Question

M 3. Consider a scenario in which supersonic flow is expanded and turned by 150 through a Prandtl-Meyer expansion wave/fan. Consider the gas to be calorically perfect Air with upstream properties as follows: M1 = 4, P = 20 kPa, T = 250 K. Find: 0-150 M2 (a) freestream Prandtl-Meyer function, Vi. (b) downstream Mach number, M2. (c) downstream static pressure, P2. (d) downstream static temperature, T2.

Answer 1

8=1-4 -4-1 Jl.4+ M = 4 e P,=20kPa b) M₂ Ti=250K | O=15. 37 a) v(M) = (JM²1 dM d.+-1m2 M =Y+ton = 1)012-) - tas" M2_1 = V(4) = J 1+ 41 tar 1.4-1 (16-D - ton J16-1 = 65.785 b) ₂ = Vito =800785° See the value of M corresponding to this ₂ is Prardtl Meyer argle table Ao or calculate usirg MATLAB M₂~5.45° (for V. = 80-785) ( P = (1 +81 MB) Sirce flow is usertropic , we can we use Stagration pressure Pt is constart = Pi (1+0=1 m;)*(1+4 L M od 13.447 kPa Sunitarly, for temper Tz = T, ( I ) ( I ) = Ti (1+ 7 = 1 M) (1+2 - 1 M)" d) = 151.285 K