Page 283 - 48Fundamentals of Compressible Fluid Mechanics

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positive
angle
14.1 Introduction

As it was discussed in Chapter (13) when
the deflection turns to the opposite direction maximum angle
of the flow and accelerated the flow to match
the boundary condition. The transition as
opposite to the oblique shock is smooth Fig. 14.1: The definition of the angle for
without any jump in properties. Here be- Prandtl–Meyer function here
cause the tradition, the deflection angle is
denoted as a positive when the it appears away from the flow (see the Figure
(14.8)). In somewhat similar concept to oblique shock there exist a “detachment”
point above which this model breaks and another model have to be implemented.
Yet, when this model breaks, the flow becomes complicate and flow separation oc-
curs and no known simple model describes the situation. As oppose to the oblique
shock, there is no limitation of the Prandtl-Meyer function to approach zero. Yet, for
very small angles, because imperfections of the wall have to be assumed insignifi-
cant.
Supersonic expansion and isentropic com-
pression (Prandtl-Meyer function), is extension U
of the Mach Line concept. Reviewing the Mach c
line shows that a disturbance in a field of su-
personic flow moves in an angle of , which is
defined as (see Figure (14.2))

(14.1) Fig. 14.2: The angles of the Mach
line triangle

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