Thermodynamic Study of Turbofan Engine in Off-Design Conditions

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1 J. Basi. ppl. Si. es., -5,, exoa uliaion ISSN - Jounal o Basi an pplie Sienii eseah heoynai Suy o uoan Engine in O-Design oniions oi Goji, in Kazei, Davoo Doii Ganji Depaen o ehanial, Baol Univesiy o ehnology, Baol, 8, Islai epuli o Ian. BS In his pape uoan engine peoane gaphs inluing hus, hus speii uel onsupion an heal, populsive an he oveall eiienies, also he gaphs o uoan oponens suh as he high pessue an low pessue opesso pessue aio, exi epeaue pessue o high pessue opesso, ouso inle epeaue, oee inle ass low ae o opesso an an an ypass aio, ha is onolle y he engine onol syse wee awn ase on inle ah nue an vaious ligh heighs. Gaphs have een analyze an he ee o eah o he aoeenione paaees was oseve on peoane gaphs. lso, in oe o yiel oe auae soluions, he eho o geneaing peoane gaphs has een oiie. KEYWODS: uoan, O-Design,ah nue.. INODUION oo heoynai analysis inlues assessing hanges in heoynais o opeaing lui passing ino engine. his suy an e ivie ino wo eniely isin goups: On-esign analysis aaei yle nalysis an O-Design nalysis engine eoane nalysis. In On-Design nalysis, he geoey o engine is no onsiee an in suying he peoane iaga elae o his analysis, eah poin epesens a ieen engine. I is sai ha On-Design nalysis exaines a ue Engine. o esiae engine peoane in ieen ai oniions, a oeling appoah is neee ha is apale o esiing he ehavio o engine oponens in he asene o On-Design oniions. In he lae sixies, i was oun suiien o opiize he engine in a speii woking poin. Bu oay, ainly o eonoi easons, exisene o an o-esign oel is neessay in ealy sages o esign.. When a gas uine engine is esigne an uil, is egee o eeo epens on availale ehnology, he eans o esigne an he engine's ain appliaions. When he engine is insalle on an aia, is eiieny hanges wih hole seing an lying oniions an is liie y engine onol syse. he goal o all O-Design oels is o alulae lui sae in ieen loaions o ain sea in engine. Using hese esuls, hus, uel onsupion an all ajo paaees o engine oponens an e eive. ohen an e al in 5 explain ha peoane popeies o iniviual oponens o he engine an e oaine o aual es. When engine oponens ae assele, he peoane ange o eah oponen is eue in engine. When he engine is opeaing in seay spee o equiliiu, epening on he ype o gas uine, equiliiu unning zone an e awn o a ange o ieen spees on he opesso haaeisi uve unil equiliiu unning line o zone is oaine. When he unning oniion is eeine, unning uves o hus o speii uel onsupion an e ahieve. Oaes in Explains ha O-Design nalysis an e one in wo ways. he is onsiee ase is ha eiienies o oponens ae unknown; heeoe hey us e esiae as a union o eoane oniions. his eho is use o alulae he piay esiae o he engine's peoane. In he seon ase, oponens o engine have een uil an ese; heeoe peoane haaeisis o he engine oponens ae availale. hus, oinaion peoane o opesso, ousion hae an uine ae peiale. hese oine haaeisis, alle puping haaeisis, an e use o pei he oveall peoane o engine. hus, ehos o oining eah o he oponens haaeisis in oe o oain puping haaeisis ae povie.one his phase has een oplee, opeaing haaeisis will e oaine. o sipliiy, he exaple o a uoje engine is pesene. is, siple gas geneao equaion is oaine an ae having een onnee o nuzzle, inal equaions ae geneae. lso Walsh aquies peoane gaphs y using β Lines an eee eoane has. aingly in an analyzes engine peoane y eplaing onsan values oaine in union o engine pessue aio an epeaue aio, in a sae o O-Design, wih values o sae union a esign poin. s will e explaine uhe in his suy, een analysis will e use o analysis o uoan engines in a sae o O-Design. Suggesions o ipoving he esuls ae also pesene. Zeo-iensional oel is use in his analysis. hese oels, wih ega o hei sipliiy an sel-explanaoy naue whih is inepenen o he exa geoey o he engine, ae aong he os oonly use oels in he wol o uo-ahiney. oesponing uho: in Kazei, Depaen o ehanial, Baol Univesiy o ehnology, Baol, 8, Islai epuli o Ian.

