Elements of Gas Dynamics

by Liepmann, H. W.; Roshko, A.

• ISBN13: 9780486419633
• ISBN10: 0486419630
• Format: Paperback
• Copyright: 2002-01-11
• Publisher: Dover Publications

Summary

First-rate text covers introductory concepts from thermodynamics, one-dimensional gas dynamics and one-dimensional wave motion, waves in supersonic flow, flow in ducts and wind tunnels, methods of measurement, the equations of frictionless flow, small-perturbation theory, transonic flow, and much more. For advanced undergraduate or graduate physics and engineering students with at least a working knowledge of calculus and basic physics. Exercises demonstrate application of material in text.

Table of Contents

Concepts from Thermodynamics
Introduction	1	(1)
Thermodynamic Systems	2	(1)
Variables of State	3	(1)
The First Principal Law	4	(2)
Irreversible and Reversible Processes	6	(1)
Perfect Gases	7	(3)
The First Law Applied to Reversible Processes. Specific Heats	10	(4)
The First Law Applied to Irreversible Processes	14	(3)
The Concept of Entropy. The Second Law	17	(3)
The Canonical Equation of State. Free Energy and Free Enthalpy	20	(2)
Reciprocity Relations	22	(1)
Entropy and Transport Processes	23	(1)
Equilibrium Conditions	24	(1)
Mixtures of Perfect Gases	25	(2)
The Law of Mass Action	27	(2)
Dissociation	29	(4)
Condensation	33	(1)
Real Gases in Gasdynamics	34	(5)
One-Dimensional Gasdynamics
Introduction	39	(1)
The Continuity Equation	40	(1)
The Energy Equation	41	(2)
Reservoir Conditions	43	(2)
Euler's Equation	45	(2)
The Momentum Equation	47	(2)
Isentropic Conditions	49	(1)
Speed of Sound; Mach Number	50	(1)
The Area-Velocity Relation	51	(2)
Results from the Energy Equation	53	(2)
Bernoulli Equation; Dynamic Pressure	55	(1)
Flow at Constant Area	56	(1)
The Normal Shock Relations for a Perfect Gas	57	(5)
One-Dimensional Wave Motion
Introduction	62	(1)
The Propagating Shock Wave	62	(3)
One-Dimensional Isentropic Equations	65	(2)
The Acoustic Equations	67	(1)
Propagation of Acoustic Waves	68	(1)
The Speed of Sound	69	(2)
Pressure and Particle Velocity in a Sound Wave	71	(1)
``Linearized'' Shock Tube	72	(2)
Isentropic Waves of Finite Amplitude	74	(2)
Propagation of Finite Waves	76	(2)
Centered Expansion Wave	78	(1)
The Shock Tube	79	(5)
Waves in Supersonic Flow
Introduction	84	(1)
Oblique Shock Waves	85	(1)
Relation between β and &thetas;	86	(2)
Supersonic Flow over a Wedge	88	(1)
Mach Lines	89	(2)
Piston Analogy	91	(1)
Weak Oblique Shocks	92	(1)
Supersonic Compression by Turning	93	(4)
Supersonic Expansion by Turning	97	(1)
The Prandtl-Meyer Function	98	(2)
Simple and Nonsimple Regions	100	(1)
Reflection and Intersection of Oblique Shocks	101	(1)
Intersection of Shocks of the Same Family	102	(1)
Detached Shocks	103	(3)
Mach Reflection	106	(1)
Shock-Expansion Theory	107	(2)
Thin Airfoil Theory	109	(4)
Flat Lifting Wings	113	(2)
Drag Reduction	115	(3)
The Hodograph Plane	118	(2)
Cone in Supersonic Flow	120	(4)
Flow in Ducts and Wind Tunnels
Introduction	124	(1)
Flow in Channel of Varying Area	124	(1)
Area Relations	125	(2)
Nozzle Flow	127	(3)
Normal Shock Recovery	130	(1)
Effects of Second Throat	131	(2)
Actual Performance of Wind Tunnel Diffusers	133	(1)
Wind Tunnel Pressure Ratio	133	(3)
Supersonic Wind Tunnels	136	(1)
Wind Tunnel Characteristics	137	(2)
Compressor Matching	139	(3)
Other Wind Tunnels and Testing Methods	142	(2)
Methods of Measurement
Introduction	144	(1)
Static Pressure	144	(3)
Total Pressure	147	(1)
Mach Number from Pressure Measurements	148	(1)
Wedge and Cone Measurements	149	(1)
Velocity	150	(1)
Temperature and Heat Transfer Measurements	151	(2)
Density Measurements	153	(1)
Index of Refraction	153	(4)
Schlieren System	157	(2)
The Knife Edge	159	(2)
Some Practical Considerations	161	(1)
The Shadow Methods	162	(2)
Interference Method	164	(1)
Mach-Zehnder Interferometer	165	(3)
Interferometer Techniques	168	(2)
X-Ray Absorption and Other Methods	170	(1)
Direct Measurement of Skin Friction	171	(1)
Hot-Wire Probe	172	(5)
Shock Tube Instrumentation	177	(1)
The Equations of Frictionless Flow
Introduction	178	(1)
Notation	178	(2)
The Equation of Continuity	180	(2)
The Momentum Equation	182	(3)
