animation panel will become se-lected.

vi. Click OK in the Solution Animation panel.

(f) Define the animation sequence for the velocity vectors.

i. Click Define... on the line for vv to set the parameters for the sequence.

The Animation Sequence panel will open.

ii. Under Storage Type, keep the default selection of Metafile.

iii. Increase the Window number to 2 and click Set.

Graphics window number 2 will open.

iv. Under Display Type, select Vectors.

The Vectors panel will open.

v. Click Display in the Vectors panel.

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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=0.0000e+00) Dec 17, 2002FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

3.10e+00

3.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+003.10e+00

Figure 11.4: Vectors of Velocity at t = 0 s

vi. Click OK in the Animation Sequence panel.

The Animation Sequence panel will close, and the checkbox in the Activecolumn next to vv in the Solution Animation panel will become selected.

vii. Click OK in the Solution Animation panel.

6. Set the time step parameters for the calculation.

Solve −→Iterate...

(a) Set the Time Step Size to 4e-6 s.

(b) Increase the Max Iterations per Time Step to 100.

In the accurate solution of a real-life time-dependent CFD problem, it is impor-tant to make sure that the solution converges at every time step to within thedesired accuracy. Here the first few time steps will only come to a reasonablyconverged solution.

(c) Click Apply.

This will save the time step size to the case file (the next time a case file issaved).

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7. Save the initial case and data files (valve.cas and valve.dat).

File −→ Write −→Case & Data...

8. Request 80 time steps.

Solve −→Iterate...

Extra: If you decide to read in the case file that is provided for this tutorial on thedocumentation CD, you will need to compile the UDF associated with this tutorialin your working directory. This is necessary because FLUENT will expect to findthe correct UDF libraries in your working directory when reading the case file.

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Step 10: Postprocessing

1. Inspect the solution at the final time step.

(a) Inspect the contours of static pressure in the valve (Figure 11.5).

Contours of Static Pressure (psi) (Time=3.2000e-04)FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Nov 22, 2002

1.74e+041.61e+041.47e+041.34e+041.20e+041.07e+049.34e+038.00e+036.65e+035.30e+033.95e+032.61e+031.26e+03-8.73e+01-1.43e+03-2.78e+03-4.13e+03-5.48e+03-6.82e+03-8.17e+03-9.52e+03

Figure 11.5: Contours of Static Pressure After 80 Time Steps

(b) Inspect the velocity vectors in the valve (Figure 11.6).

2. Optionally, inspect the solution at different intermediate time steps.

(a) Read in the corresponding case and data files (valve....cas and valve....dat).

File −→ Read −→Case & Data...

(b) Display the desired contours and vectors.

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Velocity Vectors Colored By Velocity Magnitude (m/s) (Time=3.2000e-04)FLUENT 6.1 (axi, segregated, dynamesh, ske, unsteady)

Nov 22, 2002

1.50e+041.42e+041.35e+041.27e+041.20e+041.12e+041.05e+049.74e+038.99e+038.24e+037.49e+036.74e+035.99e+035.24e+034.49e+033.75e+033.00e+032.25e+031.50e+037.49e+022.87e-01

Figure 11.6: Velocity Vectors After 80 Time Steps

3. Play back the animation of the pressure contours.

Solve −→ Animate −→Playback...

(a) In the Sequences list, select pressure.

The playback control buttons will become active.

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(b) Set the slider bar above Replay Speed about halfway in between Slow and Fast.

(c) Keep the default settings in the rest of the panel and click the play button(the second from the right in the group of buttons under Playback).

See Tutorial 4 in the Tutorial Guide and Section 24.17 of the User’s Guidefor additional information on animating the solution.

4. Play back the animation of the velocity vectors.

Solve −→ Animate −→Playback...

(a) In the Sequences list, select vv.

(b) Keep the default settings in the rest of the panel and click the play button.

Summary: In this tutorial you learned how to use the dynamic mesh feature of FLUENTto simulate the rigid-body motion of a valve poppet in a flow field, driven by theflow-generated forces, and spring and inertial forces, by means of a user definedfunction (UDF).

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Tutorial 12. Modeling Species Transportand Gaseous Combustion

Introduction: This tutorial examines chemical species mixing and combustion of agaseous fuel. A cylindrical combustor burning methane (CH4) in air is studiedusing the finite-rate chemistry model in FLUENT.

In this tutorial you will learn how to:

• Enable physical models, select material properties, and define boundary con-ditions for a turbulent flow with chemical species mixing and reaction

• Initiate and solve the combustion simulation using the segregated solver

• Compare the results computed with constant and variable specific 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 Tutorial 1 and are fa-miliar with the FLUENT interface. It also assumes that you have developed a basicfamiliarity with the solution of turbulent flows using FLUENT. You may find ithelpful to read about chemical reaction modeling in the User’s Guide. Otherwise,no previous experience with chemical reaction or combustion modeling is assumed.

Problem Description: The cylindrical combustor considered in this tutorial is shownin Figure 12.1. The flame considered is a turbulent diffusion flame. A small nozzlein the center of the combustor introduces methane at 80 m/s. Ambient air entersthe combustor coaxially at 0.5 m/s. The overall equivalence ratio is approximately0.76 (about 28% excess air). The high-speed methane jet initially expands withlittle interference from the outer wall, and entrains and mixes with the low-speedair. The Reynolds number based on the methane jet diameter is approximately5.7× 103.

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Methane, 80 m/s, 300K

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

1.8 m

0.22

5m

0.00

5m

CL

Figure 12.1: Combustion of Methane Gas in a Turbulent Diffusion Flame Furnace

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Background: In this tutorial, you will use the generalized finite-rate chemistry modelto analyze the methane-air combustion system. The combustion will be modeledusing a global one-step reaction mechanism, assuming complete conversion of thefuel to CO2 and H2O. The reaction equation is

CH4 + 2O2 → CO2 + 2H2O (12.1)

This reaction will be defined in terms of stoichiometric coefficients, formation en-thalpies, and parameters that control the reaction rate. The reaction rate will bedetermined assuming that turbulent mixing is the rate-limiting process, with theturbulence-chemistry interaction modeled using the eddy-dissipation model.

Preparation

1. Copy the file gascomb/gascomb.msh from the FLUENT documentation CD to yourworking directory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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Step 1: Grid

1. Read the grid file gascomb.msh.

File −→ Read −→Case...

After reading the grid file, FLUENT will report that 1615 quadrilateral fluid cellshave been read, along with a number of boundary faces with different zone identi-fiers.

2. Check the grid.

Grid −→Check

The grid check lists the minimum and maximum x and y values from the grid,and reports on a number of other grid features that are checked. Any errors in thegrid would be reported at this time. For instance, the cell volumes must never benegative. Note that the domain extents are reported in units of meters, the defaultunit of length in FLUENT. Since this grid was created in units of millimeters, theScale Grid panel will be used to scale the grid into meters.

3. Scale the grid.

Grid −→Scale...

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

(b) Click on Scale and confirm that the maximum x and y values are 1.8 and 0.225meters, respectively, as indicated in Figure 12.1.

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

4. Display the grid.

Display −→Grid...

Extra: You can use the right mouse button to check which zone number correspondsto each boundary. If you click the right mouse button on one of the boundariesin the graphics window, its zone number, name, and type will be printed in theFLUENTconsole window. This feature is especially useful when you have severalzones of the same type and you want to distinguish between them quickly.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 12, 2002

Figure 12.2: The Quadrilateral Grid for the Combustor Model

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Step 2: Models

1. Define the domain as axisymmetric, and keep the default (segregated) solver.

Define −→ Models −→Solver...

2. Enable the k-ε turbulence model.

Define −→ Models −→Viscous...

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The panel will expand to provide further options. Click OK to accept the defaultStandard 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...

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(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 mixtures that exist inthe FLUENT database. By selecting one of the pre-defined mixtures, you areaccessing a complete description of the reacting system. The chemical speciesin the system and their physical and thermodynamic properties are defined byyour selection of the mixture material. You can alter the mixture materialselection or modify the mixture material properties 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 under the assumptionthat chemical kinetics are fast compared to the rate at which reactants aremixed by turbulent fluctuations (eddies).

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(e) Click OK.

After you click OK in the Species Model panel, a warning about the symmetryzone 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 treated using the axisboundary condition instead of symmetry. You will change the symmetry zoneto an axis boundary in Step 4: Boundary Conditions.

The console window will also list the properties that are required for the modelsyou have enabled. You will see an Information dialog box, reminding you toconfirm the property values that have been extracted from the database.

(f) Click OK to continue.

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Step 3: Materials

Define −→Materials...

The Materials panel shows the mixture material, methane-air, that was enabled in theSpecies Model panel. The properties for this mixture material have been copied from theFLUENT database and can be modified by you.

Here, you will modify the default setting for the mixture by enabling the gas law. Bydefault, the mixture material uses constant properties: you will retain this constant prop-erty assumption for now, allowing only the mixture density to vary with temperature andcomposition. The influence of variable property inputs on the combustion prediction willbe examined in 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.

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You can add or remove species from the mixture material using this panel. Here,the species that make up the methane-air mixture are predefined and require nomodification.

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

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

This will open the Reactions panel.

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The eddy-dissipation reaction model ignores chemical kinetics (the Arrhenius rate)and uses only the Mixing Rate parameters in the Reactions panel. The ArrheniusRate section of the panel is therefore inactive. (The Rate Exponent and ArrheniusRate entries are included in the database and are employed when the alternate finite-rate/eddy-dissipation model is used.) See the User’s Guide for details.

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

6. In the Materials panel, select constant from the drop-down list next to Cp and enter1000 for the specific heat value.

7. Use the scroll bar to review the remaining properties. Click on the Change/Createbutton to accept the material property settings and then Close the panel.

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As noted above, the initial calculation will be performed assuming that all properties exceptdensity are constant. Using constant transport properties (viscosity, thermal conductivity,and mass diffusion coefficients) is acceptable here because the flow is fully turbulent. Themolecular transport properties will play a minor role compared to turbulent transport. Theassumption of constant specific heat, in contrast, has a strong effect on the combustionsolution, and you will change this property definition in Step 6: Solution Using Non-Constant Heat Capacity.

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Step 4: Boundary Conditions

1. Convert the symmetry zone to the axis type.

The symmetry zone must be converted to an axis to prevent numerical difficultieswhere the radius goes to zero.

Define −→Boundary Conditions...

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

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

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

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

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

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

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(a) Rename this zone fuel-inlet and assign inlet conditions as shown in thepanel.

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

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Note: The Backflow values in this panel are utilized only when backflow occursat the pressure outlet. Reasonable values should always be assigned, sincebackflow may occur during intermediate iterations and could affect the solutionstability.

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

Hint: Use the mouse-probe method described above for the air inlet to determinewhich zone corresponds to the outer wall. The outer wall zone will be selectedin the Boundary Conditions panel once the outer wall boundary is probed.

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

(b) Set the thermal condition to Temperature and keep the default temperature of300 K.

(c) Retain the default settings in the Momentum and Species sections of the panel.

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

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

(b) Accept the default thermal condition of Heat Flux with a value of zero (adia-batic wall).

(c) Retain the default settings in the Momentum and Species sections of the panel.

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Step 5: Initial Solution Using Constant Heat Capacity

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 Mass Fraction 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 fuel content willallow the combustion reaction to begin. The initial condition acts as a numer-ical “spark” to ignite the methane-air mixture. This initialization is especiallycritical when you include finite-rate kinetics in the overall reaction rate.

2. Set the under-relaxation factors.

The default under-relaxation parameters in FLUENT are set to high values. Fora combustion model it may be necessary to reduce the under-relaxation to stabilizethe solution. Some experimentation is typically necessary to establish the opti-mal under-relaxation. For this tutorial it is sufficient to reduce the species under-relaxation to 0.9.

Solve −→ Controls −→Solution...

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

3. Turn on residual plotting during the calculation.

Solve −→ Monitors −→Residual...

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(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 binaryfile.

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

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

5. Start the calculation by requesting 500 iterations.

Solve −→Iterate...

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The solution converges in about 350 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 file is to be overwrit-ten.

7. Review the current state of the solution by viewing contours of temperature (Fig-ure 12.3).

Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-downlist.

(b) Click Display.

The temperature contours are shown in Figure 12.3. The peak temperature, pre-dicted using a constant heat capacity of 1000 J/kg-K, is over 3000 K. This over-prediction of the flame temperature can be remedied by a more realistic model forthe temperature and composition dependence of the heat capacity, as illustrated inthe next step of the tutorial.

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Contours of Static Temperature (k)FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

3.08e+032.94e+032.80e+032.66e+032.52e+032.38e+032.24e+032.11e+031.97e+031.83e+031.69e+031.55e+031.41e+031.27e+031.13e+039.94e+028.56e+027.17e+025.78e+024.39e+023.00e+02

Figure 12.3: Temperature Contours: Constant cp

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Step 6: Solution Using Non-Constant Heat Capacity

As noted above, the strong temperature and composition dependence of the specific heatwill have a significant impact on the predicted flame temperature. In this step you willuse the temperature-varying property information in the FLUENT database to recomputethe solution.

1. Enable composition dependence of the specific heat.

Define −→Materials...

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

(b) Click on the Change/Create button to render the mixture specific heat basedon a local mass-fraction-weighted average of all the species.

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

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

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

(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.

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

The default coefficients describe the polynomial cp(T ) and are extractedfrom the FLUENT property database.

ii. Click on Change/Create in the Materials panel to accept the change inproperties for CO2.

(d) Repeat steps (b) and (c) above for the remaining species (CH4, N2, O2, andH2O). Remember to click on Change/Create to accept the change for eachspecies.

3. Request 500 more iterations.

Solve −→Iterate...

Note: The residuals will jump significantly as the solution adjusts to the new spe-cific heat representation. The solution converges after about 300 additionaliterations.

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

File −→ Write −→Case & Data...

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Step 7: Postprocessing

Review the solution by examining graphical displays of the results and performing surfaceintegrations at the combustor exit.

1. View contours of temperature (Figure 12.4).

Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-downlist.

(b) Click Display.

The temperature contours are shown in Figure 12.4. The peak temperature hasdropped to about 2300 K as a result of the temperature- and composition-dependentspecific heat.

Contours of Static Temperature (k)FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

2.30e+032.20e+032.10e+032.00e+031.90e+031.80e+031.70e+031.60e+031.50e+031.40e+031.30e+031.20e+031.10e+031.00e+039.01e+028.01e+027.01e+026.00e+025.00e+024.00e+023.00e+02

Figure 12.4: Temperature Contours: Variable cp

2. Plot contours of specific heat (Figure 12.5).

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

Display −→Contours...

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

(b) Click Display.

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The contours are shown in Figure 12.5. The mixture specific heat is largest wherethe CH4 is concentrated, near the fuel inlet, and where the temperature and com-bustion product concentrations are large. The increase in heat capacity, relative tothe constant value used before, substantially lowers the peak flame temperature.

Contours of Specific Heat (Cp) (j/kg-k)FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

2.77e+032.68e+032.59e+032.50e+032.41e+032.33e+032.24e+032.15e+032.06e+031.98e+031.89e+031.80e+031.71e+031.62e+031.54e+031.45e+031.36e+031.27e+031.19e+031.10e+031.01e+03

Figure 12.5: Contours of Specific Heat

3. Display velocity vectors (Figure 12.6).

Display −→Vectors...

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(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 magnitude varies dramatically.With fixed length vectors, the velocity magnitude is described only by colorinstead of by both vector length and color.

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

The velocity vectors are shown in Figure 12.6.

Velocity Vectors Colored By Velocity Magnitude (m/s)FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

8.24e+017.83e+017.42e+017.01e+016.60e+016.19e+015.78e+015.37e+014.96e+014.55e+014.14e+013.73e+013.32e+012.91e+012.50e+012.09e+011.68e+011.27e+018.59e+004.49e+003.86e-01

Figure 12.6: Velocity Vectors: Variable cp

4. Plot contours of stream function (Figure 12.7).

Display −→Contours...

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

(b) Click Display.

The stream function contours are shown in Figure 12.7. The entrainment of airinto the high-velocity methane jet is clearly visible in the streamline display.

5. Plot contours of mass fraction for each species.

Display −→Contours...

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

(b) Turn on the Filled button under Options.

(c) Click Display.

The CH4 mass fraction contours are shown in Figure 12.8.

(d) Repeat for the remaining species.

The mass fraction contours for O2, CO2, and H2O are shown in Figures 12.9, 12.10,and 12.11.

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Contours of Stream Function (kg/s)FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

1.55e-021.47e-021.39e-021.31e-021.24e-021.16e-021.08e-021.00e-029.27e-038.50e-037.73e-036.95e-036.18e-035.41e-034.64e-033.86e-033.09e-032.32e-031.55e-037.73e-040.00e+00

Figure 12.7: Stream Function Contours: Variable cp

Contours of Mass fraction of ch4FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

1.00e+009.50e-019.00e-018.50e-018.00e-017.50e-017.00e-016.50e-016.00e-015.50e-015.00e-014.50e-014.00e-013.50e-013.00e-012.50e-012.00e-011.50e-011.00e-015.00e-020.00e+00

Figure 12.8: CH4 Mass Fraction

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Contours of Mass fraction of o2FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

2.30e-012.19e-012.07e-011.96e-011.84e-011.73e-011.61e-011.50e-011.38e-011.27e-011.15e-011.04e-019.20e-028.05e-026.90e-025.75e-024.60e-023.45e-022.30e-021.15e-020.00e+00

Figure 12.9: O2 Mass Fraction

Contours of Mass fraction of co2FLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

1.46e-011.38e-011.31e-011.24e-011.17e-011.09e-011.02e-019.47e-028.75e-028.02e-027.29e-026.56e-025.83e-025.10e-024.37e-023.64e-022.92e-022.19e-021.46e-027.29e-030.00e+00

Figure 12.10: CO2 Mass Fraction

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Contours of Mass fraction of h2oFLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

1.19e-011.13e-011.07e-011.01e-019.55e-028.95e-028.35e-027.76e-027.16e-026.56e-025.97e-025.37e-024.77e-024.18e-023.58e-022.98e-022.39e-021.79e-021.19e-025.97e-030.00e+00

Figure 12.11: H2O Mass Fraction

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6. Determine the average exit temperature and velocity.

Report −→Surface Integrals...

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

(b) Select Temperature... and Static Temperature in the Field Variable drop-downlist.

The mass-averaged temperature will be computed as

T =

∫Tρ~v · d ~A∫ρ~v · d ~A

(12.2)

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

(d) Click Compute.

The mass-weighted average exit temperature is about 1796 K.

