Numerical Simulation of Reactive Flow

Cover......Page 1
About......Page 2
Numerical Simulation ofReactive Flow, Second edition......Page 4
Copyright - ISBN: 0521581753......Page 5
Contents......Page 8
Prologue......Page 16
1-1. Some Comments on Terminology......Page 22
1-2. A Classification of Models......Page 24
1-3. Statistical Averaging or Chunking......Page 25
1-4. The Hierarchy of Levels of Simulation......Page 26
1-5. The Growth of Computational Capability......Page 29
1-6. The Tyranny of Numbers......Page 31
1-7. A Bridge between Theory and Experiment......Page 32
1-8. Themes of This Book......Page 34
References......Page 35
2-1.1. Time-Dependent Conservation Equations......Page 36
2-1.2. Physical Phenomena Represented in the Equations......Page 40
2-1.4. Equations of State......Page 42
2-2.1. Convective Transport......Page 44
2-2.2. Reaction Kinetics......Page 46
2-2.3. Diffusive Transport......Page 47
2-2.4. Radiation Transport......Page 48
2-2.5. Wavelike Behavior......Page 49
2-3.1. Dimensionless Numbers......Page 50
2-3.2. Specific Interactions......Page 53
2-4.1. Interactions among Phases......Page 55
2-4.2. An Example of Multiphase Flow Equations......Page 56
2-4.3. The Complexity of Multiphase Models......Page 57
2-5. Finding Input Data......Page 58
References......Page 59
3 Models and Simulation......Page 61
3-1.1. Posing Scientific Problems for Modeling......Page 62
3-1.2. Selecting the Computer System to Use......Page 63
3-1.3. Choosing the Computational Representation......Page 65
3-2. Limiting Factors and Constraints......Page 66
3-2.1. Limitations in Accuracy......Page 67
3-2.2. The Costs of Complexity......Page 69
3-2.3. Using Phenomenological Models......Page 71
3-3.1. Trade-Offs in Selecting and Optimizing Models......Page 73
3-3.2. Steps in Constructing a Simulation Model......Page 74
3-3.3. Testing Programs and Models......Page 76
3-4.1. Partitioning Time among Tasks......Page 79
3-4.2. Documenting and Retrieving Results of Simulations......Page 80
3-4.3. Some General Programming Guidelines......Page 81
3-5.1. Parallel Processing: The Future of Large-Scale Scientific Computing?......Page 85
3-5.2. Programming for Parallel Computers......Page 86
References......Page 89
4 Some General Numerical Considerations......Page 91
4-1.1. Discretizing Time and Space......Page 92
4-1.2. Advancing Equations in Time and Space......Page 94
4-1.3. Qualitative Properties of Numerical Algorithms......Page 96
4-1.4. Approaches to Analyzing Accuracy......Page 98
4-1.5. Types of Finite-Difference Errors......Page 100
4-2.1. Explicit and Implicit Solutions......Page 103
4-2.2. Asymptotic Solutions......Page 107
4-3.1. The Diffusion Equation......Page 109
4-3.2. An Analytic Solution: Decay of a Periodic Function......Page 110
4-3.3. Explicit and Implicit Solutions......Page 111
4-3.5. Physical Diffusion and Numerical Diffusion......Page 114
4-4.1. Fluid Dynamic Flows: Advection and Compression......Page 115
4-4.2. The Square-Wave Test Problem......Page 117
4-4.3. Explicit and Implicit Solutions......Page 118
4-4.4. Phase and Amplitude Errors for Common Algorithms......Page 122
4-5.1. Waves from Coupling Continuity Equations......Page 125
4-5.2. An Explicit Staggered Leapfrog Algorithm......Page 126
4-5.3. A Reversible Implicit Algorithm......Page 129
4-5.4. Reversibility, Stability, and Accuracy......Page 130
