Diesel Engine Analytical Model

Transcription

1 Interntonl Journl of entf & Engneerng eer, Volume, Iue 8, Augut 0 IN Deel Engne Anlytl odel Wleed F. Fr *, Hem A., ed. Kffy, oumen Idre, l Elmoely Abtrt odellng deel engne n effetve tool to elp n developng nd eng ntellgent trnportton ytem nd tenologe well to elp n predtng ggregte vele fuel onumpton nd emon. Altoug vele nlytl model re te vele modellng type tt derbe te pyl penomen oted wt vele operton ompreenvely bed on te prnple of py wt explnble mtemtl trend, no nlytl model been developed yet of deel powertrn. reer pper preent n nlytl model of four-ylnder uperrged deel engne te ert of te deel powertrn. model erve to urtely nlyze wt explnble mtemtl trend te performne of te uperrged deel engne wt repet to bot of te trnent repone nd tedy tte repone. Index erm Deel Engne, Deel owertrn, odellng, Intellgent rnportton ytem INODUION D eel engne re mong te lrget ontrbutor to r polluton. It been reported tt lmot ll populton lvng n developed ountre re expoed frequently to deel exut t ome onentrton nd te potentl for deel exut to preent elt zrd proven []. Intellgent rnportton ytem I le t te ert of te ontnul effort of developng te deel powertrn bed on modelng n order to redue te negtve nfluene of deel powertrn on te envronment. ne te mot ontrbutng prt of te deel powertrn to deel exut te deel engne [], modellng deel engne reeved nreng ttenton. Among te emnl em-nlytl model of nternl ombuton engne te Kno Integrl odel KI w w orgnlly developed by Lvengood nd Wu, []. t model gve n mplt relton between te trt of njeton rnft ngle, trt of ombuton rnft ngle, nd te pyl n-ylnder prmeter u ylnder preure, ylnder temperture, n-ylnder burned g rte, nd te fuel/r rto. etlld nd Ntv propoed noter emnl em-nlytl model of te dynm of ngle- nd mult-ylnder reprotng engne, w my nvolve toronl flexblty n te rnft [5]. ey developed well lnerzed veron of t model to qure ngt nto ome pet of te ytem dynm u determnng te tedy-tte repone nd nvetgtng te effet of engne mfre. N, D., nd Henlewood, D., preented nd vldted te Bernoull model for vele nfrtruture ntegrtonenbled n-vele pplton [6]. Altoug te model doe not ddre n-ylnder g flow dynm, t preent n nlytl reltonp between r m flow rte, engne power, nd r tte. *W.F. Fr wt te Interntonl Ilm Unverty ly, nd wt Vrgn e, UA. E-ml: wfr@vt.edu. H.A. wt Vrgn e, UA. E-ml: H@vtt.vt.edu..I. Kffy wt te Interntonl Ilm Unverty ly,. E-ml: rffy@u.edu.my.. Idre wt te Interntonl Ilm Unverty ly,. E-ml: mdre@u.edu.my.. Elmoely wt te Interntonl Ilm Unverty ly, E-ml: elmoely@netpe.net. Oter modelng tenque ve been utlzed well n te modelng of nternl ombuton engne. mt, [7] revewed nd ompred te turbulene model for nternl ombuton engne nd found tt te ε turbulene emprl model wdely ued beue of t generl pplblty, robutne, nd eonomy. t model ont of two emprl trnport equton for te net energy nd dpton rte. Dv, et l., [8] omputtonlly modeled te deel engne ed ung Fnte Element modelng nd tu derbed te terml nterton nd menl nterton between te everl prt of te deel engne ed. Altoug vele nlytl model ve te ey dvntge, over te oter type of modellng derbed bove, of derbng te pyl penomen oted wt vele operton ompreenvely bed on te prnple of py, wt explnble mtemtl trend, no ompreenve nlytl model been developed yet of deel powertrn. reer