Introduction to Compressible Fluid Flow, Second Edition, 2nd Edition

1

1

Introduction

Compressibility

The compressibility of a uid is basically a measure of the change in density that will be

produced in the uid by a specied change in pressure. Gases are, in general, highly com-

pressible whereas most liquids have a very low compressibility. Now, in a uid ow there

are usually changes in pressure associated, for example, with changes in the velocity in the

ow. These pressure changes will, in general, induce density changes, which will have an

inuence on the ow, i.e., the compressibility of the uid involved will have an inuence

on the ow. If these density changes are important, the temperature changes in the ow

that arise due to the kinetic energy changes associated with the velocity changes also usu-

ally inuence the ow, i.e., when compressibility is important, the temperature changes in

the ow are usually important. Although the density changes in a ow eld can be very

important, there exist many situations of great practical importance in which the effects

of these density and temperature changes are negligible. Classical incompressible uid

mechanics deals with such ows in which the pressure and kinetic energy changes are

so small that the effects of the consequent density and temperature changes on the uid

ow are negligible, i.e., the ow can be assumed to be incompressible. There are, how-

ever, a number of ows that are of great practical importance in which this assumption is

not adequate, the density and temperature changes being so large that they have a very

signicant inuence on the ow. In such cases, it is necessary to study the thermodynam-

ics of the ow simultaneously with its dynamics. The study of these ows in which the

changes in density and temperature are important is basically what is known as compress-

ible uid ow or gas dynamics, it usually only being in gas ows that compressibility effects

are important.

The fact that compressibility effects can have a large inuence on a uid ow can be

seen by considering the three aircraft shown in Figure 1.1. The rst of the aircraft shown

in Figure 1.1 is designed for relatively low speed ight. It has straight wings, it is propel-

ler driven, and the fuselage (the body of the aircraft) has a “rounded” nose. The second

aircraft is designed for higher speeds. It has swept wings and tail surfaces and is powered

by turbojet engines. However, the fuselage still has a “rounded” nose and the intakes to

the engines also have rounded edges, which are approximately at right angles to the direc-

tion of ight. The third aircraft is designed for very-high-speed ight. It has highly swept

wings and a sharp nose, and the air intakes to the engines have sharp edges and are of

complex shape. These differences between the aircraft are mainly because compressibility

effects become increasingly important as the ight speed increases.

Although the most obvious applications of compressible uid ow theory are in the

design of high speed aircraft, and this remains an important application of the subject, a

2 Introduction to Compressible Fluid Flow

(a)

(b

)

(c)

FIGURE 1.1

Aircraft designed to operate at different speeds: (a) De Havilland Canada Dash 8; (b) Canadair CL-600 Regional

Jet; (c) Aerospatiale-BAC Concorde. (Courtesy of Eduard Marmet. Airliners.net.)