Progress in Wall Turbulence: Understanding and Modeling (eBook)

Foreword 6
Preface 8
Acknowledgements 9
Contents 10
Contributors 15
The WALLTURB Project 22
Invited Speakers 27
The Law of the Wall. Indications from DNS, and Opinion 29
Classical Position 30
Mean Velocity 30
Other Quantities 31
Behavior of Turbulence Models 32
Alternative Analytical Proposals 32
Conflicting Experiments 33
Proposals of Non-uniqueness 34
Essence of the Proposals 34
Conceptual Consequences 35
A Situation with Log Laws and Erratic kappa Values 35
DNS Evidence 37
Logarithmic Law 37
Law of the Wall 38
Response to Pressure Gradients 38
Highlights 39
References 40
A Web-Services Accessible Turbulence Database and Application to A-Priori Testing of a Matrix Exponential Subgrid Model 41
Introduction: The Web-Accessible Public Turbulence Database 41
The Matrix Exponential Subgrid Model for LES 42
Database-Enabled A-Priori Tests 45
Conclusions 47
References 47
Modeling Multi-point Correlations in Wall-Bounded Turbulence 48
Introduction 48
Multi-point Correlations and LES 50
Modeling Anisotropy in Wall-Bounded Turbulence 52
Discussion 54
References 55
Theoretical Prediction of Turbulent Skin Friction on Geometrically Complex Surfaces 57
Introduction 57
Mathematical Formulation 59
Skin Friction Coefficient 59
Application of the Formula to Surface Riblets 61
Componential Contributions 61
Drag Reduction 62
Straight Riblets 63
Wavy Riblets 64
Conclusions 64
Appendix 66
References 67
Scaling Turbulent Fluctuations in Wall Layers 68
Introduction 68
Composite Expansions 69
Reynolds Shear Stress 69
Vorticity Fluctuations 69
Outer Vorticity 70
Inner Vertical Vorticity 71
Inner Spanwise Vorticity 71
Inner Streamwise Vorticity 73
Outer Vorticity and Dissipation 74
Normal Reynolds Stresses 74
Vertical Velocity Fluctuations 74
Streamwise Velocity Fluctuations 75
Spanwise Velocity Fluctuations 76
Summary 78
References 79
Session 1: The WALLTURB LML Experiment 80
The WALLTURB Joined Experiment to Assess the Large Scale Structures in a High Reynolds Number Turbulent Boundary Layer 82
Introduction 83
Experimental Setup 83
Samples results 87
Conclusions 89
References 90
Calibration of the WALLTURB Experiment Hot Wire Rake with Help of PIV 91
Introduction 92
Wires Location 92
Blockage Effect 94
Calibration 97
Conclusion 99
References 100
Spatial Correlation from the SPIV Database of the WALLTURB Experiment 101
Introduction 101
Experimental Setup 102
SPIV System 103
PIV Analysis 104
Spatial Correlation 105
2D Correlations 105
3D Correlations 105
Conclusion 107
References 108
Two-Point Correlations and POD Analysis of the WALLTURB Experiment Using the Hot-Wire Rake Database 110
Two-Point Correlations of WALLTURB Experiments 111
Proper Orthogonal Decomposition 111
Eigenvalue Distribution over POD Modes 112
Eigenvalue Distribution over POD and Spanwise Fourier Modes 113
Reconstruction of Velocity Field 114
Discussion and Summary 116
References 117
Session 2: Experiments in Flat Plate Boundary Layers 118
Reynolds Number Dependence of the Amplitude Modulated Near-Wall Cycle 120
Introduction 120
Quantifying Amplitude Modulation 121
Experiments 123
Variations with Reynolds Number 123
References 126
Tomographic Particle Image Velocimetry Measurements of a High Reynolds Number Turbulent Boundary Layer 128
Introduction 128
Experimental Procedure 130
Volume Reconstruction and PIV Processing 131
Results 132
Conclusion 134
References 134
Study of Vortical Structures in Turbulent Near-Wall Flows 136
Introduction 136
Description of the Database 137
Average Properties of the Database 137
Detection Technique 139
Results: Characteristics of the Vortices 140
Density of the Vortices 140
Radius of the Vortices 141
Vorticity of the Vortices 143
Conclusion 145
References 145
Session 3: Experiments in Adverse Pressure Gradient Boundary Layers 147
Two-Point Near-Wall Measurements of Velocity and Wall Shear Stress Beneath a Separating Turbulent Boundary Layer 149
Introduction 149
Measurement Techniques 150
Results 152
Mean Wall Shear Stress, Mean Velocity and Reynolds Stresses 152
Velocity-Wall-Shear-Stress Correlation 153
Time-Lag Correlations 155
References 156
Experimental Analysis of Turbulent Boundary Layer with Adverse Pressure Gradient Corresponding to Turbomachinery Conditions 157
