Murakami Computational Wind Engineering 1

Proceedings of the 1st International Symposium on Computational Wind Engineering (CWE 92) Tokyo, Japan, August 21-23, 1992
1. Auflage 2014
ISBN: 978-0-444-59861-5
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 924 Seiten

The aim of this volume is to explore the challenges posed by the rapid development of Computational Fluid Dynamics (CFD) within the field of engineering. CFD is already essential to research concerned with fluid flow in civil engineering, and its further potential for application in wind engineering is highly promising. State-of-the-art papers from all over the world are contained here, illuminating the present parameters of the field, as well as suggesting fruitful areas for further research. Eleven papers have been contributed by invited speakers outstanding in the fields of CFD and wind engineering. This volume will serve as a vehicle to promote further development in computational wind engineering.

Autoren/Hrsg.

Murakami, S.

Inhaltsverzeichnis

1;Front Cover;1
2;Computational Wind Engineering 1;4
3;Copyright Page;5
4;Table of Contents;10
5;Preface;6
6;Symposium organization;8
7;PART I:
FUNDAMENTALS;16
7.1;Section I: Turbulence Modelling and their
Applications;16
7.1.1;Chapter 1.
On the Simulation of Turbulent Flow Past Bluff Bodies;18
7.1.1.1;ABSTRACT;18
7.1.1.2;1. INTRODUCTION;18
7.1.1.3;2. STATISTICAL TURBULENCE MODELS EMPLOYED;19
7.1.1.4;3. LES MODELS TESTED;20
7.1.1.5;4. CALCULATION EXAMPLES;22
7.1.1.6;5. CONCLUSIONS;32
7.1.1.7;6. ACKNOWLEDGEMENTS;32
7.1.1.8;REFERENCES;33
7.1.2;CHAPTER 2. COMPARISON OF VARIOUS TURBULENCE
MODELS APPLIED TO A BLUFF BODY;36
7.1.2.1;Abstract;36
7.1.2.2;1. INTRODUCTION;36
7.1.2.3;2. CHARACTERISTICS OF FLOWFIELD AROUND A BLUFF BODY;37
7.1.2.4;3. COMPARISON OF MEAN VELOCITY VECTOR FIELD;38
7.1.2.5;4. DISCREPANCY IN SURFACE PRESSURE DISTRIBUTION;39
7.1.2.6;5. COMPARISON OF k-e
AND ASM;39
7.1.2.7;6. COMPARISON OF ASM AND LES; modelling of convection and diffusion terms;42
7.1.2.8;7. IMPROVEMENT OF LES; new SGS model with
vaiable smagorinsky constant;44
7.1.2.9;8. COMPARISON OF DIFFERENT TURBULENCE MODELS FOR VARIOUS FLOWFIELDS;45
7.1.2.10;9. CONCLUSION;46
7.1.2.11;ACKNOWLEDGEMENTS;47
7.1.2.12;NOMENCLATURE;47
7.1.2.13;REFERENCES;50
7.1.3;Chapter 3.
Computational modelling of complex turbulent flow -expectations, reality and prospects;52
7.1.3.1;1. CFD - THE CHALLENGE POSED BY PRACTICAL FLOWS;52
7.1.3.2;2. CFD - SOME IMPORTANT ISSUES;56
7.1.3.3;3. CURRENT CAPABILITIES AND LIMITATIONS;59
7.1.3.4;4. CURRENT DIRECTIONS IN TURBULENCE MODELLING;62
7.1.3.5;5. CONCLUDING REMARKS;63
7.1.3.6;REFERENCES;65
7.1.4;CHAPTER
4. MODELING FLOWS AROUND BLUFF BODIES BY REYNOLDS AVERAGED TRANSPORT EQUATIONS;68
7.1.4.1;1. INTRODUCTION;68
7.1.4.2;2. TRANSPORT EFFECTS IN COMPLEX GEOMETRIES :
k-e MODEL;69
7.1.4.3;3. SECOND MOMENT CLOSURES;71
7.1.4.4;4. CONCLUDING REMARKS;81
7.1.4.5;References;82
7.1.5;Chapter 5. Subgrid–scale
modeling suggested by a two-scale DIA;84
7.1.5.1;1. INTRODUCTION;84
7.1.5.2;2. FUNDAMENTAL EQUATIONS;85
7.1.5.3;3. RESULTS OF A TWO-SCALE DIA;85
7.1.5.4;4. SGS MODELS;87
7.1.5.5;5. DISCUSSIONS;90
7.1.5.6;6. CONCLUDING REMARKS;91
7.1.5.7;Acknowledgments;91
7.1.5.8;References;91
7.1.6;Chapter 6. Estimation of anisotropic k-e model on the Backward-facing Step
Flow by LES data base;92
7.1.6.1;1. INTRODUCTION;92
7.1.6.2;2. TURBULENCE MODELS AND NUMERICAL METHOD;93
7.1.6.3;3. RESULTS AND DISCUSSIONS;94
7.1.6.4;4. A PRIORI TEST FOR REYNOLDS STRESS;97
7.1.6.5;5. FINAL REMARKS;99
7.1.6.6;REFERENCES;99
7.1.7;Chapter 7. Numerical prediction of separating and reattaching
flows with a modifled low-Reynolds-numb er k-e model;100
7.1.7.1;1. INTRODUCTION;100
7.1.7.2;2. GOVERNING EQUATIONS AND MODIFIED LOW-REYNOLDS-NUMBER
k-e MODEL;101
7.1.7.3;3. NUMERICAL PROCEDURE AND BOUNDARY CONDITIONS;103
7.1.7.4;4. DISCUSSION OF THE PRESENT MODEL;103
7.1.7.5;5. RESULTS AND DISCUSSION;105
7.1.7.6;6. CONCLUSIONS;108
7.1.7.7;REFERENCES;108
7.1.8;Chapter 8.
Influence of the Turbulence Model in Calculations of Flow over Obstacles with Second-Moment Closures;110
7.1.8.1;1. INTRODUCTION;110
7.1.8.2;2. MATHEMATICAL FORMULATION;111
7.1.8.3;3. RESULTS AND DISCUSION;114
7.1.8.4;4. CONCLUDING REMARKS;115
7.1.8.5;5. ACKNOWLEDGMENT;115
7.1.8.6;6. REFERENCES;115
7.1.9;Chapter 9.
Finite-volume computation of merging parallel channel flows by a second-moment turbulence closure model;120
7.1.9.1;1. INTRODUCTION;120
7.1.9.2;2. MATHEMATICAL MODELS;121
