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.
Front Cover 1
Computational Wind Engineering 1 4
Copyright Page 5
Table of Contents 10
Preface 6
Symposium organization 8
PART I:
16
Section I: Turbulence Modelling and their
16
Chapter 1.
18
ABSTRACT 18
1. INTRODUCTION 18
2. STATISTICAL TURBULENCE MODELS EMPLOYED 19
3. LES MODELS TESTED 20
4. CALCULATION EXAMPLES 22
5. CONCLUSIONS 32
6. ACKNOWLEDGEMENTS 32
REFERENCES 33
CHAPTER 2. COMPARISON OF VARIOUS TURBULENCE
36
Abstract 36
1. INTRODUCTION 36
2. CHARACTERISTICS OF FLOWFIELD AROUND A BLUFF BODY 37
3. COMPARISON OF MEAN VELOCITY VECTOR FIELD 38
4. DISCREPANCY IN SURFACE PRESSURE DISTRIBUTION 39
5. COMPARISON OF k-e
39
6. COMPARISON OF ASM AND LES modelling of convection and diffusion terms
7. IMPROVEMENT OF LES new SGS model with
44
8. COMPARISON OF DIFFERENT TURBULENCE MODELS FOR VARIOUS FLOWFIELDS 45
9. CONCLUSION 46
ACKNOWLEDGEMENTS 47
NOMENCLATURE 47
REFERENCES 50
Chapter 3.
52
1. CFD - THE CHALLENGE POSED BY PRACTICAL FLOWS 52
2. CFD - SOME IMPORTANT ISSUES 56
3. CURRENT CAPABILITIES AND LIMITATIONS 59
4. CURRENT DIRECTIONS IN TURBULENCE MODELLING 62
5. CONCLUDING REMARKS 63
REFERENCES 65
CHAPTER
68
1. INTRODUCTION 68
2. TRANSPORT EFFECTS IN COMPLEX GEOMETRIES :
69
3. SECOND MOMENT CLOSURES 71
4. CONCLUDING REMARKS 81
References 82
Chapter 5. Subgrid–scale
84
1. INTRODUCTION 84
2. FUNDAMENTAL EQUATIONS 85
3. RESULTS OF A TWO-SCALE DIA 85
4. SGS MODELS 87
5. DISCUSSIONS 90
6. CONCLUDING REMARKS 91
Acknowledgments 91
References 91
Chapter 6. Estimation of anisotropic k-e model on the Backward-facing Step
92
1. INTRODUCTION 92
2. TURBULENCE MODELS AND NUMERICAL METHOD 93
3. RESULTS AND DISCUSSIONS 94
4. A PRIORI TEST FOR REYNOLDS STRESS 97
5. FINAL REMARKS 99
REFERENCES 99
Chapter 7. Numerical prediction of separating and reattaching
100
1. INTRODUCTION 100
2. GOVERNING EQUATIONS AND MODIFIED LOW-REYNOLDS-NUMBER
101
3. NUMERICAL PROCEDURE AND BOUNDARY CONDITIONS 103
4. DISCUSSION OF THE PRESENT MODEL 103
5. RESULTS AND DISCUSSION 105
6. CONCLUSIONS 108
REFERENCES 108
Chapter 8.
110
1. INTRODUCTION 110
2. MATHEMATICAL FORMULATION 111
3. RESULTS AND DISCUSION 114
4. CONCLUDING REMARKS 115
5. ACKNOWLEDGMENT 115
6. REFERENCES 115
Chapter 9.
120
1. INTRODUCTION 120
2. MATHEMATICAL MODELS 121
3. NUMERICAL IMPLEMENTATION 123
4. RESULTS AND DISCUSSION 123
5. CONCLUSION 129
REFERENCES 129
Chapter 10. Numerical Analysis of Wind around Building Using High-Speed GSMAC-FEM
130
1. INTRODUCTION 130
2. BASIC EQUATIONS 131
3. VALIDATION OF DIFFERENTIAL STRESS MODEL 134
4. APPLICATION 135
5. CONCLUSIONS 135
REFERENCES 135
Chapter 11.