pper preent n nlytl model of uperrged deel engne, equpped wt n eletron trottle ontrol E, te ert of te deel powertrn wt te m of elpng n nlyzng nlytlly te performne of te deel engne. DIEEL ENGINE ANALYIAL ODEL e mn omponent of te deel engne re tmng belt, mft, ylnder ed vlve, ylnder blo, pton nd onnetng rod embly, berng nd el, nd rnft. e tmng belt ln te rnft wt te mft nd me te mft turn n te me dreton of te rnft. e mft rotte t lf te rottonl peed of te rnft for four-ylnder deel engne. model ddree te dynm nterton between te ylnder ed vlve, ylnder blo, pton nd onnetng rod embly, nd rnft. Fgure, ow te emt onfgurton of te deel engne ylnder, pton, onnetng rod, nd rnft of uperrged deel powertrn tt nvetgted n t reer. In t eton, te preure rto nd temperture rto re formulted nlytlly from te prnple of py for te ompreon troe, ombuton proe, expnon troe, IJE 0 ttp://

2 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 IN nd exut troe of te deel yle tt own on te p-v dgrm on Fg. nd on te - dgrm on Fg.. ee formulton erve bot oed nd non-oed ondton well tedy nd trnent ondton. In ddton, te tte trougout deel yle re defned nlytlly bed on te prnple of py. oreover, te n-ylnder g peed dynm re derved nlytlly from te prnple of py. Fg. : Geometry of deel engne ylnder, pton, onnetng rod, nd rnft [9] defnng nlytlly from te prnple of py te tte trougout te deel yle. e deel yle own on te p-v dgrm on Fg. nd on te - dgrm on Fg.. ee formulton erve bot oed nd nonoed ondton well tedy nd trnent ondton. ne r flow g flow, te followng follow: otl energy equl te um of te totl energy oted wt m flow nd wor done. ne, te totl energy oted wt m flow ompre nternl energy, net energy, nd potentl energy, erefore, E otl u gz V E otl te totl energy of te g flow, u Internl energy, te g peed nde ylnder, g te grvttonl elerton, z te potentl lttude. ne by defnton of te g flow nternl energy te followng follow: u V te g entlpy. Fg. : Deel yle on -V dgrm [0] Fg. : Deel yle on - dgrm [0]. ompreon troe In t eton, te preure rto nd temperture rto for te troe nd proee of te deel yle re dentfed nlytlly from te prnple of py long wt IJE 0 ttp:// u, ombnng Eq. nd togeter led to te followng: E otl gz By pplyng te frt lw of termodynm on te onervton of energy to te n-ylnder ompreon proe of te deel yle own n Fg. nd Fg., te followng follow []: gz gz Aumng te me lttude z, Eq. n tu led to te followng: 5 ne t no pe nge, t reltvely g temperture, nd/or t reltvely low preure r n be treted n del g nd t te e nde te ylnder of deel engne, g nde te ylnder of deel engne n be treted n del g. u, t follow tt: 6 te g pef et t ontnt preure, w ontnt n te e of r treted n del g. erefore, ombnng Eq. 5 nd 6 led to te followng:

3 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 IN u, Eq. 7 n be rewrtten : 8 From te prnple of te eond nd trd lw of termodynm, t n be oneved tt [, ]: δq d 9 te bolute entropy of te g flow, Q et flow. For te ompreon troe of te deel yle, te followng follow from Eq. 9: δq 0 ellng te frt lw of termodynm, t follow tt []: δ Q du δw By ombnng Eq. 0 nd togeter, te followng follow: du dw By defnton of te wor done, Eq. n be rewrtten follow []: du dv Vd By ombnng Eq. nd togeter, te followng follow: dh dv dv Vd u, mplfyng Eq. led to te followng: dh Vd 5 ombnng te del g lw for r wt te defnton of denty, t