Instabilities of Flows and Transition to Turbulence

Summary

Addressing classical material as well as new perspectives, Instabilities of Flows and Transition to Turbulence presents a concise, up-to-date treatment of theory and applications of viscous flow instability. It covers materials from classical instability to contemporary research areas including bluff body flow instability, mixed convection flows, and application areas of aerospace and other branches of engineering. Transforms and perturbation techniques are used to link linear instability with receptivity of flows, as developed by the author.

The book:

• Provides complete coverage of transition concepts, including receptivity and flow instability
• Introduces linear receptivity using bi-lateral Fourier-Laplace transform techniques
• Presents natural laminar flow (NLF) airfoil analysis and design as a practical application of classical and bypass transition
• Distinguishes strictly between instability and receptivity, which leads to identification of wall- and free stream-modes
• Describes energy-based receptivity theory for the description of bypass transitions

Instabilities of Flows and Transition to Turbulence has evolved into an account of the personal research interests of the author over the years. A conscious effort has been made to keep the treatment at an elementary level requiring rudimentary knowledge of calculus, the Fourier-Laplace transform, and complex analysis. The book is equally amenable to undergraduate students, as well as researchers in the field.

Table of Contents

Introduction to Instability and Transition
Introduction
What Is Instability?
Temporal and Spatial Instability
Some Instability Mechanisms

Computing Transitional and Turbulent Flows
Fluid Dynamical Equations
Some Equilibrium Solutions of the Basic Equation
Boundary Layer Theory
Control Volume Analysis of Boundary Layers
Numerical Solution of the Thin Shear Layer (TSL) Equation
Laminar Mixing Layer
Plane Laminar Jet
Issues of Computing Space-Time Dependent Flows
Wave Interaction: Group Velocity and Energy Flux
Issues of Space-Time Scale Resolution of Flows
Temporal Scales in Turbulent Flows
Computing Time-Averaged and Unsteady Flows
Computing Methods for Unsteady Flows: Dispersion Relation Preserving (DRP) Methods
DRP Schemes: Parameter Ranges for Creating q-Waves

Instability and Transition in Flows
Introduction
Parallel Flow Approximation and Inviscid Instability Theorems
Viscous Instability of Parallel Flows
Properties of the Orr-Sommerfeld Equation and Boundary Conditions
Instability Analysis from the Solution of the Orr-Sommerfeld Equation
Receptivity Analysis of the Shear Layer
Direct Simulation of Receptivity to Free Stream Excitation
Nonparallel and Nonlinear Effects on Instability and Receptivity

Bypass Transition: Theory, Computations and Experiments
Introduction
Transition via Growing Waves and Bypass Transition
Visualization Study of Vortex-Induced Instability as Bypass Transition
Computations of Vortex-Induced Instability as a Precursor to Bypass Transition
The Instability Mechanism in Vortex-Induced Instability
Instability at the Attachment Line of Swept Wings

Spatio-Temporal Wave Front and Transition
Introduction
Transient Energy Growth
Bromwich Contour Integral Method and Energy-Based Receptivity Analysis
Spatio-Temporal Wave Front Obtained by the Bromwich Contour Integral Method
Nonlinear Receptivity Analysis: Transition by the Spatio-Temporal Front and
Bypass Route
Calculation of the N Factor

Nonlinear Effects: Multiple Hopf Bifurcations and Proper Orthogonal Decomposition
Introduction
Receptivity of Bluff-Body Flows to Background Disturbances
Multiple Hopf Bifurcations, Landau Equation and Flow Instability
Instability of Flow Past a Cylinder
Role of FST on Critical Reynolds Number for a Cylinder
POD Modes and Nonlinear Stability
The Landau-Stuart-Eckhaus Equation
Universality of POD Modes

Stability and Transition of Mixed Convection Flows
Introduction
The Governing Equations
Equilibrium Boundary Layer Flow Equations
Linear Spatial Stability Analysis of the Boundary Layer over a Heated Plate
Nonlinear Receptivity of Mixed Convection Flow over a Heated Plate
Concluding Remarks

Instabilities of Three-Dimensional Flows
Introduction
Three-Dimensional Flows
Infinite Swept Wing Flow
Attachment Line Flow
Boundary Layer Equations in the Transformed Plane
Simplification of Boundary Layer Equations in the Transformed Plane
Instability of Three-Dimensional Flows
Linear Stability Theory for Three-Dimensional Flows
Experimental Evidence of Instability on Swept Wings
Infinite Swept Wing Boundary Layer
Stability of the Falkner-Skan-Cooke Profile
Stationary Waves over Swept Geometries
Traveling Waves over Swept Geometries
Attachment Line Problem
Empirical Transition Prediction Method for Three-Dimensional Flows

Analysis and Design of Natural Laminar Flow Airfoils
Introduction
Airfoil Nomenclature and Basic Aerodynamic Properties
Pressure Distribution and Pressure Recovery of Some Low Drag Airfoils
Flapping of Airfoils
Effects of Roughness and Fixing Transition
Effects of Vortex Generator or Boundary Layer Re-energizer
Section Characteristics of Various Profiles
High Speed NLF Airfoils
Direct Simulation of Bypass Transitional Flow Past an Airfoil

Epilogue
Introduction
Relevance of Two-Dimensional Turbulence
Role of Formulation in the Numerical Solution in Two-dimensional DNS
Dynamical System Representation of Turbulent Flows
Role of the Computational Domain
Free and Forced Turbulence

Selected Problems
Bibliography and Index

Author(s) Bio

About the author: Professor Tapan K. Sengupta is affiliated with the High Performance Computing Laboratory in the Department of Aerospace Engineering at the Indian Institute of Technology, Kanpur, India.

Reviews

"The monograph contains the following topics of hydrodynamics: 1. Classic linear hydrodynamic instability; 2. Receptivity and instability of different types; 3. Vortex-induced instability and bypass transition; 4. Transient growth and spatio-temporal instability; 5. Bifurcation and dynamical system theory of nonlinear instabilities for different flows; 6. Instability of mixed convection flows by restricted heat transfer; 7. Instability of three-dimensional flows; 8. Applications of instability and transition for flows past airfoils. These linear and nonlinear aspects of flow instabilities are studied by using analytic and computational (numerical simulation) means. … "
––Boris V. Loginov, Zentralblatt MATH

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