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FLUENT 6.3

Users Guide

September 2006

Copyright c 2006 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, FLUENT for CATIA V5, FloWizard, GAMBIT, Icemax, Icepak, Icepro, Icewave, Icechip, MixSim, and POLYFLOW are registered trademarks of Fluent Inc. All other products or name brands are trademarks of their respective holders. CHEMKIN is a registered trademark of Reaction Design Inc. Portions of this program include material copyrighted by PathScale Corporation 2003-2004.

Fluent Inc. Centerra Resource Park 10 Cavendish Court Lebanon, NH 03766

Contents

Preface 1 Starting and Executing FLUENT 1.1

UTM-1 1-1 1-1 1-1 1-2 1-5 1-8 1-9

Starting FLUENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1.1 1.1.2 1.1.3 1.1.4 1.1.5 Single-Precision and Double-Precision Solvers . . . . . . . . . . . Starting FLUENT on a UNIX System . . . . . . . . . . . . . . . Starting FLUENT on a Windows System . . . . . . . . . . . . . . Remote Simulation Facility (RSF) . . . . . . . . . . . . . . . . . Startup Options . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.2

Executing FLUENT Remotely . . . . . . . . . . . . . . . . . . . . . . . . 1-13 1.2.1 1.2.2 1.2.3 1.2.4 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 1-13 Running FLUENT on a Remote Machine . . . . . . . . . . . . . . 1-14 Starting the Solver Manually on the Remote Machine . . . . . . 1-15 Executing Remotely by Reading a Case File . . . . . . . . . . . . 1-15

1.3

Running FLUENT in Batch Mode . . . . . . . . . . . . . . . . . . . . . . 1-16 1.3.1 1.3.2 1.3.3 Background Execution on UNIX Systems . . . . . . . . . . . . . 1-16 Background Execution on Windows Systems . . . . . . . . . . . 1-18 Batch Execution Options . . . . . . . . . . . . . . . . . . . . . . 1-19

1.4 1.5 1.6

Checkpointing a FLUENT Simulation . . . . . . . . . . . . . . . . . . . . 1-20 Cleaning Up Processes From a FLUENT Simulation . . . . . . . . . . . . 1-21 Exiting the Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-22

c Fluent Inc. September 29, 2006

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2 Graphical User Interface (GUI) 2.1 GUI Components 2.1.1 2.1.2 2.1.3 2.1.4 2.2 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2-1 2-1 2-1 2-5

Console . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dialog Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-10 Graphics Display Windows . . . . . . . . . . . . . . . . . . . . . 2-17

Customizing the Graphical User Interface (UNIX Systems Only) . . . . . 2-20 Using the GUI Help System . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 2.3.1 2.3.2 2.3.3 2.3.4 2.3.5 2.3.6 2.3.7 2.3.8 2.3.9 2.3.10 2.3.11 2.3.12 Panel Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22 Context-Sensitive Help (UNIX Only) . . . . . . . . . . . . . . . . 2-23 Opening the Users Guide Table of Contents . . . . . . . . . . . 2-23 Opening the Users Guide Index . . . . . . . . . . . . . . . . . . 2-23 Opening the Reference Guide . . . . . . . . . . . . . . . . . . . . 2-23 Help on Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-26 Help for Text Interface Commands . . . . . . . . . . . . . . . . . 2-26 Accessing the Other Manuals . . . . . . . . . . . . . . . . . . . . 2-26 Accessing the User Services Center Web Site . . . . . . . . . . . 2-28 Accessing the Fluent Online Technical Support Web Site . . . . . 2-28 Obtaining a Listing of Other FLUENT License Users . . . . . . . 2-28 Version and Release Information . . . . . . . . . . . . . . . . . . 2-28 3-1 3-1 3-3 3-4 3-4 3-5

3 Text User Interface (TUI) 3.1 Text Menu System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 3.1.2 3.1.3 3.1.4 Command Abbreviation . . . . . . . . . . . . . . . . . . . . . . . Command Line History . . . . . . . . . . . . . . . . . . . . . . . Scheme Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . Aliases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.2

Text Prompt System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5 3.2.6 3.2.7 3.2.8 Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Booleans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3-5 3-6 3-6 3-6 3-6 3-7 3-7 3-8 3-9 3-9 3-9 3-9

Filenames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Default Value Binding . . . . . . . . . . . . . . . . . . . . . . . .

3.3 3.4

Interrupts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . System Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 3.4.2 System Commands for UNIX-based Operating Systems . . . . .

System Commands for Windows Operating Systems . . . . . . . 3-10

3.5 3.6

Text Menu Input from Character Strings . . . . . . . . . . . . . . . . . . 3-11 Using the Text Interface Help System . . . . . . . . . . . . . . . . . . . 3-12 4-1 4-2 4-2 4-3 4-3 4-4 4-4 4-6 4-6 4-7

4 Reading and Writing Files 4.1 Shortcuts for Reading and Writing Files . . . . . . . . . . . . . . . . . . 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5 4.1.6 4.1.7 4.1.8 Default File Suxes . . . . . . . . . . . . . . . . . . . . . . . . . Binary Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detecting File Format . . . . . . . . . . . . . . . . . . . . . . . . Recent File List . . . . . . . . . . . . . . . . . . . . . . . . . . . Reading and Writing Compressed Files . . . . . . . . . . . . . . Tilde Expansion (UNIX Systems Only) . . . . . . . . . . . . . . Automatic Numbering of Files . . . . . . . . . . . . . . . . . . . Disabling the Overwrite Conrmation Prompt . . . . . . . . . .


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4.2

Reading Mesh Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 4.2.2 4.2.3 4.2.4 Reading TGrid Mesh Files . . . . . . . . . . . . . . . . . . . . . . Reading Surface Meshes . . . . . . . . . . . . . . . . . . . . . . . Reading GAMBIT and GeoMesh Mesh Files . . . . . . . . . . . . Reading PreBFC Unstructured Mesh Files . . . . . . . . . . . . .

4-7 4-8 4-8 4-8 4-8 4-9 4-9

4.3

Reading and Writing Case and Data Files . . . . . . . . . . . . . . . . . 4.3.1 4.3.2 4.3.3 4.3.4 Reading and Writing Case Files . . . . . . . . . . . . . . . . . .

Reading and Writing Data Files . . . . . . . . . . . . . . . . . . 4-10 Reading and Writing Case and Data Files Together . . . . . . . 4-10

Automatic Saving of Case and Data Files . . . . . . . . . . . . . 4-11

4.4 4.5 4.6 4.7 4.8 4.9

Reading FLUENT/UNS and RAMPANT Case and Data Files . . . . . . . 4-13 Reading and Writing Prole Files . . . . . . . . . . . . . . . . . . . . . . 4-14 Reading and Writing Boundary Conditions . . . . . . . . . . . . . . . . 4-15

Writing a Boundary Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16 Reading Scheme Source Files . . . . . . . . . . . . . . . . . . . . . . . . 4-17 Creating and Reading Journal Files . . . . . . . . . . . . . . . . . . . . . 4-17 4.9.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-18

4.10 Creating Transcript Files . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19 4.11 Importing Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20 4.11.1 4.11.2 4.11.3 4.11.4 4.11.5 4.11.6 4.11.7 4.11.8 4.11.9 ABAQUS Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22 ANSYS Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-22 Meshes and Data in CGNS Format . . . . . . . . . . . . . . . . . 4-23 EnSight Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23 FIDAP Neutral Files . . . . . . . . . . . . . . . . . . . . . . . . . 4-24 GAMBIT and GeoMesh Mesh Files . . . . . . . . . . . . . . . . . 4-24 HYPERMESH ASCII Files . . . . . . . . . . . . . . . . . . . . . . 4-24 I-deas Universal Files . . . . . . . . . . . . . . . . . . . . . . . . . 4-24 LSTC Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25

4.11.10 Marc POST Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25

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4.11.11 NASTRAN Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26 4.11.12 PATRAN Neutral Files . . . . . . . . . . . . . . . . . . . . . . . . 4-26 4.11.13 PLOT3D Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-27 4.11.14 PTC Mechanica Design Files . . . . . . . . . . . . . . . . . . . . . 4-27 4.11.15 FLUENT 4 Case Files . . . . . . . . . . . . . . . . . . . . . . . . 4-27 4.11.16 PreBFC Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 4.11.17 Partition Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28 4.11.18 CHEMKIN Mechanism . . . . . . . . . . . . . . . . . . . . . . . 4-28 4.12 Exporting Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29 4.12.1 4.12.2 4.12.3 4.12.4 4.12.5 4.12.6 4.12.7 4.12.8 4.12.9 Using the Export Panel . . . . . . . . . . . . . . . . . . . . . . . 4-31 ABAQUS Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32 ANSYS Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-33 ANSYS Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34 ASCII Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34 AVS Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35 CGNS Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35 Data Explorer Files . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36 EnSight Case Gold Files . . . . . . . . . . . . . . . . . . . . . . . 4-36

4.12.10 FAST Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38 4.12.11 FAST Solution Files . . . . . . . . . . . . . . . . . . . . . . . . . 4-38 4.12.12 Fieldview Unstructured Files . . . . . . . . . . . . . . . . . . . . . 4-38 4.12.13 I-deas Universal Files . . . . . . . . . . . . . . . . . . . . . . . . . 4-39 4.12.14 NASTRAN Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-40 4.12.15 PATRAN Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41 4.12.16 RadTherm Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-41 4.12.17 Tecplot Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-42 4.12.18 Dening Transient Export Parameters . . . . . . . . . . . . . . . 4-43


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4.13 Grid-to-Grid Solution Interpolation . . . . . . . . . . . . . . . . . . . . . 4-44 4.13.1 4.13.2 Performing Grid-to-Grid Solution Interpolation . . . . . . . . . . 4-44 Format of the Interpolation File . . . . . . . . . . . . . . . . . . 4-46

4.14 Saving Hardcopy Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-46 4.14.1 Using the Graphics Hardcopy Panel . . . . . . . . . . . . . . . . . 4-47

4.15 Saving the Panel Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-52 4.16 The .fluent File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-52 5 Unit Systems 5.1 5.2 5.3 5.4 Restrictions on Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Units in Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Built-In Unit Systems in FLUENT . . . . . . . . . . . . . . . . . . . . . . Customizing Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1 5-2 5-2 5-3 5-4 6-1 6-2 6-2

6 Reading and Manipulating Grids 6.1 Grid Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 6.1.2 6.1.3 6.2 Examples of Acceptable Grid Topologies . . . . . . . . . . . . . .

