Turbulent Combustion Modeling (eBook)

Preface 7
Contents 10
List of Contributors 18
Introductory Concepts 21
The Role of Combustion Technology in the 21st Century 22
Introduction 22
Sustainable Energy 25
Technology Forecasts 26
Implications for Combustion Technology 31
Prospects for Advanced Computer Modeling of Combustors 33
Concluding Remarks 36
References 36
Turbulent Combustion: Concepts, Governing Equations and Modeling Strategies 38
Introduction 38
Governing Equations 41
Conservation Equations 41
Constitutive Relations, State Equations and Auxiliary Relations 43
Conventional Mathematical and Computational Frameworks for Simulating Turbulent Combustion Flows 47
Direct Numerical Simulation (DNS) 47
Reynolds-Averaged Navier-Stokes (RANS) 49
Large-Eddy Simulation (LES) 51
Addressing the Closure Problem 54
Outline of Upcoming Chapters 55
References 56
Recent Advances and Trends in Turbulent Combustion Models 59
The Flamelet Model for Non-Premixed Combustion 60
Introduction 60
Fundamental Concepts 61
The Mixture Fraction 62
The Flamelet Solution 63
The Counterflow Diffusion Flame 64
Validity of the Flamelet Approach 65
RANS Flamelet Modeling 66
Steady Flamelets 67
Transient Flamelets 70
Representative Interactive Flamelets (RIF) Model 72
Eulerian Particle Flamelet Model (EPFM) 73
Flamelet–Progress Variable (FPV) Models 73
LES Flamelet Modeling 75
Subgrid Scale Modelling 75
Conclusion 76
References 76
RANS and LES Modelling of Premixed Turbulent Combustion 79
Introduction to Premixed Flames 79
Modelling Framework for RANS and LES 80
Introduction 80
Regimes of Premixed Turbulent Combustion 81
Averaging and Filtering 82
Modelling Principles 84
Transport Modelling for Premixed Turbulent Flames 86
Reaction Rate Modelling for Premixed Turbulent Flames 87
Simple Models 87
Flame Surface Density Modelling 89
G-equation Modelling 96
Scalar Dissipation Rate Modelling 99
Other Approaches 101
Future 102
References 103
The Conditional Moment Closure Model 107
Introduction 107
Methodological Developments in CMC 109
The CMC Equations 109
Advances in Second Order Closures 112
Advances in Doubly Conditioned Moment Closures 117
Premixed Combustion 123
Liquid Fuel Combustion 124
Application to Flows of Engineering Interest 125
Dimensionality of the CMC Equation 125
Numerical Methods 126
Applications and Outlook 128
Conclusion 130
References 130
Transported Probability Density Function Methods for Reynolds-Averaged and Large-Eddy Simulations 134
Introduction 134
A Baseline PDF Formulation 135
Recent Advances in PDF Methods 139
Mixing Models 139
Hybrid Lagrangian Particle/Eulerian Mesh Methods 140
Eulerian Field Methods 141
Multiscale, Multiphysics Modeling 143
Examples 144
PDF-Based Methods for Large-Eddy Simulation 147
Spatial Filtering, FDFs, and FDF Transport Equations 148
Equivalent Representations, Models, and Algorithms 149
An Alternative Interpretation 150
Examples 151
Summary and Conclusions 153
References 154
Multiple Mapping Conditioning: A New Modelling Framework for Turbulent Combustion 158
Introduction 158
The Basic MMC Framework 161
Context and Concepts 161
Mapping Functions 162
The Deterministic MMC Model 163
The Stochastic MMC Model 167
Qualitative Properties of MMC 169
Replacement of Reference Variables 169
Generalised MMC 171
Reference Variables in Generalised MMC 171
Features of Generalised MMC Models 172
MMC with Dissipation-like Reference Variables 174
DNS/LES Simulated Reference Variables 175
Examples 176
MMC in Homogeneous Turbulence 176
MMC with RANS 179
MMC with the Binomial Langevin Model 180
MMC with LES 182
Summary and Future Directions 185
References 186
Advances and Trends in Multiscale Strategies 189
The Emerging Role of Multiscale Methods in Turbulent Combustion 190
Motivation 190
The Multiscale Nature of Turbulent Combustion Flows 191
The Case for Multiscale Strategies in Turbulent Combustion 193
Emerging Combustion Technologies 194
Emerging Multiscale Science 195
Multiscale Considerations for Turbulent Combustion 196
Basic Requirements for Multiscale Approaches in Turbulent Combustion 197
General Frameworks for the Governing Equations for Multiscale Models of Turbulent Combustion 198
Multiscale Approaches in Turbulent Combustion and Preview of Relevant Chapters 199
Time-Step Acceleration 199
Mesh Adaptive Methods 200
Flame Embedding Approaches 200
Hybrid LES-Low-Dimensional Models 201
Concluding Remarks 202
References 203
Model Reduction for Combustion Chemistry 206
Introduction 206
Traditional Methodologies for Reduction: QSSA and PEA 211
The QSSA 212
