Download Transition, Turbulence and Combustion Modelling: Lecture Notes from the 2nd ERCOFTAC Summerschool he PDF

Transition, Turbulence and Combustion Modelling: Lecture Notes from the 2nd ERCOFTAC Summerschool he
Name: Transition, Turbulence and Combustion Modelling: Lecture Notes from the 2nd ERCOFTAC Summerschool he
Author: p. h. alfredsson
Pages: 539
Year: 1999
Language: English
File Size: 38.02 MB
Downloads: 0
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ERCOFTAC SERIES VOLUME 6 Series Editors P. Hutchinson, Chairman ERCOFTAC, Cranfield University, Bedford, UK W. Rodi, Chairman ERCOFTAC Scientific Programme Committee, Universitdt Karlsruhe, Karlsruhe, Germany Aims and Scope of the Series ERCOFfAC (European Research Community on Flow, Turbulence and Combustion) was founded as an international association with scientific objectives in 1988. ERCOFTAC strongly promotes joint efforts of European research institutes and industries that are active in the field of flow, turbulence and combustion, in order to enhance the exchange of technical and scientific information on fundamental and applied research and design. Each year, ERCOFTAC organizes several meetings in the form of workshops, conferences and summerschools, where ERCOFfAC members and other researchers meet and exchange information. The ERCOFTAC Series will publish the proceedings of ERCOFTAC meetings, which cover all aspects of fluid mechanics. The series will comprise proceedings of conferences and workshops, and of textbooks presenting the material taught at summerschools. The series covers the entire domain of fluid mechanics, which includes physical modelling, computational fluid dynamics including grid generation and turbulence modelling, measuring techniques, flow visualization as applied to industrial flows, aerodynamics, combustion, geophysical and environmental flows, hydraulics, multi phase flows, non Newtonian flows, astrophysical flows, laminar, turbulent and transitional flows. The titles published in this series are listed at the end of this volume.


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CONTENTS Preface ..... 1 INTRODUCTION P.H. Alfredsson and A.D. Burden 1.1 Equations for compressible flows 1.1.1 Gas (air) material parameters. 1.2 Laminar boundary layers ...... . 1.2.1 The incompressible boundary layer. 1.2.2 Boundary layer equations for compressible flow 1.3 Combustion... ................ . 1.3.1 Gas mixtures with varying composition 1.3.2 Shocks, Detonations and Deflagrations . 1.3.3 Combustion chemistry ..... 1.3.4 Stirred reactors and extinction 1.3.5 Flame fronts v xi 1 1 7 9 9 17 35 36 40 44 45 46 References . . . . . . . . . . . . . . . . . . . 49 2 STABILITY OF BOUNDARY LAYER FLOWS 51 A. Hanifi and D.S. Henningson 2.1 Introduction...................... 51 2.2 Introduction to stability of incompressible parallel flows 52 2.2.1 Linear stability equations . . . 53 2.2.2 Inviscid linear stability theory. 55 2.2.3 Viscous instability analysis . . 57 2.2.4 Transient growth . . . . . . . . 63 2.3 Stability of compressible parallel flows 68 2.3.1 Derivation of stability equations 69 2.3.2 Exponential instabilities . . . . . 70 2.3.3 Non modal instabilities ..... 83 2.4 Stability of non parallel compressible flows. 87 2.4.1 Non local stability theory . . . . . . 87 2.4.2 Derivation of stability equations .. 88 2.4.3 Mathematical character of the non local stability equations 91 2.5 Applications. 94 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99 3 TRANSITION PREDICTION IN INDUSTRIAL APPLICATIONS 105 D. Arnal 3.1 Introduction........................ 105 3.2 Qualitative description of some transition mechanisms 106 3.2.1 "Natural" transition . . . . . . . . . . . . . . . 107 3.2.2 Transition caused by large amplitude disturbances 109 3.3 Some theoretical elements for "natural" transition .... 110