4-6. Approaches to Coupling the Terms......Page 131
References......Page 133
5 Ordinary Differential Equations: Reaction Mechanisms and Other Local Phenomena......Page 135
5-1.1. The Initial Value Problem......Page 136
5-1.2. Accuracy, Convergence, and Stability......Page 137
5-1.3. Stiff Ordinary Differential Equations (ODEs)......Page 141
5-2.1. One-Step Methods......Page 143
5-2.2. Linear Multistep Methods......Page 144
5-2.3. Extrapolation Methods......Page 147
5-2.4. Leapfrog Integration Methods......Page 148
5-3.1. Stability and Stiff ODEs.......Page 150
5-3.2. Implicit Methods for Stiff ODEs......Page 152
5-3.3. Useful Methods for Solving of Stiff ODEs......Page 153
5-3.4. Summary: Some Important Issues......Page 159
5-4. Useful Information and Techniques......Page 160
5-4.1. Solving Temperature Equations......Page 161
5-4.2. Sensitivity Analysis......Page 162
5-4.3. Integration Packages for Solving ODEs......Page 166
5-5. Reduced Reaction Mechanisms for Reactive Flows......Page 170
5-5.1. The Induction Parameter Model......Page 171
5-5.2. Computational Singular Perturbations......Page 172
5-5.3. Intrinsic Low-Dimensional Manifolds......Page 174
References......Page 175
6-1. Representations of Convective Flows......Page 180
6-1.1. Why Convection Is Difficult to Simulate......Page 181
6-1.2. The Continuity Equation......Page 182
6-1.3. Lagrangian versus Eulerian Representations......Page 183
6-2. Discretizing a Continuous Variable......Page 184
6-2.1. Grid-Based Representations......Page 185
6-2.2. Eulerian Grid Representations......Page 186
6-2.3. Expansion and Spectral Representations......Page 189
6-2.4. Lagrangian and Unstructured Grid Representations......Page 191
6-2.5. Macroparticle Representations......Page 192
6-3. Gridding to Represent Complex Geometry......Page 194
6-3.1. Eulerian, Body-Fitted Grids......Page 195
6-3.2. Overset Grids......Page 197
6-3.3. Unstructured Grids......Page 199
6-3.4. Globally Structured Cartesian Grids......Page 201
6-4.1. Strategies for Refining and Coarsening a Grid......Page 204
6-4.2. Adaptive Mesh Redistribution on Multidimensional Cartesian Grids......Page 208
6-4.3. Adaptive Mesh Refinement on Multidimensional Cartesian Grids......Page 210
6-4.4. AMR and Overset Grids......Page 213
6-4.5. AMR and Unstructured Grids......Page 215
6-5.1. Errors Introduced by Grid Representations......Page 217
6-5.3. The Connection between Resolution and Accuracy......Page 219
References......Page 220
7 Diffusive Transport Processes......Page 225
7-1.1. The Physical Origin of Diffusive Effects......Page 226
7-1.2. The d-Function Test Problem......Page 227
7-1.3. Short- and Long-Wavelength Breakdowns......Page 231
7-2.1. A Finite-Difference Formula in One Dimension......Page 232
7-2.2. Implicit Solutions Using Tridiagonal Matrix Inversions......Page 233
7-2.3. Large Variations in Δx and D......Page 234
7-3.1. Nonlinear Diffusion Effects......Page 236
7-3.2. Numerical Techniques for Nonlinear Diffusion......Page 239
7-3.4. Flux Limiters......Page 241
7-4.1. Implicit, Explicit, and Centered Algorithms......Page 242
7-5.1. The Fickian Diffusion Approximation......Page 245
7-5.2. An Efficient Iterative Algorithm......Page 247
7-6.1. Thermal Conductivity......Page 249
7-6.2. Ordinary (or Molecular or Binary) Diffusion......Page 250
7-6.4. Viscosity......Page 251
References......Page 252
