O'Reilly logo

Handbook of Compressible Aerodynamics by Jean Délery

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 Image 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:

Image

(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:

Image

The quantity w = V2V1 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:

Image

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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required