computer simulation of compression-ignition engine processes v ganesan bn.pdf

8/9/2019 Computer Simulation of Compression-Ignition Engine Processes V Ganesan BN.pdf

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CONTENTS

P n fa cc xi

L ü l o f if tn io U ziv

Ch»pt«r 1 INTRODUC TION1.t SindUlon1.2 Advuilt| et of compaUr ilmBUtio*1.3 Obj«ctiv« ef lU i book1.4 SU p-by- «t«p pproadi

C h a pU r 2 R E A C T I V E P R 0 C E S 3 E 32.1 Inlrodactios2.2 Heit oí r«»etba2.3 Mcuoremeot of 2.< MíunrtmtBt oí B, f

2 i Cilcnk tloB of h!|litr tnil iower L«tt vilae of fatliEnrcii*

C h ap tM S A D I A B A T I C r L A M E T E M P E R A T U R B3.1 Introdactioa

3.2 CompfcU combttrtlon io C/ H /O /N iyit«mi3.3 Con*tuit>voluai« adUbttU comb iutbn ÍA CoftttuiUpretittn iJitbtllc combutton3.( CklcnUUon oí »dUb«(lc flun* Itmpt rttart3.6 SolYíd cxamplet

Sxtrcbe

Chapla- l I 3 E N T R 0 P I C C HA N C E S OT STATE4.1 Introdacdon4.2 SammiTy

ExereáeC h ap le r E C O M P R ES S IO N - IG N IT I ON E N C IN E S

5.1 Intixxiaction5.2 Somc bu le dctt lb tnd DomcscUtart5.5 Cylioder preMurt iadictlor dUg mn6.4 IndicaUd poww 40


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vUl CompoUt SlmüUltoa oí d Eaíli» Pto cM itt

Chapter

Cbapter

Cbaptcr

C b t p t c r 9

iS B r^ powcr«1

j «iJt Working principie

41i j

S.7 Eagioc kiaem^icsExcrcac

AA«

a CI ENGINE 8IMULATION WITH A m A S W OH KI NG M E DI U M 47

0.1 btrodsclloa 47

e j Uctl DUm I cyck 4S

OJ SlmuUlíon wUh *Sr u the workim médium 49

S.4 Dtvi^ioa betmea utaU ta i IdeU cycli51

t s Solvtd «xunple* 62S4Cxtrcke

T C 1 E N G IN E S I M U I ^ I O N W I T H A D IA B A T IC C OM B US TI ON S5

7.1 laUodaction ss

7.2 Engíae detul* -65

7J Nu vti ly uptraied openiioa 66

7.< Work ontput u d «Sciency cak oUliou 62

T i Supercbirgcd open iioa 66

Exiutitt 72

6 C I E N G I N E 8 I M U L A T I 0 N W I T HPHOGUESSIYE COMBUSTION 7}

t, l laUodactioa . 73

ta lf*rogrtuivi comboftioQ 75

Combuilloii iiiodilEfi{ SI

&.Í 7->nw


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))

)

PREFACE

laUnikl Combnitiea Eailnti c u bt broully cU tiiled iato ipuk-i(aitiaB (SI)u>d comprttiIoD-lfnhloB (CI) Tb t ipvk*l(oUtoB eafint datci bu kto 1878 «he n Ao fiiit Otto GM derttoped the SI tafln t u d comprcatlon-iinitloB cB(ine to 1S92 whtB R«dolf Dlettl iavtB(*d tlie C1 capae. O m tbelu í OBC eeatnry, eaginet coatianed to devtlop, u onr kaowledie of engíoeproce*««< b u bc r«u «d . N


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jd l Cempatu StaiUth» • / O Eagia* Ptocmm*

wlittkcr lk« c


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LIST OF SYMBOLS

S y m ' b o l D w c r l p t l o n

Á, Á f t n x ot ihe piiton A ,x wide open cxhtiut vilve are&

Ain wide open inlet vilvf ir ei AC S letaxl cydc liraalition Á/F úr-fatl ritió AL cotfficient for ibe cdcuUtion of C ,

Sp br»ke povfer B bore

BD C bottom deid centre BL coefficient for the ulcu litio a of Cp

mcut pUlon tpMdCp ipecifie beiC tt coattul preuure

pcciGc bc*t« of úr

C( ̂ tpecific bc*l« of fa«ICr, coMliot volumí tptcific beiti of the reic linl mixture

c :( r ) meul vUoe of ipecific bett coiut»nt voliitne

C, ipe


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.. .. . ....... i ̂ -- - - -

yvi CoiDpal«rSImBl»» toooíCÍ£i i í ío#P/oe»«M*

f, Keit rtjKUdQ f tatiTpf r t k u * at c o u t u t p n t i o r c

Qv tntriy ttk u* U conitut vptuB*

r conprtMioa ntio R fW coulu il

RA F nUliv* air-fatl n lw A« lUyn oU’i Bvinbw

S lUol*S (o(4l «ttlropy

5, K»v


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V

l

INTRODUCTION

1.1 Simulation

StmnIittoD ú a broully uied »ad tomcwbtt Ul-dt6oed Urra írom the enji-nc«rin{ po bt of view. Accordiai to Wcbiter'l inUrnUiontl dict!oaary *lolimtlatc' meizu *(« fe íi n, te cttain lAc turnee «ntAo«{ t kt n M f * . How-

evcr, tbc iiznpUtt mcuiing of úmBlitioii ú ‘ ímitatún*. Thcic dictionaryn e u i n p do oot brtng ont • cltu- pkcnn of tbe worti '«tmaUtion* for ca>tinet rb( ^pticat'>oiu. Tbercfore, i definitioa of the word b duired in thucont«xt. W i(h ioroe Ircpidttion, Iht uth or d


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• ________ L ___

____ i

3 Coa pulM SImiUtliea oí Cí Ettíat Pncmtm

1.2 Advanlagu oí com putcf stmulation

In ui iaUroal corabutlion (IC) th« proctue» involvcd u e extmnclycomplcx. Uotil Ihe lu t ¿tc*dt, lb« dosta of an cngine rtlied farat¡ag adiabatic Same temperatnre calcolatioiu for heatadd itbn/ comb utioB analyi'u. Ib ibis asalytti, ioitead of air, the working

médium ú auumed to be a mixture of fuel and air. We wiU cali tbi i analyi'uu fuel-air cycle timilation (FCS) . Kere, combiutioa is aaiumed to take placeat coutant preuure and uoder adiabatic conditioa.

Síep Il¡: In tbii ttep, tbe adiabatic flame temperatnre calcutationi are modi*fied by asiomlng combuttioa to be progreulve, Le., heit release ii not ÍBstan>taneon» but ipreadi.over a period of time. In otber wordj, the duralion ofcombuition ii taken into account. In CI eaginei, the heat releaje a oalytii canbe done either by meaoj of progreuive combtutk>n at cooitant preuure, oras meani oí tero-, oae- or two-dimeiuioaal heat releau roodeli. In tbij bo okjtwo typei of a nilyili have been explained. The Sn t oae ii the progreaiivecombajtion at cooitut prcuare. The lecond oae is the progreuive combui-tion uiing a iux>-dimetuiaaal lingle -ione modeL Forther, extenaion to oae>or two^tmeuiiona] modeis niing two- or mnlti-ione approach ii alio poMÍbte.We will cali tbii analyiis progreulve combuitba lúnalatlon (PCS). However,io receot yean, attempta bave becn made to uie mnUi-dimeniional models.Thii requirei high ipeed, bigb memory computen.

SUp IV : In this taal itep, uiing limpUSed auampttoo i, the engine heat trani-fer can be takeo into account by meuu of empirical eqaatioDi. Gaa exchasgepcoceiie» are inlroduced in ordtr to analyie the engine intake and exhaiut.

We will cali tbii analyiti actual cycle limulation (ACS). In this itep, intakeand exbauit pr oceuei using Suid dynamic equatto u, heat traaifer and frictioaare included by meani of empirical equatioas. -

By means of thb itep-by-itep limulatioa, the valúes of presture, volomeand temperatnre at lalieat points in the cycle ue calcutated. Work outputai well as thermal eSciency is evaluated; Ptxmiioni have been made in theComputer program for making paramelrtc studics. Thii itep-by-step approach,it b haped, will make the reader appreciate the complexitiei Involvcd in actualengine limulation.

Compared to other proceitcs, Ihe combustión procesa is not amenableto thermodynamic analysis. However, an attempt has beea made to bríngcombustión analyiis within the purvlew of thermodynamks.

In order to get a bisic undcnlindbg of the comboitioo pcocets pertainisgto engines, tbe next two chapten are devoted to providing a bockground foranalyiing the combustión pheo omcni using thcrmodyaamics. These chaptertdeal with reactive processes and adiabitic Sune temperalure calculatioos,

reipectivelyj


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REACTIVE PROCESSES

2.1 Iniroducüon

When k fuel come» iaU) contul with oxygea or ur nndex tke properenvironmcat, t ekesücil rMc(io& ttke« plice. "^e r eictioa c»n be íioíAtnníc,whtre heit esersy ii rekued; or loinettme* ««¿otAírmiV, where Keit energyii ilMOfbed. The híU esergy releued In ta exothamic rcKtion cin be oie4,for ex&mpk, to nm ta iatemil combaition entine. In the ui üy iú of intenitlcombiutioa eagiae proctuet, we ire interated u tKe itody of cxo them ic re-actioni involviflg th o« m bitancci th»t cu i be nied u fntU. In olbtr wofdi,We woold like to mqotfe into cliemic«l reactiotu opto the extent ihit ibeíe

reactioni *tt i tonrce of he»t cscrgy for h'eU enginet, e«pec¡ally the íat«rat]

combnitioa Bafine*.

M uy booki ttlk about nactive proctuet. L«t tu ice what it meut by» reaefiM froten. A pr octíi mvolvLag eAtmúoi rtwtíon c&n be coiuidered u

reactive proceu. Then, whU ii a chemIcU rtaction? A ekemüí] rcatlwnmt y be deEoed is < rMiruigement of the atoms of

the reactanta dne to the redUtríbation of etcctrou lo form producía that aredlfereot froto rtacta«U. The iroplicatíoa of Ihit dcSnitioD ii tbat the namberof atomi of euh element partidpatlng is a reactun remami nachauged, i-«.,the coue ivat bn o f matter. Thú principie willbe oaed in writing the eqm tiou

for chemical reactiou.

It ti known that a cheniicaliy correct or itoiduooietric mixture of hydro-carbón fuel aad air reacU to produce oaly HjO or COj or both.

Fot example;

Ha + 0.5 0 } — H,0,

CO + 0.5 0 , - C 0 „

CH« + 2.0,0, -> COi + 2 H ,0 ,

C , U „ + 12.6 0 , - 8 COj + 9 H , 0 ,

ÍU i£tl n P to ctM t

C,oHn

CHjOH

CiHiOH

+++

15.S O,

hí O, —

J.0 O, —

10 CO,

CO,

I C O ,

+++

11 H ,0.

2 H3O.

S H , 0 .

No te; All the above fatU cao be a»»d ia IC cofiaca.

1 2 Heat of reaction

Ueder conditioni that promott eomboitloDi tha active cotutilueala of a furtac l witk oxy feo . Thia comboitio n proceaa bvohres the ooddatioii of thcarboB aad bydrogea preteal in lk« fatL The com butioa proce u ¡a a complereaction or, more exaclly, a rapldly occorting atriea of rtactiotu.

Whenever comboatioa occnn, the energy aasociiled wilh the chemicabon di ia the foel and oxyges molecnte* b releaaed. The chemica) energy

' coaverled into heat energy and appeart Snt u a heatbg effect in the pto ds cgue«. The final lemperaisra of the prodocta of combution dependa on nnmber of faetón. The impoitant onea ara aj foUowi.

(i) the fuel and Ita compoaitloa,

(ü) the prtaiora and tempcratorc of the reaelant mixtore,

(ui) the álate of the fael, «htthtr Uqoid or gueeoa, aad

(tv) the externa] conatrainta impoaed on the reactlng »yllera, Le. whether thcombuition takea place at conatast volome or al conatant prcaaort.

la order to ulccJate the &bi1(«mp entor* o f the ptodscla of combaiUonthe energy characteriilica of the fail ihonld bt known. The energy characteritlica of fnela are Tariouly knova aa talKaipici of comlailton, JteaKn; «o/vet Ktal of eomitution uí i ktút «f ncctian. In thiabook, the tenn heat o/nactionwiü be uaed.

2.2.1 Oelinhton of heat of reicüon

The leal of rtaclún at coiuUnC tofinu, tnJ a ( ceiutant pm ivr t , Hrp

M áefineii lu lAc t n t r f f t i i t i i o (rín; (X< prodvtU 0 / comU >l>on to the inih'aJ

Umptratun, m . 198 K, vktn > anít gMiiliry o f f nt l m i u m c t

OTfjen (u m at conitint to ltmt 0t * l uiulant prtii tn , rt iptelítclf .