Introduction 157
Experimental Setup and Measuring Techniques 158
Experimental Results and Scaling of TBL 160
Conclusion 163
References 164
Near Wall Measurements in a Separating Turbulent Boundary Layer with and without Passive Flow Control 165
Introduction 165
Experimental Apparatus and Methodology 166
Measurement Technique and Experiment Organization 167
Results and Discussion 168
Dissipation Mechanism 168
Three-Dimensional Effect of VGs 170
Conclusion 172
References 173
Session 4: Boundary Layer Structure and Scaling 174
On the Relationship Between Vortex Tubes and Sheets in Wall-Bounded Flows 176
Introduction 176
Statistical Analysis 177
Conditional Expected Fields 178
Conclusions 183
References 184
Spanwise Characteristics of Hairpin Packets in a Turbulent Boundary Layer Under a Strong Adverse Pressure Gradient 185
Introduction 185
Experimental Procedure 187
Results and Discussion 190
References 193
The Mesolayer and Reynolds Number Dependencies of Boundary Layer Turbulence 194
Historical Context 194
Spectra at Rtheta= 19,100 197
Summary and Conclusions 200
References 201
A New Wall Function for Near Wall Mixing Length Models Based on a Universal Representation of Near Wall Turbulence 202
Introduction 202
Vortices Properties in the TBL 203
Universal Representation 203
Wall Function Model 206
Channel Flow Validation 207
Conclusion 209
References 210
Session 5: DNS and LES 211
Direct Numerical Simulations of Converging-Diverging Channel Flow 213
Introduction 213
Description of the DNS 214
Results 215
Conclusions 218
References 219
Corrections to Taylor's Approximation from Computed Turbulent Convection Velocities 220
Introduction 220
The Estimation of the Convection Velocities 221
Spectral and Spatial Dependence of the Convection Velocity 222
The Effect of Taylor's Approximation 223
Conclusions 226
References 226
A Multi-scale & Dynamic Method for Spatially Evolving Flows
Introduction 229
Formulation of the Problem and Methodology 230
The Rescaling-Recycling Method: The Multi-scale Similarity Approach 230
Dynamic Approach 233
Results and Discussion 233
Conclusions 235
References 235
Statistics and Flow Structures in Couette-Poiseuille Flows 237
Introduction 237
Numerical Methodology 238
Mean and Fluctuating Properties 240
Turbulence Structure near the Moving Wall 241
Conclusions 243
References 243
Session 6: Theory 245
LES-Langevin Approach for Turbulent Channel Flow 247
Introduction 247
LES-Langevin Model for Wall Turbulence 248
Estimation of Stochastic Forcing in the Case of Channel Flow 250
A Priori Tests 250
The Filter and Spatial Resolution Dependence of the Stochastic Forcing and the Turbulent Force 251
Time Scale Separation 251
Results and Discussions 252
Conclusion 254
References 255
A Scale-Entropy Diffusion Equation for Wall Turbulence 257
Introduction 257
Scale-Entropy Diffusion Equation 258
Experimental Measurement of Structure Functions, Scaling Exponents and Intermittency Efficiency 259
Detection of Structures by a Thresholding Procedure of Velocity Fluctuations 259
The Notion of Equivalent Dispersion Scale 261
Conclusion 263
References 264
A Specific Behaviour of Adverse Pressure Gradient Near Wall Flows 265
Introduction 265
LML Experiment 266
LML Direct Numerical Simulation 266
Literature Data 268
Discussion 268
Conclusion 271
References 272
Session 7: RANS Modelling 274
A Nonlinear Eddy-Viscosity Model for Near-Wall Turbulence 276
Introduction 276
Mathematical Modeling 278
The Linear V2F Model 278
The Nonlinear V2F Model (NLV2F) 279
Results and Discussion 279
Experimental and Numerical Reference Data 280
Model Results and Discussion 281
Concluding Remarks 283
References 283
ASBM-BSL: An Easy Access to the Structure Based Model Technology 284
Introduction 284
ASBM Modelling 285
Coupling with a k - omega Model 288
Validation Results 288
Conclusions and Perspectives 291
References 292
Introduction of Wall Effects into Explicit Algebraic Stress Models Through Elliptic Blending 293
Introduction 293
Explicit Algebraic Methodology 294
Invariant and Functional Integrity Bases 295
Truncated Bases 296
Validation of the Models 298
Conclusions 302
References 302
Session 8: Dynamical Systems 304
POD Based Reduced-Order Model for Prescribing Turbulent Near Wall Unsteady Boundary Condition 306