7.1.9.3;3. NUMERICAL IMPLEMENTATION;123
7.1.9.4;4. RESULTS AND DISCUSSION;123
7.1.9.5;5. CONCLUSION;129
7.1.9.6;REFERENCES;129
7.1.10;Chapter 10. Numerical Analysis of Wind around Building Using High-Speed GSMAC-FEM
— Validation of Differential Stress Model;130
7.1.10.1;1. INTRODUCTION;130
7.1.10.2;2. BASIC EQUATIONS;131
7.1.10.3;3. VALIDATION OF DIFFERENTIAL STRESS MODEL;134
7.1.10.4;4. APPLICATION;135
7.1.10.5;5. CONCLUSIONS;135
7.1.10.6;REFERENCES;135
7.1.11;Chapter 11.
A computational study of the flow in a bluff body/flat plate junction;136
7.1.11.1;1. INTRODUCTION;136
7.1.11.2;2. GOVERNING EQUATIONS AND NUMERICAL METHOD;137
7.1.11.3;3. RESULTS;138
7.1.11.4;4. CONCLUSIONS;142
7.1.11.5;References;142
7.1.12;Chapter 12.
Numerical simulation to determine the effects of incident wind shear and turbulence level on the flow around a building;144
7.1.12.1;1. INTRODUCTION;144
7.1.12.2;2. NUMERICAL SIMULATION;144
7.1.12.3;3. RESULTS AND DISCUSSION;145
7.1.12.4;4 CONCLUSIONS;149
7.1.12.5;5 ACKNOWLEDGMENTS;149
7.1.12.6;6 REFERENCES;149
7.1.13;Chapter 13.
Numerical study of wind flow over an elevated roadway;150
7.1.13.1;1. INTRODUCTION;150
7.1.13.2;2. PHYSICAL MODEL;151
7.1.13.3;3. COMPUTATIONAL MODEL;152
7.1.13.4;4. CONCLUSIONS;158
7.1.13.5;5. ACKNOWLEDGEMENTS;158
7.1.13.6;6. References;158
7.1.14;Chapter 14. Appropriate boundary conditions for computational wind engineering models using the
k-e turbulence model;160
7.1.14.1;1. INTRODUCTION;160
7.1.14.2;2. A HOMOGENEOUS
k-e MODEL FOR THE ATMOSPHERIC SURFACE LAYER;161
7.1.14.3;3. ATMOSPHERIC SURFACE LAYER MEASUREMENTS AT SILSOE;162
7.1.14.4;4. APPROPRIATE BOUNDARY CONDITIONS;166
7.1.14.5;5. CONCLUSIONS;167
7.1.14.6;6. REFERENCES;168
7.1.15;Chapter 15.
Transport equations of conditionally averaged Reynolds stresses for computation of turbulent flows with intermittency;170
7.1.15.1;1. INTRODUCTION;170
7.1.15.2;2. THE CONDITIONAL REYNOLDS-STRESS TRANSPORT EQUATIONS;171
7.1.15.3;4. EXPERIMENTAL DATA;175
7.1.15.4;5. CONCLUSIONS;178
7.1.15.5;6. REFERENCES;179
7.1.16;Chapter 16.
Optimization of roughness parameters for staggered arrayed cubic blocks using experimental data;180
7.1.16.1;1. INTRODUCTION;180
7.1.16.2;2. WIND TUNNEL EXPERIMENT;180
7.1.16.3;3. NUMERICAL CALCULATIONS;182
7.1.16.4;4. OPTIMIZATION OF ROUGHNESS PARAMETERS;184
7.1.16.5;5. CONCLUSION;186
7.1.16.6;Acknowledgments;186
7.1.16.7;References;186
7.1.17;Chapter 17.
Modelling of Turbulent Flows within Plant/Urban Canopies;188
7.1.17.1;1. INTRODUCTION;188
7.1.17.2;2. AVERAGING PROCEDURE;188
7.1.17.3;3. AVERADING PROCEDURE FOR CONSTITUTIVE EQUATIONS;190
7.1.17.4;4. FORMATION OF REYNOLDS STRESS EQUATION MODEL;192
7.1.17.5;5. RESULTS;194
7.1.17.6;6. SUMMERY AND CONCLUSIONS;194
7.1.17.7;ACKNOWLEDGEMENTS;194
7.1.17.8;REFERENCES;195
7.1.18;DISCUSSIONS OF TURBULENCE MODELLING AND THEIR APPLICATIONS;198
7.2;Section II:
Direct and Large Eddy Simulations;208
7.2.1;Chapter 18.
Simulation of complex turbulent flows: recent advances and prospects in wind engineering;210
7.2.1.1;1. INTRODUCTION;210
7.2.1.2;2. THREE-DIMENSIONAL UNSTEADY SIMULATIONS OF TURBULENT FLOW;211
7.2.1.3;3. RECENT DEVELOPMENTS IN LARGE EDDY SIMULATION;215
7.2.1.4;4. APPLICATIONS TO FLOWS OVER BLUFF BODIES;219
7.2.1.5;5. SOME RECENT LES RESULTS FOR BLUFF BODIES;221
7.2.1.6;6. BOOTSTRAPPING;222
7.2.1.7;7. CONCLUSIONS AND PROSPECTS;226
7.2.1.8;8. ACKNOWLEDGEMENTS;226
7.2.1.9;9. REFERENCES;226
7.2.2;Chapter 19.
Large-eddy-simulation of the flow around building models;228
7.2.2.1;1. BASIC EQUATIONS AND DISCRETISATION;228
7.2.2.2;2. TIME INTEGRATION AND SUBGRID SCALE MODELLING;229
7.2.2.3;3. RESULTS;229
7.2.2.4;4. REFERENCES;230
7.2.3;Chapter 20.
Computation of Wind Flow around a Tall Building and the Large-Scale Vortex Structure;234
7.2.3.1;1. INTRODUCTION;234
7.2.3.2;2. GOVERNING EQUATIONS;235
7.2.3.3;3. MODEL VALIDATION;236
7.2.3.4;4. TALL BUILDING CASE;238
7.2.3.5;5. CONCLUSIONS;241
7.2.3.6;ACKNOWLEDGEMENTS;243
7.2.3.7;REFERENCES;243
7.2.4;Chapter 21.
Large eddy simulation of microburst winds flowing around a building;244
7.2.4.1;1. INTRODUCTION;244
7.2.4.2;2. MODEL;245
7.2.4.3;3. EXPERIMENTAL DESIGN;245
7.2.4.4;4. RESULTS;247
7.2.4.5;5. CONCLUSIONS;248
7.2.4.6;6. ACKNOWLEDGMENTS;252
7.2.4.7;7. REFERENCES;252
7.2.5;Chapter 22.
Use of large eddy simulation to measure fluctuating pressure fields around buildings with wall openings;254
7.2.5.1;1 Introduction;254
7.2.5.2;2 Outline of LES;254
7.2.5.3;3 Results of Numerical Analyses;255
7.2.5.4;4 Conclusion;256