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

The area-weighted velocity-magnitude average will be computed as

v =1

A

∫v dA (12.3)

(f) Click Compute.

The area-averaged exit velocity is about 3.14 m/s.

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Step 8: NOx Prediction

In this section you will extend the FLUENT model to include the prediction of NOx. Youwill first calculate the formation of both thermal and prompt NOx, then calculate eachseparately to determine the contribution of 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 under Turbulence Interac-tion to enable the turbulence-chemistry interaction.

If turbulence interaction is not enabled, you will be computing NOx formationwithout considering the important influence of turbulent fluctuations on thetime-averaged reaction rates.

(c) Select Partial-equilibrium in the [O] Model drop down list under Thermal NOParameters.

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

(d) Set the Equivalence Ratio to 0.76 under Prompt NO Parameters, and keep thedefault Fuel Species and Fuel Carbon Number.

The equivalence ratio defines the fuel-air ratio (relative to stoichiometric con-ditions) and is used in the calculation of prompt NOx formation. The FuelCarbon Number is the number of carbon atoms per molecule of fuel and is used

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in the prompt NOx prediction. The Fuel Species designation is also used in theprompt NOx model.

(e) Click OK to accept these changes.

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

Solve −→ Controls −→Solution...

(a) In the Equations list, deselect all variables except the NO species.

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

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

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

Solve −→ Monitors −→Residual...

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

4. Request 50 more iterations.

Solve −→Iterate...

The solution converges in about 10 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 12.12).

Display −→Contours...

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

(b) Deselect Filled under Options and click Display.

The NO mass fraction contours are shown in Figure 12.12. The peak con-centration of NO is located in a region of high temperature where oxygen andnitrogen are available.

7. Calculate the average exit NO mass fraction.

Report −→Surface Integrals...

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Contours of Mass fraction of NOFLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

4.93e-034.68e-034.43e-034.19e-033.94e-033.69e-033.45e-033.20e-032.96e-032.71e-032.46e-032.22e-031.97e-031.72e-031.48e-031.23e-039.85e-047.39e-044.93e-042.46e-040.00e+00

Figure 12.12: Contours of NO Mass Fraction: Prompt and Thermal NOx

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

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

(c) Click Compute.

The mass-weighted average exit NO mass fraction is about 0.00469.

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

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

(a) Turn off Prompt NO under Models to disable the prompt NOx mechanism, andclick OK.

(b) Request 50 iterations.

Solve −→Iterate...

The solution converges in about 10 iterations.

(c) Review the thermal NOx solution by viewing contours of NO mass fraction(Figure 12.13).

Display −→Contours...

i. Check that NOx... and Mass fraction of NO are selected in the ContoursOf drop-down list.

ii. Click Display.

The NO mass fraction contours are shown in Figure 12.13. The concen-tration of NO is slightly lower without the prompt NOx mechanism.

Contours of Mass fraction of NOFLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

4.89e-034.65e-034.40e-034.16e-033.91e-033.67e-033.42e-033.18e-032.93e-032.69e-032.45e-032.20e-031.96e-031.71e-031.47e-031.22e-039.78e-047.34e-044.89e-042.45e-040.00e+00

Figure 12.13: Contours of NO Mass Fraction: Thermal NOx Formation

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

Report −→Surface Integrals...

Hint: Follow the same procedure you used earlier for the calculation with boththermal and prompt NOx formation.

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The mass-weighted average exit NO mass fraction, with thermal but no promptNOx formation, is about 0.00457.

9. Solve for prompt NOx production only.

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

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

(b) Request 50 iterations.

The solution converges in about 10 iterations.

Solve −→Iterate...

(c) Review the prompt NOx solution by viewing contours of NO mass fraction(Figure 12.14).

Display −→Contours...

The NO mass fraction contours are shown in Figure 12.14. The prompt NOx

mechanism is most significant in fuel-rich flames. In this case the flame islean and prompt NO production is low.

Contours of Mass fraction of NOFLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

8.87e-058.43e-057.98e-057.54e-057.10e-056.65e-056.21e-055.77e-055.32e-054.88e-054.44e-053.99e-053.55e-053.11e-052.66e-052.22e-051.77e-051.33e-058.87e-064.44e-061.95e-28

Figure 12.14: Contours of NO Mass Fraction: Prompt NOx Formation

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

Report −→Surface Integrals...

Hint: Follow the same procedure you used earlier for the calculation with boththermal and prompt NOx formation.

The mass-weighted average exit NO mass fraction, with only prompt NOx for-mation, is about 0.000071.

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Note: The individual thermal and prompt NO mass fractions do not add upto the levels predicted with the two models combined. This is becausereversible reactions are involved. NO produced in one reaction can bedestroyed in another 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(12.4)

where

NO mole fraction =NO mass fraction×mixture MW

30(12.5)

and the mixture molecular weight is

mixture MW =1∑

i

mass fractionMW

(12.6)

where MW is the molecular weight of each species.

First you will create a function for Equation 12.6. Then you will substitute Equa-tion 12.5 into Equation 12.4 and create a function for Equation 12.4.

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

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

ii. Select Species... and Mass fraction of ch4 in the Field Functions drop-downlist. Click Select to add this variable to the field function Definition.

iii. Click on / and then click on 1 and 6 to enter 16 (the molecular weight ofmethane).

iv. Continue in this fashion to complete the definition of the mixture molec-ular 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 variable list.

(b) Create a field function for NO ppm.

i. Select NOx... and Mass fraction of NO in the Field Functions drop-downlist. Click Select to add this variable to the field function Definition.

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

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

iv. Click on / and then click on 3 and 0 to enter 30 (the molecular weight ofNO).

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 panel above.

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

ix. Click Define to add the new field function to the variable list.

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11. Plot contours of NO ppm (Figure 12.15).

Display −→Contours...

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

(b) Click Display.

The NO ppm contours are shown in Figure 12.15. The contours closely re-semble the mass fraction contours (Figure 12.14), as expected.

Contours of no-ppmFLUENT 6.1 (axi, segregated, spe5, ske)

Nov 12, 2002

2.24e+022.13e+022.01e+021.90e+021.79e+021.68e+021.57e+021.45e+021.34e+021.23e+021.12e+021.01e+028.95e+017.83e+016.71e+015.59e+014.48e+013.36e+012.24e+011.12e+013.11e-22

Figure 12.15: Contours of NO ppm: Prompt NOx Formation

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Summary: In this tutorial you used FLUENT to model the transport, mixing, and reac-tion of chemical species. The reaction system was defined by using and modifyinga mixture-material entry in the FLUENT database. The procedures used here forsimulation of hydrocarbon combustion can be applied to other reacting flow sys-tems.

This exercise illustrated the important role of the mixture heat capacity in theprediction of flame temperature. The combustion modeling results are summarizedin the following table. (Note that some of the values in the table were not explicitlycalculated during the tutorial.)

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

Constant cp 3077 2198 3.83Variable cp 2301 1796 3.14

The use of a constant cp results in a significant overprediction of the peak temper-ature. The average exit temperature and velocity are also overpredicted.

While the variable cp solution produces dramatic improvements in the predictedresults, further improvements are possible by considering additional models andfeatures available in FLUENT, as discussed below.

The NOx production in this case was dominated by the thermal NO mechanism.This mechanism is very sensitive to temperature. Every effort should be made toensure that the temperature solution is not overpredicted, since this will lead tounrealistically high predicted levels of NO.

Further Improvements: Further improvements can be expected by including the ef-fects of intermediate species and radiation, both of which will result in lower pre-dicted combustion temperatures.

The single-step reaction process used in this tutorial cannot account for the moder-ating effects of intermediate reaction products, such as CO and H2. Multiple-stepreactions can be used to address these species. If a multi-step Magnussen model isused, considerably more computational effort is required to solve for the additionalspecies. Where applicable, the non-premixed combustion model can be used toaccount for intermediate species at a reduced computational cost. See the User’sGuide for more details on the non-premixed combustion model.

Radiation heat transfer tends to make the temperature distribution more uniform,thereby lowering the peak temperature. In addition, radiation heat transfer tothe wall can be very significant (especially here, with the wall temperature setat 300 K). The large influence of radiation can be anticipated by computing theBoltzmann number for the flow:

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Bo =(ρUcp)inlet

σT3AF

∼ convection

radiation

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

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Tutorial 13. Using the Non-PremixedCombustion Model

Introduction: A pulverized coal combustion simulation involves modeling a continuousgas phase flow field and its interaction with a discrete phase of coal particles.The coal particles, traveling through the gas, will devolatilize and undergo charcombustion, creating a source of fuel for reaction in the gas phase. Reaction can bemodeled using either the species transport model or the non-premixed combustionmodel. In this tutorial you will model a simplified coal combustion furnace usingthe non-premixed combustion model for the reaction chemistry.

In this tutorial you will learn how to:

• Prepare a PDF table for a pulverized coal fuel using the prePDF preprocessor

• Define FLUENT inputs for non-premixed combustion chemistry modeling

• Define a discrete second phase of coal particles

• Solve a simulation involving reacting discrete phase coal particles

The non-premixed combustion model uses a modeling approach that solves trans-port equations for one or two conserved scalars, the mixture fractions. Multiplechemical species, including radicals and intermediate species, may be included inthe problem definition and their concentrations will be derived from the predictedmixture fraction distribution. Property data for the species are accessed througha chemical database and turbulence-chemistry interaction is modeled using a Betaor double-delta probability density function (PDF). See the User’s Guide for moredetail on the non-premixed combustion modeling approach.

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT, and that you have solved Tutorial 1 or its equivalent. Some steps in thesetup and solution procedure will not be shown explicitly.

Problem Description: The coal combustion system considered in this tutorial is asimple 10 m by 1 m two-dimensional duct depicted in Figure 13.1. Only half ofthe domain width is modeled because of symmetry. The inlet of the 2D duct issplit into two streams. A high-speed stream near the center of the duct enters at50 m/s and spans 0.125 m. The other stream enters at 15 m/s and spans 0.375 m.Both streams are air at 1500 K. Coal particles enter the furnace near the centerof the high-speed stream with a mass flow rate of 0.1 kg/s (total flow rate in the

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furnace is 0.2 kg/s). The duct wall has a constant temperature of 1200 K. TheReynolds number based on the inlet dimension and the average inlet velocity isabout 100,000. Thus, the flow is turbulent.

Details regarding the coal composition and size distribution are included 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 13.1: 2D Furnace with Pulverized Coal Combustion

Preparation for prePDF

1. Start prePDF.

When you use the non-premixed combustion model, you prepare a PDF file with thepreprocessor, prePDF. The PDF file contains information that relates species con-centrations and temperatures to the mixture fraction values, and is used by FLUENTto obtain these scalars during the solution procedure.

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Step 1: Define the Preliminary Adiabatic System inprePDF

1. Define the prePDF model type.

You can define either a single fuel stream, or a fuel stream plus a secondary stream.Enabling a secondary stream allows you to keep track of two mixture fractions.For coal combustion, this would allow you to track volatile matter (the secondarystream) separately from the char (fuel stream). In this tutorial, we will not followthis approach. Instead, we will model coal using a single mixture fraction.

Setup −→Case...

(a) Under Heat transfer options, keep the default setting of Adiabatic.

The coal combustor studied in this tutorial is a non-adiabatic system, withheat transfer at the combustor wall and heat transfer to the coal particles fromthe gas. Therefore, a non-adiabatic combustion system must be considered inprePDF.

Because non-adiabatic calculations are more time-consuming than those foradiabatic systems, you will start the prePDF setup by considering the resultsof an adiabatic system. By computing the PDF/equilibrium chemistry resultsfor the adiabatic system, you will determine appropriate system parametersthat will make the non-adiabatic calculation more efficient. Specifically, the

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adiabatic calculation will provide information on the peak (adiabatic) flametemperature, the stoichiometric mixture fraction, and the importance of indi-vidual components to the chemical system. This process of beginning with anadiabatic system calculation should be followed in all PDF calculations thatultimately require a non-adiabatic model.

(b) Under Chemistry models, keep the default setting of Equilibrium Chemistry.

In most PDF-based simulations, the Equilibrium Chemistry option is recom-mended. The Stoichiometric Reaction (mixed is burned) option requires lesscomputation but is generally less accurate. The Laminar Flamelets option of-fers the ability to include aerodynamic strain induced non-equilibrium effects,such as super-equilibrium radical concentration and sub-equilibrium tempera-tures. 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 it is more accuratethan the Delta PDF approach.

(d) Under Empirically Defined Streams, enable the Fuel stream option.

This will allow you to define the fuel stream using the empirical input option.The empirical input option allows you to define the composition in terms ofatom fractions of H, C, N, and O, along with the lower heating value and heatcapacity of the fuel. This is a useful option when the ultimate analysis andheating value of the coal are known.

(e) Click Apply and close the panel.

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2. Define the chemical species in the system.

The choice of which species to include depends on the fuel type and combustionsystem. Guidelines on this selection are provided in the FLUENT User’s Guide.Here, you will assume that the equilibrium system 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 defined in terms of theseatom fractions, using the “empirical” input method.

! You should include both C and C(S) in the system when the empirical inputoption is used.

Setup −→ Species −→Define...

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

(b) Select the top species in the Defined Species list (initially labeled UNDEFINED).

(c) In the Database Species drop-down list, use the slider bar to scroll the list, andselect C. The Defined Species list now shows C as the first entry.

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

(e) In the Database Species drop-down list, use the slider bar to scroll the list, andselect 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.

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Note: In other combustion systems, you might want to include additional chemicalspecies, but you should not add slow chemical species like NOx.

3. Determine the fuel composition inputs.

The fuel considered here is known, from proximate analysis, to consist of 28%volatiles, 64% char, and 8% ash. You will use this information, along with theultimate analysis given below, to define the coal composition in prePDF. The fuelstream composition (char and 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 combined into thenitrogen 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 yield the followingelemental 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

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You will enter the mole fractions in the final column, above, in order to definethe fuel composition. prePDF will use this information, along with the coal heatingvalue, to define the species present in 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 selection of Mole Fractions.

iii. Select O2 in the Defined Species list and enter 0.21 in the Species Fractionfield.

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iv. Select N2 in the Defined Species list and enter 0.79 in the Species Fractionfield.

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

Note: Because the empirical input option is enabled for the fuel stream, youwill be prompted to enter atom mole fractions for C, H, O, and N, alongwith the heating value and heat capacity of the coal.

i. Under Stream, select Fuel.

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

iii. Select C in the Defined Species list and enter 0.581 in the Atom Fractionfield.

iv. Select H in the Defined Species list and enter 0.390 in the Atom Fractionfield.

v. Select N in the Defined Species list and enter 0.016 in the Atom Fractionfield.

vi. Select O in the Defined Species list and enter 0.013 in the Atom Fractionfield.

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vii. Enter 3.53e+07 J/kg for the Lower Caloric Value and 1000 J/kg-K for theSpecific 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 the mixture densityfor the fuel. You should enter the density of solid char. This input will differfrom the coal density defined in FLUENT, which is the apparent density of theash-containing coal particles.

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6. Define the system operating conditions.

The system pressure and inlet stream temperatures are required for the equilibriumchemistry calculation. The fuel stream inlet temperature for coal combustion shouldbe the temperature at the onset of devolatilization. The oxidizer inlet temperatureshould correspond to the air inlet temperature. In this tutorial, the coal devolatiliza-tion temperature will be set to 400 K and the air inlet temperature is 1500 K. Thesystem pressure is one atmosphere.

Setup −→Operating Conditions...

(a) Enter 400 K and 1500 K as the Fuel and Oxidiser inlet temperatures.

(b) Click Apply and close the panel.

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Step 2: Compute and Review the Adiabatic SystemprePDF Look-Up Tables

1. Accept the default PDF solution parameters.

Setup −→Solution Parameters...

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

The Fuel Rich Flamability Limit allows you to perform a “partial equilibrium” cal-culation, suspending equilibrium calculations when the mixture fraction exceeds thespecified rich limit. This increases the efficiency of the PDF calculation, allowingyou to bypass the complex equilibrium calculations in the fuel-rich region, and ismore physically realistic than the assumption of full equilibrium. For empiricallydefined streams, the rich limit is always 1.0 and cannot be altered.

(a) Keep the default setting for Automatic Distribution.

This feature allows you to improve the prePDF prediction by optimizing thedistribution of the discrete mixture fraction values, clustering them around thepeak temperature value. If you choose not to use the Automatic Distribution,you should set the distribution center point on the rich side of the stoichio-metric scale mixture fraction.

(b) Click Apply and close the panel.

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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 data from the database.Then the time-averaged values of temperature, composition, and density at the dis-crete mixture-fraction/mixture-fraction-variance points (21 points as defined in theSolution Parameters panel) are calculated. The result will be a set of tables contain-ing time-averaged values of species mole fractions, density, and temperature at eachdiscrete value of these two parameters. prePDF reports the progress of the look-uptable construction in the console window.

When the calculations are complete, prePDF will warn you that equilibrium cal-culations have been performed for the fuel inlet. You can simply acknowledge thiswarning, as the equilibrium conditions predicted do not impact your modeling inputsunless the fuel stream is 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 file by default. If youare planning to use the PDF file on the same machine, you can save the fileusing the default Write Binary File option. However, if you are planning to usethe PDF file on a different machine, you should save an ASCII (formatted)file from prePDF. Note that ASCII files take up more disk space than binaryfiles.

(b) Under Solver, select FLUENT 6.

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

(d) Click OK to write the file.

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

The results of the adiabatic calculation provide insight into the system descriptionthat will be used for the non-adiabatic calculation.

Display −→PDF Table...

(a) Select TEMPERATURE from the Plot Variable list and then click Display togenerate the table (Figure 13.2).

The temperature display shows how the time-averaged system temperature varieswith the mean mixture fraction and its variance.

The temperature/mixture-fraction relationship shows that the peak flame tem-perature is about 2750 K at fuel stoichiometric mixture fractions of approxi-mately 0.1. The relatively high flame temperature is a result of the high pre-heat in the combustion air.

Note: The adiabatic flame temperature predicted by the adiabatic system cal-culation will be used to select the maximum temperature in the non-adiabaticsystem calculation.

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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 V4.11

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 13.2: Time-Averaged Temperature: Adiabatic prePDF Calculation

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Step 3: Create and Compute the Non-Adiabatic prePDFSystem

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

• Redefine the system as non-adiabatic.

• Set the peak system temperature (based on the adiabatic result of 2750 K).

After these modifications, you will recompute the system chemistry and save 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 Apply.