Introduction 307
POD Analysis and Modelling Strategy 307
Flow Reconstruction and Coupling with LES 309
Low-Order Dynamical Systems 311
Conclusions and Perspectives 312
References 313
A POD-Based Model for the Turbulent Wall Layer 314
Introduction 314
Characteristics of the Direct Numerical Simulation 315
The Proper Orthogonal Decomposition 315
Derivation Hypotheses 316
Model Validation 316
Influence of the Calibration Procedure 318
Conclusion 320
References 320
HR SPIV for Dynamical System Construction 322
Introduction 322
Experimental Setup 323
HR SPIV System 323
PIV Analysis 326
Space-Time Correlations 327
Conclusion 330
References 331
The Stagnation Point Structure of Wall-Turbulence and the Law of the Wall in Turbulent Channel Flow 332
Introduction 332
Conventional Results of DNS of Turbulent Channel Flow 333
The Stagnation Point Approach 335
Consequences of the Constancies of B1 & Cs
Conclusion 339
References 339
Session 9: Large Eddy Simulation 340
Wall Modelling for Implicit Large Eddy Simulation of Favourable and Adverse Pressure Gradient Flows 342
Introduction 342
Numerical Method and Wall Modelling 344
Cut-Cell Finite-Volume IB Method 344
Wall Model on IB Boundary 345
Validation and Application 346
Validation for Turbulent Channel Flow 346
Application to Bump Flow 349
Conclusion 350
References 350
LES of Turbulent Channel Flow with Pressure Gradient Corresponding to Turbomachinery Conditions 352
Introduction 352
Numerical Procedure 353
Analysis of the Results 355
Conclusions 358
References 359
LES Modeling of Converging Diverging Turbulent Channel Flow 360
Introduction 360
Numerical Code 361
Subgrid-Scale Models 362
Test Case Description 363
Results 364
Conclusions 367
References 368
Large-Scale Organized Motion in Turbulent Pipe Flow 369
Introduction 369
Flow Facility, Experimental Setup, and PIV Processing 370
Discussion of First Results 372
Outlook 376
References 376
Session 10: Skin Friction 378
Near-Wall Measurements and Wall Shear Stress 380
Introduction 380
Very Near Wall Measurements Using LDA 382
Analysis of Bias in Near Wall Measurements 383
Momentum Integral Method 384
Conclusions 386
References 387
Measurements of Near Wall Velocity and Wall Stress in a Wall-Bounded Turbulent Flow Using Digital Holographic Microscopic PIV and Shear Stress Sensitive Film 388
Introduction 388
Wall Shear Stress Sensor 389
Sensor Calibration and Application 390
Experimental Setup 391
Results and Discussion 392
Velocity Profile Measurement 392
Conclusion 394
References 395
Friction Measurement in Zero and Adverse Pressure Gradient Boundary Layer Using Oil Droplet Interferometric Method 396
Introduction 396
Oil Film Interferometric Method 396
Oil Droplet Interferometric Method 400
Test Surface 401
Experimental Tests: ZPG and APG Cases 401
Conclusion 404
References 404
Session 11: Modified Wall Flow 406
Scaling of Turbulence Structures in Very-Rough-Wall Channel Flow 408
Introduction 408
Experimental Technique 409
Results and Discussion 411
Conclusions 414
References 415
Characterizing a Boundary Layer Flow for Bubble Drag Reduction 416
Review of Work on Drag Reduction by Air Bubbles 416
Preparation of a Zero Pressure Gradient Developing Boundary Layer 419
Outlook 421
References 422
Direct and Large Eddy Numerical Simulations of Turbulent Viscoelastic Drag Reduction 424
Direct Numerical Simulations (DNS) 425
DNS Model Equations 425
Numerical Method 426
DNS Results 426
Temporal Large Eddy Simulations (TLES) 427
TLES Model Equations 428
TLES Results at Retau0=180 430
References 431
DNS of Supercritical Carbon Dioxide Turbulent Channel Flow 432
Introduction 432
Numerical Method 433
Turbulence Statistics 434
Turbulent Kinetic Energy Budget 435
Heat Transfer Characteristics 436
Summary 438
References 439
Session 12: Industrial Modeling 440
Evaluation of v2-f and ASBM Turbulence Models for Transonic Aerofoil RAE2822 442
Introduction 442
Turbulence Model Selection and Test on Channel and Flat Plate 444
Results for RAE2822 Aerofoil 446
Conclusions 451
References 451
Turbulence Modelling Applied to Aerodynamic Design 454
Introduction 454
Reynolds Averaged Navier-Stokes Modelling 455
Reynolds Stress Modelling 459
LES/DES Modelling 461
Conclusions and Perspectives 464
References 465