The impUcationa of the above definitlon are u foUowi.

(i) Ur ̂ and Ilrp are both negalhre.

(ü) Uff and Hrp are prbperttei of the fneL

(Si) Urf and H,p refer apeclScaQy lo chemlcalty co tm t fueUutygen mixtoreireactlng at 29t K.

it may be noled that both and i/rp are meunra ble quantltiea.


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ComftUt SüülUilo» •/ Ct SMfiat PntMMt

Foc t i t Ma iyti t o í (Bfue tombo i l ion, we wi l l dcEnc two rtl^tcd eatr jy

’ u n i u , Q , a n d Q,-, w l i « « tbc U n a < J, . U i u i* f o r e » e r * y w U u t U c o w t u i tvolomi ud Q „ tht mtrsf rtUu* al cooiUat pr«uurc.

Í Í 7 DcSattIoa ol Q , «nd Q ,

T h* t i i t m r t U u t i «I u u í t i t U 9c h m t , o«¡tive. They «rt propertií* oí th« reielmt

'.tnvtBft, r(ítrr»d to »ny Ump


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i

8 Coapattc StmaUtha o f CI Eofice Pníeuct

If Ihe •(«cific «nlliiJpitj of thí vino iu cotutUuenlt »r« kaown, t/,p cu befrom «j.(2.7).

2.4 Mcasurement of

The he»l of ríiclkm it coiut»nt prewure, i/rp, U meunied in t lUuly-aowcilorimtter. The detüb tliown in Fig.2.2 »it refaced to the b»r« eueotiJj.Fuel tnd »ir ¡n txcttt oí the ehemiciUy torree» rcqnirement enter the re»clioathimbtr it 298 K, md Ihe producU trt cookd to the inlet temp«r»tore by

the wxter circuUtiog La Ihe lorrounding jidcet.

Ccxitrol volume

Futí Air298 K ‘

Products‘ 298K

WiZír

Flg.3.3 SUa íj-flot) ealorímtltr

If the chingei in (he kínetic u d potentiil caergie* are Degligible, u Uuíuillythe e i« , for a ittadjr-fiw ceaiervilion of ener?y

/í. (2 98 ) + / f , ( t „ ) = ffp( 29 8) + i/ .(í


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„:í i....

10 ComputtíSin^UtioñctCitMglauPi

» b t ( « R ii th« onivinal ( u coajUnt, úace tbc «atliaJpy Ti «ad iatcnial caersyD v « la BuU ptr mo b. For tiqúiU kwl lolid*

K - 0 w 0.

Th« difftnac* b«lw*«a Ihe cotu iut-p rcuo n u d coiutuiU\'olaiiie k«at oíntctloa mijr (bta b« wirUUa u

u „ - v „ [N ,-N ,)R r . (2.18)

With R = t.SU kJ/kmol-K tsd T « 29$ K, lb« vilne of (he prodact JtT willbe 2477.S7, wkicb cu b« kpjiradmUtd to 2480. Tliiu,

*» 2 480(A V -/r ,), (2.19)

wbtr* Nf u d Nf dto oU , re*pc«tiv«l/, the mole niunber in the product w d islh< nictutl mutu« U thi | m ou ip«ciei for &ckemluUy correet fie)


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13 CompoUr Siniii/ítfcB of C/E afíae ProceM*»

Hrp - = /l̂ K,0 X íl/.ÍH jO).

Witk A/, (H ,0 ) = 43956 kJ/kmol, we h»ve

= 11 X 43955 = 483516 kJ/kmol.

Thcn.

- M 1 2 3 00 - «3 5 1 6

« -e795SI6 kJ/knioI,

t chuije of more {h»n 7.0%.

Similuly, it « n be «hown tliit Ibc cBinge in th< ü,p v»lue will ilf o be

of Ihe tune onler.Tte ibort cilcnUtbai «how lli»t wUl* Mcorint htxt of reMlion i^ae»

from publálied t»ble*, greite tt « r e muit be txíKÚ ed to note ihe con


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H Compatu Simulitloa ol Cí Eaflot en cta ttt

T*bl« 3.4 Utf coutul-pnwBr* btU oT nulloa for Uie cut ot (UMU HaO U U « pnxlMt

FbnauU UoL wt.

T í ü í s r "EtkMtProp»a«fvBulu*tv-P«ntuen-Hexu>«n-Htptuen-Octwi<n-NoBueiv-DccueMttbuolEtbksolB«aiutt

CiH,C,H,C«HioC»Bu

C«Hu0 , H „C»Hu

C»HmCioH»ca,ouC,H»OH

C.H.

1»904458

72sa

100lU12814232

4678

H^ttid íuel

Tj/fcaot í m r

Gutatu fae)yy tmoi í's/k¡

-2019900-2622800

-Í228200-3884600

-4441100-5047800-5654700-62lnt ?uel HiO In Üie product

Co utu t volsme Liquid Liqoid

Co njtu t volutne Ltquid Gaieouj

C ou tu t volutae Gaieona Gatepuj

Cou tast volume Gaieooi Liquid

Co&itut preuure Liquid LIquid

Conitaal preuure . Liquld Gaseous

Conttut prtuure Gueoui Gaieoui

Comlant preuure Gueoiu Ltquid

ADIABATÍCFLAME TEMPERATURE

3.1 introductíon

VirtuaUy «v«ty probUm bvotving comb oilion wiQ úrvolvt tbe ctk ok tia n of«dúbatic flime tcmpcnto n. Tli« SsU Ump


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l e Computer SimnIttloB of C1 Ecx/oe Prx eu< »

at cooíUaVprtJJure. FWther, the reutinC prainre c»n »1ío »ff«t lh« flune

Umperatu^e. AccQr»t< d ka lit io n of the a im t Umpcratnre inv olra a « ( of conipU-

ctltd tqaUioo*. Howívtr, for two reuo iu we wfli confine our alUntion only

lo a limpie fct of eqaatiou:( ] Accorate caltola tioa Un« done very eaaüy by a lytUma tic teirck

willi a compatcr. Th» main empliasa in (bii cliapter will b« toward» ttU *nd.

3.2 Complete combustión In C-H -O -N systems

AaTOtning complete combuition, we can decide the compo«itton of the conv-bwtio n prodn cli merely by inipectüig the reactant mútnre. For a reactantmUtore (bat contain* C, B, O, N aloms, we will formoUte the rolíJ ai foUomrj;

(i) AU bydrogen ú fin t caúdiied to HjO.

(ü) Alt carbón i* initially ^ .

N i^ O ,

ff , « N „c ,

U 3 = O.SNmH„

= S.liY,

A i - r - n c

(3J)

Ni throagh Nt cao be uied ai lubtcríbed vamblet in the Computer program,10 that the inbtcript* 1 lo $ can be made to denote

(3.


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IB Computv SimtJtUoB ol Cl Eaflat F n ct tt t

Rigid. IníuUud Vcuel

Flg.S.l Ci>atla»(-faUnu adiaictic Mtnlwiwa

L«t


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30 CoapnUr Simdithci of CI EnfUe Procttsc»

The vilue o( //,p whkk ú » po«ilive he»t of re»ction for COj c»n b« found

from ttimdixd hmdtxxiki to be 282ÍOO kJ/kmoL Tbtrefore,

(t / ,p)co, = 212*00-2480(1.5-1)

= 281560 kJ/kmolCO a

a 281600 kJ/kmatCO i.

The rtjulls of the two cuta of Y, vil, Y >Y, f »oJ Y < Ytt, »re tivínby


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33 CompíU/ Slmtit lha o / d £i (Jce of c


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)

34 CktmpaUr S lmditba oí CI Eít lm Pmkmm*

entrcr {cq.(3.32]| 0"ihetkal vilo* oí lie Hime Unipenture. Thtn, tbe ntw-lune Umperanro b

cttiined fron

r . . . T - m z t ó b i i l .c , ( r )

II thc difTcrtace bítweta T uid To,w ú witkin, lay, 6 deg na , tbe it«r«tk>iican be i toppcd .

For cout»&l-preuQr« corabiutioa, iniUul of Vp{T), the v» ]aet of Hp(T)

trt com pattd luint the rtUtion given ia Appcndix C.

For txiniplt;

For « » < r < l eoo

X{T) = AL + B L xT -^ CL h{T ). ( J ^ )

For 1000 < r ^ 6000,

X(T) « ÁB + B H x T + CB ln[T]. (S.S7)

SimlUrly, úuteid of ^ (7 ^ the rklati of Z^(T] are compoted nilog the

relation

= BL + CL/T,

C ; ( T ) = B H + C H ¡T

T b ,w i* ulcoUted aim{ tbe reUtion

r „ .

for 400 < r < 1600,

for 1600


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-ÍUd-S. ....

30 Com pat tf SUotaltÜoa o í CJ EagU* Pi

bttwMS ffpC^ u d N, C, h Mktom luye . Á* » cosMijatoc*, it i* UfUinkU*

to ignora (k* Umj>«rUin varálioa ia u dT]i«a, f or tk« ( ca trd cu e o í cattft>at>volBti>c kdiib«t¡c c cmbutioik witlt

n t cUsU U T „ ib* flt4au Umptntare á iñc a hf

»tic combuUoa

- F „ - // c o x M 2 S 0 0

(S.«)

fo r (Kt (tstn l ctM, tlti ueceiuor «xp rwio M íor tke Nevtoa-IUphfOBit«r«tlon Mppur sow for cauUat'Volami combu tioi u

r - B B z M i b S ic , ( n

ta i íor coBit*aUprt»iow cambailion tt

( j . « )

( 5 . « )

Whüt d«vtlo pbi( a compaUr progrun, wlcttUtíoaf for iTp(T],í/’p{7), C,(7) u d C,(T) c«a bt doat by muju ot fuctioa rabprognnu.

3.6 Sotved m m plcs %

1. Com puli tbt Sunt Umjx nture «h tn » cktmktUy correct mixtura ofUquid C|U]f 4ad air úUUUy a 400 K utd 1 Um, bonu U eooiUn t

volome.

Tbt rcactul mix(«r« k

C,Hi, + Y „O j + 3.76Yc.K3,

wh«r« Ya ú ti » chtfflktUy com ct cucy êa to íneJ r»tio. Utrt

/ / * o » í , A i» a i« W i A'm Qi“ 0.

Tbercfor«,

n . -

Ad l^a tic Fl us * Timptntan 3T

12.5.

O,

«.9,


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36 Compottí’SU nalitha af CI Eoglüt Proc^M^

U¡,{T) - / f co . ( -4 ^ + ( 5 f f - ^ ) r + < 7 £ f i a ( r ) | c o .

+ /^h . o I/ í h + ( B f f - • f i ) r+ C H l n ( r ) I i, . o

+ Nti, [A H + [B B ~R ]T + CH ln(r)I„,

= a X [93048 + (6 8^8 - Í.3J4) X SOOO- :6979 X ln{3000)]

+ 9 X [15


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.ÍJU. ñ____ ....... —~

80 CompiUr Slmoíttloo o/'C1 £ii(la« Fn>c= 68.2S .

Tlü* yieldi

ítAT) - N oo M L + B L x T + C ll a (T ]l

^Nu,o[ÁL + B L xT +C L b ( r ) ]

+ V / « , ( A ¿ + f l L x r + C L k ( r )| .

For u inl;iil Umperxtox* ot iOO K, i.e. 7 , = c o m p a t t r p r o t ra m l o c i l c o l i t t tb e a d U b u i c & u a e t e m p c ra tu re

o f u y fu e l f o r u j r g i v t s ¡ o p a l t o n d U b n i .

2. Uaing the above proprara eakuUte tbe a^Uabatíc &une («np«ritare fortbe fueU CiKtt asd CioH » (rom Y»\e¡ to Vniuci «b crc 1-6 Ytt(tnder conatant-volnme and coutaiil>preaaare comboitioB. Draw a grapbof idiabatic Baine l«raptra(sr« vergas Y aud dlscuu.


25/110

ISENTROPIC CHANCES

OF STATE

4.1 Inífoductlon

Miny o[ the combnjtion e np a« involva t tomprtMioa proíeti ind »U of »heminvolve »» «pu u'nj n proceii. The workinj Buid Ma mixture of ju e» . Thetnüo qae«tton b how to eilenlate the lempe ntore oí tbe {uc * U the cnd ofthe próce « oí compreuioii or cjcpuuioa. In the puton tDgisc, la order toulcolUe the wort don* by or oa the g u «, the*« CsaJ t«rap«atoret m t u l be

known.

IdetUy ipetldng, the comprcMtoo u d expuuion procttiei ihoaid tikeplu « npidjyi «ith negC{ib!e hest trttufer^ Reoec, compreo ioa u d cxpiAsionc^ctüitioiu ctQ be mtde on the auamptton of bentioptc bchtvioar.