7.2.5.5;References;256
7.2.6;Chapter 23.
Numerical Modelling of Flow Over A Rigid Wavy Surface by LES;260
7.2.6.1;1. INTRODUCTION;260
7.2.6.2;2. GOVERNING EQUATIONS;261
7.2.6.3;3. COORDINATE TRANSFORMATION;262
7.2.6.4;4. COMMENTS ON NUMERICAL SIMULATION;263
7.2.6.5;5. RESULTS AND DISCUSSION;264
7.2.6.6;6. ACKNOWLEDGEMENT;267
7.2.6.7;7. REFERENCES;269
7.2.7;Chapter 24.
A numerical study on the flow around flat plates at low Reynolds numbers;270
7.2.7.1;1. INTRODUCTION;270
7.2.7.2;2. FORMULATION;271
7.2.7.3;3. RESULTS;274
7.2.7.4;4. CONCLUSIONS;278
7.2.7.5;5. REFERENCES;279
7.2.8;Chapter 25.
Fourth Order Finite Difference and Multigrid Methods for Modeling Instabilities in 2-Dimensional Flat Plate Boundary Layers;280
7.2.8.1;1. INTRODUCTION;280
7.2.8.2;2. GOVERNING EQUATIONS;281
7.2.8.3;3. OUTFLOW BOUNDARY TREATMENT;282
7.2.8.4;4. NUMERICAL METHODS;284
7.2.8.5;5. COMPUTATIONAL RESULTS;286
7.2.8.6;6. CONCLUDING REMARKS;288
7.2.8.7;ACKNOWLEDGEMENTS;289
7.2.8.8;REFERENCES;289
7.2.9;Chapter 26. Numerical analysis of flows
over walls with protuberances;290
7.2.9.1;1.INTRODUCTION;290
7.2.9.2;2.GOVERNING EQUATION;291
7.2.9.3;3.NUMERICAL SCHEME;291
7.2.9.4;4.RESULTS AND DISCUSSION;292
7.2.9.5;5.CONCLUSIONS;295
7.2.9.6;6.REFERENCES;295
7.2.10;Chapter 27. A numerical study of nonlinear waves excited by an
obstacle in the flow of stratified fluid;298
7.2.10.1;1.INTRODUCTION;298
7.2.10.2;2. GOVERNING EQUATIONS AND THE NUMERICAL METHOD;299
7.2.10.3;3.RESULTS AND DISCUSSIONS;301
7.2.10.4;REFERENCES;301
7.2.11;DISCUSSIONS OF DIRECT AND LARGE EDDY SIMULATIONS;304
7.3;Section III: Numerical Methods;310
7.3.1;Chapter 28.
Finite element methods in wind engineering;312
7.3.1.1;1. INTRODUCTION;312
7.3.1.2;2. ISSUES IN THE DEVELOPMENT OF WIND ENGINEERING SIMULATION TOOLS;313
7.3.1.3;3. CONCLUSIONS;318
7.3.1.4;4. REFERENCES;319
7.3.2;Chapter 29.
High Resolution Vortex Simulation of Bluff Body Flows;330
7.3.2.1;1. INTRODUCTION;330
7.3.2.2;2. VISCOUS VORTEX METHOD;331
7.3.2.3;References;337
7.3.3;Chapter 30. Volume–fraction techniques: powerful
tools for wind engineering;342
7.3.3.1;1. INTRODUCTION: OVERVIEW OF FAVOR CONCEPT;342
7.3.3.2;2. A SIMPLE EXAMPLE AND ITS IMPLICATIONS;344
7.3.3.3;3. MAKING THE CONCEPT A PRACTICAL TOOL;346
7.3.3.4;4. ORDINARY AND NOVEL USES OF THE FAVOR METHOD;347
7.3.3.5;5. ACKNOWLEDGEMENTS;349
7.3.3.6;REFERENCES;350
7.3.4;Chapter 31. Numerical Simulation of High Reynolds Number Flows
by Petrov-Galerkin Finite Element Method;354
7.3.4.1;1. INTRODUCTION;354
7.3.4.2;2. STATEMENT OF PROBLEMS;354
7.3.4.3;3. PETROV-GALERKIN FORMULATION USING EXPONENTIAL FUNCTIONS;355
7.3.4.4;4. NUMERICAL EXAMPLES;357
7.3.4.5;5. CONCLUSIONS;361
7.3.4.6;REFERENCES;361
7.3.5;Chapter 32.
Direct third-order upwind finite element simulation of high Reynolds number flows around a circular cylinder;364
7.3.5.1;1. INTRODUCTION;364
7.3.5.2;2. INCOMPRESSIBLE NAVIER-STOKES EQUATIONS;365
7.3.5.3;3. THIRD-ORDER ACCURATE UPWIND SCHEME;365
7.3.5.4;4. FINITE ELEMENT SCHEME;367
7.3.5.5;5. NUMERICAL EXAMPLES;368
7.3.5.6;6. CONCLUSIONS;370
7.3.5.7;REFERENCES;370
7.3.6;Chapter 33.
Automatic mesh generation for FEM simulation of wind flow around tall buildings;372
7.3.6.1;1. INTRODUCTION;372
7.3.6.2;2. RECURSIVE SUBDIVISION;373
7.3.6.3;3. MESH CONVERSION;374
7.3.6.4;4. CONCLUSION;377
7.3.6.5;5. REFERENCES;377
7.3.7;Chapter 34.
Numerical Simulation of Flow around a Sphere with Vortex Blobs;378
7.3.7.1;1. INTRODUCTION;378
7.3.7.2;2. MATHEMATICAL MODEL;379
7.3.7.3;3. RESULTS;383
7.3.7.4;4. CONCLUSIONS;384
7.3.7.5;5. REFERENCES;384
7.3.8;Chapter 35.
Simulation of Turbulent Flow by Discrete Vortex Approximation;386
7.3.8.1;1. INTRODUCTION;386
7.3.8.2;2. FORMULATION AND NUMERICAL PROCEDURE;386
7.3.8.3;3. RESULT;388
7.3.8.4;4. CONCLUSION;389
7.3.8.5;REFERENCES;389
7.3.9;Chapter 36. Solution Method of the Time Transient Moving Boundary Problems
Using Generalized Porous Media Technique;396
7.3.9.1;1. Introduction;396
7.3.9.2;2. Basic Idea of the moving obstacle
treatment;397
7.3.9.3;3. FAVORITE formulation including thin plate;398
7.3.9.4;4.
Conclusion;401
7.3.9.5;Acknowledgement;401
7.3.9.6;References;401
7.3.9.7;5. Result of sample calculations;402
7.3.10;Chapter 37.
Application of Massive Parallel Computer to Computational Wind Engineering;408
7.3.10.1;1. INTRODUCTION;408
7.3.10.2;2. FLOW SIMULATION;409
7.3.10.3;3. MASSIVE PARALLEL COMPUTER USED;410
7.3.10.4;4. PARALLELIZATION OF ALGORITHM;411
7.3.10.5;5. CASES ANALYZED;411
7.3.10.6;6. RESULTS;412
7.3.10.7;7.
CONCLUSIONS;415
