3rd Edition

Analytical Fluid Dynamics

By George Emanuel Copyright 2015
    650 Pages 240 B/W Illustrations
    by CRC Press

    New Edition Now Covers Shock-Wave Analysis

    An in-depth presentation of analytical methods and physical foundations, Analytical Fluid Dynamics, Third Edition breaks down the "how" and "why" of fluid dynamics. While continuing to cover the most fundamental topics in fluid mechanics, this latest work emphasizes advanced analytical approaches to aid in the analytical process and corresponding physical interpretation. It also addresses the need for a more flexible mathematical language (utilizing vector and tensor analysis and transformation theory) to cover the growing complexity of fluid dynamics.

    Revised and updated, the text centers on shock-wave structure, shock-wave derivatives, and shock-produced vorticity; supersonic diffusers; thrust and lift from an asymmetric nozzle; and outlines operator methods and laminar boundary-layer theory. In addition, the discussion introduces pertinent assumptions, reasons for studying a particular topic, background discussion, illustrative examples, and numerous end-of-chapter problems.

    Utilizing a wide variety of topics on inviscid and viscous fluid dynamics, the author covers material that includes:

    • Viscous dissipation
    • The second law of thermodynamics
    • Calorically imperfect gas flows
    • Aerodynamic sweep
    • Shock-wave interference
    • Unsteady one-dimensional flow
    • Internal ballistics
    • Force and momentum balance
    • The Substitution Principle
    • Rarefaction shock waves
    • A comprehensive treatment of flow property derivatives just downstream of an unsteady three-dimensional shock
    • Shock-generated vorticity
    • Triple points
    • An extended version of the Navier‒Stokes equations
    • Shock-free supersonic diffusers
    • Lift and thrust from an asymmetric nozzle

    Analytical Fluid Dynamics, Third Edition outlines the basics of analytical fluid mechanics while emphasizing analytical approaches to fluid dynamics. Covering the material in-depth, this book provides an authoritative interpretation of formulations and procedures in analytical fluid dynamics, and offers analytical solutions to fluid dynamic problems.

    BASIC CONCEPTS

    Background Discussion
    Preliminary Remarks
    Euler and Lagrange Formulations
    Stress Tensor
    Relation between Stress and Deformation-Rate Tensors
    Constitutive Relations
    Problems
    References

    Conservation Equations
    Preliminary Remarks
    Mass Equation
    Transport Theorem
    Linear Momentum Equation
    Inertial Frame
    Angular Momentum Equation
    Energy Equation
    Viscous Dissipation
    Alternate Forms for the Energy Equation
    Problems
    Reference

    Classical Thermodynamics
    Preliminary Remarks
    Combined First and Second Laws
    Potential Functions
    Open System
    Coupling to Fluid Dynamics
    Compressible Liquid or Solid
    Second Law
    Rarefaction Shock Wave
    Problems
    References

    Kinematics
    Preliminary Remarks
    Definitions
    Kelvin’s Equation and Vorticity
    Helmholtz Vortex Theorems
    Problems
    Reference

    ADVANCED GAS DYNAMICS

    Euler Equations
    Preliminary Remarks
    Equations: Initial and Boundary Conditions
    Bernoulli’s Equations
    Vorticity
    Steady Flow
    Intrinsic Coordinates
    Problems
    References

    Shock-Wave Dynamics
    Preliminary Remarks
    Jump Conditions
    Steady, Two-Dimensional or Axisymmetric Flow
    Derivatives for a Two-Dimensional or Axisymmetric Shock with a Uniform Freestream
    Derivative Applications
    Problems
    References

    Vorticity and Its Substantial Derivative
    Preliminary Remarks
    Vorticity
    Substantial Derivative of the Vorticity
    Generic Shock Shape
    Slope, Curvature, Arc Length, and Sonic Point
    Results
    Problems
    References

    Shock-Wave Triple-Point Morphology
    Preliminary Remarks
    Analysis
    Solution Method
    Normal Mach Stem or Reflected Shocks
    Results and Discussion
    Problems
    References

    Derivatives When the Upstream Flow Is Nonuniform
    Preliminary Remarks
    Jump Conditions
    Tangential Derivatives
    Normal Derivatives
    Intrinsic Coordinate Derivatives
    Vorticity
    Source Flow Model
    Problems
    Reference

    General Derivative Formulation
    Preliminary Remarks
    Vector Relations
    Elliptic Paraboloid Shock
    Shock Curvatures
    Vorticity I
    Jump Conditions and Tangential Derivatives
    Normal Derivatives
    Applications
    Unsteady, Normal Derivative Formulation
    SMR and Ray Scaling
    Unsteady Intrinsic Coordinate Derivatives
    Vorticity II
    Problems
    References

    Extended Navier–Stokes Equations, Ultrasonic Absorption, and Shock Structure
    Preliminary Remarks
    Newtonian and Stokesian Fluids
    Viscous Dissipation
    Laminar Flow
    Unsteady One-Dimensional Flow
    Shock-Wave Structure
    Problems
    References

    Hodograph Transformation and Limit Lines
    Preliminary Remarks
    Two-Dimensional, Irrotational Flow
    Ringleb’s Solution
    Limit Lines
    General Solution
    Rotational Flow
    Problems
    References

    Substitution Principle
    Preliminary Remarks
    Transformation Equations
    Parallel Flow
    Prandtl–Meyer Flow
    Rotational Solutions in the Hodograph Plane
    Problems
    References

    Calorically Imperfect Flows
    Preliminary Remarks
    Thermodynamics
    Isentropic Streamtube Flow
    Planar Shock Flow
    Prandtl–Meyer Flow
    Taylor–Maccoll Flow
    Problems
    References

