1st Edition

Instabilities of Flows and Transition to Turbulence

By Tapan K. Sengupta Copyright 2012
    528 Pages 234 B/W Illustrations
    by CRC Press

    526 Pages 234 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    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.

    "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