Page 265 - 48Fundamentals of Compressible Fluid Mechanics

13.4. SOLUTION OF MACH ANGLE 227

distance from the body is a complex analysis and should be left to graduate class
and for researchers in the area. Nevertheless, a graph and general explanation to
engineers is provided. Even though there are very limited applications to this topic
some might be raised in certain situations, which this author isn’t aware of.
Analysis of the detached shock
can be carried out by looking at a
body with a round section moving in weak shock
a supper sonic flow (the absolute ve- M > 1
Strong Shock
locity isn’t important for this discus-
sion). Figure 13.12 exhibits a bul- Upstream U ∞
zone B Subsonic Area θ
let with a round tip which the shock
zone A
is detach. The distance of the de- Normal Shock
tachment determined to a large de-
gree the resistance to the body. The # $ % " & ! % ! ' ( $ ) & "
"

zone A is zone where the flow must
be subsonic because at the body the
velocity must be zero (the no slip con-
dition). In such case, the gas must
go through a shock. While at at zone Fig. 13.12: The schematic for round tip bullet in
C the flow must be supersonic (The a supersonic flow
weak oblique shock is predicted for
flow around cone.). The flow in zone A has to go thorough some acceleration
to became supersonic flow. The explanation to such phenomenon is above the
24
level of this book (where is the “throat” area question . Yet, it can be explained
as the subsonic is “sucked” into gas in zone C. Regardless the explanation, these
calculations can be summarized in the flowing equation

(13.53)
body thickness constant *
detachment distance

where * is a function of the upstream Mach number which tabulated in the
literature.

The constant and the function are different for different geometries. As gen-
eral rule the increase in the upstream Mach results in decrease of the detach-
ment. Larger shock results in smaller detachment distance, or alternatively the To insert the table for the con-
stants and functions
flow becomes “blinder” to obstacles. Thus, this phenomenon has a larger impact
for relatively smaller supersonic flow.

13.4.10 Issues related to the Maximum Deflection Angle

The issue of maximum deflection has practical application aside to the obvious
configuration shown as a typical simple example. In the typical example a wedge
or cone moves into a still medium or gas flow into it. If the deflection angle exceeds
24 See example 13.5.