Computational Wind Engineering 1: Proceedings of the 1st International Symposium on Computational Wind Engineering (CWE 92) Tokyo, Japan, August 21-23, 1992

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.

• Language: English
• Publisher: Elsevier Science
• Release date: Jun 28, 2014
• ISBN: 9780444598615

Book preview

Computational Wind Engineering 1

Proceedings of the 1st International Symposium on Computational Wind Engineering (CWE 92) Tokyo, Japan, August 21–23,1992

S. Murakami

Institute of Industrial Sciences, University of Tokyo, Tokyo, Japan

AMSTERDAM • LONDON • NEW YORK • TOKYO

Table of Contents

Cover image

Title page

Copyright

Preface

Symposium organization

Fundamentals

Turbulence modellings and their applications

Chapter 1: On the Simulation of Turbulent Flow Past Bluff Bodies

ABSTRACT

1 INTRODUCTION

2 STATISTICAL TURBULENCE MODELS EMPLOYED

3 LES MODELS TESTED

4 CALCULATION EXAMPLES

5 CONCLUSIONS

6 ACKNOWLEDGEMENTS

Chapter 2: COMPARISON OF VARIOUS TURBULENCE MODELS APPLIED TO A BLUFF BODY

Abstract

1 INTRODUCTION

2 CHARACTERISTICS OF FLOWFIELD AROUND A BLUFF BODY

3 COMPARISON OF MEAN VELOCITY VECTOR FIELD

4 DISCREPANCY IN SURFACE PRESSURE DISTRIBUTION

5 COMPARISON OF k−ε AND ASM; modelling of turbulence energy production term (Pk)

6 COMPARISON OF ASM AND LES; modelling of convection and diffusion terms

7 IMPROVEMENT OF LES; new SGS model with variable Smagorinsky constant

8 COMPARISON OF DIFFERENT TURBULENCE MODELS FOR VARIOUS FLOWFIELDS

9 CONCLUSION

ACKNOWLEDGEMENTS

NOMENCLATURE

Note 1 Model equations and numerical methods

Note 2 Mesh arrangements and boundary conditions

Appendix 1 Model equations for k−ε EVM

Appendix 2 Model equations for ASM (DSM)

Appendix 3 Model equations for LES

Appendix 4 Derivation of new model of LES with variable Smagorinsky Constant [22]

Chapter 3: Computational modelling of complex turbulent flow -expectations, reality and prospects

Abstract

1 CFD - THE CHALLENGE POSED BY PRACTICAL FLOWS

2 CFD - SOME IMPORTANT ISSUES

3 CURRENT CAPABILITIES AND LIMITATIONS

4 CURRENT DIRECTIONS IN TURBULENCE MODELLING

5 CONCLUDING REMARKS

Chapter 4: MODELING FLOWS AROUND BLUFF BODIES BY REYNOLDS AVERAGED TRANSPORT EQUATIONS

Abstract:

1 INTRODUCTION

2 TRANSPORT EFFECTS IN COMPLEX GEOMETRIES : K-ε MODEL.

3 SECOND MOMENT CLOSURES

4 CONCLUDING REMARKS

Chapter 5: Subgrid-scale modeling suggested by a two-scale DIA

Abstract

1 INTRODUCTION

2 FUNDAMENTAL EQUATIONS

3 RESULTS OF A TWO-SCALE DIA

4 SGS MODELS

5 DISCUSSIONS

6 CONCLUDING REMARKS

Acknowledgments

Chapter 6: Estimation of anisotropic k-ε model on the Backward-facing Step Flow by LES data base

Abstract

1 INTRODUCTION

2 TURBULENCE MODELS AND NUMERICAL METHOD

3 RESULTS AND DISCUSSIONS

4 A PRIORI TEST FOR REYNOLDS STRESS

5 FINAL REMARKS

Chapter 7: Numerical prediction of separating and reattaching flows with a modified low-Reynolds-number k-ε model

Abstract

1 INTRODUCTION

2 GOVERNING EQUATIONS AND MODIFIED LOW-REYNOLDS-NUMBER k-ε MODEL

3 NUMERICAL PROCEDURE AND BOUNDARY CONDITIONS

4 DISCUSSION OF THE PRESENT MODEL

5 RESULTS AND DISCUSSION

6 CONCLUSIONS

Chapter 8: Influence of the Turbulence Model in Calculations of Flow over Obstacles with Second-Moment Closures

Abstract

1 INTRODUCTION

2 MATHEMATICAL FORMULATION

3 RESULTS AND DISCUSION

4 CONCLUDING REMARKS

5 ACKNOWLEDGMENT

Chapter 9: Finite-volume computation of merging parallel channel flows by a second-moment turbulence closure model

Abstract

1 INTRODUCTION

2 MATHEMATICAL MODELS

3 NUMERICAL IMPLEMENTATION

4 RESULTS AND DISCUSSION

5 CONCLUSION

Chapter 10: Numerical Analysis of Wind around Building Using High-Speed GSMAC-FEM — Validation of Differential Stress Model —

Abstract

1 INTRODUCTION

2 BASIC EQUATIONS

3 VALIDATION OF DIFFERENTIAL STRESS MODEL

4 APPLICATION

5 CONCLUSIONS

Chapter 11: A computational study of the flow in a bluff body/flat plate junction

Abstract

1 INTRODUCTION

2 GOVERNING EQUATIONS AND NUMERICAL METHOD

3 RESULTS

4 CONCLUSIONS

Chapter 12: Numerical simulation to determine the effects of incident wind shear and turbulence level on the flow around a building

Abstract

1 INTRODUCTION

2 NUMERICAL SIMULATION

3 RESULTS AND DISCUSSION

4 CONCLUSIONS

5 ACKNOWLEDGMENTS

Chapter 13: Numerical study of wind flow over an elevated roadway

Abstract

1 INTRODUCTION

2 PHYSICAL MODEL

3 COMPUTATIONAL MODEL

4 CONCLUSIONS

5 ACKNOWLEDGEMENTS

Chapter 14: Appropriate boundary conditions for computational wind engineering models using the k-ε turbulence model

Abstract

1 INTRODUCTION

2 A HOMOGENEOUS k-ε MODEL FOR THE ATMOSPHERIC SURFACE LAYER

3 ATMOSPHERIC SURFACE LAYER MEASUREMENTS AT SILSOE

4 APPROPRIATE BOUNDARY CONDITIONS

5 CONCLUSIONS

Chapter 15: Transport equations of conditionally averaged Reynolds stresses for computation of turbulent flows with intermittency

Abstract

1 INTRODUCTION

2 THE CONDITIONAL REYNOLDS-STRESS TRANSPORT EQUATIONS

4 EXPERIMENTAL DATA

5 CONCLUSIONS

Chapter 16: Optimization of roughness parameters for staggered arrayed cubic blocks using experimental data

Abstract

1 INTRODUCTION

2 WIND TUNNEL EXPERIMENT

3 NUMERICAL CALCULATIONS

4 OPTIMIZATION OF ROUGHNESS PARAMETERS

5 CONCLUSION

Acknowledgments

Chapter 17: Modelling of Turbulent Flows within Plant/Urban Canopies

Abstract

1 INTRODUCTION

2 AVERAGING PROCEDURE

3 AVERADING PROCEDURE FOR CONSTITUTIVE EQUATIONS

4 FORMATION OF REYNOLDS STRESS EQUATION MODEL

5 RESULTS

6 SUMMERY AND CONCLUSIONS

ACKNOWLEDGEMENTS

NOMENCLATURE

others

Chapter 18: DISCUSSIONS OF TURBULENCE MODELLING AND THEIR APPLICATIONS

On The Simulation of Turbulent Flow past Bluff Bodies

Comparison of Various Turbulence Models Applied to A Bluff Body

Computational Modelling of Complex Turbulent Flow – Expectations, Reality and Prospects

