An engineer wishes to conduct experiments on a new re-entry device in a superson

Question

An engineer wishes to conduct experiments on a new re-entry device in a supersonic wind tunnel which uses air as the working fluid. The air may be treated as an ideal gas with a specific heat ratio of 1.4 and its specific heat at constant pressure is 1.121 kJ/kgK. The conditions at the entrance to the test section are: the flow is travelling at Mach 4. with a static pressure of 2 MPa and stagnation temperature of 3800 K. If the test section is made from steel with a bore of 200 mm and the test is to be performed at Mach 3, determine: a) The distance from the start of the lest section at which the re-entry device should be located. b) The static pressure and temperature of the flow at the model device. Note that: theta_p kR/k - 1 mu bT^1/2/1 + S/T b 1.458 times 10^6 kg/(m s K^1/2) S = 110.4 K

Explanation / Answer

Given data:

= 1.4

Cp=1.121KJ/Kg K

P0=2 MPa

T0= 3800K

M0=4 Mach

Test Conditions,

Me= 3Mach

Steel bore of 20mm

From given notes, 0= 87.34 and R=0.32 KJ/Kg K

Since we take air to be ideal gas, 0=P0/RT0= 1.645

Let us calculate the Reynolds no. for the steel pipe at exit,

Re= 0vDH/0,

Where DH= diamension of the bore i.e. 20mm

And v= maximum velocity given by (2RT0/-1)1/2

Thus v=2917.5 m/s

      Now, Re=1.098

     Value of fn. a0 = 1250.37

For the system considered, Re/L=(0a0M/0) *(1+[-1]M2/2).268-(1/-1) =7.0235

since we know Re, L=Re/7.0235=0.1563m. is the reqd. ans

                                      

Static Temp,T can be found from the eqn., T0/T=1+[(-1)M2]/2= 1357.14

Static pressure,P can be got from the relation given below since it is a condensation reaction,

(Change in M)2/M2 = [(1+M2)/(-M2)]{(dQ/H)-(dA/A)}

Substituting the known values, {(dQ/H)-(dA/A)}= 0.1836

and (Change in Pressure)/P=[M2/1-M2]*{(dQ/H)-(dA/A)}=0.2892

P-P0/P =.2892 or P=2.814MPa

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