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lecture_8

# lecture_8 - 16.512 Rocket Propulsion Prof Manuel...

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16.512, Rocket Propulsion Prof. Manuel Martinez-Sanchez Lecture 8: Convective Heat Transfer: Other Effects Overall Heat Loss and Performance Effects of Heat Loss (1) Overall Heat Loss The local heat loss per unit area is ( ) w p aw w q uc T T = ρ t S , and using , the integrated heat loss is 2 m u R = π i ρ L 2 w w x 0 dR Q q 2 R ds ; ds 1 dx dx dx = π = + ± ± (small angles) (1) ( ) ( ) L L w p aw w t p aw w t 2 0 0 m d Q c T T S 2 R dx m c T T S 2 R R π = π i i ± x (2) For an approximate evaluation, assume the quantity ( ) p aw w t c T T S is a weak function of x, and treat it as a constant. We then obtain ( ) ( ) L L aw w w t c c 0 0 p c T T Q T dx dx 2S 1 2S T T R x R x mc T i ± ± w t (3) For many rockets, ( ) L eff 0 L d R R x x is of the order of 6-10, and w c T 1 1 T 4 3 , so the ratio w p c Q mc T i (heat loss divided by total enthalpy flux) is of the order of 8-16 times 16.512, Rocket Propulsion Lecture 8 Prof. Manuel Martinez-Sanchez Page 1 of 6

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the Stanton number. As we found before, is itself ~ 0.001, leading to fraction heat losses of the order of 1-2%. While this is a small fraction, its absolute value may be large, because the total thermal power is enormous. As an example, for the SSME engine t S 6 p c p c F 2 10 N J mc T c T 2770 3600K C 4500 m s KgK × = × i ± × , or (the output power of four large power stations). 9 p c mc T 4.4 10 W = × i A 1.5% fraction of this means 66 MW lost to the walls (some 80,000 HP). (2) Effect on Performance As a starting guess, we could imagine that all of the losses ( ) w Q are reflected in an equal amount of kinetic energy loss in the exhaust. If is the exist velocity with no losses, e 0 u i ± 2 2 e 0 e w u u m 2 2 Q (4)
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lecture_8 - 16.512 Rocket Propulsion Prof Manuel...

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