Modeling Flows around Bluff Bodies by Reynolds Averaged Transport Equations

Subgrid – Scale Modeling Suggested by A Two – Scale DIA

Estimation of Anisotropic k-ε Model on The Backward – Facing Step Flow by LES Date Base

Numerical Prediction of Separating and Reattaching Flow with A Modified Low – Reynolds – Number k–ε Model

Influence of The Turbulence Model in Calculations of Flow over Obstacles with Second – Moment Closures

Finite – Volume Computation of Merging Parallel Channel Flows by A Second – Moment Turbulence Closure Model

Numerical Analysis of Wind around Building Using High – Speed GSMAC – FEM – Validation of Differential Stress Model –

Numerical Study of Wind Flow Over An Elevated Roadway

Appropriate Boundary Conditions for Computational Wind Engineering Models Using The k–ε Turbulence Model

Optimization of Roughness Parameters for Staggered Arrayed Cubic Blocks Using Experimental Data

Direct and large eddy simulations

Chapter 19: Simulation of complex turbulent flows: recent advances and prospects in wind engineering

Publisher Summary

1 INTRODUCTION

2 THREE-DIMENSIONAL UNSTEADY SIMULATIONS OF TURBULENT FLOW

3 RECENT DEVELOPMENTS IN LARGE EDDY SIMULATION

4 APPLICATIONS TO FLOWS OVER BLUFF BODIES

5 SOME RECENT LES RESULTS FOR BLUFF BODIES

6 BOOTSTRAPPING

7 CONCLUSIONS AND PROSPECTS

8 ACKNOWLEDGEMENTS

Chapter 20: Large-eddy-simulation of the flow around bumodelsilding

Abstract

1 BASIC EQUATIONS AND DISCRETISATION

2 TIME INTEGRATION AND SUBGRID SCALE MODELLING

3 RESULTS

Chapter 21: Computation of Wind Flow around a Tall Building and the Large–Scale Vortex Structure

Abstract

1 INTRODUCTION

2 GOVERNING EQUATIONS

3 MODEL VALIDATION

4 TALL BUILDING CASE

5 CONCLUSIONS

ACKNOWLEDGEMENTS

Chapter 22: Large eddy simulation of microburst winds flowing around a building

Abstract

1 INTRODUCTION

2 MODEL

3 EXPERIMENTAL DESIGN

4 RESULTS

5 CONCLUSIONS

6 ACKNOWLEDGMENTS

Chapter 23: Use of large eddy simulation to measure fluctuating pressure fields around buildings with wall openings

1 Introduction

2 Outline of LES

3 Results of Numerical Analyses

4 Conclusion

Chapter 24: Numerical Modelling of Flow Over A Rigid Wavy Surface by LES

Abstract

1 INTRODUCTION

2 GOVERNING EQUATIONS

3 COORDINATE TRANSFORMATION

4 COMMENTS ON NUMERICAL SIMULATION

5 RESULTS AND DISCUSSION

6 ACKNOWLEDGEMENT

Chapter 25: A numerical study on the flow around flat plates at low Reynolds numbers

Abstract

1 INTRODUCTION

2 FORMULATION

3 RESULTS

4 CONCLUSIONS

Chapter 26: Fourth Order Finite Difference and Multigrid Methods for Modeling Instabilities in 2-Dimensional Flat Plate Boundary Layers

Abstract

1 INTRODUCTION

2 GOVERNING EQUATIONS

3 OUTFLOW BOUNDARY TREATMENT

4 NUMERICAL METHODS

5 COMPUTATIONAL RESULTS

6 CONCLUDING REMARKS

ACKNOWLEDGEMENTS

Chapter 27: Numerical analysis of flows over walls with protuberances

Abstract

1 INTRODUCTION

2 GOVERNING EQUATION

3 NUMERICAL SCHEME

4 RESULTS AND DISCUSSION

5 CONCLUSIONS

Chapter 28: A numerical study of nonlinear waves excited by an obstacle in the flow of stratified fluid

Abstruct

1 INTRODUCTION

2 GOVERNING EQUATIONS AND THE NUMERICAL METHOD

3 RESULTS AND DISCUSSIONS

Chapter 29: DISCUSSIONS OF DIRECT AND LARGE EDDY SIMULATIONS

Simulation of Complex Turbulent Flows: Recent Advances and Prospects in Wind Engineering

Large – Eddy – Simulation of The Flow around Building Models

Computation of Wind Flow around A Tall Building and The Large – Scale Vortex Structure

Large Eddy Simulation of Microburst Winds Flowing around A Building

Use of Large Eddy Simulation To Measure Fluctuating Pressure Fields around Buildings with Wall Openings

Numerical Modelling of Flow over A Rigid Wavy Surface by LES

Numerical Analysis of Flows over Walls with Protuberances

A Numerical Study of Nonlinear Waves Excited by An Obstacle in The Flow of Stratified Fluid

Numerical methods

Chapter 30: Finite element methods in wind engineering

Abstract

1 INTRODUCTION

2 ISSUES IN THE DEVELOPMENT OF WIND ENGINEERING SIMULATION TOOLS

3 CONCLUSIONS

Chapter 31: High Resolution Vortex Simulation of Bluff Body Flows

Abstract

1 INTRODUCTION

2 VISCOUS VORTEX METHOD

Chapter 32: Volume-fraction techniques: powerful tools for wind engineering

Abstract

1 INTRODUCTION: OVERVIEW OF FAVOR CONCEPT

2 A SIMPLE EXAMPLE AND ITS IMPLICATIONS

3 MAKING THE CONCEPT A PRACTICAL TOOL

4 ORDINARY AND NOVEL USES OF THE FAVOR METHOD

5 ACKNOWLEDGEMENTS

Chapter 33: Numerical Simulation of High Reynolds Number Flows by Petrov-Galerkin Finite Element Method

Abstract

1 INTRODUCTION

2 STATEMENT OF PROBLEMS

3 PETROV-GALERKIN FORMULATION USING EXPONENTIAL FUNCTIONS

4 NUMERICAL EXAMPLES

5 CONCLUSIONS

Chapter 34: Direct third-order upwind finite element simulation of high Reynolds number flows around a circular cylinder

Abstract

1 INTRODUCTION

2 INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

3 THIRD-ORDER ACCURATE UPWIND SCHEME

4 FINITE ELEMENT SCHEME

5 NUMERICAL EXAMPLES

6 CONCLUSIONS

Chapter 35: Automatic mesh generation for FEM simulation of wind flow around tall buildings

Abstract

1 INTRODUCTION

2 RECURSIVE SUBDIVISION

3 MESH CONVERSION

4 CONCLUSION

Chapter 36: Numerical Simulation of Flow around a Sphere with Vortex Blobs

Abstract

1 INTRODUCTION

2 MATHEMATICAL MODEL

3 RESULTS

4 CONCLUSIONS

Chapter 37: Simulation of Turbulent Flow by Discrete Vortex Approximation

Abstract

1 INTRODUCTION

2 FORMULATION AND NUMERICAL PROCEDURE

3 RESULT

4 CONCLUSION

Chapter 38: Solution Method of the Time Transient Moving Boundary Problems Using Generalized Porous Media Technique: – FAVORITE (FAVOR ImitaTE) Program –

Abstract

1 Introduction

2 Basic Idea of the moving obstacle treatment

3 FAVORITE fondation including thin plate

4 Conclusion

Acknowledgement

5 Result of sample calculations

Chapter 39: Application of Massive Parallel Computer to Computational Wind Engineering

Abstract

1 INTRODUCTION

2 FLOW SIMULATION

3 MASSIVE PARALLEL COMPUTER USED

4 PARALLELIZATION OF ALGORITHM

5 CASES ANALYZED

6 RESULTS

7 CONCLUSIONS

ACKNOWLEDGEMENTS

Chapter 40: DISCUSSIONS OF NUMERICAL METHODS

Finite Element Methods in Wind Engineering

High Resolution Vortex Simulation of Bluff Body Flows

Volume – Fraction Techniques: Powerful Tools for Wind Engineering

Numerical Simulation of High Reynolds Number Flows by Petrov – Galerkin Finite Element Method

