The Prandtl-Meyer Function

It is known from basic studies on fluid flows that a flow which preserves its own geometry in space or time or both is called a self-similar Bow. In the simplest cases of flows, such motions are described by a single independent variable, referred to as similarity variable. The Prandtl-Meyer function is such a similarity variable.

Подпись: Y + 1 t v = arc tan Y - 1 Подпись: Y+l (M2 - 1) - arc tan у/(Mj2 - 1) Подпись: (9.181)

The Prandtl-Meyer function in terms of the Mach number M1 just upstream of the expansion fan can be written as:

Equation (9.181), expressing the Prandtl-Meyer function v in terms of the Mach number, is a very important result of supersonic flow. From this relation, it is seen that for a given Mj, there is a fixed v. For a detailed discussion about Prandtl-Meyer expansion process see Rathakrishnan (2010) [1].

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