Ch11_3_CD - MAE130B Ch 11 (3) Compressible Flow Changzheng...

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MAE130B – Ch 11 (3) Compressible Flow Changzheng Huang
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Ch 11 (3) Changzheng Huang 2 Compressible Flow 1. Isentropic converging diverging duct flow 2. Non-isentropic adiabatic flow (Fanno flow)
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Ch 11 (3) Changzheng Huang 3 1. Converging-diverging duct flow Inflow Outflow p p* M 1 x 0 x 0 Six isentropic flow cases: (i) A : sub in – sub throat – sub out (ii) B Æ C : sub in – sonic throat – sub out (iii)B Æ E : sub in – sonic throat – super out (iv) D Æ C : super in – sonic throat – sub out (v) D Æ E : super in – sonic throat – super out (vi) F : super in – super throat – super out A BC D E F A B C D E F
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Ch 11 (3) Changzheng Huang 4 1. Converging-diverging duct flow Inflow Outflow p p* M 1 x 0 x 0 A BC D E F A B C D E F T 0 , p 0 p b p I p III M III M I Suppose stagnation temperature T 0 , stagnation pressure p 0 , duct area A = A ( x ), back pressure p b Then there are five cases, (1) p0>pb>pI isentropic flow A (2) pb=pI Isentropic ( B , C ) or ( D , C ) (3) pI>pb>pIII Non-isentropic shock flow (4) pb=pIII Isentropic ( B , E ) or ( D , E ) (5) pIII>pb>0 Isentropic flow F
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Ch 11 (3) Changzheng Huang 5 1. Converging-diverging duct flow Inflow Outflow p p* M 1 x 0 x 0 A BC D E F A B C D E F T 0 , p 0 p 1 Stagnation temperature T 0 , stagnation pressure p 0 , duct area A = A ( x ), Given pressure p 1 at A 1 . How to solve duct flow p(x)? A 1 ( ) () ** * * * 1/2 * * 00 1 11 1 Ax u Au cc cuc M c kRT T MM T krT TT MT T ρ ρρ = == ⎛⎞ ⎜⎟ ⎝⎠ =
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Ch 11 (3) Changzheng Huang 6 1. Converging-diverging duct flow Inflow Outflow p p* M 1 x 0 x 0 A BC D E F A B C D E F T 0 , p 0 p 1 Stagnation temperature T 0 , stagnation pressure p 0 , duct area A = A ( x ), Given pressure p 1 at A 1 .
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Ch11_3_CD - MAE130B Ch 11 (3) Compressible Flow Changzheng...

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