Direct Third – Order Upwind Finite Element Simulation of High Reynolds Number Flows around A Circular Cylinder

Automatic Mesh Generation for FEM Simulation of Wind Flow around Tall Buildings

Numerical Simulation of Flow around A Sphere with Vortex Blobs

Simulation of Turbulent Flow by Discrete Vortex Approximation

Application of Massive Parallel Computer to Computational Wind Engineering

Applications

Wind load

Chapter 41: The generalization and simplification of wind loads and implications for computational methods

Abstract

1 COMPUTATIONAL ASPECTS OF WIND LOADING MODELLING

2 SOME BREAKTHROUGHS

3 GENERALIZATION OF RESPONSE USING INFLUENCE SURFACES

4 SIMPLIFICATION THROUGH ORTHONORMAL FUNCTIONS

5 INFLUENCE OF WIND DIRECTION AND UNCERTAINTIES

6 COMPUTATIONAL OPPORTUNITIES IN WIND LOADING AND SOME CONCLUSIONS

Chapter 42: Numerical simulation of wind-induced pressures on buildings of various geometries

Abstract

1 INTRODUCTION

2 NUMERICAL APPROACH

3 BOUNDARY CONDITIONS

4 RESULTS AND DISCUSSION

5 CONCLUSIONS

Chapter 43: Predicting r. m.s. pressures from computed velocities and mean pressures

Abstract

1 FORMULAE FOR R. M.S. PRESSURES IN HOMOGENEOUS ISOTROPIC TURBULENCE

2 FORMULAE FOR R. M.S. PRESSURES IN GENERAL FLOWS

3 THE TEXAS TECH EXPERIMENTAL DATA

4 RELATIONSHIPS BETWEEN AND

5 CONCLUSIONS

Chapter 44: A comparison of computer and wind-tunnel models of turbulence around the Silsoe Structures Building

Abstract

1 INTRODUCTION

2 FULL-SCALE MEASUREMENTS

3 WIND-TUNNEL MEASUREMENTS

4 COMPUTATIONAL SOLUTIONS

5 RESULTS AND DISCUSSION

6 CONCLUSIONS

7 ACKNOWLEDGEMENT

Chapter 45: Computational and Experimental Roof Corner Pressures on the Texas Tech Building

Abstract

1 INTRODUCTION

2 COMPUTER MODELLING

3 RESULTS AND DISCUSSIONS

4 CONCLUSIONS

5 ACKNOWLEDGEMENTS

Chapter 46: Numerical Simulation of Flowfield around Texas Tech Building by Large Eddy Simulation

Abstract

1 INTRODUCTION

2 OUTLINE OF FIELD MEASUREMENT OF THE TEXAS TECH BUILDING

3 RESULTS AND DISCUSSION

4 CONCLUSION

Chapter 47: Large eddy simulation of wind flow around dome structures by the finite element method

Abstract

1 BASIC EQUATIONS

2 FINITE ELEMENT FORMULATION

3 INDUCING THE FLOW WITH TURBULENCE

4 WIND FLOW AROUND A CYLINDRICAL DOME ROOF

5 CONCLUDING REMARKS

Chapter 48: Computation of wind flow over topography

Abstract

1 TOPOGRAPHIC MULTIPLIERS

2 RIDGE GEOMETRIES

3 COMPUTER MODELLING

4 RESULTS

5 CONCLUSIONS

Chapter 49: Analysis of hyperbolic cooling towers for wind loads with ACMC and semi-loof shell elements

Abstract

1 INTRODUCTION

2 FORMULATION FOR ANALYSIS

Chapter 50: Computing the statistical stability of integral length scale measurements by autoregressive simulation

Abstract

1 INTRODUCTION

2 BASIC ASSUMPTIONS AND DEFINITIONS

3 ESTIMATION OF MEAN, VARIANCE AND INTEGRAL TIME SCALE

4 AUTOREGRESSIVE SIMULATION

5 EXPERIMENTAL RESULTS

6 CONCLUSIONS

Chapter 51: Response analyses on along-wind and across-wind vibrations of tall buildings in time domain

Abstract

1 INTRODUCTION

2 SPECIFICATIONS OF A BUILDING

3 SIMULATION OF THE FLUCTUATING WIND FORCES

4 WIND RESPONSE ANALYSES IN TIME DOMAIN

5 CONCLUSION

Chapter 52: Proposed formulae for the power spectral densities of fluctuating lift and torque on rectangular 3-D cylinders

Abstract

1 INTRODUCTION

2 WIND TUNNEL EXPERIMENTS

3 EXPERIMENTAL RESULTS AND FORMULATION

4 CONCLUSION

5 ACKNOWLEDGEMENT

Chapter 53: NUMERICAL SIMULATION OF PRESSURE DISTRIBUTIONS UNDERNEATH ROOFING PAVER SYSTEMS

Abstract

1 INTRODUCTION

2 PHYSICAL ASSUMPTIONS

3 MATHEMATICAL EQUATIONS

4 COMPARISONS OF NUMERICAL AND EXPERIMENTAL RESULTS AND DISCUSSIONS

Chapter 54: DISCUSSIONS OF WIND LOAD

The Generalization and Simplification of Wind Loads and Implications for Computational Methods

Numerical Simulation of Wind – Induced Pressures on Buildings of Various Geometries

Predicting R. M.S. Pressures from Computed Velocities and Mean Pressures

A Comparison of Computer and Wind – Tunnel Models of Turbulence around The Silsoe Structures Building

Computational and Experimental Roof Corner Pressures on The Texas Tech Building

Numerical Simulation of Flowfield around Texas Tech Building by Large Eddy Simulation

Large Eddy Simulation of Wind Flow around Dome Structures by The Finite Element Method

Computation of Wind Flow over Topography

Analysis of Hyperbolic Cooling Towers for Wind Loads with ACMC and Semi – Loof Shell Elements

Computing The Statistical Stability of Integral Length Scale Measurements by Autoregressive Simulation

Response Analyses on Along – Wind and Across – Wind Vibrations of Tall Buildings in Time Domain

Proposed Formulae for The Power Spectral Densities of Fluctuating Lift and Torque on Rectangular 3 – D Cylinders

Numerical Simulation of Pressure Distributions Underneath Roofing Paver Systems

Wind induced vibrations

Chapter 55: Numerical study on aeroelastic instability of cylinders with a circular and rectangular cross-section

Abstract

1 INTRODUCTION

NOMENCLATURE

2 OUTLINE OF COMPUTATIONAL METHODS

3 COMPUTATIONAL RESULTS

4 CONCLUSIONS

Chapter 56: Unsteady Pressure Field around Oscillating Prism predicted by LES

Abstract

1 INTRODUCTION

2 OUTLINE OF NUMERICAL SIMULATIONS

3 RESULTS AND DISCUSSIONS

4 CONCLUSION

Acknowledgements

Nomenclature

Chapter 57: Numerical Investigation on the Aeroelastic Instability of Bluff Cylinders

Abstract

1 INTRODUCTION

2 PROBLEM FORMULATION

3 COMPUTATIONAL MODEL

4 THREE-DIMENSIONAL SIMULATIONS FOR A RECTANGULAR CYLINDER

5 AEROELASTIC BEHAVIOR OF BLUFF CYLINDERS

6 CONCLUSION

Chapter 58: Numerical simulation of flow field around an oscillating bridge using finite difference method

Abstract

1 INTRODUCTION

2 PROBLEM FORMULATION

3 RESULTS

4 CONCLUSION

5 ACKNOWLEDGEMENT

Chapter 59: A numerical investigation of the unsteady fluid force induced in the annular diffuser by the oscillating inner cylinder