The Energy Equation	185	(1)
The Eulerian Derivative	186	(2)
Splitting the Energy Equation	188	(2)
The Total Enthalpy	190	(1)
Natural Coordinates. Crocco's Theorem	191	(3)
Relation of Vorticity to Circulation and Rotation	194	(2)
The Velocity Potential	196	(1)
Irrotational Flow	197	(3)
Remarks on the Equations of Motion	200	(2)
Small-Perturbation Theory
Introduction	202	(1)
Derivation of the Pertubation Equations	203	(3)
Pressure Coefficient	206	(1)
Boundary Conditions	206	(2)
Two-Dimensional Flow Past a Wave-Shaped Wall	208	(4)
Wavy Wall in Supersonic Flow	212	(3)
Supersonic Thin Airfoil Theory	215	(1)
Planar Flows	216	(2)
Bodies of Revolution. Slender Body Theory
Introduction	218	(1)
Cylindrical Coordinates	219	(2)
Boundary Conditions	221	(3)
Pressure Coefficient	224	(1)
Axially Symmetric Flow	224	(2)
Subsonic Flow	226	(1)
Supersonic Flow	226	(3)
Velocities in the Supersonic Field	229	(1)
Solution for a Cone	230	(2)
Other Meridian Shapes	232	(1)
Solution for Slender Cone	233	(2)
Slender Body Drag	235	(4)
Yawed Body of Revolution in Supersonic Flow	239	(2)
Cross-Flow Boundary Conditions	241	(1)
Cross-Flow Solutions	242	(1)
Cross Flow for Slender Bodies of Revolution	242	(1)
Lift of Slender Bodies of Revolution	243	(3)
Slender Body Theory	246	(1)
Rayleigh's Formula	247	(5)
The Similarity Rules of High-Speed Flow
Introduction	252	(1)
Two-Dimensional Linearized Flow. Prandtl-Glauert and Gothert Rules	253	(3)
Two-Dimensional Transonic Flow. von Karman's Rules	256	(2)
Linearized Axially Symmetric Flow	258	(2)
Planar Flow	260	(2)
Summary and Application of the Similarity Laws	262	(1)
High Mach Numbers. Hypersonic Similarity	263	(7)
Transonic Flow
Introduction	270	(1)
Definition of the Transonic Range	270	(1)
Transonic Flow Past Wedge Sections	271	(5)
Transonic Flow Past a Cone	276	(2)
Transonic Flow Past Smooth Two-Dimensional Shapes. The Question of Shock-Free Flow	278	(2)
The Hodograph Transformation of the Equations	280	(4)
The Method of Characteristics
Introduction	284	(1)
Hyperbolic Equations	285	(1)
The Compatibility Relation	285	(3)
The Computation Method	288	(3)
Interior and Boundary Points	291	(1)
Axially Symmetric Flow	292	(3)
Nonisentropic Flow	295	(1)
Theorems about Plane Flow	296	(2)
Computation with Weak, Finite Waves	298	(1)
Interaction of Waves	299	(2)
Design of Supersonic Nozzles	301	(3)
Comparison of Characteristics and Waves	304	(1)
Effects of Viscosity and Conductivity
Introduction	305	(1)
Couette Flow	306	(4)
Recovery Temperature	310	(1)
Velocity Distribution in Couette Flow	311	(2)
Rayleigh's Problem. The Diffusion of Vorticity	313	(3)
The Bounary-Layer Concept	316	(3)
Prandtl's Equations for a Flat Plate	319	(1)
Characteristics Results from the Boundary-Layer Equation	320	(3)
The Displacement Effect of the Boundary Layer. Momentum and Energy Integrals	323	(2)
Change of Variables	325	(1)
Boundary Layers on Profiles Other than a Flat Plate	326	(3)
Flow through a Shock Wave	329	(3)
The Navier-Stokes Equations	332	(6)
The Turbulent Boundary Layer	338	(2)
Boundary-Layer Effects on the External Flow Field	340	(2)
Shock-Wave Boundary-Layer Interaction	342	(4)
Turbulence	346	(2)
Couette Flow of a Dissociating Gas	348	(5)
Concepts from Gaskinetics
Introduction	353	(2)
Probability Concepts	355	(4)
Distribution Functions	359	(2)
The Virial Theorem of Clausius	361	(1)
The Equation of State of a Perfect Gas	362	(1)
The Maxwell-Boltzmann Distribution	363	(3)
The Specific Heats of Gases	366	(3)
Molecular Collisions. Mean Free Path and Relaxation Times	369	(3)
Shear Viscosity and Heat Conduction	372	(1)
Couette Flow of a Highly Rarefied Gas	373	(3)
The Concepts of Slip and Accommodation	376	(2)
Relaxation Effects of the Internal Degrees of Freedom	378	(2)
The Limit of Continuum Theory	380	(3)
EXERCISES	383	(20)
SELECTED REFERENCES	403	(30)
TABLES
Critical Data and Characteristics Temperatures for Several Gases	405	(1)
Flow Parameters versus M for Subsonic Flow	406	(3)
Flow Parameters versus M for Supersonic Flow	409	(9)
Parameters for Shock Flow	418	(7)
Mach Number and Mach Angle versus Prandtl-Meyer Function	425	(3)
CHARTS
Oblique Shock Chart	428	(2)
Oblique Shock Chart	430	(3)
Appendix	433	(4)
Index	437