follow tt []: ρ 6 ρ te denty of r nde ylnder. By ombnng Eq. 5 nd 6 togeter long wt te del g lw for r, te followng follow []: dh md 7 ρ By ombnng Eq. 6 nd 7 togeter long wt te del g lw for r, te followng follow []: d d 8 Hene, t follow mtemtlly from Eq. 8 tt: 9 te pef entropy of te g flow. erefore, rerrngng Eq. 9 led to te followng: 0 From Eq., t follow tt: d du d V By ombnng Eq. wt te del g lw for r, te followng follow []: d du By dvdng bot de of Eq. by nd rellng Eq. 6 nd rellng te mlr equton to Eq. 6 for te pef et t ontnt volume, t follow tt []: V By te defnton of te rto of pef et,, Eq. n be rewrtten []: u, by rerrngng Eq. te followng follow: 5 Hene, Eq. 5 n be rerrnged follow: 6 By ubttutng Eq. 6 n Eq. 0: 7 ne te ompreon troe dbt by defnton n te deel yle, te ompreon proe n be umed entrop [, ]. erefore, te followng follow from Eq. 7: 8 By etblng n nvere logrtm operton on bot de of Eq. 8 te followng mtemtlly follow: 9 IJE 0 ttp://

4 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 IN By ubttutng Eq. 6 n Eq. 8: 0 ne number,, by defnton defned : te peed of ound. By defnton, te peed of ound,, evluted ung te followng formul [6, ]: Hene, by ombnng Eq. 0,, nd te followng follow: By rerrngng Eq. 8, te followng follow from Eq. 8: By etblng n nvere logrtm operton on bot de of Eq., te followng mtemtlly follow: 5 ne te no gnfnt et trnfer our n te ylnder durng ompreon troe, nd te ompreon troe umed to be entrop well, te followng follow from ombnng Eq. 9 nd : 6 By etblng logrtm operton on bot de of Eq. 6, te followng mtemtlly follow: 7 By rerrngng Eq. 7 nd etblng n nvere logrtm operton on bot de te followng follow: 8 By rellng te n-ylnder g peed nlytl formul from te reer pper enttled Deel owertrn Inte nfold Anlytl odel [5] nd ombnng t formul wt Eq. 8, u: π B 00 r Nm A0 en π B n θ 00 r Nm A0 en n θ 9 IJE 0 ttp:// B ylnder bore dmeter. r te ompreon rto n deel engne. N m rnft rottonl peed rev/mn. te rn lengt. A 0 en te men ro etonl re of frtonle trot t te entrne of te nte mnfold. θ te rnft ngle of rotton t tte on deel yle. θ te rnft ngle of rotton t tte on deel yle. e next proe on deel yle te ombuton proe. Hene, te temperture rto n te ombuton proe of deel yle re derved nlytlly from te prnple of py n te followng ubeton.. ombuton roe By pplyng te frt lw of termodynm on te onervton of energy to te n-ylnder ombuton proe of te deel yle own n Fg. nd Fg., te followng follow []: gz gz 0 Aumng te me lttude z, Eq. 0 n tu led to te followng: erefore, ombnng Eq. nd 6 led to te followng: u, Eq. n be rewrtten : From te prnple of te eond nd trd lw of termodynm, t n be oneved for te ombuton proe n deel yle followng from Eq. 9 tt [, ]: δq By ombnng Eq. nd togeter, te followng follow: du dw 5 By defnton of te wor done, Eq. 5 n be rewrtten follow []: du dv Vd 6 By ombnng Eq. nd 6 togeter, te followng fol-