Abstract

1 INTRODUCTION

2 METHODOLOGY OF NUMERICAL ANALYSIS

3 NUMERICAL RESULTS

4 CONCLUSION

Chapter 60: Finite element analysis of vortex-induced vibrations of bluff cylinders

Abstract

1 INTRODUCTION

2 COMPUTATIONAL METHOD

3 VORTEX-INDUCED OSCILLATIONS OF A CIRCULAR CYLINDER

4 CONCLUDING REMARK

Chapter 61: Interaction analysis between structure and fluid flow for wind engineering

Abstract

1 INTRODUCTION

2 ALGORITHM

3 FLOW AROUND A RIGID RECTANGULAR CYLINDER

4 FLOW AROUND A FLEXIBLE STUCTURE

5 CONCLUDING REMARKS

ACKNOWLEDGEMENTS

Chapter 62: Vortex induced vibration of circular cylinder

Abstract

l INTRODUCTION

2 METHOD OF SIMULATION

3 DISCUSSION OF RESULTS

4 CONCLUSION

Chapter 63: Simulation of Aerodynamic Instability of Bluff Body

Abstract

1 INTRODUCTION

2 METHOD

3 RESULTS AND DISCUSSION

4 CONCLUSION

Chapter 64: Aerodynamic loading and flow past bluff bodies using discrete vortex method

Abstract

1 INTRODUCTION

2 METHOD

3 DVM APPLICATION FOR BLUFF BODY AERODYNAMICS

4 DVM IMPLEMENTATION AT COLORADO STATE UNIVERSITY

5 REPRESENTATIVE RESULTS

6 CONCLUDING REMARKS

Acknowledgments

Chapter 65: Unsteady aerodynamic force characteristics on 2-D oscillating bluff body

Abstract

1 INTRODUCTION

2 COMPUTATIONAL METHOD

3 WIND TUNNEL APPARATUS

4 DISCUSSIONS

5 CONCLUSION

Acknowledgements

Chapter 66: Aeolian vibrations of overhead transmission lines: computation in turbulence conditions

Abstract

1 INTRODUCTION

2 MATHEMATICAL MODEL OF THE SYSTEM CABLE-FLUID ACTIONS

3 SOME ANALYTICAL RESULTS AND CONCLUSIONS

Chapter 67: DISCUSSIONS OF WIND INDUCED VIBRATIONS

Unsteady Pressure Field around Oscillating Prism Predicted by LES

Numerical Investigations on The Aeroelastic Instability of Bluff Cylinders

Numerical Simulation of Flow Field around An Oscillating Bridge Using Finite Difference Method

Finite Element Analysis of Vortex – Induced Vibrations of Bluff Cylinders

Interaction Analysis between Structure and Fluid Flow for Wind Engineering

Vortex Induced Vlbration of Circular Cylinder

Simulations of Aerodynamic Instability of Bluff Body

Aerodynamic Loading and Flow Past Bluff Bodies Using Discrete Vortex Method

Unsteady Aerodynamic Force Characteristics on 2 – D Oscillating Bluff Body

Environmental problems

Chapter 68: Numerical study of wind flow over a cooling tower

Abstract

1 INTRODUCTION

2 PHYSICAL MODEL

3 COMPUTATIONAL MODEL

4 CONCLUSIONS

5 ACKNOWLEDGEMENTS

Chapter 69: A study on the environment in an open court of high rise building with heliport

Abstract

1 INTRODUCTION

2 OUTLINE OF SIMULATION

3 RESULTS

4 DISCUSSION

5 CONCLUSIONS

Chapter 70: Modelling of flow and ventilation within petroleum process plants

Abstract

1 INTRODUCTION

2 VENTILATION AND AREA CLASSIFICATION

3 GAS AND SMOKE DISPERSION

4 CONCLUSIONS

5 ACKNOWLEDGEMENTS

Chapter 71: Simulation of diffusion phenomena under unstable conditions using a Lagrangian particle dispersion model

Abstract

1 INTRODUCTION

2 LAGRANGIAN PARTICLE DISPERSION MODEL

3 WIND TUNNEL EXPERIMENT

4 CALCULATION RESULTS OF DIFFUSION

5 CONCLUSIONS

ACKNOWLEDGEMENTS

Chapter 72: Numerical and experimental simulation of vehicle exhaust gas dispersion for complex urban roadways and their surroundings

Abstract

1 INTRODUCTION

2 NUMERICAL SIMULATION

3 EXPERIMENTAL SIMULATION

4 RESULTS OF NUMERICAL AND EXPERIMENTAL SIMULATION

5 CONCLUSION

Chapter 73: Simulation of Air Flow over a Heated Flat Plate Using Anisotropic k-ε Model

Abstract

1 INTRODUCTION

2 WIND TUNNEL EXPERIMENT

3 THE MODEL

4 RESULTS AND DISCUSSION

5 CONCLUSIONS

Chapter 74: Application of Reynolds-Stress Model to the Study of Heat Island Structure over a Slightly Inclined Terrain

Abstract

1 INTRODUCTION

2 GOVERNING EQUATIONS AND MODEL DESCRIPTION

3 NUMERICAL PROCEDURE

4 RESULTS AND DISCUSSION

5 SUMMARY

Chapter 75: Modeling of multisized particle laden turbulent low swirling free jets

Abstract

1 INTRODUCTION

2 THE NUMERICAL MODEL

3 RESULTS AND DISCUSSION

4 CONCLUSIONS

ACKNOWLEDGEMENTS

Chapter 76: Simulation of wind-driven-rain around a building

Abstract

1 INTRODUCTION

2 WIND-DRIVEN-RAIN

3 DISCUSSION

4 Acknowledgement

Chapter 77: A three-step Taylor-Galerkin finite element method for orographic rainfall

Abstract

1 INTRODUCTION

2 BASIC EQUATION

3 THREE-STEP TAYLOR-GALERKIN METHOD

4 FINITE ELEMENT FORMULATION

5 NUMERICAL EXAMPLE

6 CONCLUSION

Chapter 78: Three dimensional numerical simulation of snowdrift

Abstract

1 INTRODUCTION

2 NUMERICAL SIMULATION MODEL

3 THE RESULTS OF SIMULATIONS

4 CONCLUSION

Chapter 79: DISCUSSIONS OF ENVIRONMENTAL PROBLEMS

Numerical Study of Wind Flow over A Cooling Tower

A Study on The Environment in An Open Court of High Rise Building with Heliport

Modelling of Flow and Ventilation within Petroleum Process Plants

Simulation of Diffusion Phenomena under Unstable Conditions Using A Lagrangian Particle Dispersion Model

Numerical and Experimental Simulation of Vehicle Exhaust Gas Dispersion for Complex Urban Roadways and Their Surroundings

Simulation of Air Flow over A Heated Flat Plate Using Anisotropic k–ε Model

Application of Reynolds – Stress Model to The Study of Heat Island Structure over A Slightly Inclined Terrain

Modeling of Multisized Particle Laden Turbulent Low Swirling Free Jets

Simulation of Wind – Driven – Rain around A Building

A Three – Step Taylor – Galerkin Finite Element Method for Orographic Rainfall

Three Dimensional Numerical Simulation of Snowdrift

Pedestrain wind

Chapter 80: Numerical and experimental modelling of the three-dimensional turbulent wind flow through an urban square

Abstract

1 INTRODUCTION

2 THE EXPERIMENTAL SITE

3 NUMERICAL SIMULATION

4 COMPARISON WITH WIND TUNNEL EXPERIMENT

5 CONCLUSION

6 ACKNOWLEDGEMENTS

Chapter 81: Numerical Simulation of Flowfield around Buildings in an Urban Area

Abstract

1 INTRODUCTION

2 NUMERICAL SIMULATION OF FLOWFIELD

3 BUILDING ANALYZED

4 RESULTS AND DISCUSSIONS

5 CONCLUSIONS

Chapter 82: Numerical Study on Relationship between Building Shape and Ground-Level Wind Velocity