Where the process ii not benlropic, e.g. b compreMon u d torbmci,

the ñeatropic tímpírtto re comp otílioo ii »{ill retn»Uy, Cf »nd C, is ae ue iríth tempertture, while k decreuu. Since C, indC, dlffer by t c oni tinl iroonnt, the chtnje ¡n i wUh temperUure tt not verypredominant. However, the ippb'cxtioa oíe


26/110

s i Com pttu SlmaUtloM ot C! BagU* F nctua t

f o t »a y | u , 4i{ T) U Ibe caUopy p«r mole kt tcm pcnto re T u d 1 «t m .TkbU C.4 ú App«Bdix O glvu A t v^lac* oí ^ for (U«* Uut tr« camioo»(y

íound in comb utioa pro4ucU.T»bl«* 3.1 u lT )- -^ -¥ V L

CH

4 0 0 á T S l « 0 0 .

4 “ B H h { T ) - ~ + DH I 6 0 0 < r < í 0 0 0

Ti ú foaad by *oIvía| thi cqa&tiosj

á S « 0.

li,Tj)wkicb u a h* cJcpudcd te

AS- (̂ (r,) - f,(r,)|- iví uFor lb« lolatlos oí tb« abovt c


27/110

)

)

)

)

COMPRESSION IGNITION ENGINES

5.1 Iníroducilon

In order to umolate the compreubs ¡sq Uío d (Cl) eogtne oa &digital com<pater, Gnt of tU it tt necmvy to know the vtríoat proccuci of thc CI engioe,wtd iu workiBg príocíple u well u the nomencUinre us oci it«d with it. lathLi ch»pt«r we wiil rcview brícSy tbe wofkiai principk of a fonr-itroke CI

eagine.

5.2 Some baste dcUiIs and nomenclature

U t IU fint deEiic a cycfc. A cfcle ii a complett leqoenc* of eríct» «tuiintftom o nt it ate and rctttnúiig to the lame (tat « ii^the unt e «ray. For exunple,it may b« an intcnral or a períod of time occapíed by ene round or conne of

cvent* repeating in the Hjne order in a «trie», loth u the cycle of fe uon i, withipring, lummer, anlumn aad winter foUowing ctch other and thea recnrring.

Similtrly, an IC tnjint cfcle i« a »eríet of eveat* that aa iotem al comhs**tion engine undergoe* whSe it ij operating aad deliveríng power. Stace thcieeveoti occuT in a certaia xquence, they are MÍd to be tímed.

Al already tt ated, cor intereft lie* ia revicviag the worktng priacipteof a four-ilroke Cl engine. The com prtuia a ignítion cngine wu orífinalJydevetoped by Rndolf Diuel la Gtnn any in 1892. Moit o f the reciprocatisgengine* oper ite on a foBMtroke five-event eyd«. There are foo r itroket oíthe púton, two op and two down, for each engine operating cyc k. The baiiepower-developing compoaeati of a typical Cl engine are ihown in Fig,5.1.

They are:

(i) the cylinder,

(ü) the piitOB,(iü)

(iv)

the connecting tod,

the craakihaft.

Camp nmk» ¡ftlIloM Eaíl ntt ÍT

Pto»««lBDC

CxuMtlng n i

Creakilnfl

Fig.S.l BatU fOwt r-dtft lofÍBf com font nlt o / » CI tnfint

The cyllader ha* a imooth inrface *o that thc piitoa, with the aid of pi*-

ton tingi aad i labricu t, caá cRit< i ital todi (hU do |U uq tia p< bctwMS

tbe piiton aad the cyCnder walb. The p btoo ti eonaected to the craalahaftby meanj of a eonnectbig rod *o that the redprocaitag moiton Si converUd torotaiy tnotion by mtaaa of the coBoeeting rod and «raak auembly.

Tbo pctition of the workiag pliton aad the moving pane, whkh are inft-dhanicaQy conneeted to the piitoa, at the moment when the dircction of itimotbn u revened at either oí the cnd polnta d the atroke, m called tbe deadcentre. There are two dead centre*, vii ,, lo p dead centre (TDC ) aa d bol-kom dead centre (BDC). The limit of travel to which the p'utott can move,u calJed TOO and the limit to «hich it more* in the oppoeite directloa iicalkd BDC. For each revoloiba of the craok


28/110

iS CoapaUe SUaatillon ol aEat l t * Ptoi

As cogio e ba vliig » bore eqaU l o tEe itroka ii o lUtd » «aji ne. lítti< »troV« is lu í thu » iL t boce, U i» t«lled «a ovei^»


29/110

be cilculatd. The dUpun ninrtr»Ui tbe prt«ar« _r«K dnriag the tompre^«ion itrokí »ad comtiat prmnre daría* he»! «ddilion. Further, ¡l »howí thepríMUm drop wilb the expiniioa of the c « « duriag the povfer itroke u weü

u doricg he»t rejecfion.

ComputUioM oí tle indicUed power ir» loniewhit «únplified bjr oiinj

»he avenje prewure iít b j o q the píiton thniBghont the wor kk í »troke, T hi.

»ver»ge preunre, ofUn oU td the nwia effetlivt prw ort , tt Qormally obtuntd

frotn thú indic»lor dUpim.

^0 CompatiT Simalithn of CI Espine ProccMÉ

Flg.6.4 Prtn«re-»olum« {náiator ¿t’ajmm

5 . < IndJ c a t d p o w t r

IndicUed power b defiaed u the t«tal pw er convertid by tbe engine fromhe»t energy to mechwicil energy. It á tuniBy »bbrc viutd u «>.

If the chtnclerótici of la engine u t knoirn, the indicited power ritingc»n be CMÍly tilcoUted. The tot»l forcé «cting on the pUton in e»ch cyliaderti the product of tbe indkited mein effective preMure (K/ra’ ) uid «•«», Á,

of the pbton hetd in

The prodact of the totul forcé uid the dtitifice through which it act» i?one íecond give» the wMk done per tetond. Thii product mntlipUed by ti

ncmber of cyliaden on oper^ioa |ive* the work done by the catire engineper Krcoad, in WitU.

Indicited power b then given by

¡\^SAnK

CompntsloD !fi ilíha EaglneM 4

•F " (S.3

whert A ' K

« X » 0

u-et of the pUton ianomber of cyliaden

n » Btunber of workiaf (troke* per miaute (rpm/2) per cyliodef l* » ladieited m eu effecthre prtuur* ta N/m’S = length of the itrok* la m

5.5 Brake power

Br»ke power, ip, ii the Mt uJ power delivered by an engine tt the e r»a bh iítIt ii the dlfference between the indicited power, i>, ind the frietion power /p . FVictioa power is thtt pir t o f the tota l power aec eut ry lo overeome thftictbn of the moving pirU ia the engine «Jid lu acce»»oríe*. The relitioajhipbetween them m»y be exprttted u

»> - /p - (5.<

It m»y tlio be ttU«d thU hp ti (hit pirt of ihe tolü power developed bythe engine which cía be nied to perfortn work.

5.6 Wo fklna principie

Id 1 four'itroke cytk eofine, th i cytle of opcratb a U compitted tn four ttroke*of (he piitoa, tnch u lactioa, comprtuioa, expuuion lad exhisat. £ich

•troke coQittt« of one revolnlbn of (he crinbhift or 180* of crink rotitíon»nd henee a cyde co n« il« of 720* oí craink rotition.

The vtnotu tlrokei ire illutrated in Fig.5.5 ind (he comtponding idetlcycW p-V d iig rm it iliowa in Fig.5.8.

The working principie of the engine ii deicribed below.

$.6.1 Suctbn itroke

p e inction itroke ii repreaented by 0—1 in Fig.5.6. It itu tj when the p'utonb it TDC, ind ibout lo move downwtrdj. The blet vilve b in Ihe openpoíition lad (he exhioj l nlr e b b the cloied po*ition [Pig.5.5(»)]. DnriagIhb Itroke, dae lo ihe lucking iclion of the pbton, lir from the ilmoapherei] driwn into the cylinder. At (be end of ihe luction itroke, the inlet vilvecloiej.


30/110

42 Co mp ou i SlmiíUtioB o f C¡ Eagla» Ptoctu4t

¡tltur

latekfnimdMn

(a) SuctioB [b] Coinpres*b&

CtWtM

(c) Expauion

Fig.5.5 KaniM Uroka in C / (n ; tn (

(d)

CooiprMiiaa 2{sillaa ¿cf iiiM 43

S.6.2 ComprosJon itroks

TKe compresaloo t(roke ú repretentcd by l->2 ia Fíg-5.6. The air tikea inloihe cylmdcr doring the «action itroke, doog «riih tbe producU of comboitionof the previooi eycle, u compreited bjr Ihe return «troke of the púUin l-»2.Durúig the comprtsiioD (troke, b«t h ¡alet u d exhauiC valvet remain clo*ed|Pt{.5.S(b)j. This ú r U compre ued Uto the cleuan ce volume at the tud cí the alroke. However, joit beíore the esd of the comprtuioa itrokc, the fací úinjected with the help of as b jeetor. Even though combiutioa onght to it vtúnmediately, in actual engiaei, it itarts after a vtiy imall mterval of (¡mecalled the deUy períod.

Flg.6.0 ¡dtal p-V dii¡rcm

Durini the combualion proce u, the chemicU energy of the futí b rtleaacd

is th; f^nii of heat eaer^, prodadog a temperatuje riúe of aboat 1800 Kand the p:t«aan wUl rcmain conitaat (rtpreieated by 2->3 in FIg.5.6).

S. ( 3 Ejtpans^M tUoke

The expaniloa lUxjke á lepreM&tcd by 3-»4 ia Fig.S.O. The buming gu«aforcé the piitos towaida botto m dtad centre. During tiiii «troke, botb inlet

and exhaust v)üvei remún closed [t«e F¡g.5.5(c]|. T hsi, power ii obtim cd only

during thii «troke. Both preíJiire and temperatnre dec re« e during expajuioa.


31/110

« Computer SImdtlion cf Cí Entiat Peocetta

S.S.4 Exlutiit strol x

The cxliiiast ilro le ti rtpreitnlcd by


32/110

i6 CoBpatu SlfliBUÜM e l « E «fU « Ptottuim

DispUc(m


33/110


34/110

(O Ccwpai u Slat¡iUoB oí Cí Eaila t FnctutM

CoBiidcnBf the pr octa S->4, w« Kkvc

, h - » )

-

(«.»

(6.5)

Rom


35/110


36/110

M Cea palt r SlatUÜoM ot Ct Pr

HtU »ad.

Thtrtíoi»,

aci *n>fk doa«,

tltcmiAl «fficUncy

L 0 0 4 x ( J « 7 . « - « ( » . i )

17S9.1 kJ/k i,

K̂ tnp +

1109.6 + 7ÍJ~4MJ>

1455.7 kJ/kj,

ty..i

lÍ M

U5S.7

J7J9.1

m tu t ffecüv* pr tMwrt o . f lS L íL ÍÍ )\ViuJ\ItTxJ\ 101305 J

14S8.7 101S2S X 6Í9.8 X 10“* 10» X itf* X — — — X

SS2.9

» I B .» b u .

2S7X300 101S25

ffotr, la (U« «z uip it, tk< cat>offntlo ¡f tmamúd w 4 which ú • iiUla tooUt(c . Hidm, th« «SciicBcy i( ooly SS.lX . NonnkUr, U wül b« b«hr Ma 2 u d

S. TliSi QliutraU* tkU Ihf cal-oS rU b b ako » de cidkf f tclor in a Dictclcycla.

Exercise

WríK » profru n to ilmaltU CI eaglat proccuc* u b | u ideal I>ies«l cycle.C«acn t« tki rM)iür«l daU »t


37/110

S 6Cemp ii l « Sím oUIfoo o f CTEaf be Pra cet ttt

Ftg.T.l Diticl t fclc al tuiiunlly aipiraltá eowíiltsn

Tkbla r. l Dttalbolthtciitiattortiinslaüoii

B Bore 80.0 Eun

S Stroke 110.0 mm L Conaectiai rod lengtb 2J0.0 mm

T Compreuioa ritió ie.5

Kiup DkpUcemeat voldine 552.9 cc

V kí. Volttiae it TDC 35.7 te

Vuc Voloine U BDC 68S.( ce

7.3 Nítura lly asplrated operalion

Miximum powcr of thc compríMioa-i fni lbu «afiní wM bt obtúned wl i t i i itU n a U fall lotd md tW» condilion, *n hivt,

Pi Pi P.

V,

imbitnt preMUrt

V w c

1 Um{My)

L«C Tt unbicnl ur Umperalsre uid

= ialil* mui/bld tempcritut;

Tkert wiD be no Umpcratara drop ú Iht icttlu m uifo ld u lliii foci Uúij

C¡ Enflat SlwaUtloa irltk Ad/t&il/c Combiulha 5T

T„ r .. (7.1)

Lh «i >o » ikEnt ccrtaía temu thit are lutd qoilc of ua in th« limaUtion.