2 Goji e al.,. Solving ehos an Hypoheses Desiing an peiing he engine peoane in ieen ligh oniions an hole seings is one using elaionships whih ae ase on he appliaion o ass, enegy, oenu an enopy onsieaion o he seay low o pee gas, in a seay sae opeaing poin o engine. lso i he elaionship eween epeaue aio an pessue aio, in a seay sae opeaing poin, is equal o onsan value, he onsan value an e evaluae a a eeene esign oniion ha is expesse y he suiles. hus:, e, his eho ha is ase on he eplaeen o onsan values o pessue aio an epeaue aio unions in a sae o an o-esign, wih he sae union in oniion o esign poin, is alenaively use in pole analysis. Sea-Level Sai oniions ae onsiee as esign poin oniions o values o he gas uine engine vaiales an. In uoan engines he onsiee ase is ha high-pessue an lowpessue uine inle will hoke as soni sea in inle guie vanes in uine will e supesoni in he is sage o he oo an his leas o a oe pouive powe in he uine. uheoe, we assue he hoa aeas whee hoking in high pessue an low-pessue uine enane nozzle oues ae onsan. his uines is alle ixe-aea uine. hese hypoheses ae vali in a wie opeaing ange o oen gas uine engines. s well, ase on eeene hypoheses, pessue aio o ousion hae π, ain exi nozzle π n an ypass exi nozzle π n an eiieny o oponens owas esign poin values o no hange. uine ooling an he leakage ees ae ignoe an no powe is eove o uine o ive aessoies. Gas in upsea an ownsea o he ousion hae is onsiee aloially pee.. O-esign equaions o uoan igue shows a uoan engine. uine an opesso ae ivie ino wo pas o low pessue an high pessue. High-pessue uine ives he high-pessue opesso hough High essue Spool.also Low-pessue uine ives an an low pessue opesso hough Low essue Spool. igue uoan engine ass low passing hough he engine oe an an ae an espeively. he aio o passing ass low o he an o passing ass low o he oe is inoue as Bypass aio an is shown wih α hus: he ass low paaee is a union o ah nue an is eine as ollows:, V g V V g g lso ass low aio o ai o uel in he ousion hae is eine as ollows: uel ai Sine he exhaus nozzles have ixe aeas, his gas uine has ou inepenen vaiales inluing,,,. lso epenen vaiales ae oaine as ollows: High pessue uine - inle ass low ae o low pessue uine an high pessue is equal o eah ohe. heeoe: g

3 J. Basi. ppl. Si. es., -5, ssuing onsan aea an hoking in hese seions ause an. 5 o have onsan values:.5.5 H H e lso, aoing o he onsan value o H H an H will have ix values. Low-pessue uine - inle ass low ae o low-pessue uine is equal o oule ass low ae o he exi nozzle: oing o he onsan value o an.5, hoking in he low pessue uine inle, an equiy 5, he aove equaion wih espe o wha was expesse in equaion, an e sipliie ino he ollowing equaions: L L 5.5 L L.5 e L L L L L L L L L High pessue opesso - aoing o powe alane eween uine an he high-pessue opesso: 5 lso H p.5.5 p.5 H p H p. 5 H.5.5.5, H p H H H e H H / H / H H p Low pessue opessos eause he low pessue opesso an an ae on a spool, ineasing lowpessue opesso enhalpy is popoional wih ineasing an enhalpy heeoe: L L.5 K L K K n aios o epeaue an pessue o he low pessue opesso ae oaine: 7 8

4 Goji e al., L L L L L o he powe alane eween he low-pessue uine, he an an low pessue opesso we have: p L p p.5.5.5,,, H H p L p p p p H L L L p p H L L L e / / L L L L an also: Bypass aio - in engine oe, aoing o ouene o hoking in high-pessue uine eneane, ixe inle aea o uine an onsane value o uel o ai aio, an eplaing a onsan value wih eeene values, we have: e Siilaly o passing low o ypass u we have: e By eplaing elaions - an -7 oh in elaion elae o ypass aio: oing o:.5.5, L H n L H n