5 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 5 IN IJE 0 ttp:// low: Vd dv dv dh 7 u, mplfyng Eq. 7 led to te followng: Vd dh 8 By ombnng Eq. 8 nd 6 togeter long wt te del g lw for r, te followng follow []: md dh ρ 9 By ombnng Eq. 6 nd 9 togeter long wt te del g lw for r, te followng follow []: d d 50 Hene, t follow mtemtlly from Eq. 50 tt: 5 erefore, rerrngng Eq. 5 led to te followng: 5 By ubttutng Eq. 6 n Eq. 5: 5 Aumng frtonle ombuton, Eq. 5 n tu be rewrtten : 0 0 q q q q 5 q te mount of et ext n te ylnder jut before reng tte n deel yle. q o te mount of et ext n te ylnder jut fter reng tte n deel yle. q te mount of et ext n te ylnder jut before reng tte n deel yle. q o te mount of et ext n te ylnder jut fter reng tte n deel yle. By rewrtng Eq. 5 []: 55 te g temperture jut before te begnnng of te ombuton proe n deel yle. te g temperture jut fter te end of te ombuton proe n deel yle. erefore, te followng follow from Eq. 55: 56 ne te ombuton proe n deel yle obr, te followng follow by etblng n nvere logrtm operton on Eq. 56: e 57 By ombnng Eq. 6 nd : 58 By ombnng Eq.,, nd 58: 59 By ombnng Eq. 57 nd 59: 60 Equton 60 n be rewrtten follow: 6 By rellng te n-ylnder g peed nlytl formul from te reer pper enttled Deel owertrn Inte nfold Anlytl odel [5] nd ombnng t formul wt Eq. 6, u: 0 00 θ π n A N r B en m 6 e expnon troe ppen next to te ombuton proe n deel yle. u, te preure rto n te expnon troe of deel yle re derved nlytlly from te prnple of py n te followng ubeton.. Expnon troe By pplyng te frt lw of termodynm on te onervton of energy to te n-ylnder expnon proe of te deel yle own n Fg. nd Fg., te followng follow []: gz gz 6 Aumng te me lttude z, Eq. 6 n tu led to te followng: 6 erefore, ombnng Eq. 6 nd 6 led to te followng: 65

6 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 6 IN IJE 0 ttp:// u, Eq. 65 n be rewrtten : 66 For te expnon troe of te deel yle, te followng follow from Eq. 9: Q δ 67 By ombnng Eq. 67 nd togeter, te followng follow: dw du 68 By defnton of te wor done, Eq. 68 n be rewrtten follow []: Vd dv du 69 By ombnng Eq. nd 69 togeter, te followng follow: Vd dv dv dh 70 u, mplfyng Eq. 70 led to te followng: Vd dh 7 By ombnng Eq. 7 nd 6 togeter long wt te del g lw for r, te followng follow []: md dh ρ 7 By ombnng Eq. 6 nd 7 togeter long wt te del g lw for r, te followng follow []: d d 7 Hene, t follow mtemtlly from Eq. 7 tt: 7 erefore, rerrngng Eq. 7 led to te followng: 75 By ubttutng Eq. 6 n Eq. 75: 76 ne te expnon troe dbt by defnton n te deel yle, te expnon proe n be umed entrop [, ]. erefore, te followng follow from Eq. 76: 77 By etblng n nvere logrtm operton on bot de of Eq. 8 te followng mtemtlly follow: 78 By ubttutng Eq. 6 n Eq. 66: 79 Hene, by ombnng Eq. 79,, nd te followng follow: 80 By rerrngng Eq. 77, te followng follow: 8 By etblng n nvere logrtm operton on bot de of Eq. 8, te followng mtemtlly follow: 8 ne te no gnfnt et trnfer our n te ylnder durng ompreon troe, nd te ompreon troe umed to be entrop well, te followng follow from ombnng Eq. 80 nd 8: 8 By etblng logrtm operton on bot de of Eq. 8, te followng mtemtlly follow: 8 By rerrngng Eq. 8 nd etblng n nvere logrtm operton on bot de te followng follow: 85 By rellng te n-ylnder g peed nlytl formul from te reer pper enttled Deel owertrn Inte nfold Anlytl odel [5] nd ombnng t formul wt Eq. 85, u: en m en m n A N r B n A N r B θ π θ π 86