Face-Node Connectivity in FLUENT . . . . . . . . . . . . . . . . 6-11 Choosing the Appropriate Grid Type . . . . . . . . . . . . . . . 6-17

Grid Requirements and Considerations . . . . . . . . . . . . . . . . . . . 6-19 6.2.1 6.2.2 Geometry/Grid Requirements . . . . . . . . . . . . . . . . . . . 6-19

Mesh Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-20

6.3

Grid Import . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5 6.3.6 6.3.7 GAMBIT Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . 6-24 GeoMesh Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . 6-24 TGrid Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24 PreBFC Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25 ICEMCFD Grid Files . . . . . . . . . . . . . . . . . . . . . . . . . 6-26 Grid Files from Third-Party CAD Packages . . . . . . . . . . . . 6-26 FLUENT/UNS and RAMPANT Case Files . . . . . . . . . . . . . 6-32

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6.3.8 6.3.9 6.3.10 6.3.11 6.4

FLUENT 4 Case Files . . . . . . . . . . . . . . . . . . . . . . . . 6-32 FIDAP Neutral Files . . . . . . . . . . . . . . . . . . . . . . . . . 6-32 Reading Multiple Mesh/Case/Data Files . . . . . . . . . . . . . 6-33

Reading Surface Mesh Files . . . . . . . . . . . . . . . . . . . . . 6-37

Non-Conformal Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-37 6.4.1 6.4.2 6.4.3 6.4.4 Non-Conformal Grid Calculations . . . . . . . . . . . . . . . . . 6-37 Requirements and Limitations of Non-Conformal Grids . . . . . 6-41 Using a Non-Conformal Grid in FLUENT . . . . . . . . . . . . . 6-43 Starting From a FLUENT/UNS or RAMPANT Case . . . . . . . . 6-45

6.5

Checking the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-46 6.5.1 6.5.2 Grid Check Information . . . . . . . . . . . . . . . . . . . . . . . 6-46 Repairing Duplicate Shadow Nodes . . . . . . . . . . . . . . . . 6-48

6.6

Reporting Grid Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 6-48 6.6.1 6.6.2 6.6.3 6.6.4 Grid Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-48 Memory Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-49 Grid Zone Information . . . . . . . . . . . . . . . . . . . . . . . 6-51

Partition Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . 6-51

6.7

Converting the Grid to a Polyhedral Mesh . . . . . . . . . . . . . . . . . 6-52 6.7.1 6.7.2 6.7.3 Converting the Domain to a Polyhedra . . . . . . . . . . . . . . 6-52 Converting Skewed Cells to Polyhedra . . . . . . . . . . . . . . . 6-58 Steps in Converting Skewed Cells to Polyhedral Cells . . . . . . . 6-59

6.8

Modifying the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-60 6.8.1 6.8.2 6.8.3 6.8.4 6.8.5 6.8.6 6.8.7 Merging Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-61 Separating Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-62 Fusing Face Zones . . . . . . . . . . . . . . . . . . . . . . . . . . 6-69 Creating Periodic Zones . . . . . . . . . . . . . . . . . . . . . . . 6-71 Slitting Periodic Zones . . . . . . . . . . . . . . . . . . . . . . . 6-72

Slitting Face Zones . . . . . . . . . . . . . . . . . . . . . . . . . . 6-73 Extruding Face Zones . . . . . . . . . . . . . . . . . . . . . . . . 6-74


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6.8.8 6.8.9 6.8.10 6.8.11 6.8.12

Replacing, Deleting, Deactivating, and Activating Zones . . . . . 6-75 Reordering the Domain and Zones . . . . . . . . . . . . . . . . . 6-79 Scaling the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-80 Translating the Grid . . . . . . . . . . . . . . . . . . . . . . . . . 6-83 Rotating the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 6-84 7-1 7-3 7-3 7-4 7-5 7-6 7-7 7-8 7-8 7-9 7-9

7 Boundary Conditions 7.1 Overview of Dening Boundary Conditions . . . . . . . . . . . . . . . . 7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.1.6 7.1.7 7.1.8 7.1.9 7.1.10 7.2 Available Boundary Types . . . . . . . . . . . . . . . . . . . . . The Boundary Conditions Panel . . . . . . . . . . . . . . . . . . . Changing Boundary Zone Types . . . . . . . . . . . . . . . . . . Setting Boundary Conditions . . . . . . . . . . . . . . . . . . . . Copying Boundary Conditions . . . . . . . . . . . . . . . . . . . Selecting Boundary Zones in the Graphics Display . . . . . . . . Changing Boundary Zone Names . . . . . . . . . . . . . . . . . . Dening Non-Uniform Boundary Conditions . . . . . . . . . . .

Dening Transient Boundary Conditions . . . . . . . . . . . . . .

Saving and Reusing Boundary Conditions . . . . . . . . . . . . . 7-12

Flow Inlet and Exit Boundary Conditions . . . . . . . . . . . . . . . . . 7-12 7.2.1 7.2.2 Using Flow Boundary Conditions . . . . . . . . . . . . . . . . . . 7-13 Determining Turbulence Parameters . . . . . . . . . . . . . . . . 7-14

7.3

Pressure Inlet Boundary Conditions . . . . . . . . . . . . . . . . . . . . 7-21 7.3.1 7.3.2 7.3.3 Inputs at Pressure Inlet Boundaries . . . . . . . . . . . . . . . . 7-21 Default Settings at Pressure Inlet Boundaries . . . . . . . . . . . 7-27 Calculation Procedure at Pressure Inlet Boundaries . . . . . . . 7-27

7.4

Velocity Inlet Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 7-29 7.4.1 7.4.2 7.4.3 Inputs at Velocity Inlet Boundaries . . . . . . . . . . . . . . . . 7-30

Default Settings at Velocity Inlet Boundaries . . . . . . . . . . . 7-36 Calculation Procedure at Velocity Inlet Boundaries . . . . . . . . 7-36

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7.5

Mass Flow Inlet Boundary Conditions . . . . . . . . . . . . . . . . . . . 7-38 7.5.1 7.5.2 7.5.3 Inputs at Mass Flow Inlet Boundaries . . . . . . . . . . . . . . . 7-39 Default Settings at Mass Flow Inlet Boundaries . . . . . . . . . . 7-44 Calculation Procedure at Mass Flow Inlet Boundaries . . . . . . 7-45

7.6

Inlet Vent Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 7-47 7.6.1 Inputs at Inlet Vent Boundaries . . . . . . . . . . . . . . . . . . 7-47

7.7

Intake Fan Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 7-49 7.7.1 Inputs at Intake Fan Boundaries . . . . . . . . . . . . . . . . . . 7-49

7.8

Pressure Outlet Boundary Conditions . . . . . . . . . . . . . . . . . . . 7-51 7.8.1 7.8.2 7.8.3 7.8.4 Inputs at Pressure Outlet Boundaries . . . . . . . . . . . . . . . 7-52 Default Settings at Pressure Outlet Boundaries . . . . . . . . . . 7-56 Calculation Procedure at Pressure Outlet Boundaries . . . . . . 7-57 Other Optional Inputs at Pressure Outlet Boundaries . . . . . . 7-59

7.9

Pressure Far-Field Boundary Conditions . . . . . . . . . . . . . . . . . . 7-61 7.9.1 7.9.2 7.9.3 Inputs at Pressure Far-Field Boundaries . . . . . . . . . . . . . . 7-62 Default Settings at Pressure Far-Field Boundaries . . . . . . . . 7-64 Calculation Procedure at Pressure Far-Field Boundaries . . . . . 7-64

7.10 Outow Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 7-65 7.10.1 7.10.2 7.10.3 7.10.4 FLUENTs Treatment at Outow Boundaries . . . . . . . . . . . 7-66 Using Outow Boundaries . . . . . . . . . . . . . . . . . . . . . . 7-66 Mass Flow Split Boundary Conditions . . . . . . . . . . . . . . . 7-68 Other Inputs at Outow Boundaries . . . . . . . . . . . . . . . . 7-69

7.11 Outlet Vent Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 7-70 7.11.1 Inputs at Outlet Vent Boundaries . . . . . . . . . . . . . . . . . 7-70

7.12 Exhaust Fan Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 7-73 7.12.1 Inputs at Exhaust Fan Boundaries . . . . . . . . . . . . . . . . . 7-73


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7.13 Wall Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 7-75 7.13.1 7.13.2 7.13.3 7.13.4 Inputs at Wall Boundaries . . . . . . . . . . . . . . . . . . . . . 7-75 Default Settings at Wall Boundaries . . . . . . . . . . . . . . . . 7-93 Shear-Stress Calculation Procedure at Wall Boundaries . . . . . 7-94 Heat Transfer Calculations at Wall Boundaries . . . . . . . . . . 7-95

7.14 Symmetry Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . 7-97 7.14.1 7.14.2 Examples of Symmetry Boundaries . . . . . . . . . . . . . . . . . 7-98 Calculation Procedure at Symmetry Boundaries . . . . . . . . . 7-100

7.15 Periodic Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . 7-100 7.15.1 7.15.2 7.15.3 7.15.4 Examples of Periodic Boundaries . . . . . . . . . . . . . . . . . . 7-101 Inputs for Periodic Boundaries . . . . . . . . . . . . . . . . . . . 7-101 Default Settings at Periodic Boundaries . . . . . . . . . . . . . . 7-104 Calculation Procedure at Periodic Boundaries . . . . . . . . . . . 7-104

7.16 Axis Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 7-105 7.17 Fluid Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-106 7.17.1 Inputs for Fluid Zones . . . . . . . . . . . . . . . . . . . . . . . . 7-106

7.18 Solid Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-109 7.18.1 Inputs for Solid Zones . . . . . . . . . . . . . . . . . . . . . . . . 7-110

7.19 Porous Media Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 7-112 7.19.1 7.19.2 7.19.3 7.19.4 7.19.5 7.19.6 7.19.7 7.19.8 7.19.9 Limitations and Assumptions of the Porous Media Model . . . . 7-113 Momentum Equations for Porous Media . . . . . . . . . . . . . . 7-113 Treatment of the Energy Equation in Porous Media . . . . . . . 7-116 Treatment of Turbulence in Porous Media . . . . . . . . . . . . . 7-117 Eect of Porosity on Transient Scalar Equations . . . . . . . . . 7-117 User Inputs for Porous Media . . . . . . . . . . . . . . . . . . . . 7-117 Modeling Porous Media Based on Physical Velocity . . . . . . . . 7-131 Solution Strategies for Porous Media . . . . . . . . . . . . . . . . 7-132 Postprocessing for Porous Media . . . . . . . . . . . . . . . . . . 7-133

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7.20 Fan Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 7-134 7.20.1 7.20.2 7.20.3 Fan Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-134 User Inputs for Fans . . . . . . . . . . . . . . . . . . . . . . . . . 7-135 Postprocessing for Fans . . . . . . . . . . . . . . . . . . . . . . . 7-143

7.21 Radiator Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . 7-144 7.21.1 7.21.2 7.21.3 Radiator Equations . . . . . . . . . . . . . . . . . . . . . . . . . 7-144 User Inputs for Radiators . . . . . . . . . . . . . . . . . . . . . . 7-146 Postprocessing for Radiators . . . . . . . . . . . . . . . . . . . . 7-151

7.22 Porous Jump Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 7-153 7.23 Non-Reecting Boundary Conditions . . . . . . . . . . . . . . . . . . . . 7-155 7.23.1 7.23.2 Turbo-Specic Non-Reecting Boundary Conditions . . . . . . . 7-156 General Non-Reecting Boundary Conditions . . . . . . . . . . . 7-168

7.24 User-Dened Fan Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-176 7.24.1 7.24.2 Steps for Using the User-Dened Fan Model . . . . . . . . . . . . 7-176 Example of a User-Dened Fan . . . . . . . . . . . . . . . . . . . 7-177

