Basics of Fluid Mechanics, 2014a

CHAPTER 12
Compressible Flow 2–Dimensional
12.1 Introduction
In Chapter 11 the discussed dealt with one–dimensional and semi one–dimensional flow.
In this Chapter the focus is around the two diminsional effect which focus around the
oblique shock and Prandtl–Meyer flow (in other word it focus around Theodor Meyer’s
thesis). This Chapter present a simplified summary of two chapters from the book
“Fundamtals of Compressible Flow” by this author.
12.1.1 Preface to Oblique Shock
In Section (11.5), a discussion on a normal
shock was presented. A normal shock
is a special type of shock wave. Another
type of shock wave is the oblique
shock. In the literature oblique shock, normal
shock, and Prandtl–Meyer function
are presented as three separate and different
issues. However, one can view all
these cases as three different regions of a
flow over a plate with a deflection section.
θ δ= 0
U 1 U 2
Fig. -12.1. A view of a straight normal shock
as a limited case for oblique shock.
Clearly, variation of the deflection angle from a zero (δ =0) to a positive value results
in oblique shock (see Figure 12.1). Further changing the deflection angle to a negative
value results in expansion waves. The common representation is done by ignoring the
boundaries of these models. However, this section attempts to show the boundaries
and the limits or connections of these models.
A normal shock occurs when there is a disturbance downstream which imposes
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