5 J. Basi. ppl. Si. es., -5, lso onsie ha L H n L H n L H e 5 ] / [ / L H L H ass low ae o he engine: L H.5.5 L H L H e H L H L he oule ah nue a he ain hannel: 7 / I he oule o he ain hannel is no hoking ohewise n L H H exi ah nue in ypass hannel: 8 / I he oule o he ain hannel is no hoking Ohewise n

6 Goji e al., oing o aove oaine equaions, L, L,, L, L, H, H,,,, ae he epenen vaiales o uoan engine, whih onsiue a syse onsising o equaions. hese equaions shoul e solve y Ieaive appoah o oain values.. esign vaiales, ojeive unions an onsains ong inpu paaees, he hee paaees inluing lying heigh h, inle ah nue, an ouse exi epeaue, ae onsiee as esign vaiales. s seen in he ollowing elaion, inle ai ass ino he engine is a union o inle ah nue an aliue o aiplane. i i i i i ouse exi epeaue is also one o he aos ha he engine eiieny is sensiive o is hange. s shown in eeenes an, uping haaeisi o a gas geneao is a union o.he os ipoan oule paaees assue as ojeive unions in uoan engine inlue hus, hus Speii uel onsupion, opulsive eiieny, heal eiieny, an Oveall Eiieny. hese unions o uoan engine ae as ollow : a V a V a a S / a o V / / a / V / a / V / a V / a V / a V / a V / a V / a h Engine onol us keep high-pessue an low-pessue opesso pessue aio, opesso exi epeaue, oee ass low ae o an an opesso an ypass aio o exeeing speiie value. opesso exi epeaue as a union o opesso oal epeaue as well as he oee ass low ae as a union o inle ass low ae will e alulae as ollows: /.5.5 H L i i i i... 5 Solving equaions he oaine equaions in he hi pa us e solve y ieaive eho. eeene values o engine ae onsiee as he iniial guess. L L,, L L, L 8 5

7 J. Basi. ppl. Si. es., -5, Wih his assupion, unions o he nue 7 o 8 ae alulae, his poess is epeae unil he ieene eween he values oaine o ypass aio, low pessue uine epeaue aio L, high pessue opesso epeaue aio H, low pessue epeaue aio L an an epeaue aio, ae less han. o he oesponing values o evious sep. I he enione oniion is esalishe, soluions oaine as onvege soluions ae use o alulae he values o peoane in elaions o 5. aove ehos an e use o awing o-esign peoane gaphs.on he ohe han, he engine onol syse onols he vaious oponens peoane o gas uine so ha he ouse exi epeaue, high-pessue an low-pessue opesso aio,, an pessue aio, he opesso exi epeaue H L, oee ass low ae o opesso an ypass aio o no exee o peissile values. Soe o hese liiaions inluing exi epeaue o ouse an exi epeaue o he opesso ae ue o liie epeaue oleane o he pas.i also onols ass low ae in opesso an opesso pessue aio o low an high pessue opesso o peven he ouene o suge an sall in he engine.onolling he aove-enione paaees wihin he esie ange is one y euing.igue shows he lowha o awing peoane has o uoan engine. eeene values o oo esign poin Iniial guess o he values o epeaue aio an pessue aio o low pessue uine, epeaue aio o an an low pessue opesso aoing o Equaion 8 Solving equaions 7 o 8 eplaeen values oaine o aio o epeaue aio an pessue aio o low pessue uine, epeaue aio o an an low pessue opesso wih pevious values. No Dieene eween he values oaine o,,,, ae less L H L han. o he oesponing values o pevious sep. Yes e onsains in peissile ange? No euion Yes alulaion o peoane unions igue lowha o awing peoane iagas o uoan engine. eoane has In his pa, peoane has o a uoan engine in o-esign oniion ae oaine. eee values o engine esign poin in sea level an zeo ah nue ae as ollow: 5