136
1. INTRODUCTION 136
2. GOVERNING EQUATIONS AND NUMERICAL METHOD 137
3. RESULTS 138
4. CONCLUSIONS 142
References 142
Chapter 12.
144
1. INTRODUCTION 144
2. NUMERICAL SIMULATION 144
3. RESULTS AND DISCUSSION 145
4 CONCLUSIONS 149
5 ACKNOWLEDGMENTS 149
6 REFERENCES 149
Chapter 13.
150
1. INTRODUCTION 150
2. PHYSICAL MODEL 151
3. COMPUTATIONAL MODEL 152
4. CONCLUSIONS 158
5. ACKNOWLEDGEMENTS 158
6. References 158
Chapter 14. Appropriate boundary conditions for computational wind engineering models using the
160
1. INTRODUCTION 160
2. A HOMOGENEOUS
161
3. ATMOSPHERIC SURFACE LAYER MEASUREMENTS AT SILSOE 162
4. APPROPRIATE BOUNDARY CONDITIONS 166
5. CONCLUSIONS 167
6. REFERENCES 168
Chapter 15.
170
1. INTRODUCTION 170
2. THE CONDITIONAL REYNOLDS-STRESS TRANSPORT EQUATIONS 171
4. EXPERIMENTAL DATA 175
5. CONCLUSIONS 178
6. REFERENCES 179
Chapter 16.
180
1. INTRODUCTION 180
2. WIND TUNNEL EXPERIMENT 180
3. NUMERICAL CALCULATIONS 182
4. OPTIMIZATION OF ROUGHNESS PARAMETERS 184
5. CONCLUSION 186
Acknowledgments 186
References 186
Chapter 17.
188
1. INTRODUCTION 188
2. AVERAGING PROCEDURE 188
3. AVERADING PROCEDURE FOR CONSTITUTIVE EQUATIONS 190
4. FORMATION OF REYNOLDS STRESS EQUATION MODEL 192
5. RESULTS 194
6. SUMMERY AND CONCLUSIONS 194
ACKNOWLEDGEMENTS 194
REFERENCES 195
DISCUSSIONS OF TURBULENCE MODELLING AND THEIR APPLICATIONS 198
Section II:
208
Chapter 18.
210
1. INTRODUCTION 210
2. THREE-DIMENSIONAL UNSTEADY SIMULATIONS OF TURBULENT FLOW 211
3. RECENT DEVELOPMENTS IN LARGE EDDY SIMULATION 215
4. APPLICATIONS TO FLOWS OVER BLUFF BODIES 219
5. SOME RECENT LES RESULTS FOR BLUFF BODIES 221
6. BOOTSTRAPPING 222
7. CONCLUSIONS AND PROSPECTS 226
8. ACKNOWLEDGEMENTS 226
9. REFERENCES 226
Chapter 19.
228
1. BASIC EQUATIONS AND DISCRETISATION 228
2. TIME INTEGRATION AND SUBGRID SCALE MODELLING 229
3. RESULTS 229
4. REFERENCES 230
Chapter 20.
234
1. INTRODUCTION 234
2. GOVERNING EQUATIONS 235
3. MODEL VALIDATION 236
4. TALL BUILDING CASE 238
5. CONCLUSIONS 241
ACKNOWLEDGEMENTS 243
REFERENCES 243
Chapter 21.
244
1. INTRODUCTION 244
2. MODEL 245
3. EXPERIMENTAL DESIGN 245
4. RESULTS 247
5. CONCLUSIONS 248
6. ACKNOWLEDGMENTS 252
7. REFERENCES 252
Chapter 22.
254
1 Introduction 254
2 Outline of LES 254
3 Results of Numerical Analyses 255
4 Conclusion 256
References 256
Chapter 23.
260
1. INTRODUCTION 260
2. GOVERNING EQUATIONS 261
3. COORDINATE TRANSFORMATION 262
4. COMMENTS ON NUMERICAL SIMULATION 263
5. RESULTS AND DISCUSSION 264
6. ACKNOWLEDGEMENT 267
7. REFERENCES 269
Chapter 24.