8 Computational Fluid Dynamics: Continuity Equations......Page 254
8-1.1. The Basic One-Step Method......Page 256
8-1.2. Two-Step Richtmyer Methods......Page 258
8-1.3. The MacCormack Method......Page 259
8-1.4. Pad´e or Compact Finite-Difference Methods......Page 260
8-2. Positivity, Monotonicity, and Accuracy......Page 261
8-3. Monotone Convection Algorithms and Flux Limiting......Page 267
8-3.1. The Basic Idea of Flux-Corrected Transport......Page 268
8-3.2. Generalizations and Extensions of FCT Algorithms......Page 270
8-3.3. The Effects of Order on FCT......Page 272
8-3.4. Other Approaches to Monotonicity......Page 275
8-4.1. Lax-Wendroff Methods......Page 277
8-4.2. FCT for Coupled Continuity Equations......Page 279
8-4.3. Multidimensions through Timestep Splitting......Page 281
8-4.4. Considerations for Multidimensional Monotone Algorithms......Page 284
8-4.5. Flux-Corrected Transport Packages......Page 288
8-5.1. Galerkin, Tau, and Collocation Approximations......Page 291
8-5.2. Spectral Methods......Page 293
8-5.3. Finite-Element Methods......Page 296
8-5.4. Spectral-Element Methods......Page 298
8-5.5. Wavelet Methods......Page 299
8-6. Resolution and Reynolds-Number Limitations......Page 300
References......Page 302
9 Computational Fluid Dynamics: Using More Flow Physics......Page 307
9-1.1. Equations of Compressible and Incompressible Flow......Page 308
9-1.2. Characteristic Trajectories......Page 311
9-1.3. Time Integration......Page 312
9-2. Methods for Fast Flows......Page 313
9-2.1. The Riemann Problem and Godunov Methods......Page 316
9-2.2. The Boltzmann Gas-Kinetic and Flux-Vector Splitting Methods......Page 318
9-2.3. Comparisons and Caveats......Page 320
9-2.4. Shock Fitting and the Method of Characteristics......Page 324
9-3. Methods for Incompressible Flows......Page 326
9-3.1. Pseudocompressibility Methods......Page 328
9-3.2. Projection Methods......Page 329
9-3.3. Implicit Pressure Formulations......Page 331
9-4. Methods for Slow Flows......Page 332
9-4.1. The Slow-Flow Methods......Page 333
9-4.2. An Implicit Flux-Corrected Transport Algorithm......Page 335
9-4.3. Several Implicit Algorithms......Page 339
9-5. Lagrangian Fluid Dynamics......Page 341
9-5.1. Advantages and Limitations of Lagrangian Methods......Page 342
9-5.2. A One-Dimensional Implicit Lagrangian Algorithm......Page 344
9-5.3. Multidimensional Lagrangian Algorithms......Page 351
9-5.4. Free-Lagrange Methods......Page 352
9-6. Lagrangian Particle and Quasiparticle Methods......Page 355
9-6.1. Quasiparticle Methods......Page 356
9-6.2. Smooth-Particle Hydrodynamics......Page 359
9-6.3. Lattice-Gas (Cellular) Automata......Page 361
9-7.1. Vortex Dynamics......Page 363
9-7.3. Contour Dynamics......Page 365
9-7.4. Some Comments on Vortex Methods......Page 366
References......Page 367
10 Boundaries, Interfaces, and Implicit Algorithms......Page 374
10-1.1. General Comments on Boundary Conditions......Page 375
10-1.2. Boundary Conditions for Confined Domains......Page 377
10-1.3. Boundary Conditions for Unconfined Domains......Page 383
10-1.4. Conditions for a Thermal Boundary Layer......Page 387
10-2. Boundary Conditions for High-Order Algorithms......Page 390
10-2.1. Use of Characteristics......Page 392
10-2.2. Problems with Acoustic Radiation in CFD......Page 395
10-3. Interfaces and Discontinuities......Page 396
10-3.1. Resolving Active Interfaces......Page 397
