Frontiers of computational fluid dynamics 2006

Contents......Page 10
Dedication......Page 6
1.1 Introduction......Page 20
1.2 Shock Wave Structure and Sonic Boom......Page 21
1.3 Potential Flow Simulations......Page 22
1.4 Solutions of Euler Equations......Page 23
1.5 Solutions of Navier-Stokes Equations......Page 29
1.6 Simulation of Turbulent Reactive Flows......Page 32
1.7 Special Topics......Page 33
1.8 Review Articles......Page 34
1.9 Fluid Mechanics: An Interactive Text......Page 35
1.10 Concluding Remarks......Page 36
1-A Ph.D. Students Supervised by David A. Caughey......Page 38
1-B Publications of David A. Caughey......Page 40
I. Design and Optimization......Page 54
2.1 Introduction......Page 56
2.2 Flow Modeling for Fire Control Strategies and Scenario Planning in an Underground Road Tunnel......Page 57
2.3 Flow Modeling in a Hard Disk Drive Enclosure......Page 62
2.4 Concluding Remarks......Page 64
2.5 Bibliography......Page 65
3.1 Introduction......Page 68
3.2.1 Gradient Calculation......Page 71
3.3 Design using the Euler Equations......Page 74
3.4 The Reduced Gradient Formulation......Page 80
3.5.1 The Need for a Sobolev Inner Product in the Definition of the Gradient......Page 82
3.5.2 Sobolev Gradient for Shape Optimization......Page 84
3.5.3 Outline of the Design Procedure......Page 85
3.6.1 Two-Dimensional Studies of Transonic Airfoil Design......Page 86
3.6.2 B747 Euler Planform Result......Page 88
3.7 Super P51 Racer......Page 90
3.7.1 Shape Optimization for a Transonic Business Jet......Page 92
3.8 Conclusion......Page 94
3.10 Bibliography......Page 95
4.1 Introduction......Page 100
4.2 Formulation as a Control Problem......Page 101
4.2.1 Cost Functions for Propeller Blades......Page 102
4.2.2 Search Procedure......Page 103
4.4 Optimization of a Blade Section for Low Cav- it at ion......Page 105
4.4.1 Comparisons with Water Tunnel Measurements......Page 109
4.5 Conclusions......Page 113
4.6 Bibliography......Page 114
5.1 Introduction......Page 116
5.2 Geometry concept for 4-dimensional problems......Page 117
5.4 Adaptive configurations......Page 120
5.6 Bio-fluidmechanic applications......Page 121
5.8 Bibliography......Page 123
II. Algorithms and Accuracy......Page 124
6.1 Introduction......Page 126
6.2 Implicit schemes description......Page 127
6.3 Direct solver efficiency......Page 131
6.4 Implicit treatment description......Page 133
6.5 Iterative solver efficiency and stability......Page 139
6.6 Concluding remarks......Page 142
6.7 Bibliography......Page 145
7.1 Abstract......Page 148
7.2 Introduction......Page 149
7.3 Governing Equations in Arbitrary-Lagrangian-Eulerian (ALE) Form and Base Flow Solver......Page 150
7.4 Higher-order Time Integration and the Discrete Geometric Conservation Law......Page 151
7.5 Mesh Motion Strategies......Page 153
7.5.2 Linear elasticity analogy......Page 154
7.7 Mesh Motion Results......Page 156
7.7.1 Convergence of the mesh motion equations......Page 158
7.8.1 Multigrid Convergence Efficiency......Page 160
7.8.2 Time-Accuracy Validation......Page 163
7.9 Implicit-Runge-Kutta Methods for Dynamic Mesh Problems......Page 166
7.10 Conclusions......Page 170
7.12 Bibliography......Page 171
7-A The Geometric Convervation Law for BDF3......Page 174
8.1 Introduction......Page 180
8.2.1 Governing Equations......Page 181
Far field boundary and the perfectly matched layer......Page 182
8.4.2 Discretisation in space......Page 183
8.4.3 Computational details......Page 184
8.5 Numerical examples......Page 186
8.5.2 PEC almond......Page 187
8.6 Dealing with electrically larger scatterers......Page 188
8.6.1 Higher order Taylor-Galerkin time stepping schemes......Page 190
8.6.2 Higher order spatial discretisation......Page 192
8.7 Conclusions......Page 195
8.8 Bibliography......Page 197
9.1 Introduction......Page 202
9.2 Classification of Methods......Page 203
9.3 Overview of the Discrete Error Transport Equation......Page 205
9.4 DETEs for FV Solutions of the Euler Equations......Page 207
9.4.1 Finite-Volume Method of Solution......Page 208
9.4.2 DETE for the FV Method......Page 210
9.5.1 Test Problem 1: Inviscid Flow over an Airfoil......Page 211
9.5.2 Test Problem 2: Viscous Flow over an Iced Airfoil......Page 212
9.6 Final Remarks......Page 214
9.7 Bibliography......Page 215
10.1 Abstract......Page 218
10.2 Introduction......Page 219
10.2.1 Basic Concepts......Page 220
10.3 Illustrative One-Dimensional Example......Page 223
10.4 Vorticity Confinement......Page 226
10.4.1.1 VC1 Formulation......Page 229
10.4.1.2 VC2 Formulation......Page 230
10.4.1.3 Boundary Conditions......Page 231
10.4.2 Comparison of the VC2 Formulation to Conventional Discontinuity Steepening Schemes......Page 233