2. Set the system temperature limits.

Minimum and maximum temperatures in the system are required when the PDFcalculation is non-adiabatic.

The minimum temperature should be a few degrees lower than the lowest bound-ary condition temperature (e.g., the inlet temperature or wall temperature). In coal

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combustion systems, the minimum system temperature should also be set below thetemperature at which the volatiles begin to evolve from the coal. Here, the vapor-ization temperature at which devolatilization begins will be set to 400 K. Thus, theminimum system temperature is set to 298 K (the default).

The maximum temperature should be at least 100 K higher than the peak flametemperature found in the preliminary adiabatic calculation. Here, the maximumtemperature will be taken as 3000 K, well above the peak adiabatic system temper-ature of 2750 K.

Setup −→Operating Conditions...

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

(b) Click Apply and close the panel.

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

File −→ Write −→Input...

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

Calculate −→PDF Table

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The non-adiabatic prePDF calculation requires much more computation than theadiabatic calculation. prePDF begins by accessing the thermodynamic data from thedatabase. Next, the enthalpy field is initialized and the enthalpy grid adjusted to ac-count for inlet conditions and solution parameters. Time-averaged values of temper-ature, composition, and density at the discrete mixture-fraction/mixture-fraction-variance/enthalpy points (21 points, as defined in the Solution Parameters panel) arethen calculated. The result will be a set of tables containing time-averaged valuesof species mole fractions, density, and temperature at each discrete value of thesethree parameters.

When the calculations are complete, prePDF will warn you that equilibrium cal-culations have been performed for the fuel inlet. As noted above, you can simplyacknowledge this warning, which has no impact on your inputs when you are mod-eling coal or liquid fuels.

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.

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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 list and click Display(Figure 13.3).

Note: Review of the 3D look-up tables is accomplished on a slice-by-slice basis.By default, the slice selected is that corresponding to the adiabatic enthalpyvalues. This display should look very similar to the look-up table created duringthe adiabatic calculation. You can select other slices of constant enthalpy fordisplay, as well.

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

Display −→Nonadiabatic Table...

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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 V4.11

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 13.3: Non-Adiabatic Temperature Look-Up Table on the Slice Corresponding toAdiabatic Enthalpy

(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 andclick OK.

(c) Click Display in the Nonadiabatic-Table panel to generate the table (Figure 13.4).

8. Follow the steps above to plot the instantaneous mole fractions for CO (Figure 13.5).

9. Exit from prePDF.

File −→Exit

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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 V4.11

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

MEAN ENTHALPY SLICE NUMBER 23

Figure 13.4: Time-Averaged C(S) Mole Fractions: Non-Adiabatic prePDF 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 V4.11

3.0E-01

2.4E-01

1.8E-01

1.2E-01

6.0E-02

0.0E+00

Fluent Inc.

F-MEAN

SPECIES CO FROM 3D-PDF-TABLE

MEAN ENTHALPY SLICE NUMBER 23

Figure 13.5: Time-Averaged CO Mole Fractions: Non-Adiabatic prePDF Calculation

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Preparation for FLUENT Calculation

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

1. Copy the file coal/coal.msh from the FLUENT documentation CD to your workingdirectory (as described in Tutorial 1).

The mesh file coal.msh is a quadrilateral mesh describing the system geometryshown in Figure 13.1.

2. Start the 2D version of FLUENT.

Step 4: Grid

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

File −→ Read −→Case...

The FLUENT console window reports that the mesh contains 1357 quadrilateralcells.

2. Check the grid.

Grid −→Check

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

3. Display the grid (Figure 13.6).

Display −→Grid...

Due to the grid resolution and the size of the domain, you may find it more usefulto display just the outline, or to zoom in on various portions of the grid display.

Note: You can use the mouse probe button (right button, by default) to find outthe boundary zone labels. As annotated in Figure 13.7, the upstream boundarycontains two velocity inlets (for the low-speed and high-speed air streams), thedownstream boundary is a pressure outlet, the top boundary is a wall, and thebottom boundary is a symmetry plane.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 26, 2002

Figure 13.6: 2D Coal Furnace Mesh Outline Display

wall-7

symmetry

velocity-inlet-8

velocity-inlet-2

GridFLUENT 6.1 (2d, segregated, lam)

Nov 26, 2002

Figure 13.7: Mesh Display with Annotated Boundary Types

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Step 5: Models: Continuous (Gas) Phase

1. Accept the default segregated solver.

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

Define −→ Models −→Solver...

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

Define −→ Models −→Viscous...

Note: As indicated in the problem description, the Reynolds number of the flow isabout 105. Thus, the flow is turbulent and the high-Re k-ε model is suitable.

3. Turn on the non-premixed combustion model.

Define −→ Models −→Species...

(a) Select Non-Premixed Combustion under Model.

The panel will expand to show the related inputs.

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When you click OK, FLUENT will open the Select File dialog box, requestinginput of the PDF file to be used in the simulation.

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

FLUENT reports in the console window that it is reading the nonadiabaticPDF file containing 13 species. It also reports that a new material, calledpdf-mixture, has been created. This mixture contains the 13 species that youdefined in prePDF and their thermodynamic properties.

FLUENT will present an Information dialog box telling you that available ma-terial properties have changed. You will be setting properties later, so you cansimply click OK in the dialog box to acknowledge this information.

Note: FLUENT will automatically activate solution of the energy equationwhen it reads the non-adiabatic PDF file, so you do not need to visit theEnergy panel to enable heat transfer.

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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 for the exchange ofradiation between gas and particulates.

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Step 6: Models: Discrete Phase

The flow of pulverized coal particles will be modeled by FLUENT using the discrete phasemodel. This model predicts the trajectories of individual coal particles, each represent-ing a continuous stream (or mass flow) of coal. Heat, momentum, and mass transferbetween the coal and the gas will be included by alternately computing the discrete phasetrajectories and the gas phase continuum equations.

1. Enable the discrete phase coupling to the continuous phase flow prediction.

Define −→ Models −→Discrete Phase...

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

This option enables coupling, in which the discrete phase trajectories (alongwith heat and mass transfer to the particles) are allowed to impact the gasphase equations. If you leave this option turned off, you can track particlesbut they will have no impact on the continuous phase flow.

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(b) Set the coupling parameter, the Number of Continuous Phase Iterations perDPM Iteration, to 20.

You should use higher values of this parameter in problems that include a highparticle mass loading or a larger grid size. Less frequent trajectory updates canbe beneficial in such problems, in order to converge the gas phase equationsmore completely prior to repeating the trajectory calculation.

(c) Under Tracking Parameters, set the Max. Number of Steps to 10000.

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

(d) Turn on Specify Length Scale and retain the default Length Scale of 0.01 m.

The Length Scale controls the time step size used for integration of the discretephase trajectories. The value of 0.01 m used here implies that roughly 1000time steps will be used to compute trajectories along the 10 m length of thedomain.

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

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2. Create the discrete phase coal injections.

The flow of the pulverized coal is defined by the initial conditions that describe thecoal as it enters the gas. FLUENT will use these initial conditions as the startingpoint for its time integration of the particle equations of motion (the trajectorycalculations).

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 to obey a Rosin-Rammlersize distribution between 70 and 200 micron diameter. Other initial conditions(velocity, temperature, position) are detailed below along with the appropriate inputprocedures.

Define −→ Injections...

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

This will open the Set Injection Properties panel where you will define the initialconditions defining the flow of coal particles.

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In the Set Injection Properties panel you will define the initial conditions ofthe flow of coal particles. The particle stream will be defined as a group of 10distinct initial conditions, all identical except for diameter, which will obey theRosin-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 specified initial conditionsby 10 discrete particle streams, each with its own set of discrete initial condi-tions. Here, this will result in 10 discrete particle diameters, as the diameterwill be varied within the injection group.

(d) Select Combusting under Particle Type.

By selecting Combusting you are activating the submodels for coal devolatiliza-tion and char burnout. Similarly, selecting Droplet would enable the submodelsfor droplet evaporation and boiling.

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

The Material list contains the combusting particle materials in the FLUENTdatabase. You can select an appropriate coal from this list and then review ormodify its properties in the Materials panel (see Step 8: Materials: DiscretePhase).

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

The coal particles have a nonuniform size distribution with diameters rangingfrom 70 µm to 200 µm. The size distribution fits the Rosin-Rammler equation,with a mean diameter of 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 Properties starting with thefollowing 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, velocity, and tempera-ture.

(j) Define the turbulent dispersion.

i. Click on Turbulent Dispersion.

The panel will change to show the related inputs.

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ii. Under Stochastic Tracking, turn on Stochastic Model.

Stochastic tracks model the effect of turbulence in the gas phase on theparticle trajectories. Including stochastic tracking is important in coalcombustion simulations, to simulate realistic particle dispersion.

iii. Set the Number of Tries to 10.

Note: The new injection (named injection-0, by default) now appears in theInjections panel.

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This panel can be used to copy and delete injection definitions. You can alsoselect an existing injection and list the initial conditions of particle streamsdefined by that injection in the console window. The listing for the injection-0group will show 10 particle streams, each with a unique diameter between thespecified minimum and maximum value, obtained from the Rosin-Rammlerdistribution, and a unique mass flow rate.

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Step 7: Materials: Continuous Phase

All thermodynamic data including density, specific heat, and formation enthalpies areextracted from the prePDF chemical database when the non-premixed combustion modelis used. These properties are transferred to FLUENT as the pdf-mixture material, forwhich only transport properties, such as viscosity and thermal conductivity, need to bedefined.

Define −→Materials...

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 Absorption Coefficient.

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

4. Click the Change/Create button.

Note: You can click on the View... button next to Mixture Species to view the speciesincluded in the pdf-mixture material. These are the species included during thesystem chemistry setup in prePDF. Note that the Density and Cp laws cannot bealtered: these properties are stored in the non-premixed combustion look-up tables.prePDF uses the gas law to compute the mixture density and a mass-weighted mixinglaw to compute the mixture cp. Although it is possible for you to alter the propertiesof the individual species, you should not do so when the non-premixed combustionmodel is used. This would create an inconsistency with the look-up table created inprePDF.

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Step 8: Materials: Discrete Phase

Define −→Materials...

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

The combusting-particle material type appears because you have activated combustingparticles using the Set Injection Properties panel. Other discrete phase materialtypes (droplets, inert particles) will appear in this list if you have created injectionsof those types.

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

This is the combusting particle material type that you selected from the list ofdatabase options in the Set Injection Properties panel. Additional combusting parti-cle materials can be copied from the property database, if desired. You can click the

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Database... button in order to view the combusting-particle materials that are avail-able. Here, you will simply modify the property settings for the selected material,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 the gravitationalacceleration is non-zero).

• Cp determines the heat required to change the particle temperature.

• Latent Heat is the heat required to vaporize the volatiles. This can usually be setto zero when the non-premixed combustion model is used for coal combustion.If the volatile composition has been selected in order to preserve the heatingvalue of the fuel, the latent heat has been effectively included. (You would,however, use a non-zero latent heat if water content had been included in thevolatile definition as vapor phase H2O.)

• Vaporization Temperature is the temperature at which the coal devolatilizationbegins. It should be set equal to the fuel inlet temperature used in prePDF.

• Volatile Component Fraction determines the mass of each coal particle that isdevolatilized.

• Binary Diffusivity is the diffusivity of oxidant to the particle surface and is usedin the diffusion-limited char burnout rate.

• Particle Emissivity is the emissivity of the particles. It is used to computeradiation heat transfer to the particles.

• Particle Scattering Factor is the scattering factor due to particles.

• Swelling Coefficient determines the change in diameter during coal devolatiliza-tion. A swelling coefficient of 2 implies that the particle size will double as thevolatile fraction is released.

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• Burnout Stoichiometric Ratio is used in the calculation of the diffusion-controlledburnout rate. Otherwise, this parameter has no impact when the non-premixedcombustion model is used. When finite-rate chemistry is used instead, the sto-ichiometric ratio defines the mass of oxidant required per mass of char. Thedefault value represents oxidation of C(s) to CO2.

• Combustible Fraction is the mass fraction of char in the coal particle. It de-termines the mass of each coal particle that is consumed by the char burnoutsubmodel.

! The settings for the Vaporization Temperature, Combustible Fraction, and Vol-atile Component Fraction inputs should all be consistent with your prePDF in-puts. (See Step 1: Define the Preliminary Adiabatic System in prePDF.)

4. Select the Single Rate Devolatilization Model for Devolatilization Model.

(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 Combustion Model drop-downlist.

This opens the Kinetics/Diffusion Limited Combustion Model panel.

(b) Accept the default values.

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

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Step 9: Boundary Conditions

Define −→Boundary Conditions...

Hint: You can click your mouse probe button (the right button, by default) on the desiredboundary zone in the graphics display window. FLUENT will then select that zonein the Boundary Conditions panel.

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

Note: Turbulence parameters are defined here based on intensity and hydraulicdiameter. The relatively large turbulence intensity of 10% may be typical forcombustion air flows. The hydraulic diameter has been set to twice the heightof the 2D inlet stream.

For the non-premixed combustion calculation, you need to define the inlet MeanMixture Fraction and Mixture Fraction Variance. For coal combustion, all fuelcomes from the discrete phase and thus the gas phase inlets have zero mixturefraction. Therefore, you can accept the zero default settings.

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

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

The exit gauge pressure of zero simply defines the system pressure at the exit tobe the operating pressure. The backflow conditions for scalars (temperature, mix-ture fraction, turbulence parameters) will be used only if flow is entrained into thedomain through the exit. It is a good idea to use reasonable values in case flowreversal occurs at the exit at some point during the solution process.

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

The furnace wall will be treated as an isothermal boundary with a temperature of1200 K.

(a) Under Thermal Conditions, select Temperature.

(b) Enter 1200 in the Temperature field.

Note: The default boundary condition for particles that hit the wall is reflect, asshown under DPM. Alternate treatments can be selected, using the BC Typelist, for particles that hit the wall.

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Step 10: Solution

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

Solve −→ Controls −→Solution...

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

Solve −→ Initialize −→Initialize...

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

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

! The Apply button does not initialize the flow field data. You must use the Initbutton. (Apply simply allows you to store your initialization parameters forlater use.)

Note: Here, with very high pre-heat of the oxidizer stream, you can start the com-bustion calculation from the inlet-based initialization. In general, you mayneed to start your coal combustion calculations by patching a high-temperatureregion and performing a discrete phase trajectory calculation. This provides theinitial volatile and char release required to initiate combustion. The Solve/Initialize/Patch... menu item and the solve/dpm-update text command can be used toperform this initialization.

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

Solve −→ Monitors −→Residual...

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

File −→ Write −→Case...

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5. Begin the calculation by requesting 400 iterations.

Solve −→Iterate...

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

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

File −→ Write −→Data...

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Step 11: Postprocessing

1. Display the predicted temperature field (Figure 13.8).

Display −→Contours...

The peak temperature in the system is about 2260 K.

Hint: Use the Views panel (Display/Views...) to mirror the display about the sym-metry plane.

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Contours of Static Temperature (k)FLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

2.26e+032.21e+032.16e+032.10e+032.05e+032.00e+031.94e+031.89e+031.84e+031.79e+031.73e+031.68e+031.63e+031.57e+031.52e+031.47e+031.41e+031.36e+031.31e+031.25e+031.20e+03

Figure 13.8: Temperature Contours

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2. Display the Mean Mixture Fraction distribution (Figure 13.9).

Display −→Contours...

The mixture-fraction distribution shows where the char and volatiles released fromthe coal exist in the gas phase.

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Contours of Mean Mixture FractionFLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

3.76e-023.57e-023.38e-023.20e-023.01e-022.82e-022.63e-022.44e-022.26e-022.07e-021.88e-021.69e-021.50e-021.32e-021.13e-029.40e-037.52e-035.64e-033.76e-031.88e-030.00e+00

Figure 13.9: Mixture-Fraction Distribution

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3. Display the devolatilization rate (Figure 13.10).

Display −→Contours...

(a) Select Discrete Phase Model... and DPM Evaporation/Devolatilization in thedrop-down lists under Contours Of.

4. Display the char burnout rate (Figure 13.11) by selecting DPM Burnout from thelower drop-down list.

Note: The display of devolatilization rate shows that volatiles are released after thecoal travels about one eighth of the furnace length. (The onset of devolatiliza-tion occurs when the coal temperature reaches the specified value of 400 K.) Thechar burnout occurs following complete devolatilization. Figure 13.11 showsthat burnout is complete at about three-quarters of the furnace.

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Contours of DPM Evaporation/Devolatilization (kg/s)FLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

2.79e-032.65e-032.51e-032.37e-032.23e-032.09e-031.95e-031.81e-031.67e-031.53e-031.39e-031.25e-031.12e-039.76e-048.37e-046.97e-045.58e-044.18e-042.79e-041.39e-040.00e+00

Figure 13.10: Devolatilization Rate

Contours of DPM Burnout (kg/s)FLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

4.13e-043.93e-043.72e-043.51e-043.31e-043.10e-042.89e-042.69e-042.48e-042.27e-042.07e-041.86e-041.65e-041.45e-041.24e-041.03e-048.27e-056.20e-054.13e-052.07e-050.00e+00

Figure 13.11: Char Burnout Rate

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5. Display the particle trajectory of one particle stream (Figure 13.12).

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 to 5.

(d) Click Display.

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Particle Traces Colored by Particle Residence Time (s)FLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

3.82e-013.63e-013.44e-013.25e-013.06e-012.87e-012.68e-012.48e-012.29e-012.10e-011.91e-011.72e-011.53e-011.34e-011.15e-019.56e-027.64e-025.73e-023.82e-021.91e-020.00e+00

Figure 13.12: Trajectories of Particle Stream 5 Colored by Particle Residence Time

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6. Display the oxygen distribution (Figure 13.13).

Display −→Contours...

Note: Although transport equations are solved only for the mixture fraction and itsvariance, you can still display the predicted chemical species concentrations.These are predicted by the PDF equilibrium chemistry model.

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Contours of Mass fraction of o2FLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

2.33e-012.27e-012.22e-012.16e-012.10e-012.05e-011.99e-011.94e-011.88e-011.82e-011.77e-011.71e-011.65e-011.60e-011.54e-011.49e-011.43e-011.37e-011.32e-011.26e-011.20e-01

Figure 13.13: O2 Distribution

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7. Select other species and display their mass fraction distributions (e.g., Figures 13.14–13.16).