270
1. INTRODUCTION 270
2. FORMULATION 271
3. RESULTS 274
4. CONCLUSIONS 278
5. REFERENCES 279
Chapter 25.
280
1. INTRODUCTION 280
2. GOVERNING EQUATIONS 281
3. OUTFLOW BOUNDARY TREATMENT 282
4. NUMERICAL METHODS 284
5. COMPUTATIONAL RESULTS 286
6. CONCLUDING REMARKS 288
ACKNOWLEDGEMENTS 289
REFERENCES 289
Chapter 26. Numerical analysis of flows
290
1.INTRODUCTION 290
2.GOVERNING EQUATION 291
3.NUMERICAL SCHEME 291
4.RESULTS AND DISCUSSION 292
5.CONCLUSIONS 295
6.REFERENCES 295
Chapter 27. A numerical study of nonlinear waves excited by an
298
1.INTRODUCTION 298
2. GOVERNING EQUATIONS AND THE NUMERICAL METHOD 299
3.RESULTS AND DISCUSSIONS 301
REFERENCES 301
DISCUSSIONS OF DIRECT AND LARGE EDDY SIMULATIONS 304
Section III: Numerical Methods 310
Chapter 28.
312
1. INTRODUCTION 312
2. ISSUES IN THE DEVELOPMENT OF WIND ENGINEERING SIMULATION TOOLS 313
3. CONCLUSIONS 318
4. REFERENCES 319
Chapter 29.
330
1. INTRODUCTION 330
2. VISCOUS VORTEX METHOD 331
References 337
Chapter 30. Volume–fraction techniques: powerful
342
1. INTRODUCTION: OVERVIEW OF FAVOR CONCEPT 342
2. A SIMPLE EXAMPLE AND ITS IMPLICATIONS 344
3. MAKING THE CONCEPT A PRACTICAL TOOL 346
4. ORDINARY AND NOVEL USES OF THE FAVOR METHOD 347
5. ACKNOWLEDGEMENTS 349
REFERENCES 350
Chapter 31. Numerical Simulation of High Reynolds Number Flows
354
1. INTRODUCTION 354
2. STATEMENT OF PROBLEMS 354
3. PETROV-GALERKIN FORMULATION USING EXPONENTIAL FUNCTIONS 355
4. NUMERICAL EXAMPLES 357
5. CONCLUSIONS 361
REFERENCES 361
Chapter 32.
364
1. INTRODUCTION 364
2. INCOMPRESSIBLE NAVIER-STOKES EQUATIONS 365
3. THIRD-ORDER ACCURATE UPWIND SCHEME 365
4. FINITE ELEMENT SCHEME 367
5. NUMERICAL EXAMPLES 368
6. CONCLUSIONS 370
REFERENCES 370
Chapter 33.
372
1. INTRODUCTION 372
2. RECURSIVE SUBDIVISION 373
3. MESH CONVERSION 374
4. CONCLUSION 377
5. REFERENCES 377
Chapter 34.
378
1. INTRODUCTION 378
2. MATHEMATICAL MODEL 379
3. RESULTS 383
4. CONCLUSIONS 384
5. REFERENCES 384
Chapter 35.
386
1. INTRODUCTION 386
2. FORMULATION AND NUMERICAL PROCEDURE 386
3. RESULT 388
4. CONCLUSION 389
REFERENCES 389
Chapter 36. Solution Method of the Time Transient Moving Boundary Problems
396
1. Introduction 396
2. Basic Idea of the moving obstacle
397
3. FAVORITE formulation including thin plate 398
4.
401
Acknowledgement 401
References 401
5. Result of sample calculations 402
Chapter 37.
408
1. INTRODUCTION 408
2. FLOW SIMULATION 409
3. MASSIVE PARALLEL COMPUTER USED 410
4. PARALLELIZATION OF ALGORITHM 411
5. CASES ANALYZED 411
6. RESULTS 412
7.
415
ACKNOWLEDGEMENTS 415
REFERENCES 415
DISCUSSIONS OF NUMERICAL METHODS 416
PART II: APPLICATIONS 422
Section I: Wind Load 422
Chapter 38.
