Instabilities of Flows and Transition to Turbulence

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ISBN: 9781439879443 | 1439879443
Cover: Hardcover
Copyright: 4/24/2012

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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.

Symbol Description	p. ix
List of Figures	p. xv
List of Tables	p. xxvii
Preface	p. xxix
Introduction to Instability and Transition	p. 1
Introduction	p. 1
What Is Instability?	p. 4
Temporal and Spatial Instability	p. 4
Some Instability Mechanisms	p. 5
Dynamic Stability of Still Atmosphere	p. 5
Kelvin-Helmholtz Instability	p. 7
Computing Transitional and Turbulent Flows	p. 11
Fluid Dynamical Equations	p. 11
Equation of Continuity	p. 12
Momentum Conservation Equation	p. 12
Energy Conservation Equation	p. 14
Alternate Forms of the Energy Equation	p. 15
Equations of Motion in Terms of Derived Variables	p. 15
Some Equilibrium Solutions of the Basic Equation	p. 16
Couette Flow between Parallel Plates	p. 18
Flow between Concentric Rotating Cylinders	p. 19
Couette Flow between Parallel Plates, Driven by Pressure	p. 21
Steady Stagnation Point Flow	p. 24
Flow Past a Rotating Disc	p. 26
Boundary Layer Theory	p. 30
Control Volume Analysis of Boundary Layers	p. 35
Displacement Thickness	p. 36
Momentum Thickness	p. 36
Separation of a Steady Boundary Layer	p. 37
Accelerated Flows (dp/dx < 0)	p. 38
Retarded Flow (dp/dx > 0)	p. 38
Numerical Solution of the Thin Shear Layer (TSL) Equation	p. 40
Falkner-Skan Similarity Profile	p. 43
Separation Criterion for Wedge Flow	p. 44
Blasius Profile	p. 44
Hiemenz or Stagnation Point Flow	p. 44
Laminar Mixing Layer	p. 44
Plane Laminar Jet	p. 46
Issues of Computing Space-Time Dependent Flows	p. 48
Waves - Building Blocks of a Disturbance Field	p. 49
Plane Waves	p. 50
Wave Interaction: Group Velocity and Energy Flux	p. 51
Physical and Computational Implications of Group Velocity	p. 52
Wave Packets and Their Propagation	p. 53
Issues of Space-Time Scale Resolution of Flows	p. 54
Spatial Scales in Turbulent Flows	p. 54
Two- and Three-Dimensional DNS	p. 55
Temporal Scales in Turbulent Flows	p. 57
Computing Time-Averaged and Unsteady Flows	p. 59
Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methods	p. 61
Spectral or Numerical Amplification Factor	p. 62
Quantification of Dispersion Error	p. 65
DRP Schemes: Parameter Ranges for Creating q-Waves	p. 68
Instability and Transition in Flows	p. 75
Introduction	p. 75
Parallel Flow Approximation and Inviscid Instability Theorems	p. 76
Inviscid Instability Mechanism	p. 78
Viscous Instability of Parallel Flows	p. 79
Eigenvalue Formulation for Instability of Parallel Flows	p. 80
Temporal and Spatial Amplification of Disturbances	p. 83
Temporal Amplification Theory	p. 83
Spatial Amplification Theory	p. 83
Relationship between Temporal and Spatial Theories	p. 84
Properties of the Orr-Sommerfeld Equation and Boundary Conditions	p. 85
Compound Matrix Method	p. 87
Instability Analysis from the Solution of the Orr-Sommerfeld Equation	p. 91
Local and Total Amplification of Disturbances	p. 95
Effects of the Mean Flow Pressure Gradient	p. 97
Transition Prediction Based on Stability Calculation	p. 102
Effects of Free Stream Turbulence	p. 103
Receptivity Analysis of the Shear Layer	p. 106
Receptivity Mechanism by a Linearized Approach: Connection to Stability Theory	p. 107
A Brief Review of Laplace-Fourier Transforms	p. 107
Fourier and Laplace Transforms	p. 108
Inversion Formula for Laplace Transforms	p. 110
A Short Tutorial on Fourier Integral and Transforms	p. 112
Some Useful Laplace-Fourier Transforms	p. 115
Receptivity to Wall Excitation and Impulse Response	p. 118
Near-Field Response Created by Localized Excitation	p. 120
Outer Solution	p. 122
Inner Solution	p. 122
Vibrating Ribbon at the Wall	p. 127
Receptivity to Free Stream Excitation	p. 130
General Excitation and Upstream Propagating Modes	p. 132
Low Frequency Free Stream Excitation and the Klebanoff Mode	p. 138
Direct Simulation of Receptivity to Free Stream Excitation	p. 140
Coupling between the Wall and Free Stream Modes	p. 144
Receptivity to a Train of Convected Vortices in the Free Stream	p. 147
Further Explanation of Free Stream Periodic Excitation	p. 151
Nonparallel and Nonlinear Effects on Instability and Receptivity	p. 155
Time Varying Receptivity Problem vis-a-vis the Signal Problem	p. 158
Evidence of Nonparallel and Nonlinear Effects	p. 159
Limitations of Linearized Nonparallel Theories	p. 166
Bypass Transition: Theory, Computations, and Experiments	p. 171
