16100lectre41_cj

# 16100lectre41_cj - M shock Upstream Mach: 1 > L M...

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Normal Shock Waves In our quasi-1D flows, shocks can occur from a supersonic-to-subsonic state. These shocks are discontinuous in our inviscid flow model (recall that shocks are very thin and their thickness scales with e R 1 ): The shock jump relationships come from the conservation equations we have seen before: Since the jump is discontinuous (i.e. it has zero thickness) 0 = = = dA A A A R L Here are some important things to know about shock waves from these relationships: Mathematically, “shocks” exist which jump from subsonic-to-supersonic flow. However, these “shocks” can be shown to violate the 2 nd Law ( 0 < s ). Only shocks which jump from supersonic-to-subsonic states satisfy the 2 nd Law. The Mach number downstream of shocks is given by : And it can be shown that 0 > s . 1 M Throat L M R

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Unformatted text preview: M shock Upstream Mach: 1 > L M Downstream Mach: 1 < R M R o R R L o L L A A R R R R L L L L R R R L L L A h u A h u pdA A p u A p u A U A U R L R L ρ = − + = + = ∫ ) ( ) ( 2 2 R L o R R L L R R R L L L R R L L h u h u p u p u u u = + = + = 2 2 Ranhine-Hugoniot Shock Jump Relationships ) 1 ( 2 1 ) 1 ( 2 1 1 2 2 2 − − − + = γ L L R M M M where 1 > L M Normal Shock Waves 16.100 2002 2 ∗ The stagnation enthalpy (and therefore the total temperature) is constant through a shock (shocks are adiabatic). ⇒ ∗ Total pressure decreases through a shock (this is a direct result of the entropy Increasing while . const T = ): ⇒ R L h h = or, equivalently, R L T T = R s s L R L R e p p ) ( − − =...
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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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16100lectre41_cj - M shock Upstream Mach: 1 > L M...

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