Shock wave

A common irreversibility occurring in supersonic internal or external flows is the
normal-shock wave Except at near-vacuum pressures such shock waves
are very thin (a few micrometers thick) and approximate a discontinuous change in flow
properties. We select a control volume just before and after the wave, as in Fig. 9.8.
The analysis is identical to that of a shock wave is a fixed strong pres-
sure wave. To compute all property changes rather than just the wave speed, we use
all our basic one-dimensional steady-flow relations, letting section 1 be upstream and
section 2 be downstream:
The stagnation temperature remains the same, but the stagnation pressure and den-
sity decrease in the same ratio; i.e., the flow across the shock is adiabatic but non-
isentropic. Other basic principles governing the behavior of shock waves can be sum-
marized as follows:
1. The upstream flow is supersonic, and the downstream flow is subsonic.
2. For perfect gases (and also for real fluids except under bizarre thermodynamic
conditions) rarefaction shocks are impossible, and only a compression shock can
exist.
3. The entropy increases across a shock with consequent decreases in stagnation
pressure and stagnation density and an increase in the effective sonic-throat area.
4. Weak shock waves are very nearly isentropic.
Normal-shock waves form in ducts under transient conditions, e.g., shock tubes, and
in steady flow for certain ranges of the downstream pressure. Figure 9.10a shows a
normal shock in a supersonic nozzle. Flow is from left to right. The oblique wave pat-
tern to the left is formed by roughness elements on the nozzle walls and indicates that
the upstream flow is supersonic. Note the absence of these Mach waves (see Sec. 9.10)
in the subsonic flow downstream.