7.3.10.8;ACKNOWLEDGEMENTS;415
7.3.10.9;REFERENCES;415
7.3.11;DISCUSSIONS OF NUMERICAL METHODS;416
8;PART II: APPLICATIONS;422
8.1;Section I: Wind Load;422
8.1.1;Chapter 38.
The generalization and simplification of wind loads and implications for computational methods;424
8.1.1.1;1. COMPUTATIONAL ASPECTS OF WIND LOADING MODELLING;424
8.1.1.2;2. SOME BREAKTHROUGHS;425
8.1.1.3;3. GENERALIZATION OF RESPONSE USING INFLUENCE SURFACES;426
8.1.1.4;4. SIMPLIFICATION THROUGH ORTHONORMAL FUNCTIONS;428
8.1.1.5;5. INFLUENCE OF WIND DIRECTION AND UNCERTAINTIES;429
8.1.1.6;6. COMPUTATIONAL OPPORTUNITIES IN WIND LOADING AND SOME CONCLUSIONS;430
8.1.2;Chapter 39.
Numerical simulation of wind-induced pressures on buildings of various geometries;434
8.1.2.1;1. INTRODUCTION;434
8.1.2.2;2. NUMERICAL APPROACH;435
8.1.2.3;3. BOUNDARY CONDITIONS;437
8.1.2.4;4. RESULTS AND DISCUSSION;438
8.1.2.5;5. CONCLUSIONS;443
8.1.2.6;6. REFERENCES;444
8.1.3;Chapter 40.
Predicting r.m.s. pressures from computed velocities and mean pressures;446
8.1.3.1;1. FORMULAE FOR R.M.S. PRESSURES IN HOMOGENEOUS ISOTROPIC TURBULENCE;446
8.1.3.2;2. FORMULAE FOR R.M.S. PRESSURES IN GENERAL FLOWS;447
8.1.3.3;3. THE TEXAS TECH EXPERIMENTAL DATA;448
8.1.3.4;4. RELATIONSHIPS BETWEEN C'p AND Cp;448
8.1.3.5;5. CONCLUSIONS;451
8.1.3.6;6. REFERENCES;451
8.1.4;Chapter 41.
A comparison of computer and wind-tunnel models of turbulence around the Silsoe Structures Building;454
8.1.4.1;1. INTRODUCTION;454
8.1.4.2;2. FULL-SCALE MEASUREMENTS;454
8.1.4.3;3. WIND-TUNNEL MEASUREMENTS;455
8.1.4.4;4. COMPUTATIONAL SOLUTIONS;455
8.1.4.5;6. CONCLUSIONS;461
8.1.4.6;7. ACKNOWLEDGEMENT;462
8.1.4.7;8. REFERENCES;462
8.1.5;Chapter 42.
Computational and Experimental Roof Corner Pressures on the Texas Tech Building;464
8.1.5.1;1. INTRODUCTION;464
8.1.5.2;2. COMPUTER MODELLING;464
8.1.5.3;3. RESULTS AND DISCUSSIONS;466
8.1.5.4;4. CONCLUSIONS;468
8.1.5.5;5. ACKNOWLEDGEMENTS;469
8.1.5.6;6. REFERENCES;469
8.1.6;Chapter 43.
Numerical Simulation of Flowfield around Texas Tech Building by Large Eddy Simulation;470
8.1.6.1;1. INTRODUCTION;470
8.1.6.2;2. OUTLINE OF FIELD MEASUREMENT OF THE TEXAS TECH BUILDING;470
8.1.6.3;3. RESULTS AND DISCUSSION;471
8.1.6.4;4. CONCLUSION;473
8.1.6.5;Acknowledgement;473
8.1.6.6;References;475
8.1.7;Chapter 44. Large eddy simulation of wind flow around dome
structures by the finite element method;476
8.1.7.1;1. BASIC EQUATIONS;476
8.1.7.2;2. FINITE ELEMENT FORMULATION;477
8.1.7.3;3. INDUCING THE FLOW WITH TURBULENCE;478
8.1.7.4;4. WIND FLOW AROUND A CYLINDRICAL DOME ROOF;480
8.1.7.5;5. CONCLUDING REMARKS;485
8.1.7.6;REFERENCES;485
8.1.8;Chapter 45.
Computation of wind flow over topography;486
8.1.8.1;1. TOPOGRAPHIC MULTIPLIERS;486
8.1.8.2;2. RIDGE GEOMETRIES;487
8.1.8.3;3. COMPUTER MODELLING;487
8.1.8.4;4. RESULTS;488
8.1.8.5;5. CONCLUSIONS;491
8.1.8.6;6. REFERENCES;491
8.1.9;Chapter 46.
Analysis of hyperbolic cooling towers for wind loads with ACMC and semi-loof shell elements;492
8.1.9.1;1. INTRODUCTION;492
8.1.9.2;2. FORMULATION FOR ANALYSIS;493
8.1.10;Chapter 47. Computing the statistical stability of integral length scale measurements by autoregressive
simulation;502
8.1.10.1;1. INTRODUCTION;502
8.1.10.2;2. BASIC ASSUMPTIONS AND DEFINITIONS;502
8.1.10.3;3. ESTIMATION OF MEAN, VARIANCE AND INTEGRAL TIME SCALE;503
8.1.10.4;4. AUTOREGRESSIVE SIMULATION;507
8.1.10.5;5. EXPERIMENTAL RESULTS;508
8.1.10.6;6. CONCLUSIONS;510
8.1.10.7;References;511
8.1.11;Chapter 48.
Response analyses on along-wind and across-wind vibrations of tall buildings in time domain;512
8.1.11.1;1. INTRODUCTION;512
8.1.11.2;2. SPECIFICATIONS OF A BUILDING;513
8.1.11.3;3. SIMULATION OF THE FLUCTUATING WIND FORCES;514
8.1.11.4;4. WIND RESPONSE ANALYSES IN TIME DOMAIN;517
8.1.11.5;5. CONCLUSION;517
8.1.11.6;References;521
8.1.12;Chapter 49.
Proposed formulae for the power spectral densities of fluctuating lift and torque on rectangular 3-D cylinders;522
8.1.12.1;1. INTRODUCTION;522
8.1.12.2;2. WIND TUNNEL EXPERIMENTS;523
8.1.12.3;3. EXPERIMENTAL RESULTS AND FORMULATION;523
8.1.12.4;4. CONCLUSION;530
8.1.12.5;5. ACKNOWLEDGEMENT;530
8.1.12.6;6. REFERENCES;531
8.1.13;CHAPTER 50. NUMERICAL SIMULATION OF PRESSURE DISTRIBUTIONS UNDERNEATH ROOFING PAVER SYSTEMS;532
8.1.13.1;1. INTRODUCTION;532
8.1.13.2;2. PHYSICAL ASSUMPTIONS;532
8.1.13.3;3. MATHEMATICAL EQUATIONS;533
8.1.13.4;4. COMPARISONS OF NUMERICAL AND EXPERIMENTAL RESULTS AND DISCUSSIONS;539
8.1.13.5;5. REFERENCES;541
8.1.14;DISCUSSIONS OF WIND LOAD;542
