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Oblique Shock and Expansion Waves Lecture 27-28 ME EN 412 Andrew - - PDF document
Oblique Shock and Expansion Waves Lecture 27-28 ME EN 412 Andrew - - PDF document
Oblique Shock and Expansion Waves Lecture 27-28 ME EN 412 Andrew Ning aning@byu.edu Outline Oblique Shock Waves Expansion Waves Applications Oblique Shock Waves NASA, Public Domain V 1 n V 1 t V 2 V 1 V 2 t V 2 n M > 1
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NASA, Public Domain
V2t V1t V1n V2n V2 V1
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β M > 1 θ
- shock angle: β
- turning angle: θ
M1n = M1 sin β M2n = M2 sin(β − θ)
10 20 30 40 50 θ: deflection angle (degrees) 10 20 30 40 50 60 70 80 90 β: shock angle (degrees) M =1.5 M =2 M =3 M =∞
tan θ = 2 cot β(M 2
1 sin2 β − 1)
M 2
1(γ + cos(2β)) + 2
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Bow shock
1 2 3 4 5 1 2 3 4 5 θ β
subsonic supersonic
Example
Uniform supersonic flow (M1 = 3, p1 = 1 atm, T1 = 300 K) encounters a corner and deflects by 20◦. Find the shock wave angle and p2, T2, M2, pT 2, TT 2.
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Expansion Waves Expansion Waves
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Prandtl-Meyer function
ν(M) = γ + 1 γ − 1 tan−1 γ − 1 γ + 1(M 2 − 1) − tan−1 M 2 − 1 The turning angle is a function of this equation θ = ν(M2) − ν(M1)
Applications
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Applications
What must exist at the exit of an overexpanded and underexpanded nozzle?
External Flow
Diamond airfoil at zero angle of attack.
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Example: Flat plate at 5◦ angle of attack in M = 2.6
- freestream. What are lift and drag coefficients.