7 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 7 IN θ te rnft ngle of rotton t tte on deel yle. θ te rnft ngle of rotton t tte on deel yle. e lt troe on deel yle te exut troe. e temperture rto n te exut troe of deel yle re derved nlytlly from te prnple of py n te followng ubeton.. Exut troe By pplyng te frt lw of termodynm on te onervton of energy to te n-ylnder exut proe of te deel yle own n Fg. nd Fg., te followng follow []: gz gz 87 Aumng te me lttude z, Eq. 87 n tu led to te followng: 88 erefore, ombnng Eq. 88 nd 6 led to te followng: 89 u, Eq. 89 n be rewrtten : 90 From te prnple of te eond nd trd lw of termodynm, t n be oneved for te ombuton proe n deel yle followng from Eq. 9 tt [, ]: δq 9 By ombnng Eq. 9 nd togeter, te followng follow: du dw 9 By defnton of te wor done, Eq. 9 n be rewrtten follow []: du dv Vd 9 By ombnng Eq. nd 9 togeter, te followng follow: dh dv dv Vd 9 u, mplfyng Eq. 9 led to te followng: dh Vd 95 By ombnng Eq. 95 nd 6 togeter long wt te del g lw for r, te followng follow []: dh md 96 ρ By ombnng Eq. 6 nd 96 togeter long wt te del g lw for r, te followng follow []: d d 97 Hene, t follow mtemtlly from Eq. 97 tt: 98 erefore, rerrngng Eq. 98 led to te followng: 99 By ubttutng Eq. 6 n Eq. 99: 00 Aumng frtonle ombuton, Eq. 00 n tu be rewrtten : q q0 q q0 0 q te mount of et ext n te ylnder jut before reng tte n deel yle. q o te mount of et ext n te ylnder jut fter reng tte n deel yle. q te mount of et ext n te ylnder jut before reng tte n deel yle. q o te mount of et ext n te ylnder jut fter reng tte n deel yle. By rewrtng Eq. 0 []: 0 te g temperture jut before te begnnng of te exut proe n deel yle. te g temperture jut fter te end of te exut proe n deel yle. erefore, te followng follow from Eq. 0: 0 ne te exut proe n deel yle oor, te followng follow by pplyng te del g lw to Eq. IJE 0 ttp://

8 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 8 IN : 0 u, te followng follow by etblng n nvere logrtm operton on Eq. 0: e 05 By ombnng Eq. 6 nd 90: 06 By ombnng Eq.,, nd 06: 07 By ombnng Eq. 05 nd 07: 08 Equton 08 n be rewrtten follow: 09 By rellng te n-ylnder g peed nlytl formul from te reer pper enttled Deel owertrn Inte nfold Anlytl odel [5] nd ombnng t formul wt Eq. 09, u: π B r N m n θ 00 A0 en 0 θ te rnft ngle of rotton t tte on deel yle. erefore, te tte trougout deel yle n be determned nlytlly bed on te prnple of py. e followng ubeton preent t..5 Determnng te tte Anlytlly rougout Deel yle e four tte n te deel yle n be determned nlytlly ung te prnple of py. e frt tte mong tem tte, w determned nlytlly follow: ompreor ompreor te preure t te outlet of te uperrgng ompreor tted n te ompreor mp orrepondng to te mxmum effeny of te ompreor nd te requred r flow rte. Interooler η Interooler te nte mnfold temperture. Interooler te temperture t te outlet of te nterooler tted n te nterooler tlogue. η Interooler te nterooler effeny w depend on te rnge of temperture of nlet r flow nd tted n te nterooler tlogue. e nterooler effeny nlytlly formulted follow: InletInterooler Interooler η Interooler InletInterooler e f Amb Inlet-Interooler te nterooler nlet temperture or pot ompreor temperture. ef-amb te mbent referene temperture. By ombnng te equton of tte for del ge,.e. Eq. 6, long wt Eq. nd, te volume of te g n be determned well nlytlly: Interooler v ηinterooler ompreor v te pef volume of g t tte. e eond tte n te deel yle n be determned nlytlly well followng from te prnple of py. tte on deel yle n be nlytlly formulted follow: e 5 e te pe preure nde ylnder w ommerlly et n te deel engne tlogue for e tegory of deel engne. In order to determne, let u rell Eq. 9 for te ompreon troe: ompreor e By ombnng Eq. 6 nd : Interooler ompreor η Interooler e By ombnng Eq. 6, 5, nd 7: Interooler v ompreor η Interooler e e v te pef volume of g t tte By pplyng Eq. 6 to e of tte nd of te on- IJE 0 ttp://