10-3.3. Surface-Tracking Methods......Page 402
10-3.4. Volume-Tracking Methods......Page 405
10-3.5. Some Concluding Remarks......Page 408
10-4.1. Statement of the Problem......Page 409
10-4.2. Exact Solution of the Matrix Equation......Page 411
10-4.3. Tridiagonal Matrices......Page 412
10-4.4. Direct Solutions of the Poisson Equation......Page 414
10-4.5. Iterative Solutions of Elliptic Equations......Page 416
10-4.6. Multigrid Iteration Methods......Page 420
10-4.7. Summary......Page 421
References......Page 422
11 Coupling Models of Reactive-Flow Processes......Page 426
11-1.1. Global-Implicit Coupling......Page 427
11-1.2. Timestep Splitting......Page 429
11-1.3. Trade-Offs in the Choice of Methods......Page 430
11-2. Coupling Physical Processes in Reactive Flows......Page 432
11-2.1. Coupling for Fluid Dynamics, Species Reactions, and Diffusion......Page 433
11-2.2. Timestep Control......Page 439
11-3. More on Coupling: Warnings and Extensions......Page 441
11-3.1. General Comments......Page 442
11-3.2. Including Gravity......Page 446
11-3.3. Implicit, Lagrangian, and Navier-Stokes Fluid Dynamics......Page 447
11-3.4. Multiphase Flows......Page 449
11-4.1. The General Formulation......Page 452
11-4.2. An Example......Page 454
11-5. More-Complex Spatial and Temporal Coupling......Page 457
11-5.1. A Classification of Time and Space Scales......Page 458
11-5.2. Intermittent Embedding: An Advanced Coupling Problem......Page 460
References......Page 462
12 Turbulent Reactive Flows......Page 464
12-1.1. An Overview of Current Concepts and Approaches......Page 465
12-1.2. Direct Numerical Simulation......Page 468
12-1.3. Turbulence-Averaged Navier-Stokes Equations......Page 469
12-1.4. Turbulence Modeling and Reynolds-Stress Models......Page 472
12-1.5. Probability Distribution-Function Methods......Page 473
12-2. Large-Eddy Simulation and Subgrid Models......Page 474
12-2.1. Overview of Large-Eddy Simulation......Page 475
12-2.2. The Ideal Subgrid Turbulence Model......Page 478
12-2.3. Four Fortunate Circumstances for Turbulence Simulations......Page 480
12-3.1. Some Problems in Modeling Turbulent Reactive Flows......Page 483
12-3.2. Overview of Turbulent Combustion......Page 487
12-3.3. DNS and LES of Turbulent Reactive Flows......Page 489
12-3.4. Turbulent Combustion Models......Page 491
12-4. Monotone-Integrated Large-Eddy Simulation......Page 494
12-4.1. Why MILES Should Work......Page 495
12-4.2. Tests of the Underlying Concepts......Page 497
12-4.3. Empirical Evidence that MILES Works for Complex Flows......Page 499
12-4.4. Conclusions and Speculations......Page 501
References......Page 504
13 Radiation Transport and Reactive Flows......Page 509
13-1. The Physical Basis of Radiation Transport......Page 510
13-2.1. The Radiative-Transfer Equation......Page 513
13-2.2. The Radiant Energy Flux......Page 517
13-2.3. Important Limiting Cases......Page 518
13-2.4. Monte Carlo Methods......Page 519
13-3. Radiation Diffusion Approximations......Page 520
13-3.2. The Variable Eddington Approximation......Page 521
13-4. Other Solution Methods......Page 524
13-4.1. The Zonal Method......Page 525
13-4.2. Flux or Expansion Methods......Page 528
13-4.3. The Discrete-Ordinate or Sn Method......Page 530
13-5. Using These Models for Reactive Flows......Page 533
References......Page 539
Index......Page 542