Nao Iflomolt» oí »ir pío» fuel viponr ia a mu tgn coatiia iag1 kmol of fnd.

Npt küomolcj oí prodscU formtd from Ibe combu tioa of ffgto-küomolct of úr tUen In dariot tactioa.

kQomoIo of fucl iiijKttd.

tfx küamolet of retidokl uh ttu l from tk« previooi cycU lo tbecBfíae darías tba compmiioa itroke.

ffp kilomolci oí prodocU formed from ibe comboition of N, + Ni-i- Nt.

ipocific b«U of tir.

C ,f iptcifie b«it oí íuel.

A/F ili^foe] rttio.

7J.1 iMfltropk compftulon pro cai l-*2

U l M tonada tbe «ajía e cyele (rij.7 .1) » aí it irt from poiat l. InilUUy,we h»ve to «wi ne tbe vilnet oí N, u d Ti, bolh depead'mg on tbe prtviooicycle, wbkb !n tora, dependí oa tbe cyde before tbit, wid to on. To iltrtwithi let iti uiame

// , = 0 tad r j B r , ,

Pi V ^ RTy •

(7.2)

(7.J)

Al tbe be jian ún of t be comprt$iJon proee*$, there m mole* of tbe workiaf Raid.

Let Cf, be tbe coulint-preuurt beU e»p»c¡ty (kJ/kmol K} for tht re-ICtMt ff ̂+ A , .

Tbea tbe polytroplc índex for compresjíon [k


38/110

68 Conpoo]iUan«rCTS»/ia»Ffo«»*«

r . = T i r ^ - ‘ . (7.5)

pi = Pit^'i(7.6)

Vi = Vtd.. (7.7)

7 J J AdUbatk combuitloa ̂ oce w 2->3

Lcl iii uium e tbU tha comb ution pUc« uliibatic&Uy «J>d co ni tu l

preuore. S ínct Ihm is ao beU (r uuíer , tke cncrgy e« laffixt* r, f and p dcaoU Ike moles oí nactanU, fael *ad

t]i« prodacti of coabottioii.

Tka (o la lka oí c^.(7.S) wiU k« U kta np akortljr. By aolvútg ecn,Uf bi •q.(7.11). W* wiO «valaal* IhtM mok aomb en in Un ni of tbe actsalvaloe* hr U i « apaa aadar coajIdcxaUoo.

?or CI tnfia u aornally dleiel, C ieH », i* tbt fue) iu«d. Ecnc*, Iho

vitieu prodocU moUi trt m I u

• N ,- C O ; N t -C O t; AT*= K,; » O,.

L il Y Kprt wal m olu oí O j per mole oí CtoH j], thea the reactanl foel-air

mixture i*C,oHn + YO ,+3.7 f lYN j (7.12)

We bive

CI Eefüit Süoahtha n iti ÁdUbttíc CoabasUoD 60

í f » . - = 1 + 0 9 7 (7.1J)

(7.14)

= 17+ 3.70 y, füC 10.5 < y < 15.5

= 4JS + 4 .7 6 r , í o r Y ¿ l 6 .S

* From Tibie 2.3 in Cliipter 2, tbe valué of ¿Trp c u be oblaine d, whicb iido»« to -6,796,000 kJ/kfflot oí CioH » v»poiii.

Han tbe aote nnmbera and tbe vake of Qp r«q


39/110


40/110

6 3 C o m p o U r S i a a U l h a o í C t E e f h i t P t o c t M t

itroke (iq.(7J}|. A lhir4 cyclc c u foUow th« *«x>nd tjid to oa. The costpalk-üoat u t to b« halu d w bu »accc«*>ye cyclo prodnce Umcat tbc um e vtlac*.Gtatri lly , ibt co nvtriwc* b ^oi lc npkl .

Tibl* 7.3 fivcs lh« rottb* ai Uii compntuioa (wtlh (cmr decimai kcca-ncjrl] for thc cogin* dt*cjib«


41/110

1

1

M Compattr Slmttltiha o( CI EniUit Procttttt

T^blc T.s EffKt cl r oa m ioo j tuflni pins itUn(re«iltJ Iroia tli* conruted cycU)

Input eondlUonj tad pwdlcted rerolU

FVUJo»d open tioa CkemÍHUy «ar ect mixloreF\iel Ci oH u Spe«d 1500 rpmr , SOOK P j l » t m

FViclioa »J>d Ji«»l truufer ncglected

r 12.0000 14.0000 16.5000 18.0000 M.OOOO

TtT,TiTiTi

Pi?i Pt

K1K1

¡SI;k iitm]itmj«tmj

fe K

N J [N ,+ N ,}PlkW)

Pto.f [»»ml

-í.h \%\

321.12&8M2.025828I2.58S42127.7612im. l483

52.2125Í2.2125'.7.7«7'3.8U21.39741.2Í340.M12

10.2394M.621339.3949

317.7575907.39712B52.29962054.31931386.5930

39.975039.9750

7.45403.62941.39761.24310.9836

10.9807

15.67994^7958

314.S340960.03202397.66721981.39001347.9358

50.313950.31397.18813.44641J9771.24270.9858

n.722716.739346.3199

313.4828989.7369

2923.W0Í1944.90091328.5470

56.8301S6.Í3017.04763.3S491.39781.24250.9869

12.0982

17.275547.9S6Í

512.01701027.4467

2955.36161902.84731306.0485

6S.85M65A584

6.88853.24901.39781.24230.9981

12.540017.906550.0008

««mptntu re »nd with = 3.44. Howí w , H Buy b« noted th»t die»*l tniineinonnilíy^ opent « oa lein mixtorc* »nd rtrtly oa chemktJly correct mxtam.

Tht-importuit ftUarc fti eq.(7.41) ii the í« t »b»t Ihe coraprewton ntio,

prtnore, tmper^ urc imd mole ntio quintitin t1i»t apptir oa the rigKt-kud(ide «re iateiuivc paran cten; that U, the ilie of the eogine doet oot mflDcncethem.

Alí o, e«. Theie two factorsmay improve the fuej vaponiation when the futí i» injected.


42/110

08 Compal*/Sietíillei e/CZ Íi/U * Pa k w w

VTOC''ol

VBDC

Flg.r.S Th* ti Kéut -UUU loof /or an ti U u t H t K m tvpenhirgtr

Tb« p«titioa ct tic vilv« detcrmÍAet tke frtclioB ol the exhaast Sowtbkt puMU tkroa|h lb« tu bU t. Thtu, th« povcr ootpat oí Ui« tarbine !icoDUÓlUbU. TkU (cilurt ii aot avtlUbU b • {u x lm ta lapercbuier. la

gttiMlrivtn lapcrcbtrgtr, to codUoI tbe poixr mpot to tbe compreuor, t gt«r box would b« rt


43/110

10 Compattr SIiobIíUoii of C¡ Eaílnt Proctut*

Tib ie ?. { EíIkí of »ope/ti«x ii>f on Tirloiu enxim piruDíttn(|nr-dthftttli»rt«r)

laput coadlllooa md predicted reíult*

F\ül lotd operttion Chíinic illy corrt tl mixtureFtiel CioH jj Sptfd 1500 rpmr „ JOOK r 16.6

FHctioa and hent truufer neglMted

Pl 1.1000 1.2000l.SOOO 1.4000 1.6000

Ti K J09.2019 317.S242 325.9474 33J.63S9 340.9414Ti K M0.6609 964.3538 986.619» 1007.5700 1027.3920

Ti K 2902.6280 2920.9390 2938.9660 2956.8630 2973.8S40

Ti K 1966.3790 1970.3440 1974.9880 1980.2970 1985.5200

Ti K 1351.W70 1360.7770 13704310 1373.7920 1388.7940

T» K 1351.047S 1360.7ni 1370.3314 1379.7920 1388.7930

atm 65.2197 60.0797 64.9276 69.7813 74.5816

Pi atm 65.2167 60.0797 54.927669.7813 74.8816

P« atm 7.6170 7,9939 8.4M28.9292 9.3866

Pi 1.0000 1.0000 1.0000 1.00001.0000

p» 1.1000 1.2000 1.3000 1.40001.5000

re 3.S157 3.2546 3.2009 3.1534 3.1104

i . 1.3969 1.3960 1.3951 1.39431.3935

Jto 1.2«7 1.2425 1.2424 1.2422 1.2421

+ 1.0000 1.0000 1.0000 1.0000 1.0000

PlkWI 12.3116 13.0984 13.BM7 14.6195 15.3540

PI-^I latml 17.5B02 1B.7038 19.8009 20.8757 21.9246

niU 45.4824 45.5938 45.6939 45.7885 45.8660

íb power ontpat ii oetrly tke txme for tfce two lyitenu when tJl th« «xh»uitflowi throB|h the turbint,

Hovcvcr, ‘IVble 7.6 dou not reprcaecC t trae exunple of ui exhioit tar-biao lyttcra btíiu st it b u been calcnlittd on the uiumption of foU «xliíoi tSoir (broQgb tb< tnrbiae. Thtre it tbe ticit uium ptios tbat tbe raútu jce tbetorbíne offeri to gu flow cin b« kltered by »oroe meini, tbewby »lttriag pr«»-lure p( npstreant from tbe tnrbiae. la tbeory thix could be tccompUihcd bycKuigínt tbe blude lettiag; bowever, in prxctice tbii wouU be diEBcull to do.Wbtt cui be done t« {Uaitnted tn Fig.7.0. The exiiiuit control nlv e deter-minet tbe qntntity of exb«iut pi ul a; throsgh the tnrbiae, with tbe remimiosdlverted directty to the »tmo»phere.

U &[rutloa / of the exhiuut pis stt through the torbine, the equition for

turbine work oatput ü now given by

IVjatb = /AfpCpy (T s—T i) íjiu/b- (7.S1)

T.ble T.8

CI En flít SbavUtloa witk Ádltb tllc Combutloa T

EfKt of igptixhirxisi os nrioo i pu^m«t«n(ezlitait drlrta topcrchtrpr)

laput condit lona and predicted r «u lts

Pb U b» d operatioa Chenticilly corrtct mixtnrruel CjoH n Speed J600 rpmr „ JOO K r 18.6FVictian uid bett truufer oeilected

Pi 1.1000 1.2000 l.SOOO 1.4000 1.5000

Ti K 809.2019 317.8242325.9474 333.6359 340.9414n K 940.6669 964.3836 986.6198 1007.5700 I027J920

r . K 2902.6280 2920.9390 2938.9660 2956.8630 2973.8840r . K 1966.3790 1970.3440 1974.9880 1980.2970 1985.5200n K 1332.6730 132S.8850 1320.4380 1316.1500 1312.4820r . K 1351.0476 1390.7771 1370.3314 1379.7920 1388.7936

Pi |«m 55.2167 60.0797 64.9276 #9.7613 74.5816 Fi ¡átra 55.2167 60.0797 64.9276 69.7613 74.8816 PA ¡atm 7.8170 T.9939 8.4642 Í.9292 9J866 Pi 1.0255 1.0505 1.0749 1.0989 1.1225 P* 1.1000 1.2000 UOOO 1.4000 1.5000r< S.S157 3.2546 3.2009 3.1534 3.1104ir 1.3969 1.3960 1J951 1.3943 U935¿p 1.2427 L2425 1.2424 1.2422 1.2421

f f M + K ) 1.0000 1.0000 1.0000 1.0000 1.0000PjkW) 12.3796 13.2400 14.0866 14.9223 15.74J7Pu«f 1atm] 17.6775 18.9059 20.1149 21.3081 22.4812r;ib 45.7337 46.0864 46.4186 46.7369 47JM03

Then in eq.(7.49), for f wül tppew la th* dcnomlmtor of the Mcosdpart of the expreuioD, with > re«allu| In crtiM in p*. The a tl effect on powerü to detreiíe (Fi|.7.5), thtn by decreu laf lh« power outpnt.

Tbt (nd uiot of tbe futor, / n tb« ttkuUtloa* doet not preieat uycorapatUiontl diffcnlty, ralhtr th« probitm ii «Be of knonring how • reiltorbine opertte* U coajunctiott witb «o exhtnit control v*Ke, which c«n bepoiltioaed u we pleue. Tb t vtive for / ii Exed in iccordance with the reUtiveBow resbtince* o f the torblae u d tbe control valve, and we htve a probiemtn fluid tnechasiu dcUiag with divided flow.

Note that with increue in p», which wili occur with dccr ctsísg / valnes,not oniy will Wu,tf be reduced, but alio when earricd to the poiot wherc pi exce^dj pi, the islike maoifold preasure, the eaglne will no looger Kiveagemid ua] exhaujt gaie* completely. One of the deiírabU featurei of tapet-charged engiaei ii thea loat. AU thii meas i that the tarblne mait be matchedlo tbe enginei and, to aoWe the proWem properly, power ca)culatioat requlrt a


44/110

73 C o api l4i Sim»¡*tion oí Ct S ttlat Procttttt

d et 4ÍJewut control Tahre

l e o m c l r y .

