Analytical Fluid Dynamics, Third Edition / Edition 3

by George Emanuel

Overview

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.

Product Details

ISBN-13:	9781498715690
Publisher:	Taylor & Francis
Publication date:	10/28/2015
Edition description:	3rd ed.
Pages:	650
Product dimensions:	8.40(w) x 10.90(h) x 1.60(d)

About the Author

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.

Table of Contents

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

Editorial Reviews

"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

"Analytical Fluid Dynamics, 3rd Ed. is a must-have reference useful for a variety of advanced undergraduate and graduate courses in fluid dynamics, and more specialized courses in aerodynamics. The scope and in-depth coverage of topics is unique in contemporary fluid mechanics literature. With increasing emphasis on computational methods in research and industrial applications, the greatest value of Analytical Fluid Dynamics for those communities is twofold: 1) mathematically elegant analyses that expand physical insight into basic concepts and the development of advanced fluid-flow theory, and 2) analytical solutions of complex flow phenomena that can be used to verify CFD methods and codes. Examples include chapters devoted to sweep, the substitution principle, calorically imperfect flows, and supersonic diffusers that can be found nowhere else. Particularly relevant for high-speed aerodynamics and CFD are chapters presenting a general approach to shock waves and related phenomena that include their structure, vorticity generation, and downstream flow derivatives. A chapter on thermodynamics discusses the use of a potential function for CFD that is consistent with the modelling of real gas flows that produce rarefaction shock waves. Additional chapters are devoted to one-dimensional flows, a force and momentum analysis, and first-and-second-order boundary-layer theory. In keeping with the analytical approach, appendices cover vector and tensor analysis, Jacobian theory (useful for transforming thermodynamic derivatives and transforming fluid dynamic equations), and characteristic theory for the solution of first-order PDEs. Illustrative examples are included throughout that show stepwise development of theory and application to relevant problems."
—Brian Argrow, Department Aerospace Engineering Sciences, University of Colorado Boulder

From the Publisher