Consider a Mach 4 airflow at a pressure of 1 atm. We wish to slow this flow to subsonic speed through a system of shock waves with as small a loss in total pressure as possible. Compare the loss in total pressure for the following three shock systems:
a. A single normal shock wave
b. An oblique shock with a deflection angle of
c. An oblique shock with a deflection angle of
From the results of (a), (b), and (c), what can you induce about the efficiency of the various shock systems?
(a)
The comparison in total pressure loss for the single normal shock wave.
Answer to Problem 9.8P
The loss in pressure is
Explanation of Solution
Given:
The Mach number is
The pressure is
Formula used:
The expression for
The expression for
The expression for loss in pressure is given as,
Calculation:
The pressure
The pressure
The loss in pressure can be calculated as,
Conclusion:
Therefore, the loss in pressure is
(b)
The comparison in pressure for an oblique shock with a deflection angle of
Answer to Problem 9.8P
The loss in pressure is
Explanation of Solution
Given:
The Mach number is
The pressure is
The deflection angle of oblique shock wave is
Formula used:
The expression for
The expression for
The expression for
The expression for loss in pressure is given as,
Calculation:
From
Figure (1)
The Mach number
The pressure ratio for Mach number
From appendix B
The Mach number
The pressure ratio for Mach number
The pressure
The pressure loss can be calculated as,
Conclusion:
Therefore, the loss in pressure is
(c)
The comparison in pressure for the an oblique shock with a deflection angle of
Answer to Problem 9.8P
The loss in pressure is
Explanation of Solution
Given:
The Mach number is
The pressure is
The deflection angle of second oblique shock wave is
Formula used:
The expression for the Mach number
The expression for Mach number
The expression for the pressure
The expression for loss in pressure is given as,
Calculation:
From
Figure (2)
The Mach number
The pressure ratio for Mach number from appendix B is given as,
Refer to appendix B
The Mach number
The pressure ratio for Mach number
The pressure
The pressure loss can be calculated as,
From a, b and c it is clear that the most efficient way to decrease supersonic flow to subsonic flow is through a combination of supersonic diffuser and then normal shock wave at the end.
Conclusion:
Therefore, the loss in pressure is
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Chapter 9 Solutions
Fundamentals of Aerodynamics
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