Compressible Flows

In the preceding sections of this chapter, the discussions were for incompressible flows, where the density can be regarded as constant. But in many engineering applications, such as designing buildings to withstand winds, the design of engines and of vehicles of all kinds – cars, yachts, trains, aeroplane, missiles and launch vehicles require a study of the flow with velocities at which the gas cannot be treated as incompressible. Indeed, the flow becomes compressible. Study of such flows where the changes in both density and temperature associated with pressure change become appreciable is called gas dynamics. In other words, gas dynamics is the science of fluid flows where the density and temperature changes become important. The essence of the subject of gas dynamics is that the entire flow field is dominated
by Mach waves, expansion waves and shock waves, when the flow speed is supersonic. It is through these waves that the change of flow properties from one state to another takes place. In the theory of gas dynamics, change of state in flow properties is achieved by three means: (a) with area change, treating the fluid to be inviscid and passage to be frictionless, (b) with friction, treating the heat transfer between the surrounding and system to be negligible and (c) with heat transfer, assuming the fluid to be inviscid. These three types of flows are called isentropic flow, frictional or Fanno type flow and Rayleigh type flow, respectively.

All problems in gas dynamics can be classified under the three flow processes described above, of course with the assumptions mentioned. Although it is impossible to have a flow process which is purely isentropic or Fanno type or Rayleigh type, in practice it is justified in assuming so, since the results obtained with these treatments prove to be accurate enough for most practical problems in gas dynamics. Even though it is possible to solve problems with mathematical equations and working formulae asso­ciated with these processes, it is found to be extremely useful and time saving if the working formulae are available in the form of tables with a Mach number which is the dominant parameter in compressible flow analysis.