lecture_3

# lecture_3 - 16.512 Rocket Propulsion Prof Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 3: Ideal Nozzle Fluid Mechanics Ideal Nozzle Flow with No Separation (1-D) - Quasi 1-D (slender) approximation - Ideal gas assumed ( ) = + ± e e a F mu P P A e F c t F C P A Optimum expansion : = e a P P - For less , > e e t A P P A a , could derive more forward push by additional expansion 16.512, Rocket Propulsion Lecture 3 Prof. Manuel Martinez-Sanchez Page 1 of 10

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- For more , < e e t A P P A a , and the extra pressure forces are a suction , backwards Compute at = ± m u ρ A sonic throat: ( ) γ γ γ ρ γ γ γ γ + = = + + + ± 1 1 1 2 1 2 2 2 ; 1 1 1 c t c g c t g c P A R m R T A g M R T = g R call 2 3 Γ ± call ( ) γ = Γ * c (“characteristic velocity”) g c R T * = ± c t P A m c Can express u P etc in terms of either M , , e e e , A e or e c P P or e t A A : γ γ γ γ γ γ + = + + ⎞ ⎛ = = = ⎟ ⎜ ⎟ ⎜ + ⎠ ⎝ 1 2 1 1 2 1 2 1 ; 1 1 2 1 1 1 1 2 1 2 e c e e e t t t t t e e e e e e P P M M A P u P T A P u P M T M ( ) γ γ + 1 2 1 γ γ γ γ γ γ γ γ = = + + = + = 1 2 2 2 , 1 and , 1 1 2 2 1 2 1 e e c c e c e e e Because p e p c g e e g c P T P T T T M u M c T c T R T RT R T 16.512, Rocket Propulsion Lecture 3 Prof. Manuel Martinez-Sanchez Page 2 of 10
( ) γ γ γ γ γ γ + = + = + + = = + + Γ ± * 1 2 2 1 * 2 1 1 2 2 1 1 1 2 e a e e e a e F e c t c t c c t e e e e P P A u P P A m C u P A P A P P A c M R M u M c R Tc M Tc γ e g g In vacuum, ( ) 0 = a P ( ) ( ) ( ) γ γ γ γ γ γ γ γ γ γ γ γ γ + + + + = + = + + + + 1 1 2 1 1 2 2 1 2 1 * 1 2 2 1 1 1 2 2 1 1 1 1 1 2 2 e e e e e F v c t e e e M u P A M C P A M c M M ( ) ( ) γ γ γ γ

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