In this lecture... Ideal gas turbine cycles Thrust and efficiency The thrust equation Other engine performance parameters Ideal cycle for jet engines

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2 Lct-3 In this lctur... Idl gs turbin cycls Thrust nd icincy Th thrust qution Othr ngin prormnc prmtrs Idl cycl or jt ngins Turbojt ngin Turbojt ngin with trburning Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby

3 Lct-3 Gs turbin cycls Gs turbin ngins oprt on Bryton cycls. Idl Bryton cycl is closd cycl, whrs gs turbins oprt in th opn cycl mod. Idl cycl ssums tht thr r no irrvrsibilitis in th procsss, ir bhvs lik n idl gs with constnt spciic hts, nd tht thr r no rictionl losss. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 3

4 Lct-3 Thrust nd icincy W will now driv xprssions or thrust nd icincy o ir-brthing ngins rom th momntum nd nrgy qutions. W shll considr gnrlizd thrust producing dvic with singl inlt nd singl xhust. W ssum tht th thrust nd conditions t ll points within th control volum do not chng with tim. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 4

5 Th thrust qution Control surc I (Rction) Lct-3 u A i A u u, P Thrust producr A, P u y 1 s x Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 5

6 Th thrust qution Lct-3 Th rction to th thrust,, is trnsmittd to th support. Th ngin thrust is thus th vctor summtion o ll orcs on th intrnl nd xtrnl surcs o th ngin. Thror, F u ρ ( u. n) da CS Considring th componnts o orc nd th momntum lux in th x-dirction only, F x ux ρ( u. n) da CS I Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 6

7 Th thrust qution Lct-3 Th prssur nd vlocity cn b ssumd to b constnt ovr th ntir control surc, xcpt ovr th xhust r, A. Th nt prssur orc cting on this control volum is (P P )A. Th only othr orc cting on th control volum is th rction to th thrust, I. Adding up th orcs in th x-dirction, F ( P P ) A x + I Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 7

8 Th thrust qution Th mss low tht ntrs th cptur r, A i, is Similrly, th mss low crossing th xhust r A, is, Also, Or, Continuity qution or th CV givs, Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 8 Lct-3 ua i m ρ A u m ρ i m m m + i ua A u m ρ ρ ) ( Which is, Rrrnging, 0 ) ( i s s s A A u m A u ua m m ua m m A A u A u ρ ρ ρ ρ ρ ρ

9 Th thrust qution Control surc I (Rction) Lct-3 u A i A u u, P Thrust producr A, P u y 1 s x Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 9

10 Th thrust qution From th momntum blnc cross th CV, u ρ( u. n) da u + u + ρu( A A ) u u ρu( A A ) u CS x This is th nt outwrd lux o x-momntum. This qution rducs to uxρ( u. n) da u CS s From th orc blnc qution, w hv, I u m u u + ( P P ) A Lct-3 i Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 10

11 Th thrust qution I w din ul-ir rtio, / I [( 1+ ) u ] u + ( P P A m ) Lct-3 This is th gnrlisd thrust qution or ir-brthing ngins. Th trm (P P )A is not zro only i th xhust jt is suprsonic nd th nozzl dos not xpnd th xhust jt to mbint prssur. Howvr i P «P, it cn b substntil contribution. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 11

12 Lct-3 Engin prormnc prmtrs Th ngin prormnc is dscribd by dirnt icincy dinitions, thrust nd th ul consumption. Th icincy dinitions tht w shll now b discussing r pplicbl to n ngin with singl propllnt strm (turbojts or rmjts). For othr typs o jt ngins (turbon, turboprop) th qutions nd to b ppropritly modiid. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 1

13 Engin prormnc prmtrs Propulsion icincy: Th rtio o thrust powr to th rt o production o propllnt kintic nrgy. Iu ηp m (1 + )( u / ) u / [ ] I w ssum tht «1 nd th prssur thrust trm is ngligibl, η P u ( u / u) u u / u / u 1+ u / u Lct-3 Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 13

14 Lct-3 Engin prormnc prmtrs Thrml icincy: Th rtio o th rt o production o propllnt kintic nrgy to th totl nrgy consumption rt η th whr, Q [(1 )( / ) / ] [(1 )( / ) / ] + u u + u u R, is Q R th ht o rction o th ul. For turboprop or turbosht ngin, th output is lrgly sht powr. In this cs, Ps ηth whr, Ps, is th sht powr output o th ngin. Q R Q R Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 14

15 Engin prormnc prmtrs Ovrll icincy: Th product o thrml icincy nd propulsion icincy. η η o p η th Lct-3 In th cs o ircrt tht gnrt thrust using propllrs, η η o pr η Whr, η th pr is th propllr icincy. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 15

16 Engin prormnc prmtrs Thrust spciic ul consumption, TSFC TSFC I (1 + ) u u [ ] Lct-3 For turbin ngins tht produc sht powr, brk spciic ul consumption, BSFC BSFC P For ngin (lik turboprop) tht produc both, quivlnt brk spciic ul consumption, EBSFC P P + Iu s s s 16 Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby

17 Idl cycl or jt ngins Lct-3 All ir-brthing jt ngins oprt on th Bryton cycl (opn cycl mod). Th most bsic orm o jt ngin is turbojt ngin. Som o th prmtrs o jt ngin cycl r usully dsign prmtrs nd hnc otn ixd priori: g. comprssor prssur rtio, turbin inlt tmprtur tc. Cycl nlysis involvs dtrmining th prormnc prmtrs o th cycl with th known dsign prmtrs. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 17

18 Idl cycl or jt ngins Lct-3 Diusr Combustion chmbr/burnr Comprssor Turbin Nozzl Atrburnr Schmtic o turbojt ngin nd sttion numbring schm Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 18

19 Idl cycl or jt ngins Lct-3 Th dirnt procsss in turbojt cycl r th ollowing: -1: Air rom r upstrm is brought to th ir intk (diusr) with som cclrtion/dclrtion 1-: Air is dclrtd s is psss through th diusr -3: Air is comprssd in comprssor (xil or cntriugl) 3-4 Th ir is htd using combustion chmbr/burnr Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 19

20 Idl cycl or jt ngins Lct-3 4-5: Th ir is xpndd in turbin to obtin powr to driv th comprssor 5-6: Th ir my or my not b urthr htd in n trburnr by dding urthr ul 6-7: Th ir is cclrtd nd xhustd through th nozzl. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 0

21 Idl cycl or jt ngins Lct-3 T Idl turbojt cycl (without trburning) on T-s digrm s Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 1

22 Idl cycl or jt ngins Lct-3 For cycl nlysis w shll tk up ch componnt nd dtrmin th xit conditions bsd on known inlt prmtrs. Intk: Ambint prssur, tmprtur nd Mch numbr r known, P, T nd M Intk xit stgntion tmprtur nd prssur r dtrmind rom th isntropic rltions: T P 0 0 T P 1+ T T 0 γ 1 M γ /( γ 1) Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby

23 Idl cycl or jt ngins Lct-3 Comprssor: Lt th known comprssor prssur rtio b dnotd s P T π P T c 0 0 ( )( γ 1)/ γ π Combustion chmbr: From nrgy blnc, h h + Q 04 or, 03 Q R Hnc, w cn dtrmin th ul-ir rtio. c T / c R 04 p 03 π c / T03 1 T T / T Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 3

24 Idl cycl or jt ngins Lct-3 Turbin: Sinc th turbin producs work to driv th comprssor, W turbin W comprssor t c p ( T 04 T 05 ) c p ( T 03 T 0 ) or, T 05 (1 + T 04 )( T ( T T T 05 0 ) ( T 03 ) /(1 + ) T 0 ) γ /( γ 1) T 05 Hnc, P05 P04 T 04 For n idl combustion chmbr, P 04 P 03 Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 4

25 Idl cycl or jt ngins Lct-3 Nozzl: With no trburnr, T 06 T 05, P 06 P 05 Thror, u h07 Sinc, h u 07 c p T th nozzl xit kintic nrgy, h 7 06 h 06 [ ( ) ] ( γ 1) /γ 1 P / P Thrust, TSFC nd icincis cn now b dtrmind using th ormul drivd rlir. 06 Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 5

26 Thrust, I TSFC I Idl cycl or jt ngins I I ( P Propulsion icincy, η Thrml icincy, [(1 + ) u u] P ) A [(1 + ) u u] [(1 + ) u u] + ( P is ngligibl, η P th m P Iu ) A Lct-3 [(1 )( / ) / ] + u u [(1 )( u / ) u / ] + Q R Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 6

27 Idl cycl or jt ngins Lct-3 T 6 4 5, Idl turbojt cycl with trburning on T-s digrm s Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 7

28 Idl cycl or jt ngins Lct-3 Atrburning: usd whn th ircrt nds substntil incrmnt in thrust. For g. to cclrt to nd cruis t suprsonic spds. Sinc th ir-ul rtio in gs turbin ngins r much grtr thn th stoichiomtric vlus, thr is suicint mount o ir vilbl or combustion t th turbin xit. Thr r no rotting componnts lik turbin in th trburnr, th tmprturs cn b tkn to much highr vlus thn tht t turbin ntry. Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 8

29 Idl cycl or jt ngins Lct-3 For clculting th ul low rt rquird to chiv tmprtur o T 6, w crry out n nrgy blnc, h 06 or, h Whr, 05 Q + low rtio, R T / c / T05 1 T T / T in th min combustor. 1 Q 06 1 p R + 05, 06 is 05 th totl is th ul low rtio ul Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 9

30 Lct-3 In this lctur... Idl gs turbin cycls Thrust nd icincy Th thrust qution Othr ngin prormnc prmtrs Idl cycl or jt ngins Turbojt ngin Turbojt ngin with trburning Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 30

31 Lct-3 In th nxt lctur... Idl cycl or jt ngins Turbon ngin Dirnt conigurtions o turbon ngins Turboprop ngins Turbosht ngins Rmjts Pro. Bhskr Roy, Pro. A M Prdp, Dprtmnt o Arospc, IIT Bomby 31