8.2;Section II:
Wind Induced Vibrations;554
8.2.1;Chapter 51.
Numerical study on aeroelastic instability of cylinders with a circular and rectangular cross-section;556
8.2.1.1;1. INTRODUCTION;556
8.2.1.2;2. OUTLINE OF COMPUTATIONAL METHODS;557
8.2.1.3;3. COMPUTATIONAL RESULTS;557
8.2.1.4;4. CONCLUSIONS;565
8.2.1.5;References;565
8.2.2;Chapter 52.
Unsteady Pressure Field around Oscillating Prism predicted by LES;566
8.2.2.1;1. INTRODUCTION;566
8.2.2.2;2. OUTLINE OF NUMERICAL SIMULATIONS;567
8.2.2.3;3. RESULTS AND DISCUSSIONS;568
8.2.2.4;4. CONCLUSION;571
8.2.2.5;Acknowledgements;571
8.2.2.6;References;571
8.2.3;Chapter 53.
Numerical Investigation on the Aeroelastic Instability of Bluff Cylinders;572
8.2.3.1;1. INTRODUCTION;572
8.2.3.2;2. PROBLEM FORMULATION;573
8.2.3.3;3. COMPUTATIONAL MODEL;573
8.2.3.4;4. THREE-DIMENSIONAL SIMULATIONS FOR A RECTANGULAR CYLINDER;574
8.2.3.5;5. AEROELASTIC BEHAVIOR OF BLUFF CYLINDERS;576
8.2.3.6;6. CONCLUSION;581
8.2.3.7;REFERENCES;581
8.2.4;Chapter 54.
Numerical simulation of flow field around an oscillating bridge using finite difference method;582
8.2.4.1;1 INTRODUCTION;582
8.2.4.2;2 PROBLEM FORMULATION;582
8.2.4.3;3 RESULTS;584
8.2.4.4;4 CONCLUSION;586
8.2.4.5;5 ACKNOWLEDGEMENT;586
8.2.4.6;References;586
8.2.5;Chapter 55.
A numerical investigation of the unsteady fluid force induced in the annular diffuser by the oscillating inner cylinder;592
8.2.5.1;1. INTRODUCTION;592
8.2.5.2;2. METHODOLOGY OF NUMERICAL ANALYSIS;592
8.2.5.3;3. NUMERICAL RESULTS;594
8.2.5.4;4. CONCLUSION;600
8.2.5.5;References;600
8.2.6;Chapter 56.
Finite element analysis of vortex-induced vibrations of bluff cylinders;602
8.2.6.1;1. INTRODUCTION;602
8.2.6.2;2. COMPUTATIONAL METHOD;603
8.2.6.3;3. VORTEX-INDUCED OSCILLATIONS OF A CIRCULAR CYLINDER;605
8.2.6.4;4. CONCLUDING REMARK;608
8.2.6.5;References;609
8.2.7;Chapter 57.
Interaction analysis between structure and fluid flow for wind engineering;610
8.2.7.1;1.INTRODUCTION;610
8.2.7.2;2.ALGORITHM;611
8.2.7.3;3. FLOW AROUND A RIGID RECTANGULAR CYLINDER;613
8.2.7.4;4.FLOW AROUND A FLEXIBLE STRUCTURE;615
8.2.7.5;5.CONCLUDING REMARKS;619
8.2.7.6;ACKNOWLEDGEMENTS;619
8.2.7.7;REFERENCES;619
8.2.8;Chapter 58.
Vortex induced vibration of circular cylinder;620
8.2.8.1;1.
INTRODUCTION;620
8.2.8.2;2. METHOD OF SIMULATION;621
8.2.8.3;3. DISCUSSION OF RESULTS;621
8.2.8.4;4. CONCLUSION;625
8.2.8.5;REFERENCES;625
8.2.9;Chapter 59.
Simulation of Aerodynamic Instability of Bluff Body;626
8.2.9.1;1. INTRODUCTION;626
8.2.9.2;2. METHOD;626
8.2.9.3;3. RESULTS AND DISCUSSION;630
8.2.9.4;4. CONCLUSION;633
8.2.9.5;References;633
8.2.10;Chapter 60.
Aerodynamic loading and flow past bluff bodies using discrete vortex method;634
8.2.10.1;1. INTRODUCTION;634
8.2.10.2;2. METHOD;634
8.2.10.3;3. DVM APPLICATION FOR BLUFF BODY AERODYNAMICS;637
8.2.10.4;4. DVM IMPLEMENTATION AT COLORADO STATE UNIVERSITY;638
8.2.10.5;5.
REPRESENTATIVE RESULTS;639
8.2.10.6;6. CONCLUDING REMARKS;642
8.2.10.7;REFERENCES;642
8.2.11;Chapter 61.
Unsteady aerodynamic force characteristics on 2-D oscillating bluff body;644
8.2.11.1;1. INTRODUCTION;644
8.2.11.2;2. COMPUTATIONAL METHOD;645
8.2.11.3;3. WIND TUNNEL APPARATUS;646
8.2.11.4;4. DISCUSSIONS;646
8.2.11.5;5. CONCLUSION;651
8.2.11.6;Acknowledgements;651
8.2.11.7;References;651
8.2.12;Chapter 62.
Aeolian vibrations of overhead transmission lines: computation in turbulence conditions;654
8.2.12.1;1.INTRODUCTION;654
8.2.12.2;2. MATHEMATICAL MODEL OF THE SYSTEM CABLE-FLUID ACTIONS;657
8.2.12.3;3. SOME ANALYTICAL RESULTS AND CONCLUSIONS;659
8.2.12.4;REFERENCES;663
8.2.13;DISCUSSIONS OF WIND INDUCED VIBRATIONS;664
8.3;Section III:
Environmental Problems;670
8.3.1;Chapter 63.
Numerical study of wind flow over a cooling tower;672
8.3.1.1;1. INTRODUCTION;672
8.3.1.2;2. PHYSICAL MODEL;673
8.3.1.3;3. COMPUTATIONAL MODEL;675
8.3.1.4;4. CONCLUSIONS;679
8.3.1.5;5.
ACKNOWLEDGEMENT;679
8.3.1.6;6. REFERENCES;679
8.3.2;Chapter 64.
A study on the environment in an open court of high rise building with heliport;680
8.3.2.1;1. INTRODUCTION;680
8.3.2.2;2. OUTLINE OF SIMULATION;681
8.3.2.3;3. RESULTS;683
8.3.2.4;4. DISCUSSION;689
8.3.2.5;5. CONCLUSIONS;689
8.3.2.6;References;689
8.3.3;Chapter 65.
Modelling of flow and ventilation within petroleum process plants;690
8.3.3.1;1. INTRODUCTION;690
8.3.3.2;2. VENTILATION AND AREA CLASSIFICATION;691
8.3.3.3;3. GAS AND SMOKE DISPERSION;694
8.3.3.4;4. CONCLUSIONS;694
8.3.3.5;5. ACKNOWLEDGEMENTS;694
8.3.3.6;6. REFERENCES;695