Contours of Mass fraction of co2FLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

1.23e-011.17e-011.10e-011.04e-019.82e-029.20e-028.59e-027.98e-027.36e-026.75e-026.13e-025.52e-024.91e-024.29e-023.68e-023.07e-022.45e-021.84e-021.23e-026.13e-030.00e+00

Figure 13.14: CO2 Distribution

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Contours of Mass fraction of h2oFLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

1.66e-021.58e-021.49e-021.41e-021.33e-021.25e-021.16e-021.08e-029.97e-039.14e-038.31e-037.47e-036.64e-035.81e-034.98e-034.15e-033.32e-032.49e-031.66e-038.31e-040.00e+00

Figure 13.15: H2O Distribution

Contours of Mass fraction of coFLUENT 6.1 (2d, segregated, pdf13, ske)

Nov 26, 2002

6.43e-036.11e-035.79e-035.47e-035.15e-034.82e-034.50e-034.18e-033.86e-033.54e-033.22e-032.89e-032.57e-032.25e-031.93e-031.61e-031.29e-039.65e-046.43e-043.22e-040.00e+00

Figure 13.16: CO Distribution

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Step 12: Energy Balances and Particle Reporting

FLUENT can provide many useful reports, including overall energy accounting and de-tailed information regarding heat and mass transfer from the discrete phase. Here, youwill 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 val-ues indicate heat leaving the domain. In reacting flows, the heat report usestotal enthalpy (sensible heat plus heat of formation of the chemical species).Here, the net “imbalance” of total enthalpy (about 14 kW) represents the totalenthalpy addition from the discrete phase.

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2. Compute the volume sources of heat transferred between the gas and discrete par-ticle phase.

Report −→Volume Integrals...

(a) Select Sum under Options.

(b) Select Discrete Phase Model... and DPM Enthalpy Source in the drop-down listsunder Field Variable.

(c) Select fluid-1 under Cell Zones.

(d) Click Compute.

The total enthalpy transfer to the discrete phase from the gas is about -13.4 kW, asexpected based on the boundary flux report above. This represents the total enthalpyaddition from the discrete phase to the gas during the devolatilization and charcombustion processes.

3. Obtain a summary report on the particle trajectories.

The discrete phase model summary report provides detailed information about theparticle residence time, heat and mass transfer between the continuous and discretephases, and (for combusting particles) char conversion and volatile yield.

Display −→Particle Tracks...

(a) Select Summary under Report Type.

(b) Select injection-0.

(c) Click Track.

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

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

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DPM Iteration ....

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

Fate Number Elapsed Time (s) InjMin Max Avg Std Dev

---- ------ ---------- ---------- ---------- ---------- -------Escaped - Zone 6 100 2.574e-01 5.153e-01 3.317e-01 5.311e-02 inj

(*)- Mass Transfer Summary -(*)

Fate Mass Flow (kg/s)Initial Final Change

---- ---------- ---------- ----------Escaped - Zone 6 1.000e-01 7.999e-03 -9.200e-02

(*)- Energy Transfer Summary -(*)

Fate Heat Content (W)Initial Final Change

---- ---------- ---------- ----------Escaped - Zone 6 -3.712e+03 9.849e+03 1.356e+04

(*)- Combusting Particles -(*)

Fate Volatile Content (kg/s) Char Content (kg/s)Initial Final %Conv Initial Final %Conv

---- ---------- ---------- ------- ---------- ---------- -------Escaped - Zone 6 2.800e-02 0.000e+00 100.00 6.400e-02 0.000e+00 100.00

The report shows that the average residence time of the coal particles is about 0.33seconds. Volatiles are completely released within the domain and the char conver-sion is 100% .

Extra: You can obtain a detailed report of the particle position, velocity, diameter, andtemperature along the trajectories of individual particles. This type of detailed trackreporting can be useful if you are trying to understand unusual or important detailsin the discrete model behavior. To generate the report, visit the Particle Trackspanel. Select Step By Step under Report Type, and File under Report to. Enablethe Track Single Particle Stream option, and set the Stream ID to the desired particlestream. Clicking Track will bring up the Select File dialog box, where you will enterthe name of the file to be written. This file can then be viewed with a text editor.

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Summary: Coal combustion modeling involves the prediction of volatile evolution andchar burnout from the pulverized coal along with simulation of the combustionchemistry occurring in the gas phase. In this tutorial you learned how to usethe non-premixed combustion model to represent the gas phase combustion chem-istry. In this approach the fuel composition was defined in prePDF and the fuelwas assumed to react according to the equilibrium system data. This equilibriumchemistry model can be applied to other turbulent, diffusion-reaction systems. Notethat you can also model coal combustion using the finite-rate chemistry model.

You also learned how to set up and solve a problem involving a discrete phase ofcombusting particles. You created discrete phase injections, activated coupling tothe gas phase, and defined the discrete phase material properties. These procedurescan be used to set up other simulations involving reacting or inert particles.

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Tutorial 14. Modeling Surface Chemistry

Introduction: In chemically reacting laminar flows, such as those encountered in chem-ical vapor deposition (CVD) applications, accurate modeling of time-dependenthydrodynamics, heat and mass transfer, and chemical reactions (including wallsurface reactions) is important. Tutorials 12 and 13 deal with reacting flows withapplications in gaseous fuel and coal combustion.

In this tutorial, surface reactions are considered. Modeling the reactions takingplace at gas-solid interfaces is complex and involves several elementary physico-chemical processes like adsorption of gas-phase species on the surface, chemicalreactions occurring on the surface, and desorption of gases from the surface backto the gas phase.

In this tutorial, you will learn how to:

• Create new materials and set the mixture properties.

• Model surface reactions involving site species.

• Enable physical models and define boundary conditions for a chemically re-acting laminar flow involving wall surface reactions.

• Calculate the deposition solution using the segregated solver.

• Examine the flow results using graphics.

Prerequisites: This tutorial assumes that you are familiar with the FLUENT user in-terface, and that you have solved Tutorial 1. Some steps in the setup and solutionprocedure will not be shown explicitly.

Before beginning, you should read Sections 13.1 and 13.2 in the User’s Guide. Sec-tion 13.1 deals with species transport and chemically reacting flows. In particular,you should be familiar with the Arrhenius rate equation, as this equation is used forthe surface reactions modeled in this tutorial. Section 13.2 describes wall surfacereaction modeling and chemical vapor deposition.

Problem Description: A rotating disk CVD reactor for the growth of Gallium Ar-senide (GaAs) shown in Figure 14.1 will be modeled.

The process gases, Trimethyl Gallium (GaCh3) and Arsine (AsH3) enter the reactorat 293 K through the inlet at the top. These gases flow over the hot, spinningdisk depositing thin layers of gallium and arsenide on it in a uniform, repeatablemanner. The disk rotation generates a radially pumping effect, which forces the

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Inlet

Outlet

RotatingDisk

Figure 14.1: An Outline of the Reactor Configuration

gases to flow in a laminar manner down to the growth surface, outward across thedisk, and finally to be discharged from the reactor.

The semiconductor materials Ga(s) and As(s) are deposited on the heated surfacegoverned by the following surface reactions.

AsH3 +Ga s→ Ga+ As s+ 1.5H2 (14.1)

GaCH3 + As s→ As+Ga s+ 3CH3 (14.2)

As mentioned earlier, the inlet gas is a mixture of trimethyl gallium and arsine. Inthe inlet mixture the mass fraction of GaCH3 is 0.15 and AsH3 is 0.4. The mixturevelocity at the inlet is 0.02189 m/s. The disk rotates at 80 rad/sec, and the top wall(wall-1) is heated to 473 K, and the sidewalls (wall-2) of the reactor are maintainedat 343 K. The susceptor (wall-4) is heated to a uniform temperature of 1023 K,and the bottom wall (wall-6) is at 303 K.

In this tutorial, simultaneous deposition of Ga and As is simulated and examined.The mixture properties and the mass diffusivity are determined based on kinetictheory. Detailed surface reactions with multiple sites and site species, and fullmulti-component/thermal diffusion effects are also included in the simulation.

Preparation

1. Copy the files surface/surface.msh from the FLUENT documentation CD to yourworking directory (as described in Tutorial 1).

2. Start the 3ddp version of FLUENT.

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Step 1: Grid

1. Read in the mesh file surface.msh.

File −→ Read −→Case...

2. Check the grid.

Grid −→Check

Note: The grid check lists the minimum and maximum x and y values from thegrid, and reports on a number of other grid features that are checked. Anyerrors in the grid would be reported at this time. For instance, the cell volumesmust never be negative. Note that the domain extents are reported in units ofmeters, the default unit of length in FLUENT. Since this grid was created inunits of centimeters, the Scale Grid panel will be used to scale the grid intometers.

3. Scale the grid.

Grid −→Scale...

(a) In the Units Conversion drop-down list, select cm to complete the phrase GridWas Created In cm (centimeters).

(b) Click 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 tochange any units.

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4. Display the grid (Figure 14.2).

Display −→Grid...

Extra: You can use the left mouse button to rotate the image and view it fromdifferent angles. You can use the right mouse button to check which zonenumber corresponds to each boundary. If you click the right mouse buttonon one of the boundaries in the graphics window, its name and type will beprinted in the FLUENT console window. This feature is especially useful whenyou have several zones of the same type and you want to distinguish betweenthem quickly. Use the middle mouse button to zoom the image.

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ZY

X

GridFLUENT 6.1 (3d, dp, segregated, spe4, lam)

Sep 20, 2002

Figure 14.2: Grid Display

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Step 2: Models

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

1. Keep the default solver settings.

Define −→ Models −→Solver...

2. Enable heat transfer by activating the energy equation.

Define −→ Models −→Energy...

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3. Enable chemical species transport and reaction.

Define −→ Models −→Species...

(a) Under Model, select Species Transport.

This will expand the Species Model panel.

(b) Under Reactions, select Volumetric and Wall Surface.

(c) Under Wall Surface Reaction Options, select Mass Deposition Source.

Mass Deposition Source is selected because there is a certain loss of mass dueto the surface deposition reaction, i.e., As(s) and Ga(s) are being depositedout. If you were to do an overall mass balance without taking this fact intoaccount, you would end up with a slight imbalance.

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

Note: This includes the effect of enthalpy transport due to species diffusionin the energy equation, which contributes to the energy balance, especiallyfor the case of Lewis numbers far from unity.

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(e) Select Full Multicomponent Diffusion and Thermal Diffusion.

Note: The Full Multicomponent Diffusion activates Stefan-Maxwells equationsand computes the diffusive fluxes of all species in the mixture to all con-centration gradients. The Thermal Diffusion effects cause heavy moleculesto diffuse less rapidly, and light molecules to diffuse more rapidly, towardsheated surfaces.

(f) Click OK.

The console window will list the properties that are required for the modelsthat you have enabled. You will see an Information dialog box, reminding youto confirm the property values that have been extracted from the database.

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

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Step 3: Materials

Define −→Materials...

1. Create the gas-phase species (AsH3, GaCH3, CH3, H2), the site species (Ga s andAs s), and solid species (Ga and As).

(a) Create species AsH3.

i. In the Materials panel, select fluid under Material Type.

ii. Select nitrogen under Fluid Materials to create the new material.

iii. Set the Mixture to none.

iv. Enter arsine under Name.

v. Enter ash3 under Chemical Formula.

vi. Specify the following for each of the properties:

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Parameter ValueCp kinetic-theoryThermal Conductivity kinetic-theoryViscosity kinetic-theoryMolecular Weight 77.95

Standard State Enthalpy 0

Standard State Entropy 130579.1

Reference Temperature 298.15

L-J Characteristic Length 4.145

L-J Energy Parameter 259.8

Degrees of Freedom 0

Ignore the Density parameter as the density will be set to incompressible-ideal-gas-law for mixture.

vii. Click Change/Create to create the new material.

viii. FLUENT will ask if you would like to overwrite nitrogen. Click No in theQuestion panel.

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(b) Create the other species following the same procedure as for AsH3.

i. The parameter values for each of the species is as per the table givenbelow:

Parameter GaCH3 CH3 H2 Ga s As s Ga AsName tmg ch3g hydrogen ga s as s ga as

Chemical For-mula

gach3 ch3 h2 ga s as s ga as

Cp kinetic-theory

kinetic-theory

kinetic-theory

520.64 520.64 1006.43 1006.43

Thermal Con-ductivity

kinetic-theory

kinetic-theory

kinetic-theory

0.0158 0.0158 kinetic-theory

kinetic-theory

Viscosity kinetic-theory

kinetic-theory

kinetic-theory

2.125

e-05

2.125

e-05

kinetic-theory

kinetic-theory

MolecularWeight

114.83 15 2.02 69.72 74.92 69.72 74.92

Standard StateEnthalpy

0 2.044

e+07

0 -3117.71 -3117.71 0 0

Standard StateEntropy

130579.1 257367.6 130579.1 154719.3 154719.3 0 0

ReferenceTemperature

298.15 298.15 298.15 298.15 298.15 298.15 298.15

L-J Character-istic Length

5.68 3.758 2.827 - - 0 0

L-J Energy Pa-rameter

398 148.6 59.7 - - 0 0

Degrees ofFreedom

0 0 5 - - - -

ii. Click Change/Create to create the new material.

iii. Click No in the Question panel.

2. Set the mixture species.

(a) Under Material Type, select mixture.

(b) Enter gaas deposition under Name.

(c) Click Change/Create.

(d) To overwrite the mixture-template, click Yes in the Question panel.

(e) Under Properties, click the Edit... button to the right of Mixture Species.

This will open the Species panel. Here you will set the Selected Species, SelectedSite Species, and Selected Solid Species from the Available Materials list usingthe Add and Remove buttons.

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The species under each species type are:

Selected Species Selected Site Species Selected Solid Speciesash3 ga s gagach3 as s asch3 - -h2 - -

The species should appear in the same order as shown in the above table.!

(f) To set the species follow the procedure listed below:

i. To remove an unwanted species from the Selected Species list, select thespecies and click Remove under Selected Species.

ii. Select the required species in the Available Materials list.

iii. Click Add under the corresponding species list.

iv. Click OK after all the species are set under the respective categories.

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3. Set the mixture reactions.

(a) In the Materials panel, under Properties, click the Edit... button to the right ofReaction.

This will open the Reactions panel.

(b) In the Reactions panel, increase the Total Number of Reactions to 2, and definethe following reactions, where PEF = Pre-Exponential Factor, AE = Activa-tion Energy, and TE = Temperature Exponent.

AsH3 +Ga s→ Ga+ As s+ 1.5H2 (14.3)

GaCH3 + As s→ As+Ga s+ 3CH3 (14.4)

Reaction Name gallium-dep arsenic-dep

Reaction ID 1 2Reaction Type Wall Surface Wall SurfaceNumber of Reactants 2 2Species ash3, ga s gach3, as sStoich. Coefficient ash3=1, ga s=1 gach3=1, as s=1Rate Exponent ash3=1, ga s=1 gach3=1, as s=1Arrhenius Rate PEF=1e+06, AE=0,

TE=0.5PEF=1e+12, AE=0,TE=0.5

Number of Products 3 3Species ga, as s, h2 as, ga s, ch3Stoich. Coefficient ga=1, as s=1, h2=1.5 as=1, ga s=1, ch3=3Rate Exponent as s=0, h2=0 ga s=0, ch3=0

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(c) Change the ID to 2 and set the parameters for the second equation as shownin the above table.

(d) Click OK to save your data and close the panel.

4. Set the reaction mechanisms for the mixture.

(a) In the Materials panel, under Properties, click the Edit... button to the right ofMechanism.

This will open the Reaction Mechanisms panel.

(b) Enter gaas-ald under Name.

(c) Retain the Number of Mechanisms as 1.

(d) Set the Reaction Type to Wall Surface.

(e) Under Reactions, select gallium-dep and arsenic-dep.

(f) Increase the Number of Sites to 1.

(g) Set the Site Density as 1e-08.

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(h) Click Define... to the right of site-1.

This opens the Site Parameters panel.

i. In the Site Parameters panel, set the Total Number of Site Species to 2.

ii. Select ga s as the first site species and set the Site Coverage to 0.7.

iii. Select as s as the second site species and set the Site Coverage to 0.3.

(i) Click Apply and Close the panel.

(j) Click OK in the Reaction Mechanisms panel to close the panel.

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5. In the Materials panel, set Density to incompressible-ideal-gas.

6. Set Cp to mixing-law.

7. Set Thermal Conductivity to mass-weighted-mixing-law.

8. Set Viscosity to mass-weighted-mixing-law.

9. Set Mass Diffusivity to kinetic-theory.

10. Set Thermal Diffusion Coefficient to kinetic-theory.

11. Click Change/Create and close the Materials panel.

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Step 4: Operating Conditions

Define −→Operating Conditions...

1. Set the Operating Pressure to 10000 pascals.

2. Enable Gravity.

3. Set the Gravitational Acceleration in the Z direction as 9.81.

4. Set the Operating Temperature to 303 K.

5. Click OK to close the panel.

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Step 5: Boundary Conditions

Define −→Boundary Conditions...

1. Keep the default settings for outflow.

2. Set the conditions for velocity-inlet.

(a) Retain the default Velocity Specification Method as Magnitude,Normal to Bound-ary.

(b) Retain the default Reference Frame as Absolute.

(c) Set the Velocity Magnitude to 0.02189 m/s

(d) Set the Temperature to 293 K.

(e) Set the Species Mass Fractions for ash3 as 0.4, gach3 as 0.15, and ch3 as 0.

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(f) Click OK to close the panel.

3. Set the boundary conditions for wall-1.

(a) Under Thermal Conditions, select Temperature and set the Temperature to473 K.

(b) Click OK to close the panel.

4. Similarly, set the boundary conditions for wall-2.

(a) Under Thermal Conditions, select Temperature and set the Temperature to343 K.

(b) Click OK to close the panel.

5. Set the boundary conditions for wall-4.

(a) Under Thermal Conditions, select Temperature and set the Temperature to1023 K.

(b) In the Momentum section of the panel, set Wall Motion to Moving Wall, Motionto Absolute and Rotational and set the Speed to 80 rad/s.

(c) Retain other defaults.

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(d) Under the Species section of the panel, enable Reaction and set Mechanisms togaas-ald.

(e) Click OK to close the panel.

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6. Set the boundary conditions for wall-5.

(a) Under Thermal Conditions, select Temperature and set the Temperature to720 K.

(b) In the Momentum section of the panel, set Wall Motion to Moving Wall, Motionto Absolute and Rotational and set the Speed to 80 rad/s.

(c) Retain other defaults.

(d) Click OK to close the panel.

7. Set the boundary conditions for wall-6.

(a) Under Thermal Conditions, select Temperature and set the Temperature to303 K.

(b) Click OK to close the panel.

