FLUENT 15.0 Tutorial Guide

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fluent 15.0 官方指南
Table of contents Using This Manual……,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,……xi What's In this manual XI 2. The Contents of the fluent manuals 3. Where to find the files used in the tutorials 4. How To Use this manual . 4.1. For the Beginner… 4.2. For the Experienced User……… 鲁番着鲁 1 Introduction to Using ANSYS Fluent in ANSYS Workbench: Fluid Flow and Heat Transfer in a Mixing + v 5. Typographical Conventions Used In This Manual………….…….….………… E|boW.…1 1.1. Introduction 1.2. Prerequisites……,…,…,…,…,…,…,……………… 1.3. Problem Description............................... 1.4. Setup and Solution……….........,…,.,.,,…… :··:··············:······· 14.1. Preparation… 4 14.2. Creating a Fluent Fluid Flow Analysis System in ANSYS Workbench……………….4 1.4.3. Creating the Geometry in ANSYS Design Modeler 1.4.4. Meshing the Geometry in the ANSYS Meshing application......... 20 1.4.5. Setting Up the CFD Simulation in ANSYS Fluent 27 1.4.6. Displaying results in ansys fluent and cfd-Post..………….51 7. Duplicating the Fluent-Based Fluid Flow Analysis System 60 14.:8. Changing the geometry in ANSYS Design Modeler……………,……,………………………161 1.4.9. Updating the Mesh in the aNsys Meshing Application 63 1.4.10. Calculating a New Solution in ANSYS Fluent ··.:·;· 65 14.1. Comparing the Results of Both Systems in CFD-Post……….….….….….….….….…....67 1.5. Summary,….……,,… 2. Parametric Analysis in ANSYS Workbench Using ANSYS Fluent………,…,…,…,…,……………,73 2.1. Introduction 73 2,2. Prerequisites………,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,… ∴,74 2.3. Problem Description 74 24. Setup and Solution…………,…,…,…,…,……,…,…,…,…,…,…,…,…,……,…,…,…,…,…,…,,,77 2.4.1. Preparation............. 78 2.4.2. Adding Constraints to ANSYS Design Modeler Parameters in ANSYS Workbench 78 2.4.3. Setting Up the CFD Simulation in ANSYS Fluent 87 24.4. Defining Input Parameters in ANSYS Fluent and Running the Simulation…………)91 2.4.5. Postprocessing and Setting the output Parameters in ANSYS CFD-Post 100 2.4.6. Creating Additional Design Points in ANSYS Workbench........... ,112 2.4.7. Postprocessing the New design Points in CFD-Post 115 2.4.8. Summary………,,…,…,…,…,…,…,…,…,…,…,…,…,…,,…,…,……,121 3. Introduction to Using ANSYS Fluent: Fluid Flow and Heat Transfer in a Mixing Elbow 123 3.1. ntroduction∩.……………………123 3.2. Prerequisites∴,.,…,…,…,…,…,,,,123 3.3. Problem Description 34. Setup and Solution….…..….…..…..….….…,…,.,….,….,… 124 3. 4.1. Preparation 125 3.4.2. Launching ansys fluent.................. 125 3.4.3 Reading the mesh 128 344. General Settings……,…,,…,…,…,…,…,,…,…,…,…,…,…,…,…,…,…………,133 3. 4.5. Models 着。音自 135 3. 4.6. Materials 138 Release 15.0-@ SAS /P Inc. Al/rights reserved. -Contains proprietary and confidential in/ormation of ansys inc and its Tutorial guide 3. 47 Cell Zone Conditions 141 3.4.8. Boundary Conditions ∴143 3.4.9. Solution……………………,……………147 4.10. Displaying the Preliminary Solution…….….….….…..….….….…...…...…….…...,157 3.4.11. Using the Coupled Solver............................... 172 3.4.12. Adapting the Mesh... 。自非·非非·非··非非非·非。是非非非自·非非·非·非··非·自非非非 175 3.5.5 ummary..... 191 4. Modeling Periodic Flow and Heat Transfer………,…,…,…,…,…,…,…,……,…,………………,193 4.1. Introduction 193 4.2. Prerequisites….........,.,..,,.,… 193 4.3. Problem Description ..194 4.4. Setup and Solution............ 