Fundamentals of Gas Dynamics

Compressible flows are encountered in many applications in aerospace and mechanical engineering. Some examples are flows in nozzles, compressors, turbines, and diffusers. In aerospace engineering, in addition to these examples, compressible flows are seen in external aerodynamics, aircraft, and rocket engines. In almost all of these applications, air (or some other gas or mixture of gases) is the working fluid. However, steam can be the working substance in turbomachinery applications. Thus, the range of engineering applications in which compressible flow occurs is quite large and hence a clear understanding of the dynamics of compressible flow is essential for engineers.

In this chapter, we discuss some fundamental concepts in the study of compressible flows. Throughout this book, we assume the flow to be one-dimensional or quasi-one-dimensional. A flow is said to be one-dimensional, if the flow properties change only along the flow direction. The fluid can have velocity either along the flow direction or both along and perpendicular to it. Oblique shock waves and Prandtl Meyer expansion/compression waves discussed in later chapters are examples of the latter. We begin with a discussion of one-dimensional flows which belong to the former category i.e., with velocity along the flow direction only.

Normal shock waves are compression waves that are seen in nozzles, turbomachinery blade passages, and shock tubes, to name a few. In the first two examples, normal shock usually occurs under off-design operating conditions or during start-up. The compression process across the shock wave is highly irreversible and so it is undesirable in such cases. In the last example, a normal shock is designed to achieve extremely fast compression and heating of a gas with the aim of studying highly transient phenomena. Normal shocks are seen in external flows also. The term “normal” is used to denote the fact that the shock wave is normal (perpendicular) to the flow direction, before and after passage through the shock wave. This latter fact implies that there is no change in flow direction as a result of passing through the shock wave. In this chapter, we take a detailed look at the thermodynamic and flow aspects of normal shock waves.

In this chapter, we look at one-dimensional flow in a constant area duct with heat addition. Heat interaction would be more appropriate, since the theory that is developed applies equally well to situations where heat is removed. However, such a situation is rarely, if ever, encountered. Hence the predominant interest is on flows with heat addition, which are encountered in combustors ranging from those in aviation gas turbine engines through ramjet engines to scramjet engines. The corresponding combustor entry Mach number in these applications range from low subsonic through high subsonic to supersonic.

In this chapter, we look at one-dimensional adiabatic flow in a duct with friction at the walls of the duct. This type of flow occurs, for example, when gases are transported through pipes over long distances. It is also of practical importance when equipment handling gases are connected to high-pressure reservoirs, which may be located some distance away. Knowledge of this flow will allow us to determine the mass flow rate that can be handled, pressure drop and so on.

In the previous chapters, one-dimensional compressible flow solutions were presented, wherein the flow was either across a wave or through a constant area passage. A very important class of compressible flow is flow through a passage of finite but varying cross-sectional areas such as flow-through nozzles, diffusers, and blade passages in turbomachines.

Oblique shock waves are generated in compressible flows whenever a supersonic flow is turned into itself through a finite angle. In some applications such as intakes of supersonic vehicles, ramjet and scramjet engines, the intended objective is to decelerate and compress the incoming air through a series of such oblique shocks thereby eliminating the need for the compressor and the turbine. In other applications, the dynamics of the flow triggers oblique shock waves. This is the case, for instance, when an over-expanded supersonic jet issues from a nozzle into the ambient. Oblique shocks are generated from the corners in the exit plane of the nozzle to compress the jet and increase the static pressure to the ambient value.

In the previous chapters, we looked at flow across normal and oblique shock waves. In both cases, the fluid undergoes compression and the flow decelerates. There is also an attendant loss of stagnation pressure. It was also shown that an “expansion shock” solution, while mathematically possible, is forbidden by the second law of thermodynamics as the entropy decreases across such a shock wave, which is adiabatic.

In the earlier chapters, we studied the gas dynamics of a perfect gas. In this chapter, we will study the dynamics of the flow of steam through nozzles. Historically, the theory of the flow of steam through nozzles was developed first in the late 1800 and early 1900 s.