424
1. COMPUTATIONAL ASPECTS OF WIND LOADING MODELLING 424
2. SOME BREAKTHROUGHS 425
3. GENERALIZATION OF RESPONSE USING INFLUENCE SURFACES 426
4. SIMPLIFICATION THROUGH ORTHONORMAL FUNCTIONS 428
5. INFLUENCE OF WIND DIRECTION AND UNCERTAINTIES 429
6. COMPUTATIONAL OPPORTUNITIES IN WIND LOADING AND SOME CONCLUSIONS 430
Chapter 39.
434
1. INTRODUCTION 434
2. NUMERICAL APPROACH 435
3. BOUNDARY CONDITIONS 437
4. RESULTS AND DISCUSSION 438
5. CONCLUSIONS 443
6. REFERENCES 444
Chapter 40.
446
1. FORMULAE FOR R.M.S. PRESSURES IN HOMOGENEOUS ISOTROPIC TURBULENCE 446
2. FORMULAE FOR R.M.S. PRESSURES IN GENERAL FLOWS 447
3. THE TEXAS TECH EXPERIMENTAL DATA 448
4. RELATIONSHIPS BETWEEN C'p AND Cp 448
5. CONCLUSIONS 451
6. REFERENCES 451
Chapter 41.
454
1. INTRODUCTION 454
2. FULL-SCALE MEASUREMENTS 454
3. WIND-TUNNEL MEASUREMENTS 455
4. COMPUTATIONAL SOLUTIONS 455
6. CONCLUSIONS 461
7. ACKNOWLEDGEMENT 462
8. REFERENCES 462
Chapter 42.
464
1. INTRODUCTION 464
2. COMPUTER MODELLING 464
3. RESULTS AND DISCUSSIONS 466
4. CONCLUSIONS 468
5. ACKNOWLEDGEMENTS 469
6. REFERENCES 469
Chapter 43.
470
1. INTRODUCTION 470
2. OUTLINE OF FIELD MEASUREMENT OF THE TEXAS TECH BUILDING 470
3. RESULTS AND DISCUSSION 471
4. CONCLUSION 473
Acknowledgement 473
References 475
Chapter 44. Large eddy simulation of wind flow around dome
476
1. BASIC EQUATIONS 476
2. FINITE ELEMENT FORMULATION 477
3. INDUCING THE FLOW WITH TURBULENCE 478
4. WIND FLOW AROUND A CYLINDRICAL DOME ROOF 480
5. CONCLUDING REMARKS 485
REFERENCES 485
Chapter 45.
486
1. TOPOGRAPHIC MULTIPLIERS 486
2. RIDGE GEOMETRIES 487
3. COMPUTER MODELLING 487
4. RESULTS 488
5. CONCLUSIONS 491
6. REFERENCES 491
Chapter 46.
492
1. INTRODUCTION 492
2. FORMULATION FOR ANALYSIS 493
Chapter 47. Computing the statistical stability of integral length scale measurements by autoregressive
502
1. INTRODUCTION 502
2. BASIC ASSUMPTIONS AND DEFINITIONS 502
3. ESTIMATION OF MEAN, VARIANCE AND INTEGRAL TIME SCALE 503
4. AUTOREGRESSIVE SIMULATION 507
5. EXPERIMENTAL RESULTS 508
6. CONCLUSIONS 510
References 511
Chapter 48.
512
1. INTRODUCTION 512
2. SPECIFICATIONS OF A BUILDING 513
3. SIMULATION OF THE FLUCTUATING WIND FORCES 514
4. WIND RESPONSE ANALYSES IN TIME DOMAIN 517
5. CONCLUSION 517
References 521
Chapter 49.