8.3.4;Chapter 66. Simulation of diffusion phenomena under unstable conditions using a Lagrangian particle dispersion
model;696
8.3.4.1;1. INTRODUCTION;696
8.3.4.2;2. LAGRANGIAN PARTICLEDIS PERSION MODEL;697
8.3.4.3;3. WIND TUNNEL EXPERIMENT;698
8.3.4.4;4. CALCULATION RESULTS OF DIFFUSION;700
8.3.4.5;5. CONCLUSIONS;703
8.3.4.6;REFERENCES;703
8.3.5;Chapter 67.
Numerical and experimental simulation of vehicle exhaust gas dispersion for complex urban roadways and their surroundings;704
8.3.5.1;1. INTRODUCTION;704
8.3.5.2;2. NUMERICAL SIMULATION;704
8.3.5.3;3. EXPERIMENTAL SIMULATION;706
8.3.5.4;4. RESULTS OF NUMERICAL AND EXPERIMENTAL SIMULATION;707
8.3.5.5;5. CONCLUSION;710
8.3.5.6;References;710
8.3.6;Chapter 68. Simulation of Air Flow over a Heated Flat Plate Using Anisotropie k-e
Model;712
8.3.6.1;1. INTRODUCTION;712
8.3.6.2;2. WIND TUNNEL EXPERIMENT;713
8.3.6.3;3 . THE MODEL;714
8.3.6.4;4. RESULTS AND DISCUSSION;716
8.3.6.5;5 . CONCLUSIONS;719
8.3.6.6;References;719
8.3.7;Chapter 69.
Application of Reynolds-Stress Model to the Study of Heat Island Structure over a Slightly Inclined Terrain;720
8.3.7.1;1. INTRODUCTION;720
8.3.7.2;2. GOVERNING EQUATIONS AND MODEL DESCRIPTION;721
8.3.7.3;3. NUMERICAL PROCEDURE;723
8.3.7.4;4. RESULTS AND DISCUSSION;724
8.3.7.5;5. SUMMARY;726
8.3.7.6;Acknowledgement;726
8.3.8;Chapter 70.
Modeling of multisized particle laden turbulent low swirling free jets;728
8.3.8.1;1. INTRODUCTION;728
8.3.8.2;2. THE NUMERICAL MODEL;729
8.3.8.3;3. RESULTS AND DISCUSSION;730
8.3.8.4;4. CONCLUSIONS;734
8.3.8.5;ACKNOWLEDGEMENTS;734
8.3.8.6;REFERENCES;735
8.3.9;Chapter 71.
Simulation of wind-driven-rain around a building;736
8.3.9.1;1. INTRODUCTION;736
8.3.9.2;2. WIND-DRIVEN-RAIN;736
8.3.9.3;3. DISCUSSION;744
8.3.9.4;4. Acknowledgement;744
8.3.9.5;5. REFERENCES;744
8.3.10;Chapter 72.
A three-step Taylor-Galerkin finite element method for orographie rainfall;746
8.3.10.1;1. INTRODUCTION;746
8.3.10.2;2. BASIC EQUATION;746
8.3.10.3;3. THREE-STEP TAYLOR-GALERKIN METHOD;748
8.3.10.4;4. FINITE ELEMENT FORMULATION;750
8.3.10.5;5. NUMERICAL EXAMPLE;751
8.3.10.6;6. CONCLUSION;755
8.3.10.7;References;755
8.3.11;Chapter 73.
Three dimensional numerical simulation of snowdrift;756
8.3.11.1;1. INTRODUCTION;756
8.3.11.2;2. NUMERICAL SIMULATION MODEL;756
8.3.11.3;3. THE RESULTS OF SIMULATIONS;758
8.3.11.4;4. CONCLUSION;758
8.3.11.5;References;761
8.3.12;DISCUSSIONS OF ENVIRONMENTAL PROBLEMS;762
8.4;Section IV:
Pedestrian Wind;768
8.4.1;Chapter 74.
Numerical and experimental modelling of the three-dimensional turbulent wind flow through an urban square;770
8.4.1.1;1. INTRODUCTION;770
8.4.1.2;2. THE EXPERIMENTAL SITE;771
8.4.1.3;3. NUMERICAL SIMULATION;771
8.4.1.4;4. COMPARISON WITH WIND TUNNEL EXPERIMENT;774
8.4.1.5;5. CONCLUSION;778
8.4.1.6;6. ACKNOWLEDGEMENTS;778
8.4.1.7;7. REFERENCES;778
8.4.2;Chapter 75.
Numerical Simulation of Flowfield around Buildingsin an Urban Area;780
8.4.2.1;1. INTRODUCTION;780
8.4.2.2;2. NUMERICAL SIMULATION OF FLOWFIELD;780
8.4.2.3;3. BUILDING ANALYZED;782
8.4.2.4;4. RESULTS AND DISCUSSIONS;782
8.4.2.5;5. CONCLUSIONS;786
8.4.2.6;REFERENCES;786
8.4.3;Chapter 76.
Numerical Study on Relationship between Building Shape and Ground-Level Wind Velocity;788
8.4.3.1;1. INTRODUCTION;788
8.4.3.2;2. OUTLINE OF NUMERICAL ANALYSIS;789
8.4.3.3;3. RESULTS OF ANALYSIS AND DISCUSSION;790
8.4.3.4;4. APPLICATION TO ACTUAL BUILDING(Case 10, Fig. 6);793
8.4.3.5;5. CONCLUSIONS;793
8.4.3.6;References;793
8.4.4;DISCUSSIONS OF PEDESTRIAN WIND;794
8.5;Section V:
Vehicle Aerodynamics and Others;798
8.5.1;Chapter 77.
Numerical Analysis and Visualization of Flow in Automobile Aerodynamics Development;800
8.5.1.1;1. INTRODUCTION;800
8.5.1.2;2. DRAG4D SYSTEM;801
8.5.1.3;3. AERODYNAMIC DRAG FORCE;803
8.5.1.4;4. Engine Cooling;804
8.5.1.5;5. CONCLUSION;804
8.5.1.6;6. REFERENCES;805
8.5.2;Chapter 78.
Flow Structure around a 3D Bluff Body in Ground Proximity: A computational Study;806
8.5.2.1;ABSTRACT;806
8.5.2.2;I. INTRODUCTION;806
8.5.2.3;II, MATHEMATICAL FORMULATION;807
8.5.2.4;III. METHOD OF COMPUTATION;809
8.5.2.5;IV. RESULTS AND DISCUSSION;811
8.5.2.6;V. CONCLUDING REMARKS;812
8.5.2.7;ACKNOWLEDGEMENTS;812
8.5.2.8;REFERENCES;812
8.5.2.9;APPENDIX A;813
8.5.3;Chapter 79.
Finite element analysis of air flow around an Automatic Guided Vehicle;816
8.5.3.1;1. INTRODUCTION;816
8.5.3.2;2. A MATHEMATICAL MODEL;816
8.5.3.3;3. NUMERICAL METHOD;818
8.5.3.4;4. RESULTS;820
8.5.3.5;5. CONCLUDING REMARKS;820
8.5.3.6;References;825