8 Goji e al., 8.. L.. n H L n p L ax H. p 8K. H 7kg se.758 H H.5 L h.5 8kJ kg.7.7 L. he opesso pessue aio is liie o. lso axiu exi epeaue o he ouse an opesso ae 8 an 8 Kelvin espeively. In his ase, ypass aio, an an he opesso pessue aio, ouse an opesso exi epeaues an oee ass low ae o opesso an he an ae onolle y engine onolle. uoan engine peoane has ase on vaiales o ligh spee, a ieen aliue ae awn an pesene. In igue hanges in he hus is awn vesus ah nue a vaious ligh heighs. s an e seen, as aliue ineases, ligh spee hange has less ee on he hus. s in h hus is alos onsan. lso in h an h. 5 an inease in ligh spee le o a signiian eease in he hus oe. o a lose look, hee heighs o h, h an h ae eing invesigae. Invesigaion in h k In igues an oee ass low o he opesso an an ae awn espeively. igue will eue o Design aoun 85. kg se in zeo ah nue o kg se in ah nue one. Siilay igue will eue o Design aoun 8.8 kg se o 5. kg se. In oh has o igues an i an e seen ha he aoun o an ae elow he iial values. In igue 8, wih an inease in ligh ah nue, ineases o aoun esigne in zeo ah nue 7 kg se, o aoun kg se. igue shows hanges o an pessue aio ase on ah nue. an pessue aio eease o a value o in zeo ah nue o value.58 in ah nue one. igue 5 shows he opesso pessue aio eeases wih ineasing ah nue. In igues an, hese hanges ae pesene sepaaely o he low-pessue opesso an high pessue opesso. In igue 5, wih ineasing ah nue o zeo o one, opesso pessue aio eease a he ae o 57% o he aoun o. Siilaly his eeasing in he low-pessue opesso an in high pessue opesso is 87% an % igue an. he ineenal hange o Bypass aio o is esign poin in zeo ah nue o. in ah nue one is shown in igue. lso Ineenal hanges o opesso exi epeaue vesus ineases in ligh spee is shown in igue. hese hanges sa o 88 K in Zeo ah nue an oninue o ah nue.. o ah nue. o ah nue one, he axiu inease in epeaue woul e onolle a 8 K. his onol is one y euing he exi epeaue o he ouso.heeoe, as seen in igue 7,in ah nue ange eween an., eains in esign aoun o 8K an hen is eue o ainain a is axiu value an his oninues unil ah nue one. his poin eahes 87 K.In igue 8 he oe aio o inle pessue o exi pessue, o value o. in zeo ah nue eahes o. 85 in ah nue one. his gaph has eak in a ligh ah nue o., whih is ue o onol. In igue, ypass inle o exi pessue hanges aes, ineases y ineasing he ah nue. lso his union eease o value o. in zeo ah nue o value o. in ah nue one. Invesigaion in h k s i an e seen in igue, he ha has a eakpoin in ligh ah nue.. lso, i is seen ha hus eeases wih an inease in ah nue. he eakpoin is ue o he a ha all o onsains unions in igue o have eahe hei esign value in ah nue., hus, y eeasing igue 7 hey ae ainaine a hei esign value. s seen in igue 7, in ligh ah nues less han. is less han is esign value. lso, in ah nues highe han.7 he value o eease o is axiu value. his is ue o he a ha in his ange, union o igue has eahe is axiu value. s