194 4.4.1. Preparation 195 44.2.Mesh∴ ……195 4.4.3. General Settings.……,…,…,…,,,…,…,…,…,,…,,…,,,… 198 4.4.4.Mode|s….…………198 44.5. Materials… 4.4.6. Cell zone conditions…….…201 4.47. Periodic conditions . 4.4.8. Boundary Conditions……..……,…,………,……,…,……,…………………………,203 449 Solution ∴…………204 4.4.10. postprocessing 鲁·音自非 209 4.5.5 ummary………….….….…….….….219 4.6. Further Improvements 220 5. Modeling External Compressible Flow…… 221 5.1. Introduction .221 5.2. Prerequisites…,..,....,….., ·;·····:··:······:······:···:·:.········:······;····4·:· 221 5.3. Problem Description…...…… .222 5.4. Setup and solution 5.4.1. Preparation 222 5. 4.2. Mesh 223 5.4.3. General Settings 226 5.4.4. Models….26 5.4.5. Materials… ·····4·:········:·:··.·4·:···:·····:····:·中···· 227 5.4.6. Boundary Conditions 229 5.4.7.Operating Conditions .····:········ 231 5. 4. 8. Solution 232 54.9. Postprocessing………,…,…,…,…,…,…,,…,………,………,………,…,249 55.5 ummary… 255 5.6. Further Improvements……...….,...,….…,.….,….…….………,255 6. Modeling Transient Compressible Flow.....................257 6.1. Introduction 257 6.2. Prerequisites….….,….,…..,., ··..··················· 257 6.3. Problem Description........,.,….,….,…,……….………258 64. Setup and Solution…… 258 6.4.1. Preparation…,…,…,…,…,…,…,…,…,…,……,………,258 64.2. Reading and Checking the mesh……. 259 6.4.3. Specifying Solver and Analysis type............ 香音非 着非·非·普。音非着·非。番··非非非 261 64.4. Specifying the Models…… ················:···············:······:···:·····:·.·······:··················:··········· 263 6.4.5. Editing the material Properties. 646. Setting the Operating Conditions……… 265 647. Creating the boundary Conditions…… 266 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates Tutorial guide 6.4.8. Setting the Solution Parameters for Steady Flow and Solving............... 26 6.4.9. Enabling Time Dependence and Setting Transient Conditions 282 6.4.10. Specifying Solution Parameters for Transient Flow and Solving..............285 6.4.11. Saving and Postprocessing Time-Dependent Data Sets……………………,…,288 6.5.5 ummary….....,.,…,,…,…,…,…,,…,…,,…,,,302 66. Further Improvements……,…,…,…,…,…,…,…,…,…,…,…,……,………303 7. Modeling Radiation and Natural Convection 305 7.1. Introduction∴ ···非·非非非音。1 305 7.2. Prerequisites 305 7.3. Problem Description 7. 4. Setup and Solution ......... .306 7.4.1. Preparation…,…,…,…,…,…,…,…,…,,…,…,……,306 7.4.2. Reading and Checking the Mesh ············市···,··市·· 307 74.3. Specifying Solver and Analysis Type…........,,….…,…,08 7.4.4. Specifying the Models ∴309 7.4.5. Defining the materials 312 7.4.6. Specifying Boundary Conditions ,314 74.7.0 btaining the solution…….….……………………………318 7.4.8 Postprocessing ··:······:·····:··············:······*· 324 7.4.9. Comparing the Contour Plots after Varying Radiating Surfaces .....................339 74.10.52 S Definition, Solution, and postprocessing with Partial Enclosure…………………,351 7.5. Summary… 音音着鲁D自自鲁非4自非音自。自自非自曲非自鲁鲁自非鲁非着自自自自。自着鲁D 355 7.6. Further Improvements…..,..,.,..,.,…,…,…,…,… 356 8. Using the Discrete Ordinates Radiation Model 357 8.1. Introduction .. 8.2. Prerequisites ................................................................................................................................357 83. Problem Description…...........,.,,.,…,…,…,……,……358 8.4. Setup and Solution 358 84.1. Preparation……,…,…,,…,…,…,…,…,,,…,…,…………59 8.4.2.MeSh 359 843. General Settings..........