Problem Set 5 (75 points) - Waves

Problem 1 (5)
Sea level air at M = 2 is turned isentropically in an expansion direction through an angle of 15⁰.  By dividing the turn into three 5⁰ increments, find the approximate Mach number after turning.

Problem 2 (15)
Sea level air at M = 1.5 is turned in a compressive direction through an angle of 10⁰.  Find the Mach number, speed, pressure temperature and density of the flow after turning (all in SI units) using the 3 different methods described below and tabulate your results:
A. Assume the flow is turned isentropically through a Mach wave (approximate method for isentropic flow)
B. Assume the flow is turned isentropically through a Prandlt-Meyer compression wave (exact method for isentropic flow)
C. Assume the flow is turned non-isentropically through an oblique shock wave (exact method for non-isentropic flow)

(a) Which method yields the most accurate results?
(b) Which method yields the least accurate results?
(c) Which method yields the greatest changes in flow conditions?

Problem 3 (5)
A supersonic flow at M₁ = 3, T₁ = 285 K and p₁ = 1 atm is deflected upward through a compression corner with q = 30.6⁰ and then is subsequently expanded around a corner of the same angle such that the flow direction is the same as the original direction.  Calculate M₃, p₃, T₃ downstream of the expansion corner.  Since the resulting flow is in the same direction as the original flow, would you expect M₃ = M₁, p₃ = p₁, T₃ = T₁? Explain.

Problem 4 - 4.8 (5)
A single normal shock OR an oblique shock followed by a normal shock? Calculate also the total pressure loss in each case.

Problem 5 - 4.16 (10)
Diamond airfoil in supersonic flow.

Problem 6 - 4.17 (10)
Flat plate in supersonic flow.

Problem 7 - 4.9 (10)
Intersection of shock waves

Problem 8 - 4.20 & 4.21 (15)
Chemically reacting gas