Handbook of Compressible Aerodynamics

Chapter 22

Unsteady Shock Wave, Contact Surface, and Wave Reflections

22.1. The shock wave equations and relations

We examine the problem of a shock wave (Ω) propagating parallel to the velocity of the upstream fluid in a fixed reference frame (A) (see Figure 22.1). We denote with D the propagation velocity of the shock wave in relation to the upstream fluid counted positive upstream: D is called the shock wave celerity.

The absolute velocity of the wave in the reference frame (A) is:

(since the flow is one-dimensional, we omit the vector sign above V₁). The velocity V₁ undergoes a discontinuity across (Ω) to take a value V₂ and we write:

The quantity w = V₂ – V₁ represents the velocity difference experienced by the fluid across the shock (Ω). To make the shock wave steady, we consider a reference frame (R) moving with the velocity of the shock; i.e. V₁ + D (see Figure 22.2). In (R), the upstream flow (1) encounters the shock wave with a velocity:

and becomes a state (2) with the velocity in (R):

Figure 22.1. Shock wave in the absolute reference frame

Figure 22.2. Shock wave in ...