522
1. INTRODUCTION 522
2. WIND TUNNEL EXPERIMENTS 523
3. EXPERIMENTAL RESULTS AND FORMULATION 523
4. CONCLUSION 530
5. ACKNOWLEDGEMENT 530
6. REFERENCES 531
CHAPTER 50. NUMERICAL SIMULATION OF PRESSURE DISTRIBUTIONS UNDERNEATH ROOFING PAVER SYSTEMS 532
1. INTRODUCTION 532
2. PHYSICAL ASSUMPTIONS 532
3. MATHEMATICAL EQUATIONS 533
4. COMPARISONS OF NUMERICAL AND EXPERIMENTAL RESULTS AND DISCUSSIONS 539
5. REFERENCES 541
DISCUSSIONS OF WIND LOAD 542
Section II:
554
Chapter 51.
556
1. INTRODUCTION 556
2. OUTLINE OF COMPUTATIONAL METHODS 557
3. COMPUTATIONAL RESULTS 557
4. CONCLUSIONS 565
References 565
Chapter 52.
566
1. INTRODUCTION 566
2. OUTLINE OF NUMERICAL SIMULATIONS 567
3. RESULTS AND DISCUSSIONS 568
4. CONCLUSION 571
Acknowledgements 571
References 571
Chapter 53.
572
1. INTRODUCTION 572
2. PROBLEM FORMULATION 573
3. COMPUTATIONAL MODEL 573
4. THREE-DIMENSIONAL SIMULATIONS FOR A RECTANGULAR CYLINDER 574
5. AEROELASTIC BEHAVIOR OF BLUFF CYLINDERS 576
6. CONCLUSION 581
REFERENCES 581
Chapter 54.
582
1 INTRODUCTION 582
2 PROBLEM FORMULATION 582
3 RESULTS 584
4 CONCLUSION 586
5 ACKNOWLEDGEMENT 586
References 586
Chapter 55.
592
1. INTRODUCTION 592
2. METHODOLOGY OF NUMERICAL ANALYSIS 592
3. NUMERICAL RESULTS 594
4. CONCLUSION 600
References 600
Chapter 56.
602
1. INTRODUCTION 602
2. COMPUTATIONAL METHOD 603
3. VORTEX-INDUCED OSCILLATIONS OF A CIRCULAR CYLINDER 605
4. CONCLUDING REMARK 608
References 609
Chapter 57.
610
1.INTRODUCTION 610
2.ALGORITHM 611
3. FLOW AROUND A RIGID RECTANGULAR CYLINDER 613
4.FLOW AROUND A FLEXIBLE STRUCTURE 615
5.CONCLUDING REMARKS 619
ACKNOWLEDGEMENTS 619
REFERENCES 619
Chapter 58.
620
1.
620
2. METHOD OF SIMULATION 621
3. DISCUSSION OF RESULTS 621
4. CONCLUSION 625
REFERENCES 625
Chapter 59.
626
1. INTRODUCTION 626
2. METHOD 626
3. RESULTS AND DISCUSSION 630
4. CONCLUSION 633
References 633
Chapter 60.
634
1. INTRODUCTION 634
2. METHOD 634
3. DVM APPLICATION FOR BLUFF BODY AERODYNAMICS 637
4. DVM IMPLEMENTATION AT COLORADO STATE UNIVERSITY 638
5.
639
6. CONCLUDING REMARKS 642
REFERENCES 642
Chapter 61.
644
1. INTRODUCTION 644
2. COMPUTATIONAL METHOD 645
3. WIND TUNNEL APPARATUS 646
4. DISCUSSIONS 646
5. CONCLUSION 651
Acknowledgements 651
References 651
Chapter 62.
654
1.INTRODUCTION 654
2. MATHEMATICAL MODEL OF THE SYSTEM CABLE-FLUID ACTIONS 657
3. SOME ANALYTICAL RESULTS AND CONCLUSIONS 659
REFERENCES 663
DISCUSSIONS OF WIND INDUCED VIBRATIONS 664
Section III:
670
Chapter 63.
672
1. INTRODUCTION 672
2. PHYSICAL MODEL 673
3. COMPUTATIONAL MODEL 675
4. CONCLUSIONS 679
5.
679
6. REFERENCES 679
Chapter 64.
680
1. INTRODUCTION 680
2. OUTLINE OF SIMULATION 681
3. RESULTS 683
4. DISCUSSION 689
5. CONCLUSIONS 689
References 689
Chapter 65.
