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Ch11_2_CD

# Ch11_2_CD - MAE130B Ch 11(2 Isentropic Duct Flow Changzheng...

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MAE130B – Ch 11 (2) Isentropic Duct Flow Changzheng Huang

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Ch 11 (2) Changzheng Huang 2 Isentropic Duct Flow 1. Stagnation (M=0) and chocked condition (M=1) 2. Temperature-entropy diagram 3. Converging-diverging duct flow
Ch 11 (2) Changzheng Huang 3 1. Stagnation (M=0) and chocked condition (M=1) 0 0 kk p p ρ = Isentropic flow: Energy equation: 2 0 2 dp V d ⎛⎞ + = ⎜⎟ ⎝⎠ 1/ 22 2 00 0 2 k k pp dp V dp V V dd p d p d p ρρ += 0 2 0 0 0 0 2 k pV k p p V pd p d ∫∫ 0 2 (1 ) / 0 0 0 12 k p p p kV p k ⎡⎤ + = ⎣⎦ () 2 ) / ) / 0 0 0 0 k p k −−

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Ch 11 (2) Changzheng Huang 4 0 0 kk p p ρ = Isentropic flow: () 1/ 2 (1 ) / ) / 0 0 0 0 12 k p kV pp k −− −+ = 2 ) / ) / 0 0 0 0 k k p kp V k ρρ ⎛⎞ += ⎜⎟ ⎝⎠ 2 0 0 0 p V k = 2 0 0 kR V TT k 2 0 2 V cT =+ 2 0 2 V hh 1. Stagnation (M=0) and chocked condition (M=1)
Ch 11 (2) Changzheng Huang 5 2 0 2 pp V cT = + 2 0 2 V hh = + We now have, Or 222 2 0 2 11 1 1 1 1 2 p T Vk M Tc T k R T c −−− =+ What about p 0 /p and ρ 0 / ρ ? 1. Stagnation (M=0) and chocked condition (M=1)

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Ch 11 (2) Changzheng Huang 6 2 0 1 1 2 T k M T =+ 0 0 kk p p ρ = p RT = 00 k p p ⎛⎞ = ⎜⎟ ⎝⎠ 0 p T p T = 1 1 k T T = 1 k k pT = 1 2 0 1 1 2 k k p k M p 1 1 2 0 1 1 2 k k M 1. Stagnation (M=0) and chocked condition (M=1)
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Ch11_2_CD - MAE130B Ch 11(2 Isentropic Duct Flow Changzheng...

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