Ch11_5_NS - MAE130B Ch 11 (5) Normal Shock Wave Changzheng...

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MAE130B – Ch 11 (5) Normal Shock Wave Changzheng Huang
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Ch 11 (5) Changzheng Huang 2 Compressible Flow 1. Normal shock wave 2. Examples
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Ch 11 (5) Changzheng Huang 3 (1) Normal shock wave ( x )( y ) M >1 M <1 Fanno flow Rayleigh flow Normal shock Mass Momentum Energy V const ρ = V const = V const = 2 p V const +≠ 2 2 V h const += 2 p V const + = 2 2 V h const 2 p V const + = 2 2 V h const s T s T s T M<1 M>1 M>1 M<1 x y Second law of thermodynamics: entropy must increase across shock. M<1 M>1
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Ch 11 (5) Changzheng Huang 4 (1) Normal shock wave ( x )( y ) M >1 M <1 Normal shock V const ρ = 2 p V const + = 2 2 V h const += s T x y M<1 M>1 Knowing M x , to find M y 22 x xx y yy p Vp V + 2 2 12 kRT V kRT V kk + −− 2 2 11 xy V V pk kp kp ⎛⎞ + ⎜⎟ ⎝⎠ () ( ) x y p kM p kM + 2 2 p V pV ρρ + 2 2 x y p V p k k p +• =
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Ch 11 (5) Changzheng Huang 5 (1) Normal shock wave ( x )( y ) M >1 M <1 Normal shock V const ρ = 2 p V const + = 2 2 V h const += s T x y M<1 M>1 () ( ) 22 11 x xy y p kM p kM + 2 2 yy xx x y p V pV kk kp kp ρρ ⎛⎞ −− +• = ⎜⎟ ⎝⎠ x y pM + 1/2 0 0 y y y x yx x x x x x x vM cM T M T T T M T T == = = 2 0 2 0 1 1 2 1 1 2 y y x x x x k M MT T M k T M M + +
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Ch 11 (5) Changzheng Huang 6 (1) Normal shock wave ( x )( y ) M >1 M <1 Normal shock V const ρ = 2 p V const + = 2 2 V h const += s T x y M<1 M>1 () ( ) 22 11 x xy y p kM p kM + x xx yy y kk pM −− ⎛⎞ + ⎜⎟ ⎝⎠ 1/2 2 0 2 0 1 1 2 1 1 2 y y x yx x x x k M MT T M k T M M + == + x y p MM p + x y M M kM kM ++ =
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Ch 11 (5) Changzheng Huang 7 (1) Normal shock wave ( x )( y ) M >1 M <1 Normal shock V const ρ = 2 p V const + = 2 2 V h const += s T x y M<1 M>1 () ( ) 22 11 x xy y p kM p kM + 1/2 x y kk M MM M
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Ch11_5_NS - MAE130B Ch 11 (5) Normal Shock Wave Changzheng...

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