8. Use the TUI commands to turn off diffusion at the inlet. In the console window,type the commands shown in boxes in the dialog below.

Hint: You may need to enter press the <Enter> key to get the > prompt.

> define/models/species/inlet-diffusion?

Include diffusion at inlets? [yes] no

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Step 5: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Change the Under-Relaxation Factor as follows:

Parameter URF Parameter URFPressure 0.1 ash3 1

Density 0.3 gach3 1

Body Forces 1 ch3 1

Momentum 0.2 Energy 0.9

Hint: You will need to scroll down the Under-Relaxation Factors list to see thespecies and Energy.

(b) Under Discretization, retain the default First Order Upwind for Momentum, allthe species and Energy.

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

Solve −→ Initialize −→Initialize...

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

(b) Click Init, and Close the panel.

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3. Turn on residual plotting during the calculation.

Solve −→ Monitors −→Residual...

(a) Select Plot under Options.

(b) Set the Convergence Criterion for Continuity to 1e-05.

(c) Click OK to close the panel.

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

File −→ Write −→Case...

5. Start the calculation by requesting 2000 iterations.

Solve −→Iterate...

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The solution converges in about 1900 iterations.

ZYX

Scaled ResidualsFLUENT 6.1 (3d, dp, segregated, spe4, lam)

Sep 17, 2002

Iterations

2000180016001400120010008006004002000

1e+01

1e+00

1e-01

1e-02

1e-03

1e-04

1e-05

1e-06

1e-07

1e-08

ch3gach3ash3energyz-velocityy-velocityx-velocitycontinuityResiduals

Figure 14.3: Scaled Residuals

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

File −→ Write −→Case & Data...

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Step 7: Postprocessing

1. Create an iso-surface near wall-4.

Surface −→Iso-Surface...

(a) In the Iso-Surface panel, select Grid and Z-Coordinate under Surface of Constant.

(b) Click Compute.

(c) Enter 0.075438 under Iso-Values.

(d) Enter z=0.07 under New Surface Name.

(e) Click Create.

2. Display contours of temperature on the plane surface. (Figure 14.4).

Display −→Contours...

(a) Select Temperature... and Static Temperature in the Contours Of drop-downlist.

(b) Enable Filled under Options.

(c) Select z=0.07 under Surfaces.

(d) Click Display.

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Contours of Static Temperature (k)FLUENT 6.1 (3d, dp, segregated, spe4, lam)

Sep 24, 2002

1.02e+039.86e+029.50e+029.14e+028.77e+028.40e+028.04e+027.68e+027.31e+026.94e+026.58e+026.22e+025.85e+025.48e+025.12e+024.76e+024.39e+024.02e+023.66e+023.30e+022.93e+02

Z Y

X

Figure 14.4: Temperature Contours near wall-4

The temperature contours shows the temperature distribution across a plane justabove the rotating disk. You can see that the disk has a temperature of 1023 K..

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3. Display contours of surface deposition rates of ga.(Figure 14.5).

Display −→Contours...

(a) Select Species... and Surface Deposition Rate of ga in the Contours Of drop-down list.

(b) Select wall-4 under Surfaces.

(c) Click Display.

You may need to use the left mouse button to rotate the image so that you cansee the contours on the top side of wall-4 where the deposition takes place.

Contours of Surface Deposition Rate of ga (kg/m2-s)FLUENT 6.1 (3d, dp, segregated, spe4, lam)

Sep 24, 2002

4.58e-054.35e-054.12e-053.90e-053.67e-053.44e-053.21e-052.98e-052.75e-052.52e-052.29e-052.06e-051.83e-051.60e-051.37e-051.15e-059.17e-066.87e-064.58e-062.29e-060.00e+00

Z Y

X

Figure 14.5: Contours of Surface Deposition Rate of ga

Figure 14.5 shows the gradient of surface deposition rate of ga. The maximumdeposition is seen at the center of the disk.

4. Display contours of surface coverage of ga s. (Figure 14.6).

Display −→Contours...

(a) Select Species... and Surface Coverage of ga s in the Contours Of drop-downlist.

(b) Select wall-4 under Surfaces.

(c) Click Display.

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Contours of Surface Coverage of ga_sFLUENT 6.1 (3d, dp, segregated, spe4, lam)

Sep 24, 2002

2.04e-011.94e-011.84e-011.73e-011.63e-011.53e-011.43e-011.33e-011.22e-011.12e-011.02e-019.18e-028.16e-027.14e-026.12e-025.10e-024.08e-023.06e-022.04e-021.02e-020.00e+00

Z Y

X

Figure 14.6: Contours of Surface Coverage of ga s

Figure 14.6 shows the rate of surface coverage of the site species ga s.

5. Create a line surface from the center of wall-4 to the edge.

Surface −→Line/Rake...

(a) In the Line/Rake Surface panel, select Select Points with Mouse.

(b) In the graphic display, click at the center of wall-4 and at the edge with theright mouse button.

(c) Click Create.

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6. Plot the surface deposition rate of Ga v/s radial distance(Figure 14.7).

Plot −→XY Plot...

(a) Select Species... and Surface Deposition Rate of ga in the Y Axis Functiondrop-down list.

(b) Under Options, deselect Node Values.

The source/sink terms due to the surface reaction are deposited in the celladjacent to the wall cells, so it is necessary to plot the cell values and not thenode values.

(c) In the Surfaces list, select line-7.

(d) To set the scale of the XY plot, click Axes.

i. In the Axes - Solution XY Plot panel, select Y under Axis.

ii. Disable Auto Range under Options.

iii. Under Range, set Minimum to 2e-05 and Maximum to 5e-05, click Applyand Close the panel.

(e) In the Solution XY Plot, click Plot.

The peak of the surface deposition rate occurs at the center of wall-4 (where theconcentration of the mixture is highest).

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Z

Y

X

Surface Deposition Rate of gaFLUENT 6.1 (3d, dp, segregated, spe4, lam)

Sep 24, 2002

Position (m)

(kg/m2-s)gaof

RateDeposition

Surface

0.250.20.150.10.051.38778e-17-0.05-0.1-0.15-0.2-0.25

5.500000e-05

5.000000e-05

4.500000e-05

4.000000e-05

3.500000e-05

3.000000e-05

2.500000e-05

2.000000e-05

line-7

Figure 14.7: Plot of Surface Deposition Rate of Ga

Extra: You can also perform all the above postprocessing steps to analyze the depositionof As.

Summary: The main focus of this tutorial is the accurate modeling of macroscopic gasflow, heat and mass transfer, species diffusion, and chemical reactions (includingsurface reactions) in a rotating disk CVD reactor. In this tutorial, you learnedhow to use the two-step surface reactions involving site species, and computedsimultaneous deposition of gallium and arsenide from a mixture of precursor gaseson a rotating susceptor. Note that the same approach is valid if you are simulatingmulti-step reactions with multiple sites/site species.

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Tutorial 15. Modeling Evaporating LiquidSpray

Introduction: In this tutorial, FLUENT’s air-blast atomizer model is used to predict thedroplet behavior of an evaporating methanol spray. The air flow is modeled firstas a steady-state problem without droplets. To predict the behavior of individualdroplets in the atomizer, several other discrete-phase models, including collisionand breakup, are used in an unsteady calculation.

In this tutorial you will learn how to:

• Create periodic zones

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

• Calculate a transient solution using the second-order implicit unsteady formu-lation

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: The geometry to be considered in this tutorial is shown in Fig-ure 15.1. Methanol is cooled to −10C before being introduced into an air-blastatomizer. The atomizer contains an inner air stream surrounded by a swirling an-nular stream. (The species include the components of air as well as water vapor,so the model can be expanded to include combustion, if desired.) To make useof the periodicity of the problem, only a 30-degree section of the atomizer will bemodeled.

Preparation

1. Copy the file spray/sector.msh from the FLUENT documentation CD to yourworking directory (as described in Tutorial 1).

2. Start the 3D version of FLUENT.

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ZY

X

inner air stream

swirling annular stream

Figure 15.1: Problem Specification

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Step 1: Grid

1. Read in the mesh file sector.msh.

File −→ Read −→Case...

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid.

Display −→Grid...

(a) Under Options, select Faces.

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

(c) Click the Colors... button.

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

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

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

The graphics display will be updated to show the grid. You will now changethe display again to zoom in on an isometric view of the atomizer section.

4. Change the display to an isometric view.

Display −→Views...

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

(b) Zoom in and rotate with your mouse to obtain the view shown in Figure 15.2.

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ZY

X

GridFLUENT 6.1 (3d, segregated, lam)

Nov 18, 2002

Figure 15.2: Air-Blast Atomizer Mesh Display

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5. Using the text interface, change zones periodic-a and periodic-b from wall zonesto periodic zones.

(a) In the console window, type the commands shown in boxes in 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 face

11 default-interior interior face

/grid/modify-zones> make-periodic

Periodic zone [()] 7Shadow 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.

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6. Reorder the grid.

To speed up the solution procedure, the mesh should be reordered, which will sub-stantially 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.

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Step 2: Models

1. Keep the default solver settings.

Define −→ Models −→Solver...

2. Enable heat transfer by activating the energy equation.

Define −→ Models −→Energy...

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3. Enable the realizable k-ε turbulence model.

Define −→ Models −→Viscous...

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

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4. Enable chemical species transport and reaction.

Define −→ Models −→Species...

(a) Select Species Transport under Model.

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

The Mixture Material list contains the set of chemical mixtures that exist inthe FLUENT database. By selecting one of the pre-defined mixtures, you areaccessing a complete description of the reacting system. The chemical speciesin the system and their physical and thermodynamic properties are defined byyour selection of the mixture material. You can alter the mixture materialselection or modify the mixture material properties using the Materials panel(see Step 6: Solution: Unsteady Flow).

! When you click OK, the console window will list the properties that arerequired for the models you have enabled. You will see an Informationdialog box, reminding you to confirm the property values that have beenextracted from the database.

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

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Step 3: Boundary Conditions

Define −→Boundary Conditions...

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

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

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

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

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

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Step 4: Initial Solution Without Droplets

The airflow will first be solved and analyzed without droplets.

1. Initialize the flow field.

Solve −→ Initialize −→Initialize...

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

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

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2. Keep the default under-relaxation factors.

Solve −→ Controls −→Solution...

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3. Turn on residual plotting during the calculation.

Solve −→ Monitors −→Residual...

(a) Under Options, select Plot.

(b) Click OK.

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

File −→ Write −→Case...

5. Start the calculation by requesting 200 iterations.

Solve −→Iterate...

The solution will converge after about 175 iterations.

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

File −→ Write −→Case & Data...

Note: FLUENT will ask you to confirm that the previous case file is to be overwrit-ten.

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

Surface −→Iso-Surface...

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

(b) Click on Compute to update the minimum and maximum values.

(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.

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8. Review the current state of the solution by examining contours of velocity magni-tude (Figure 15.3).

Display −→Contours...

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

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

This will open the Grid Display panel.

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(c) Keep the current grid display settings and close the Grid Display 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 15.3.

Contours of Velocity Magnitude (m/s)FLUENT 6.1 (3d, segregated, spe5, ske)

Nov 18, 2002

9.91e+019.41e+018.92e+018.42e+017.92e+017.43e+016.93e+016.44e+015.94e+015.45e+014.95e+014.46e+013.96e+013.47e+012.97e+012.48e+011.98e+011.49e+019.91e+004.95e+000.00e+00

ZY

X

Figure 15.3: Velocity Magnitude at Mid-Point of Atomizer Section

9. Display path lines of the air in the swirling annular stream (Figure 15.4).

Display −→Path Lines...

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(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.

This will open the Grid Display panel.

(d) Keep the current grid display settings and close the Grid Display panel.

(e) Click Display in the Path Lines panel.

(f) Use your mouse to obtain the view shown in Figure 15.4.

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Path Lines Colored by Particle IDFLUENT 6.1 (3d, segregated, spe5, ske)

Nov 18, 2002

4.90e+014.65e+014.41e+014.17e+013.92e+013.68e+013.43e+013.19e+012.94e+012.70e+012.45e+012.20e+011.96e+011.71e+011.47e+011.22e+019.80e+007.35e+004.90e+002.45e+000.00e+00

ZY

X

Figure 15.4: Path Lines of Air in the Swirling Annular Stream

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Step 5: Enable Time Dependence and Create a SprayInjection

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

1. Enable a time-dependent flow calculation.

Define −→ Models −→Solver...

(a) Under Time, select Unsteady.

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

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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 trajectories on the con-tinuous phase.

ii. Under Number of Continuous Phase Iterations per DPM Iteration, enter avalue of 1000.

This option controls the iterative solution of the discrete phase within eachgas-phase time step. Higher values are more desirable for sprays.

(b) Specify the Tracking Parameters.

i. Deselect the Specify Length Scale option.

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ii. Keep the default value of Step Length Factor.

(c) Set the Unsteady Options.

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

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 at t = 0.

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

The dynamic-drag law is available only when the Droplet Breakup model 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.

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(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 introduced into the do-main 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 injection to 0, 0, and0.0015.

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 of the atomizer. Theactual atomizer flow rate is 12 times this value.

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

For this problem, the injection should begin at t = 0 and not stop untillong after the time period of interest. A large value for the stop time (e.g.,100 s) will ensure that the injection will essentially never stop.

vi. Set the Injector Inner Diam. to 0.0035 m, and the Injector Outer Diam. to0.0045 m.

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

The spray angle is the angle between the liquid sheet trajectory and theinjector centerline. In this case, the value is negative because the sheet isinitially converging toward the centerline.

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

The relative velocity is the expected relative velocity between the atomizingair and the liquid sheet.

ix. Keep the default Azimuthal Start Angle of 0 deg and set the AzimuthalStop Angle to 30 deg.

This will restrict the injection to the 30-degree section of the atomizer thatis being modeled.

(g) Define the turbulent dispersion.

i. Click the Turbulent Dispersion tab.

The lower half of the panel will change to show options for the turbulentdispersion model.

ii. Under Stochastic Tracking, turn on the Stochastic Model and Random EddyLifetime options.

These models will account for the turbulent dispersion of the droplets.

Note: In the case that the spray injection would be striking a wall, you would needto define the wall boundary conditions to reflect that event. In the Wall panel,you would select the DPM tab, and then select wall-jet from the Boundary Cond.Type drop-down list. Though this tutorial case does have wall zones, they area part of the atomizer apparatus. Because these walls are not in the path ofthe spray droplets, you do not need to change the wall boundary conditions anyfurther.

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4. Set the droplet material properties.

Because the secondary atomization models (breakup and coalescence) are used, thedroplet properties must be set.

Define −→Materials...

(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 0.0222 N/m for DropletSurface Tension.

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

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Step 6: Solution: Unsteady Flow

1. Set the initial condition for the discrete phase.

Resetting the discrete phase model sources will make sure that the interphase cou-pling is initialized.

Solve −→ Initialize −→Reset DPM Sources

2. Set the time step parameters.

The selection of the time step is critical for accurate time-dependent flow predic-tions.

Solve −→Iterate...

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

(b) Click Apply.

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

File −→ Write −→Case...

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4. Calculate a solution for one time step.

Solve −→Iterate...

It is a good idea to do one time step initially so you can check the position of theatomizer droplets before they are significantly dispersed.

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

(b) Click Iterate.

! You will notice that FLUENT will perform less than 20 iterations for the firsttime step. Since this is the specified Max Iterations per Time Step, the solutionis converged. For a real problem, it is important that you allow the solution toconverge at each time step, so you may need to increase the Max Iterations perTime Step. The default of 20 is used in this tutorial to speed up the calculation.

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

File −→ Write −→Case & Data...

6. Display the trajectories of the droplets in the spray injection (Figure 15.5).

This will allow you to review the location of the atomizer droplets after just onetime step. They should therefore still be near their initial injection positions.

Display −→Particle Tracks...

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(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.

This will open the Grid Display panel.

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

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

This will display the location of the droplets colored by their diameters.

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

(h) Click Display.

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(i) Use your mouse to obtain the view shown in Figure 15.4.

Particle Traces Colored by Particle Diameter (m) (Time=5.0000e-05)FLUENT 6.1 (3d, segregated, spe5, ske, unsteady)

Nov 18, 2002

5.91e-055.63e-055.35e-055.07e-054.79e-054.51e-054.23e-053.95e-053.67e-053.39e-053.11e-052.83e-052.56e-052.28e-052.00e-051.72e-051.44e-051.16e-058.80e-066.01e-063.22e-06

ZY

X

Figure 15.5: Particle Tracks for the Spray Injection After 1 Time Step

The air-blast atomizer model assumes that a cylindrical liquid sheet exits theatomizer, which then disintegrates into ligaments and droplets. Appropriately,the model determines that the droplets should be input into the domain in aring. The radius of this disk is determined from the inner and outer radii ofthe injector.

Note that the maximum diameter of the droplets is about10−4 m, or 0.1 mm. This is slightly smaller than the film height, which makessense. Recall that the inner diameter and outer diameter of the injector are3.5 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-blastatomizer automatically uses a droplet distribution.

Also note that the droplets are placed a slight distance away from the injector.Once the droplets are injected into the domain, they can collide/coalesce withother droplets as determined by the secondary models (breakup and collision).However, once a droplet has been introduced into the domain, the air-blastatomizer model no longer affects the droplet.

7. Request 10 more time steps.

Solve −→Iterate...

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

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Step 7: Postprocessing

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

Display −→Particle Tracks...

(a) Click Display in the Particle Tracks panel.

(b) Use your mouse to obtain the view shown in Figure 15.6.

Particle Traces Colored by Particle Diameter (m) (Time=5.5000e-04)FLUENT 6.1 (3d, segregated, spe5, ske, unsteady)

Nov 18, 2002

1.52e-041.45e-041.37e-041.30e-041.22e-041.15e-041.07e-049.95e-059.19e-058.43e-057.68e-056.92e-056.17e-055.41e-054.65e-053.90e-053.14e-052.39e-051.63e-058.74e-061.18e-06

ZY

X

Figure 15.6: Particle Tracks for the Spray Injection After 11 Time Steps

2. Create an isosurface of the methanol mass fraction.

Surface −→Iso-Surface...

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

(b) Click on Compute to update the minimum and maximum values.

(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).

Display −→Grid...

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

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(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 red in the Colors list.

This will ensure that the isosurface is displayed in red, which contrasts betterwith 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.

Display −→Views...

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

(b) Click Apply in the Views panel.

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

The graphics display will be updated to show the entire atomizer.

(d) Use your mouse to obtain the view shown in Figure 15.7.