10.4.3 Computational Details for the VC2 Formulation......Page 234
10.5.1 Wing Tip Vortices......Page 236
10.5.2 Cylinder Wake......Page 237
10.5.3 Dynamic Stall......Page 238
10.6.2 Blade Vortex Interaction (BVI)......Page 239
10.7 Conclusions......Page 240
10.8 Acknowledgements......Page 241
10.9 Bibliography......Page 242
III. Flow Stability and Control......Page 258
11.1 Abstract......Page 260
11.2 Introduction......Page 261
11.3 CFD Flow-solvers Employed......Page 262
11.4 Results & Discussion......Page 263
11.6 Acknowledgments......Page 279
11.7 Bibliography......Page 281
12.1 Nomenclature......Page 284
12.2 Introduction......Page 285
12.3 Second Order Analytical Model of EMHD......Page 287
12.4 Least-Squares Finite Element Method......Page 288
12.4.1 Nondimensional First Order Form for Simplified EMHD......Page 289
12.4.2 Verification of Accuracy......Page 292
12.5 Numerical Results......Page 293
12.6 Conclusion......Page 296
12.8 Bibliography......Page 297
13.1 Introduction......Page 304
13.3 Analysis of the lift coefficient as a function of M......Page 305
13.4 Analysis of stability with respect to variation of......Page 308
13.6 Conclusion......Page 309
13.7 Bibliography......Page 310
14.1 Abstract......Page 316
14.2 Introduction......Page 317
14.3 The Euler Solver and the Flow Model......Page 321
14.4 Computational Grid and Boundary Conditions......Page 322
14.5.1 Temporal Asymmetric Perturbations......Page 325
14.5.2 Stationary Symmetric Vortex Flow......Page 326
14.5.3 Stability of the Stationary Symmetric Vortex Flow......Page 327
14.5.4 Stability of the Stationary Asymmetric Vortex Flow......Page 329
14.5.5 A Mirror-Image of the Asymmetric Vortex Flow......Page 330
14.5.6 Symmetry Nature of the Present Euler Solver......Page 332
14.5.8 Comparison with Experimental Data on Stability......Page 333
14.6.1 Computational Result......Page 334
14.6.2 Comparison with Experimental Data......Page 339
14.7 Summary and Conclusions......Page 341
14.8 Bibliography......Page 342
15.1 Introduction......Page 348
15.2 Singular inviscid pressure gradient......Page 349
15.3 Governing equations......Page 350
15.4 Inviscid sublayer 1......Page 351
15.6 Outer turbulent sublayer 3......Page 352
15.7 Pressure-dominated flow pattern......Page 353
15.9 Conclusion......Page 355
15.10 Bibliography......Page 356
16.1 Abstract......Page 360
16.3 Introduction......Page 361
16.4 Governing equations......Page 363
16.5 Plasma models......Page 365
16.6 Elect ro-Fluid-Dynamic Interact ion......Page 368
16.7 Magnet o-Fluid-Dynamic Interact ion......Page 373
16.8 Concluding Remarks......Page 378
16.10 Bibliography......Page 380
IV. Multiphase and Reacting Flows......Page 384
17.1 Abstract......Page 386
17.2 Introduction......Page 387
17.3.1 Thermodynamic Equilibrium Model [14]......Page 388
17.3.2 Two-fluid Model......Page 392
17.3.3 Multiphase Stratified Fluid Model......Page 395
17.3.4 Convection fluxes......Page 398
17.3.5 Pressure fluxes,......Page 399
17.3.6 The interfacial pressure correction term......Page 400
17.4.1 Ransom's faucet problem......Page 402
17.4.2 Air-water shock tube problem......Page 404
17.4.3 Shock-bubble interaction problem......Page 405
17.5 Concluding Remarks......Page 408
17.7 Bibliography......Page 410
17-A Numerical Flux Formulas......Page 413
18.1 Introduction......Page 414
18.2 Mat hematical Formulation......Page 416
18.3 Numerical Method......Page 418
18.3.1 Integration of the Flow Equations......Page 419
18.3.2 Front- Tracking Met hod......Page 421
18.3.3 The Overall Solution Procedure......Page 423
18.4 Results and Discussion......Page 424
18.4.1 Oscillating Drop......Page 425
18.4.2 Buoyancy-Driven Falling Drop in a Straight Channel......Page 426
18.4.3 Buoyancy-Driven Rising Drops in a Continuously Constricted Channel......Page 429
18.4.4 Chaotic Mixing in a Drop Moving through a Winding Channel......Page 432
18.5 Conclusions......Page 433
18.6 Bibliography......Page 434
18-A Optimal Artificial Compressibility in the Stokes Limit......Page 438
19.1 Introduction......Page 440
19.2 PDF Calculations of Turbulent Flames......Page 441
19.2.2 Lifted Jet Flame in a Vitiated Co-Flow......Page 442
19.3 Modelling of Turbulent Mixing......Page 444
19.5 Bibliography......Page 446
V. Education......Page 450
20.1 Introduction......Page 452
20.2 Course Overview......Page 453
20.3 Conceptual Understanding and Active Learning......Page 454
20.5 Project-based Learning......Page 457
20.5.1 Military Aircraft Design Project......Page 458
20.6.1 Effectiveness of Pedagogy......Page 459
20.6.2 Impact of Pre-Class Homework......Page 461
20.6.3 Student Comments......Page 463
20.7 Outlook......Page 464
20.9 Bibliography......Page 465