7.25 Heat Exchanger Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-186 7.25.1 7.25.2 7.25.3 7.25.4 7.25.5 Overview and Restrictions of the Heat Exchanger Models . . . . 7-186 Heat Exchanger Model Theory . . . . . . . . . . . . . . . . . . . 7-189 Using the Heat Exchanger Model . . . . . . . . . . . . . . . . . . 7-196 Using the Heat Exchanger Group . . . . . . . . . . . . . . . . . . 7-208 Postprocessing for the Heat Exchanger Model . . . . . . . . . . . 7-211

7.26 Boundary Proles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-216 7.26.1 7.26.2 7.26.3 7.26.4 Boundary Prole Specication Types . . . . . . . . . . . . . . . 7-216 Boundary Prole File Format . . . . . . . . . . . . . . . . . . . . 7-217 Using Boundary Proles . . . . . . . . . . . . . . . . . . . . . . . 7-220 Reorienting Boundary Proles . . . . . . . . . . . . . . . . . . . 7-223

7.27 Fixing the Values of Variables . . . . . . . . . . . . . . . . . . . . . . . . 7-228 7.27.1 7.27.2 Overview of Fixing the Value of a Variable . . . . . . . . . . . . 7-228 Procedure for Fixing Values of Variables in a Zone . . . . . . . . 7-230


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7.28 Dening Mass, Momentum, Energy, and Other Sources . . . . . . . . . . 7-233 7.28.1 Procedure for Dening Sources . . . . . . . . . . . . . . . . . . . 7-234

7.29 Coupling Boundary Conditions with GT-Power . . . . . . . . . . . . . . 7-238 7.29.1 7.29.2 Requirements and Restrictions . . . . . . . . . . . . . . . . . . . 7-238 User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-239

7.30 Coupling Boundary Conditions with WAVE . . . . . . . . . . . . . . . . 7-241 7.30.1 7.30.2 Requirements and Restrictions . . . . . . . . . . . . . . . . . . . 7-241 User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7-242 8-1 8-2 8-3 8-4

8 Physical Properties 8.1 Dening Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 8.1.2 8.1.3 8.2 Material Types and Databases . . . . . . . . . . . . . . . . . . . Using the Materials Panel . . . . . . . . . . . . . . . . . . . . . .

Using a User-Dened Materials Database . . . . . . . . . . . . . 8-10

Dening Properties Using Temperature-Dependent Functions . . . . . . 8-19 8.2.1 8.2.2 8.2.3 8.2.4 Inputs for Polynomial Functions . . . . . . . . . . . . . . . . . . 8-20 Inputs for Piecewise-Linear Functions . . . . . . . . . . . . . . . 8-21 Inputs for Piecewise-Polynomial Functions . . . . . . . . . . . . . 8-22 Checking and Modifying Existing Proles . . . . . . . . . . . . . 8-23

8.3

Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-24 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5 8.3.6 8.3.7 Dening Density for Various Flow Regimes . . . . . . . . . . . . 8-24 Input of Constant Density . . . . . . . . . . . . . . . . . . . . . 8-25

Inputs for the Boussinesq Approximation . . . . . . . . . . . . . 8-25 Density as a Prole Function of Temperature . . . . . . . . . . . 8-26 Incompressible Ideal Gas Law . . . . . . . . . . . . . . . . . . . . 8-26 Ideal Gas Law for Compressible Flows . . . . . . . . . . . . . . . 8-27 Composition-Dependent Density for Multicomponent Mixtures . 8-28

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8.4

Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-30 8.4.1 8.4.2 8.4.3 8.4.4 8.4.5 Input of Constant Viscosity . . . . . . . . . . . . . . . . . . . . . 8-30 Viscosity as a Function of Temperature . . . . . . . . . . . . . . 8-31 Dening the Viscosity Using Kinetic Theory . . . . . . . . . . . 8-34 8-34

Composition-Dependent Viscosity for Multicomponent Mixtures

Viscosity for Non-Newtonian Fluids . . . . . . . . . . . . . . . . 8-35

8.5

Thermal Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-41 8.5.1 8.5.2 8.5.3 8.5.4 8.5.5 Constant Thermal Conductivity . . . . . . . . . . . . . . . . . . 8-42 Thermal Conductivity as a Function of Temperature . . . . . . . 8-43 Thermal Conductivity Using Kinetic Theory . . . . . . . . . . . 8-43 Composition-Dependent Thermal Conductivity for Multicomponent Mixtures . . . . . . . . . . . . . . . . . . . . . . 8-44 Anisotropic Thermal Conductivity for Solids . . . . . . . . . . . 8-45

8.6

User-Dened Scalar (UDS) Diusivity . . . . . . . . . . . . . . . . . . . 8-50 8.6.1 8.6.2 8.6.3 Isotropic Diusion . . . . . . . . . . . . . . . . . . . . . . . . . . 8-51 Anisotropic Diusion . . . . . . . . . . . . . . . . . . . . . . . . 8-54 User-Dened Anisotropic Diusivity . . . . . . . . . . . . . . . . 8-58

8.7

Specic Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-59 8.7.1 8.7.2 8.7.3 8.7.4 Input of Constant Specic Heat Capacity . . . . . . . . . . . . . 8-59 Specic Heat Capacity as a Function of Temperature . . . . . . . 8-60 Dening Specic Heat Capacity Using Kinetic Theory . . . . . . 8-60 Specic Heat Capacity as a Function of Composition . . . . . . . 8-61

8.8

Radiation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-61 8.8.1 8.8.2 8.8.3 8.8.4 Absorption Coecient . . . . . . . . . . . . . . . . . . . . . . . . 8-62 Scattering Coecient . . . . . . . . . . . . . . . . . . . . . . . . 8-64 Refractive Index . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-65 Reporting the Radiation Properties . . . . . . . . . . . . . . . . 8-65


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8.9

Mass Diusion Coecients 8.9.1 8.9.2 8.9.3 8.9.4 8.9.5

. . . . . . . . . . . . . . . . . . . . . . . . . 8-65

Fickian Diusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-65 Full Multicomponent Diusion . . . . . . . . . . . . . . . . . . . 8-67 Thermal Diusion Coecients . . . . . . . . . . . . . . . . . . . 8-68 Mass Diusion Coecient Inputs . . . . . . . . . . . . . . . . . . 8-69 Mass Diusion Coecient Inputs for Turbulent Flow . . . . . . . 8-75

8.10 Standard State Enthalpies . . . . . . . . . . . . . . . . . . . . . . . . . . 8-76 8.11 Standard State Entropies . . . . . . . . . . . . . . . . . . . . . . . . . . 8-76 8.12 Molecular Heat Transfer Coecient . . . . . . . . . . . . . . . . . . . . . 8-76 8.13 Kinetic Theory Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 8-77 8.14 Operating Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-78 8.14.1 8.14.2 8.14.3 The Eect of Numerical Roundo on Pressure Calculation in Low-Mach-Number Flow . . . . . . . . . . . . . . . . . . . . . 8-78 Operating Pressure, Gauge Pressure, and Absolute Pressure . . . 8-79 Setting the Operating Pressure . . . . . . . . . . . . . . . . . . . 8-79

8.15 Reference Pressure Location . . . . . . . . . . . . . . . . . . . . . . . . . 8-80 8.15.1 Actual Reference Pressure Location . . . . . . . . . . . . . . . . 8-81

8.16 Real Gas Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8-81 8.16.1 8.16.2 The NIST Real Gas Models . . . . . . . . . . . . . . . . . . . . . 8-84 The User-Dened Real Gas Model . . . . . . . . . . . . . . . . . 8-88 9-1 9-2 9-3 9-5 9-5 9-5 9-7

9 Modeling Basic Fluid Flow 9.1 9.2 9.3 Overview of Physical Models in FLUENT . . . . . . . . . . . . . . . . . . Continuity and Momentum Equations . . . . . . . . . . . . . . . . . . . User-Dened Scalar (UDS) Transport Equations . . . . . . . . . . . . . . 9.3.1 9.3.2 9.3.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UDS Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Setting Up UDS Equations in FLUENT . . . . . . . . . . . . . .

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9.4

Periodic Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-15 9.4.1 9.4.2 9.4.3 9.4.4 9.4.5 9.4.6 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 9-15 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-17 User Inputs for the Pressure-Based Solver . . . . . . . . . . . . . 9-18 User Inputs for the Density-Based Solvers . . . . . . . . . . . . . 9-20 Monitoring the Value of the Pressure Gradient . . . . . . . . . . 9-20 Postprocessing for Streamwise-Periodic Flows . . . . . . . . . . . 9-21

9.5

Swirling and Rotating Flows . . . . . . . . . . . . . . . . . . . . . . . . . 9-22 9.5.1 9.5.2 9.5.3 9.5.4 9.5.5 Overview of Swirling and Rotating Flows . . . . . . . . . . . . . 9-23 Physics of Swirling and Rotating Flows . . . . . . . . . . . . . . 9-24 Turbulence Modeling in Swirling Flows . . . . . . . . . . . . . . 9-26 Grid Setup for Swirling and Rotating Flows . . . . . . . . . . . . 9-27 Modeling Axisymmetric Flows with Swirl or Rotation . . . . . . 9-27

9.6

Compressible Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-32 9.6.1 9.6.2 9.6.3 9.6.4 9.6.5 9.6.6 When to Use the Compressible Flow Model . . . . . . . . . . . . 9-34 Physics of Compressible Flows . . . . . . . . . . . . . . . . . . . 9-35 Modeling Inputs for Compressible Flows . . . . . . . . . . . . . . 9-36 Floating Operating Pressure . . . . . . . . . . . . . . . . . . . . 9-38 Solution Strategies for Compressible Flows . . . . . . . . . . . . 9-40 Reporting of Results for Compressible Flows . . . . . . . . . . . 9-41

9.7

Inviscid Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-41 9.7.1 9.7.2 9.7.3 9.7.4 Euler Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 9-42 Setting Up an Inviscid Flow Model . . . . . . . . . . . . . . . . . 9-43 Solution Strategies for Inviscid Flows . . . . . . . . . . . . . . . 9-44 Postprocessing for Inviscid Flows . . . . . . . . . . . . . . . . . . 9-44


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10 Modeling Flows with Rotating Reference Frames 10.1 Introduction

10-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-2

10.2 Flow in a Rotating Reference Frame . . . . . . . . . . . . . . . . . . . . 10-4 10.2.1 10.2.2 10.2.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-4 Equations for a Rotating Reference Frame . . . . . . . . . . . . . 10-4 Single Rotating Reference Frame (SRF) Modeling . . . . . . . . 10-7

10.3 Flow in Multiple Rotating Reference Frames . . . . . . . . . . . . . . . . 10-9 10.3.1 10.3.2 The Multiple Reference Frame Model . . . . . . . . . . . . . . . 10-9 The Mixing Plane Model . . . . . . . . . . . . . . . . . . . . . . 10-15

10.4 Grid Setup for a Single Rotating Reference Frame . . . . . . . . . . . . . 10-21 10.5 Grid Setup for a Multiple Rotating Reference Frame . . . . . . . . . . . 10-22 10.6 Steps in Using Rotating Reference Frames . . . . . . . . . . . . . . . . . 10-22 10.7 Setting Up a Single Rotating Reference Frame Problem . . . . . . . . . . 10-25 10.7.1 Choosing the Relative or Absolute Velocity Formulation . . . . . 10-27

