Compressible Flows

9.1 Introduction

Our discussions so far were on incompressible flow past lifting surfaces. That is, the effect of com­pressibility of the air has been ignored. But we know that the incompressible flow is that for which the Mach number is zero. This definition of incompressible flow is only of mathematical interest, since for Mach number equal to zero there is no flow and the state is essentially a stagnation state. Therefore, in engineering applications we treat the flow with density change less than 5% of the freestream density as incompressible[1]. This corresponds to M = 0.3 for air at standard sea level state. Thus, flow with Mach number greater than 0.3 is treated compressible. Compressible flows can be classified into subsonic, su­personic and hypersonic, based on the flow Mach number. Flows with Mach number from 0.3 to around 1 is termed compressible subsonic, flows with Mach number greater than 1 and less than 5 are referred to as supersonic and flows with Mach number in the range from 5 to 40 is termed hypersonic. In our discussions here, only subsonic and supersonic flows will be considered. In Chapter 2, we discussed some aspects of compressible flows only briefly. Therefore, it will be of great value to read books specializing on gas dynamics and its application aspects, such as Rathakrishnan (2010) [1], before getting into this chapter.

In our discussion in this chapter, the air will be treated as a perfect, compressible and inviscid fluid. In other words, the important consequence of viscosity, namely, the skin friction drag due to the viscous effects in the boundary layer will not be considered in our discussions.