Contents 10
Dedication 6
Chapter 1 The Contributions of David Caughey to Computational Fluid Dynamics Mohamed M. Hafez 20
1.1 Introduction 20
1.2 Shock Wave Structure and Sonic Boom 21
1.3 Potential Flow Simulations 22
1.4 Solutions of Euler Equations 23
1.5 Solutions of Navier-Stokes Equations 29
1.6 Simulation of Turbulent Reactive Flows 32
1.7 Special Topics 33
1.8 Review Articles 34
1.9 Fluid Mechanics: An Interactive Text 35
1.10 Concluding Remarks 36
1-A Ph.D. Students Supervised by David A. Caughey 38
1-B Publications of David A. Caughey 40
I. Design and Optimization 54
Chapter 2 Computational Fluid Dynamics in the Analysis and Design of Engineered Systems M. Damodaran, S. Alil and S. Dayanandan 56
2.1 Introduction 56
2.2 Flow Modeling for Fire Control Strategies and Scenario Planning in an Underground Road Tunnel 57
2.3 Flow Modeling in a Hard Disk Drive Enclosure 62
2.4 Concluding Remarks 64
2.5 Bibliography 65
Chapter 3 Advances in Aerodynamic Shape Optimization Antony Jameson 68
3.1 Introduction 68
3.2 Formulation of the Optimization Procedure 71
3.2.1 Gradient Calculation 71
3.3 Design using the Euler Equations 74
3.4 The Reduced Gradient Formulation 80
3.5 Optimization Procedure 82
3.5.1 The Need for a Sobolev Inner Product in the Definition of the Gradient 82
3.5.2 Sobolev Gradient for Shape Optimization 84
3.5.3 Outline of the Design Procedure 85
3.6 Case Studies 86
3.6.1 Two-Dimensional Studies of Transonic Airfoil Design 86
3.6.2 B747 Euler Planform Result 88
3.6.3 Super B747 90
3.7 Super P51 Racer 90
3.7.1 Shape Optimization for a Transonic Business Jet 92
3.8 Conclusion 94
3.9 Acknowledgment 95
3.10 Bibliography 95
Chapter 4 Design Optirnization of Propeller Blades Luigi Martinellil and James. Dreyer 100
4.1 Introduction 100
4.2 Formulation as a Control Problem 101
4.2.1 Cost Functions for Propeller Blades 102
4.2.2 Search Procedure 103
4.3 Implement at ion 105
4.4 Optimization of a Blade Section for Low Cav- it at ion 105
4.4.1 Comparisons with Water Tunnel Measurements 109
4.5 Conclusions 113
4.6 Bibliography 114
Chapter 5 Flow Boundary Conditions Modeling in 4D for Optimized, Adaptive and Unsteady Configurations Helmut Sobieczky 116
5.1 Introduction 116
5.2 Geometry concept for 4-dimensional problems 117
5.3 Optimization 120
5.4 Adaptive configurations 120
5.5 Unsteady boundary conditions 121
5.6 Bio-fluidmechanic applications 121
5.7 Conclusion 123
5.8 Bibliography 123
II. Algorithms and Accuracy 124
Chapter 6 Stability and Efficiency of Implicit Residual-Based Compact Schemes C. Corre & A. Lerat 126
6.1 Introduction 126
6.2 Implicit schemes description 127
6.3 Direct solver efficiency 131
6.4 Implicit treatment description 133
6.5 Iterative solver efficiency and stability 139
6.6 Concluding remarks 142
6.7 Bibliography 145
Chapter 7 Higher- Order Time-Integration Schemes for Dynamic Unstructured Mesh CFD Simulations Dimitri J. Mavriplis and Zhi Yang 148
7.1 Abstract 148
7.2 Introduction 149
7.3 Governing Equations in Arbitrary-Lagrangian-Eulerian (ALE) Form and Base Flow Solver 150
7.4 Higher-order Time Integration and the Discrete Geometric Conservation Law 151
7.5 Mesh Motion Strategies 153
7.5.1 Tension spring analogy 154
7.5.2 Linear elasticity analogy 154
7.6 Acceleration Strategies 156
7.7 Mesh Motion Results 156
7.7.1 Convergence of the mesh motion equations 158
7.8 Unsteady Flow Simulations using Backwards Difference Schemes 160
7.8.1 Multigrid Convergence Efficiency 160
7.8.2 Time-Accuracy Validation 163
7.9 Implicit-Runge-Kutta Methods for Dynamic Mesh Problems 166
7.10 Conclusions 170
7.11 Acknowledgments 171
7.12 Bibliography 171
7-A The Geometric Convervation Law for BDF3 174
