16100lectre38_cj

16100lectre38_cj - Behavior of Isentropic Flow in Quasi-1D...

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Unformatted text preview: Behavior of Isentropic Flow in Quasi-1D Recall cons. of mass: . const uA = ρ Consider a perturbation in the area . . . ) )( )( ( = + + ⇒ + + + + = + + + = udA Adu uAd T O H udA Adu uA d uA dA A du u d uA ρ ρ ρ ρ ρ ρ ρ ρ ρ ρ Or (1) Similar manipulations to x-momentum gives: (2) Also, since the flow is assumed isentropic, we can use the definition of the speed of sound to relate ρ d and dp : ⇒ ∂ ∂ = = . 2 const s p a ρ A A u u p p L L L L = = = = ρ ρ L x R x dA A A du u u dp p p d L R L R L R L R + = + = + = + = ρ ρ ρ = + udu dp ρ ρ d a dp 2 = = + + A dA u du d ρ ρ Since we have assumed . const s = in the flow (3) Behavior of Isentropic Flow in Quasi-1D 16.10 2002 2 We are interested in how the flow properties change when the area changes. So, we use (2) and (3) to eliminate terms from (1). For example, let’s determine how u changes with A : ) 1 ( 2 2 2 = + − = + + − = + + = + + A dA u du M A dA u du a udu A dA u du a dp A dA u du d ρ ρ ρ ρ ρ ⇒ When...
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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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16100lectre38_cj - Behavior of Isentropic Flow in Quasi-1D...

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