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vi 3.3.1 Linear stability theory: local approach 111 3.3.2 Linear stability: nonlocal approach 117 3.3.3 Receptivity.... 118 3.3.4 Non linear effects. 119 3.4 The eN method. . . . . . 119 3.4.1 Local approach . . 120 3.4.2 Nonlocal approach 123 3.5 Application to transonic flows: laminar flow control 123 3.5.1 Effect of streamwise pressure gradients. . . . 125 3.5.2 Suction . . . . . . . . . . . . . . . . . . . . . 126 3.5.3 How to prevent leading edge contamination? 133 3.5.4 Examples of flight experiments with transition control 136 3.6 Application to high speed flows . . . . . . . . . . 140 3.6.1 Factors acting on the stability properties 141 3.6.2 Transition prediction. 142 3.7 Conclusion 152 References . . . . . . . . . . . . . . 153 4 AN INTRODUCTION TO TURBULENCE MODELLING 159 A.V. Johansson and A.D. Burden 4.1 Introduction ........ . 159 4.2 Basic properties of turbulence and the mean flow equation. . . .. 160 4.2.1 Decomposition and mean flow equation for incompressible flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 162 4.2.2 Decomposition and mass weighted, Favre, averaging for com pressible flow . . . . . . . . . . . . . . . . . . . 163 4.2.3 The mean flow equation for compressible flows 165 4.2.4 Averaged conservation equations for e, h, Ya . . . 165 4.2.5 Methodology of single point model development 166 4.2.6 Basic properties of near wall incompressible turbulence. 167 4.2.7 The compressible turbulent boundary layer 172 4.2.8 The energy cascade in turbulence. . . . . . . . 173 4.3 Transport equations for single point moments. . . . . 174 4.3.1 The exact K equation for incompressible flow. 176 4.3.2 The exact Reynolds stress transport equation for incom pressible flow . . . . . . . . . . . . . . . . . . . . . . . 177 4.3.3 The dissipation rate equation for incompressible flow . 179 4.3.4 The K equation for compressible flow . . . 179 4.4 The hierarchy and history of single point closures. 180 4.4.1 The eddy viscosity hypothesis. 180 4.4.2 One equation models. . . . . . . 183 4.4.3 Two equation models ...... 183 4.4.4 Reynolds stress transport models 184 4.4.5 Algebraic Reynolds stress models 185 4.5 What should a closure fulfill? . . . . . . 185


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vii 4.5.1 Coordinate invariance . . . 185 4.5.2 Material frame indifference 186 4.5.3 Invariant modelling. . 187 4.5.4 Realizability ..... 189 4.5.5 Near wall asymptotics 193 4.6 Purely algebraic models . . . 195 4.6.1 The mixing length model with a van Driest damping function195 4.7 Eddy viscosity based two equation models 197 4.7.1 The K c: model. . . . . . . . . . . . . . . . . . . . 199 4.7.2 The K w model ................... 207 4.8 Differential Reynolds stress models for incompressible flow. 209 4.8.1 The dissipation rate tensor ... . . . . . . . . . 211 4.8.2 The pressure strain rate term . . . . . . . . . . . 213 4.8.3 Rotating channel flow and illustrative example 221 4.8.4 The c: equation in RST closures. . . . . . . . . . 223 4.8.5 Wall boundary conditions and low Reynolds number formu lations . . . . . . . . . . . . . . . . . . . . 223 4.9 Algebraic Reynolds stress models . . . . . . . . . . . . 224 4.9.1 Explicit algebraic Reynolds stress models . . . 229 4.9.2 The WJ model for two dimensional mean flows 231 4.9.3 The WJ model for three dimensional mean flow. 234 4.9.4 Compressible EARSM 235 References. . . . . . . . . . . . . . . . . . 237 5 MODELLING OF TURBULENCE IN COMPRESSIBLE FLOWS 243 R. Friedrich 5.1 Introduction.................. 243 5.1.1 Equations of motion . . . . . . . . . 245 5.1.2 Transport of dilatation and vorticity 250 5.2 Averaged equations. . . . . . . . . . . . 252 5.2.1 Definition of averages . . . . . . . . 252 5.2.2 Averaged conservation equations . . 254 5.2.3 Turbulent stress transport equations 257 5.2.4 Transport equations for the pressure variance and the tur bulent heat flux. . . . . . . . . . . . . . . . . . . . . . . . . 260 5.2.5 Transport equations for homogeneous shear flow . . . . . . 263 5.3 Compressibility effects due to turbulent fluctuations and modelling of explicit compressibility terms . . . . . . 269 5.3.1 Homogeneous isotropic turbulence 269 5.3.2 Homogeneous shear turbulence 281 5.3.3 Compressible channel flow. . 309 5.4 Transport equation models ..... 322 5.4.1 Eddy viscosity based models 323 5.4.2 Algebraic stress models . 329 5.4.3 Reynolds stress transport . . 330