Exerdse

1. O tvclop » comtiaUr progm a to «tmnUu u C1 «a fb t U ntionU)' u{4>r«Ud u d fop rnliu fed condilioM. D «v(] ^ »ho Üw po*ligni£cuit effect oa tbe ptiformicce oí tbe eagiae.

Figure 8.L computa tbe meua red u d cikoU ted power autpat for >.•Ingle cylmder reciprocttiag eogine ntto nUy uplr^ted conditio oi kt fallload. It ii ues tb it peak power occo n troond ISOO rpm. [f IdeiJ Cyd«SimolitioB (ICS) ú cm ied ontwitb idübatie combiutioD for tbe «uaa eagine,

the oatput versus ipeed plot wül be u tliova m Pis.R.l, » itriigbt Une puiio gtbrougb tbc origm.

Oor imiaedute concera U not wUb tbe dtfference in valcej between thetwo curves; tbe c&kulaled p«wer u expected to excecd the meunred perfor-mmce . The ib»pe of tbe weunred p we r curve i< tbe feature of int«re«l. AU natortliy' upl rtle d engines exbibit a. power peak witb retpect to ipet d.Henee, it is cleu tb»t adiib itic combaition utl yt ii miut be tr.odiSed b &

, lúttbls wiy to u bkv e clo»er tpproxiinatioo in order to itudy tbe bebkviouroí actual eagins.

Witbin tbe metbod» and tactic» of tbermodynamícj, modification* can beattempted in tbe foUowing tbree pr«^t*ítt»:

[i) tbe combuition proceUi

(ü) tbe g u Mcbaoge proceu , and

(iii) the beat trmfer proceM.

We wilt ttJie up the firat modification in thÍ9 cbapter and will ca li it

prcgreuive combiution limulatios (PCS),


45/110

í

k

í

74 Cooputtf Simal»!»!! oíC I Ent/o«

Spad(tpm)

Plg.8.1 PouK r e ulp vt n tpet J « / an C¡ tnp'íie

CotnbtulioD ¡At a actax] compreulon-ignition engise a nol iiu Unt uieo u.

The injeclloa itaxU well befort TOC uid combulion dependí oq muy fae

tón, ihc promintnl oaei btln*

(») the iraount oí fuel injected

(b) deUy period

(c) the togise ipeed,

(d) the injeclor locUíon,

(e) combiutiott ckimber lUe ind geometry.

Thennodyaunk* laggetU í wty lo deil wUh tombo»liott that proceed» Utome Sttile r»t«, dthongh it «hedí no üght whiUoevtr on the centnl quatioAoí the rite itietf. ProgreMÍve combtutíon u whit we »« joi nj to diíCttít ift

thú chapter.In order to calcsUtc the net wol-k done by the |u«« btlween the il»rt

of ignition uid (he end o( combiution, iuUUUy, we hrre to deSne thete twoevenl* in the cycle in iddilion to the p-V Irtce dnring


46/110

TO Compattt SlmaUtlot ol Ct Eaflai Pracatc*

N o n ' w « c u e xu n i n c the t im e n t4 oí biunini, rcprtMotcd by the r&tiodnjdt , wrítlni th« qnotúnt in tkc (oQowiot fornu

dv d> adt

(í.


47/110

.....

I

78 Cc api Ui Simtli-tioa o f Cl Enih* Procetset

Once ihe bnniiüg r»U rtaclíc* the raiximnm allowibk, In pUce of «¡.(3.7)

An -w t A

At (8.8)

for »U üttbMqacnt ¡ncr«menti in lime. Tbí íiit«;ratioa ú completed (j.e. com-

baittoD tj complete*]] wkeB

X ;A n = 1 (Í.9)

4fld the work of expiniion ú ctkulai«il from

where the lomnutioD ippliei for the «ntire combnjtion pnxeu, and Tj b thetcmper&ture *t the tnil of combo ition.

Figure 8.3 iliiutntei how the prtuure-volume trice of the CI engbe cytk¡1 iltered when (he mudimim «Uowable boming nt e í i reached. When themudma m »Uow»ble bumln| nt e ñ Urge, i»jr 450 it i> readhed, ia thi»cue, jojt befóte the end of combiutlon; whereu a rate of 500 allowablcboraing rate b reached early in (he combuition proceu, foUowed by i ih updecreaie in preuore and in power OQtpnt.

60

50

.4 0

| 3 0i?E0.20

CRsIÓJ

SpeedsISOOipni

,1-----3001/i ydn p-661.45 ct

TM-300K

RAF«U

' Ctsmbuttion poHx) ioijjcucd

b)f w IkI Uo c s

0.2 0.4 0.6 0.8 1 1.2

C¡ Eofls* SímalilJoa trlli PnfrtttlrÉ Cbo&utfoa T

Figure 8.4(a) ii aaother «ray of lookiag at tho lame caknlaCiatuInjection and combiution begúu at TDC. At (ha maxúnnm tUoirable bom iairate increaae*, ít !i reached latcr and tater m (he combatlioo procet*; tk« total cranluhaft «pan nta tion for combnation decr


48/110

BO Com j» Ur SlmaUtiaa o/ C l PiocMu*

Fi{ur« S.5 illiutrUtft jnrt bow dnjtktUy th« prenare-voliunt Utct oí thacyck c«n ciita(« u Ib* lUxt oí th» mjc«tioo is du aft d. WUli Miiy !nJ«ctioa,10* bUoR TDC, Uer« ú » n U lts tiil |ua is po «cr boC U (he expense of utqoUiy laUtuitúI iacTC«M ia p«>i prtuorc. On tJU oUitr hud, b)' deUjÍJifUjcctioo ttnin 10* kiUr TOC. puk preuurc ii redacté cooiUtrib))', bat toalto U p«wcr. H t «karp cb ug u ia tl i « combojtiaa corvo vi th 10* l>«for«TDC , u d TDC iaJactliMi, iadic«U tbat (be mm lmam alWftbIe bo rniaf r»t«

hu bees reicbed.

70

¿O

JO

e < o

§ ■

r20

10

)O

Coatatk» peiMlaJeaioabctiasM lOCbTDC

\j^úodbe» l í i «TOC

[ajcojos bcfiiu tt l(T *TOC

CR-IUSjxola UOOî av£ipaMI.45CCm - X O K RAF-W

- - - - - - - - - -0.4 0.6

V_OJ 1 u

f Í2.8.( Pniiurt-toUmc tracci Jor Ihnt i njutí et timioft

U^oriunitity, thennodyskmíu doe* not proride nt wi(b (be «mxUett

(bred of iaícroution t«(wdiag probable vaiuu /or (be mudmum b&roúg rate.Lu(«a d, wt m u t (orn to wbttever cxpertmentil erideace may be availabte.Tbe potat of útr odacisc (be ootioa of • maximam allowable btm is f rat«b u bees to dtm onjlrste 'tbat U caa «xerl a aifnificant ioSneiice oa CI engiaeperformance. Of cootm, tbt notion of *one* maximnm boniing rate k «a*doabledly an ovenimpCficalion. It b more Iban liU y tbat Uj va]a« cban fciu combusltos proceed«, rtfiecting Ibe d co ta u in Bomben of avsilable oxyges

molecolei. lí Itiii k lt« « - tbat rnuámoiik buruAf nt« de o«u «f in vilue ucombiutioa proUtdi - tbca the tSect oa power, uy, nhich ma lu whea themaúniun bo m k i rat« i* itacbed^ wiU be more pronouiced tbas b ng gat edin F i(i .j J and t.4. Note tbat tbe isaxiaiun bsialag rat« i* aot likely to bercaebed ia eUfioca openting at ,nód*nt« ip«ed *or ia engiacj operatiug witbwaal! futí Sow /jo tbat (be dontiou of con ¿ail ioa b ibort, to bcgin witb.

Cí BafiaM Simsiilfoa witk P/ogrt(tirt Ooobul/a n 81

Aj » final commcnt, note tbat it ¡J not ne« eu uy to ertKaea of anbnraed carbón, indlcating tbat tbe esgine tnay beoperating at the Umit of maximnis boming rate or at the Umit of avaüableoxygen, or botb.

8.3 Combustión moddling

In tbe prevíoui lection we deaii witb progrcuive Datare of combnjtion.Some general obiervation* abont modeli of cugine proceue* provide a contextfor tbe detaili tbat foliow. In cnginea, the proceues tbemielvei are extremetycomplex. Wb ik mncb it Icnown about tbeae proceaaet, tbey are not adeqaatelyunderatood at a fandameatal kvcL At pretent, it is not pouib le to con itructmodeli tbat predict engine operation (rom the bu ic goreming eqaatio u alone.Th u, the objectivei of any modd development «ffort iboold be cleirly defined,and tht ttructnre and tbe detaied coatent of tbe m odd ibonld be appropriateto tbe«e objectivei. It it impractvcal to conit mct modeti tbat attempt todescribe all important atpects of cjg bc operation. Henee, limited objectívcsaze appropriate.

Dae to tbe complexity of engine processes and our inadeqaate onder-stu din g at a fundamental level, most engine modeli are incoroplete. Emplri-cal reUtions and ad boc approxlmationi are often needed to btidge gapi in ourundenta adlng of critical pbenomena. SInce nod els wül continne lo developover a period witb greater eompUtenesj, the erapbatit Ln this cbapter ii oathe batic relatiooships oied in engine proceu modeb ratber Iban tbe currentilatus of tbese modeb,

Tbe progre«ive combustioa model we have di»cussed in the prevíous tec-tion b a littie over^iimplified. In tbe modem ilm ulalion techniques, vaxiousmodeb like tero-, one-, two- and multi- loae/dimetuional modeb are beingatlempted.

Fot the procesies that govem eagine performance and emistions, twobatic types of modeb bave been developed. Tbe te can be cit ego rbe d astbermodyiiamJc or fluid 4ynunJc in nature, depending on whether theequatioM wbich give the model it« predomiuant ttnictur e u « based oa en-

ergy conservation or on a íuU analyib of the Soid m otion. Other labeb gtvento thermodynainic energy-cooservatioa-based mode b are: tcro>dimenxiona](lince in the absence of any flow modeliag, geometric featuret of tbe fluid mo-tion canoot be predicted], phenomenokigictl (tince additional detall beyondthe energy conservation eqaations b added for eacb phenomenon in tum ), andquasi.dimcasioaal (where tpecific geomctric featurei, e.g., the «pu l'ign itlon


49/110

...

)

)

)

8 } CompBlw SlmoiilioB of CI En fkc Pn>ce**u

Bu ne o r i h e d i a t l fuel » p r i / t h t p t t , ue idded lo the b i«c thenaodynunic

ipproick). Fluid -dynuiúe-bued roodel» u t o fun ctlkd mnl lHÜni íni ioD» !

raodeli due to llicir inherínt ibüity lo pmride delwkd feom rtñc iafonnUion

Ott the flow field, b« «d on loIatloD of tlie joYeram* flow eqnakH u.

rin»Uy, »n importmt tune is «a u y ovtrUl tní ino nwdtl b i l ince ¡a

compltjQty ind deti í ) u no sp t th» proctn lub-inodeU. A m odd U no more

nwurUe thia iU weakut Uni . Thiu, cr i l i ct l phenom eoi i l ioold b« dtícri lxd

i l com p»r»bl í leveh of fop lBl ic i l i jn U> »cUíve better retal t».

8.4 ZeicMÍlmenslonal combus tión model

In thU MClion w« will dUcuu Ifct ieri>-dimenjioDtl modcl. Tht loítwwecorretponding to both progmitví combaítioa *i well m lero-dúnemioiiilmodeú k»ye btta incorporated In ike eompoUr progwa (ivta is ibt Aj>-pcndix . In th« lero -dimciuioBU modcl we klx> tale into accoanC tli< ifnition

dcUy.Tlii» model b b« ed oo tbe £nl Uw of ihemod yBumc», The •tiitíni

potnl of íbe ihermodynimlc cüctilUloa u tboten it the inítint ti whkí tbe

InUl nlv e clotei,

The «aeriy cquuioa for the clowd cyde period cía be writtea u

(


50/110

t i CoiapuUt SlauUtlon of CI BAfint Pn cttta

Bolii u d (B.tT) irc BOB-dimeasioiullic4 eq ot tb u. Eqaatioa y úulu itcrwtk u| t« U tke tt»rt of combniCioa

kbiucloa. WUb« uxtm ed Ssws ^ O.KQ «ad, henee, a «= 9.90S.