690
1. INTRODUCTION 690
2. VENTILATION AND AREA CLASSIFICATION 691
3. GAS AND SMOKE DISPERSION 694
4. CONCLUSIONS 694
5. ACKNOWLEDGEMENTS 694
6. REFERENCES 695
Chapter 66. Simulation of diffusion phenomena under unstable conditions using a Lagrangian particle dispersion
696
1. INTRODUCTION 696
2. LAGRANGIAN PARTICLEDIS PERSION MODEL 697
3. WIND TUNNEL EXPERIMENT 698
4. CALCULATION RESULTS OF DIFFUSION 700
5. CONCLUSIONS 703
REFERENCES 703
Chapter 67.
704
1. INTRODUCTION 704
2. NUMERICAL SIMULATION 704
3. EXPERIMENTAL SIMULATION 706
4. RESULTS OF NUMERICAL AND EXPERIMENTAL SIMULATION 707
5. CONCLUSION 710
References 710
Chapter 68. Simulation of Air Flow over a Heated Flat Plate Using Anisotropie k-e
712
1. INTRODUCTION 712
2. WIND TUNNEL EXPERIMENT 713
3 . THE MODEL 714
4. RESULTS AND DISCUSSION 716
5 . CONCLUSIONS 719
References 719
Chapter 69.
720
1. INTRODUCTION 720
2. GOVERNING EQUATIONS AND MODEL DESCRIPTION 721
3. NUMERICAL PROCEDURE 723
4. RESULTS AND DISCUSSION 724
5. SUMMARY 726
Acknowledgement 726
Chapter 70.
728
1. INTRODUCTION 728
2. THE NUMERICAL MODEL 729
3. RESULTS AND DISCUSSION 730
4. CONCLUSIONS 734
ACKNOWLEDGEMENTS 734
REFERENCES 735
Chapter 71.
736
1. INTRODUCTION 736
2. WIND-DRIVEN-RAIN 736
3. DISCUSSION 744
4. Acknowledgement 744
5. REFERENCES 744
Chapter 72.
746
1. INTRODUCTION 746
2. BASIC EQUATION 746
3. THREE-STEP TAYLOR-GALERKIN METHOD 748
4. FINITE ELEMENT FORMULATION 750
5. NUMERICAL EXAMPLE 751
6. CONCLUSION 755
References 755
Chapter 73.
756
1. INTRODUCTION 756
2. NUMERICAL SIMULATION MODEL 756
3. THE RESULTS OF SIMULATIONS 758
4. CONCLUSION 758
References 761
DISCUSSIONS OF ENVIRONMENTAL PROBLEMS 762
Section IV:
768
Chapter 74.
770
1. INTRODUCTION 770
2. THE EXPERIMENTAL SITE 771
3. NUMERICAL SIMULATION 771
4. COMPARISON WITH WIND TUNNEL EXPERIMENT 774
5. CONCLUSION 778
6. ACKNOWLEDGEMENTS 778
7. REFERENCES 778
Chapter 75.
780
1. INTRODUCTION 780
2. NUMERICAL SIMULATION OF FLOWFIELD 780
3. BUILDING ANALYZED 782
4. RESULTS AND DISCUSSIONS 782
5. CONCLUSIONS 786
REFERENCES 786
Chapter 76.
788
1. INTRODUCTION 788
2. OUTLINE OF NUMERICAL ANALYSIS 789
3. RESULTS OF ANALYSIS AND DISCUSSION 790
4. APPLICATION TO ACTUAL BUILDING(Case 10, Fig. 6) 793
5. CONCLUSIONS 793
References 793
DISCUSSIONS OF PEDESTRIAN WIND 794
Section V:
798
Chapter 77.
800
1. INTRODUCTION 800
2. DRAG4D SYSTEM 801
3. AERODYNAMIC DRAG FORCE 803
4. Engine Cooling 804
5. CONCLUSION 804
6. REFERENCES 805
Chapter 78.