9 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 9 IN tnt volume exut troe n deel yle nd dvdng te reult, te followng follow: ompreor 9 By ombnng Eq. 9, Eq., nd Eq. 8 for entrop expnon troe, te followng follow: 0 ompreor Interooler η Interooler ne te ombuton proe n deel yle obr, te followng tu follow from te p-v dgrm of deel yle on Fg. : e e followng follow well from te - dgrm of deel yle on Fg. : e e te pe temperture nde ylnder w ommerlly et n te deel engne tlogue for e tegory of deel engne. Hene, by ombnng Eq. 0,, nd, te followng follow mtemtlly from Eq. 0 tt: Interooler ompreor e η Interooler e erefore, by ubttutng Eq. n Eq. 8 for entrop expnon troe: e e η Interooler Interooler ompreor In order to determne v, ombnng Eq. 6 nd Eq. 8 for entrop expnon troe led to te followng: e e v v v te pef volume of g t tte. v te pef volume of g t tte. 5 ne te exut troe n deel yle oor, te followng tu follow from Eq. : Interooler v v 6 η Interooler ompreor erefore, te followng mtemtlly follow from Eq. 5: e v v By ombnng Eq. 7 nd 6: 7 e e v 8 v Hene, te followng mtemtlly follow from Eq. 8: e v 9 v u, ombnng Eq. 9,, nd led to te followng: Interooler e v Interooler η ompreor e Interooler e Interooler η ompreor 0 Hene, te followng mtemtlly follow from Eq. 0: η v e Interooler Interooler e ompreor In n endevour to over te ey prmeter n deel powertrn n t tudy, te n-ylnder g peed dynm re derved nlytlly from te prnple of py n te next ubeton..6 In-ylnder G peed Dynm In order to evlute te n-ylnder g dynm veloty, te momentum onervton ten nto onderton. onderng te ontrol volume n te deel engne ylnder own n Fg., ne tere no re nge over te nfnteml lengt of te engne ylnder, dx, n te engne ylnder, te flow tu umed to be qu onedmenonl flow. e momentum onervton equton tte tt te net preure fore plu te wll er fore tng on te ontrol volume urfe equl te rte of nge of momentum wtn te ontrol volume plu te net flow of momentum out of te ontrol volume [9]. u, te net fore n te ontrol volume own n Fg., te rte of nge of momentum wtn te ontrol volume, te net flow of momentum ro te ontrol volume urfe, nd te totl momentum re nvetgted n t eton, repetvely. IJE 0 ttp://

10 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 0 IN ζ ρ π D F er dx 7.6. e rte of nge of momentum wtn te ontrol volume e rte of nge of momentum wtn te ontrol volume n te engne ylnder own n Fg., oment, n be evluted from te fundmentl defnton of momentum nd fore follow [9]: oment F oment 8 Fg. : ontrol volume n deel engne ylnder for onedmenonl flow nly.6. e net fore e net fore n te ontrol volume own n Fg. ont of preure fore nd er fore. e net preure fore, F re, n be evluted follow: yl F e yl A yl dx A x r A te ro etonl re of te engne ylnder. yl te preure nde ylnder. By rerrngng Eq., te followng follow: yl Fr e A dx e net er fore, F er, n be evluted follow: Fer τ W π D dx τ W te flow er tre per unt re, D te dmeter of te engne ylnder. By defnton of te flow er tre nd flow frton oeffent, te followng follow [9]: τ ζ 5 W E Kn ζ te flow frton oeffent, E Kn te net energy per unt re. e net energy per unt