Modern Developments in Gas Dynamics

During the last decade, the rapid growth of knowledge in the field of fluid mechanics and heat transfer has resulted in many significant ad­ vances of interest to students, engineers, and scientists. Accordingly, a course entitled "Modern Developments in Fluid Mechanics and Heat Transfer" was given at the University of California to present significant recent theoretical and experimental work. The course consisted of seven parts: I-Introduction; II-Hydraulic Analogy for Gas Dynamics; 111- Turbulence and Unsteady Gas Dynamics; IV-Rarefied and Radiation Gas Dynamics; V-Biological Fluid Mechanics; VI-Hypersonic and Plasma Gas Dynamics; and VII-Heat Transfer in Hypersonic Flows. The material, presented by the undersigned as course instructor and by various guest lecturers, could easily be adapted by other universities for use as a text for a one-semester senior or graduate course on the subject. Due to the extensive notes developed during the University of California course, it was decided to publish the material in three volumes, of which the present is the first. The succeeding volumes will be entitled "Selected Topics in Fluid and Bio-Fluid Mechanics" and "Introduction to Steady and Unsteady Gas Dynamics." Finally, I must express a word of appreciation to my wife Irene and to my children, Wellington Jr. and Victoria, who made it possible for me to write and edit this book in the very quiet atmosphere of our home.

1 Theory of the Hydraulic Analogy for Steady and Unsteady Gas Dynamics.- 1. Two-Dimensional Steady Flow Analogy.- 1.1. Energy Equation.- 1.2. Continuity Equation.- 1.3. Irrotational Motion.- 1.4. Summary.- 2. Hydraulic Jumps (Shocks).- 2.1. Shock Polars.- 2.2. Water Depths in Hydraulic Jump.- 2.3. Energy Loss during Hydraulic Jump.- 2.4. Summary.- 3. One-Dimensional Unsteady Gas Dynamics by Hydraulic Analogy.- 3.1. Two-Dimensional Steady Flow.- 3.2. One-Dimensional Unsteady Flow.- 3.3. Equations of Standing Waves.- 3.4. Summary of Analogous Equations.- 3.5. Discussion.- 4. Hydraulic Analogy for Longitudinal Plane Waves. Derivation of Equations of Standing Waves.- 4.1. Continuity Equation.- 4.2. Equation of Thermodynamics and Equation of Hydraulics.- 4.3. Equation of Motion.- 4.4. Wave Equations,.- 4.5. Equation of Wave Propagation Velocity.- 4.6. Summary.- 5. Experimental Verification.- 5.1. Equations for Experimental Model.- 5.2. Analogous Quantities for Hydraulic Model Design.- Appendix A.- Appendix B.- Notation.- References.- 2 Combined Heat and Mass Transfer Processes.- 1. Conservation Equations.- 2. Constitutive Equations.- 3. Laminar Boundary Layer Equations.- 4. Solutions of the Laminar Boundary Layer Equations.- 4.1. Heat Transfer.- 4.2. Mass Transfer.- 4.3. Example.- 5. Turbulent Boundary Layers.- 6. Correction Equations for Pr ? 1 and Le ? 1.- Notation.- References.- 3 Hypersonic Viscous Flows.- 1. Induced-Pressure Effects.- 1.1. Introduction.- 1.2. Basic Considerations.- 1.3. Flat Plate ? = 0.- 1.4. Blunt Wedge.- 2. Closed-Form Local Similarity.- 2.1. Local Similarity Defined.- 2.2. Compressible Similar Solutions.- 2.3. Closed-Form Local-Similarity Solutions.- 3. Boundary Layer Transition.- 4. Turbulent Boundary Layer.- 4.1. Effect of Wall-Temperature Ratio.- 4.2. Virtual Origin.- 4.3. Transformation of Compressible Boundary Layer Profiles.- Notation.- References.- 4 Hypersonic Gas Dynamics of Slender Bodies.- 1. Inviscid Flows and Related Problems.