Chapter 8 Explicit Time Domain Finite Element Methods for Electromagnetics Kenneth Morgan, Mohamed El hachemi, Oubay Hassan, and Nigel Weatherill 180
8.1 Introduction 180
8.2 Electromagnetic Scattering 181
8.2.1 Governing Equations 181
8.2.2 Boundary conditions 182
Perfect electrical conductor surface 182
Far field boundary and the perfectly matched layer 182
8.3 Mesh generation 183
8.4 Numerical solution algorithm 183
8.4.1 Time discretisation 183
8.4.2 Discretisation in space 183
8.4.3 Computational details 184
8.5 Numerical examples 186
8.5.1 PEC sphere 187
8.5.2 PEC almond 187
8.6 Dealing with electrically larger scatterers 188
8.6.1 Higher order Taylor-Galerkin time stepping schemes 190
8.6.2 Higher order spatial discretisation 192
8.7 Conclusions 195
8.8 Bibliography 197
Chapter 9 Estimating Grid-Induced Errors in CFD Solutions T. I-P. Shih 202
9.1 Introduction 202
9.2 Classification of Methods 203
9.3 Overview of the Discrete Error Transport Equation 205
9.4 DETEs for FV Solutions of the Euler Equations 207
9.4.1 Finite-Volume Method of Solution 208
9.4.2 DETE for the FV Method 210
9.5 Usefulness of the DETEs 211
9.5.1 Test Problem 1: Inviscid Flow over an Airfoil 211
9.5.2 Test Problem 2: Viscous Flow over an Iced Airfoil 212
9.6 Final Remarks 214
9.7 Bibliography 215
Chapter 10 Treatment of Vortical Flow Using Vorticity Confinement John Steinhoff & Nicholas Lynn 218
10.1 Abstract 218
10.2 Introduction 219
10.2.1 Basic Concepts 220
10.3 Illustrative One-Dimensional Example 223
10.4 Vorticity Confinement 226
10.4.1 Basic Formulation 229
10.4.1.1 VC1 Formulation 229
10.4.1.2 VC2 Formulation 230
10.4.1.3 Boundary Conditions 231
10.4.2 Comparison of the VC2 Formulation to Conventional Discontinuity Steepening Schemes 233
10.4.3 Computational Details for the VC2 Formulation 234
10.5 Results 236
10.5.1 Wing Tip Vortices 236
10.5.2 Cylinder Wake 237
10.5.3 Dynamic Stall 238
10.6 Other Studies 239
10.6.1 Missile Base Drag Computation 239
10.6.2 Blade Vortex Interaction (BVI) 239
10.6.3 Turbulent Flow Simulations for Special Effects 240
10.7 Conclusions 240
10.8 Acknowledgements 241
10.9 Bibliography 242
III. Flow Stability and Control 258
Chapter 11 Flow Control Applications with Synthetic and Pulsed Jets R. Agarwal, J. Vadillo, Y. Tan, J. Cui, D. Guo, H. Jain A. W. Cary & W. W. Bower 260
11.1 Abstract 260
11.2 Introduction 261
11.3 CFD Flow-solvers Employed 262
11.4 Results & Discussion 263
11.5 Conclusions 279
11.6 Acknowledgments 279
11.7 Bibliography 281
Chapter 12 Control of Flow Separation over a Circular Cylinder Using Electro-Magnetic Fields: Numerical Simulation Brian H. Dennis and George S. Dulikravich 284
12.1 Nomenclature 284
12.2 Introduction 285
12.3 Second Order Analytical Model of EMHD 287
12.4 Least-Squares Finite Element Method 288
12.4.1 Nondimensional First Order Form for Simplified EMHD 289
12.4.2 Verification of Accuracy 292
12.5 Numerical Results 293
12.6 Conclusion 296
12.7 Acknowledgements 297
12.8 Bibliography 297
Chapter 13 Bifurcation of Transonic Flow Over a Flattened Airfoil Alexander G. Kuz\u2019min 304
13.1 Introduction 304
13.2 Problem statement and a numerical method 305
13.3 Analysis of the lift coefficient as a function of M 305
13.4 Analysis of stability with respect to variation of 308
13.5 Summary of the results 309
13.6 Conclusion 309
13.7 Bibliography 310
Chapter 14 Study of Stability of Vortex Pairs over a Slender Conical Body by Euler Computations Jinsheng Cai, Her-Mann Tsai, Shijun Luo, and Feng Liu 316
14.1 Abstract 316
14.2 Introduction 317
14.3 The Euler Solver and the Flow Model 321
14.4 Computational Grid and Boundary Conditions 322
14.5 Stationary Symmetric and Asymmetric Solutions and Their Stability 325
14.5.1 Temporal Asymmetric Perturbations 325
14.5.2 Stationary Symmetric Vortex Flow 326