10.8 Solution Strategies for a Single Rotating Reference Frame . . . . . . . . 10-29 10.8.1 Gradual Increase of the Rotational Speed to Improve Solution Stability . . . . . . . . . . . . . . . . . . . . . . . . . . 10-30

10.9 Postprocessing for a Single Rotating Reference Frame . . . . . . . . . . . 10-30 10.10 Setting Up a Multiple Rotating Reference Frame Problem . . . . . . . . 10-32 10.10.1 Setting Up Multiple Reference Frames . . . . . . . . . . . . . . . 10-32 10.10.2 Setting Up the Mixing Plane Model . . . . . . . . . . . . . . . . 10-35 10.11 Solution Strategies for MRF and Mixing Plane Problems . . . . . . . . . 10-40 10.11.1 MRF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-40 10.11.2 Mixing Plane Model . . . . . . . . . . . . . . . . . . . . . . . . . 10-40 10.12 Postprocessing for MRF and Mixing Plane Problems . . . . . . . . . . . 10-40

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11 Modeling Flows Using Sliding and Deforming Meshes 11.1 Introduction 11.1.1

11-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-1

Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . 11-3

11.2 Sliding Mesh Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-4 11.2.1 11.2.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-4 Sliding Mesh Concept . . . . . . . . . . . . . . . . . . . . . . . . 11-10

11.3 Dynamic Mesh Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-12 11.3.1 11.3.2 11.3.3 11.3.4 11.3.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-12 Dynamic Mesh Update Methods . . . . . . . . . . . . . . . . . . 11-12 Volume Mesh Update Procedure . . . . . . . . . . . . . . . . . . 11-34 Solid-Body Kinematics . . . . . . . . . . . . . . . . . . . . . . . 11-35 Steady-State Dynamic Mesh Applications . . . . . . . . . . . . . 11-39

11.4 Steps in Using Sliding Meshes . . . . . . . . . . . . . . . . . . . . . . . . 11-42 11.4.1 11.4.2 Grid Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . 11-42 Setting Up the Problem . . . . . . . . . . . . . . . . . . . . . . . 11-43

11.5 Solution Strategies for Sliding Meshes . . . . . . . . . . . . . . . . . . . 11-45 11.6 Postprocessing for Sliding Meshes . . . . . . . . . . . . . . . . . . . . . . 11-49 11.7 Steps in Using Dynamic Meshes . . . . . . . . . . . . . . . . . . . . . . . 11-50 11.7.1 11.7.2 11.7.3 11.7.4 11.7.5 11.7.6 11.7.7 Setting Dynamic Mesh Modeling Parameters . . . . . . . . . . . 11-51 Specifying the Motion of Dynamic Zones . . . . . . . . . . . . . 11-60 Previewing the Dynamic Mesh . . . . . . . . . . . . . . . . . . . 11-70 Dening Dynamic Mesh Events . . . . . . . . . . . . . . . . . . . 11-73 Using the In-Cylinder Model . . . . . . . . . . . . . . . . . . . . 11-83 Using the 2.5D Model . . . . . . . . . . . . . . . . . . . . . . . . 11-99 Using the Six DOF Solver . . . . . . . . . . . . . . . . . . . . . . 11-101


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12 Modeling Turbulence 12.1 Introduction

12-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-2

12.2 Choosing a Turbulence Model . . . . . . . . . . . . . . . . . . . . . . . . 12-3 12.2.1 12.2.2 12.2.3 12.2.4 Reynolds-Averaged Approach of the DES Model vs. LES . . . . 12-3 Reynolds (Ensemble) Averaging . . . . . . . . . . . . . . . . . . 12-4 Boussinesq Approach vs. Reynolds Stress Transport Models . . . 12-5 Computational Eort: CPU Time and Solution Behavior . . . . 12-6

12.3 Spalart-Allmaras Model Theory . . . . . . . . . . . . . . . . . . . . . . . 12-7 12.3.1 12.3.2 12.3.3 12.3.4 12.3.5 12.3.6 12.3.7 12.3.8 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-7 Transport Equation for the Spalart-Allmaras Model . . . . . . . 12-7 Modeling the Turbulent Viscosity . . . . . . . . . . . . . . . . . 12-8 Modeling the Turbulent Production . . . . . . . . . . . . . . . . 12-8 Modeling the Turbulent Destruction . . . . . . . . . . . . . . . . 12-10 Model Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-10 Wall Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 12-10 Convective Heat and Mass Transfer Modeling . . . . . . . . . . . 12-11

12.4 Standard, RNG, and Realizable k- Models Theory . . . . . . . . . . . . 12-12 12.4.1 12.4.2 12.4.3 12.4.4 12.4.5 12.4.6 12.4.7 Standard k- Model . . . . . . . . . . . . . . . . . . . . . . . . . 12-12 RNG k- Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-14 Realizable k- Model . . . . . . . . . . . . . . . . . . . . . . . . . 12-18 Modeling Turbulent Production in the k- Models . . . . . . . . 12-22 Eects of Buoyancy on Turbulence in the k- Models . . . . . . . 12-23 Eects of Compressibility on Turbulence in the k- Models . . . 12-24 Convective Heat and Mass Transfer Modeling in the k- Models . 12-25

12.5 Standard and SST k- Models Theory . . . . . . . . . . . . . . . . . . . 12-26 12.5.1 12.5.2 12.5.3 Standard k- Model . . . . . . . . . . . . . . . . . . . . . . . . . 12-26 Shear-Stress Transport (SST) k- Model . . . . . . . . . . . . . 12-31 Wall Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 12-35

12.6 The v 2 -f Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-36

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12.7 Reynolds Stress Model (RSM) Theory . . . . . . . . . . . . . . . . . . . 12-37 12.7.1 12.7.2 12.7.3 12.7.4 12.7.5 12.7.6 12.7.7 12.7.8 12.7.9 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-37 Reynolds Stress Transport Equations . . . . . . . . . . . . . . . 12-38 Modeling Turbulent Diusive Transport . . . . . . . . . . . . . . 12-38 Modeling the Pressure-Strain Term . . . . . . . . . . . . . . . . . 12-39 Eects of Buoyancy on Turbulence . . . . . . . . . . . . . . . . . 12-44 Modeling the Turbulence Kinetic Energy . . . . . . . . . . . . . 12-44 Modeling the Dissipation Rate . . . . . . . . . . . . . . . . . . . 12-45 Modeling the Turbulent Viscosity . . . . . . . . . . . . . . . . . 12-45 Wall Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 12-46

12.7.10 Convective Heat and Mass Transfer Modeling . . . . . . . . . . . 12-47 12.8 Detached Eddy Simulation (DES) Model Theory . . . . . . . . . . . . . 12-47 12.8.1 12.8.2 12.8.3 Spalart-Allmaras RANS Model . . . . . . . . . . . . . . . . . . . 12-48 Realizable k- RANS Model . . . . . . . . . . . . . . . . . . . . . 12-48 SST k- RANS Model . . . . . . . . . . . . . . . . . . . . . . . . 12-49

12.9 Large Eddy Simulation (LES) Model Theory . . . . . . . . . . . . . . . . 12-49 12.9.1 12.9.2 12.9.3 12.9.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-49 Filtered Navier-Stokes Equations . . . . . . . . . . . . . . . . . . 12-50 Subgrid-Scale Models . . . . . . . . . . . . . . . . . . . . . . . . 12-52 Inlet Boundary Conditions for the LES Model . . . . . . . . . . 12-56

12.10 Near-Wall Treatments for Wall-Bounded Turbulent Flows . . . . . . . . 12-58 12.10.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-58 12.10.2 Standard Wall Functions . . . . . . . . . . . . . . . . . . . . . . 12-61 12.10.3 Non-Equilibrium Wall Functions . . . . . . . . . . . . . . . . . . 12-65 12.10.4 Enhanced Wall Treatment . . . . . . . . . . . . . . . . . . . . . . 12-68 12.10.5 User-Dened Wall Functions . . . . . . . . . . . . . . . . . . . . 12-74 12.10.6 LES Near-Wall Treatment . . . . . . . . . . . . . . . . . . . . . . 12-74 12.11 Grid Considerations for Turbulent Flow Simulations . . . . . . . . . . . 12-75 12.11.1 Near-Wall Mesh Guidelines . . . . . . . . . . . . . . . . . . . . . 12-75


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12.12 Steps in Using a Turbulence Model . . . . . . . . . . . . . . . . . . . . . 12-77 12.13 Setting Up the Spalart-Allmaras Model . . . . . . . . . . . . . . . . . . . 12-80 12.14 Setting Up the k- Model . . . . . . . . . . . . . . . . . . . . . . . . . . 12-81 12.14.1 Setting Up the Standard or Realizable k- Model . . . . . . . . . 12-81 12.14.2 Setting Up the RNG k- Model . . . . . . . . . . . . . . . . . . . 12-82 12.15 Setting Up the k- Model . . . . . . . . . . . . . . . . . . . . . . . . . . 12-84 12.15.1 Setting Up the Standard k- Model . . . . . . . . . . . . . . . . 12-84 12.15.2 Setting Up the Shear-Stress Transport k- Model . . . . . . . . . 12-85 12.16 Setting Up the Reynolds Stress Model . . . . . . . . . . . . . . . . . . . 12-86 12.17 Setting Up the Detached Eddy Simulation Model . . . . . . . . . . . . . 12-89 12.18 Setting Up the Large Eddy Simulation Model . . . . . . . . . . . . . . . 12-90 12.19 Setup Options for all Turbulence Modeling . . . . . . . . . . . . . . . . . 12-92 12.19.1 Including the Viscous Heating Eects . . . . . . . . . . . . . . . 12-92 12.19.2 Including Turbulence Generation Due to Buoyancy . . . . . . . . 12-92 12.19.3 Vorticity- and Strain/Vorticity-Based Production . . . . . . . . . 12-92 12.19.4 Detached Eddy Simulation (DES) Modeling . . . . . . . . . . . . 12-92 12.19.5 Dierential Viscosity Modication . . . . . . . . . . . . . . . . . 12-93 12.19.6 Swirl Modication . . . . . . . . . . . . . . . . . . . . . . . . . . 12-93 12.19.7 Transitional Flows . . . . . . . . . . . . . . . . . . . . . . . . . . 12-93 12.19.8 Shear Flow Corrections . . . . . . . . . . . . . . . . . . . . . . . 12-93 12.19.9 Including Pressure Gradient Eects . . . . . . . . . . . . . . . . 12-93 12.19.10 Including Thermal Eects . . . . . . . . . . . . . . . . . . . . . 12-94 12.19.11 Including the Wall Reection Term . . . . . . . . . . . . . . . . 12-94 12.19.12 Solving the k Equation to Obtain Wall Boundary Conditions . . 12-94 12.19.13 Quadratic Pressure-Strain Model . . . . . . . . . . . . . . . . . 12-94 12.19.14 Low-Re Stress-Omega Pressure-Strain . . . . . . . . . . . . . . . 12-95 12.19.15 Subgrid-Scale Model . . . . . . . . . . . . . . . . . . . . . . . . 12-95

