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A cylindrical object is reentering at a Mach number of say 25 at an altitude of 80 km. I like to calculate static pressure and static temperature inside the cylinder.

Yes Obvious, normal shock will form. But the problem is a small orifice (say 20 cm ) is available in the cylinder, the air starts entering the cylinder through this orifice until the total pressure outside is equal to inside pressure.

I have solved/attempted this problem in the following way

Step1: I assumed cylinder as a CD nozzle having convergent portion ,orifice (as throat) and divergent portion as my cylindrical volume and also assumed sonic flow in throat. Since I know the critical mass flow rate, I calculated the density inside the cylinder and using the isentropic relation I calculated the Mach number (Initially flow reaches supersonic speed in the cylinder) inside the cylinder and subsequently pressure and temperature also calculated. This process exist until static pressure inside reaches the pressure at throat.

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Step2: Reduction in Mach number from 1 to 0 until it reaches the outside pressure.

Is this process is correct? Static temperature inside the cylinder also will reach the temperature behind the shock?