Transonic flow is a mixed subsonic-supersonic flow where the local Mach number is near 1.  A typical example is the flow over the wing of a high-speed subsonic transport, such as the Boeing 777 shown in Fig. 1.4. When the airplane is flying at a free-stream Mach number on the order of 0.85 , there will be a pocket of locally supersonic flow over the wing, as sketched in Fig. 1.10b. This pocket is terminated by a weak shock wave, also shown in Fig. 1.10b. Early numerical calculations of such transonic flows over an airfoil assumed the flow to be isentropic, hence ignoring the entropy increase and total pressure loss across the shock wave. Making the assumption that the shock wave in Fig. \(1.10 b\) is locally a normal shock, calculate the total pressure ratio and entropy increase across the shock for \(M_{1}=1.04,1.08,1.12\), 1.16, and 1.2. Comment on the appropriateness of the isentropic flow assumption for the solution of transonic flows involving shocks of this nature.

Figure 1.10b:

Figure 1.4:

Transcribed Image Text:

0.8 I Shock wave MAI (b)