9 J. Basi. ppl. Si. es., -5, an e seen in igue, ineases wih inease in ligh ah nue. he enione igue has wo eakpoins, in ligh ah., ue o a eease in he aoun o in oe o onol onsains an in ligh ah nue.7, as has eahe is axiu value. s an e seen in igues 8 an, wo unions an eease wih inease in ah nue values an have eak poins in ah nue.. Invesigaion in h k s an e seen in igue, in all ah nue values, hus is nealy onsan. hee is no eak in he uve. his is ue o he a ha all onsains have eahe he values o esign exea igues - an have een onolle as eeases o value 8K igue 7. heeoe, in igue 7, he gaph o all values o ligh ah nues is less han 8K an I is evien ha i ineases as ligh ah nue ineases. s seen in igue, values o o all ligh ah nue ange is less han he axiu values an he hanges en is ising wih ineasing ligh ah nue. Know we'll exaine ohe ojeive unions. igue shows hanges o speii uel onsupion in es o he ah nue. s an e seen, speii uel onsupion will e inease wih onsan ae wih ineasing o ah nue. igue 5 shows he hange o heal eiieny wih ligh ah Nue a vaious heighs. I is seen ha heal eiieny eeases when ah nue ineases. lso, in ange o ligh ah values o. heal eiieny eains onsan in all ligh heighs. igue shows ineasing hange o hus eiieny y ligh ah nue. s i is seen, in ligh ah values o.5 hus eiieny oesn hange in vaious heighs. his ieene eahes is axiu aoun in ah nue one. igue 7 shows hanges gaph o oveall eiieny in es o ah nue values. s an e seen, in zeo kiloees heigh, he oveall eiieny ineases as ah nue ineases an eahes is axiu.8 in ah nue. an hen eeases. lso in he ange o ligh ah values o., hus eiieny is no aee y hange o heigh. 7

10 Goji e al., 5 h= k hus N hus speii uel onsupion [g/se/n] 8 h=,.5,,.5,,7.5k h=, k ah nue igue hus ase on ligh ah nue a vaious heighs....8 ah nue igue hus Speii uel onsupion ase on ligh ah nue a vaious heighs.5. h=,.5,,.5k..8 heal eiieny h=,7.5,,,k h=,.5,,.5k opulsive eiieny h=,7.5,,,k ah nue igue 5 heal eiieny ase on ligh ah nue a vaious heighs ah nue igue populsive eiieny ase on ligh ah nue a vaious heighs. h=,.5,,.5k 8 h= k Oveal eiieny.5..5 h=,7.5,,,k ass low ae kg/se ah nue igue 7 oveall eiieny ase on ligh ah nue a vaious heighs....8 ah nue igue 8 ass low ae ase on ligh ah nue a vaious heighs 8

11 J. Basi. ppl. Si. es., -5, oee ass low ae o opesso kg/se h=7.5,,,k.5.5 h= k oee ass low ae o an kg/se h=7.5,,,k.5.5 h= k ah nue igue oee ass low ae o opesso ase on ligh ah nue a vaious heighs ah nue igue oee ass low ae o an ase on ligh ah nue a vaious heighs. Bypass aio h= k.5.5 an pessue aio..8.7 h=7.5,,,k.5.5 h= k ah nue h=7.5,,,k igue ypass aio ase on ligh ah nue a vaious heighs ah nue igue an pessue aio ase on ligh ah nue a vaious heighs. high pessue opesso pessue aio h=7.5,,,k.5.5 h= k Low pessue opeso pessue aio h=7.5,,,k.5.5 h= k ah nue igue high pessue opesso pessue aio ase on ligh ah nue a vaious heighs ah nue igue Low pessue opesso pessue ase on ligh ah nue a vaious heighs

12 Goji e al., opesso pessue aio 8 h= k ah nue h=7.5,,,k igue 5 opesso pessue aio ase on ligh ah nue a vaious heighs.5.5 opesso exi epaaue- K h= k , ah nue igue opesso exi epeaue ase on ligh ah nue a vaious heighs ouse exi epeauehole seing- K h= k ,....8 ah nue igue 7 ouse exi epeaue hole seing ase on ligh ah nue a vaious heighs Inle pessue/exi pesue o oe sea-/ ah nue h= k.5.5 h=7.5,,,k igue 8 Inle o exi pessue o oe sea ase on ligh ah nue a vaious heighs Inle pessue/exi pesue o ypass sea-/ ah nue h=7.5,,,k h=,.5,,.5,k igue Inle o exi pessue o ypass sea ase on ligh ah nue a vaious heighs 5