Abstract

1 INTRODUCTION

2 OUTLINE OF NUMERICAL ANALYSIS

Nomenclature

3 RESULTS OF ANALYSIS AND DISCUSSION

4 APPLICATION TO ACTUAL BUILDING(Case 10, Fig. 6)

5 CONCLUSIONS

Chapter 83: DISCUSSIONS OF PEDESTRIAN WIND

Numerical and Experimental Modelling of The Three – Dimensional Turbulent Wind Flow through An Urban Square

Numerical Simulation of Flowfield around Buildings in An Urban Area

Numerical Study on Relationship between Building Shape and Ground – Level Wind Velocity

Vehicle aerodynamics and others

Chapter 84: Numerical Analysis and Visualization of Flow in Automobile Aerodynamics Development

Abstract

1 INTRODUCTION

2 DRAG4D SYSTEM

3 AERODYNAMIC DRAG FORCE

4 Engine Cooling

5 CONCLUSION

Chapter 85: Flow Structure around a 3D Blufaf Body in Ground Proximity :: A computational Study

ABSTRACT

I. INTRODUCTION

II. MATHEMATICAL FORMULATION

III. METHOD OF COMPUTATION

IV. RESULTS AND DISCUSSION

V. CONCLUDING REMARKS

ACKNOWLEDGEMENTS

APPENDIX A

Chapter 86: Finite element analysis of air flow around an Automatic Guided Vehicle

Abstract

1. INTRODUCTION

2. A MATHEMATICAL MODEL

3. NUMERICAL METHOD

4. RESULTS

5. CONCLUDING REMARKS

Chapter 87: UNSTEADY AERODYNAMICS AND WAKE OF THE SAVONIUS WIND TURBINE : A NUMERICAL STUDY

Abstract

1 INTRODUCTION

2 APPROACH TO THE PROBLEM

Chapter 88: DISCUSSIONS OF VEHICLE AERODYNAMICS AND OTHERS

Flow Structure around A 3D Bluff Body in Ground Proximity: A Computational Study

Finite Element Analysis of Air Flow around An Automatic Guided Vehicle

Unsteady Aerodynamics and Wake of The Savonius Wind Turbine: A Numerical Study

Computer aided experiments and computer graphics

Chapter 89: Turbulence measurement in a separated and reattaching flow over a backward-facing step with the aid of three-dimensional particle tracking velocimetry

Abstract

1 INTRODUCTION

2 EXPERIMENTAL APPARATUS AND PROCEDURE

3 EXPERIMENTAL RESULTS

4 CONCLUSIONS

Chapter 90: Study on three-dimensional characteristics of natural ventilation in half-enclosed buildings using video imaging techniques

Abstract

1 INTRODUCTION

2 OUTLINE OF EXPERIMENTS

3 RESULTS AND DISCUSSIONS

4 CONCLUSION

Acknowledgment

Chapter 91: A Computer-Controlled Wind Tunnel

Abstract

1. INTRODUCTION

2. EXPERIMENTAL WIND TUNNELS

3. CONTROL VARIABLES OF FANS

4. MEAN WIND VELOCITY PROFILES AND TURBULENCE INTENSITIES

5. CONTROL OF TURBULENCE INTENSITY

6. CONTROL OF INTEGRAL LENGTH SCALE OF TURBULENCE

7. CONCLUSIONS

Chapter 92: Computer Animation for Incompressible Viscous Flow Problems by Using Graphic Engineering Work Station

ABSTRACT

1. INTRODUCTION

2. ANIMATION SYSTEM

3. DISPLAY EXAMPLES

4. CONCLUSIONS

Chapter 93: VVG & LEONARDO as interactive visualization systems for Computer Fluid Mechanics

Abstract

1. OBJECTIVE OF THE WORK

2. ADVANCED SYSTEM FEATURES IN AN INTERACTIVE USER ENVIRONMENT

3. PECULIARITIES OF DATA REPRESENTATIONS

4. PRINTOUT

5. CONCLUSIONS

Chapter 94: DISCUSSIONS OF COMPUTER AIDED EXPERIMENTS AND COMPUTER GRAPHICS

Turbulence Measurement in A Separated and Reattaching Flow over A Backward – Facing Step with The Aid of Three – Dimensional Particle Tracking Veloclmetry

A Computer – Controlled Wind Tunnel

Discrete – Vortex Simulation of Pulsating Flow behind A Normal Plate

Workshop

Chapter 95: Prospects for Numerical Analysis of Interaction between Fluid Flow and Structural Vibration

Publisher Summary

1 INTRODUCTION

2 SUMMARIES OF WORKSHOP PRESENTATIONS

3 CWE IN STRUCTURAL DESIGN

4 ACCURACY AND RELIABILITY OF THE NUMERICAL SOLUTIONS

5 THE ROLE OF EXPERIMENT AND WIND TUNNEL TESTING IN CWE

6 LIST OF WORKSHOP PARTICIPANTS

Appendix (Abstract)

Chapter 96: FOR THE ADVANCE OF THE COMPUTATIONAL STRUCTURAL AEROELASTICITY

Publisher Summary

1 INTRODUCTION

2 BASIC PROBLEMS FOR THE DISCUSSION OF STRUCTURAL AEROELASTICITY

3 EXPECTATIONS AND PROBLEMS FOR THE COMPUTATIONAL APPROACH

4 CONCLUSION

Chapter 97: Survey for the Aeroelasticity of Structures

Publisher Summary

1 CLASSIFICATION

2 MECHANISM OF BLUFF BODY AERODYNAMICS

3 RECENT TOPICS

4 WHAT IS REQUIRED OF CWE?

Chapter 98: A Computational Fluid Dynamicist’s View of CWE

Publisher Summary

1 NUMERICAL ERRORS

2 DATA NEEDS

3 PROSPECTS FOR LARGE EDDY SIMULATION

Chapter 99: Brief Review: Numerical Analysis of the Flow around Vibrating Cylinders

Publisher Summary

Chapter 100: Numerical Simulations of Aerodynamic Instability of Bluff Body by the Discrete Vortex Method

Publisher Summary

1 INTRODUCTION

2 METHODS AND RESULTS

3 CONCLUDING REMARKS

Chapter 101: Current Research by the FDM

Publisher Summary

1 OBJECTIVES

2 PROBLEM FORMULATION

3 DEFINITIONS

4 NUMERICAL EXAMPLES

Chapter 102: Current researches by FEM

Publisher Summary

1 INTRODUCTION

2 NUMERICAL EXAMPLES

3 COMPUTATIONAL TECHNIQUES

Chapter 103: A contribution to the workshop on computational wind engineering

Publisher Summary

INTRODUCTION

BUILDINGS

BRIDGES

OTHER STRUCTURES

OTHER RELATED PROBLEMS

MAJOR FACTORS IN PRACTICAL APPLICATIONS OF CWE

CONCLUSIONS

Summary of Video Presentation

SUMMARY OF VIDEO PRESENTATION

Author Index Volume 46–47 (1993)

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Preface

The First International Symposium on Computational Wind Engineering (CWE92) was held at the University of Tokyo in August 1992, under the auspices of the Japan Association for Wind Engineering and the Institute of Industrial Science, University of Tokyo.

The aim of this Symposium was 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.

CFD developed mainly in the fields of mechanical and aeronautical engineering. Great success has been achieved in predicting such relatively simple flows as channel flow, air flow around a wing, etc. However, problems concerning air flow in wind engineering are far more complicated. In many cases, the current CFD technology borrowed from other fields is thus inadequate and new research and development are urgently required in this field.

State-of-the-art papers from all over the world were presented at this Symposium, affording researchers in wind engineering the opportunity to present their most recent findings contributing to the overall development of the field. A host of researchers and engineers representing both industry and the academic world attended this Symposium, which was designed to illuminate the present parameters of the field, as well as to suggest fruitful areas for further research.