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12.19.16 Customizing the Turbulent Viscosity . . . . . . . . . . . . . . . 12-95 12.19.17 Customizing the Turbulent Prandtl Numbers . . . . . . . . . . . 12-96 12.19.18 Modeling Turbulence with Non-Newtonian Fluids . . . . . . . . 12-96 12.20 Dening Turbulence Boundary Conditions . . . . . . . . . . . . . . . . . 12-96 12.20.1 The Spalart-Allmaras Model . . . . . . . . . . . . . . . . . . . . 12-96 12.20.2 k- Models and k- Models . . . . . . . . . . . . . . . . . . . . . 12-97 12.20.3 Reynolds Stress Model . . . . . . . . . . . . . . . . . . . . . . . 12-98

12.20.4 Large Eddy Simulation Model . . . . . . . . . . . . . . . . . . . 12-100 12.21 Providing an Initial Guess for k and (or k and ) . . . . . . . . . . . . 12-100

12.22 Solution Strategies for Turbulent Flow Simulations . . . . . . . . . . . . 12-101 12.22.1 Mesh Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-101 12.22.2 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-101 12.22.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-102 12.22.4 RSM-Specic Solution Strategies . . . . . . . . . . . . . . . . . . 12-102 12.22.5 LES-Specic Solution Strategies . . . . . . . . . . . . . . . . . . 12-103 12.23 Postprocessing for Turbulent Flows . . . . . . . . . . . . . . . . . . . . . 12-105 12.23.1 Custom Field Functions for Turbulence . . . . . . . . . . . . . . 12-109 12.23.2 Postprocessing Turbulent Flow Statistics . . . . . . . . . . . . . 12-109 12.23.3 Troubleshooting . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-111 13 Modeling Heat Transfer 13.1 Introduction 13-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-1

13.2 Modeling Conductive and Convective Heat Transfer . . . . . . . . . . . . 13-2 13.2.1 13.2.2 13.2.3 13.2.4 13.2.5 13.2.6 Heat Transfer Theory . . . . . . . . . . . . . . . . . . . . . . . . 13-2 Steps in Solving Heat Transfer Problems . . . . . . . . . . . . . . 13-7 Solution Strategies for Heat Transfer Modeling . . . . . . . . . . 13-10 Postprocessing Heat Transfer Quantities . . . . . . . . . . . . . . 13-12 Natural Convection and Buoyancy-Driven Flows . . . . . . . . . 13-14 Shell Conduction Considerations . . . . . . . . . . . . . . . . . . 13-21


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13.3 Modeling Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-24 13.3.1 13.3.2 13.3.3 13.3.4 13.3.5 13.3.6 13.3.7 13.3.8 13.3.9 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 13-25 Radiative Transfer Equation . . . . . . . . . . . . . . . . . . . . 13-29 P-1 Radiation Model Theory . . . . . . . . . . . . . . . . . . . . 13-30 Rosseland Radiation Model Theory . . . . . . . . . . . . . . . . 13-34 Discrete Transfer Radiation Model (DTRM) Theory . . . . . . . 13-36 Discrete Ordinates (DO) Radiation Model Theory . . . . . . . . 13-40 Surface-to-Surface (S2S) Radiation Model Theory . . . . . . . . 13-61 Radiation in Combusting Flows . . . . . . . . . . . . . . . . . . 13-64

Choosing a Radiation Model . . . . . . . . . . . . . . . . . . . . 13-68

13.3.10 Steps in Using the Radiation Models . . . . . . . . . . . . . . . . 13-69 13.3.11 Setting Up the DTRM Model . . . . . . . . . . . . . . . . . . . . 13-71 13.3.12 Setting Up the S2S Model . . . . . . . . . . . . . . . . . . . . . . 13-74 13.3.13 Setting Up the DO Model . . . . . . . . . . . . . . . . . . . . . . 13-84 13.3.14 Dening Material Properties for Radiation . . . . . . . . . . . . 13-88 13.3.15 Dening Boundary Conditions for Radiation . . . . . . . . . . . 13-89 13.3.16 Solution Strategies for Radiation Modeling . . . . . . . . . . . . 13-99 13.3.17 Postprocessing Radiation Quantities . . . . . . . . . . . . . . . . 13-104 13.3.18 Solar Load Model . . . . . . . . . . . . . . . . . . . . . . . . . . 13-109 13.4 Modeling Periodic Heat Transfer . . . . . . . . . . . . . . . . . . . . . . 13-137 13.4.1 13.4.2 13.4.3 13.4.4 13.4.5 13.4.6 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 13-137 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13-138 Steps in Using Periodic Heat Transfer . . . . . . . . . . . . . . . 13-140 Solution Strategies for Periodic Heat Transfer . . . . . . . . . . . 13-142 Monitoring Convergence . . . . . . . . . . . . . . . . . . . . . . . 13-142 Postprocessing for Periodic Heat Transfer . . . . . . . . . . . . . 13-143

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14 Modeling Species Transport and Finite-Rate Chemistry

14-1

14.1 Volumetric Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-2 14.1.1 14.1.2 14.1.3 14.1.4 14.1.5 14.1.6 14.1.7 14.1.8 14.1.9 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-3 Overview of User Inputs for Modeling Species Transport and Reactions . . . . . . . . . . . . . . . . . . . . . . 14-12 Enabling Species Transport and Reactions and Choosing the Mixture Material . . . . . . . . . . . . . . . . . . . 14-15 Dening Properties for the Mixture and Its Constituent Species . 14-17 Dening Boundary Conditions for Species . . . . . . . . . . . . . 14-34 Dening Other Sources of Chemical Species . . . . . . . . . . . . 14-35 Solution Procedures for Chemical Mixing and Finite-Rate Chemistry . . . . . . . . . . . . . . . . . . . . . . . . 14-35 Postprocessing for Species Calculations . . . . . . . . . . . . . . 14-40 Importing a Volumetric Kinetic Mechanism in CHEMKIN Format . . . . . . . . . . . . . . . . . . . . . . . . . 14-41

14.2 Wall Surface Reactions and Chemical Vapor Deposition . . . . . . . . . 14-44 14.2.1 14.2.2 14.2.3 14.2.4 14.2.5 14.2.6 Overview of Surface Species and Wall Surface Reactions . . . . . 14-44 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-44 User Inputs for Wall Surface Reactions . . . . . . . . . . . . . . 14-49 Solution Procedures for Wall Surface Reactions . . . . . . . . . . 14-51 Postprocessing for Surface Reactions . . . . . . . . . . . . . . . . 14-51 Importing a Surface Kinetic Mechanism in CHEMKIN Format . 14-52

14.3 Particle Surface Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 14-56 14.3.1 14.3.2 14.3.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14-56 User Inputs for Particle Surface Reactions . . . . . . . . . . . . . 14-61 Using the Multiple Surface Reactions Model for Discrete-Phase Particle Combustion . . . . . . . . . . . . . . . . 14-62

14.4 Species Transport Without Reactions . . . . . . . . . . . . . . . . . . . . 14-63


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15 Modeling Non-Premixed Combustion 15.1 Introduction 15.1.1

15-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-2

Overview of the Non-Premixed Approach . . . . . . . . . . . . . 15-2

15.2 Non-Premixed Combustion and Mixture Fraction Theory . . . . . . . . . 15-2 15.2.1 15.2.2 15.2.3 15.2.4 15.2.5 Mixture Fraction Theory . . . . . . . . . . . . . . . . . . . . . . 15-3 Modeling of Turbulence-Chemistry Interaction . . . . . . . . . . 15-8 Non-Adiabatic Extensions of the Non-Premixed Model . . . . . . 15-12 Chemistry Tabulation . . . . . . . . . . . . . . . . . . . . . . . . 15-15 Restrictions and Special Cases for Using the Non-Premixed Model . . . . . . . . . . . . . . . . . . . . . . . . 15-18

15.3 The Laminar Flamelet Models Theory . . . . . . . . . . . . . . . . . . . 15-24 15.3.1 15.3.2 15.3.3 15.3.4 Restrictions and Assumptions . . . . . . . . . . . . . . . . . . . . 15-24 The Flamelet Concept . . . . . . . . . . . . . . . . . . . . . . . . 15-24 Flamelet Generation . . . . . . . . . . . . . . . . . . . . . . . . . 15-28 Flamelet Import . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-28

15.4 The Steady Laminar Flamelet Model Theory . . . . . . . . . . . . . . . 15-30 15.4.1 15.4.2 15.4.3 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-31 Multiple Steady Flamelet Libraries . . . . . . . . . . . . . . . . . 15-31 Non-Adiabatic Steady Laminar Flamelets . . . . . . . . . . . . . 15-32

15.5 The Unsteady Laminar Flamelet Model Theory . . . . . . . . . . . . . . 15-32 15.5.1 15.5.2 The Generalized Unsteady Laminar Flamelet Model . . . . . . . 15-33 The Diesel Unsteady Laminar Flamelet Model . . . . . . . . . . 15-36

15.6 Steps in Using the Non-Premixed Model . . . . . . . . . . . . . . . . . . 15-37 15.6.1 15.6.2 15.6.3 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-37 Dening the Problem Type . . . . . . . . . . . . . . . . . . . . . 15-38 Overview of the Problem Setup Procedure . . . . . . . . . . . . . 15-38

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15.7 Setting Up the Equilibrium Chemistry Model . . . . . . . . . . . . . . . 15-42 15.7.1 15.7.2 15.7.3 15.7.4 15.7.5 Choosing Adiabatic or Non-Adiabatic Options . . . . . . . . . . 15-43 Specifying the Operating Pressure for the System . . . . . . . . . 15-43 Enabling a Secondary Inlet Stream . . . . . . . . . . . . . . . . . 15-44 Choosing to Dene the Fuel Stream(s) Empirically . . . . . . . . 15-45 Enabling the Rich Flammability Limit (RFL) Option . . . . . . 15-46

15.8 Setting Up the Steady and Unsteady Laminar Flamelet Models . . . . . 15-46 15.8.1 15.8.2 15.8.3 15.8.4 15.8.5 Choosing Adiabatic or Non-Adiabatic Options . . . . . . . . . . 15-47 Specifying the Operating Pressure for the System . . . . . . . . . 15-47 Specifying a Chemical Mechanism File for Flamelet Generation . 15-48 Importing a Flamelet . . . . . . . . . . . . . . . . . . . . . . . . 15-49 Using the Diesel Unsteady Laminar Flamelet Model . . . . . . . 15-49

15.9 Dening the Stream Compositions . . . . . . . . . . . . . . . . . . . . . 15-51 15.9.1 15.9.2 15.9.3 15.9.4 15.9.5 Setting Boundary Stream Species . . . . . . . . . . . . . . . . . . 15-54 Modifying the Database . . . . . . . . . . . . . . . . . . . . . . . 15-54 Composition Inputs for Empirically-Dened Fuel Streams . . . . 15-55 Modeling Liquid Fuel Combustion Using the Non-Premixed Model . . . . . . . . . . . . . . . . . . . . . . . . 15-55 Modeling Coal Combustion Using the Non-Premixed Model . . . 15-56

