Internal Flow: Concepts and Applications
Providing students and practicing engineers with a range of analytical tools, this book describes the analysis and behavior of internal flows encountered in propulsion systems, fluid machinery, and ducts.
TABLE OF CONTENTS Internal Flow: Concepts and Applications
10.9: Flow Angle, Mach Number, and Pressure Changes in Isentropic Supersonic Flow
10.9 Flow Angle, Mach Number, and Pressure Changes in Isentropic Supersonic Flow
Much of this chapter has focused on flows which can be described within the quasi-one-dimensional framework, neglecting pressure differences normal to the stream. In this section we address the effect of normal pressure gradients on flow angle changes in a supersonic stream. The causal link between pressure gradient and streamline deflection is unchanged from subsonic flow, in that the deflections are in the direction of the low pressure, but the manner in which the flow angle change occurs is different in supersonic and subsonic regimes.
10.9.1 Differential relationships for small angle changes
The issue can be illustrated through examination of the relation between pressure and turning at a bounding solid surface, confining the discussion to two dimensions. Consider the geometry in Figure 10.39 with a flat wall and a bump made up of straight-line segments. If the angles the segments make with the wall are small, the disturbances will also be small, the flow field will be described by a linear analysis, and the flow pattern can be built up by a superposition of small disturbances emanating from the boundary.
Figure 10.39: Supersonic flow around a straight-line segment bump; ?x, ?y are projections of the control volume on the x- and y-axes, u ? = undisturbed velocity.
In Figure 10.39 a uniform parallel supersonic stream of velocity u strikes the first non-parallel element of the surface, AB, whose inclination to the stream direction...
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