Twenty-three technical sessions were organized including four special sessions featuring twelve invited speakers outstanding in the fields of computational fluid dynamics and wind engineering, a workshop focused upon numerical analysis of the interaction between fluid flow and structural vibration, and a video session which delved into computer graphics for turbulent flowfields around structures.

Selected papers from the Symposium are compiled in this Proceedings volume. The summaries of the workshop and the video session are also included. The editor wishes this Proceedings to serve as a vehicle to promote further development in computational wind engineering. I would like to express my sincere gratitude to all the authors for their contributions.

Finally, I extend my sincere thanks to the many individuals and the organizations who assisted in the staging of CWE92 listed in the following page. In particular I would like to express my special thanks to Professor M. Matsumoto, Kyoto University, and Doctor A. Mochida, I.I.S., University of Tokyo, for their great contributions as the chairman of the Programming Committee and the secretary general of the Symposium, respectively.

Symposium Chairman. Shuzo Murakami

Symposium organization

S. Akabayashi⁸, H. Akao⁷, J.E. Cermak⁶, H. Daiguuji⁶, A.G. Davenport⁶, K. Deguchi⁸, M. Endo⁷, J.H. Ferziger⁶, K. Fujii⁷,⁸, Y. Fujino⁷,⁸, K. Hama⁷, K. Hibi⁸,⁹, M. Hino⁶, J.C.R. Hunt⁶, I. Imai⁶, T. Inamuro⁸⁹–10, Y. Ishida⁸, H. Ishizaki⁶, M. Ito⁶, J. Kanda⁷⁸⁹–10, S. Kato⁷⁸⁹–10, A. Kawaguchi⁸, H. Kawai⁷⁸⁹–10, H. Kitamura⁷, M. Kiya⁷, N. Kobayashi⁸, T. Kobayashi⁷, B.E. Launder⁶, Y. Matagi⁸, M. Matsumoto⁴,⁷,⁸,¹⁰, T. Miyata⁷, T. Mizutani⁷, A. Mochida⁷⁸⁹–10, Y. Morikawa⁸, S. Murakami¹²–3,⁹,¹⁰, T. Nomura⁸⁹–10, K. Ogawa⁸, A. Okajima⁷,⁸,¹⁰, M. Ohba⁸, T. Ohkuma⁵,⁷,⁸, Y. Ohsaki⁷, W. Rodi⁶, T. Saito⁸, H. Sakata⁷, K. Sato⁷, M. Shimura⁸,⁹, N. Shiraishi⁶, H. Shirato⁸, T. Stathopoulos⁷, Y. Suyama⁸, T. Takeda⁷, T. Tamura⁸⁹–10, Y. Tamura⁷⁸⁹–10, T. Tanaka⁸ and A. Yoshizawa⁷

---

¹Chairman of CWE92

²Chairman of Organizing Committee

³Chairman of Executive Committee

⁴Chairman of Programming Committee

⁵Chairman of Working Group

⁶Members of Scientific Advisory Board

⁷Members of Organizing Committee

⁸Members of Executive Committee

⁹Members of Programming Committee

¹⁰Members of Working Group

Fundamentals

Outline

Chapter 1: On the Simulation of Turbulent Flow Past Bluff Bodies

Chapter 2: COMPARISON OF VARIOUS TURBULENCE MODELS APPLIED TO A BLUFF BODY

Chapter 3: Computational modelling of complex turbulent flow -expectations, reality and prospects

Chapter 4: MODELING FLOWS AROUND BLUFF BODIES BY REYNOLDS AVERAGED TRANSPORT EQUATIONS

Chapter 5: Subgrid-scale modeling suggested by a two-scale DIA

Chapter 6: Estimation of anisotropic k-ε model on the Backward-facing Step Flow by LES data base

Chapter 7: Numerical prediction of separating and reattaching flows with a modified low-Reynolds-number k-ε model

Chapter 8: Influence of the Turbulence Model in Calculations of Flow over Obstacles with Second-Moment Closures

Chapter 9: Finite-volume computation of merging parallel channel flows by a second-moment turbulence closure model

Chapter 10: Numerical Analysis of Wind around Building Using High-Speed GSMAC-FEM — Validation of Differential Stress Model —

Chapter 11: A computational study of the flow in a bluff body/flat plate junction

Chapter 12: Numerical simulation to determine the effects of incident wind shear and turbulence level on the flow around a building

Chapter 13: Numerical study of wind flow over an elevated roadway

Chapter 14: Appropriate boundary conditions for computational wind engineering models using the k-ε turbulence model

Chapter 15: Transport equations of conditionally averaged Reynolds stresses for computation of turbulent flows with intermittency

Chapter 16: Optimization of roughness parameters for staggered arrayed cubic blocks using experimental data

Chapter 17: Modelling of Turbulent Flows within Plant/Urban Canopies

Chapter 18: DISCUSSIONS OF TURBULENCE MODELLING AND THEIR APPLICATIONS

Chapter 19: Simulation of complex turbulent flows: recent advances and prospects in wind engineering

Chapter 20: Large-eddy-simulation of the flow around bumodelsilding

Chapter 21: Computation of Wind Flow around a Tall Building and the Large–Scale Vortex Structure

Chapter 22: Large eddy simulation of microburst winds flowing around a building

Chapter 23: Use of large eddy simulation to measure fluctuating pressure fields around buildings with wall openings

Chapter 24: Numerical Modelling of Flow Over A Rigid Wavy Surface by LES

Chapter 25: A numerical study on the flow around flat plates at low Reynolds numbers

Chapter 26: Fourth Order Finite Difference and Multigrid Methods for Modeling Instabilities in 2-Dimensional Flat Plate Boundary Layers

Chapter 27: Numerical analysis of flows over walls with protuberances

Chapter 28: A numerical study of nonlinear waves excited by an obstacle in the flow of stratified fluid

Chapter 29: DISCUSSIONS OF DIRECT AND LARGE EDDY SIMULATIONS

Chapter 30: Finite element methods in wind engineering

Chapter 31: High Resolution Vortex Simulation of Bluff Body Flows

Chapter 32: Volume-fraction techniques: powerful tools for wind engineering

Chapter 33: Numerical Simulation of High Reynolds Number Flows by Petrov-Galerkin Finite Element Method

Chapter 34: Direct third-order upwind finite element simulation of high Reynolds number flows around a circular cylinder

Chapter 35: Automatic mesh generation for FEM simulation of wind flow around tall buildings

Chapter 36: Numerical Simulation of Flow around a Sphere with Vortex Blobs

Chapter 37: Simulation of Turbulent Flow by Discrete Vortex Approximation

Chapter 39: Application of Massive Parallel Computer to Computational Wind Engineering

Chapter 40: DISCUSSIONS OF NUMERICAL METHODS

Turbulence modellings and their applications

Outline

Chapter 1: On the Simulation of Turbulent Flow Past Bluff Bodies

Chapter 2: COMPARISON OF VARIOUS TURBULENCE MODELS APPLIED TO A BLUFF BODY

Chapter 3: Computational modelling of complex turbulent flow -expectations, reality and prospects

Chapter 4: MODELING FLOWS AROUND BLUFF BODIES BY REYNOLDS AVERAGED TRANSPORT EQUATIONS

Chapter 5: Subgrid-scale modeling suggested by a two-scale DIA

Chapter 6: Estimation of anisotropic k-ε model on the Backward-facing Step Flow by LES data base

Chapter 7: Numerical prediction of separating and reattaching flows with a modified low-Reynolds-number k-ε model

Chapter 8: Influence of the Turbulence Model in Calculations of Flow over Obstacles with Second-Moment Closures

Chapter 9: Finite-volume computation of merging parallel channel flows by a second-moment turbulence closure model

Chapter 10: Numerical Analysis of Wind around Building Using High-Speed GSMAC-FEM — Validation of Differential Stress Model —

Chapter 11: A computational study of the flow in a bluff body/flat plate junction

Chapter 12: Numerical simulation to determine the effects of incident wind shear and turbulence level on the flow around a building

Chapter 13: Numerical study of wind flow over an elevated roadway

Chapter 14: Appropriate boundary conditions for computational wind engineering models using the k-ε turbulence model

Chapter 15: Transport equations of conditionally averaged Reynolds stresses for computation of turbulent flows with intermittency

Chapter 16: Optimization of roughness parameters for staggered arrayed cubic blocks using experimental data

Chapter 17: Modelling of Turbulent Flows within Plant/Urban Canopies

Chapter 18: DISCUSSIONS OF TURBULENCE MODELLING AND THEIR APPLICATIONS

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. [the periodic fluctuation, f˙ the stochastic turbulent flucuation and 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

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

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 through the following eddy-viscosity relation:

(1)

The variation of the eddy viscosity 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, is calculated basically from the velocity gradient at a position where this gradient, weighted with the wall distance, reaches a maximum. In wake regions, 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 to the turbulent kinetic energy 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.