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viii 5.4.4 Heat flux transport. 5.4.5 Applications 333 335 References . . . . . . . . . . . . . 343 6 LARGE EDDY SIMULATIONS OF INCOMPRESSIBLE AND COMPRESSIBLE TURBULENCE 349 O. Metais, M. Lesieur and P. Comte 6.1 Introduction................ 349 6.2 Large eddy simulation (LES) formalism 350 6.2.1 LES and unpredictability growth 351 6.3 Smagorinsky's model .......... . 6.4 Spectral Eddy viscosity and eddy diffusivity models 6.4.1 Temporal mixing layer ... . 6.4.2 Spectral dynamic model .. . 6.4.3 Incompressible plane channel 6.5 Return to physical space ...... . 6.5.1 Structure function models .. 6.5.2 Selective and filtered structure function models 6.5.3 Generalized hyperviscosities ... . 6.5.4 Hyper viscosity .......... . 6.5.5 Scale similarity and mixed models 6.5.6 Dynamic models ........ . 6.5.7 Anisotropic subgrid scale models 6.6 Vortex control in a round jet 6.6.1 The natural jet 6.6.2 The forced jet ... . 6.7 Rotating flows ....... . 6.7.1 Rotating channel flow 6.7.2 Spatial organization . 6.7.3 Statistics ...... . 6.7.4 Flows of geophysical interest 6.7.5 Separated flows: the backward facing step 6.7.6 Statistics ...... . 6.7.7 Coherent structures ...... . 6.8 Compressible LES formalism ..... . 6.8.1 compressible filtering procedure. 6.8.2 The simplest possible closure .. 352 353 356 358 359 364 364 367 371 372 373 373 376 376 377 378 383 383 385 385 390 391 392 392 397 398 399 6.9 Compressible mixing layer. . . . . . . . 402 6.10 Compressible boundary layers on a flat plate 405 6.10.1 LES of a spatially developing boundary layer at Mach 0.5 405 6.10.2 Boundary layer upon a groove 409 6.11 Conclusion 412 References . . . . . . . . . . . . . . . . . . . 414


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7 DIRECT NUMERICAL SIMULATIONS OF COMPRESSIBLE TURBULENT FLOWS: FUNDAMENTALS AND APPLICATIONS S.K. Lele 7.1 Introduction .................. . 7.2 Physical nature of compressible turbulent flows 7.3 Governing equations .............. . 7.3.1 Non dimensionalization ........ . 7.3.2 Linearized equations and modal decomposition 7.4 Numerical methods .............. . 7.4.1 Basic discretization in space and time 7.4.2 Boundary conditions ........ . 7.4.3 Artifacts of numerical discretization 7.5 DNS of compressible free shear flows 7.5.1 Flow definition .......... . 7.5.2 Incompressible mixing layer ... . 7.5.3 Convective/relative Mach number 7.5.4 Turbulence and eddy structures. 7.5.5 Proposed explanations/modeling 7.5.6 Insights from recent DNS studies 7.6 DNS of shock turbulence interaction .. 7.6.1 Idealized shock turbulence interaction 7.6.2 Linearized analysis of shock turbulence interaction 7.6.3 Observations from DNS ........ . 7.7 DNS of aerodynamically generated sound .. . 7.7.1 Direct computation of sound generation 7.7.2 Predictions based on acoustic analogies 7.8 Concluding remarks References . . . . . . . . . . . . . . . . . . . . . . . . 8 TURBULENT COMBUSTION MODELLING J.J. Riley 8.1 Introduction ......... . 8.1.1 General features .. . 8.1.2 Predictive approaches 8.1.3 Mathematical problem. 8.1.4 Important parameters 8.2 Mixture fraction based theories 8.2.1 Fast chemistry limit 8.2.2 Finite rate chemistry. 8.3 Large eddy simulations ... . 8.3.1 Introduction .... . 8.3.2 LES of chemically reacting flows References . . . . . . . . . . . . . . . . . . . . ix 421 421 422 423 424 430 436 436 440 448 451 452 453 . ,454 454 455 459 462 463 463 466 468 469 475 481 482 489 489 489 491 496 499 500 502 508 512 512 516 526


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