Analytical Fluid Dynamics, Third Edition

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.

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 ß 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