Analytical Fluid Dynamics

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

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