U ii tb« puuntter cbu^teríitag (be r*tt ol combiution. Tbe«nuU vkluu for m roeisi » hi(b rale »t tbe be{inmn{ ot conv-biution, wbile lirgt valuu of m meuu » U(b r»t« by tba ead of

comboitioD.The ploU of tbe fuactioa x u d a fl-BO) for Mv«r«l

valoe* ofm tst ihowu la Ftgf.8.6 «ad S,7.

m

Fig.t.B N u t nl cé ie u « /« b c’ ío » o / nlaíiet duntien o f comitulion

Tb« bcU releue nU dtp cndt npoa over&U equivalenee rfttio. Kaowmglb« fuel-air ralio, w« c u fix (be miH o( »ir «dmitted. It ibould be &o(«d(b»( Ibt »bove modil e«niio( (»k« cut of premüed tad diínsive combutioo.

(0-fl ,)/A9

Fig.S.T Heal nieat t nl t


51/110

....

1

86 Ccmptttr SlaalUha a[ CI Eaflat PrvctM f

Tliú ú the ditxicUn itic oí iKe diatl eogioe wlúcb eonld not be prtdictedby Ibe Fbel Oyele Súnolitioa (FCS). Il » fr*tífym | l on ok tkU »1>* pre


52/110

88 Caapaltr Slatlitioa oí C! Eafbii Ptxtctutt

dM

. . . i . . . P-

)

wbere Ap u the púton area and dy tt poúttve as ihowo ia Fig.9.1.

During túne dt, let lorae air dŜ mole* enler the control volume bringingio eneigy givea by

Kd N, (y.+Pow.)


53/110

90 ’ CoBjpotaf Súnul»tío« of CTEoflaf P ro« «t«

E>{uition (9.2) couU htvt hto|h tii»loiJ j'it i, mertly by ncxing thaC tfae gu tb it remúiu iniid e the cyllodcr luder-

jíx a *a «d ub itic , rerír aiblí e bu ge ol «lite; wiethqf tht diuit< l i cutMd bypiiU>a mation or by fu flcrwo r by »ome combisUion of tbc two u im mitcm LSince we wüh io [oUotr ennlt u tb* putos uiove», we wtíu ttrok


54/110

g3 CcmptUt Siathiloa •( a SMfU* Procmtm

M OTuUppUf oí ikt vtjvu, thea txhiuil valir woold ]i*ve jiut clotedU TO C, umI u lh« pútoa movei, tk* inttic vxlve will btfln to op«A. TbUvoUmt iacrtkM wUl ct«M k redoctioa la tiie preusn m (kt workinf ip&c«,u il U tkc u m « time, *x^4U»t |*« wUl low bwik Uto tkc intiJM muüf otd,d'MpUcíni Ihc (rcib air. T bá b ¡deniified is fig .9.2 u Región I. Tbe oatwardEow ot citliuul vUi coalinn* ontil p u rcduced to p .. Wilb (urtlier píslonisoli oa, p wiU f«U bcknr u> tbe intaJie rouúíold wül rctuni to tbc cyl úder, u

cTÍdeat tn Refioa IL

iVeib atr will aot begia to CDlcr the cyliodtr notil tU Ihc exba.uit hu betaRliuned to tbe workisf iput . It ú ntttuuy to idea'.ify tbe iastut wbcnU = Mxit to get thc co m ct reiult from timulUioa. T bu coadttioa mwk* theitart of £tmK air flow ¡ato tb« cyiíadcr. Tbe paipOM ot t detiíled trtUmcatot thc ¡Btak* itnik* k, Cor tbc ue on tc eompatUion of tbe mau o f (rcih airic tba eafiat at Ib* itart of tbc compreuioB proccM; aad tbis ii «cbievtd byIviun iaj ap ib t «ouU amosaU of írcth air, ¿Af, tb ai flotr ia duríog


55/110

Oi‘ Coiupatt/S/fflTx/*tíofl of CT

Flg.0.3 fío» chart for inteíntion of ci¡t.(9.3) and fS.Sj [ite ti¡.(9.Il)}

However, »orae forra of control mtut overiM the inUgrition, A nnifonn Ae kC «»th lUp miy le»d to A P vilae» lh»t rtduce cyllnder pr wn re b«lowpo dming th« eihnut procea», or «bove Pm duriog the inlike procm.

On the other hind, with i fixtd AP vilue. MC«wiv«ljr Urge Ai vJuet

jn»jr rcíull ¡o over»IiootÍDg the ümiti oí puton tnvel .The tcheme describid »bove wUl work lUiifictorily for the «ntire exhiuit

(troke, u>d for th it portk>& of the inttlie itro lu identified u Repo n III inFig.9.2. Bul it m»y not work doring the eirly per iod of the intake itroke,bec&tue if we lúnlt pretiore cJiuigei to

Apmt.P - P o

p cinnot drop below po or, in other wordi, we íuinot uie the relitioa

Po - Po

m

for the inttke itroke untUpbecomeskH lhxn P e Once TDC á re»died on the(jchiust Itroke, the proctdtire ii to decreue p repestedly by emtU, pr«itríbí¿

OI 5iü)a/At/ofi trítb G ms EkcJiájige Pioc ets O

unountj, ttíiai ef, m ------------- ---------------- .PoK)t.|.

(9.15)

(9.18)

In order to carry out cycle cakalationi that incorpórate detaüi ofth e g uexchange procesi, it b oeceuary to ipecify the variatlon of the effectiye ralreare» A, that appean in eq».(9.7 ) and (9.B) u a function of the crank angle.Thii vahre aro» calcolation dependí opon the engine geometry and ihould beipeciGed by the reader.


56/110


57/110

)

J

98 Compíl ff SlmoíitJoii of Cí £oi ¡«e PrwroM»

T»b1e 9.1 Eff«t of v»1yo »«» . on powtr ind Yotaia«lric clEcknqr[for tht (le««l by cq.(O.I9])

Spetd :Cem¿ur :

1500 rpm50*

r :Start of injection :

18.Í RAF 15J*

: 1.5

x « / Ti N .. Power Ala (K) «I» Nu, + N. (kW)

>7tk

2,0/2.0 3«.530 «5.116 0.980 3.918 28.882

2.6/2.S 312.099 90.771 0.9S2 4.586 31.458

3.0/2.5 311.440 0O.8S3 O.9S0 4.635 31.744S.0/3.0 299.173 94.008 0.950 4.912 32.413J.$/3.S 289.797 96.612 0.949 6.145 32.938

i.O/i.O 279.816 99. M5 0.943 5.347 53.220

Fipire 9.S ihoiri tliít i( 1500 rpm, witk / ( „ *> /iu =*


58/110

100 CompaUr SlaalíUoB et Cl Eat¡»*

TibU 9.3 iUiulrtU* Ihe tfftct ofen jint »p t«d on ihe powtr Mtpo t. Il e»ab« ob«


59/110

720

Flg.9.7 A iypkii *a/ct-íímítij ¿ía;rotn/or a CI «nji'ne

T«ble 9A Effect of nlve-linúsg on povrer »t ml oo i

r : 16.5 Aft/Ain : S.0/2.5cm* EVC : 554* RA F : 1.5

ASc : 60* Start of injection : 153* IVO : 527“

EVO/IVC Spted (rpm)

(deg) 1200 ISOO 1800 2100 2300

Power (kW)

360/720 3.326 S.926 Í.120 4.149 3,963SÍO/735 3.632 4.288 -«.622 4.727 4.77ÍS


60/110

10< Compou/ 5I»iil*lí»» oí Cl Enjliit FtOiMut

TibU •.» Eftcl of nhr*-Ual>( oa p o w « d roluDiUk «aScUncy(.p««l - tSOOip s]

r t UJ Á..lÁi^ : 9.0/J.6 cm» i: i'C ; SS4* ; 1J A f, : SO* Sti rt oí ia jtcltoB : >U* ÍVO : S27* Sp« «a : ISOO tpta

BriJc* power (kW) t ad Volmacuic cScka cy (^ }

EVO (def)

(* Ifurr» U bcMkcu


61/110

100 Compul í f Slnioi«lfon ofCI Enfim Procatet

T» ble 9 .5 V»ri»tion oí ip»cillc powet wUh €i¡jin« tlj«

(|com«trlc»U)r tlmlUr tritw««)

Coniv- •'Ion r*tio

CRLStrolcefor exhitut vjve

16.52.875 borí1.375 bore¿2 /W = 3.5/M.O

Rá F Sptíd

132200 rpm

m - ^0.05S

for blet vibre ; a. 02 = 2.5/64.0 = 0.039

Bore

(mm)

AnIMa

(cm’ )

Bnke

Power (kW)

A#c

(CA)

^tol

( « )

r ,

(K) A'^ + Wx

40 1.00/0.7S 0,862 25.00 95.559 0.948 288.950

60 2.00/1.50 2.645 37.50 89.724 0.953 312.377

80 J.EO/2.50 5.241 50,00' 78.316 0.984 359.4Í6

100 5.50/4.00 8.775 62.50 70.850 0.980 388.245

120 8,00/6.75 11.683 75.00 60.006 0.982 397.879

UO 11.00/7.7S 11.171 87.50 60.683 0.983 401 j0«3

Sltrt of injíction - (tic = 153*)

T«bl« ».fl M «t oí »]r-fael ntio od p6«wr[fot Ihe «Bglnn ducribod by «q.(9.19), O 1500 rpm)

ComprcMÍoa ratio

Stirt of bjeclion

5 16.6 Speed : 1500 rpm

RAF Y Bnke

Power (kW)

Illh L h

1.06 16.5 4.118 28.265 61.57

1.13 17.5 6,001 31.344 65.17

1.19 18.5 5.714 31.133 58.69

1.26 19.5 5.312 30.623 63,07

1.32 20.5 4.996 30.177 66.96

1.50 23.6 4.121 28.277 78.67

9.3 Kea t transfer process

H »t truufer ú t muit m !C « oginn to miúitún cylinder wtlli, cxlináer heidiand píitoa fice> tt •Je optniting Umperttn m. HeU ii trutrerred from orto the worklng finid during evíry p»rt of í»ch cyde, ind th« ntt work done

C¡ Ea¡ln» Slwaltlloa wilh Cu Emhutfe Procat 107

by tbe worlÍD| flaid in one complete cycle It (ivcn by

wbcre Ap ú the prcn on chtnge tniüle tbc cytiadcr u t rc fotl of pUton motion,combutioa , lo v b to or oat of tbe cylúider lod bt»( truiifer.

The preusrt cbutge áp dae to heat trájufcr it fiven by

P MC,T.

where A, 8 heit trinifer coefScicot, A B bterior mrf»e» trtt of eogise volume,T. “ bterior intfue lemperttiire,U m m uí of workmg fluid,c. X2 workbg Buid ipeclEc beU,T XI workiag fluid temperature.

The Duls problem with c kncnni aboat the |u motloD íoiidej itb common to s u lome empirical fomo lie for CAkalatinf K,. Tbe fortnalic oí( i ) Alhle y-Cun pbell, (ü) Sitkei ud RuiuntUb, (üi) Haheobeiti (ir) Pflkamu d (v) AnAud irt widely aied.

(I) Aihley-Campbcll cquatlon

kJ/i K. (9.24)

where B

PT

Z

cytiiider bore ia m,

cyliader pre»jure in ttm,worktnj Suid temperituie in K,worklng íuid velocity tn m/f.

(II) Sltkel tnd Rjunaoal&b e^uatloD

0.0< (1 + i) Kc»J/m»h*C. (9.24)

where b O- 0.03 fpr He»»elin»n-lypt direetion combuilion chunbeO.OS - 0.10 for piiton chunbe x,0.1$ - 0.25 for iwirl chunber,0.25 - 0.35 for precoinbuilioa chunber,gu prtuure b tlm,


62/110

....t....

103 Compuiw SlmaUtlat « lC ¡ Etf lu* F/aMM»

Cm * m


63/110

l i o Compvttr SimB/ífJbt ’í’dj/ii í Pe oc

wbcre np, - -i-mber oCrinji.

(¡ii) MEP »b »o rM ü>frictioQ dae lo pUton and riagi

whtre P,i » p’utoD lUrt-leaftli (mm).

(ív) BJow-by lo9» fatp* ~ V'P» ~ Pliaí

0.121r‘' ‘ - (0.03« + 0.00105Sr) x j

whert // = «peíd ia rpm.

(v) MEP loít in ovucoming inlet « d itroUling I o « «Pr

2.7S+ Pioif

♦ rhew p, =


64/110


65/110

n i Conjpu(«/SímufitioB ofCJ Eoí/ü* Proce»»*»

Í3 x>

a

X»

CR0 I6-5Spoedo iSOOrpraníniS

* EKpenmáu]

- ~ Tworonc---- , Single ytfie

130 140 ¡50 160 170 ISO

Inj’cclion tíming (dcg CA)

Flg.9.9 Ef f tc t of {n j cct io tí tíming on iroAí mean c^íclí*e ffíMiirt

9.1 0 Brake thermat effidency

Fijure 9.10 ih ow» the effect of injíCtloB timiag on brike ihermil elEcieney. Itu ttta Ihil mudnwm br i^ ihe m il efBcitncy occan ilm dv d injectiontirain*, vu. 153*. On «iOjer ikie of tb« tt uia ira injettion timinj (i.t., ±20*)the thtTroU «ffick ncy fiUj. Al c» a b« « etn, th« two-Jone tnodct prtdicta ihew u ti on bttte r cotnpwred to the lero- dime uioa al modcL Pnrther refinemtnt*

io ttie combtutioa model b a moit for bcíter predktioiu.