- 1.1. Entropy and Speed Defects.- 1.2. The Shock-Layer/Entropy-Wake Interaction.- 1.3. Blow-Hard.- 1.4. Minimizing Drag.- 2. The Outer-Edge Problem of the Hypersonic Boundary Layer on a Slender Body.- 2.1. The Outer-Edge Problem.- 2.2. The Scales Associated with the Viscous Transition Layer.- 2.3. The Transition Layer in the Strong- and Weak-Interaction Regimes Involving Power-Law Shocks.- 2.4. The Outer-Edge Problem for the Flat Plate in the Strong-Interaction Regime: ? = 1.- 3. Transverse Curvature and Cross Flow in the Strong-Interaction Regime.- 3.1. A Strong-Interaction Formulation of Hypersonic Viscous Flow around Asymmetrical Slender Bodies.- 3.2. The Needle in the Strong-Interaction Regime.- 3.3. The Needle Problem in the Weak-Shock Regimes.- Acknowledgment.- References.- 5 Hypersonic Blunt-Body Gas Dynamics.- 1. Classification of Body Shapes.- 2. Blunt-Body Flow Fields.- 3. Flow Regimes.- 4. Flow-Field Gas Properties.- 5. Inviscid-Flow Analysis.- 5.1. Methods of Analysis—Subsonic-Transonic Region.- 5.2. Method of Analysis—Supersonic Region.- 6. Viscous-Flow Analysis.- 6.1. Methods of Analysis—Boundary Layer.- 6.2. Improved Boundary-Layer Analysis.- 7. Interactions of Viscous-Inviscid Flow.- 7.1. Separated Flow.- 7.2. Base and Wake Flow Fields.- 8. Wake Flows.- 9. Summary.- Notation.- References.- 6 Rarefied Gas Dynamics.- 1. Elements of Kinetic Theory.- 2. Free-Molecular Flow.- 3. Slip Flow.- References.- 7 Fundamentals of Radiation Gas Dynamics.- 1. Fundamentals of Radiative Transfer.- 2. Fundamental Equations of Radiation Gas Dynamics.- 3. Initial and Boundary Conditions of Radiation Gas Dynamics.- 4. Similarity Parameters of Radiation Gas Dynamics.- 4.1. Dimensionless Parameters of Ordinary Gas Dynamics.- 4.2. Dimensionless Parameters of Radiation Gas Dynamics.- 5. Radiation Mean Free Path.- 6. Wave Motion in a Radiating Gas.- 7. Shock Waves.- 7.1. Rankine-Hugoniot Relations in Radiation Gas Dynamics.- 7.2. Shock-Wave Structure.- 8. Two-Dimensional Channel Flows of an Ionized, Radiating Gas.- 9. Unsteady Laminar Boundary Layer on an Infinite Plate.- 10. A Uniform Flow of a Radiating Gas Over a Semiinfinite Plate.- 11. Stagnation-Point Heat Transfer in Radiation Gas Dynamics.- Acknowledgment.- Notation.- References.- 8 Some Problems of Radiative Transfer.- 1. Absorption Coefficients for Radiative Transfer Calculation.- 1.1. Gray-Gas Approximations.- 1.2. Piecewise Gray Models.- 1.3. Models for Band Radiation.- 2. The Differential Approximation.- 2.1. For a Nongray Gas.- 2.2. Difficulties near Surfaces.- 2.3. The Three-Dimensional Difficulty.- 3. A Problem of Thermal Choking by Radiation.- Notation.- References.- 9 Plasma Dynamics.- 1. Plasmas and Plasma Dynamics.- 2. Fundamental Equations of the Dynamics of an Electrically-Conducting Fluid.- 3. Equations and Boundary Conditions of Electromagnetic Fields.- 4. Magnetogasdynamic Approximations.- 5. Electrogasdynamic Approximations.- 6. Important Parameters of Electromagnetofluid Dynamics.- 7. One-Dimensional Flow in Magnetogasdynamics.- 8. One-Dimensional Flow in Electrogasdynamics.- 9. Channel Flow in Magnetohydrodynamics.- 10. Waves and Shocks in Magnetogasdynamics.- 11. Boundary Layer Flow in Magnetofluid Dynamics.- 12. Wakes in Magnetohydrodynamics.- 13. Tensor Electrical Conductivity.- 14. Turbulent Flow in Magnetohydrodynamics.- 15. Multifluid Theory of Magnetofluid Dynamics.- Acknowledgment.- Notation.- References.- Author Index.