The PEA 213
Comments on the QSSA and PEA 214
A Common Set-up for the QSSA and PEA 214
The Need for Algorithmic Methodologies for Reduction 217
Reduction Algorithms 219
Interaction of Chemistry with Diffusion 221
Manifold Methods and Tabulation Strategies 222
Principles of Manifold Methods 222
Calculation of Low-Dimensional Manifolds 224
Tabulation 227
Concluding Remarks 229
References 229
The Linear-Eddy Model 234
Motivation 234
Triplet Map 235
Map Sizes and Frequency of Occurrence 236
Application to Passive Mixing 238
Application to Reacting Flows 239
Application to Reacting Flows as a Subgrid Model 241
The LEM Subgrid Model 244
Large-Scale Advection of the Subgrid Field 245
LEMLES Applications to Reacting Flows 250
Summary and Future Prospects 256
References 257
The One-Dimensional-Turbulence Model 261
Motivation 261
Constant-Property ODT 263
Model Formulation 263
Numerical Implementation 267
Generalizations and Couplings 267
Features of the ODT Representation of Turbulent Flow 268
Applications of ODT in Combustion 270
Governing Equations 270
Stand-Alone ODT Simulations 273
Hybrid ODTLES 277
Concluding Remarks 284
References 286
Unsteady Flame Embedding 289
Introduction 290
Historical Perspective on the Flame Embedding Concept 292
Elemental Flame Model Formulation 295
Numerical Solution for the Elemental Flame Model 298
UFE LES Sub-grid Combustion Model 300
Numerical Results 303
Conclusions 308
References 310
Adaptive Methods for Simulation of Turbulent Combustion 313
Introduction 313
Mathematical Formulation 314
AMR Basic Concepts 317
Creating and Managing the Grid Hierarchy 317
AMR Discretization 319
Hyperbolic Conservation Laws 319
Elliptic 323
Parabolic Systems 326
AMR for Low Mach Number Combustion 327
Implementation Issues and Software Design 331
Performance of Adaptive Projection 332
Application – Lean Premixed Hydrogen Flames 333
Background 333
Models and Setup 335
Simulation Results 336
Summary 339
References 339
Wavelet Methods in Computational Combustion 342
Introduction 342
Wavelet Transforms 344
Orthogonal Wavelets 344
Biorthogonal Wavelet Transforms 346
Second Generation Wavelets 347
Wavelets as a Method for DNS 348
The Wavelet Representation of the Derivative 351
Higher Dimensional Discretizations 352
An Application of Wavelets to Reacting Flows 354
Governing Equations 354
Results 356
Conclusions 360
References 361
Cross-Cutting Science 363
Design of Experiments for Gaining Insights and Validating Modeling of Turbulent Combustion 364
Introduction 364
The Turbulent Combustion Domain 367
Basic Considerations 369
Design Issues 369
Operational Envelopes 371
Experimental Considerations 373
Numerical Considerations 375
Case Studies 376
The Swirl Stabilised Burner 376
The Premixed Burner in Vitiated Coflows 379
The Piloted Spray Burner 381
Concluding Remarks 384
References 386
Uncertainty Quantification in Fluid Flow 390
Introduction 390
Polynomial Chaos 393
Challenges in PC UQ Methods 398
Polynomial Chaos UQ in Fluid Flow Applications 401
Incompressible Flow 402
Reacting Flow 405
Compressible Flow 407
Turbulence 408
Closure 410
References 410
Computational Frameworks for Advanced Combustion Simulations 417
Introduction 417
Literature Review of Computational Frameworks 418
The Common Component Architecture 421
Features of the Common Component Architecture 422
Computational Facility for Reacting Flow Science 424
Numerical Methods and Capabilities 424
The Need for Componentization 425
Computational Investigations Using CCA 428
Fourth-order Combustion Simulations with Adaptive Mesh Refinement 429
Computational Singular Perturbation and Tabulation 433
Research Topics in Computational Frameworks 439
Conclusion 440
References 441
The Heterogeneous Multiscale Methods with Application to Combustion 446
The Heterogeneous Multiscale Method 446
The Basic Framework 447
The Seamless Algorithm 450
Stability and Accuracy 453
Capturing Macroscale Interface Dynamics 454
Macroscale Solver: The Interface Tracking Methods 454
Estimating The Macroscale Interface Velocity 455
HMM Interface Tracking of Combustion Fronts 458
Majda's Model 458
Reactive Euler Equations 461
Conclusions 463
References 464
Lattice Boltzmann Methods for Reactive and Other Flows 467
Introduction 467
The Boltzmann Equation 469
Basic Considerations 469
Lattice Boltzmann Model 471
Variations on the LBM Theme 476
Initial and Boundary Conditions 478
Computational Cost 479
Applications 479
Isothermal Flows 479
Non-Isothermal Flows 482
Multicomponent Mixtures 484
Reactive Flows 485
Conclusions 487
References 488
Index 493