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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 () =+ ± ee a Fm u PPA e F ct F C PA Optimum expansion : = ea PP - For less , > e e t A 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 PP A a , and the extra pressure forces are a suction , backwards Compute at = ± mu ρ A sonic throat: () γ γγ ργ + −− ⎛⎞ == ⎜⎟ ++ + ⎝⎠ ± 11 12 1 22 2 ; 1 ct cg c t gc PA R mR T A g M RT = g R call 2 3 Γ ± call = Γ * c (“characteristic velocity”) * →= ± m c Can express uP etc in terms of either M ,, ee e , A e or e c P P or e t A A : + = + + ⎛⎞⎛⎞ = ⎜⎟⎜⎟ + ⎝⎠⎝⎠ 1 2 21 2 1 ; 1 1 2 1 1 2 1 2 e c e e et t t t te e e e ee P P M M AP u P T u P M T M + 1 = = + += + = 1 2 , 1 and , 1 1 2 2 1 cc e c e Because p ep c g e e g c PT T T M uM cT 16.512, Rocket Propulsion Lecture 3 Prof. Manuel Martinez-Sanchez Page 2 of 10
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() γ + ⎛⎞ =+ = + ⎜⎟ ⎝⎠ + == + + Γ ± * 1 2 21 * 2 1 1 2 2 1 1 1 2 eae e e ae Fe ct c t c c t e e e e PPA u P PA m Cu P A P P A c MR M uM c RTc M Tc eg g In vacuum, 0 = a P γγ + −− + + + = + + + + 1 1 21 1 2 2 1 * 1 2 1 1 2 1 1 1 1 2 2 e ee e e F v e e e M uP A M C M c M M + + = + + 1 2 1 2 1 1 1 2 e e F v e M M C M and otherwise, 16.512, Rocket Propulsion Lecture 3 Prof. Manuel Martinez-Sanchez Page 3 of 10
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⎛⎞ =− ⎜⎟ ⎝⎠ ea FF v tc M e AP CC Note: For , = PP () γ + == + + 1 21 * Matched 2 2 1 1 1 2 ee F e uM C c M For 0 γγ + = −+ 1 Max,Vac 22 11 F C Choice of Optimum Expansion For a Rocket Flying Through an Atmosphere ( varying) a P The thrust coefficient = F ct F C PA was derived in class in the form ae vac (1) + + = + + 1 2 1 2 1 1 1 2 e e F vac e M M C M (2) and we also found + + = + 1 2 1
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This note was uploaded on 11/07/2011 for the course AERO 16.512 taught by Professor Manuelmartinez-sanchez during the Fall '05 term at MIT.

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lecture_3 - 16.512 Rocket Propulsion Prof Manuel...

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