Handbook of Compressible Aerodynamics

Chapter 13

Discontinuity Surfaces: Shock Wave and Slip Line

13.1. Existence of shock waves

For reasons we will not analyze here, a supersonic flow can be the seat of shock waves. This phenomenon results from the hyperbolic nature of equations governing the supersonic flow of non-viscous fluids. In this case, the disturbances propagating at the speed of sound cannot propagate against the flow and, thus, are not perceived upstream of the body that has induced them. Thus, the supersonic flow arriving ahead of the body is not “warned” of the presence of the obstacle which inflicts a velocity reduction. It follows that the adjustment of the velocity, and other properties of the flow, will have to happen abruptly through a quasi-discontinuity. The requirement of shock waves can be introduced in a less intuitive way by the wave theory described in Chapter 21 dealing with wave propagation. Here, we accept the existence of shock waves as a fact or evidence, characteristic for supersonic flow and proven by experience. Thus, we seek the relations which have to exist between the properties of the fluid downstream and upstream of the shock wave, understanding that these properties, or more precisely their variations, must satisfy the fundamental equations of fluid mechanics.

The visualizations in Figure 13.1 show some configurations where shock waves are formed in aerodynamic flows. In the case of Figure 13.1a, a sudden change of the direction of a wall causes the formation of an oblique shock ...