…..,….,…,…,,……,…………360 8. 4. Models 363 8. 4.5. Materials ···········4······4·····::·· 鲁,看 ,364 8.4.6. Cell zone conditions∴.……366 84.7. Boundary Conditions….........,.…….….…………368 8. 8. Solution 376 8.4.9. Postprocessing................... 380 84.10. terate for higher Pixels……,,…,…,…,…,…,…,…,,,…,,…,…,,…,…,,……,,388 8.4.11. Iterate for Higher Divisions ....... 392 84.12. Make the Reflector Completely Diffuse………………,,,,,,,.,400 8.4.13. Change the boundary type of 8.5. Summary………,…,…,…,… ∴404 8.6. Further Improvements 404 9. Using a Non- Conformal Mesh 405 9.1. Introduction 看看 405 9.2. Prerequisites…,,… 405 9.3. Problem Description 406 9.4. Setup and solution ·非.非·着·,非·非非着非非。非自。··非非音自。鲁·非。非非。非非看 407 9.4.1. Preparation……,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,………,407 94.2.Mesh. ··:·:····:·················· ·····:····:···:··:·····: 408 9.4.3. General Settings…,…,…,…,…,…,…,…,…,…,,…,…,,,,411 9. 4. Models 412 Release 15.0-@ SAS /P Inc. All rights reserved -Contains proprietary and con/idential in/ormation of ansys inc and its subsidiaries and affiliates Tutorial guide 9.45. Materials .. 9. 4.6. Cell zone conditions 带看 414 9.4.7. Operating Conditions....................... ,416 94.8. Boundary Conditions………………………………416 9. 4.9. Mesh Interfaces 426 9.4.10. Solution 428 9.4.11. Postprocessing ∴431 9.5.5 ummary………,…,….……….……….3 9.6. Further Improvements...... 10. Modeling F| ow Through Porous Media……… 443 ··:·····:···· 445 10.1. Introduction 445 10.2. Prerequisites……,…,…,…,…,…,…,…,…,…,…,,…,,445 10.3. Problem Description 446 10.4. Setup and Solution 446 10.4.1. Preparation .:·····:·.···········:···· 447 10.4.2.Mesh.….………………447 10.4.3. General Settings 449 10.44. Models………………………………………………………450 10.4.5. Materⅰals… ……………………………………………………451 10.4.6. Cell zone conditions……9453 10.4.7. Boundary Conditions……………….………….………………………2457 10.4.8. Solution 自着 ,非B非 460 10.4.9. Postprocessing………,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,,…,,.,…,465 10.5. Summary 479 10.6. Further Improvements…,…,…,…,…,…,…,…,…,…,…,…,…,…,,…479 11. Using a Single Rotating Reference Frame. 11.1 Introduction ···········:····:··············:··········:·····:····:···· 481 11. 2. Prerequisites .481 11.3. Problem Description....................................................482 11.4. Setup and solution 483 11.4.1. Preparation……,…,…,…,…,…,…,…,… 483 114,2.Mesh 484 114.3. General Settings............….….….….….…..….…4.84 11.4.4. Models∴487 11.45 Materials 488 114.6, Cell zone conditions 489 11.4.7. Boundary Conditions a·:...·:··a...:·· ..:.···.:· 490 11.4.8. Solution Using the Standard k-ε Model………….……,…,………,…,…,…,…,……………,494 11.4.9. Postprocessing for the standard k-E Solution .......502 114.10. Solution Using the rng k-ε Model……….…………………………………………512 11.4.11. Postprocessing for the rng k-E Solution. ..........................................................................514 11.5. Summary…….………,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…………,518 11.6. Further Improvements 518 11.7. References……………….1519 12. Using Multiple Reference Frames 521 12.1. Introduction .·:····:·····:··········:······:·························· 521 12. 