^ 3 4

^ 3 205 30’ü£ 2 8

1 2 6

I 24O

m 20

CK-16ÍSpccr(ncnul— -----------Twoione----- , Single ywt

130 140 150 160 170 180

Injection üming (dcg C A)

Plg.9.10 ESc


66/110

9.13 EtTect oí ipeed on paío íma nce

Figur» 9.U lh« viiUtion oí p«*k príMure wUh ra pe ct to iajectioatimini. It b «Mil tliil the two-»one model prédieti the det»fl» belU r th u thíxcTO-


67/110

l i s Coo)p»(«rSliaEUt»a OÍCÍ £«xla* FrocíM*»

Tbc m ole it t&c unosat af a «obituice of i $yitem tbit conlaiiu u mu ytUm«cíSed and tEey roty be atoms, moUcolu, tkcCroa*, otbtf {>articlet, or ipecíEed |Toup« o( incb parikies.

In th« SI sait lytUm, tbe mole repUeti the pa n mole ((m ol).

The nQmVer of estitie* in a mote ii 6.022 x 10 ^, whkh k alio known u

A vo fu bo ’l co oi tu t.

1 Biol of 0 } hti a mau of 32 g,

1 mol of H} hu a muí of 2 g,

1 mol of K} hii a mau of 28 (,

1 mol of O hai a mau of ISg, etc.

The £ n ( three are known aa moleco lir wei{hU and the laat U known u

atórale weight.

The íntcrnal enerty, u, and enthalpy, h, are rtlated by

For ideal (aaei, we can alio wríte

ti + pV.

u + JtT.

lA.l)

(X.2)

Inlernal eoerf y u d enthalpy are deGned by

du =• C,tlT,

dh «

C , -C . = R.

The ratio of the «pecific heata t« deiipiated by k, given by

‘ =I-

(/l.S)

(^4 )

The heat capacitita Cp and C, ar« weak fonctloni of pretisre but itrongfuoctioni of temperatore. The valuea of C, are tabnlated tn Table C.2. Theinperacript * m ein i that the valuea are for 1 atra pre uiu t. l^b le C.S gWeicoeScienta to calcúlale C,, for gaao normally eneoontered in internal cora-boilioD engine calculitlobj. The expreuíon ii of (he fonn

C, « a + i r ( k J / k m o l K )

and b vaüd for the temperature rangc 298 < 7 < 900 K.

AppiadlxA 110

Internal energy and enthalpy are itroag fonctiont of temperatore:

u ( r) - r c . j T + u i T o ) , ( A.e) Jr ,

M r ) - r C,dT + x>{To) + RTo. (X.7) J t ,

The temperatore Ti and u{7o) or /i(7o) may b* aaiigned arbitraríly.

Entropy ú a more compUeated function and ii derived from the Ent law,

T ‘

which c*B tikc aajr ene of tke íoUowídj Ihrte forma (for pV m /JT);

it

dt

C .- 5T + A - ,

' T p ’

V p

(>1.*)

Inlrodocbi a function ^(T) deGned by

(/1.9)

the entropy diferente between two itatea 1 and 2 can be writteB u

•2-> i “ ^ ( r , ) - ^ ( r , ) - / í b > {A.10)

The Ubalated valaca o( ^(T) are Uited in Table C.S (lee Appendlx C).Since k |e


68/110

130 Cowfattr SlmaUth» elC l Saglet Pn rmtm

la k mixtar« of fWM, «Ub »,• 4uoUa| Ü>« mole aambcr ot gu Uie

loUl moU B«mb«r íf i* fiv » by

N -

laUrnU w«riy U, tsUiUpy JET, isd tslio py ^ of » mUtni* w«obtuatd bf uldiof tkt cOBtdbatioiu bom «ick coulUacst |u:

Ápptadlx A 131

y ( r ) -

B[T) -

SÍPiT) * X^N ííÍWiT),

nhttt tbi partía! pm m « ft b

(A.12)

fi

P

’ ÜLe

E « -

(>(.«)

Tk* iBUraal «Bwor, «atbalpy »m í «oUopjr o í • mtxtwrt p(.J5)

* (p i31 « . 53» . »


69/110

1J3 CcapiiUr SímiUtha otC í E at lf Peocoff*

The »ppnudm»tí chuicltr oí tq.(A.22) c»a bo obMTved by notinf tbitur hu k lirger i vilse tbui botb O] tuá N j.

Aii- coaiit U ot BÍtrogeD, oxyf en tad tmtU unoiuiU of tcverkl other |u«t .Fot CDtmecnni cücnUlioa», the lilUr m«y b« ¡2nort


70/110

l l l ComptUt SimtUth» tf ct E a^ t Pto cttf

Newtoft-fiaphion kertüon lechnique

tr u cf y o f tbit Ucratioa tcud« »t Tj , t a i bjf dcfialiúa lh« «lopc U 7i U

wWdi cm b« íoWed íor T» lo gívt

Ta =

( T i - r , ) *( f l j )

T , - [BA )

wbicli U kntwn u tbc rtcontoa tqaition for Tj; & IxlUr «ppradnution t»tk* Miatioo i h u T| MB bt compn(«d firom Ti. By itp«at«d tppUeUion of

toh lloa UA b« »ppñneli«d u cloMly u we dtiire.

PCD

OT2 TI

ff tv to n- It a fl u o» íU nH on

^ a («aerU rale, Vke Newtoa-lUphioa iUnlio a eoavtrga more npidfyIbui tbc otber ac lb c^ . But w« ne«d to know more tboat the cbiracUr ol

U ordcr to um tbe Newioo-IUphwo hcrstioa sñtb utnrad incctf i. Forooe tbiai, f lT } mw t U difiiutAtUbl*. Tbii b Mldom 4 probkm.

Figtitt B^ illiulnXt* lb« lott of probtemi wbkh may wím; bowiver,*^


71/110

136 CompBUJ-S/aufitfoii oíCl EsíÍdi Ptocattt

lurb in Fi*.B.2(»), where llit cnrrUurt ii toncive downw*nü. Ü we rt»rt UB, hr eu ap k, (ie t iopc U th*t poiot miy be tadt m lo c*hk the tuiftat lo íc(cnccl (omrwbert oa tbe scgUrrt T-ax». U i (̂T] conu lu k>{(7 ,̂ uü tbe CMC oí tí, h u d ^ foiictiou, the pro{run »kodd ibort. Tbli c u bt«voided by atartúf «t A , u d (be «ohtioD «hostd be «pproaclied from bttow.Sincc the tbcnnodynuníc ronctio&i are compvted wUb cxprtuiooi IbU uenot viltd betow 400 K or ibove 8000 K, T viluei osUide theM túniu mutbe kvoided. (ActuaU)’, tbe U|lf te»p erUQ re limít ti »eldom » re tí probWm.)Figure B.3 Acmt í fiow cbu t for the NewloD- Ripkto a iteration. The ñcnrcbirt is immjed to ctrrf tbe ctkuUtbni to a »olatioa for «ny Ta, providedit ú gnate r tb u 400 K, by fyitem»tic»Uy rtdada| T by DELT sutil (bertcnnion exprtuíon prodacet ui tcceptkble vtlae.

But tbere ire circimutuice* nodcr wkicb the flow chvt ia Fi^-BJ wíHnot coaverje. Thii m»y otenr ¡f tbe derivitive f (T ] dt>«* nol bcreue oc dem tM oni/onniy wd coBtmnouily with 7. When (hli condition ii not met, F[T), irhiJe inono(oajc, cu y be S-ihaped. la thu ctte, lome cualpsiitiooiux rtíjaired to di»cover »a isitii l T vilue thit wlU faariatee coaverjence.

Appendix C

Aígebfalc expresslons for thefmodynamlc functlons

For huid caicüUtioiif, the labsUted valae* of Cf, tbe conitut-preunr* htiitcapaclty, h, the eothalpy, the tem pen tore portion of entropy aod K ,, thereaction coMta st, are adeqvtte. Por compaler pro{rami, a ljcb nk expre*-lioiit are re


72/110

' D i b i * C . 1 Co«ffieS*aU f o t c t k s U t l o n a « í t l i « m e t l o B e o s a U a b K , t l M • q m k t l e a

X , - «* p [ i + ( * + j ; ) la (r ) + á ] f»n


73/110

ST ^ 55 £ S S S 2^ SZ. SZ. ^ ÍE

TkU« C.S E»pr««*km» for tb» *p*clSc he»t cf k'm* »b


74/110

IeE

I8-

TkbU C.S «i e j ^ K alMolau «atra^ tí 1 tím (kj kmol“ * K~*) fcr fSMi-

• c o . CO, H ü> H ,0 N N» NO 0 0 , OH208.10 187^10 213.840 114X11 13a590 188.720 153.195 191.490 210.820 180.954 205ÍM0 183.830500.00 213 j0«O 234.780 126.357 145.840 208.480 183.941 208.830 220.140 172.091 220.810 198.980

lOOOXK) 2S4.7W 289.181 139.784 188.122 232.708 178.348 228J)8e 248.404 188.883 243J0S 219.822I SOOJOO 24 ». v n 292.098 148.192 178.752 250.491 188.778 241.778 282.579 195.147 257.997 232.494 .2000.00 m . 9 6 7 S09.2S8 154.172 188.327 284.433 192.758 251.978 273.018 201.140 288.68S 242.2353C00.00 2«7.125

322.*48 168.810 198.151 275.907 197.399 280.083 281.28$ 205.789 277J38 250.1373000.00 2TS.«74 334.334 182.800 202.797 285.825 201.208 288.805 288.084 209.597 284.427 S58.794asoo.00 2T9.«3« 344.098 185.804 208.591 294.032 204.459 272.545 293.898 212.835 290.855 282.5524000.00 2M.MÍ 362.ftM 188.580 213.748 30L 424 2 07 .Í M 277j a i 298.970 215,885 298.158 287.8304S00J» 289.115 S80.23S 171.028 218.401 508.011 209.944 281.993 303.471 218.188 301X184 272.1775000.00 293.110 387.081 m . 3 l8 222.855 818.950 212.388 285.98S 30T.C19 220.471 305.541 278.298SSOO.OO 298.781 S7S.318 175.199 228.579 319.381 214.853 289.811 311.200 222.581 309.808 280.069eooo.00 300JOSO 379.052 177 JXM 230.225 324.333 218.831 292.438 314.578 224.490 313J39 283.548

— i i

í >*0► C

na Ch

5


75/110

1 J 6 C o n p a l * / 5 / i n c I it f e a o í C l E a í ío o P t o c a t a

........................................................................................................................

C SDí UUnOK OP 4-BTBOKE CCJffHtSSIOS ICKinON EKQIKE................................. .......................

8L0CI OKU ......................................................................................................................................... ..

C IH THIS f fUBROUTIKE VALUES VHICH AfiE KOI UKEL T TO CHAKCE ASE

C or VEH AS DATA REAL U,n>.Kli,KC.KHP.KH.l(O.WJLin?.W,K.X.HH.HAOHAX.KKO.

# KP.KPO.KX.KBRUÍTEGE» EVD.EVCLoaicAL n>ma.iPRi (r r.i 6UPca,is wET,HT_iKDEX

CHA8ACTEH.10 XV.YZCOHMOH/OEOV/B,CT,C8I..8,VBDC.VDIB?.VI1VBI>C(T20) .VOLÜHE(eoO),

f VTOCC0KN0H/THEW


76/110

X38 C o m p a U r S lm a U Ü o a c í a E a f ia t P n o ú M*

C MOT E: p a z s s u i z I S I H A T K0 S PB Z S2 8 k I D l P E a A m Z M E L V I H

itppudix D 180

DATA

- C

C

TI

3 0 0 . 0 0

PA

1.00TA

9 0 0 . 0 0Pl

1 1.00 ,DATA W j l . t /

KCEXG : NUKBER COMSTmJ UnS I N TBZ EXEAUffT SA8.

DATA CI>A,IIZ.IICEXa/30.0.0.,e/ B U U Z 18 K A X I MW A 1 UV A BL 8 BUUlUO KATE ( L m e S / S )TB 18 18 m i e z j w ) r o í p u k k e s s i v b c o x B u m o H mo oe l .

DATA BBKAX/WO.O/

a c 18 THE CKAMK AMOLE AT VHIC8 F Ua 18 li I JECTEO

U P M0 BE 8 S I V E C OJ f f l US HOK W) D E I . ( kOD a 1 ) 1 8 Ü8 E D T HE H I BC - I BO

DATA IBC/1S3/

DK 18 A COMBTAMT CBQ8EX BETVEZJi 3 0 i 60 IK P S OOm S I VE COMBUS

TION KOOa. TO DETEUlIKE B UAU. IMCBZUUrt S DP CSAXK AHOLE.