Introduction	p. 171
Transition via Growing Waves and Bypass Transition	p. 177
Visualization Study of Vortex-Induced Instability as Bypass Transition	p. 179
Computations of Vortex-Induced Instability as a Precursor to Bypass Transition	p. 189
Instability Mechanism in Vortex-Induced Instability	p. 192
Instability at the Attachment Line of Swept Wings	p. 195
Spatio-Temporal Wave Front and Transition	p. 201
Introduction	p. 201
Transient Energy Growth	p. 205
Bromwich Contour Integral Method and Energy-Based Receptivity Analysis	p. 206
Spatio-Temporal Wave Front Obtained by the Bromwich Contour Integral Method	p. 207
Nonlinear Receptivity Analysis: Transition by the Spatio-Temporal Front and Bypass Route	p. 217
Governing Equations and Boundary Condition	p. 219
Nonlinear Receptivity to Vortical Wall Excitation	p. 223
Low Amplitude, Moderate Frequency Excitation	p. 226
High Amplitude Cases and Spot Regeneration Mechanism	p. 229
Low Frequency Excitation Cases: Different Route of Transition	p. 234
Calculation of the N Factor	p. 240
Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decomposition	p. 245
Introduction	p. 245
Receptivity of Bluff-Body Flows to Background Disturbances	p. 246
Numerical Simulation of Flow Past a Cylinder	p. 251
Multiple Hopf Bifurcations, Landau Equation and Flow Instability	p. 256
Instability of Flow Past a Cylinder	p. 258
Role of FST on Critical Reynolds Number for a Cylinder	p. 260
POD Modes and Nonlinear Stability	p. 263
Landau-Stuart-Eckhaus Equation	p. 274
Universality of POD Modes	p. 276
Stability and Transition of Mixed Convection Flows	p. 293
Introduction	p. 293
Governing Equations	p. 297
Equilibrium Boundary Layer Flow Equations	p. 298
Schneider's Similarity Solution	p. 299
Linear Spatial Stability Analysis of the Boundary Layer over a Heated Plate	p. 305
Fundamental Solutions of the OSE	p. 310
Compound Matrix Method for the Sixth Order OSE	p. 312
Initial Conditions for an Auxiliary System of Equations	p. 315
Dispersion Relation	p. 316
The Grid Search Method and the Newton-Raphson Technique for Obtaining Eigenspectrum	p. 316
Neutral Curve and Wavenumber Contours	p. 319
Precision in Computing	p. 321
Results of the Linear Spatial Stability Theory	p. 322
Nonlinear Receptivity of Mixed Convection Flow over a Heated Plate	p. 333
Boundary and Initial Conditions	p. 336
Eigenfunction Structure and DNS of the Mixed Convection Problem	p. 356
Concluding Remarks	p. 358
Instabilities of Three-Dimensional Flows	p. 361
Introduction	p. 361
Three-Dimensional Flows	p. 361
Infinite Swept Wing Flow	p. 364
Attachment Line Flow	p. 365
Boundary Layer Equations in the Transformed Plane	p. 367
Simplification of Boundary Layer Equations in the Transformed Plane	p. 368
Instability of Three-Dimensional Flows	p. 369
Effects of Sweep Back and Cross Flow Instability	p. 370
Linear Stability Theory for Three-Dimensional Flows	p. 372
Temporal Instability of Three-Dimensional Flows	p. 373
Spatial Instability of Three-Dimensional Flows	p. 374
Experimental Evidence of Instability on Swept Wings	p. 376
Infinite Swept Wing Boundary Layer	p. 377
Stability of the Falkner-Skan-Cooke Profile	p. 381
Stationary Waves over Swept Geometries	p. 384
Traveling Waves over Swept Geometries	p. 386
Attachment Line Problem	p. 387
Empirical Transition Prediction Method for Three-Dimensional Flows	p. 389
Streamwise Transition Criterion	p. 389
Cross Flow Transition Criteria	p. 389
Leading Edge Contamination Criterion	p. 390
Analysis and Design of Natural Laminar Flow Airfoils	p. 393
Introduction	p. 393
Airfoil Nomenclature and Basic Aerodynamic Properties	p. 394
Pressure Distribution and Pressure Recovery of Some Low Drag Airfoils	p. 402
Flapping of Airfoils	p. 406
Effects of Roughness and Fixing Transition	p. 407
Effects of Vortex Generator or Boundary Layer Re-Energizer	p. 409
Section Characteristics of Various Profiles	p. 410
High Speed NLF Airfoils	p. 412
Direct Simulation of Bypass Transitional Flow Past an Airfoil	p. 420
Epilogue	p. 425
Introduction	p. 425
Relevance of Two-Dimensional Turbulence	p. 426
Role of Formulation in the Numerical Solution in Two-Dimensional DNS	p. 427
Dynamical System Representation of Turbulent Flows	p. 429
Role of the Computational Domain	p. 431
Renewal Mechanism and Intermittent Nature of Turbulence	p. 433
Free and Forced Turbulence	p. 437
Selected Problems	p. 441
Bibliography	p. 447
Index	p. 473
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Instabilities of Flows and Transition to Turbulence

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