    Sweep
    Preliminary Remarks
    Oblique Shock Flow
    Prandtl-Meyer Flow
    Problems
    References

    Interaction of an Expansion Wave with a Shock Wave and a Shock-Wave Curvature
    Preliminary Remarks
    Flow Topology
    Solution for Regions I, II, and III
    Curvature Singularity
    Numerical Procedure
    Shock Wave with Longitudinal Curvature Sign Change
    Problems
    References

    Unsteady, One-Dimensional Flow
    Preliminary Remarks
    Incident Normal Shock Waves
    Reflected Normal Shock Waves
    Characteristic Theory
    Rarefaction Waves
    Compression Waves
    Internal Ballistics
    Nonsimple Wave Region
    Problems
    References

    Supersonic Diffusers
    Preliminary Remarks
    General Discussion
    Prandtl-Meyer Diffuser
    Lens-Analogy Diffuser
    Results and Discussion
    Problems
    References

    VISCOUS/INVISCID FLUID DYNAMICS

    Coordinate Systems and Related Topics
    Preliminary Remarks
    Orthogonal Coordinates
    Similarity Parameters
    Bulk Viscosity
    Viscous Flow in a Heated Duct
    Problems
    References

    Force and Moment Analysis
    Preliminary Remarks
    Momentum Theorem
    Surface Integral
    Angular Momentum
    Hydrostatics
    Flow in a Duct
    Acyclic Motion
    Jet–Plate Interaction
    Syringe with a Hypodermic Needle
    Shock-Expansion Theory
    Forces on a Particle
    Entropy Generation
    Forces and Moments on a Supersonic Vehicle
    Lift and Thrust of an Asymmetric Nozzle
    Problems
    References

    EXACT SOLUTIONS FOR A VISCOUS FLOW

    Rayleigh Flow
    Preliminary Remarks
    Solution
    Problems
    References

    Couette Flow
    Preliminary Remarks
    Solution
    Adiabatic Wall
    Problems
    Reference

    Stagnation Point Flow
    Preliminary Remarks
    Formulation
    Velocity Solution
    Temperature Solution
    Problems
    Reference

    LAMINAR BOUNDARY-LAYER THEORY FOR STEADY TWO-DIMENSIONAL OR AXISYMMETRIC FLOW

    Incompressible Flow over a Flat Plate
    Preliminary Remarks
    Derivation of the Boundary-Layer Equations
    Similarity Solution
    Problems
    References

    Large Reynolds Number Flow
    Preliminary Remarks
    Matched Asymptotic Expansions
    Problems
    References

    Incompressible Boundary-Layer Theory
    Preliminary Remarks
    Primitive Variable Formulation
    Solution of the Boundary-Layer Equations
    Problems
    References

    Compressible Boundary-Layer Theory
    Preliminary Remarks
    Boundary-Layer Equations
    Solution of the Similarity Equations
    Solution of the Energy Equation
    The β and gw Parameters
    Local Similarity
    Boundary-Layer Parameters
    Comprehensive Tables
    Adiabatic Wall
    Critique of the Prandtl Number and Chapman–Rubesin Parameter Assumptions
    Nonsimilar Boundary Layers: I
    Nonsimilar Boundary Layers: II
    Problems
    References

    Supersonic Boundary-Layer Examples
    Preliminary Remarks
    Thin Airfoil Theory
    Compressive Ramp
    Zero Displacement Thickness Wall Shape
    Performance of a Scramjet Propulsion Nozzle
    Problems
    References

    Second-Order Boundary-Layer Theory
    Preliminary Remarks
    Inner Equations
    Outer Equations
    Boundary and Matching Conditions
    Decomposition of the Second-Order Boundary-Layer Equations
    Example: First-Order Solution
    Example: Second-Order Outer Solution
    Example: Second-Order Inner Equations
    Appendix R

    Problems

    References

    Appendices

    Biography

    George Emanuel earned his PhD in aeronautical sciences from Stanford University, California. Subsequently, he was employed at the Aerospace Corp., TRW, and Los Alamos National Laboratory as a research engineer. He spent 19 years as a professor in the School of Aerospace and Mechanical Engineering at the University of Oklahoma. He is the author of numerous books that include Analytical Fluid Dynamics, Second Edition, Solution of Ordinary Differential Equations by Continuous Groups, and Shock Wave Dynamics (CRC Press). He is also the author of four chapters in three handbooks and the author or coauthor of more than 100 peer-reviewed articles.

    "The author has formulated curved shock theory with vector notation. This is a new and useful approach that has led to new results and insights and independent verification of the complex algebraic results of earlier tensor methods, the theory is surrounded by careful and thorough treatment of assumptions and limitations. Problems at the end of the chapter are well-chosen to promote a deeper understanding. This is a must-read for anyone searching for an appreciation of curved shock wave theory."
    —Sannu Mölder, Ryerson University, Toronto, Ontario, Canada

    "In the modern era where computational techniques dominate, it is refreshing to see a book that returns to the fundamentals in depth and breadth. Emanuel’s book is a solid treatment of basic fluid physics. It provides elegant and yet easy-to-follow mathematical treatments of a wide range of topics that are important in contemporary applications. One of the useful aspects of the work is its clear elucidation of the flow physics that is firmly grounded in the mathematics. Such revelations are difficult if not impossible to come by from numerical analysis. Thus, another value of this book is to provide checks to computational results."
    —Frank K. Lu, University of Texas at Arlington

    "Professor Emanuel extends the conventional thermodynamic development to include the nonclassical dynamics of a dense gas—and for the first time explains why expansion shock waves cannot exist. … one of the very few texts that even mentions the ‘nonclassical’ behavior of certain dense gases."
    —Brian Argrow, Department Aerospace Engineering Sciences, University of Colorado Boulder