In this lecture... Subsonic and supersonic nozzles Working of these nozzles Performance parameters for nozzles

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1 Lct-30

2 Lct-30 In this lctur... Subsonic and suprsonic nozzls Working of ths nozzls rformanc paramtrs for nozzls rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay

3 Lct-30 Variation of fluid vlocity with flow ara 0, 0 M (sonic) M< (subsonic) 0, 0 M (sonic) Sonic vlocity will occur at th xit of th convrging xtnsion, instad of th xit of th original nozzl, and th mass flow rat through th nozzl will dcras bcaus of th rducd xit ara. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 3

4 Lct-30 Variation of fluid vlocity with flow ara M<, dcrass V, M incrass M<, incrass V, M dcrass Subsonic nozzl Subsonic diffusr M>, dcrass V, M incrass M>, incrass V, M dcrass Suprsonic nozzl Suprsonic diffusr rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 4

5 Lt through a nozzl. h mass m his m us ρua A 0 on R Lct-30 Govrning quations considr a calorically prfct flow through th nozzl is MA R R ( M R ) { + (( ) / )M } { + (( ) / )M } simplication A rducs { } ( + (( ) / )M / /( ) + ) / ( ) rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay M (MA) to 0 gas 0 flow R 0 5

6 Lct-30 Isntropic flow through convrging nozzls Convrging nozzl in a subsonic flow will hav dcrasing ara along th flow dirction. W shall considr th ffct of back prssur on th xit vlocity, mass flow rat and prssur distribution along th nozzl. W assum flow ntrs th nozzl from a rsrvoir so that inlt vlocity is zro. Stagnation tmpratur and prssur rmains unchangd in th nozzl. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 6

7 Lct-30 Isntropic flow through convrging nozzls Rsrvoir 0, 0 b : back prssur / 0 x b 0 b > * */ b * b < * b 0 Chokd flow rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 7

8 Lct-30 Isntropic flow through convrging nozzls mmax m / 0.0 */ 0.0 b / 0 */ h ffct of back prssur b on th mass flow rat and th xit prssur. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 8

9 Lct-30 Isntropic flow through convrging nozzls From th abov figur, b for for For all back prssurs lowr that th critical prssur, xit prssur critical prssur, Mach numbr is unity and th mass flow rat is maximum (chokd flow). A back prssur lowr than th critical prssur cannot b snsd in th nozzl upstram flow and dos not affct th flow rat. b b < rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 9

10 Nozzl fficincy Lct-30 h 0 0t 0 s s rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 0

11 Convrging nozzls Lct-30 h η n at th th In η n th trms fficincy h h h h s nozzl nozzl nozzl of s, xit,h xit. th of whr inlt, s is h s is th corrsponding a nozzl h / / is 0 is th th dfind actual isntropic as stagnation static static tmpraturs, nthalpy nthalpy nthalpy at at rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay

12 If Convrging nozzls For chokd flow, M, ( /( + )) ηn ( ) / ( / ) h prssur ratio is thrfor, C C < a C, ( ( / η n )(( ) /( + ))) /( ) Lct-30 th nozzl is oprating undr chokd condition. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay

13 Convrging nozzls Lct-30 If a convrgnt nozzl is oprating undr chokd condition, th xit Mach numbr is unity. h xit flow paramtrs ar thn dfind by th critical paramtrs. o dtrmin whthr a nozzl is chokd or not, w calculat th actual prssur ratio and thn compar this with th critical prssur ratio. If th actual prssur ratio > critical prssur ratio, th nozzl is said to b chokd. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 3

14 Lct-30 Isntropic flow through convrgingdivrging nozzls Maximum Mach numbr achivabl in a convrging nozzl is unity. For suprsonic Mach numbrs, a divrging sction aftr th throat is rquird. Howvr, a divrging sction alon would not guarant a suprsonic flow. h Mach numbr at th xit of th convrging-divrging nozzl dpnds upon th back prssur. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 4

15 Lct-30 hroat 0 b 0 * Sonic flow at throat Inlt M hroat A B C D A B C D E F G Exit b Subsonic flow at nozzl xit No shock Subsonic flow at nozzl xit Shock in nozzl Suprsonic flow at nozzl xit No shock in nozzl x Shock in nozzl.0 D C B A Suprsonic flow at nozzl xit No shock in nozzl Subsonic flow at nozzl xit Shock in nozzl Subsonic flow at nozzl xit No shock rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 5

16 Lct-30 Convrging-divrging nozzls h flow through nozzls is normally assumd to b adiabatic as th hat transfr pr unit mass is much smallr than th diffrnc in nthalpy btwn th inlt and outlt. h flow from th inlt to th throat can b assumd to b isntropic, but th flow from th throat to xit may not b du th possibl prsnc of shocks. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 6

17 rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 7 Lct-30 Convrging-divrging nozzls ) /( ) / ( n ) /( ) / ( n 0 ) / ( ) / ( 0 s 0 s s n Sinc, hrfor, ) / ( ) / ( / / h h h h as dfind is nozzl a of fficincy h η η η

18 Lct-30 Convrging-divrging nozzls h xit vlocity can b calculatd from u (h h ) η n (h h s ) c p η n ( s ) c p η n ( ) / R ( ) η n ( ) / rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 8

19 rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 9 Lct-30 Convrging-divrging nozzls { } { } + + η η η ) / ( n ) / ( n ) / ( i i n 0 ) / ( ) / ( M M M Sinc, R u a u M is Mach numbr xit h

20 From th th A A A A t * Lct-30 Convrging-divrging nozzls assumin g throat 0 ot 0 M + (( Mt + (( If th throat is M 0 * M M govrning t isntropic ara and + (( + (( quation flow upto th ) / )M ) / )M ) / )M t ) / )M chokd, M xit ( + ) / ) + (( ) / )M ( + / ( )) t t ara is, ( + / ( )), discussd throat, th ( + / ( )) arlir, and ratio also btwn rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 0

21 m Lct-30 Convrging-divrging nozzls h mass flow rat will thrfor b, A R * * * ( + ) / ( ) (( + ) / ) h mass flow rat is a function of th inlt stagnation prssur, tmpratur and throat ara. By dsign on would lik to kp th ara ratio A /A as clos as possibl to unity. his is to kp th xtrnal drag undr control. Howvr this may rsult in th nozzl xit prssur to b diffrnt from th ambint prssur :incomplt xpansion. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay i

22 Lct-30 Convrging-divrging nozzls Undrxpandd nozzl: > a h flow is capabl of additional xpansion. Expansion wavs originating from th lip of th nozzl. Ovrxpandd nozzl: < a Shock wavs originat from th nozzl lip. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay

23 Lct-30 Convrging-divrging nozzls Fully xpandd nozzl: a No shock wavs/xpansion wavs. If << a Shock wavs will occur within th divrgnt sction of th nozzl. rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 3

24 Lct-30 Convrging-divrging nozzls Expansion wavs Fully xpandd: a Undrxpandd: a Obliqu shocks Ovrxpandd: a << a rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 4

25 Lct-30 In this lctur... Subsonic and suprsonic nozzls Working of ths nozzls rformanc paramtrs for nozzls rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 5

26 Lct-30 In th nxt lctur... utorial on intaks and nozzls rof. Bhaskar Roy, rof. A M radp, Dpartmnt of Arospac, II Bombay 6