. 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 -equations are related to the equivalent terms in the -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 the walls. In this model, functions involving the viscosity and the wall distance appear which are absent in the standard k-ε model. Franke and Rodi [7] and Jansson [10] tested a two-layer approach in which, both in connection with the k-ε model and the RSE or ASM model, the viscous sublayer was resolved with a simpler one-equation model due to Norris and Reynolds [13]. In this, the velocity scale of the turbulent motion is also determined from the -equation, but the length scale is not determined from an <ε>-equation. Rather, the length-scale distribution is prescribed, and in particular a linear distribution is used which is damped near the wall as in the van Driest mixing-length model.

3 LES MODELS TESTED

In large-eddy simulations, the three-dimensional time-dependent Navier-Stokes equations are solved numerically; thereby all motions having scales larger than the mesh size are resolved, including the 2D periodic shedding fluctuations. This simulation does not distinguish between these fluctuations and the larger-scale turbulent stochastic fluctuations. Of course, the finer the numerical grid used, the finer is the scale of the motions that can be resolved. As was mentioned already, at low Reynolds numbers all fluctuating motions can be resolved, but not at high Reynolds numbers. The effect of the unresolved small-scale motion on the resolved larger-scale motion needs to be modelled. Tamura et al. [14] leave this simply to the damping effect of their third-order upwind scheme used for discretizing the convection terms. They do not call their method a large-eddy simulation technique but a direct finite-difference method, yet it is a quasi-LES technique because, at the higher Reynolds numbers considered by them, the small-scale motion could certainly not be resolved but only the larger-scale motion. With this approach, there is no direct control on the damping effect and this must be expected to depend on the grid employed. The approach produces surprisingly good results (see next section) but its implications are not clear and should be examined.

The more usual, and also considered more proper way to account for the effect of the unresolved small-scale motion is to simulate this with the aid of a subgrid-scale model. The 3D time-dependent Navier-Stokes equations solved represent equations averaged over the control volumes of the numerical grid or, what is equivalent, equations from which the small-scale motion has been filtered out. The averaging or filtering introduces correlations between the unresolved fluctuating velocities which act as stresses on the resolved motions and need to be simulated with a model. Models similar to the statistical turbulence models are in use, the main difference being that the length scale does not need to be determined but can be taken as the mesh size. Most common is the simple eddy-viscosity model due to Smagorinsky [15]. In this, the subgrid-scale eddy viscosity is related to the strain rate of the resolved motion and the mesh size. Murakami et al. [16, 17] employed the standard Smagorinsky model in their LES calculations.

Near the wall, especially in the viscous sublayer, the scales of the motions contributing most to the turbulent moment transfer is small and cannot be resolved in a large-eddy simulation at high Reynolds numbers. In most LES calculations at high Reynolds numbers, like the ones of Murakami et al. [16, 17], this region is not resolved at all but bridged by using a relation between the wall shear stress and the velocity at the first grid away from the wall. Murakami et al [16] used a relation based on the assumption of a logarithmic velocity distribution of the time-mean flow. Murakami et al [17] adopted Werner and Wengle′s [18] approach in which a linear (y+≤ 11.81) or 1/7 power law (y+≥ 11.81) distribution of the instantaneous velocity is assumed. It should be mentioned that Tamura et al. [14] did not introduce any special near-wall treatment in their quasi-LES calculations.

Tamura et al. [14] and Murakami et al. [16] report also on 2D LES calculations of vortex-shedding flow past cylinders. In these, the 2D time-dependent Navier-Stokes equations are solved and the damping effect of the unresolved small-scale motion is again left either to numerical damping [14] or is simulated with the Smagorinsky model [16]. Sung and Yuan [19] also report on 2D LES calculations of vortex-shedding flow past a circular cylinder using the Smagorinsky subgrid-scale model. As the turbulent motion and the essential vortex-stretching mechanism associated with this is always three-dimensional, an important ingredient is missing in 2D calculations and these are therefore not large-eddy simulations in the true sense. Spanwise turbulent structures have been observed in experiments and 3D LES calculations, and these can of course not be simulated in 2D calculations. These are rather like the 2D time-dependent calculations using statistical turbulence models, but the damping introduced by either the numerical scheme or the Smagorinsky subgrid-scale model is probably considerably smaller than that introduced by the statistical turbulence models and hence smaller-scale motions (not necessarily periodic) will appear when the grid is sufficiently fine. The calculation examples presented in the next section show that 3D LES calculations are clearly superior to 2D LES calculations. It should be added here that in the 2D calculations of Sung and Yuan [14], the boundary layer was not resolved at all as the grid used was coarser than the boundary-layer thickness. A mixture of slip, partial-slip and no-slip conditions was introduced to account for this, and the separation point was not predicted by their flow calculations but was put in through empirical relations.

4 CALCULATION EXAMPLES

In this section, calculations of vortex-shedding flows past cylinders of various geometries obtained with statistical turbulence models and LES techniques are presented and discussed. Some remarks on the accuracy of the procedures are in place here. For vortex-shedding calculations, the numerical accuracy of the scheme employed is of particular importance as it can introduce damping of the fluctuating motion. In Tamura et al.′s [14] quasi-LES calculations a certain amount of such damping is wanted and necessary since no model is introduced for the damping effect of the unresolved small-scale motion. However, in other calculations which simulate the damping effect of the turbulent motion through a special model (be it for the entire stochastic motion or only for the small-scale part of it), the introduction of numerical damping is undesirable. In some cases if was found that upwind differencing for the convection terms introduces so much numerical damping that vortex shedding could not be obtained and a steady solution resulted. Hence, discretization schemes of at least second-order accuracy have been used in most of the calculations reported. It should be noted, however, that other details of the numerical codes employed also influence the ability to produce and sustain a periodic shedding motion.

Detailed experimental data are crucial for the testing of simulation procedures. In the case of unsteady vortex-shedding flows, proper testing is possible only when time-resolved measurements are available which give information on the temporal variation of the ensemble-averaged quantities and separate the fluctuations into periodic and turbulent ones. To the author’s knowledge, only two experiments of this kind have been carried out, namely Lyn′s [20] LDA measurements of the flow past a square cylinder at Re = 22,000 (unfortunately not yet published) and Cantwell and Coles′ [6] flying hot-wire measurements of the flow past a circular cylinder at Re = 1.4 × 10⁵. The square-cylinder flow has the advantage that separation is fixed at the corners where also laminar-turbulent transition takes place, while for the flow around a circular cylinder the separation point has to be determined as part of the calculation, and transition of the laminar boundary layer before separation (supercritical flow) may have to be accounted for. Hence, the most detailed model testing was carried out for the square cylinder.

Flow past square cylinders.

