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Hang on, why you're taking supersonic aerodynamics and compressibility into the equation?
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Ok, I gave you the report and a few days to digest it. Now lets explain it so you can get a grip on what is going on with the P51 radiator system.
First let's talk a second about supersonic aerodynamics. Just because the airplane is going subsonic does not mean the LOCAL mach number is not supersonic.
How does that happen? Well basic physics explains it very well. I am sure you are familiar with a venturi. If we take a given diameter pipe filled with gas at a constant mass flow and suddenly decrease the diameter, what happens to the velocity of the gas traveling thru the pipe?
Answer is the velocity of the gas increases!! It goes faster. Look at the design of the P51 radiator system and you will see this in the flow interaction with the oil cooler intake.
That is what happens in the P-51 ducting. The air enters the intake and very quickly encounters the oil cooler intake just before the radiator element expansion chamber. The volume is smaller because of the oil cooler intake so the velocity of the air flow increases.
At some point, it increase enough to go supersonic. Whenever we have supersonic flow at the local mach number a normal shock will form. A normal shock has specific characteristics. At the point of the shock, a "wall" of air will form. In front of the normal shock is supersonic flow and behind this "wall of air" is a flow reversal followed by subsonic flow. This flow reversal is essential a vacuum at the boundary layer which is why it is called suction.
This suction dynamically increase the amount of pressure drag. The effect is our aircraft slows down as the drag dramatically increases. The airplane slows down....
Once it slows down to subsonic flow, the shock will disappear. Our thrust available has not changed so the aircraft will immediately accelerate as the pressure drag has dramatically decreased. Once it accelerates enough to create a local supersonic flow our normal shock will reform and the cycle starts all over again.
This cycle happens rather quickly and the pilot will perceive it as a "rumbling" noise in the ducts of the intake as the airplane accelerates/decelerates rapidly in a very short time period.
How did this happen? How could the designers at NAA make such a mistake?
Well we just did not understand normal shock formation at the time.
Today we know it is all about the angle of the shock. The relationship is fixed to velocity at the sine of the normal shock is equal to the reciprocal of the local mach number. We also know that in any corner, oblique shocks are formed further dissipating our available energy.
They did not know that then however and were just beginning to understand compressibility and normal shock formation.
Got it now?