For a given Prandtl-Meyer expansion, the upstream Mach number is 3 and the pressure ratio across the wave is P2/P1 = 0.4. Calculate teh angl

Question

For a given Prandtl-Meyer expansion, the upstream Mach number is 3 and the pressure ratio across the wave is P2/P1 = 0.4. Calculate teh angles of the forward and rearward mach lines of the expansion fan relative to the free-stream direction

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Sigridomena 2 months 2021-07-21T12:17:05+00:00 1 Answers 3 views 0

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    2021-07-21T12:18:21+00:00

    Answer:

    The angle for the forward Mach line is 19.47°

    The angle for the rearward Mach line is 5.21°

    Explanation:

    From table A-1 (Modern Compressible Flow: with historical perspective):

    \frac{P_{o} }{P_{1} } =36.73 (M₁ = 3)

    If Po₁ = Po₂

    \frac{P_{o2} }{P_{2} } =\frac{P_{o1} }{P_{1} } *\frac{P_{1} }{P_{2} } =36.73*\frac{1}{4} =91.825

    Table A-1:

    \frac{P_{o2} }{P_{2} } =91.825,M_{2} =3.63

    Table A-5:

    v₁ = 49.76°

    μ₁ = 19.47°

    v₂ = 60.55°

    μ₂ = 16°

    θ = 60.55 – 49.76 = 10.79°

    The angle for the forward Mach line is:

    μ₁ = 19.47°

    The angle for the rearward Mach line is:

    θr = μ₂ – θ = 16 – 10.79 = 5.21°

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