Page 247 - 48Fundamentals of Compressible Fluid Mechanics

13.3. OBLIQUE SHOCK 209

the upstream Mach number increases
and determined the downstream Mach number and the “negative” deflection angle.
One has to point that both oblique shock and Prandtl–Meyer Function have
. However, the maximum point for Prandtl–Meyer
Function is match larger than the Oblique shock by a factor of more than two.
maximum point for
The reason for the larger maximum point is because of the effective turning (less
entropy) which will be explained in the next chapter (see Figure (13.2)).

13.2.3 Introduction to zero inclination

What happened when the inclination angle is zero? Which model is correct to
use? Can these two conflicting models co-exist? Or perhaps a different model
better describes the physics. In some books and in the famous NACA report 1135
it was assumed that Mach wave and oblique shock co–occur in the same zone.
Previously (see Chapter 5 ), it also assumed that normal shock occurs in the same
time. In this chapter, the stability issue will be examined in some details.

13.3 Oblique Shock
The shock occurs in reality in situations where the shock has three–dimensional
effects. The three–dimensional effects of the shock make it appears as a curved
plan. However, for a chosen arbitrary accuracy requires a specific small area,
a one dimensional shock can be considered. In such a case the change of the
orientation makes the shock considerations a two dimensional. Alternately, using
an infinite (or two dimensional) object produces a two dimensional shock. The two
dimensional effects occur when the flow is affected from the “side” i.e. change in
4
the flow direction .
To match the boundary conditions, the flow turns after the shock to be parallel
to the inclination angle. In Figure 13.3 exhibits the schematic of the oblique shock.
The deflection angle, c , is the direction of the flow after the shock (parallel to the
wall). The normal shock analysis dictates that after the shock, the flow is always
subsonic. The total flow after oblique shock can be also supersonic which depends
boundary layer.
Only the oblique shock’s normal component undergoes the “shock.” The tan-
gent component doesn’t change because it doesn’t “moves” across the shock line.
Hence, the mass balance reads ! !

(13.1)

The momentum equation reads ! " " !

(13.2)
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