Aircraft Propulsion, 2nd Edition

2.14 Expansion Waves

The oblique shocks are compression waves in a supersonic flow that abruptly turn the flow and compress the gas in the process. An expansion wave causes a supersonic flow to turn and the static pressure to drop. The expansion waves are Mach waves that make a Mach angle with respect to the local flow. The flow through expansion waves is inherently isentropic, as the Mach waves are of infinitesimal strength and hence reversible. An expansion Mach wave is capable of only turning the flow incrementally and accelerates the flow incrementally. Such a flow turning and flow acceleration is shown in Figure 2.28 with exaggeration of the turning angle and the flow acceleration increment. The local wave angle with respect to upstream flow is at the Mach angle μ. The incremental turning angle is labeled as dθ. The change of velocity is shown by a magnitude of dV and a direction dθ with respect to upstream flow. Since the velocity downstream of the Mach wave has to have the same tangential component as the upstream flow, the right triangles that share the same tangential velocity are labeled with V and V + dV vectors in Figure 2.28.

FIGURE 2.28 Incremental turning across a Mach wave

We may apply the law of sines to the triangle with sides V and V + dV to relate the turning ...