Instabilities of Flows and Transition to Turbulence

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  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2012-04-24
  • Publisher: CRC Press

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This book covers material ranging from classical hydrodynamic instability to contemporary research areas, including bluff body flow instability and mixed convection flows. It also examines applications in aerospace and other branches of engineering such as fluid mechanics. The author addresses classical material as well as new perspectives and presents comprehensive coverage of receptivity to complement the instability material. This book presents a concise, up-to-date treatment of theory and applications of viscous flow instability, providing both current knowledge and techniques.

Table of Contents

Symbol Descriptionp. ix
List of Figuresp. xv
List of Tablesp. xxvii
Prefacep. xxix
Introduction to Instability and Transitionp. 1
Introductionp. 1
What Is Instability?p. 4
Temporal and Spatial Instabilityp. 4
Some Instability Mechanismsp. 5
Dynamic Stability of Still Atmospherep. 5
Kelvin-Helmholtz Instabilityp. 7
Computing Transitional and Turbulent Flowsp. 11
Fluid Dynamical Equationsp. 11
Equation of Continuityp. 12
Momentum Conservation Equationp. 12
Energy Conservation Equationp. 14
Alternate Forms of the Energy Equationp. 15
Equations of Motion in Terms of Derived Variablesp. 15
Some Equilibrium Solutions of the Basic Equationp. 16
Couette Flow between Parallel Platesp. 18
Flow between Concentric Rotating Cylindersp. 19
Couette Flow between Parallel Plates, Driven by Pressurep. 21
Steady Stagnation Point Flowp. 24
Flow Past a Rotating Discp. 26
Boundary Layer Theoryp. 30
Control Volume Analysis of Boundary Layersp. 35
Displacement Thicknessp. 36
Momentum Thicknessp. 36
Separation of a Steady Boundary Layerp. 37
Accelerated Flows (dp/dx < 0)p. 38
Retarded Flow (dp/dx > 0)p. 38
Numerical Solution of the Thin Shear Layer (TSL) Equationp. 40
Falkner-Skan Similarity Profilep. 43
Separation Criterion for Wedge Flowp. 44
Blasius Profilep. 44
Hiemenz or Stagnation Point Flowp. 44
Laminar Mixing Layerp. 44
Plane Laminar Jetp. 46
Issues of Computing Space-Time Dependent Flowsp. 48
Waves - Building Blocks of a Disturbance Fieldp. 49
Plane Wavesp. 50
Wave Interaction: Group Velocity and Energy Fluxp. 51
Physical and Computational Implications of Group Velocityp. 52
Wave Packets and Their Propagationp. 53
Issues of Space-Time Scale Resolution of Flowsp. 54
Spatial Scales in Turbulent Flowsp. 54
Two- and Three-Dimensional DNSp. 55
Temporal Scales in Turbulent Flowsp. 57
Computing Time-Averaged and Unsteady Flowsp. 59
Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methodsp. 61
Spectral or Numerical Amplification Factorp. 62
Quantification of Dispersion Errorp. 65
DRP Schemes: Parameter Ranges for Creating q-Wavesp. 68
Instability and Transition in Flowsp. 75
Introductionp. 75
Parallel Flow Approximation and Inviscid Instability Theoremsp. 76
Inviscid Instability Mechanismp. 78
Viscous Instability of Parallel Flowsp. 79
Eigenvalue Formulation for Instability of Parallel Flowsp. 80
Temporal and Spatial Amplification of Disturbancesp. 83
Temporal Amplification Theoryp. 83
Spatial Amplification Theoryp. 83
Relationship between Temporal and Spatial Theoriesp. 84
Properties of the Orr-Sommerfeld Equation and Boundary Conditionsp. 85
Compound Matrix Methodp. 87
Instability Analysis from the Solution of the Orr-Sommerfeld Equationp. 91
Local and Total Amplification of Disturbancesp. 95
Effects of the Mean Flow Pressure Gradientp. 97
Transition Prediction Based on Stability Calculationp. 102
Effects of Free Stream Turbulencep. 103
Receptivity Analysis of the Shear Layerp. 106
Receptivity Mechanism by a Linearized Approach: Connection to Stability Theoryp. 107
A Brief Review of Laplace-Fourier Transformsp. 107
Fourier and Laplace Transformsp. 108
Inversion Formula for Laplace Transformsp. 110
A Short Tutorial on Fourier Integral and Transformsp. 112
Some Useful Laplace-Fourier Transformsp. 115
Receptivity to Wall Excitation and Impulse Responsep. 118
Near-Field Response Created by Localized Excitationp. 120
Outer Solutionp. 122
Inner Solutionp. 122
Vibrating Ribbon at the Wallp. 127
Receptivity to Free Stream Excitationp. 130
General Excitation and Upstream Propagating Modesp. 132
Low Frequency Free Stream Excitation and the Klebanoff Modep. 138
Direct Simulation of Receptivity to Free Stream Excitationp. 140
Coupling between the Wall and Free Stream Modesp. 144
Receptivity to a Train of Convected Vortices in the Free Streamp. 147
Further Explanation of Free Stream Periodic Excitationp. 151