15.10 Setting Up Control Parameters . . . . . . . . . . . . . . . . . . . . . . . 15-60 15.10.1 Forcing the Exclusion and Inclusion of Equilibrium Species . . . 15-60 15.10.2 Dening the Flamelet Controls . . . . . . . . . . . . . . . . . . . 15-62 15.10.3 Zeroing Species in the Initial Unsteady Flamelet . . . . . . . . . 15-63 15.11 Calculating the Flamelets . . . . . . . . . . . . . . . . . . . . . . . . . . 15-65 15.11.1 Steady Flamelet . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-65 15.11.2 Unsteady Flamelet . . . . . . . . . . . . . . . . . . . . . . . . . . 15-67 15.11.3 Saving the Flamelet Data . . . . . . . . . . . . . . . . . . . . . . 15-70 15.11.4 Postprocessing the Flamelet Data . . . . . . . . . . . . . . . . . 15-70


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15.12 Calculating the Look-Up Tables . . . . . . . . . . . . . . . . . . . . . . . 15-74 15.12.1 Stability Issues in Calculating Look-Up Tables . . . . . . . . . . 15-77 15.12.2 Saving the Look-Up Tables . . . . . . . . . . . . . . . . . . . . . 15-77 15.12.3 Postprocessing the Look-Up Table Data . . . . . . . . . . . . . . 15-78 15.13 Dening Non-Premixed Boundary Conditions . . . . . . . . . . . . . . . 15-85 15.13.1 Input of Mixture Fraction Boundary Conditions . . . . . . . . . 15-85 15.13.2 Diusion at Inlets . . . . . . . . . . . . . . . . . . . . . . . . . . 15-86 15.13.3 Input of Thermal Boundary Conditions and Fuel Inlet Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-86 15.14 Dening Non-Premixed Physical Properties . . . . . . . . . . . . . . . . 15-87 15.15 Coal Modeling Inputs in FLUENT . . . . . . . . . . . . . . . . . . . . . . 15-88 15.16 Solution Strategies for Non-Premixed Modeling . . . . . . . . . . . . . . 15-89 15.16.1 Single-Mixture-Fraction Approach . . . . . . . . . . . . . . . . . 15-89 15.16.2 Two-Mixture-Fraction Approach . . . . . . . . . . . . . . . . . . 15-90 15.16.3 Starting a Non-Premixed Calculation From a Previous Case File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-90 15.16.4 Solving the Flow Problem . . . . . . . . . . . . . . . . . . . . . . 15-92 15.17 Postprocessing the Non-Premixed Model Results . . . . . . . . . . . . . 15-94 16 Modeling Premixed Combustion 16-1

16.1 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1 16.1.1 16.1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16-2

16.2 Premixed Combustion Theory . . . . . . . . . . . . . . . . . . . . . . . . 16-3 16.2.1 16.2.2 16.2.3 16.2.4 16.2.5 Propagation of the Flame Front . . . . . . . . . . . . . . . . . . 16-3 Turbulent Flame Speed . . . . . . . . . . . . . . . . . . . . . . . 16-4 Premixed Combustion Model Formulation in FLUENT . . . . . . 16-9 Calculation of Temperature . . . . . . . . . . . . . . . . . . . . . 16-9 Calculation of Density . . . . . . . . . . . . . . . . . . . . . . . . 16-10

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16.3 Using the Premixed Combustion Model . . . . . . . . . . . . . . . . . . 16-11 16.3.1 16.3.2 16.3.3 16.3.4 16.3.5 16.3.6 16.3.7 Enabling the Premixed Combustion Model . . . . . . . . . . . . 16-12 Choosing an Adiabatic or Non-Adiabatic Model . . . . . . . . . 16-12

Modifying the Constants for the Premixed Combustion Model . . 16-13 Dening Physical Properties for the Unburnt Mixture . . . . . . 16-13 Setting Boundary Conditions for the Progress Variable . . . . . . 16-14 Initializing the Progress Variable . . . . . . . . . . . . . . . . . . 16-14 Postprocessing for Premixed Combustion Calculations . . . . . . 16-15 17-1

17 Modeling Partially Premixed Combustion

17.1 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1 17.1.1 17.1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-1

17.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17-2 17.2.1 17.2.2 Calculation of Scalar Quantities . . . . . . . . . . . . . . . . . . 17-2 Laminar Flame Speed . . . . . . . . . . . . . . . . . . . . . . . . 17-3

17.3 Using the Partially Premixed Combustion Model . . . . . . . . . . . . . 17-3 17.3.1 17.3.2 Setup and Solution Procedure . . . . . . . . . . . . . . . . . . . 17-4 Modifying the Unburnt Mixture Property Polynomials . . . . . . 17-6 18-1

18 Modeling a Composition PDF Transport Problem

18.1 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . 18-1 18.2 Composition PDF Transport Theory . . . . . . . . . . . . . . . . . . . . 18-1 18.2.1 18.2.2 18.2.3 18.2.4 18.2.5 Solution of the PDF Transport Equation . . . . . . . . . . . . . 18-3 Particle Convection . . . . . . . . . . . . . . . . . . . . . . . . . 18-3 Particle Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-4 Particle Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-6 The ISAT Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 18-7


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18.3 Steps for Using the Composition PDF Transport Model . . . . . . . . . 18-9 18.3.1 18.3.2 18.3.3 18.3.4 18.3.5 18.3.6 18.3.7 18.3.8 18.3.9 Enabling the Composition PDF Transport Model . . . . . . . . . 18-10 Setting Integration Parameters . . . . . . . . . . . . . . . . . . . 18-11 Enabling KINetics from Reaction Design . . . . . . . . . . . . . 18-12 Enabling Liquid Micro-Mixing . . . . . . . . . . . . . . . . . . . 18-13 Selecting the Particle Mixing Model . . . . . . . . . . . . . . . . 18-13 Dening the Solution Parameters . . . . . . . . . . . . . . . . . . 18-13 Monitoring the Solution . . . . . . . . . . . . . . . . . . . . . . . 18-15 Monitoring ISAT . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-16 Using ISAT Eciently . . . . . . . . . . . . . . . . . . . . . . . . 18-17

18.3.10 Reading and Writing ISAT Tables in Parallel . . . . . . . . . . . 18-18 18.3.11 Running Unsteady Composition PDF Transport Simulations . . 18-19 18.3.12 Running Compressible Composition PDF Transport Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18-19 18.3.13 Running Composition PDF Transport Simulations with Conjugate Heat Transfer . . . . . . . . . . . . . . . . . . . 18-19 18.3.14 Postprocessing for Composition PDF Transport Calculations . . 18-19 19 Modeling Engine Ignition 19-1

19.1 Spark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-1 19.1.1 19.1.2 19.1.3 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 19-1 Spark Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . 19-2 Using the Spark Model . . . . . . . . . . . . . . . . . . . . . . . 19-3

19.2 Autoignition Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-5 19.2.1 19.2.2 19.2.3 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 19-6 Ignition Model Theory . . . . . . . . . . . . . . . . . . . . . . . . 19-7 Using the Autoignition Models . . . . . . . . . . . . . . . . . . . 19-11

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19.3 Crevice Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-14 19.3.1 19.3.2 19.3.3 19.3.4 19.3.5 19.3.6 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-14 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19-17 Crevice Model Theory . . . . . . . . . . . . . . . . . . . . . . . . 19-17 Using the Crevice Model . . . . . . . . . . . . . . . . . . . . . . 19-19 Crevice Model Solution Details . . . . . . . . . . . . . . . . . . . 19-21 Postprocessing for the Crevice Model . . . . . . . . . . . . . . . 19-21 20-1

20 Modeling Pollutant Formation

20.1 NOx Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-1 20.1.1 20.1.2 20.1.3 20.1.4 20.1.5 20.1.6 20.1.7 20.1.8 20.1.9 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-2 Governing Equations for NOx Transport . . . . . . . . . . . . . . 20-3 Thermal NOx Formation . . . . . . . . . . . . . . . . . . . . . . 20-4 Prompt NOx Formation . . . . . . . . . . . . . . . . . . . . . . . 20-8 Fuel NOx Formation . . . . . . . . . . . . . . . . . . . . . . . . . 20-12 NOx Formation from Intermediate N2 O . . . . . . . . . . . . . . 20-24 NOx Reduction by Reburning . . . . . . . . . . . . . . . . . . . . 20-26 NOx Reduction by SNCR . . . . . . . . . . . . . . . . . . . . . . 20-30 NOx Formation in Turbulent Flows . . . . . . . . . . . . . . . . 20-36

20.1.10 Using the NOx Model . . . . . . . . . . . . . . . . . . . . . . . . 20-39 20.1.11 Solution Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 20-51 20.1.12 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-52 20.2 SOx Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-53 20.2.1 20.2.2 20.2.3 20.2.4 20.2.5 20.2.6 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-54 Governing Equations for SOx Transport . . . . . . . . . . . . . . 20-55 Reaction Mechanisms for Sulfur Oxidation . . . . . . . . . . . . 20-56 SO2 and H 2 S Production in a Gaseous Fuel . . . . . . . . . . . . 20-58 SO2 and H 2 S Production in a Liquid Fuel . . . . . . . . . . . . 20-59 SO2 and H 2 S Production from Coal . . . . . . . . . . . . . . . . 20-59


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20.2.7 20.2.8 20.2.9

SOx Formation in Turbulent Flows . . . . . . . . . . . . . . . . . 20-60 Using the SOx Model . . . . . . . . . . . . . . . . . . . . . . . . 20-61 Solution Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . 20-71

20.2.10 Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-72 20.3 Soot Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-73 20.3.1 20.3.2 20.3.3 Overview and Limitations . . . . . . . . . . . . . . . . . . . . . . 20-73 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-74 Using the Soot Models . . . . . . . . . . . . . . . . . . . . . . . 20-78 21-1

21 Predicting Aerodynamically Generated Noise

21.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-1 21.1.1 21.1.2 21.1.3 Direct Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-2 Integral Method Based on Acoustic Analogy . . . . . . . . . . . 21-2 Broadband Noise Source Models . . . . . . . . . . . . . . . . . . 21-3

21.2 Acoustics Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 21-4 21.2.1 21.2.2 The Ffowcs Williams and Hawkings Model . . . . . . . . . . . . 21-4 Broadband Noise Source Models . . . . . . . . . . . . . . . . . . 21-7

21.3 Using the Ffowcs Williams and Hawkings Acoustics Model . . . . . . . . 21-12 21.3.1 21.3.2 21.3.3 21.3.4 Enabling the FW-H Acoustics Model . . . . . . . . . . . . . . . 21-13

Specifying Source Surfaces . . . . . . . . . . . . . . . . . . . . . 21-17 Specifying Acoustic Receivers . . . . . . . . . . . . . . . . . . . . 21-20 Postprocessing the FW-H Acoustics Model Data . . . . . . . . . 21-21

21.4 Using the Broadband Noise Source Models . . . . . . . . . . . . . . . . . 21-25 21.4.1 21.4.2 Enabling the Broadband Noise Source Models . . . . . . . . . . . 21-26 Postprocessing the Broadband Noise Source Model Data . . . . . 21-27

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22 Modeling Discrete Phase 22.1 Introduction 22.1.1 22.1.2