2. Prerequisites 522 12.3. Problem Description ··来自··非非非·非非··。非非着非。非·非非·非非着非非非非着非非非非非。自非非非。非非非鲁自D非自非非鲁看 522 12.4. Setup and Solution…………,…,…,…,…,…,…,…,…,…,…,…,,… 523 12.4.1. Preparation…… 523 1242. Reading and Checking the Mesh and Setting the Units………………………,…,524 12.4.3. Specifying Solver and Analysis Type . 看 526 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates Tutorial guide 1244. Specifying the models.......,.,,.,….,,……,…,,526 124.5. Specifying Materials……… 527 124.6. Specifying Cell Zone Conditions...,.,.,,.,,,,,…,…,………,…,529 124.7. Setting Boundary Conditions……….1532 12. 4.8. Defining Mesh Interfaces........ ··:··· 534 12.4.9.0 btaining the Solution………….….……… 鲁垂·非·。。非非非 ∴535 124.10.step9: Postprocessing....,...,.,.,,…,…,,… 541 125. Summary……………………,…,,….………,….,………………………547 12.6. Further Improvements 548 13. Using the Mixing Plane Model…..….….….…….,…,,…,………,……………549 3.1. Introduction 549 13.2. Prerequisites……,…,…,…,,…,…,…,……………………,549 33. Problem Description…… 549 13.4. Setup and Solution............. ·············:··:····::.····:·············:··:··:·: 550 13.4.1. Preparation……,…, 550 13.4.2.Mesh.……………551 134.3. General| Settings………,…,…, 551 1344. Models…554 134.5. Mixing Plane………,…,…,…,…,…,…,…,…,…,…,,…,…,…, ····:·····:··· 555 13.4.6. Materia5∴557 13.4.7. Cell zone conditiⅰons∴.,,,…11 558 134.8. Boundary Conditions.....…...….5 13.49 Solution 569 13.. Postprocessing 578 13.5. Summary………… 586 13.6. Further Improvements ·.·++·:··+···:···++·+·+··· 586 4. Using Sliding Meshes........ ·4······:·····:·.·······:···:··:········:····:·.:···:···· 587 41. Introduction 587 14.2. Prerequisites…,,,….,.,.,…,,,,,, 587 14.3. Problem Description 587 144. Setup and Solution..........….…588 14.4.1. Preparation……… 588 144.2.Mesh∴ ·着。音。·自。非非着普非音·D。 ,非非非非。·。。。自,··非。。,。非非.非音着非D。音非。· ,589 144.3. General Settings.……,…,… ·············:·······:····.···:·······:········· 589 14.4. 4 Models 593 14.4.5. Materials ∴593 14.46 Cell Zone conditions 594 1447. Boundary Conditions…………….…………………….597 14.4.8. Operating Conditions................. ·····“··4· 601 14.49. Mesh interface5………602 14.4.10 Solution 603 144.11. Postprocessing……,…,…,…,…,……………………,.622 4.5.Summary 630 146. Further Improvements….......,.,,.,,…,…,…,………………630 15. Using Dynamic Meshes 631 15.1. Introduction∴ ····:····:···········:········.········ 631 15.2. Prerequisites 631 15.3. Problem Description 54. Setup and Solution……..…..….…,…,,…,,…… 632 15.4.1. Preparation………,…,…,………,…,…………….632 15.4.2.MeSh 633 15.4.3. General Settings.............. 633 Release 15.0-@ SAS /P Inc. All rights reserved -Contains proprietary and con/idential in/ormation of ansys inc and its subsidiaries and affiliates Tutorial guide 1544. Models∴ 636 154.5 Materials 637 15.4.6. Boundary Conditions. ...................................................................................639 154.7. Solution: Steady Flow……….………,…,…,,…,…,…,…,…,…,…,……,… 644 15.4.8. Time-Dependent Solution Setup 648 15.4.9. Mesh Motion ∴649 15.4.10. Time-Dependent Solution... 655 154.1. Postprocessing………………,…,…,…,……,…,…,……,…,…,…,…,…,,……………,665 15.5. Summary 669 156. Further Improvements……......…......….669 16. Modeling Species Transport and Gaseous Combustion .671 16.1.Introduction..........wm.w.m.w..www.w....w........671 16.2. Prerequisites… 671 16.3. Problem Description 16.4. Background……,… 672 16.5. Setup and Solution ...........................................................672 16.5.1. Preparation… ∴673 16.52.Mesh ·:·.