Grid (Time=5.5000e-04)FLUENT 6.1 (3d, segregated, spe5, rke, unsteady)

Aug 29, 2002

ZY

X

Figure 15.7: Full Atomizer Display with Surface of Constant Methanol Mass Fraction

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Summary: In this tutorial, you defined a discrete-phase spray injection for an air-blastatomizer and calculated a transient solution using the second-order implicit un-steady formulation. You viewed the location of methanol droplet particles afterthey had exited the atomizer and examined an isosurface of the methanol massfraction.

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Tutorial 16. Using the VOF Model

Introduction: This tutorial illustrates the setup and solution of the two-dimensionalturbulent fluid flow in a partially filled spinning bowl.

In this tutorial you will learn how to:

• Set up and solve a transient free-surface problem using the segregated 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 velocity vectors andvolume fraction contours

Prerequisites: This tutorial requires a basic familiarity with FLUENT. You may alsofind it helpful to read about VOF multiphase flow modeling in the FLUENT User’sGuide. Otherwise, no previous experience with multiphase modeling is required.

Problem Description: The information relevant to this problem is shown in Figure 16.1.A large bowl, 1 m in radius, is one-third filled with water and is open to the atmo-sphere. The bowl spins with an angular velocity of 3 rad/sec. Based on the rotatingwater, the Reynolds number is about 106, so the flow is modeled as turbulent.

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2 m

1 m

=Bowl: Ω 3 rad/s3

-5

-3

Air: ρ = 1.225 kg/m

µ = 1.7894 x 10Water: ρ = 998.2 kg/m3

µ = 1 x 10

kg/m-s

kg/m-s

Figure 16.1: Water and Air in a Spinning Bowl

Preparation

1. Copy the file vof/bowl.msh from the FLUENT documentation CD to your workingdirectory (as described in Tutorial 1).

The mesh file bowl.msh is a quadrilateral mesh describing the system geometryshown in Figure 16.1.

2. Start the 2D version of FLUENT.

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Step 1: Grid

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

File −→ Read −→Case...

2. Display the grid (Figure 16.2).

Display −→Grid...

As shown in Figure 16.2, half of the bowl is modeled, with a symmetry boundary atthe centerline. The bowl is shown lying on its side, with the region to be modeledextending from the centerline to the outer wall. When you begin to display datagraphically, you will need to rotate the view and mirror it across the centerline toobtain a more realistic view of the model. This step will be performed later in thetutorial.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 15, 2002

Figure 16.2: Grid Display

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Step 2: Models

1. Specify a transient model with axisymmetric swirl.

Define −→ Models −→Solver...

(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.

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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 is recommended formost transient VOF calculations.

When you click OK, FLUENT will report that one of the zone types will needto be changed before proceeding with the calculation. You will take care of thisstep when you input boundary conditions for the problem.

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

Define −→ Models −→Viscous...

(a) Select k-epsilon as the Model, and retain the default setting of Standard underk-epsilon Model.

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Step 3: Materials

1. Copy water from the materials database so that it can be used for the secondaryphase.

Define −→Materials...

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

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

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

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Step 4: Phases

Here, water is defined as the secondary phase mainly for convenience in setting up theproblem. When you define the initial solution, you will be patching an initial swirl velocityin the bottom third of the bowl, where the water is. It is more convenient to patch a watervolume fraction of 1 there than to patch an air volume fraction of 1 in the rest of thedomain. Also, the default volume fraction at the pressure inlet is 0, which is the correctvalue if water is the secondary phase.

In general, you can specify the primary and secondary phases whichever way you prefer.It is a good idea, especially in more complicated problems, to consider how your choicewill affect the ease of problem setup.

1. Define the air and water phases within the bowl.

Define −→Phases...

(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.

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(b) Specify water as the secondary phase.

i. Select phase-2 and click the Set... button.

ii. In the Secondary Phase panel, enter water for the Name.

iii. Select water-liquid from the Phase Material drop-down list.

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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 9.81 m/s2.

Since the centerline of the bowl is the x axis, gravity points in the positive xdirection.

2. Set the operating density.

(a) Under Variable-Density Parameters, turn on the Specified Operating Density op-tion and accept the Operating Density of 1.225.

It is a good idea to set the operating density to be the density of the lighterphase. This excludes the buildup of hydrostatic pressure within the lighterphase, improving the round-off accuracy for the momentum balance.

Note: The Reference Pressure Location (0,0) is situated in a region where the fluidwill always be 100% of one of the phases (air), a condition that is essentialfor smooth and rapid convergence. If it were not, you would need to change itto a more appropriate location.

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Step 6: Boundary Conditions

Define −→Boundary Conditions...

1. Change the bowl centerline from a symmetry boundary to an axis boundary.

For axisymmetric models, the axis of symmetry must be an axis zone.

(a) Select symmetry-2 in the Zone list in the Boundary Conditions panel.

(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.

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 thatapply to all phases) and also conditions that are specific to the secondary phase.There are no conditions to be specified for the primary phase.

(a) Set the conditions for the mixture.

i. In the Boundary Conditions panel, keep the default selection of mixture inthe Phase drop-down list and click Set....

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ii. Set the Turb. Kinetic Energy to 2.25e-2 and the Turb. Dissipation Rate to7.92e-3.

Since there is initially no flow passing through the pressure inlet, you needto specify k and ε explicitly rather than using one of the other turbulencespecification methods. 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:

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 multiplying 0.07 by the maximum radius of thebowl, which is 1). See the User’s Guide for details about the specificationof turbulence 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 the Phase drop-downlist and click Set....

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ii. Retain the default Volume Fraction of 0.

A water volume fraction of 0 indicates that only air is present at thepressure inlet.

3. Set the conditions for the spinning bowl (the wall boundary).

For a wall boundary, all conditions are specified for the mixture. There are noconditions to be specified for the individual phases.

(a) In the Boundary Conditions panel, select mixture in the Phase drop-down listand click Set....

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(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 rotational Speed (Ω) to 3

rad/s.

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Step 7: Solution

In simple flows, the under-relaxation factors can usually be increased at the start of thecalculation. This is particularly true when the VOF model is used, where high under-relaxation on all variables can greatly improve the performance of the solver.

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Set all Under-Relaxation factors to 1.

! Be sure to use the scroll bar to access the under-relaxation factors thatare initially out of view.

(b) Under Discretization, choose the Body Force Weighted scheme in the drop-downlist next to Pressure.

The body-force-weighted pressure discretization scheme is recommended whenyou solve a VOF problem involving gravity.

(c) Also under Discretization, select PISO as the Pressure-Velocity Coupling method.

PISO is recommended for transient flow calculations.

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

Solve −→ Monitors −→Residual...

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(a) Under Options, select Plot.

(b) Click the OK button.

3. Enable the plotting of the axial velocity of water near the outer edge of the bowlduring the calculation.

For transient calculations, it is often useful to monitor the value of a particularvariable to see how it changes over time. Here you will first specify the point atwhich 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...

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i. Set the x0 and y0 coordinates to 0.75 and 0.65.

ii. Enter point for the New Surface Name.

iii. Click Create.

(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 Surface Monitors panel, thevelocity history will be written to a file. If you do not select the Writeoption, the history information will be lost when you exit FLUENT.

iii. In the drop-down list under Every, choose Time Step.

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iv. Click on Define... to specify the surface monitor parameters in the DefineSurface Monitor panel.

v. Select Vertex Average from the Report Type drop-down list.

This is the recommended choice when you are monitoring the value at asingle 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 in the SurfaceMonitors panel.

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4. Initialize the solution.

Solve −→ Initialize −→Initialize...

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

All initial values will be set to zero, except for the turbulence quantities.

(b) Click Init and close the panel.

5. Patch the initial distribution of water (i.e., water volume fraction of 1.0) and aswirl velocity of 3 rad/s in the bottom third of the bowl (where the water is).

In order to patch a value in just a portion of the domain, you will need to definea cell “register” for that region. You will use the same tool that is used to mark aregion of cells for adaption. Also, you will need to define a custom function for theswirl velocity.

(a) Define a register for the bottom third of the domain.

Adapt −→Region...

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i. Set the (Xminimum,Yminimum) coordinate to (0.66,0), and the (Xmaxi-mum,Ymaximum) coordinate to (1,1).

ii. Click the Mark button.

This creates a register containing the cells in this region.

(b) Check the register to be sure it is correct.

Adapt −→Manage...

i. Select the register (hexahedron-r0) in the Registers list and click Display.

The graphics display will show the bottom third of the bowl in red.

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(c) Define a custom field function for the swirl velocity w = 3r.

Define −→Custom Field Functions...

i. Click the 3 button on the calculator pad.

The 3 will appear in the Definition field. If you make a mistake, click theDEL button to delete the last item you added to the function definition.

ii. Click the X button on the calculator pad.

iii. In the Field Functions drop-down list, select Grid... and Radial 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, click on the Manage...button and select swirl-init.

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(d) Patch the water volume fraction in the bottom third of the bowl.

Solve −→ Initialize −→Patch...

i. In the Phase drop-down list, select water.

ii. Select Volume Fraction in the Variable list.

iii. Select hexahedron-r0 in the Registers To Patch list.

iv. Set the Value to 1.

v. Click Patch.

This sets the water volume fraction to 1 in the lower third of the bowl. Thatis, you have defined the lower third of the bowl to be filled with water.

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(e) Patch the swirl velocity in the bottom third of the bowl.

i. In the Phase drop-down list, select mixture.

ii. Choose Swirl Velocity in the Variable list.

iii. Enable the Use Field Function option and select swirl-init in the Field Func-tion list.

iv. Click Patch.

It’s a good idea to check your patch by displaying contours of the patched fields.

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(f) Display contours of swirl velocity.

Display −→Contours...

i. Select Velocity... and Swirl Velocity in the Contours Of lists.

ii. Enable the Filled option and turn off the Node Values option.

Since the values you patched are cell values, you should view the cell values,rather than the node values, to check that the patch has been performedcorrectly. (FLUENT computes the node values by averaging the cell val-ues.)

iii. Click Display.

To make the view more realistic, you will need to rotate the display and mirrorit across the centerline.

(g) Rotate the view and mirror it across the centerline.

Display −→Views...

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i. Select axis-2 in the Mirror Planes list and click Apply.

ii. Use your middle and left mouse buttons to zoom and translate the viewso that the entire bowl is visible in the graphics display.

iii. Click on the Camera... button to open the Camera Parameters panel.

iv. Using your left mouse button, rotate the dial clockwise until the bowlappears upright in the graphics window (90).

v. Close the Camera Parameters panel.

vi. In the Views panel, click on the Save button under Actions to save themirrored, upright view, and then close the panel.

When you do this, view-0 will be added to the list of Views.

The upright view of the bowl in Figure 16.3 correctly shows that w = 3r in theregion of the bowl that is filled with water.

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Contours of Swirl Velocity (mixture) (m/s) (Time=0.0000e+00)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

2.35e+002.23e+002.12e+002.00e+001.88e+001.76e+001.65e+001.53e+001.41e+001.29e+001.18e+001.06e+009.41e-018.23e-017.06e-015.88e-014.70e-013.53e-012.35e-011.18e-010.00e+00

Figure 16.3: Contours of Initial Swirl Velocity

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(h) Display contours of water volume fraction.

i. Select Phases... and Volume fraction of water in the Contours Of lists.

ii. Select water in the Phase drop-down list.

iii. Set the number of contour Levels to 2 and click Display.

There are only two possible values for the volume fraction at this point: 0or 1.

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Contours of Volume fraction (water) (Time=0.0000e+00)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.00e+00

5.00e-01

0.00e+00

Figure 16.4: Contours of Initial Water Volume Fraction

Figure 16.4 correctly shows that the bottom third of the bowl contains water.

6. Set the time-step parameters for the calculation.

Solve −→Iterate...

(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 time a case file issaved).

7. Request saving of data files every 100 time steps.

File −→ Write −→Autosave...

(a) Set the Autosave Case File Frequency to 0 and the Autosave Data File Frequencyto 100.

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(b) Enter the Filename bowl and then click OK.

FLUENT will append the time step value to the file name prefix (bowl). Thestandard .dat extension will also be appended. This will yield file names ofthe form bowl100.dat, where 100 is the time step number.

8. Save the initial case and data files (bowl.cas and bowl.dat).

File −→ Write −→Case & Data...

9. Request 1000 time steps.

Solve −→Iterate...

Since the time step is 0.002 seconds, you will be calculating up to t= 2 seconds.FLUENT will automatically save a data file after every 0.2 seconds, so you willhave 10 data files for postprocessing.

Figure 16.5 shows the time history for the axial velocity. The velocity is clearlyoscillating, and the oscillations appear to be decaying over time (as the peaks becomesmaller). This periodic oscillation has a cycle of 1 second. The switch from apositive to a negative axial velocity indicates that the water is sloshing up and downthe sides of the bowl in an attempt to reach an equilibrium position. The fact thatthe amplitude is decaying suggests that equilibrium will be reached at some point.The periodic behavior in evidence will therefore be present only during the initialstartup phase of the bowl rotation.

Convergence history of Axial Velocity on point (Time=2.0000e+00)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

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 16.5: Time History of Axial Velocity

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Step 8: Postprocessing

As indicated by changes in axial velocity in Figure 16.5, the flow field is oscillating peri-odically. In this step, you will examine the flow field at several different times. (Recallthat FLUENT saved 10 data files for you during the calculation.)

1. Read in the data file of interest.

File −→ Read −→Data...

2. Display filled contours of water volume fraction.

Display −→Contours...

Hint: Follow the instructions in substep 5h of Step 7: Solution (on page 16-28),but turn Node Values back on.

Figures 16.6–16.9 show that the water level decreases from t = 0.4 to t = 0.6, thenincreases from t = 0.6 to t = 1. At t = 1, the water level in the center of thebowl has risen above the initial level, so you can expect the cycle to repeat as thewater level begins to decrease again in an attempt to return to equilibrium. (Youcan read in the data files between t = 1 and t = 2 to confirm that this is in factwhat happens.

Since the time history of axial velocity (Figure 16.5) shows that the velocity os-cillation is decaying over time, you can expect that if you were to continue thecalculation, the water level would eventually reach some point where the gravita-tional and centrifugal forces balance and the water level reaches a new equilibriumpoint.

Extra: Try continuing the calculation to determine how long it takes for the axialvelocity oscillations in Figure 16.5 to disappear.

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Contours of Volume fraction (water) (Time=4.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.00e+00

5.00e-01

0.00e+00

Figure 16.6: Shape of the Free Surface at t = 0.4

Contours of Volume fraction (water) (Time=6.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.00e+00

5.00e-01

0.00e+00

Figure 16.7: Shape of the Free Surface at t = 0.6

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Contours of Volume fraction (water) (Time=8.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.00e+00

5.00e-01

0.00e+00

Figure 16.8: Shape of the Free Surface at t = 0.8

Contours of Volume fraction (water) (Time=1.0000e+00)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.00e+00

5.00e-01

0.00e+00

Figure 16.9: Shape of the Free Surface at t = 1

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3. Plot contours of stream function.

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

(b) Turn off the Filled option and increase the number of contour Levels to 30.

(c) Click on Display.

In Figures 16.10–16.13, you can see a recirculation region that falls and rises asthe water level changes. To get a better sense of these recirculating patterns, youwill next look at velocity vectors.

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Contours of Stream Function (mixture) (kg/s) (Time=4.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

2.64e+01

2.46e+01

2.29e+01

2.11e+01

1.93e+01

1.76e+01

1.58e+01

1.41e+01

1.23e+01

1.05e+01

8.79e+00

7.03e+00

5.27e+00

3.52e+00

1.76e+00

0.00e+00

Figure 16.10: Contours of Stream Function at t = 0.4

Contours of Stream Function (mixture) (kg/s) (Time=6.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

2.62e+01

2.45e+01

2.27e+01

2.10e+01

1.92e+01

1.75e+01

1.57e+01

1.40e+01

1.22e+01

1.05e+01

8.74e+00

6.99e+00

5.24e+00

3.49e+00

1.75e+00

0.00e+00

Figure 16.11: Contours of Stream Function at t = 0.6

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Contours of Stream Function (mixture) (kg/s) (Time=8.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

4.76e+01

4.45e+01

4.13e+01

3.81e+01

3.49e+01

3.18e+01

2.86e+01

2.54e+01

2.22e+01

1.91e+01

1.59e+01

1.27e+01

9.53e+00

6.35e+00

3.18e+00

0.00e+00

Figure 16.12: Contours of Stream Function at t = 0.8

Contours of Stream Function (mixture) (kg/s) (Time=1.0000e+00)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

8.42e+00

7.86e+00

7.30e+00

6.74e+00

6.18e+00

5.62e+00

5.05e+00

4.49e+00

3.93e+00

3.37e+00

2.81e+00

2.25e+00

1.68e+00

1.12e+00

5.62e-01

0.00e+00

Figure 16.13: Contours of Stream Function at t = 1

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4. Plot velocity vectors in the bowl.

Display −→Vectors...

(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 to 1.

(c) Click on Vector Options... to open the Vector Options panel.

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i. Turn off the Z Component.

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

ii. Click Apply and close the panel.

(d) Click on Display.

Figures 16.14–16.17 show the changes in water and air flow patterns between t = 0.4and t = 1. In Figure 16.14, you can see that the flow in the middle of the bowl isbeing pulled down by gravitational forces, and pushed out and up along the sides ofthe bowl by centrifugal forces. This causes the water level to decrease in the centerof the bowl, as shown in the volume fraction contour plots, and also results in theformation of a recirculation region in the air above the water surface.

In Figure 16.15, the flow has reversed direction, and is slowly rising up in the mid-dle of the bowl and being pulled down along the sides of the bowl. This reversaloccurs because the earlier flow pattern caused the water to overshoot the equilib-rium position. The gravity and centrifugal forces now act to compensate for thisovershoot.