22-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-2

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-3

22.2 Particle Motion Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-5 22.2.1 22.2.2 Equations of Motion for Particles . . . . . . . . . . . . . . . . . . 22-5 Turbulent Dispersion of Particles . . . . . . . . . . . . . . . . . . 22-10

22.3 Multicomponent Particle Theory . . . . . . . . . . . . . . . . . . . . . . 22-17 22.4 Wall-Film Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-19 22.4.1 22.4.2 22.4.3 22.4.4 22.4.5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-19 Interaction During Impact with a Boundary . . . . . . . . . . . . 22-20 Splashing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-22 Separation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 22-26

Conservation Equations for Wall-Film Particles . . . . . . . . . . 22-26

22.5 Particle Erosion and Accretion Theory . . . . . . . . . . . . . . . . . . . 22-31 22.6 Dynamic Drag Model Theory . . . . . . . . . . . . . . . . . . . . . . . . 22-32 22.7 Spray Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-33 22.7.1 22.7.2 Droplet Collision Model . . . . . . . . . . . . . . . . . . . . . . . 22-34 Droplet Breakup Models . . . . . . . . . . . . . . . . . . . . . . 22-37

22.8 Atomizer Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-46 22.8.1 22.8.2 22.8.3 22.8.4 22.8.5 The Plain-Orice Atomizer Model . . . . . . . . . . . . . . . . . 22-47 The Pressure-Swirl Atomizer Model . . . . . . . . . . . . . . . . 22-55 The Air-Blast/Air-Assist Atomizer Model . . . . . . . . . . . . . 22-60 The Flat-Fan Atomizer Model . . . . . . . . . . . . . . . . . . . 22-61 The Eervescent Atomizer Model . . . . . . . . . . . . . . . . . 22-62

22.9 One-Way and Two-Way Coupling . . . . . . . . . . . . . . . . . . . . . . 22-63 22.9.1 22.9.2 Coupling Between the Discrete and Continuous Phases . . . . . . 22-64 Particle Types in FLUENT . . . . . . . . . . . . . . . . . . . . . 22-67

22.10 Discrete Phase Model (DPM) Boundary Conditions . . . . . . . . . . . . 22-91


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22.11 Steps for Using the Discrete Phase Models . . . . . . . . . . . . . . . . . 22-91 22.11.1 Options for Interaction with the Continuous Phase . . . . . . . . 22-93 22.11.2 Steady/Transient Treatment of Particles . . . . . . . . . . . . . . 22-93 22.11.3 Parameter Tracking for the Discrete Phase Model 22.11.4 Alternate Drag Laws . . . . . . . . 22-96

. . . . . . . . . . . . . . . . . . . . . . . . 22-99

22.11.5 Physical Models for the Discrete Phase Model . . . . . . . . . . . 22-100 22.11.6 Options for Spray Modeling . . . . . . . . . . . . . . . . . . . . . 22-102 22.11.7 Numerics of the Discrete Phase Model . . . . . . . . . . . . . . . 22-103 22.11.8 User-Dened Functions . . . . . . . . . . . . . . . . . . . . . . . 22-106 22.11.9 Parallel Processing for the Discrete Phase Model . . . . . . . . . 22-106 22.12 Setting Initial Conditions for the Discrete Phase . . . . . . . . . . . . . . 22-109 22.12.1 Injection Types . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-110

22.12.2 Particle Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22-126 22.12.3 Creating, Modifying, Copying, Deleting, and Listing Injections . 22-127 22.12.4 Dening Injection Properties . . . . . . . . . . . . . . . . . . . . 22-129 22.12.5 Modeling Turbulent Dispersion of Particles . . . . . . . . . . . . 22-134 22.12.6 Custom Particle Laws . . . . . . . . . . . . . . . . . . . . . . . . 22-137 22.12.7 Dening Properties Common to More than One Injection . . . . 22-138 22.13 Setting Boundary Conditions for the Discrete Phase . . . . . . . . . . . 22-140 22.13.1 Discrete Phase Boundary Condition Types . . . . . . . . . . . . 22-141 22.13.2 Setting Particle Erosion and Accretion Parameters . . . . . . . . 22-146 22.14 Setting Material Properties for the Discrete Phase . . . . . . . . . . . . . 22-146 22.14.1 Summary of Property Inputs . . . . . . . . . . . . . . . . . . . . 22-146 22.14.2 Setting Discrete-Phase Physical Properties . . . . . . . . . . . . 22-150 22.15 Solution Strategies for the Discrete Phase . . . . . . . . . . . . . . . . . 22-156 22.15.1 Integration of Particle Equation of Motion . . . . . . . . . . . . . 22-157 22.15.2 Performing Trajectory Calculations . . . . . . . . . . . . . . . . 22-159 22.15.3 Resetting the Interphase Exchange Terms . . . . . . . . . . . . . 22-163

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22.16 Postprocessing for the Discrete Phase . . . . . . . . . . . . . . . . . . . . 22-163 22.16.1 Displaying of Trajectories . . . . . . . . . . . . . . . . . . . . . . 22-164 22.16.2 Reporting of Trajectory Fates . . . . . . . . . . . . . . . . . . . . 22-167 22.16.3 Step-by-Step Reporting of Trajectories . . . . . . . . . . . . . . . 22-172 22.16.4 Reporting of Current Positions for Unsteady Tracking . . . . . . 22-174 22.16.5 Reporting of Interphase Exchange Terms and Discrete Phase Concentration . . . . . . . . . . . . . . . . . . . . 22-175 22.16.6 Sampling of Trajectories . . . . . . . . . . . . . . . . . . . . . . . 22-176 22.16.7 Histogram Reporting of Samples . . . . . . . . . . . . . . . . . . 22-178 22.16.8 Summary Reporting of Current Particles . . . . . . . . . . . . . 22-179 22.16.9 Postprocessing of Erosion/Accretion Rates . . . . . . . . . . . . 22-181 23 Modeling Multiphase Flows 23.1 Introduction 23.1.1 23.1.2 23-1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-2

Multiphase Flow Regimes . . . . . . . . . . . . . . . . . . . . . . 23-2 Examples of Multiphase Systems . . . . . . . . . . . . . . . . . . 23-5

23.2 Choosing a General Multiphase Model . . . . . . . . . . . . . . . . . . . 23-5 23.2.1 23.2.2 23.2.3 23.2.4 Approaches to Multiphase Modeling . . . . . . . . . . . . . . . . 23-6 Model Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . 23-7 Time Schemes in Multiphase Flow . . . . . . . . . . . . . . . . . 23-11 Stability and Convergence . . . . . . . . . . . . . . . . . . . . . . 23-12

23.3 Volume of Fluid (VOF) Model Theory . . . . . . . . . . . . . . . . . . . 23-12 23.3.1 23.3.2 23.3.3 23.3.4 23.3.5 23.3.6 Overview and Limitations of the VOF Model . . . . . . . . . . . 23-12 Volume Fraction Equation . . . . . . . . . . . . . . . . . . . . . 23-14 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . 23-19 Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . 23-19 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-20 Additional Scalar Equations . . . . . . . . . . . . . . . . . . . . 23-20


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23.3.7 23.3.8 23.3.9

Time Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 23-20 Surface Tension and Wall Adhesion . . . . . . . . . . . . . . . . 23-21 Open Channel Flow . . . . . . . . . . . . . . . . . . . . . . . . . 23-26

23.4 Mixture Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-29 23.4.1 23.4.2 23.4.3 23.4.4 23.4.5 23.4.6 23.4.7 23.4.8 23.4.9 Overview and Limitations of the Mixture Model . . . . . . . . . 23-29 Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . . . 23-31 Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . . 23-32 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-32 Relative (Slip) Velocity and the Drift Velocity . . . . . . . . . . . 23-33 Volume Fraction Equation for the Secondary Phases . . . . . . . 23-34 Granular Properties . . . . . . . . . . . . . . . . . . . . . . . . . 23-35 Granular Temperature . . . . . . . . . . . . . . . . . . . . . . . . 23-36 Solids Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-36 . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-37

23.5 Eulerian Model Theory 23.5.1 23.5.2 23.5.3 23.5.4 23.5.5 23.5.6 23.5.7 23.5.8 23.5.9

Overview and Limitations of the Eulerian Model . . . . . . . . . 23-37 Volume Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . 23-39 Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . 23-40 Interphase Exchange Coecients . . . . . . . . . . . . . . . . . . 23-44 Solids Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-50 Maximum Packing Limit in Binary Mixtures . . . . . . . . . . . 23-53 Solids Shear Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 23-54 Granular Temperature . . . . . . . . . . . . . . . . . . . . . . . . 23-57 Description of Heat Transfer . . . . . . . . . . . . . . . . . . . . 23-58

23.5.10 Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . . . 23-60 23.5.11 Solution Method in FLUENT . . . . . . . . . . . . . . . . . . . . 23-70

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23.6 Wet Steam Model Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 23-71 23.6.1 23.6.2 23.6.3 23.6.4 Overview and Limitations of the Wet Steam Model . . . . . . . . 23-71 Wet Steam Flow Equations . . . . . . . . . . . . . . . . . . . . . 23-72 Phase Change Model . . . . . . . . . . . . . . . . . . . . . . . . 23-74 Built-in Thermodynamic Wet Steam Properties . . . . . . . . . . 23-75

23.7 Modeling Mass Transfer in Multiphase Flows . . . . . . . . . . . . . . . 23-78 23.7.1 23.7.2 23.7.3 23.7.4 Source Terms due to Mass Transfer . . . . . . . . . . . . . . . . 23-78 Unidirectional Constant Rate Mass Transfer . . . . . . . . . . . . 23-80 UDF-Prescribed Mass Transfer . . . . . . . . . . . . . . . . . . . 23-80 Cavitation Models . . . . . . . . . . . . . . . . . . . . . . . . . . 23-81

23.8 Modeling Species Transport in Multiphase Flows . . . . . . . . . . . . . 23-89 23.8.1 23.8.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-90 Mass and Momentum Transfer with Multiphase Species Transport23-91

23.9 Steps for Using a Multiphase Model . . . . . . . . . . . . . . . . . . . . 23-94 23.9.1 23.9.2 23.9.3 23.9.4 23.9.5 23.9.6 23.9.7 23.9.8 Enabling the Multiphase Model . . . . . . . . . . . . . . . . . . . 23-96 Solving a Homogeneous Multiphase Flow . . . . . . . . . . . . . 23-97 Dening the Phases . . . . . . . . . . . . . . . . . . . . . . . . . 23-98 Including Body Forces . . . . . . . . . . . . . . . . . . . . . . . . 23-99 Modeling Multiphase Species Transport . . . . . . . . . . . . . . 23-100 Specifying Heterogeneous Reactions . . . . . . . . . . . . . . . . 23-102 Including Mass Transfer Eects . . . . . . . . . . . . . . . . . . . 23-103 Dening Multiphase Boundary Conditions . . . . . . . . . . . . . 23-106