····· 673 16.5.3. General settings.………,…,…,…,…,…,…,…,……………674 16.54. Model∴ ∴.677 16.5.5. Materials …680 16.5.6. Boundary 16.5.7. Initial Reaction solution.wwwwwwwwwwwwwwwwwwwooo.w.. 690 16.5..Postprocesing...........… .696 16.59. NOx Prediction…………………………,,706 16.6. Summary ·····:·············=·4······:············ 720 16.7. Further Improvements .............. ∴721 17. Using the Non-Premixed Combustion Model 723 17.1. Introduction ··。自着非着非鲁 ···:··········:······.···;·:···· ·····;·;·.········;···.·中····· 723 17,2. Prerequisites….………… 723 173. Problem Description...................1724 17.4. Setup and solution……,,,,… 725 17.4.1. Preparation…,…,,…,….,…..,…, 725 1742. Reading and Checking the mesh….……..….….………,….…,…,…………………,726 17.43 Specifying Solver and analysis type.................. 730 174.4. Specifying the Models…… 731 17. 4.5. Defining Materials and Properties....... 738 174.6. Specifying Boundary Conditions…………,…,…,…,…,…,…,……,,…,………,740 17.4.7. Specifying Operating Conditions . 17.4.8.Obtaining Solution 748 17.4.9. Postprocessing 751 174.10. Energy Balances Reporting......…...….….…..….…………,755 17.5. Summary...... 757 17.6. References 自。·非非非非非非·非看···非非··D··非,非自非,着非串非非非非非非·非非···非非非·非非着非非非非鲁音·非·是··非·非·垂 ∴757 17.7. Further Improvements ··.···:············ 758 18. Modeling Surface Chemistry...,.,.,….…,…,…,…….,159 18.1. Introduction 759 18.2. Prerequisites 音着·D··非。··着音着。音着非非非非非自非非非·‖。·非。着音·音着·非非。·非 759 18.3. Problem Description ················:····:·····:··········:·····+·····················.····:····:············· 760 184. Setup and Solution............................….1761 18.4.1. Preparation 761 18.4.2. Reading and Checking the mesh ...::a 762 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates Tutorial guide 18.4.3. Specifying Solver and Analysis 18.4.4. Specifying the Models ∴765 18.4.5. Defining Materials and Properties. 18.4.6. Specifying Boundary Conditions∴… :.····:·· ∴776 1847. Setting the Operating Conditions….......….......….….…………,782 18.4.8. Simulating non- Reacting Flow.……,…,…,…,…,…,…,,,…,… 783 18.4.9. Simulating Reacting Flow 786 18.4.10. Postprocessing the Solution Results………,…,,…,…,,…,…,…,…,… 793 18.5. Summary 801 18.6. Further Improvements ··;··申 ∴801 19. Modeling Evaporating Liquid Spray............….….….….….….….…803 9.1.Introduction.......ww..w.www.ww..w....w...................803 9. 2. Prerequisites ······,······ ···,·· 803 9.3. Problem Description 19.4. Setup and solution 着看垂看, .·.·.············· 804 19.4.1. Preparation………,…,…,…,…,…,…,…,……,……,…,.804 19.42. Reading the mesh….….…..….,….,….,,…,…,…, 805 1943. General Settings......,.…...,.,……,…,………,806 194.4. Specifying the Models………………………,….…….….,…,….….….809 19.45 Materials 812 194.6. Boundary Conditions…… ∴814 19.4.7. Initial Solution Without Droplets ∴819 1948. Create a Spray Injection…………… 829 19.49. Solution 837 194.10. Postprocessing…………,…,…,…,…,…,…,…,…,…,…,…,…,…,……,……,…,…,…,,842 195. Summary… ·:···:·············=·4······:···········4····:···=·· 853 19.6. Further Improvements.............. 853 20. Using the vof Model 855 20.1. Introduction…, ·;········中······· ……855 20.2. Prerequisites∴ 855 20.3. Problem Description 20.4. Setup and solution…,…,,…,… 857 20.4.1. Preparation… 非。·,。。。