16100lectre45_cj

16100lectre45_cj - Oblique Shock Waves Heres a quick refresher on oblique shock waves We start with the oblique shock as shown below w2 M t 2(1(2)1

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Oblique Shock Waves Here’s a quick refresher on oblique shock waves. We start with the oblique shock as shown below: (1) (2) Also, the specific flow quantities above are: v : flowspeed M : Mach number = a v u : normal velocity to shock n M : Normal Mach a u = # w : tangential velocity to shock t M : Tangential Mach a w = # The next step is to apply the 2-D Euler equations to derive jump conditions. Let’s consider the following (well-chosen) control volume across the shock: Where: d a & are parallel to shock e c f b , , , are parallel to local flow Apply conservation of mass: = s ds n V 0 v v ρ But 0 = n V v v on , & , , e c f b thus: ∫∫ = + = + ad s s ds n V ds n V ds n V ds n V 0 0 2 2 1 1 v v v v v v v v 1 u 2 u y x 1 1 , t M w 1 1 , M v 1 1 , n M u β θ 2 2 , M v 2 2 , n M u 2 2 , t M w ( ) 1 : upstream flow condition ( ) 2 : downstream flow condition : angle of shock wave . . . t r w upstream flow : deflection angle of flow b c a f e d g a n n v v = 1 v 2 v s d n n v v + = s n v Control volume s s t v Shock wave
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Oblique Shock Waves 16.100 2002 2 0 2 2 1 1 = +
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lectre45_cj - Oblique Shock Waves Heres a quick refresher on oblique shock waves We start with the oblique shock as shown below w2 M t 2(1(2)1

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