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 ( ) wp a w w qu c TT =− ρ t S , and using , the integrated heat loss is 2 mu R i L 2 ww x0 dR Q q 2 R ds ; ds 1 dx dx dx = ⎛⎞ π= + ⎜⎟ ⎝⎠ ±± (small angles) (1) () () LL a w w t p a w w t 2 00 md Qc T T S 2 R d x m c T T S 2 R R −π = π ∫∫ i i ± x (2) For an approximate evaluation, assume the quantity ( ) pa w wt cT TS is a weak function of x, and treat it as a constant. We then obtain () aw w w t cc pc QT dx dx 2S 1 Rx mc T i w t (3) For many rockets, L eff 0 Ld RR x x is of the order of 6-10, and w c T 11 T 43 , so the ratio w Q 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 pc F2 1 0 N J mc T c T 2770 3600K C4 5 0 0 m s K g K × i ± × , or (the output power of four large power stations). 9 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 0e w u u m 22 Q (4) But a little reflection shows that the kinetic energy loss must be less than w Q .
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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_8 - 16.512, Rocket Propulsion Prof. Manuel...

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