806
ABSTRACT 806
I. INTRODUCTION 806
II, MATHEMATICAL FORMULATION 807
III. METHOD OF COMPUTATION 809
IV. RESULTS AND DISCUSSION 811
V. CONCLUDING REMARKS 812
ACKNOWLEDGEMENTS 812
REFERENCES 812
APPENDIX A 813
Chapter 79.
816
1. INTRODUCTION 816
2. A MATHEMATICAL MODEL 816
3. NUMERICAL METHOD 818
4. RESULTS 820
5. CONCLUDING REMARKS 820
References 825
CHAPTER 80. UNSTEADY AERODYNAMICS AND WAKE OF THE SAVONIUS WIND TURBINE : A NUMERICAL STUDY 826
1. INTRODUCTION 826
2. APPROACH TO THE PROBLEM 826
3. TYPICAL RESULTS AND DISCUSSION 827
4. CONCLUDING REMARKS 829
5. ACKNOWLEDGMENT 829
6. REFERENCES 829
DISCUSSIONS OF VEHICLE AERODYNAMICS AND OTHERS 832
Section VI: Computer Aided Experiments and Computer Graphics 834
Chapter 81. Turbulence measurement in a separated and reattaching flow
836
1. INTRODUCTION 837
2. EXPERIMENTAL APPARATUS AND PROCEDURE 837
3. EXPERIMENTAL RESULTS 839
4. CONCLUSIONS 843
REFERENCES 843
Chapter 82. Study on three-dimensional characteristics of natural ventilation in halfenclosed
846
1. INTRODUCTION 846
2. OUTLINE OF EXPERIMENTS 847
3. RESULTS AND DISCUSSIONS 848
4. CONCLUSION 851
Acknowledgment 851
References 851
Chapter 83. A Computer–Controlled Wind
852
1. INTRODUCTION 852
2. EXPERIMENTAL WIND TUNNELS 853
3. CONTROL VARIABLES OF FANS 853
4. MEAN WIND VELOCITY PROFILES AND TURBULENCE INTENSITIES 855
5. CONTROL OF TURBULENCE INTENSITY 857
6. CONTROL OF INTEGRAL LENGTH SCALE OF TURBULENCE 859
7. CONCLUSIONS 861
REFERENCES 861
Chapter 84. Computer Animation for Incompressible Viscous Flow Problems by
862
ABSTRACT 862
1. INTRODUCTION 862
2. ANIMATION SYSTEM 863
3. DISPLAY EXAMPLES 864
4. CONCLUSIONS 867
References 867
Chapter 85. WC & LEONARDO as interactive visualization
868
1. OBJECTIVE OF THE WORK 868
2. ADVANCED SYSTEM FEATURES IN AN INTERACTIVE USER ENVIRONMENT 868
3. PECULIARITIES OF DATA REPRESENTATIONS 869
4. PRINTOUT 871
5. CONCLUSIONS 871
REFERENCES 871
DISCUSSIONS OF COMPUTER AIDED EXPERIMENTS AND COMPUTER GRAPHICS 872
Part III: WORKSHOP: Prospects for
876
Chapter 86.
878
1. INTRODUCTION 878
2. SUMMARIES OF WORKSHOP PRESENTATIONS 878
3. CWE IN STRUCTURAL DESIGN 879
4. ACCURACY AND RELIABILITY OF THE NUMERICAL SOLUTIONS 880
5. THE ROLE OF EXPERIMENT AND WIND TUNNEL TESTING IN CWE 881
6. LIST OF WORKSHOP PARTICIPANTS 881
CHAPTER 87.
884
1. INTRODUCTION 884
2. BASIC PROBLEMS FOR THE DISCUSSION OF STRUCTURAL AEROELASTICITY 885
3. EXPECTATIONS AND PROBLEMS FOR THE COMPUTATIONAL APPROACH 887
4. CONCLUSION 887
Reference 887
Chapter 88.
