Instabilities of Flows: With and Without Heat Transfer and Chemical Reaction (eBook)

Prefaces 6
Table of Contents 10
Chapter 1 GENERAL INTRODUCTION ON INSTABILITY AND TRANSITION 12
1.1 Introduction 12
1.2 What is Instability? 18
1.3 Temporal and Spatial Instability 18
1.4 Elements of Wave Mechanics 19
1.5 Some Instability Mechanisms 23
1.5.1 Dynamic Stability of Still Atmosphere 24
1.5.2 Kelvin - Helmholtz Instability 26
Chapter 2 INSTABILITY AND TRANSITION IN FLUID MECHANICS 31
2.1 Introduction 31
2.2 Parallel Flow Approximation and Inviscid Instability Theorems 35
2.2.1 Inviscid Instability Mechanism 36
2.3 Viscous Instability of Parallel Flows 38
2.3.1 Eigenvalue Formulation for Instability of Parallel Flows 39
2.3.2 Temporal and Spatial Ampli.cation of Disturbances 42
2.3.2.1 Temporal Ampli.cation Theory 42
2.3.2.2 Spatial Ampli.cation Theory 43
2.3.2.3 Relationship Between Temporal and Spatial Theories 44
2.4 Properties of Orr-Sommerfeld Equation and Boundary Conditions 45
2.4.1 Compound Matrix Method 48
2.5 Instability Analysis from Solution of Orr-Sommerfeld Equation 53
2.5.1 Local and Total Amplication of Disturbances 58
2.5.2 Effect of Mean Flow Pressure Gradient 61
2.5.3 Transition Prediction Based on Stability Calculation 69
2.5.4 Effects of Free Stream Turbulence 70
2.6 Receptivity Analysis of Shear Layer 74
2.6.1 Receptivity Mechanism by Linearized Approach: Connection to Stability Theory 76
2.6.1.1 A Brief Review of Laplace-Fourier Transform 76
2.6.1.2 Fourier and Laplace Transform 77
2.6.1.2(a) The Inversion Formula for Laplace Transform 80
2.6.1.3 A Short Tutorial on Fourier Integral and Transforms 83
2.6.1.4 Some Useful Fourier Transforms 87
2.6.2 Receptivity to Wall Excitation and Impulse Response 90
2.6.2.1 Near-Field Response Created by Localized Excitation 93
2.6.2.1a Outer Solution 95
2.6.2.1b Inner Solution 96
2.6.3 Vibrating Ribbon at The Wall 102
2.6.4 Receptivity to Free Stream Excitation 107
2.6.5 General Excitation and Upstream Propagating Mode 110
2.6.6 Low frequency freestream excitation and the Klebano. mode 119
2.7 Direct Simulation of Receptivity to Freestream Excitation: 124
2.7.1 Coupling Between Wall- and Freestream-Modes 127
2.7.2 Receptivity to Train of Convected Vortices in Freestream 130
2.7.3 Further Explanation of Freestream Periodic Excitation: 136
Chapter 3 BYPASS TRANSITION 142
3.1 Introduction 142
3.2 Transition via Growing Waves and Bypass Transition: 143
3.3 Visualization Study of Vortex-Induced Instability as Bypass Transition 145
3.4 Computations of Vortex-Induced Instability as A Precursor to Bypass Transition 156
3.5 The Instability Mechanism in Vortex-Induced Instability 158
3.6 Instability on The Attachment-Line of Swept Wings 162
Chapter 4 SPATIO-TEMPORAL INSTABILITY AND TRANSITION 169
4.1 Introduction 169
4.2 Transient Energy Growth 171
4.3 Energy-Based Receptivity Analysis 173
Chapter 5 LANDAU EQUATION AND MULTIPLE HOPF-BIFURCATION 188
5.1 Landau’s Equation and Its Application for Flow Past a Cylinder 188
5.2 Instability of Flow Past a Cylinder 190
5.3 Nonlinear Instability and Amplitude Equation 191
5.4 Numerical Simulation of Flow Past a Circular Cylinder 193
Chapter 6 STABILITY OF MIXED CONVECTION BOUNDARY LAYER 201
6.1 Introduction 201
6.2 The Governing Equations 205
6.3 Mean Flow Equations 206
6.4 Stability Equations and Numerical Method 208
6.4.1 Compound Matrix Method For The 6th Order System 211
6.4.2 Initial Conditions for The Induced System 213
6.4.3 Dispersion Relation 214
6.4.4 Eigen-function for The Mixed Convection Problem 215
6.5 Results and Discussion 216
6.5.1 Eigen-spectrum For Mixed Convection Problem 217
6.5.2 Neutral Curves For Mixed Convection Problem 222
6.5.3 Eigenfunctions of The Mixed Convection Problem 231
6.6 Conclusions and Outlook 237
Chapter 7 COMBUSTION AND CFD FOR COMBUSTION 239
7.1 Introduction 239
7.2 Combustion and Energy Production 240
7.3 Combustion and Optimization 240
7.4 Combustion and Instabilities 242
7.5 Turbulent Combustion 244
7.6 DNS, LES and RANS for Combustion 245
Chapter 8 WAVES IN REACTING FLOWS 251
8.1 Physical Waves In Reacting Flows 251
8.2 Numerical Waves in High-Fidelity Simulations of Reacting Flows 254
Chapter 9 LARGE EDDY SIMULATION OF REAL COMBUSTORS 257
9.1 Introduction 257
9.2 Case 1: Small Scale Gas Turbine Burner 258
Configuration and Boundary Conditions 258
Nonreacting Flow 259
Average Fields 259
Structure of Unsteady Swirling Nonreacting Flows 259
Coexistence of Acoustic Modes and Precessing Vortex Core 262
Stable Reacting Flow 264
9.3 Case 2: Self-Excited Staged Burner 268
Configuration 268
Stable Flow 269
Controlling Oscillations Through Boundary Conditions 269
Chapter 10 TWO-PHASE FLOW COMBUSTION 273
10.1 Equations 276
Carrier Phase 276
Dispersed Phase 278
Phase Exchange Source Terms 279
The Random Uncorrelated Motion (RUM) 280
LES Approach 280
Numerical Approach 282
10.2 Reacting Flow in An Aircraft Combustion Chamber 283
Configuration 283
Steady Spray Flame 284
Ignition Sequence 288
Chapter 11 THE GROWTH OF ROUNDING ERRORS IN LES 292
11.1 Introduction 292
11.2 Effects of The Number of Processors on LES 294
11.3 Sensitivity of LES in Laminar and Turbulent Flows 297
A Fully Deterministic LES? 298
Influence of Turbulence 298
Influence of Initial Conditions 301
Effects of Graph Ordering 301
Effects of Time Step 303
Effects of Machine Precision 304
11.4 Conclusions 305
Bibliography 307