3. Supersonic shear layer interaction at off-design conditions a. Consider a flow at M = 3.0 with p = 90 kPa and T = 800 K exhausting into an ambient environment with no flow at p = 100 kPa and T = 300 K. The mismatch in pressure requires the formation of an oblique shock at the lip of the channel. See Fig. 3a. i. [5 pts] Determine the Mach number of the exhaust M3. ii. [5 pts] Determine the angle made by the shock a. M = 3.0 P = 90 kPa T = 800 K M3 a P2 = 100 kPa T = 300 K Figure 3.a. Overexpanded jet into the ambient. b. Consider a flow at M = 3.0 with p = 90 kPa and T = 800 K exhausting into a coflowing i. ii. stream at M = 2.9 with p = 50 kPa and T = 250 K. The mismatch in pressure requires the formation of a Prandtl-Meyer expansion at the lip of the channel. See Fig. 3b. [5 pts] Determine the Mach number of the exhaust M3 downstream of the expansion fan. [5 pts] Determine the angle made by the downstream flow with respect to the incoming direction a. P = 90 kPa M = 3.0 T = 800 K M3 P2 = 50 kPa M = 2.9 T = 250 K Figure 3.b. Underexpanded jet into a coflowing stream. The gas constant for air is R = 287 J/(kg.K) and the specific heat ratio is y = 1.4. Assume that the flow is inviscid. Problem 3a. Supersonic shear layer interaction at off-design conditions Overexpanded jet exiting into an ambient P1 P = 90 kPa M = 3.0 1 T = 800 K 2 M3 P2 = 100 kPa T = 300 K p3=100 kPa p3/p1=100/90=1.11 Alpha = 1.4 deg Problem 3. Supersonic shear layer interaction. at off-design conditions Underexpanded jet exiting into a coflowing supersonic stream P = 90 kPa M = 3.0 1 T = 800 K P = 50 kPa M3 2 T = 250 K M = 2.9