Introduction to Prandtl-Meyer Function

Figure: The regions where oblique shock or Prandtl-Meyer function exist. Notice that both have a maximum point and a ``no solution'' zone, which is around zero. However, Prandtl-Meyer function approaches closer to a zero deflection angle.

Decreasing the deflection angle results in the same effects as before. The boundary conditions must match the geometry. Yet, for a negative deflection angle (in this section's notation), the flow must be continuous. The analysis shows that the flow velocity must increase to achieve this requirement. This velocity increase is referred to as the expansion wave. As it will be shown in the next chapter, as opposed to oblique shock analysis, the increase in the upstream Mach number determines the downstream Mach number and the ``negative'' deflection angle. It has to be pointed out that both the oblique shock and the Prandtl-Meyer function have a maximum point for $M_1 \rightarrow \infty$ . However, the maximum point for the Prandtl-Meyer function is much larger than the oblique shock by a factor of more than 2. What accounts for the larger maximum point is the effective turning (less entropy production) which will be explained in the next chapter (see Figure (13.2)).