Elements of Gas Dynamics

H. W. Liepmann, A. Roshko

• Publisher: Dover Publications
• Year: 2013
• ISBN:
  9780486316857
• Topic: Technology & Engineering
• Subtopic: Aeronautic & Astronautic Engineering
• Index: Technology & Engineering

The increasing importance of concepts from compressible fluid flow theory for aeronautical applications makes the republication of this first-rate text particularly timely. Intended mainly for aeronautics students, the text will also be helpful to practicing engineers and scientists who work on problems involving the aerodynamics of compressible fluids.
Covering the general principles of gas dynamics to provide a working understanding of the essentials of gas flow, the contents of this book form the foundation for a study of the specialized literature and should give the necessary background for reading original papers on the subject. Topics include introductory concepts from thermodynamics, including entropy, reciprocity relations, equilibrium conditions, the law of mass action and condensation; one-dimensional gasdynamics, 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, effects of viscosity and conductivity, and much more. The text includes numerous detailed figures and several useful tables, while concluding exercises demonstrate the application of the material in the text and outline additional subjects.
Advanced undergraduate or graduate physics and engineering students with at least a working knowledge of calculus and basic physics will profit immensely from studying this outstanding volume.

CHAPTER 1

Concepts from Thermodynamics

1.1 Introduction

The basis of any physical theory is a set of experimental results. From these special primary observations, general principles are abstracted, which can be formulated in words or in mathematical equations. These principles are then applied to correlate and explain a group of physical phenomena and to predict new ones.

The experimental basis of thermodynamics is formalized in the so-called principal laws. The law of conservation of energy, which thermodynamics shares with mechanics, electrodynamics, etc., is one of these principal laws. It introduces the concept of internal energy of a system. The other principal laws of thermodynamics introduce and define the properties of entropy and temperature, the two concepts which are particular and fundamental for thermodynamics.

The principles laid down in these fundamental laws apply to the relations between equilibrium states of matter in bulk. For instance, thermodynamics yields the relation between the specific heats at constant pressure and at constant volume; it relates the temperature dependence of the vapor pressure to the latent heat of evaporization; it gives upper bounds for the efficiency of cyclic processes, etc.

Fluid mechanics of perfect fluids, i.e., fluids without viscosity and heat conductivity, is an extension of equilibrium thermodynamics to moving fluids. The kinetic energy of the fluid has now to be considered in addition to the internal energy which the fluid possesses when at rest. The ratio of this kinetic energy per unit mass to the internal energy per unit mass is a characteristic dimensionless quantity of the flow problem and in the simplest cases is directly proportional to the square of the Mach number. Thermodynamic results are taken over to perfect fluid flow almost directly.

Fluid mechanics of real fluids goes beyond classical thermodynamics. The transport processes of momentum and heat are of primary interest here, and a system through which momentum, heat, matter, etc., are being transported is not in a state of thermodynamic equilibrium, except in some rather trivial cases, such as uniform flow of matter through a fixed system.

But, even though thermodynamics is not fully and directly applicable to all phases of real fluid flow, it is often extremely helpful in relating the initial and final conditions. This complex of problems is best illustrated with a simple example. Assume a closed, heat-insulating container divided into two compartments by a diaphragm. The compartments contain the same gas but at different pressures p₁ and p₂, and different temperatures T₁ and T₂. If the diaphragm is removed suddenly, a complicated system of shock and expansion waves occurs, and finally subsides due to viscous damping. Thermodynamics predicts the pressure and temperature in this final state easily. Fluid mechanics of a real fluid should tackle the far more difficult task of computing the pressure, temperature, etc., as a function of time and location within the container. For large times, pressure and temperature will approach the thermodynamically given values. Sometimes we need only these final, equilibrium values and hence can make very good use of thermodynamic reasoning even for problems that involve real fluid flow.

In fluid mechanics of low-speed flow, thermodynamic considerations are not needed: the heat content of the fluid is then so large compared to the kinetic energy of the flow that the temperature remains nearly constant even if the whole kinetic energy is transformed into heat.

In modern high-speed flow problems, the opposite can be true. The kinetic energy can be large compared to the heat content of the moving gas, and the variations in temperature can becom...