re, E Kn, n be evluted by defnton follow [9]: E Kn ρ 6 erefore, ombnng Eq., 5, nd 6 te followng follow: F oment te fore tt generted t momentum. e fore tt generted t momentum, F oment, n be evluted from t fundmentl defnton follow [9]: F ρ 9 oment V yl u, ombnng Eq. 8 nd 9 togeter led to te followng: oment ρ A dx 0.6. e net flow of momentum ro te ontrol volume urfe e net flow of momentum ro te ontrol volume urfe n te engne ylnder own n Fg., Net, n be evluted from te fundmentl defnton of momentum follow [9]: Net ρ ρ dx dx A ρ A Equton n be rerrnged follow: ρ ρ dx d x dx A ρ A Net x x x Equton n be furter rerrnged follow: Net ρ ρ d x ρ dx ρ A ρ ρ ρ dx dx d x dx dx x x x x x A Equton n be furter rerrnged follow: ρ Net A ρ A ρ d x A ρ dx A dx ρ ρ A dx d x A dx dx ρ A IJE 0 ttp://

11 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 IN By mplfyng, gnorng mtemtlly trvl term, nd rerrngng Eq., te followng follow: ρ Adx 5 Net.6. e totl momentum erefore followng from te fundmentl defnton of te momentum onervton nd by ombnng Eq., 7, 0, nd 5 te followng follow: yl ρ A dx ζ π D dx ρ A dx ρ A dx 6 By mplfyng Eq. 6, te followng follow: yl ρ A ζ π D ρ A ρ A 7 Equton 7 n be rewrtten follow: yl ρ A ζ π D ρ A ρ A 8 Equton 8 n be rerrnged follow: yl ρ A ζ π D ρ A ρ A 9 Equton 9 n be rerrnged follow: yl ζ π D 0 50 ρ A u, te n-ylnder g dynm veloty n be expreed follow followng from Eq. 50: yl ζ x ρ x 5 D By llng te n-ylnder g peed nlytl formul from te reer pper enttled Deel owertrn Inte nfold Anlytl odel [5] nd ombnng t formul wt Eq. 5, te dynm g peed n be repreented nlytlly follow: yl ζ 5 ρ x D Equton 5 n be furter rewrtten by llng te nylnder g peed nlytl formul from te reer pper enttled Deel owertrn Inte nfold Anlytl odel [5] follow: yl ζ π B r N m n θ 5 ρ x 800 D DIUION AND ONLUION A te vele modellng type tt derbe te pyl penomen oted wt vele operton ompreenvely bed on te prnple of py wt explnble mtemtl trend, t pper preent n nlytl model of te deel engne of te gly promng deel powertrn. e ompreon rto nd temperture rto on te ompreon troe, ombuton proe, expnon troe, nd exut troe of deel yle ve been modelled n t tudy nlytlly bed on te prnple of py. Equton 9 provde n nlytl model of te preure rto over te ompreon troe of deel yle. It ow nlytlly te relton between te ngle of rotton of te rnft nd te preure rto on te ompreon troe of deel yle. e temperture rto over te ombuton proe of deel yle been modelled nlytlly well bed on te prnple of py. Equton 6 ow nlytlly te relton between te ngle of rotton of te rnft nd te temperture rto on te ombuton proe of deel yle. Equton 86 provde n nlytl model of te preure rto over te expnon troe of deel yle. It ow nlytlly te relton between te ngle of rotton of te rnft nd te preure rto on te expnon troe of deel yle. e temperture rto over te exut proe of deel yle been modelled nlytlly well bed on te prnple of py. Equton 0 ow nlytlly te relton between te ngle of rotton of te rnft nd te temperture rto on te exut proe of deel yle. e tudy derved nlytlly well te tte trougout deel yle from te frt prnple of py. e preure, temperture, nd pef volume t tte on deel yle ve been nlytlly modelled n Eq.,, nd, repetvely. tte on deel yle been fully defned nlytlly well. e preure, temperture, nd pef volume t tte on deel yle ve been nlytlly modelled n