DATA DN/E6.0/

IPTTIUl 18 7 «UE OMLY TOí IDEAL CY CU ¥ ITB SUFEECHA&OES

DA TA I P T T H K , I P l I l l T / . P A U E . , . n U E . /

ISUPET U .nUB . rOJl EZBAUST DUVE K SUPEMHAj UKK.i s i ip ca u . n uE . p o j i c o u f b z s s o k d r i y e i c s u P E s c H A &aan o t o e a k o a i m

I ? A X y OXE 0 7 T HE A BOV S I S T BUE , T HE M I P T i m 8 E 0 UU) BE . T US .

DA T A I 6 UP E T . I S UP C H /. P A L 8 E . . . T W1 E . /

DA TA I S U P E T , I 8 U P c a / .T S Ü E . , . F A I Í B , /

DA TA I S U P E T . f S ü P C H /. r A I S ? . . . P A l f i E . /

EPOCOM AMD EPOTUl AAE EPTICI EMOIES OP C0KPBE8S0K k T U E B Q S .

DA T A E P Oe ON , E P 0 1 V I /0 . 9 , 0 . 9 /

AEV 4 AI V Al E HAZ. A UA OP OP E NUO QP GCEAUST i INTA CE

V A L V U U Sq UAI E CM.

DA TA A E V . A I V / a . O . a . í /

VALV C 1011 1108 I

DA TA E V 0 . E V C , 1 V 0 , I V C / M 0 . 5 S 4 . I 2 T , 7 M /

CP t CV A U TES 8PEC1P1C BEAT AT COmA XT VOUlXB

AND COUSTAVT P U 8 8 U U l ES PE CTI YE LY (CJ /KXOL )

DA TA U , C V / 1 . 4 , 2 Ó . a 9 « /

PiKP t PENP m ULET k m u jsT KAvzpou) n E s s o m .P8L 18 TUS PI8T0M BKUT LEVOTa k KPS 18 THE VOHBEX OP

P I ST OK u n o s .

DA TA P D t P . P Z X P . P S L . K P i / l . O . l . O . f l . O . S /

KODPBT I B THE EEAT TUMSPEB MODEL V8ES U THE 8UBU3UTIKE

EZAT TSANSPEE (STKANS)

DATA KOOPHT/Í /

KOOrVA 18 KOCEL POl VALVS AEEA l »E D IN THE SUBaOUTXXE

VA LVA E. SF ECI PY E m DI k BETA IP KODPYA 2 IS U8ED.

DATA HOOPV A/l /

CAIMT 18 TES CRAKK AMOLE IKTESVAL - I AX IS AKOTSUPACTOI. T V m AlE V m IN SWROUmB OÁSa JUOTHEU VALUE8 6B0UU) BB BETVEEJI 3 t 1 0 .'

DATA CA INT, AM/6., 4./

C ‘U* 18 TEE C0Ü8TANT USED Dt VI EEE'8 BEAT KELEASE EQUATIOH;C n 18 CENEEALLY DETEBXIll EO PROM P- THETA DIACUX 05TAINEDC PIDM TEE ACTUAL ESfl IKE

DATA K/3.00/C COKDUK Z8 DUIATION OP CONBOSTIOH IH KCBEE8 CUA)nC AKQLEC n KAY BE ASSUXED B S n m 40 n 80 DEOKSES.

DATA Caa xi K/SO.O/

C VT 18 THE MOLECUUE VEIQHT 0? TSE PUEL AKD.CONQT 18 COK-

C BUSTIOl f EPFICIEMCr( HOJUALLY BETVEEH 0. 8 k 0. 9)DATA l f T,COKEFP/142.0.0 .a6/

CPSIUX 18 KAXI WM ALLOVABLE PtES SUKE E18E BATE 01 ATX/DEC.CA DATA PBXAX/IO.O/

C NODCOK IS THE COMBUSTION XOOa USEO.

C POS ZE£ 0 DIKEJISI ONAL COMBUSTION MOOa UQOCOH - 2 k C PO» PaOOBESBIVE COXBÜ8TI01I MODEL KOOCOH - 1C DATA MOOCOM/3/

C MODBE 18 TEE BEAT RELEAS E HOOEL USHODATA K i a W i /

C KOlVS P 18 TEE XOISL POS ENOOIE PKICTI OK

DATA KOOPSP/1/

C SPEED. OP TEE ENQIKE

D A T A E P K /1 6 0 0 . 0 /

EKO

NAIK FKOaUX

COMMaM/GEOK/B. CE,CU. ,(.VBDC, VDI8P. VDVBOC(T30).VOLUXElBOO),« VTDO

C0MK0H/OEN/CB(4O,4).A(tO,16) .0 (5 ).D(6),E ETAH.KAP.P(E).I . . PFM,PVN,a(6),M£P,PID4.P0y£B,RFM

C0M}


77/110

1^0 Compattf SlotUtha oí C! EniiaoPratatt*

cccccccc

c

c

cccc

c

ccc

c

c

cccc

c

c

c

c

ccc

c

ccc

ccc

c

c

ccc

IT CALCinUl TCS P, V, T VALUES AT STATE P0IKT8 í TO 4 IX

THE CYCLE.mSKIKO KE MW IS AE8UHB0 It) BE AIR ¥ 1TH COHSTAKT C?

AMD CV VALUES.THEXH 18 KO PÍ ESSUHE XISB DUSDÍO.COMBUSTION AXD DHLYCUT m 8ATI0 IS TO BE QIVEK.COKBUSTIOK IB ASSUKED TO BE ADIA BAHC AHD AT COKETAÍIT

PEESSURE.

CAIi. FC8

IN THI8 6UBR0ÜTIKE FUEL- AIR CYCU (FC8) 18 SI HUUTEO.

IT CALCUUTES P .V .T VALUES AT STATE POIHTS O TO « IH THETHE CYCLETHE IfCRKIKO KEDIUK IS ASSWED TO BE FUEL AKD AIS WII B

VASIABLE CP AND CV VALUES.P82SSURE CUAUQE DUE TO COKBUSTIOK I S CALCUUTEO USIHQ

THE AOIABAnC H.AHE TEXPESATUBE CALCUUnOKS.THE CDKBUSri OH I S ASSUKED TO BE I KSTAJÍ TAJÍ EOUS AKD AT

CONSIAKT PHESBURE.

CAa PCSTHIS SUBRQUTIHE SIKULATES l OEAi DIESEL CY CU If ITH PROCRESSIVE

COKBl/STIOH (PCS)IT CALCUUTES P.V.T VALUES AT VARKWS POIHTS O? IHTEREST

AKD ALSO VALUES OF PRESSURE k VOLÜXE POR EVESY DECEEE

CRAMK AKCLE.THE lí OBJflHC KEOrUH 18 AKSÜXEO 10 BE FUEI. m AIÍ VITH

VA8IABLE CP m CV VALUESCOMBUSTION I S A SSWED TQ TAKE PUCE OVER PERIOD 07 CBANK

AKCLE ROTATIOH ANO THE PRESSURE SIBE DUE TU COKBUSTIOH

18 CALCUUTEO USIKQ PBEORESSI VE COKBUSTIOK.K E A T T I U N S F E K E F T E C T I S I U C L W K D .

CALI ACS

THIS SUBROUTir a SI HUUTES AM ACTUAL DIES EL CYCLK (ACS) .IT CALCUUTES P .V .t VALUES AT THE VARIOUS POIHT OF I KIEBES T

AHD ALSO VALUES OP PRESSURE t VDLÜKE AT VARIOUS CRAKK AKCLES.

THE VOaXIHQ KEOIUH 18 ASSUKED TO BE FUEL AHD AIR VITH

VARIABLE CP AKD CV VALUES.PROGRESSIVE COKBUSTIOK 18 ASSUXEO AHD HEAT TRAHSFER

EFTECT IS IHCLUDED.PROVISI OMS ARE KADE Tt) I NCORPORATE VARIOUS HODELS FOR

COKBUSTIOH. KEAT TRAKSFER ANO VALVE AREA CALCUUTIONS.

CAS EXCHAJÍ CE PROCESES IB INCLUDED AND THE E mCT OF

VALVE OVERLAP CAN BE STUDIED.

Ápp tad bsD 141

CccC

CALL P R i mT8I 8 SOBROUriKE P8IKTS OUT RESVLTS

ALTEBATI0N8 KAY BE KADE TO OET THE PEIKT OUT I«THE IBJUIRED Srf LE

CLOSB(UHIT - 11)STOPEXD

SUBROUnKB í es

REAL U.KP.Kt.KC.KEP. KH. «O, WJLVTP.IIA, K.MADKAX.ÍIKQ.HP.KPO.HX

CHAKACm*10 XV,YZ

UX5ICAL IPTTHR.IPRI HI.I BUPCB.lBUPET.PVPRJ fT

COKK0X/0E0K/B,C«.CRL. S.VBDC,VDIS P.VDVBDC(72O),V0LÜXE(8 OO), VT K

COKMOH/TKERM/HRP,MOLYTP(6 ), P1 .PJ ,PJ . P4, TI . r a. TJ ,T4 . TS.T6. TA, Vl .V2 .V3 .V4

COKMOX/CKEH/EA, KP. KR, K (S ), HA, KAIDIAX. m . NP, KPO. NX. m , m .

HC,KH,KO.R,RUTAI.MIX,T,YCC,YNIN.PMOLlf TCOKMO«/C? CCEF/CV.ACPF.f iCPF.ACPA.BCPA,AL(6), Af l (6).

BL(5) ,BB(E),a(S) ,CB(S)

CO»IOK/ARRAY/DELV(r 60) .DV(T60). PCBOO) ,DEU((8 00) ,DELP( 800 ).THETA(800),V(800)

COHKOX/OEH/CB(4 0 ,4 ) ,A (1 0, 1 6 ) , 0 ( 5 ),D(5) .E ETAH.RAF,F (6 ) .FPH ,m,0(6) .KEP.Pm.POm.RPK

COKMOX/IOnS/FA. VR. STUKE

COKXOS/PSS A/CPR. DT, DTHDDT,IBC,IECPC.IEC,QAB)(AS,WCOKP. nJCP. HCEIO, VKET.IfUWP.PSPS.KL

CO«KOX/PRIKT8/JV(16). YZ (M )COKKOH/ABC/WT. COKEFP, CPA. HK

••••• STATEKEHT FUHCTION CEPUtl TIOH FOR THE CALCUUTIO* OF'•••• VOLUKE AT VARIOUS CRAHÍ AKQLE8.

VOL(THETAS)- VDISP*( CR/(CR- 1.) - (t . - C08(THETAK)>/2. ♦

(CRL/S) - . 6.5(JRT( (3. «CRL/Í ) ♦«J- (AB8 (SIH(rtí ETAI))) •♦? )) WIT E dt .S SS )

65S F0 R) aT( 20X .'8DWUTI 0H OF AIR STANDARD DIESEL CYCLE ',//J OI.1 3 8( Í B- ) )

IPRI- 0

PVPRKT- .TRUE.PSPS- RPN/120.

C I F( BTÍ OKE. EQ.2 .) PS P8 - R PH/6 0. VDISP - PI M»B*B* 8* l .0E - O9

VBDC •CÍ /{CR- 1.) *VDI8P VTTC - YBDC- VBISP


78/110

3 CoaptUr S imuhOf el Cl £ « < b « f r e c e i w

va - VIDC V« - VB6C Vi - V3« Vt

n - T i » a » «( a - i . )r a - p t « c x * * u n - v i * t a « - paT 4 - n * ( V 3 / V B 0 C) * * ( U - l . )P 4 - P 9 / ( (V 4 / V 9 ) * * u )KA - (P l «n'K)«CV MC*m)*l OOO.O/C»»Tl )

o •••••• VU u m KUKBa c p k x o u ik t be c y c u .« coxp - c v*( n - Ti) * iu

VC0K8 - K * (n - n) * i uvaof - C V« (T3- T4)» IU .m r • m p * vcoxn - «coxpB T M - ( l. O - ( T 4 - r i ) / ( U * ( n - T 3 ) } } * l (» . 0

p o m - ra T*P8Pi* . ooi

KEP - mT/(VDISP* Pr M)iF(iFU.Bq.o) n x n i i i . x )

as pouu T(y /a,7a (iH- )m. 'cb* .ex, - t i ío •.bx. ' l a u) •,6X, ' l a m •.n .l *1 4(0 ',ax , •METaJ /KOL) * ,*X. ‘OmH' ./6X,73{Ut- ))

n m d i . u } c K .n ,n .n .T 4.r a T ,i K r i a

computer simulation of compression-ignition engine processes v ganesan bn.pdf

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