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Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=4.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.93e+00

1.80e+00

1.67e+00

1.54e+00

1.42e+00

1.29e+00

1.16e+00

1.03e+00

9.05e-01

7.77e-01

6.49e-01

5.21e-01

3.93e-01

2.65e-01

1.37e-01

8.68e-03

Figure 16.14: Velocity Vectors for the Air and Water at t = 0.4

Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=6.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

1.95e+00

1.82e+00

1.69e+00

1.56e+00

1.43e+00

1.30e+00

1.17e+00

1.04e+00

9.11e-01

7.81e-01

6.51e-01

5.21e-01

3.91e-01

2.61e-01

1.30e-01

3.43e-04

Figure 16.15: Velocity Vectors for the Air and Water at t = 0.6

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Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=8.0000e-01)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

2.13e+00

1.99e+00

1.85e+00

1.71e+00

1.56e+00

1.42e+00

1.28e+00

1.14e+00

9.97e-01

8.55e-01

7.14e-01

5.72e-01

4.30e-01

2.88e-01

1.47e-01

4.92e-03

Figure 16.16: Velocity Vectors for the Air and Water at t = 0.8

Velocity Vectors Colored By Velocity Magnitude (mixture) (m/s) (Time=1.0000e+00)FLUENT 6.1 (axi, swirl, segregated, vof, ske, unsteady)

Nov 18, 2002

2.12e+00

1.98e+00

1.84e+00

1.70e+00

1.56e+00

1.42e+00

1.28e+00

1.13e+00

9.93e-01

8.51e-01

7.10e-01

5.69e-01

4.27e-01

2.86e-01

1.45e-01

3.17e-03

Figure 16.17: Velocity Vectors for the Air and Water at t = 1

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In Figure 16.16 you can see that the flow is rising up more quickly in the middle ofthe bowl, and in Figure 16.17 you can see that the flow is still moving upward, butmore slowly. These patterns correspond to the volume fraction plots at these times.As the upward motion 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 free surface modelto solve a problem involving a spinning bowl of water. The time-dependent VOFformulation is used in this problem to track the shape of the free surface and theflow field inside the spinning bowl.

You observed the changing pattern of the water and air in the bowl by displayingvolume fraction contours, stream function contours, and velocity vectors at t = 0.4,t = 0.6, t = 0.8, and t = 1 second.

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Tutorial 17. Modeling Cavitation

Introduction: This tutorial examines the pressure-driven cavitating flow of waterthrough a sharp-edged orifice. This is a typical configuration in fuel injectors,and brings a challenge to the physics and numerics of cavitation models, because ofthe high pressure differentials involved, and the high ratio of liquid to vapor den-sity. Using FLUENT’s multiphase modeling capability, you will be able to predictthe strong cavitation near the orifice after flow separation at a sharp edge. In thistutorial you will learn how to:

• Set boundary conditions for internal flow

• Use the mixture model with cavitation effects

• Calculate a solution using the segregated solver

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: The problem considers the cavitation caused by the flow sepa-ration after a sharp-edged orifice. The flow is pressure driven, with an inlet pressureof 5 × 105 Pa, and an outlet pressure of 9.5 × 104 Pa. The orifice diameter is 4× 10−3 m, and geometrical parameters of the orifice are D/d = 2.88 and L/d =8, where D, d, and L are inlet diameter, orifice diameter, and orifice length respec-tively. The geometry of the orifice is shown in Figure 17.1.

Preparation

1. Copy the file cav/cav.msh from the FLUENT documentation CD to your workingdirectory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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pressureinlet = 5e5 Pa

pressureoutlet = 9.5e4 Pa

Axis

Wall

Figure 17.1: Problem Specification

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Modeling Cavitation

Step 1: Grid

1. Read the grid file (cav.msh).

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid.

Display −→Grid...

(a) Display the grid using the default settings (Figure 17.2).

As shown in Figure 17.2, half of the problem geometry is modeled, with anaxis boundary (consisting of two separate lines) at the centerline. Especiallywhen you begin to display data graphically, you may want to mirror the viewacross the centerline to obtain a more realistic view of the model. This stepwill be performed later in the tutorial.

The mesh is quadrilateral, slightly graded in the plenum to be finer toward theorifice. In the orifice, the mesh is uniform, with aspect ratios close to 1, asthe flow is expected to exhibit two-dimensional gradients.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 26, 2002

Figure 17.2: The Grid in the Orifice

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Step 2: Models

1. Specify a steady-state axisymmetric model.

Define −→ Models −→Solver...

The segregated solver must be used for multiphase calculations.

(a) Under Space, select Axisymmetric.

(b) Keep the default settings for everything else.

Note: A computationally-intensive unsteady calculation is necessary to accuratelysimulate the irregular cyclic process of bubble formation, growth, filling bywater jet re-entry, and breakoff. In this tutorial, you will perform a steady-state calculation to simulate the presence of a bubble in the separation regionin the time-averaged flow.

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2. Enable the multiphase mixture model with cavitation effects.

Define −→ Models −→Multiphase...

(a) Select Mixture as the Model.

The panel will expand.

(b) Under Mixture Parameters, turn off the Slip Velocity option.

Since there is no significant difference in velocities for the different phases,there is no need to solve for the slip velocity equation.

(c) Select Cavitation under Interphase Mass Transfer.

The panel will expand again to show the cavitation inputs.

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(d) Enter 3540 for the Vaporization Pressure.

The vaporization pressure is a property of the working liquid, which dependsmainly on the liquid temperature. The default value is the vaporization pressureof water at a temperature of 300 K.

(e) Enter 1.5e-5 for Non Condensable Gas.

This is the mass fraction of non condensable gas dissolved in the workingliquid. 1.5e− 5 (15 ppm) is a typical value for air dissolved in water.

(f) Enter 0.0717 for the Liquid Surface Tension.

Like the vaporization pressure, the liquid-vapor surface tension is a property ofthe liquid, which depends mainly on temperature. Here too, the default valueis the surface tension for water and vapor at a temperature of 300 K.

3. Turn on the standard k-ε turbulence model with standard wall functions.

Define −→ Models −→Viscous...

(a) Select k-epsilon as the Model.

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(b) Keep the default selection of Standard under k-epsilon Model.

The standard k-εmodel used in conjunction with standard wall functions is asuitable choice for this problem. For different cavitation problems, you mayuse other turbulence models. See Chapter 22 of the User’s Guide for moreinformation on the choice of turbulence models to be used in conjunction withFLUENT’s cavitation model.

(c) Keep the default selection of Standard Wall Functions under Near-Wall Treat-ment.

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Step 3: Materials

1. Create a new material to be used for the primary phase. Copy water vapor fromthe materials database so that it can be used for the secondary phase, and modifyits density.

Define −→Materials...

(a) In the Name field, type water.

(b) Clear the Chemical Formula field.

(c) In the Density drop-down list, keep the default selection of constant, and entera value of 1000.

(d) In the Viscosity drop-down list, keep the default selection of constant, and entera value of 0.001.

(e) Click Change/Create, and then click Yes in the dialog box prompting whetheryou want to overwrite the definition of air.

(f) Click the Database... button in the Materials panel.

The Database Materials panel will open.

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i. In the list of Fluid Materials, select water-vapor (h2o).

ii. Click Copy to copy the information for water vapor to your model.

iii. Close the Database Materials panel.

(g) Change the value of Density for water-vapor (h2o) to 0.02558.

(h) Change the value of Viscosity for water-vapor (h2o) to 1.26e-6.

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Step 4: Phases

1. Define the liquid water and water vapor phases that flow through the orifice.

Define −→Phases...

(a) Specify liquid water as the primary phase.

i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter liquid for the Name.

iii. Select water from the Phase Material drop-down list.

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(b) Specify water vapor as the secondary phase.

i. Select phase-2 and click the Set... button.

ii. In the Secondary Phase panel, enter vapor for the Name.

iii. Select water-vapor from the Phase Material drop-down list.

Step 5: Operating Conditions

1. Set the operating pressure to 0 pascal.

Define −→Operating Conditions...

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Step 6: Boundary Conditions

For this problem, you need to set the boundary conditions for two boundaries: the pressureinlet (consisting of two boundary zones), and the pressure outlet. The pressure outlet isthe downstream boundary, opposite the pressure inlets.

1. Set the conditions for the pressure inlets (inlet-1, inlet-2).

For the multiphase mixture model, you will specify conditions for the mixture (i.e.,conditions that apply to all phases) and also conditions that are specific to theprimary and secondary phases. In this tutorial, boundary conditions are needed forthe mixture and secondary phase only.

(a) Set the conditions for the mixture.

Define −→Boundary Conditions...

i. In the Boundary Conditions panel, keep the default selection of mixture inthe Phase drop-down list and click Set....

ii. Enter 500000 for the Gauge Total Pressure.

iii. Enter 449000 for the Supersonic/Initial Gauge Pressure.

If you choose to initialize the solution based on the pressure-inlet con-ditions, the Supersonic/Initial Gauge Pressure will be used in conjunctionwith the specified stagnation pressure (the Gauge Total Pressure) to com-pute initial values according to the isentropic relations (for compressibleflow) or Bernoulli’s equation (for incompressible flow). Otherwise, in anincompressible flow calculation, the Supersonic/Initial Gauge Pressure inputwill be ignored by FLUENT. In this problem the velocity will be initializedbased on the difference between these two values.

iv. In the Direction Specification Method drop-down list, keep the default se-lection of Normal to Boundary.

v. In the Turbulence Specification Method drop-down list, keep the defaultselection of K and Epsilon.

vi. Under Turb. Kinetic Energy, enter 0.02.

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(b) Check the volume fraction of the secondary phase.

i. In the Boundary Conditions panel, select vapor from the Phase drop-downlist and click Set....

ii. Keep the default Volume Fraction of 0.

(c) Copy the boundary conditions defined for the first pressure inlet zone (inlet-1)to the second one (inlet-2).

i. In the Boundary Conditions panel, select mixture from the Phase drop-downlist.

ii. In the Boundary Conditions panel, click Copy...

This will open the Copy BCs panel.

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Modeling Cavitation

iii. Select inlet-1 in the From Zone list, and then select inlet-2 in the To Zoneslist.

iv. Click Copy.

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

The turbulence conditions you input at the pressure outlet will be used only if flowenters the domain through this boundary. You can set them equal to the inletvalues, as no flow reversal is expected at the pressure outlet. In general, however,it is important to set reasonable values for these downstream scalar values, in caseflow reversal occurs at some point during the calculation.

(a) Set the conditions for the mixture.

i. In the Boundary Conditions panel, keep the default selection of mixture inthe Phase drop-down list and click Set....

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Modeling Cavitation

ii. Under Gauge Pressure, enter 95000.

iii. Keep the default selection of K and Epsilon for the Turbulence SpecificationMethod.

iv. Set the Backflow Turb. Kinetic Energy to 0.02.

(b) Check the volume fraction of the secondary phase.

i. In the Boundary Conditions panel, select vapor from the Phase drop-downlist and click Set....

ii. Retain the default Volume Fraction of 0.

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Step 7: Solution

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Under Under-Relaxation Factors, set the under-relaxation factor for Pressure to0.4.

(b) Set the under-relaxation factor for Momentum to 0.4.

(c) Scroll down and set the under-relaxation factors for Turbulence Kinetic Energy,Turbulence Dissipation Rate, and Turbulent Viscosity to 0.5.

FLUENT’s new cavitation model follows a different numerical approach fromthe previous one. In general it is more robust and gives more accurate results.Typically, for more complex cases, with very high pressure drops or large liquid-vapor density ratios, the under-relaxation factors may need to be reduced tobetween 0.1 and 0.2. For the Vaporization Mass, it is generally advised to use avalue of 0.1, even though for this term you can use an under-relaxation factorof 0.001 to 1, as necessary.

(d) Under Discretization, select Linear in the Pressure drop-down list and SIMPLECin the Pressure-Velocity Coupling drop-down list.

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2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

(a) Change the convergence criterion for continuity to 1e-7 for improved accuracy.

(b) Change all other convergence criteria except for vf-vapor to 1e-5 for improvedaccuracy.

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

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3. Initialize the solution from either of the pressure inlet zones (inlet-1 or inlet-2).

Solve −→ Initialize −→Initialize...

(a) Select inlet-1 or inlet-2 in the Compute From drop-down list.

(b) Under Reference Frame, select Absolute.

(c) Click Init to initialize the solution.

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

File −→ Write −→Case...

5. Start the calculation by requesting 2500 iterations.

The solution will converge to within the specified criteria in approximately 2100iterations.

Solve −→Iterate...

6. Save the data file (cav.dat).

File −→ Write −→Data...

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Step 8: Postprocessing

1. Plot the pressure in the orifice.

Display −→Contours...

(a) Select Pressure... and Static Pressure in the drop-down lists under Contours Of.

(b) Select Filled under Options.

(c) Click Display.

Note the dramatic pressure drop at the flow restriction in Figure 17.3. Lowstatic pressure is the major factor to cause cavitation, though turbulence alsocontributes to cavitation, due to the effect of pressure fluctuation and turbulentdiffusion, as will be shown in the following plots.

To make the view more realistic, you will need to mirror it across the center-line.

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Contours of Static Pressure (mixture) (pascal)FLUENT 6.1 (axi, segregated, mixture, ske)

Nov 26, 2002

4.99e+054.74e+054.50e+054.25e+054.00e+053.75e+053.50e+053.25e+053.00e+052.75e+052.51e+052.26e+052.01e+051.76e+051.51e+051.26e+051.01e+057.64e+045.15e+042.67e+041.77e+03

Figure 17.3: Contours of Static Pressure

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2. Mirror the display across the centerline.

Display −→Views...

(a) Select symm-1 and symm-2 in the Mirror Planes list and click Apply.

Contours of Static Pressure (mixture) (pascal) Dec 17, 2002FLUENT 6.1 (axi, segregated, mixture, ske)

4.99e+05

1.77e+032.67e+045.15e+047.64e+041.01e+051.26e+051.51e+051.76e+052.01e+052.26e+052.51e+052.75e+053.00e+053.25e+053.50e+053.75e+054.00e+054.25e+054.50e+054.74e+05

Figure 17.4: Mirrored View of Contours of Static Pressure

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3. Plot the turbulent kinetic energy.

Display −→Contours...

(a) Select Turbulence... and Turbulent Kinetic Energy in the drop-down lists underContours Of.

(b) Click Display.

Contours of Turbulent Kinetic Energy (k) (mixture) (m2/s2) Dec 17, 2002FLUENT 6.1 (axi, segregated, mixture, ske)

2.48e+01

6.01e-031.24e+002.48e+003.72e+004.96e+006.20e+007.44e+008.67e+009.91e+001.12e+011.24e+011.36e+011.49e+011.61e+011.73e+011.86e+011.98e+012.11e+012.23e+012.35e+01

Figure 17.5: Contours of Turbulent Kinetic Energy

In this example, the grid used is fairly coarse. However, in cavitating flows thepressure distribution is the dominant factor, and is not very sensitive to grid size.

4. Plot the volume fraction of water vapor.

Display −→Contours...

(a) Select Phases... and Volume fraction in the drop-down lists under Contours Of.

(b) Select vapor in the Phase drop-down list.

(c) Click Display.

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Contours of Volume fraction (vapor) Dec 17, 2002FLUENT 6.1 (axi, segregated, mixture, ske)

1.00e-00

2.59e-035.24e-021.02e-011.52e-012.02e-012.52e-013.02e-013.52e-014.01e-014.51e-015.01e-015.51e-016.01e-016.51e-017.01e-017.50e-018.00e-018.50e-019.00e-019.50e-01

Figure 17.6: Contours of Vapor Volume Fraction

Note that the high turbulent kinetic energy region near the neck of the orifice (Fig-ure 17.5) coincides with the highest volume fraction of vapor in Figure 17.6. Thisindicates the correct prediction of a localized high phase change rate. The vaporthen gets convected downstream by the main flow.

Summary: This tutorial demonstrated how to set up and resolve a strongly cavitatingpressure driven flow through an orifice, using FLUENT’s multiphase mixture modelwith cavitation effects. You learned how to set the boundary conditions for aninternal flow. A steady-state solution was calculated to simulate the formation ofa vapor bubble in the neck of the flow after the section restriction at the orifice.A more computationally-intensive unsteady calculation is necessary to accuratelysimulate the irregular cyclic process of bubble formation, growth, filling by waterjet re-entry, and breakoff.

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Tutorial 18. Using the Mixture and EulerianMultiphase Models

Introduction: This tutorial examines the flow of water and air in a tee junction. Firstyou will solve the problem using the less computationally-intensive mixture model,and then you will turn to the more accurate Eulerian model. Finally, you willcompare the results obtained with the two approaches.

In this tutorial you will learn how to:

• Use the mixture model with slip velocities

• Set boundary conditions for internal flow

• Calculate a solution using the segregated solver

• Use the Eulerian model

• Compare the results obtained with the two approaches

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: This problem considers an air-water mixture flowing upwardsin a duct and then splitting in a tee-junction. The ducts are 25 mm in width, theinlet section of the duct is 125 mm long, and the top and the side ducts are 250mm long. The geometry and data for the problem are shown in Figure 18.1.

Preparation

1. Copy the file tee/tee.msh from the FLUENT documentation CD to your workingdirectory (as described in Tutorial 1).

2. Start the 2D version of FLUENT.

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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

3 3

velocity inletwater: v = - 0.31 m/sair: v = - 0.45 m/s

pressure outlet

Figure 18.1: Problem Specification

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Step 1: Grid

1. Read the grid file (tee.msh).

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid.

Display −→Grid...

(a) Display the grid using the default settings (Figure 18.2).

Extra: You can use the right mouse button to check which zone number cor-responds to each boundary. If you click the right mouse button on oneof the boundaries in the graphics window, its zone number, name, andtype will be printed in the FLUENT console window. This feature is espe-cially useful when you have several zones of the same type and you wantto distinguish between them quickly.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 18, 2002

Figure 18.2: The Grid in the Tee Junction

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Step 2: Models

1. Keep the default settings for the 2D segregated steady-state solver.

Define −→ Models −→Solver...

The segregated solver must be used for multiphase calculations.

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2. Enable the multiphase mixture model with slip velocities.

Define −→ Models −→Multiphase...

(a) Select Mixture as the Model.

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

(b) Under Mixture Parameters, keep the Slip Velocity turned on.

Since there will be significant difference in velocities for the different phases,you need to solve the slip velocity equation.

(c) Under Body Force Formulation, select Implicit Body Force.

This treatment improves solution convergence by accounting for the partialequilibrium of the pressure gradient and body forces in the momentum equa-tions. It is used when body forces are large in comparison to viscous andconvective forces, namely in VOF and mixture problems.

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3. Turn on the standard k-ε turbulence model with standard wall functions.

Define −→ Models −→Viscous...

(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 effective in accurately re-solving mixture problems when standard wall functions are used.

(c) Keep the default selection of Standard Wall Functions under Near-Wall Treat-ment.

This problem does not require a particularly fine grid, and standard wall func-tions will be used.

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4. 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 Y direction to -9.81 m/s2.

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Step 3: Materials

1. Copy liquid water from the materials database so that it can be used for the primaryphase.

Define −→Materials...

(a) Click the Database... button in the Materials panel.

The Database Materials panel will open.

(b) In the list of Fluid Materials, select water-liquid (h2o<l>).

