Instabilities of Flows: With and Without Heat Transfer and Chemical Reaction (CISM International Centre for Mechanical Sciences)

The articles in the book treat flow instability and transition starting with classical material dealt with in an innovative and rigorous way, some newer physical mechanisms explained for the first time and finally with the very complex topic of bombustion and two-phase flow instabilities. front-matter 1 Title Page 3 Copyright Page 4 Prefaces 5 Table of Contents 9 Chapter 01 11 Chapter 1 GENERAL INTRODUCTION ON INSTABILITY AND TRANSITION 11 1.1 Introduction 11 1.2 What is Instability? 17 1.3 Temporal and Spatial Instability 17 1.4 Elements of Wave Mechanics 18 1.5 Some Instability Mechanisms 22 1.5.1 Dynamic Stability of Still Atmosphere 23 1.5.2 Kelvin - Helmholtz Instability 25 Chapter 02 30 Chapter 2 INSTABILITY AND TRANSITION IN FLUID MECHANICS 30 2.1 Introduction 30 2.2 Parallel Flow Approximation and Inviscid Instability Theorems 34 2.2.1 Inviscid Instability Mechanism 35 2.3 Viscous Instability of Parallel Flows 37 2.3.1 Eigenvalue Formulation for Instability of Parallel Flows 38 2.3.2 Temporal and Spatial Ampli.cation of Disturbances 41 2.3.2.1 Temporal Ampli.cation Theory 41 2.3.2.2 Spatial Ampli.cation Theory 42 2.3.2.3 Relationship Between Temporal and Spatial Theories 43 2.4 Properties of Orr-Sommerfeld Equation and Boundary Conditions 44 2.4.1 Compound Matrix Method 47 2.5 Instability Analysis from Solution of Orr-Sommerfeld Equation 52 2.5.1 Local and Total Amplication of Disturbances 57 2.5.2 Effect of Mean Flow Pressure Gradient 60 2.5.3 Transition Prediction Based on Stability Calculation 68 2.5.4 Effects of Free Stream Turbulence 69 2.6 Receptivity Analysis of Shear Layer 73 2.6.1 Receptivity Mechanism by Linearized Approach: Connection to Stability Theory 75 2.6.1.1 A Brief Review of Laplace-Fourier Transform 75 2.6.1.2 Fourier and Laplace Transform 76 2.6.1.2(a) The Inversion Formula for Laplace Transform 79 2.6.1.3 A Short Tutorial on Fourier Integral and Transforms 82 2.6.1.4 Some Useful Fourier Transforms 86 2.6.2 Receptivity to Wall Excitation and Impulse Response 89 2.6.2.1 Near-Field Response Created by Localized Excitation 92 2.6.2.1a Outer Solution 94 2.6.2.1b Inner Solution 95 2.6.3 Vibrating Ribbon at The Wall 101 2.6.4 Receptivity to Free Stream Excitation 106 2.6.5 General Excitation and Upstream Propagating Mode 109 2.6.6 Low frequency freestream excitation and the Klebano. mode 118 2.7 Direct Simulation of Receptivity to Freestream Excitation: 123 2.7.1 Coupling Between Wall- and Freestream-Modes 126 2.7.2 Receptivity to Train of Convected Vortices in Freestream 129 2.7.3 Further Explanation of Freestream Periodic Excitation: 135 Chapter 03 141 Chapter 3 BYPASS TRANSITION 141 3.1 Introduction 141 3.2 Transition via Growing Waves and Bypass Transition: 142 3.3 Visualization Study of Vortex-Induced Instability as Bypass Transition 144 3.4 Computations of Vortex-Induced Instability as A Precursor to Bypass Transition 155 3.5 The Instability Mechanism in Vortex-Induced Instability 157 3.6 Instability on The Attachment-Line of Swept Wings 161 Chapter 04 168 Chapter 4 SPATIO-TEMPORAL INSTABILITY AND TRANSITION 168 4.1 Introduction 168 4.2 Transient Energy Growth 170 4.3 Energy-Based Receptivity Analysis 172 Chapter 05 187 Chapter 5 LANDAU EQUATION AND MULTIPLE HOPF-BIFURCATION 187 5.1 Landau’s Equation and Its Application for Flow Past a Cylinder 187 5.2 Instability of Flow Past a Cylinder 189 5.3 Nonlinear Instability and Amplitude Equation 190 5.4 Numerical Simulation of Flow Past a Circular Cylinder 192 Chapter 06 200 Chapter 6 STABILITY OF MIXED CONVECTION BOUNDARY LAYER 200 6.1 Introduction 200 6.2 The Governing Equations 204 6.3 Mean Flow Equations 205 6.4 Stability Equations and Numerical Method 207 6.4.1 Compound Matrix Method For The 6th Order System 210 6.4.2 Initial Conditions for The Induced System 212 6.4.3 Dispersion Relation 213 6.4.4 Eigen-function for The Mixed Convection Problem 214 6.5 Results and Discussion 215 6.5.1 Eigen-spectrum For Mixed Convection Problem 216 6.5.2 Neutral Curves For Mixed Convection Problem 221 6.5.3 Eigenfunctions of The Mixed Convection Problem 230 6.6 Conclusions and Outlook 236 Chapter 07 238 Chapter 7 COMBUSTION AND CFD FOR COMBUSTION 238 7.1 Introduction 238 7.2 Combustion and Energy Production 239 7.3 Combustion and Optimization 239 7.4 Combustion and Instabilities 241 7.5 Turbulent Combustion 243 7.6 DNS, LES and RANS for Combustion 244 Chapter 08 250 Chapter 8 WAVES IN REACTING FLOWS 250 8.1 Physical Waves In Reacting Flows 250 8.2 Numerical Waves in High-Fidelity Simulations of Reacting Flows 253 Chapter 09 256 Chapter 9 LARGE EDDY SIMULATION OF REAL COMBUSTORS 256 9.1 Introduction 256 9.2 Case 1: Small Scale Gas Turbine Burner 257 Configuration and Boundary Conditions 257 Nonreacting Flow 258 Average Fields 258 Structure of Unsteady Swirling Nonreacting Flows 258 Coexistence of Acoustic Modes and Precessing Vortex Core 261 Stable Reacting Flow 263 9.3 Case 2: Self-Excited Staged Burner 267 Configuration 267 Stable Flow 268 Controlling Oscillations Through Boundary Conditions 268 Chapter 10 272 Chapter 10 TWO-PHASE FLOW COMBUSTION 272 10.1 Equations 275 Carrier Phase 275 Dispersed Phase 277 Phase Exchange Source Terms 278 The Random Uncorrelated Motion (RUM) 279 LES Approach 279 Numerical Approach 281 10.2 Reacting Flow in An Aircraft Combustion Chamber 282 Configuration 282 Steady Spray Flame 283 Ignition Sequence 287 Chapter 11 291 Chapter 11 THE GROWTH OF ROUNDING ERRORS IN LES 291 11.1 Introduction 291 11.2 Effects of The Number of Processors on LES 293 11.3 Sensitivity of LES in Laminar and Turbulent Flows 296 A Fully Deterministic LES? 297 Influence of Turbulence 297 Influence of Initial Conditions 300 Effects of Graph Ordering 300 Effects of Time Step 302 Effects of Machine Precision 303 11.4 Conclusions 304 back-matter 306 Bibliography 306