Eq. 5, 7, nd 8, repetvely. At tte on deel yle, te preure, temperture, nd pef volume ve been nlytlly modelled n Eq.,, nd, repetvely. tte on deel yle been fully defned nlytlly well. e preure, temperture, nd pef volume t tte on deel yle ve been nlytlly modelled n Eq.,, nd 6, repetvely. Fnlly, te pper eludted te n-ylnder g peed dynm n deel engne. Equton 5 preent n nlytl model of te n-ylnder g peed dynm funton of g preure nde ylnder, g denty, flow frton oeffent, nd ylnder bore dmeter. e developed nlytl model n t tudy ddre flw n model preented n ey referene n t reer re. All of te nlytl model preented n t tudy ve been derved tep by tep from te prnple of py wy of vldtng tee model. e preented model n t reer wor n elp n nlyzng nlytlly wt explnble mtemtl trend te performne of uperrged deel engne wt repet to bot of te trnent repone nd tedy tte repone. ere re two ey dvntge of tee developed nlytl model: Wdely vld model tt not retrted to pef dtet; n be elpful n developng nd eng deel powertrn tenologe. reer erve te I by flttng te nlytl modellng of deel powertrn fuel onumpton nd exut emon rte w re of prme nteret n deel tenologe development. tudy ex- IJE 0 ttp://

12 Interntonl Journl of entf & Engneerng eer Volume, Iue 8, Augut 0 IN bt reer on furter vldtng expermentlly te developed nlytl model. AKNOWLEDGEN e fnnl upport provded by te Interntonl Ilm Unverty ly IIU for t reer under reer grnt # G 09-0 tnfully nowledged. e tenl upport provded by te enter for utnble oblty t Vrgn olyten Inttute nd tte Unverty Vrgn e tnfully nowledged well. [] G. Grnn nd F. urry, Ar polluton nd elt n rpdly developng ountre, Ertn, 00. [] llpp,.. eddy, nd..n. uty, erformne nd Emon rtert of ttonry I Engne wt rdnol Bo Fuel Blend, Int. J. entf nd Engneerng eer, vol., no., 0. [] K. Bl owry nd A.V. t m ju, multon of Injeton Angle on ombuton erformne Ung ultple Injeton trtegy n HDI Deel Engne by FD, Int. J. Engneerng nd enology, vol., no., pp. -9, 00. [] J.. Lvengood nd.. Wu, orrelton of Auto Ignton enomen n Internl ombuton Engne nd pd ompreon ne, ro. 5t Int. ympoum on ombuton, pp. 7 56, 995. [5]. etlld nd. Ntv, Lner nd Nonlner Dynm of eprotng Engne, Int. J. Non-Lner en, vol. 8, pp. 7-78, 00. [6] D. N nd D. Henlewood, mple Engne odel for Vele Infrtruture Integrton-enbled In-vele Applton, IEEE rn. Veulr enology, vol. 57, no. 5, pp , 008. [7] J.J.. mt, odelng of Flud Flow n n Internl ombuton Engne, eer eport # WV 006., Endoven Unverty of enology, 006. [8]. Dv,. ne nd. pnel, Het rnfer Anly of Deel Engne Hed, eer eport, Joef Boze eer enter of Engne nd Automotve Engneerng, ze enl Unverty, 00. [9] J. Heywood, Internl ombuton Engne Fundmentl, Grw Hll, New Yor, 988. [0].E. onntg,. Borgne nd G.J. Vn Wylen, Fundmentl of ermodynm, Wley, 7t edton, 008. [] E.F. Obert, onept of ermodynm, Grw-Hll New Yor, 960. [] G. Br er, Fundmentl of ompreble Flud en, Free oftwre Foundton, In., 00. [] D. Kummongol,. nr nd W. Aryprnee, Het rnfer Between Impngng Ar nd Impnged urfe: Ftorl Degn, ro. Jont Int. onf. on utnble Energy nd Envronment EE, Hu Hn, lnd, per # -00 O, 00. [] A. Holmgren, en Vlue odellng of te Inte nfold emperture, ter e, Lnopng Unvertet, 005. [5] W.F. Fr, H.A.,.. Kffy,. Idre nd. Elmoely, Deel owertrn Inte nfold Anlytl odel, Internl eport, e Interntonl Ilm Unverty ly, 0. EFEENE IJE 0 ttp://