Page 128 - 48Fundamentals of Compressible Fluid Mechanics
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90 CHAPTER 5. NORMAL SHOCK
the larger number of iterations
is required to achieve the same accuracy. Yet, for most practical purpose sufficient
(see Figure (5.9(b))). The larger value of the
results can be achieved after 3-4 iterations.
5.3.2.2 Supersonic Issues of Moving Shock
Assuming that gas velocity is supersonic (in stationary coordinates) before the
shock moves, what is the maximum velocity that can be approached before this
model fails. In other words is there point where the moving shock is fast enough
to reduce the “upstream” relative velocity below the speed of sound. This is the
point where no matter what the pressure difference be, the shock velocity cannot
be increased.
This shock chocking phe- Shock in A Suddenly Open Valve
nomenon is similar to the chocking Maximum M y ’ possible
2.5
phenomenon that will be discussed
2.25 M y (max)
earlier in nozzle flow and will ap-
2
pear in the nozzle flow and in other 1.75
pipe flows models (later chapters). Maximum M y ’ 1.5
It must be noted that in the previ- 1.25
ous case of suddenly and complete
1
closing of valve results in no limit (at
0.75
least from the model point of view). 0.5
The spesific heat ratio, k
To explain this phenomenon look at
the normal shock. Consider when Thu Aug 24 17:46:07 2006
the shock wave approaches infinity,
the downstream Fig. 5.9: The Maximum of Mach number of “down-
stream” as function of the specific heat
Mach number, according to equa-
. One can view this as the source for
the shock chocking phenomenon.
tion (5.38), is approaching to
To study this limit consider that the maximum Mach number is obtained
. Applying equation (5.23)
to this situation yields
when the pressure ratio is approaching infinity
(5.64)
From the mass conservation leads into
(5.65)
,