8.5.4;CHAPTER 80. UNSTEADY AERODYNAMICS AND WAKE OF THE SAVONIUS WIND TURBINE : A NUMERICAL STUDY;826
8.5.4.1;1. INTRODUCTION;826
8.5.4.2;2. APPROACH TO THE PROBLEM;826
8.5.4.3;3. TYPICAL RESULTS AND DISCUSSION;827
8.5.4.4;4. CONCLUDING REMARKS;829
8.5.4.5;5. ACKNOWLEDGMENT;829
8.5.4.6;6. REFERENCES;829
8.5.5;DISCUSSIONS OF VEHICLE AERODYNAMICS AND OTHERS;832
8.6;Section VI: Computer Aided Experiments and Computer Graphics;834
8.6.1;Chapter 81. Turbulence measurement in a separated and reattaching flow
over a backward-facing step with the aid of three-dimensional particle tracking velocimetry;836
8.6.1.1;1. INTRODUCTION;837
8.6.1.2;2. EXPERIMENTAL APPARATUS AND PROCEDURE;837
8.6.1.3;3. EXPERIMENTAL RESULTS;839
8.6.1.4;4. CONCLUSIONS;843
8.6.1.5;REFERENCES;843
8.6.2;Chapter 82. Study on three-dimensional characteristics of natural ventilation in halfenclosed
buildings using video imaging techniques;846
8.6.2.1;1. INTRODUCTION;846
8.6.2.2;2. OUTLINE OF EXPERIMENTS;847
8.6.2.3;3. RESULTS AND DISCUSSIONS;848
8.6.2.4;4. CONCLUSION;851
8.6.2.5;Acknowledgment;851
8.6.2.6;References;851
8.6.3;Chapter 83. A Computer–Controlled Wind
Tunnel;852
8.6.3.1;1. INTRODUCTION;852
8.6.3.2;2. EXPERIMENTAL WIND TUNNELS;853
8.6.3.3;3. CONTROL VARIABLES OF FANS;853
8.6.3.4;4. MEAN WIND VELOCITY PROFILES AND TURBULENCE INTENSITIES;855
8.6.3.5;5. CONTROL OF TURBULENCE INTENSITY;857
8.6.3.6;6. CONTROL OF INTEGRAL LENGTH SCALE OF TURBULENCE;859
8.6.3.7;7. CONCLUSIONS;861
8.6.3.8;REFERENCES;861
8.6.4;Chapter 84. Computer Animation for Incompressible Viscous Flow Problems by
Using Graphic Engineering Work Station;862
8.6.4.1;ABSTRACT;862
8.6.4.2;1. INTRODUCTION;862
8.6.4.3;2. ANIMATION SYSTEM;863
8.6.4.4;3. DISPLAY EXAMPLES;864
8.6.4.5;4. CONCLUSIONS;867
8.6.4.6;References;867
8.6.5;Chapter 85. WC & LEONARDO as interactive visualization
systems for Computer Fluid Mechanics;868
8.6.5.1;1. OBJECTIVE OF THE WORK;868
8.6.5.2;2. ADVANCED SYSTEM FEATURES IN AN INTERACTIVE USER ENVIRONMENT;868
8.6.5.3;3. PECULIARITIES OF DATA REPRESENTATIONS;869
8.6.5.4;4. PRINTOUT;871
8.6.5.5;5. CONCLUSIONS;871
8.6.5.6;REFERENCES;871
8.6.6;DISCUSSIONS OF COMPUTER AIDED EXPERIMENTS AND COMPUTER GRAPHICS;872
9;Part III: WORKSHOP: Prospects for
Numerical Analysis of Interaction between Fluid Flow and Structural Vibration;876
9.1;Chapter 86.
Prospects for Numerical Analysis of Interaction between Fluid Flow and Structural Vibration;878
9.1.1;1. INTRODUCTION;878
9.1.2;2. SUMMARIES OF WORKSHOP PRESENTATIONS;878
9.1.3;3. CWE IN STRUCTURAL DESIGN;879
9.1.4;4. ACCURACY AND RELIABILITY OF THE NUMERICAL SOLUTIONS;880
9.1.5;5. THE ROLE OF EXPERIMENT AND WIND TUNNEL TESTING IN CWE;881
9.1.6;6. LIST OF WORKSHOP PARTICIPANTS;881
9.2;CHAPTER 87.
FOR THE ADVANCE OF THE COMPUTATIONAL STRUCTURAL AEROELASTICITY;884
9.2.1;1. INTRODUCTION;884
9.2.2;2. BASIC PROBLEMS FOR THE DISCUSSION OF STRUCTURAL AEROELASTICITY;885
9.2.3;3. EXPECTATIONS AND PROBLEMS FOR THE COMPUTATIONAL APPROACH;887
9.2.4;4. CONCLUSION;887
9.2.5;Reference;887
9.3;Chapter 88.
Survey for the Aeroelasticity of Structures;888
9.3.1;1. CLASSIFICATION;888
9.3.2;2. MECHANISM OF BLUFF BODY AERODYNAMICS;888
9.3.3;3. RECENT TOPICS;889
9.3.4;4. WHAT IS REQUIRED OF CWE ?;891
9.4;Chapter 89. A Computational Fluid Dynamicist's View of
CWE;894
9.4.1;1. NUMERICAL ERRORS;894
9.4.2;2. DATA NEEDS;894
9.4.3;3. PROSPECTS FOR LARGE EDDY SIMULATION;895
9.4.4;4. REFERENCES;895
9.5;Chapter 90.
Brief Review: Numerical Analysis of the Flow around Vibrating Cylinders;896
9.5.1;REFERENCES;899
9.6;Chapter 91.
Numerical Simulations of Aerodynamic Instability of Bluff Body by the Discrete Vortex Method;900
9.6.1;1. INTRODUCTION;900
9.6.2;2. METHODS AND RESULTS;900
9.6.3;3. CONCLUDING REMARKS;901
9.6.4;References;901
9.7;Chapter 92.
Current Research by the FDM;908
9.7.1;1. OBJECTIVES;908
9.7.2;2. PROBLEM FORMULATION;908
9.7.3;3. DEFINITIONS;908
9.7.4;4. NUMERICAL EXAMPLES;909
9.7.5;REFERENCES;909
9.8;Chapter 93.
Current researches by FEM;912
9.8.1;1. INTRODUCTION;912
9.8.2;2. NUMERICAL EXAMPLES;912
9.8.3;3. COMPUTATIONAL TECHNIQUES;913
9.9;Chapter 94.
A contribution to the workshop on computational wind engineering;914
9.9.1;INTRODUCTION;914
9.9.2;BUILDINGS;914
9.9.3;BRIDGES;915
9.9.4;OTHER STRUCTURES;915
9.9.5;OTHER RELATED PROBLEMS;915
9.9.6;MAJOR FACTORS IN PRACTICAL APPLICATIONS OF CWE;916
9.9.7;CONCLUSIONS;916
10;Part IV: SUMMARY OF VIDEO PRESENTATION;918
10.1;1 Video Presentation Report;920
10.2;2 Program;921
11;Author Index Volume
46–47 (1993);924