Nonparallel and Nonlinear Effects on Instability and Receptivityp. 155
Time Varying Receptivity Problem vis-a-vis the Signal Problemp. 158
Evidence of Nonparallel and Nonlinear Effectsp. 159
Limitations of Linearized Nonparallel Theoriesp. 166
Bypass Transition: Theory, Computations, and Experimentsp. 171
Introductionp. 171
Transition via Growing Waves and Bypass Transitionp. 177
Visualization Study of Vortex-Induced Instability as Bypass Transitionp. 179
Computations of Vortex-Induced Instability as a Precursor to Bypass Transitionp. 189
Instability Mechanism in Vortex-Induced Instabilityp. 192
Instability at the Attachment Line of Swept Wingsp. 195
Spatio-Temporal Wave Front and Transitionp. 201
Introductionp. 201
Transient Energy Growthp. 205
Bromwich Contour Integral Method and Energy-Based Receptivity Analysisp. 206
Spatio-Temporal Wave Front Obtained by the Bromwich Contour Integral Methodp. 207
Nonlinear Receptivity Analysis: Transition by the Spatio-Temporal Front and Bypass Routep. 217
Governing Equations and Boundary Conditionp. 219
Nonlinear Receptivity to Vortical Wall Excitationp. 223
Low Amplitude, Moderate Frequency Excitationp. 226
High Amplitude Cases and Spot Regeneration Mechanismp. 229
Low Frequency Excitation Cases: Different Route of Transitionp. 234
Calculation of the N Factorp. 240
Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decompositionp. 245
Introductionp. 245
Receptivity of Bluff-Body Flows to Background Disturbancesp. 246
Numerical Simulation of Flow Past a Cylinderp. 251
Multiple Hopf Bifurcations, Landau Equation and Flow Instabilityp. 256
Instability of Flow Past a Cylinderp. 258
Role of FST on Critical Reynolds Number for a Cylinderp. 260
POD Modes and Nonlinear Stabilityp. 263
Landau-Stuart-Eckhaus Equationp. 274
Universality of POD Modesp. 276
Stability and Transition of Mixed Convection Flowsp. 293
Introductionp. 293
Governing Equationsp. 297
Equilibrium Boundary Layer Flow Equationsp. 298
Schneider's Similarity Solutionp. 299
Linear Spatial Stability Analysis of the Boundary Layer over a Heated Platep. 305
Fundamental Solutions of the OSEp. 310
Compound Matrix Method for the Sixth Order OSEp. 312
Initial Conditions for an Auxiliary System of Equationsp. 315
Dispersion Relationp. 316
The Grid Search Method and the Newton-Raphson Technique for Obtaining Eigenspectrump. 316
Neutral Curve and Wavenumber Contoursp. 319
Precision in Computingp. 321
Results of the Linear Spatial Stability Theoryp. 322
Nonlinear Receptivity of Mixed Convection Flow over a Heated Platep. 333
Boundary and Initial Conditionsp. 336
Eigenfunction Structure and DNS of the Mixed Convection Problemp. 356
Concluding Remarksp. 358
Instabilities of Three-Dimensional Flowsp. 361
Introductionp. 361
Three-Dimensional Flowsp. 361
Infinite Swept Wing Flowp. 364
Attachment Line Flowp. 365
Boundary Layer Equations in the Transformed Planep. 367
Simplification of Boundary Layer Equations in the Transformed Planep. 368
Instability of Three-Dimensional Flowsp. 369
Effects of Sweep Back and Cross Flow Instabilityp. 370
Linear Stability Theory for Three-Dimensional Flowsp. 372
Temporal Instability of Three-Dimensional Flowsp. 373
Spatial Instability of Three-Dimensional Flowsp. 374
Experimental Evidence of Instability on Swept Wingsp. 376
Infinite Swept Wing Boundary Layerp. 377
Stability of the Falkner-Skan-Cooke Profilep. 381
Stationary Waves over Swept Geometriesp. 384
Traveling Waves over Swept Geometriesp. 386
Attachment Line Problemp. 387
Empirical Transition Prediction Method for Three-Dimensional Flowsp. 389
Streamwise Transition Criterionp. 389
Cross Flow Transition Criteriap. 389
Leading Edge Contamination Criterionp. 390
Analysis and Design of Natural Laminar Flow Airfoilsp. 393
Introductionp. 393
Airfoil Nomenclature and Basic Aerodynamic Propertiesp. 394
Pressure Distribution and Pressure Recovery of Some Low Drag Airfoilsp. 402
Flapping of Airfoilsp. 406
Effects of Roughness and Fixing Transitionp. 407
Effects of Vortex Generator or Boundary Layer Re-Energizerp. 409
Section Characteristics of Various Profilesp. 410
High Speed NLF Airfoilsp. 412
Direct Simulation of Bypass Transitional Flow Past an Airfoilp. 420
Epiloguep. 425
Introductionp. 425
Relevance of Two-Dimensional Turbulencep. 426
Role of Formulation in the Numerical Solution in Two-Dimensional DNSp. 427
Dynamical System Representation of Turbulent Flowsp. 429
Role of the Computational Domainp. 431
Renewal Mechanism and Intermittent Nature of Turbulencep. 433
Free and Forced Turbulencep. 437
Selected Problemsp. 441
Bibliographyp. 447
Indexp. 473
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