Page 126 - 48Fundamentals of Compressible Fluid Mechanics
P. 126
88 CHAPTER 5. NORMAL SHOCK
5.3.2 Moving Shock Into Stationary Medium
5.3.2.1 General Velocities Issues
When valve or membrane is suddenly opened a shock is created and propagate
the downstream. With the exception of a close proximity to the valve, the shock is
moving in a constant velocity (see Figure (5.8)). Converting the moving shock to a
coordinates system that attached to the shock results in a stationary shock when
the flow is moving to left. The “upstream” is on the right (see Figure (5.8)).
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(a) The reflective shock into (b) The reflective shock into
close end pipe in stationary close end pipe in moving co-
coordinates ordinates
Fig. 5.8: The reflective shock into close end pipe coordinates
Similar definitions of the right and the left side shock Mach numbers for are
utilized. It has to be noticed that the “upstream” and “downstream” are the reverse
from the previous case. The “upstream” Mach number is
(5.59)
The “downstream” Mach number is
(5.60)
Note that in this case the stagnation temperature in stationary coordinate
changes (as in the previous case) where the thermal energy (due to pressure dif-
ference) is converted into velocity. The stagnation temperature (of moving coordi-
nates) is
(5.61)
After similar rearrangement as in the previous case results in
(5.62)