Leseproben

On the Simulation of Turbulent Flow Past Bluff Bodies

W. RODI,     Institute for Hydromechanics, University of Karlsruhe, D-7500 Karlsruhe, Germany

ABSTRACT

The paper reviews calculations performed to-date of vortex-shedding flow past long cylinders at high Reynolds numbers where the effect of stochastic turbulent fluctuations superimposed on the 2D periodic shedding motion needs to be simulated. The experiences gathered with various statistical turbulence models ranging from algebraic eddy-visocity models to Reynolds-stress-equation models are summarised and discussed, and calculations of vortex-shedding flow past cylinders of various cross-sections are presented. These calculations are confronted with large-eddy simulations whenever possible, and a comparative discussion on the various calculation methods is given.

1 INTRODUCTION

The flow past slender, bluff bodies is frequently associated with periodic vortex shedding causing dynamic loading on the bodies. Methods for calculating the unsteady flow and the dynamic loading are of great practical importance. In this paper, only vortex-shedding flow past long cylinders is considered which is two-dimensional in the mean. At low Reynolds numbers the flow is a laminar, 2D periodic motion which can be calculated fairly well with present-day numerical methods (e. g. [1, 2]). At higher Reynolds numbers, which usually occur in practice, stochastic three-dimensional turbulent fluctuations are superimposed on the 2D periodic vortex-shedding motion. This is illustrated in Fig. 1, where f is the instantaneous value of a quantity, is the time-mean value, the periodic fluctuation, f? the stochastic turbulent flucuation and

Fig 1 Periodic and stochastic fluctuations in vortex shedding flow

A method that can be applied to situations at high Reynolds numbers is the large-eddy simulation (LES) which resolves only the larger-scale motion. The effect of the small-scale motion that cannot be resolved on a given grid needs to be modelled. This effect is mainly dissipative, i. e. energy is withdrawn from the part of the spectrum that can be resolved. The effect can be achieved in two ways: The usual one is through a subgrid-scale model for determining turbulent stresses introduced by the subgrid-scale fluctuations; the other possibility is to leave the energy withdrawal to numerical damping by a numerical scheme that introduces a certain amount of numerical dissipation. The LES method is potentially very powerful, but LES calculations are very costly and hence there is interest in more economic calculation methods. Attempts were therefore made to simulate turbulence in vortex-shedding flows with statistical models which do not resolve any of the stochastic turbulent motion but average it out altogether. For the flows considered in this paper, only 2D equations need to be solved, which are the ensemble-averaged Navier-Stokes equations containing Reynolds stresses due to the averaging procedure. These stresses, which also undergo periodic variations, need to be determined by a statistical turbulence model. So far, turbulence models developed and tested extensively for steady flows were taken over and adapted for use in vortex-shedding calculations. The adaptation involves relating the Reynolds stresses to ensemble-averaged velocities and the addition of time-dependent terms in transport equations for turbulence parameters.

When the periodic fluctuations are also averaged out, equations describing the time-mean flow are obtained. In these, in addition to the Reynolds stresses, correlations involving the periodic fluctuations appear which then also need to be modelled. As it is difficult to arrive at a general model for these correlations and since no information on the dynamic loading results from steady calculations, this approach is of limited interest and is not discussed further here. The paper reviews the experience gained so far with turbulence models for vortex-shedding calculations of flows around cylinders of various cross-sections and confronts these with the few LES calculations available.

2 STATISTICAL TURBULENCE MODELS EMPLOYED

Statistical turbulence models have the task of determining the Reynolds stresses appearing in the ensemble-averaged Navier-Stokes equations. In this section, the turbulence models are introduced briefly which have been used in the vortex-shedding calculations reported in the next section.

Eddy-viscosity models.

In simpler models, the Reynolds stresses are related to the gradients of the ensemble-averaged velocities

(1)

The variation of the eddy viscosity

A conceptually more general model is the k-e model which relates the eddy viscosity

Franke et al. [5] evaluated Cantwell and Coles' [6] data for vortex-shedding flow past a circular cylinder and found that substantial regions exist where the eddy viscosity is negative and hence the eddy-viscosity concept is invalid. These regions correspond to flow areas where history and transport effects of turbulence quantities are dominant. These processes are poorly (if at all) described by eddy-viscosity modelsand hence these models must be expected to show poor performance for vortex-shedding flows.

Reynolds-stress-equation models and derivatives.

Reynolds-stress-equation (RSE) models account for history and transport effects by solving model transport equations for the individual Reynolds stresses . Again straightforward extensions of steady models are employed. Franke and Rodi [7] adopted the standard RSE model of Launder, Reece and Rodi [8], with wall corrections to the pressure-strain terms due to Gibson and Launder [9]. Jansson [10] used an algebraic stress model (ASM) in which the differential stress equations were simplified to algebraic equations by model assumptions about the convection and diffusion terms. The assumption of Rodi [11] is adopted in which history and transport terms in the

Near-wall treatment.

With the various turbulence models, different approaches were tested for handling the near-wall region. One approach adopted was the use of wall functions in which the viscous sublayer is not resolved but the first grid point is located outside this layer. Basically, the quantities at this grid point are related to the friction velocity based on the assumption of a logarithmic velocity distribution and of local equilibrium of turbulence (production = dissipation). Deng et al. [3] employed the low-Reynolds-number version of the k-e model due to Nagano and Tagawa [12] very near...