Franke and Rodi [7] calculated the flow past a square cylinder at Re = 22,000 studied experimentally by Lyn [20] with the k-ε model and the RSE model, in both cases with wall functions and the two-layer approach in which the near-wall region is resolved with a one-equation model. At the suggestion of the author, Murakami et al. [17] performed calculations for the same test case with their 3D LES method, using the same calculation domain in the plane perpendicular to the cylinder as Franke and Rodi. This extends to 4.5D upstream of the cylinder, 14.5 D downstream and to 6.5 D on either side of the cylinder. In the span wise direction, the width of the calculation domain was 2D. 104 × 69 × 10 grid points were placed in the streamwise, lateral and spanwise directions, respectively. Grid lines were concentrated near the cylinder walls, and the distance of the first grid point from the wall was .022 D which is the same as in Franke and Rodi′s calculations when they employed wall functions. At the inflow boundary, the streamwise velocity was set at the uniform approach flow velocity and no velocity fluctuations were prescribed. At the outflow boundary, zero gradient conditions were imposed, on the upper and lower side boundaries symmetry conditions were employed, and for the boundary planes perpendicular to the cylinder periodicity conditions. The calculations required 150,000 time steps to reach periodic conditions and were then continued for another 100,000 time steps covering 13 shedding periods. The ensemble-averaged values were determined by ensemble-averaging over these 13 periods as well as averaging over the spanwise direction. The calculation took altogether 100 CPU hours on a Fujitsu VP 2600 (peak performance 2GFLOPS) machine. For comparison, the 2D calculations with a statistical turbulence model of Franke and Rodi [7] took 1/2 hour for the RSE model with wall functions and 5 hours for the two-layer RSE model on an IBM 3090 (scalar machine, peak performance 7 MFLOPS).

Franke and Rodi′s calculations with the k-ε model using wall functions yielded a steady solution and no vortex shedding. These calculations were carried out with an extended version of the program TEACH [21] employing a staggered grid. Bosch [22] has recently repeated the calculations with a newly developed code (2D version of the code described in [23]) which uses a non-staggered grid arrangement. He did obtain a sustained vortex-shedding solution. Periodic vortex shedding was also obtained by Franke and Rodi with the other three model variants and in Murakami et al’s [17] LES calculation. Values of various integral parameters predicted with the various calculation methods are compared in Table 1 with experimental values. The parameters considered are the dimensionless shedding frequency (Strouhal number St = fD/Uo), the time-mean drag coefficient cD and the amplitudes of the oscillations in drag coefficient cD and lift coefficient cL, indicated by a tilde. The k-ε model yielded too low shedding frequency and drag coefficient, while the RSE model with wall functions predicted these parameters in good agreement with the measurements. The LES calculations produced slightly lower values which are, however, still in fairly good agreement with the measurements. On the other hand, the two-layer RSE model predicted too high Strouhal number and drag coefficient. Consistent with the increase in cD is a reduction of the base pressure, as can be seen from Fig. 2. This figure compares the pressure distributions predicted with the various methods around the cylinder surface with measurements [24, 25] at somewhat higher Reynolds numbers. At the base (CD in Fig. 2) the LES calculations reproduce the measured cp-value of about −1.4 fairly well, while the k-ε model and the two-layer RSE model under- and overpredict cp, respectively. In the approaching stagnation flow (AB) there is fairly good agreement between all calculations and measurements. Along the side walls of the cylinder (BC) the difference between the measurements and the various calculations is considerably higher. There, both versions of the RSE model as well as the LES calculation underpredict the pressure, a fact that needs further examination.

Table 1

Integral Parameters

Fig. 2 Pressure distribution along surface of cylinder

Fig. 3 displays the distribution of the time-mean velocity ū along the centreline and gives information on the length of the time-averaged separation zone behind the cylinder. Experimental data due to Lyn [20] and Durao et al [26] are included. The data agree fairly well in the near-cylinder region, but the approach to the free-stream velocity is quite different for reasons that are not clear. In front of the cylinder, the results are again not much influenced by the calculation method used, but there are fairly large differences in the wake region. The k-ε model overpredicts the length of the separation zone considerably. This finding of Franke et al [7] is supported by Deng et al’s [3] calculations with the low-Re version of the k-ε model due to Nagano and Tagawa [12]. It appears that the k-ε model produces too little momentum exchange, which in vortex-shedding flow is mainly due to the periodic fluctuations. Hence, these are underpredicted. On the other hand, both RSE-model variants predict too short separation bubbles, and there is little difference between the results obtained with the two versions near the cylinder; there are larger differences further downstream which may, however, be partly due to the relatively coarse grid used in this region. The LES calculations underpredict the length of the separation region to a lesser extent, but the agreement with the data is not entirely satisfactory. Further downstream the velocity approaches the free-stream velocity in a similar way as predicted by the RSE model with wall functions. The best agreement with the distribution measured by Lyn was obtained by Deng et al [3ū-distribution is the only result available from these calculations, a full appraisal of the performance of this model would be premature.

Fig. 3 Time-mean velocity ū along centre-line

Fig. 4 presents the distribution of the total (periodic plus turbulent) fluctuating kinetic energy along the centreline. The two-layer k-ε model can be seen to underpredict severely the fluctuation level behind the cylinder, while the RSE models give approximately the correct level and distribution of the total fluctuations. The differences between the RSE calculations using wall functions and the two-layer approach are of the same order as the differences between the experimental values of Lyn [20] and Durao et al [26]. In front of the cylinder, the k-ε model yields an unrealistically high fluctuation level (here turbulent fluctuations) which is due to the now well known excessive k-production by this model in stagnation regions. The RSE model does not have this problem. The LES calculation predicts the correct distribution of the fluctuations, but the level is too low, in the region of the maximum by almost a factor of 2. In view of this, it is somewhat surprising that the LES calculations produce a somewhat too short mean separation zone. Franke and Rodi [7] have shown that all turbulence models tested by them produce too low turbulent fluctuations in the wake of the cylinder. For the RSE models this means that, because they produce the correct level of total fluctuations, the periodic fluctuations are overpredicted. The LES calculations produce a higher turbulent fluctuation level, which is nearly correct further downstream but is too low by about a factor of 2 in the peak region around x/D ≈ 2. Hence, both periodic and turbulent fluctuations are underpredicted in these simulations, but individually they are both closer to the measured levels than those produced by the RSE models.

Fig. 4 Total kinetic energy of fluctuations (periodic + turbulent) along centre-line

Fig. 5 shows the streamlines predicted by the RSE model using wall functions and by the LES simulation at three phases; at two of the phases experimentally determined streamlines are available and are also given. The streamlines predicted with the two-layer RSE model are not significantly different [27], and there is surprising agreement between the RSE-model and LES calculations. Both methods can be seen to predict the alternating vortex shedding in reasonable agreement with the measurements. However, certain differences can be noted. At some phases the predictions show a positive -velocity on the leeward side of the cylinder while the experiments indicate that the velocity is negative at all times. Also, both methods predict temporary reattachment of the separated flow on the side walls near the rear corner (e. g. phase 1, top side) which was not found in the experiments. This can be seen more clearly in Fig. 6 where the-velocity distribution at the x-position of the rear cylinder wall is given. Here, in addition to Lyn′s [20] two-channel measurements also Lyn′s [28] one-channel measurements extending closer to the wall are included. At the two phases considered (1 and 9), none of the calculations shows negative velocities on both walls, while in the experiments the velocity near the wall is always negative. The LES calculations are slightly worse than the RSE model calculations, which may be a resolution problem. Fig. 7 displays the variation of the ensemble-averaged lateral velocity along the centreline for phases 1 and 9. The agreement of both RSE-model and LES calculations with the measurements is fairly good. There are no significant differences here between the RSE model using wall functions and the two-layer approach, and the LES calculations are also fairly close. However, it is clear from this figure that the amplitude of the v-fluctuations is predicted smaller in the LES calculations than by the RSE models and, overall, appear to be in somewhat better agreement with the measurements.

Fig. 5 Streamlines at 3 phases (phase 1 = 1/20 T) phase 9 = 9/20 T, phase 17 = 17/20 T)

Fig. 6 Profiles of at x-location of rear cylinder wall for 2 phases