888
1. CLASSIFICATION 888
2. MECHANISM OF BLUFF BODY AERODYNAMICS 888
3. RECENT TOPICS 889
4. WHAT IS REQUIRED OF CWE ? 891
Chapter 89. A Computational Fluid Dynamicist's View of
894
1. NUMERICAL ERRORS 894
2. DATA NEEDS 894
3. PROSPECTS FOR LARGE EDDY SIMULATION 895
4. REFERENCES 895
Chapter 90.
896
REFERENCES 899
Chapter 91.
900
1. INTRODUCTION 900
2. METHODS AND RESULTS 900
3. CONCLUDING REMARKS 901
References 901
Chapter 92.
908
1. OBJECTIVES 908
2. PROBLEM FORMULATION 908
3. DEFINITIONS 908
4. NUMERICAL EXAMPLES 909
REFERENCES 909
Chapter 93.
912
1. INTRODUCTION 912
2. NUMERICAL EXAMPLES 912
3. COMPUTATIONAL TECHNIQUES 913
Chapter 94.
914
INTRODUCTION 914
BUILDINGS 914
BRIDGES 915
OTHER STRUCTURES 915
OTHER RELATED PROBLEMS 915
MAJOR FACTORS IN PRACTICAL APPLICATIONS OF CWE 916
CONCLUSIONS 916
Part IV: SUMMARY OF VIDEO PRESENTATION 918
1 Video Presentation Report 920
2 Program 921
Author Index Volume
924
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 <f> the ensemble (or phase-) averaged value. The turbulent fluctuations have a considerable effect on the periodic motion which needs to be simulated in a calculation method. There are various possibilities for doing so. One would be to simulate the entire fluctuating motion by solving numerically the 3D unsteady Navier-Stokes equations. This method called direct numerical simulation (DNS) is presently feasible only at relatively low Reynolds numbers (say below Re = 104). At the higher Reynolds numbers of practical interest the dissipative part of the turbulent motion has such small scales compared with the cylinder diameter that it cannot be resolved in a numerical calculation. The number of grid points required to resolve this motion increases approximately as Re3.
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 <ui> through the following eddy-viscosity relation:
<u′iu′j>=<vt>(∂<ui>∂xj+∂<uj>∂xi)−23<k>δij (1)
The variation of the eddy viscosity <vt> over space and time must be determined by the turbulence model. For this, Deng et al. [3] used the algebraic eddy-viscosity model due to Baldwin and Lomax [4]. This employs the van Driest mixing-length model in the near-wall region, including the viscous sublayer. In regions further away from the wall, the eddy viscosity is related directly to a single velocity and length-scale characteristic of this region. In boundary layers, <vt> is calculated basically from the velocity gradient at a position where this gradient, weighted with the wall distance, reaches a maximum. In wake regions, <vt> is determined by the maximum deficit velocity and the maximum velocity gradient in the wake at a particular cross-section. Conceptually, this simple eddy-viscosity model does not seem to be very suited for flows with larger separation regions.
A conceptually more general model is the k-ε model which relates the eddy viscosity <vt> to the turbulent kinetic energy <k> and its dissipation rate <ε> and determines the distribution of these two turbulence parameters from model transport equations. The model employed in vortex-shedding calculations is a straightforward extension of the widely tested k-ε model for steady flows.
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 <uiuj>-equations are related to the equivalent terms in the <k>-equation. In their evaluation of Cantwell and Coles′data, Franke et al. [5] found that this approximation is considerably more realistic than neglecting the history and transport terms altogether for the normal stresses but that it is not so suitable for the shear stresses. As the k-ε eddy-viscosity model basically implies the neglect of history and transport terms, the use of an algebraic stress model can be expected to bring a modest improvement.
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-ε model due to Nagano and Tagawa [12] very near...
| Erscheint lt. Verlag | 28.6.2014 |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Naturwissenschaften ► Physik / Astronomie ► Angewandte Physik | |
| Naturwissenschaften ► Physik / Astronomie ► Mechanik | |
| Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik | |
| Technik ► Bauwesen | |
| Technik ► Elektrotechnik / Energietechnik | |
| Technik ► Maschinenbau | |
| ISBN-10 | 0-444-59861-8 / 0444598618 |
| ISBN-13 | 978-0-444-59861-5 / 9780444598615 |
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