14.5.3 Stability of the Stationary Symmetric Vortex Flow 327
14.5.4 Stability of the Stationary Asymmetric Vortex Flow 329
14.5.5 A Mirror-Image of the Asymmetric Vortex Flow 330
14.5.6 Symmetry Nature of the Present Euler Solver 332
14.5.7 Comparison with Theoretical Predictions on Stability 333
14.5.8 Comparison with Experimental Data on Stability 333
14.6 Structure of the Vortex Core 334
14.6.1 Computational Result 334
14.6.2 Comparison with Experimental Data 339
14.7 Summary and Conclusions 341
14.8 Bibliography 342
Chapter 15 Effect of Upstream Conditions on Velocity Deficit Profiles of the Turbulent Boundary Layer at Global Separation Oleg S. Ryzhov 348
15.1 Introduction 348
15.2 Singular inviscid pressure gradient 349
15.3 Governing equations 350
15.4 Inviscid sublayer 1 351
15.5 Outer turbulent sublayer 2 352
15.6 Outer turbulent sublayer 3 352
15.7 Pressure-dominated flow pattern 353
15.8 Comparison with experiment 355
15.9 Conclusion 355
15.10 Bibliography 356
Chapter 16 Hypersonic Magnet o-Fluid-Dynamic Interact ions J. S. Shang 360
16.1 Abstract 360
16.2 Nomenclature 361
16.3 Introduction 361
16.4 Governing equations 363
16.5 Plasma models 365
16.6 Elect ro-Fluid-Dynamic Interact ion 368
16.7 Magnet o-Fluid-Dynamic Interact ion 373
16.8 Concluding Remarks 378
16.9 Acknowledgment 380
16.10 Bibliography 380
IV. Multiphase and Reacting Flows 384
Chapter 17 Computing Multiphase Flows Using AUSM+-up Scheme Meng-Sing Liou and Chih-Hao Chang 386
17.1 Abstract 386
17.2 Introduction 387
17.3 Governing Equations (Models) for Multiphase Flows 388
17.3.1 Thermodynamic Equilibrium Model [14] 388
17.3.2 Two-fluid Model 392
17.3.3 Multiphase Stratified Fluid Model 395
17.3.4 Convection fluxes 398
17.3.5 Pressure fluxes, 399
17.3.6 The interfacial pressure correction term 400
17.4 Calculated Examples and Discussion 402
17.4.1 Ransom's faucet problem 402
17.4.2 Air-water shock tube problem 404
17.4.3 Shock-bubble interaction problem 405
17.4.4 Shock-water column interaction problem 408
17.5 Concluding Remarks 408
17.6 Acknowledgments 410
17.7 Bibliography 410
17-A Numerical Flux Formulas 413
Chapter 18 A Finite-Volume Front-Tracking Method for Computations of Multiphase Flows in Complex Geometries Metin Muradoglu 414
18.1 Introduction 414
18.2 Mat hematical Formulation 416
18.3 Numerical Method 418
18.3.1 Integration of the Flow Equations 419
18.3.2 Front- Tracking Met hod 421
18.3.3 The Overall Solution Procedure 423
18.4 Results and Discussion 424
18.4.1 Oscillating Drop 425
18.4.2 Buoyancy-Driven Falling Drop in a Straight Channel 426
18.4.3 Buoyancy-Driven Rising Drops in a Continuously Constricted Channel 429
18.4.4 Chaotic Mixing in a Drop Moving through a Winding Channel 432
18.5 Conclusions 433
18.6 Bibliography 434
18-A Optimal Artificial Compressibility in the Stokes Limit 438
Chapter 19 Computational Modeling of Turbulent Flames Stephen B. Pope 440
19.1 Introduction 440
19.2 PDF Calculations of Turbulent Flames 441
19.2.1 Piloted Jet Flames 442
19.2.2 Lifted Jet Flame in a Vitiated Co-Flow 442
19.3 Modelling of Turbulent Mixing 444
19.4 Acknowledgment 446
19.5 Bibliography 446
V. Education 450
Chapter 20 Educating the fiture: Impact of Pedagogical Reform in Aerodynamics David L. Darmofal 452
20.1 Introduction 452
20.2 Course Overview 453
20.3 Conceptual Understanding and Active Learning 454
20.4 Integration of Theory, Computation, and Experiment 457
20.5 Project-based Learning 457
20.5.1 Military Aircraft Design Project 458
20.5.2 Blended-Wing Body Design Project 459
20.6 Results 459
20.6.1 Effectiveness of Pedagogy 459
20.6.2 Impact of Pre-Class Homework 461
20.6.3 Student Comments 463
20.7 Outlook 464
20.8 Acknowledgements 465
20.9 Bibliography 465