(c) Click Copy to copy the information for liquid water to your model.

(d) Close the Database Materials panel and the Materials panel.

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Step 4: Phases

1. Define the liquid water and air phases that flow in the tee junction.

Define −→Phases...

(a) Specify liquid water as the primary phase.

i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter water for the Name.

iii. Select water-liquid from the Phase Material drop-down list.

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(b) Specify air as the secondary phase.

i. Select phase-2 and click the Set... button.

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.

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2. Check the slip velocity formulation to be used.

(a) Click the Interaction... button in the Phases panel.

(b) In the Phase Interaction panel, click the Slip tab.

(c) Keep the default selection of manninen-et-al in the Slip Velocity drop-down list.

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Step 5: Boundary Conditions

For this problem, you need to set the boundary conditions for three boundaries: the upperand lower velocity inlets and the pressure outlet.

Define −→Boundary Conditions...

1. Set the conditions for the lower velocity inlet (velocity-inlet-4).

For the multiphase mixture model, you will specify conditions at a velocity inlet forthe mixture (i.e., conditions that apply to all phases) and also conditions that arespecific to the primary and secondary phases.

(a) Set the conditions at velocity-inlet-4 for the mixture.

i. In the Boundary Conditions panel, keep the default selection of mixture inthe Phase drop-down list and click Set....

ii. In the Turbulence Specification Method drop-down list, select Intensity andLength Scale.

iii. Set Turbulence Intensity to 10% and Turbulence Length Scale to 0.025 m.

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(b) Set the conditions for the primary phase.

i. In the Boundary Conditions panel, select water from the Phase drop-downlist and click Set....

ii. Keep the default Velocity Specification Method and Reference 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 Phase drop-down listand click Set....

ii. Keep the default Velocity Specification Method and Reference Frame.

iii. Set the Velocity Magnitude to 1.6.

iv. Set the Volume Fraction to 0.02.

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2. Set the conditions for the upper velocity inlet (velocity-inlet-5).

(a) Set the conditions at velocity-inlet-5 for the mixture.

i. In the Boundary Conditions panel, select mixture in the Phase drop-downlist and click Set....

ii. In the Turbulence Specification Method drop-down list, select Intensity andLength Scale.

iii. Set Turbulence Intensity to 10% and Turbulence Length Scale to 0.025 m.

(b) Set the conditions for the primary phase.

i. In the Boundary Conditions panel, select water from the Phase drop-downlist and click Set....

ii. Keep the default Velocity Specification Method and Reference Frame.

iii. Set the Velocity Magnitude to -0.31.

In this problem, outflow characteristics at the upper velocity inlet are as-sumed to be known, and therefore imposed as a boundary condition.

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(c) Set the conditions for the secondary phase.

i. In the Boundary Conditions panel, select air from the Phase drop-down listand click Set....

ii. Keep the default Velocity Specification Method and Reference Frame.

iii. Set the Velocity Magnitude to -0.45.

iv. Set the Volume Fraction to 0.02.

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3. Set the boundary conditions for the pressure outlet (pressure-outlet-3).

For the multiphase mixture model, you will specify conditions at a pressure outletfor the mixture and for the secondary phase. There are no conditions to be set forthe primary phase.

The turbulence conditions you input at the pressure outlet will be used only if flowenters the domain through this boundary. You can set them equal to the inletvalues, as no flow reversal is expected at the pressure outlet. In general, however,it is important to set reasonable values for these downstream scalar values, in caseflow reversal occurs at some point during the calculation.

(a) Set the conditions at pressure-outlet-3 for the mixture.

i. In the Boundary Conditions panel, select mixture in the Phase drop-downlist and click Set....

ii. In the Turbulence Specification Method drop-down list, select Intensity andLength Scale.

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.

i. In the Boundary Conditions panel, select air from the Phase drop-down listand click Set....

ii. Set the Backflow Volume Fraction to 0.02.

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Step 6: Solution Using the Mixture Model

1. Set the solution parameters.

Solve −→ Controls −→Solution...

(a) Keep all default Under-Relaxation Factors.

(b) Under Discretization, select PRESTO! in the Pressure drop-down list.

2. Enable the plotting of residuals during the calculation.

Solve −→ Monitors −→Residual...

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3. Initialize the solution.

Solve −→ Initialize −→Initialize...

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

File −→ Write −→Case...

5. Start the calculation by requesting 1000 iterations.

Solve −→Iterate...

The solution will converge in approximately 600 iterations.

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

File −→ Write −→Case & Data...

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Step 7: Postprocessing for the Mixture Solution

1. Display the pressure field in the tee (Figure 18.3).

Display −→Contours...

(a) Select Pressure... and Static Pressure in the Contours Of drop-down lists.

(b) Select Filled under Options.

(c) Click Display.

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Contours of Static Pressure (mixture) (pascal)FLUENT 6.1 (2d, segregated, mixture, ske)

Nov 18, 2002

2.34e+032.15e+031.95e+031.76e+031.56e+031.36e+031.17e+039.73e+027.77e+025.81e+023.85e+021.89e+02-7.51e+00-2.04e+02-4.00e+02-5.96e+02-7.92e+02-9.88e+02-1.18e+03-1.38e+03-1.58e+03

Figure 18.3: Contours of Static Pressure

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2. Display contours of velocity magnitude (Figure 18.4).

Display −→Contours...

(a) Select Velocity... and Velocity Magnitude in the Contours Of drop-down lists.

(b) Click Display.

Contours of Velocity Magnitude (mixture) (m/s)FLUENT 6.1 (2d, segregated, mixture, ske)

Nov 18, 2002

2.23e+002.12e+002.01e+001.90e+001.78e+001.67e+001.56e+001.45e+001.34e+001.23e+001.12e+001.00e+008.92e-017.81e-016.69e-015.58e-014.46e-013.35e-012.23e-011.12e-010.00e+00

Figure 18.4: Contours of Velocity Magnitude

3. Display the volume fraction of air (Figure 18.5).

Display −→Contours...

(a) Select Phases... and Volume fraction in the Contours Of drop-down lists.

(b) Select air in the Phase drop-down list.

(c) Click Display.

In Figure 18.5, note the small bubble of air that separates at the sharp edge of thehorizontal arm of the tee junction, and the small layer of air that floats in the samearea above the water, marching towards the pressure outlet.

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Contours of Volume fraction (air) FLUENT 6.1 (2d, segregated, mixture, ske)

Nov 18, 2002

9.48e-019.01e-018.53e-018.06e-017.58e-017.11e-016.64e-016.16e-015.69e-015.21e-014.74e-014.27e-013.79e-013.32e-012.84e-012.37e-011.90e-011.42e-019.48e-024.74e-021.09e-13

Figure 18.5: Contours of Air Volume Fraction

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Step 8: Setup and Solution for the Eulerian Model

You will use the solution obtained with the mixture model as an initial condition for thecalculation with the Eulerian model.

1. Turn on the Eulerian model.

Define −→ Models −→Multiphase...

(a) Under Models, select Eulerian.

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2. Specify the drag law to be used for computing the interphase momentum transfer.

Define −→Phases...

(a) Click the Interaction... button in the Phases panel.

(b) In the Phase Interaction panel, keep the default selection of schiller-naumann inthe Drag Coefficient drop-down list.

Note: For this problem there are no parameters to be set for the individual phases,other than those that you specified when you set up the phases for the mixturemodel calculation. If you use the Eulerian model for a flow involving a granularsecondary phase, there are additional parameters that you need to set. Thereare also other options in the Phase Interaction panel that may be relevant forother applications. See the User’s Guide for complete details on setting up anEulerian multiphase calculation.

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3. Select the multiphase turbulence model.

Define −→ Models −→Viscous...

(a) Under k-epsilon Multiphase Model, keep the default selection of Mixture.

The mixture turbulence model is applicable when phases separate, for stratified(or nearly stratified) multiphase flows, and when the density ratio betweenphases is close to 1. In these cases, using mixture properties and mixturevelocities is sufficient to capture important features of the turbulent flow. SeeChapter 22 of the User’s Guide for more information on turbulence models forthe Eulerian multiphase model.

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4. Continue the solution by requesting 1000 additional iterations.

Solve −→Iterate...

The solution will converge after about 300 additional iterations.

5. Save the case and data files (tee2.cas and tee2.dat).

File −→ Write −→Case & Data...

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Step 9: Postprocessing for the Eulerian Model

1. Display the pressure field in the tee (Figure 18.6).

Display −→Contours...

Contours of Static Pressure (mixture) (pascal)FLUENT 6.1 (2d, segregated, eulerian, ske)

Nov 18, 2002

2.54e+032.34e+032.14e+031.94e+031.75e+031.55e+031.35e+031.15e+039.54e+027.55e+025.57e+023.59e+021.61e+02-3.74e+01-2.36e+02-4.34e+02-6.32e+02-8.30e+02-1.03e+03-1.23e+03-1.42e+03

Figure 18.6: Contours of Static Pressure

2. Display contours of velocity magnitude for the water (Figure 18.7).

Display −→Contours...

(a) In the Contours Of drop-down lists, select Velocity... and water Velocity Mag-nitude.

Because the Eulerian model solves individual momentum equations for eachphase, you have the choice of which phase to plot solution data for.

(b) Click Display.

3. Display the volume fraction of air (Figure 18.8).

Display −→Contours...

Note that the air bubble at the tee junction in Figure 18.8 is slightly different fromthe one that you observed in the solution obtained with the mixture model (Fig-ure 18.5). The Eulerian model generally offers better accuracy than the mixturemodel, as it solves separate sets of equations for each individual phase, rather thanmodeling slip velocity between phases. See Chapter 22 of the User’s Guide for moreinformation about the mixture and Eulerian models.

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Contours of Velocity Magnitude (water) (m/s)FLUENT 6.1 (2d, segregated, eulerian, ske)

Nov 18, 2002

2.25e+002.14e+002.03e+001.91e+001.80e+001.69e+001.58e+001.46e+001.35e+001.24e+001.13e+001.01e+009.01e-017.88e-016.76e-015.63e-014.51e-013.38e-012.25e-011.13e-010.00e+00

Figure 18.7: Contours of Water Velocity Magnitude

Contours of Volume fraction (air) FLUENT 6.1 (2d, segregated, eulerian, ske)

Nov 18, 2002

9.41e-018.94e-018.47e-018.00e-017.53e-017.06e-016.59e-016.12e-015.65e-015.18e-014.70e-014.23e-013.76e-013.29e-012.82e-012.35e-011.88e-011.41e-019.41e-024.70e-022.22e-29

Figure 18.8: Contours of Air Volume Fraction

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Summary: This tutorial demonstrated how to set up and solve a multiphase problemusing the mixture model and the Eulerian model. You learned how to set boundaryconditions for the mixture and both phases. The solution obtained with the mixturemodel was used as a starting point for the calculation with the Eulerian model.After completing calculations with both models, you compared the results obtainedwith the two approaches.

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Tutorial 19. Using the Eulerian MultiphaseModel for Granular Flow

Introduction: Mixing tanks are used to maintain solid particles or droplets of heavyfluids in suspension. Mixing may be required to enhance reaction during chemicalprocessing or to prevent sedimentation. In this tutorial, you will use the Eulerianmultiphase model to solve the particle suspension problem. The Eulerian multi-phase model solves momentum equations for each of the phases, which are allowedto mix in any proportion.

In this tutorial you will learn how to:

• Use the granular Eulerian multiphase model

• Specify fixed velocities with a user-defined function (UDF) to simulate animpeller

• Set boundary conditions for internal flow

• Calculate a solution using the segregated solver

• Solve a time-accurate transient problem

Prerequisites: This tutorial assumes that you are familiar with the menu structure inFLUENT and that you have solved or read Tutorial 1. Some steps in the setup andsolution procedure will not be shown explicitly.

Problem Description: The problem involves the transient startup of an impeller-driven mixing tank. The primary phase is water, while the secondary phase consistsof sand particles with a 111 micron diameter. The sand is initially settled at thebottom of the tank, to a level just above the impeller. A schematic of the mixingtank and the initial sand position is shown in Figure 19.1. The domain is modeledas 2D axisymmetric.

The fixed-values option will be used to simulate the impeller. Experimental dataare used to represent the time-averaged velocity and turbulence values at the im-peller location. This approach avoids the need to model the impeller itself. Theseexperimental data are provided in a user-defined function.

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.4446 m

.4446 m

water

settledsandbed

impeller

.1728 m

.116 m.0864 m

.016 m

Figure 19.1: Problem Specification

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Preparation

1. Copy the files mixtank/mixtank.msh and mixtank/fix.c from the FLUENT doc-umentation 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 (mixtank.msh).

File −→ Read −→Case...

As FLUENT reads the grid file, it will report its progress in the console window.

2. Check the grid.

Grid −→Check

FLUENT will perform various checks on the mesh and will report the progress in theconsole window. Pay particular attention to the reported minimum volume. Makesure this is a positive number.

3. Display the grid.

Display −→Grid...

(a) Display the grid using the default settings (Figure 19.2).

Extra: You can use the right mouse button to check which zone number cor-responds to each boundary. If you click the right mouse button on oneof the boundaries in the graphics window, its zone number, name, andtype will be printed in the FLUENT console window. This feature is espe-cially useful when you have several zones of the same type and you wantto distinguish between them quickly.

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GridFLUENT 6.1 (2d, segregated, lam)

Nov 18, 2002

Figure 19.2: Grid Display

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(b) Click the Colors... button.

This will open the Grid Colors panel. The Grid Colors panel allows you to controlthe colors that are used to draw grids.

i. In the Grid Colors panel, select Color By ID.

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

(c) In the Grid Display panel, click Display. (Figure 19.3).

The graphics display will be updated to show the grid.

GridFLUENT 6.1 (2d, segregated, lam)

Nov 18, 2002

Figure 19.3: Grid Display (Color by ID option)

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4. Manipulate the grid display to show the full tank upright.

Display −→Views...

(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 display without changingits orientation (Figure 19.4).

GridFLUENT 6.1 (2d, segregated, lam)

Nov 18, 2002

Figure 19.4: Grid Display with Both Sides of the Tank

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(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 dial and drag it in thecounter-clockwise direction till the upright view is displayed (Figure 19.5).

(f) Click Apply and close the Camera Parameters and Views panels.

GridFLUENT 6.1 (2d, segregated, lam)

Nov 18, 2002

Figure 19.5: Grid Display of the Upright Tank

Note: When experimenting with different view manipulation techniques, you mayaccidentally “lose” your geometry in the display. You can easily return to thedefault (front) view by clicking on the Default button in the Views panel.

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Step 2: Models

1. Specify a transient, axisymmetric model.

Define −→ Models −→Solver...

(a) Retain the default Segregated solver.

The segregated solver must be used for multiphase calculations.

(b) Under Space, select Axisymmetric.

(c) Under Time, select Unsteady.

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2. Enable the Eulerian multiphase model.

Define −→ Models −→Multiphase...

(a) Select Eulerian as the Model.

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

(b) Keep the default settings for the Eulerian model.

3. Turn on the k-ε turbulence model with standard wall functions.

Define −→ Models −→Viscous...

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(a) Select k-epsilon as the Model.

(b) Keep the default selection of Standard Wall Functions under Near-Wall Treat-ment.

This problem does not require a particularly fine grid, and standard wall func-tions will be used.

(c) Under k-epsilon Multiphase Model, select the Dispersed model.

The dispersed turbulence model is applicable in this case because there is clearlyone primary continuous phase and the material density ratio of the phases isabout 2.5. Furthermore, the Stokes number is much less than 1. Therefore,the particle’s kinetic energy will not depart significantly from that of the liquid.

4. 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 -9.81 m/s2.

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Step 3: Materials

In this step, you will add liquid water to the list of fluid materials by copying it from thematerials database, and create a new material called sand.

Define −→Materials...

1. Copy liquid water from the materials database so that it can be used for the primaryphase.

(a) Click the Database... button in the Materials panel.

The Database Materials panel will open.

(b) In the list of Fluid Materials, select water-liquid (h2o<l>).

(c) Click Copy to copy the information for liquid water to your model.

(d) Close the Database Materials panel.

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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 appear, asking youif water-liquid should be overwritten. Click No to retain water-liquid and addthe new material, sand, to the list. The Materials panel will be updated to showthe new material name in the Fluid Materials list.

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Step 4: Phases

1. Define the primary (water) and secondary (sand) phases.

Define −→Phases...

(a) Specify water as the primary phase.

i. Select phase-1 and click the Set... button.

ii. In the Primary Phase panel, enter water for the Name.

iii. Select water-liquid from the Phase Material drop-down list.

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(b) Specify sand as the secondary phase.

i. Select phase-2 and click the Set... button.

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.

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(c) Specify the drag law to be used for computing the interphase momentumtransfer.

i. Click the Interaction... button in the Phases panel.

ii. In the Phase Interaction panel, select gidaspow in the Drag Coefficient drop-down list.

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Step 5: Boundary Conditions

For this problem, there are no conditions to be specified on the outer boundaries. Withinthe domain, there are three fluid zones, representing the impeller region, the region wherethe sand is initially located, and the rest of the tank. There are no conditions to bespecified in the latter two zones, so you will need to set conditions only in the zonerepresenting the impeller.

As mentioned earlier, a UDF is used to specify the fixed velocities that simulate theimpeller. The values of the time-averaged impeller velocity components and turbulencequantities are based on experimental measurement. The variation of these values may beexpressed as a function of 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 function being fitted.For this tutorial, the polynomial coefficients shown in Table 19.1 are provided in the UDFfix.c.

Table 19.1: 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 using the DEFINE PROFILE

macro. Note that, while this macro is usually used to specify a profile condition on aboundary face zone, it is used in fix.c to specify the condition in a fluid cell zone. Thearguments of the macro have been changed accordingly.

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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 your mesh file residein your working directory. If your source code is not in your working di-rectory, then when you compile the UDF you must enter the file’s completepath in the 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 a listing of the as-sembly language code to appear in your console window when the functioncompiles.

(d) Click Compile to compile your UDF.

Note: The name and contents of your UDF will be stored in your case filewhen you write the case file.

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2. Set the conditions for the fluid zone representing the impeller (fix-zone).

You will specify the conditions for the water and the sand separately. There are noconditions to be specified for the mixture (i.e., conditions that apply to all phases);the default conditions for the mixture are acceptable.

Define −→Boundary Conditions...

(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 the Phase drop-downlist and click Set....

ii. Turn on the Fixed Values option.

The panel will expand to show the related inputs.

iii. Select udf fixed u from the drop-down list to the right of Axial 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.

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