23.10 Setting Up the VOF Model . . . . . . . . . . . . . . . . . . . . . . . . . 23-121 23.10.1 Choosing a VOF Formulation . . . . . . . . . . . . . . . . . . . . 23-121 23.10.2 Modeling Open Channel Flows . . . . . . . . . . . . . . . . . . . 23-124 23.10.3 Dening the Phases for the VOF Model . . . . . . . . . . . . . . 23-131 23.10.4 Setting Time-Dependent Parameters for the VOF Model . . . . . 23-135 23.10.5 Modeling Compressible Flows . . . . . . . . . . . . . . . . . . . . 23-137 23.10.6 Modeling Solidication/Melting . . . . . . . . . . . . . . . . . . 23-138


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23.11 Setting Up the Mixture Model

. . . . . . . . . . . . . . . . . . . . . . . 23-138

23.11.1 Dening the Phases for the Mixture Model . . . . . . . . . . . . 23-138 23.11.2 Including Cavitation Eects . . . . . . . . . . . . . . . . . . . . . 23-144 23.11.3 Modeling Compressible Flows . . . . . . . . . . . . . . . . . . . . 23-146 23.12 Setting Up the Eulerian Model . . . . . . . . . . . . . . . . . . . . . . . 23-147 23.12.1 Additional Guidelines for Eulerian Multiphase Simulations . . . . 23-147 23.12.2 Dening the Phases for the Eulerian Model . . . . . . . . . . . . 23-147 23.12.3 Modeling Turbulence . . . . . . . . . . . . . . . . . . . . . . . . 23-156 23.12.4 Including Heat Transfer Eects . . . . . . . . . . . . . . . . . . . 23-158 23.12.5 Modeling Compressible Flows . . . . . . . . . . . . . . . . . . . . 23-159 23.13 Setting Up the Wet Steam Model . . . . . . . . . . . . . . . . . . . . . . 23-160 23.13.1 Using User-Dened Thermodynamic Wet Steam Properties . . . 23-160 23.13.2 Writing the User-Dened Wet Steam Property Functions (UDWSPF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-161 23.13.3 Compiling Your UDWSPF and Building a Shared Library File . 23-164 23.13.4 Loading the UDWSPF Shared Library File . . . . . . . . . . . . 23-166 23.13.5 UDWSPF Example . . . . . . . . . . . . . . . . . . . . . . . . . 23-167 23.14 Solution Strategies for Multiphase Modeling . . . . . . . . . . . . . . . . 23-175 23.14.1 Setting Initial Volume Fractions . . . . . . . . . . . . . . . . . . 23-175 23.14.2 VOF Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-175 23.14.3 Mixture Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-177 23.14.4 Eulerian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-178 23.14.5 Wet Steam Model . . . . . . . . . . . . . . . . . . . . . . . . . . 23-179 23.15 Postprocessing for Multiphase Modeling . . . . . . . . . . . . . . . . . . 23-181 23.15.1 Model-Specic Variables . . . . . . . . . . . . . . . . . . . . . . . 23-181 23.15.2 Displaying Velocity Vectors . . . . . . . . . . . . . . . . . . . . . 23-185 23.15.3 Reporting Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . . 23-185 23.15.4 Reporting Forces on Walls . . . . . . . . . . . . . . . . . . . . . 23-185 23.15.5 Reporting Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . 23-186

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24 Modeling Solidication and Melting

24-1

24.1 Overview and Limitations of the Solidication/Melting Model . . . . . . 24-1 24.1.1 24.1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-1 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-2

24.2 Theory for the Solidication/Melting Model . . . . . . . . . . . . . . . . 24-2 24.2.1 24.2.2 24.2.3 24.2.4 24.2.5 24.2.6 Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-3 Momentum Equations . . . . . . . . . . . . . . . . . . . . . . . . 24-4 Turbulence Equations . . . . . . . . . . . . . . . . . . . . . . . . 24-5 Species Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 24-5 Pull Velocity for Continuous Casting . . . . . . . . . . . . . . . . 24-6 Contact Resistance at Walls . . . . . . . . . . . . . . . . . . . . 24-7

24.3 Using the Solidication/Melting Model . . . . . . . . . . . . . . . . . . . 24-9 24.3.1 24.3.2 24.3.3 24.3.4 Setup Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-9 Procedures for Modeling Continuous Casting . . . . . . . . . . . 24-11 Solution Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 24-12

Postprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24-12 25-1

25 Using the Solver

25.1 Overview of Flow Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . 25-2 25.1.1 25.1.2 Pressure-Based Solver . . . . . . . . . . . . . . . . . . . . . . . . 25-3 Density-Based Solver . . . . . . . . . . . . . . . . . . . . . . . . 25-5

25.2 General Scalar Transport Equation: Discretization and Solution . . . . . 25-8 25.2.1 Solving the Linear System . . . . . . . . . . . . . . . . . . . . . . 25-9

25.3 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-10 25.3.1 25.3.2 25.3.3 Spatial Discretization . . . . . . . . . . . . . . . . . . . . . . . . 25-10 Temporal Discretization . . . . . . . . . . . . . . . . . . . . . . . 25-17 Evaluation of Gradients and Derivatives . . . . . . . . . . . . . . 25-19


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25.4 Pressure-Based Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-22 25.4.1 25.4.2 25.4.3 25.4.4 25.4.5 Discretization of the Momentum Equation . . . . . . . . . . . . . 25-23 Discretization of the Continuity Equation . . . . . . . . . . . . . 25-25 Pressure-Velocity Coupling . . . . . . . . . . . . . . . . . . . . . 25-26 Steady-State Iterative Algorithm . . . . . . . . . . . . . . . . . . 25-32 Time-Advancement Algorithm . . . . . . . . . . . . . . . . . . . 25-33

25.5 Density-Based Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-37 25.5.1 25.5.2 25.5.3 25.5.4 25.5.5 Governing Equations in Vector Form . . . . . . . . . . . . . . . . 25-37 Preconditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-38 Convective Fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . 25-41 Steady-State Flow Solution Methods . . . . . . . . . . . . . . . . 25-43 Unsteady Flows Solution Methods . . . . . . . . . . . . . . . . . 25-45

25.6 Multigrid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-48 25.6.1 25.6.2 25.6.3 25.6.4 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-48 Multigrid Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-50 Algebraic Multigrid (AMG) . . . . . . . . . . . . . . . . . . . . . 25-54 Full-Approximation Storage (FAS) Multigrid . . . . . . . . . . . 25-61

25.7 How To Use the Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-63 25.7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-63 . . . . . . . . . . . . . . . . . . . . 25-67

25.8 Choosing the Discretization Scheme 25.8.1 25.8.2 25.8.3 25.8.4 25.8.5

First-Order Accuracy vs. Second-Order Accuracy . . . . . . . . . 25-67 Other Discretization Schemes . . . . . . . . . . . . . . . . . . . . 25-68 Choosing the Pressure Interpolation Scheme . . . . . . . . . . . . 25-68 Choosing the Density Interpolation Scheme . . . . . . . . . . . . 25-69 User Inputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-70

25.9 Pressure-Based Solver Settings . . . . . . . . . . . . . . . . . . . . . . . 25-71 25.9.1 25.9.2 25.9.3 Choosing the Pressure-Velocity Coupling Method . . . . . . . . . 25-71 Setting Under-Relaxation Factors . . . . . . . . . . . . . . . . . 25-74 Setting Solution Controls for the Non-Iterative Solver . . . . . . 25-76

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25.10 Density-Based Solver Settings . . . . . . . . . . . . . . . . . . . . . . . . 25-80 25.10.1 Changing the Courant Number . . . . . . . . . . . . . . . . . . . 25-80 25.10.2 Convective Flux Types . . . . . . . . . . . . . . . . . . . . . . . 25-82 25.10.3 Turning On FAS Multigrid . . . . . . . . . . . . . . . . . . . . . 25-82 25.11 Setting Algebraic Multigrid Parameters . . . . . . . . . . . . . . . . . . 25-84 25.11.1 Additional Algebraic Multigrid Parameters . . . . . . . . . . . . 25-87 25.11.2 Setting FAS Multigrid Parameters . . . . . . . . . . . . . . . . . 25-91 25.12 Setting Solution Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-94 25.13 Setting Multi-Stage Time-Stepping Parameters . . . . . . . . . . . . . . 25-97 25.14 Initializing the Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-98 25.14.1 Initializing the Entire Flow Field . . . . . . . . . . . . . . . . . . 25-99 25.14.2 Patching Values in Selected Cells . . . . . . . . . . . . . . . . . . 25-101 25.15 Using Full Multigrid (FMG) Initialization . . . . . . . . . . . . . . . . . 25-103 25.15.1 Overview of FMG Initialization . . . . . . . . . . . . . . . . . . . 25-103 25.15.2 Steps in Using FMG Initialization . . . . . . . . . . . . . . . . . 25-105 25.15.3 Convergence Strategies for FMG Initialization . . . . . . . . . . 25-106 25.16 Performing Steady-State Calculations . . . . . . . . . . . . . . . . . . . . 25-106 25.17 Performing Time-Dependent Calculations . . . . . . . . . . . . . . . . . 25-108 25.17.1 User Inputs for Time-Dependent Problems . . . . . . . . . . . . 25-110 25.17.2 Adaptive Time Stepping . . . . . . . . . . . . . . . . . . . . . . 25-116

25.17.3 Variable Time Stepping . . . . . . . . . . . . . . . . . . . . . . . 25-119 25.17.4 Postprocessing for Time-Dependent Problems . . . . . . . . . . . 25-121 25.18 Monitoring Solution Convergence . . . . . . . . . . . . . . . . . . . . . . 25-122 25.18.1 Monitoring Residuals . . . . . . . . . . . . . . . . . . . . . . . . 25-122 25.18.2 Monitoring Statistics . . . . . . . . . . . . . . . . . . . . . . . . 25-133 25.18.3 Monitoring Forces and Moments . . . . . . . . . . . . . . . . . . 25-134 25.18.4 Monitoring Surface Integrals . . . . . . . . . . . . . . . . . . . . 25-138 25.18.5 Monitoring Volume Integrals . . . . . . . . . . . . . . . . . . . . 25-142


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25.19 Executing Commands During the Calculation . . . . . . . . . . . . . . . 25-146 25.19.1 Specifying the Commands to be Executed . . . . . . . . . . . . . 25-146 25.19.2 Dening Macros . . . . . . . . . . . . . . . . . . . . . . . . . . . 25-148 25.19.3 Saving Files During the Calculation . . . . . . . . . . . . . . . . 25-149 25.20 Additional Options in the Solver Menu . . . . . . . . . . . . . . . . . . . 25-149 25.20.1 Animating the Solution . . . . . . . . . . . . . . . . . . . . . . . 25-149 25.20.2 Importing and Exporting Particle History Data . . . . . . . . . . 25-159 25.20.3 Managing Acoustic Signal Data . . . . . . . . . . . . . . . . . . . 25-163 25.21 Checking Your Case Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 25-163 25.21.1 Checking the Grid . . . . . . . . . . . . . . . . . . . . . . . . . . 25-166 25.21.2 Checking Model Selections . . . . . . . . . . . . . . . . . . . . . 25-168 25.21.3 Checking Boundary Conditions . . . . . . . . . . . . . . . . . . . 25-170 25.21.4 Checking Material Properties . . . . . . . . . . . . . . . . . . . . 25-173 25.21

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