音。。非。。音非 857 20.4,2. Reading and manipulating the mesh……………,…,……,…………858 2043. General Settings……… ∴863 20.4.4. Models 866 20.45 Materials 8 20.4.6. Phases∴868 20.4.7. Operating Conditions..................…….870 20.4.8. User-Defined Function (UDF) ·····:··.·:··········:······· …871 20.4.9. Boundary Conditions. 872 20.4.10. Solution.……..875 20.4.11 Postprocessing 882 20.5.5 ummary.… ∴888 20.6. Further Improvements 带看 888 21 Modeling Cavitation...............,.,.,….,,……………891 21.1 Introduction 891 21.2. Prerequisites… D着非·非···非音。·非非···自非。。非非··非。·音非音着非普非非非·非 春鲁非着非···非自·。··非非··。非 891 21.3. Problem Description………,…,…,…,…,…,,…,…,…,…,…,…,…,…,,…,…,…………891 214. Setup and Solution....................1892 21.4.1. Preparation………,…, 892 21.4.2. Reading and checking the mesh D ·非自4垂 893 Release 15.0-@ SAS /P Inc. All rights reserved -Contains proprietary and con/idential in/ormation of ansys inc and its subsidiaries and affiliates Tutorial guide 214.3. General Settings…...….…..….….….…,…,….…,……………895 144. Models 896 21. 45. Materials 898 2146. Phases…………………………………………………………… ∴901 2147. Boundary Conditions…,… ··;··················· 904 21.4.8. Operating Conditions……,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…,………,909 21. 49 Solution ,B音。着鲁非自非自 909 21.4.10. Postprocessing………,…,…,…,…,…,…,……,…,…………,,914 21.5. Summary 919 21.6. Further Improvements....,.,.,.,.,.,,….,….,…,…,…,…,……,…,……920 22. Using the Mixture and Eulerian Multiphase Models 921 22.1. Introduction.…………………921 22.2. Prerequisites……….,…., 921 22.3. Problem Description 22.4. Setup and Solution……… 着看垂看, .·.·.············· :··.·.···· 922 224.1. Preparation,...,.,….,…,….,….,…,….……,…,……923 22.4,2.Mesh .923 224.3. General Settings..............,.,,….…,…,….…924 22.4.4. Models∴926 224.5. Materia|s………………928 22.4.6. Phases… 929 2247. Boundary Conditions…….…........…..….………931 224.8.0 perating Conditions………,…,…,…,…,…,…,…,…,…,…,,…,…,………….,94 22. 4.9. Solution Using the Mixture Model 935 22.4.10 Postprocessing for the Mixture Solution 940 22.. Higher Order Solution using the mixture Model 943 224.12. Setup and Solution for the eulerian model....…..….…………945 22.4.13 Postprocessing for the eulerian Model 950 22.5.5 ummary...,..,.,.,,… ····:·.··· 953 22.6. Further Improvements 954 23. Using the Eulerian Multiphase Model for Granular Flow.….….….……955 231. Introduction 955 23.2. Prerequisites…,…,,…,… 955 23.3. Problem Description 956 234. Setup and Solution..................…....956 234.1. Preparation……… ∴956 234.2.Mesh :....::·· 957 234.3. General Settings…,………,…,…,…,…,…,…,…,…,…,…,…,…,…,…,…………….,958 23.44 Models ···· 965 234.5 Materials ················ ∴…967 23.4.6. Phases ·4·.+·.4·“·· 969 23.4.7. User-Defined Function(UDF) 972 234.8 Cell Zone Conditions 973 23.4.9. Solution∴.……976 23.4.10 Postprocessing 990 23.5.5 summary……….….,….,….,….,,….,.,…,…,,…,…,,,….,….,…,…………,94 23.6. Further Improvements……… 994 24 Modeling Solidification...................................995 24.1. Introduction 非。非非·。章 995 24.2. Prerequisites….…,…,….,….,…,.,…,,…,…,…,….,……,……………995 24.3. Problem Description 着非音音看D。音非D音非着非非 995 24.4. Setup and Solution 鲁,音普垂 ∴996 Release 15.0-@ SAS /P, Inc. All rights reserved -Contains proprietary and confidential information of ansys inc and its subsidiaries and affiliates

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