13 J. Basi. ppl. Si. es., -5, 7 oeive suggesion s illusae in pa, o oain he peoane gaph in vaious ligh oniions, equaions se 7 o 8 shoul e solve espeively o uoan engines y ieaive eho. s suggese In eeene, his epeiion oninues unil he ieene eween he epeaue aio o he low pessue uine, in wo onseuive seps is less han.. Howeve, as an e seen in ale, epeaue aio an pessue aio values o an oaine o his eho ae no appliale o elaion. Beause as seen in elaion 5, when, he new value o pessue aio will no hange o is pevious sae an when is susiue in he elaion, he sae values will e poue o epeaue aio an he ile will sop. heeoe, aoing o pa 5 an he lowha in igue, in his suy epeiion oninues unil he ieene eween values o ypass aio, low pessue uine epeaue aio, high pessue opesso epeaue aio H, he low pessue opesso epeaue aio L L an an epeaue aio o oesponing values o he pevious sep will e less han.. an pessue an epeaue aio values oaine o wo ehos ae shown in ale. he values oaine o he oiie eho ae appliale o elaion. In his seion, engine eee values esign poin in sea level an zeo ah nue ae as ollow: K 5.57 kg se h H H 78. kj kg. L L. L..7.5 H L... H p. n L n p.8. ax H.7.8 ale : vaious values o an epeaue an pessue aio, oaine o eseah an eee popose eho, a vaious ligh ah h k, K = =. =. =. =.8 = esuls o he pesen suy: esuls o he pesen suy: esuls o elaion - ase on oaine o he pesen suy. esuls o eee popose eho : esuls o eee popose eho : esuls o elaion - ase on oaine o eee popose eho : In oninue,pesen esuls will e opae wih he esuls oaine o E * sowae uploae y Jak aingly- he wie o an he - on his pesonal wesie 7. his poga alulaes hus an uel speii onsupion o uoan engine.in igues o, he esuls oaine o he E sowae an his suy ae opae.s i an e seen, Sligh ieenes in es o ligh ah vaiale ae seen in highe ah nues, whih ae esule y eho o solving equaions whih is exaine in his seion., * eoane nalysis o Gas uine Engines-Vesion. 5

14 Goji e al., hus N e....8 ah nue his eseah igue hus ase on ah nue: opaison o esuls oaine o his eseah an he esuls oaine o. e sowae hus speii uel onsupion [g/se/n] e ah nue his eseah igue Speii uel onsupion ase on ah nue: opaison o esuls oaine o his eseah an he esuls oaine o. e sowae e his eseah e his eseah 7.5 opesso pessue aio 5 an pessue aio ah nue igue opesso essue aio ase on ah nue: opaison o esuls oaine o his eseah an he esuls oaine o. e sowae ah nue igue an pessue aio ase on ah nue: opaison o esuls oaine o his eseah an he esuls oaine o. e sowae e his eseah Bypass aio ah nue igue ypass aio ase on ah nue: opaison o esuls oaine o his eseah an he esuls oaine o. e sowae 5

15 J. Basi. ppl. Si. es., -5, 8. ESUL Vaious ehos exaine o hek o-esign peoane o uoan engine,ha have een geneally aesse in vaious eeenes. By invesigaing hese ehos o oain peoane gaphs o uoan engines, he eho pesene in eeenes an he wee use an also soluion algoih o oe auae soluions oaine wee oee. uoan engine peoane gaphs as well as he onsains unions ha ae onolle y he onolle ase on ligh ah nue an in vaious heighs wee auaely awn an isusse. EEENES. aingly, J D; Heise, W H; a, D ;. ia Engine Design. n. eson : I Euaion Seies,. ISBN-: NO ehnial epo. eoane eiion an Siulaion o Gas uine Engine Opeaion. Hull : S. joseph opoaion opany,. O-- /V-8/.. Walsh, h an lehe,. Gas uine eoane. n. Dey : WileyBlakwell,. ISBN- :X.. Oaes, G. eoheoynais o Gas uine an oke opulsion.. eson : I Euaion Seies, 7. ISBN-: ohen, H, oges, G an Saavanauoo, H. Gas uine heoy. 5h Eiion. New Jesey : enie Hall,. ISBN:587X.. aingly, J D. Eleens o Gas uine opulion. Viginia : I Euaion seies,. ISBN: aingly, Jak. hp:// [Online] 5

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s

ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN