(heat loss divided by total enthalpy flux) is of the order of 8-16 times

Transcription

1 16.51, Rok Prolson Prof. Manl Marnz-Sanhz r 8: Convv Ha ransfr: Ohr Effs Ovrall Ha oss and Prforman Effs of Ha oss (1) Ovrall Ha oss h loal ha loss r n ara s q = ρ ( ) ngrad ha loss s a S, and sng m = ρπr, h dr Q qπ R ds ; ds = 1 + (small angls) (1) x= m Q ( ) S π R = m ( ) S R a a πr () For an aroxma valaon, assm h qany ( ) fnon of x, and ra as a onsan. W hn oban S s a ak a Q m a R x S 1 S (3) ( ) R( x) For many roks, rao Q m R R x s of h ordr of 6-1, and 1 1, so h 4 3 ff ( ) (ha loss dvdd by oal nhaly flx) s of h ordr of 8-16 ms 16.51, Rok Prolson r 8 Prof. Manl Marnz-Sanhz Pag 1 of 6

2 h Sanon nmbr. As fond bfor, s slf ~.1, ladng o fraon ha losss of h ordr of 1-%. Whl hs s a small fraon, s absol val may b larg, bas h oal hrmal or s normos. As an xaml, for h SSME ngn S 6 F 1 N J m = 77 36K, C 45 m s KgK or m = W 9 (h o or of for larg or saons). A 1.5% fraon of hs mans 66 MW los o h alls (som 8, HP). () Eff on Prforman As a sarng gss, old magn ha all of h losss ( Q ) ar rfld n an qal amon of kn nrgy loss n h xhas. If no losss, s h xs vloy h m Q (4) B a ll rflon shos ha h kn nrgy loss ms b lss han Q. Indd, ha losss ha or nar h nozzl x lan ar almos rrlvan for rforman, bas h hrmodynam ffny of h rmanng xanson from h on of loss o h xhas s vry small, so vry ll of ha loss s rfld n a kn nrgy dras. So, for h m bng, smly aknoldg hs by rng m < Q (5) Q or > m Q or > 1 m (6) P = = P Rmmbrng ha ( ), 16.51, Rok Prolson r 8 Prof. Manl Marnz-Sanhz Pag of 6

3 Q > 1 P 1 P m (7) If h fraonal loss Q m s of ordr 1.5% and h xanson ffny P 1.15 η= 1 s of ordr 75%, hn > =.1 (.., a loss of lss P.75 han 1% n sf mls, gnorng h x rssr onrbon). h allaon an b mad mor rs by rakng h volon of h gas mrar. h oal nrgy qaon, aonng for h losss, s dh d d = S R + π = π m ρa q R ρ ( a ) d d S or + = ( ) R (8) B h momnm qaon (gnorng, somha nonssnly, h ffs of d d d 1 d fron), gvs ρ + =, or =. Sbsng n (8), ρ d 1 d S = ρ R Dvd by and no ha ( ) 1 d 1 d = ρ 1d 1d S = R (9) Who h ha loss rm, hs old ngra o (snro) rlaon. Mor gnrally no, P = P 1, h dal flo 16.51, Rok Prolson r 8 Prof. Manl Marnz-Sanhz Pag 3 of 6

4 P S = x (1) P R and sn h xonn s a small nmbr, P S = (11) P R o vala h orron rm, s for h ndsrbd, as f no ha loss had hand. hs gvs P = 1 P 1 and also assm ha S s narly onsan: P P S P P R (1) and, n arlar, a h x lan, P P S P P R (13) W no xrss h x kn nrgy as ( ) = (14) hr boh and ar affd by h losss. For h oal nrgy loss, hav and so ( ) m = Q 16.51, Rok Prolson r 8 Prof. Manl Marnz-Sanhz Pag 4 of 6

5 Q R = = S m (15) hr hav sd h rsl n qaon (3). For h loss of sa nrgy, hav h rsl n (13). Usng boh n (14), 1 1 P P = S + S R P P R or P P = P P 1 S 1 1 R (16) P 1 W s no ha h faor 1 orrng n h ngral of (16) s js h P hrmodynam rlf had mnond arlr, hh maks h loss of kn nrgy b lss han h ha loss. Indd, hs faor boms zro as P P, so, as anad, ha losss nar h x ar rrlvan. o smlfy h rng, s P = P and dfn P P η, = and η x, = ( ) P P x 1 : η x, = S η, R (17) ηx, and, agan, h rgh-hand-sd mns h faor old b h rlav ha η, loss (qaon 3). Nmral valaon shos ha h modfd ngral n (17) s 16.51, Rok Prolson r 8 Prof. Manl Marnz-Sanhz Pag 5 of 6

6 abo 3 of h orgnal ngral rlav I s R. Rmmbrng or arlr sma of h loss ( < 1%), onld ha a br sma s abo.67%. hs amons o 3 s. o of I 4s. s 16.51, Rok Prolson r 8 Prof. Manl Marnz-Sanhz Pag 6 of 6