u. J. mecti. Sei. I'crg.uuon PrC$:-'.U)j5. Yo1. 17, pp. fli-1~L Print-cd in Ureat Brltain- ----

\ J,oA SIMULATION MODEL INCLUDING INTAKE AND EXHAUSTSYSTEMS FOH A SINGLE CYLINDEH FOUH-STROKE CYCLE

SPARK IGNITION ENGINE

R.~. HEC;SO);,* W. J. D. Ax x.vx n ] and P. ('. R

98

;1:

XXi

-"ferh

Zl,'oeff

Suffi xes

R. S. BENSON, \V. J. D. ANNAND and P. C. BARUAH

U,'U(i,ij

VIV

internal energy coefficient for ith terminternal e-nergy coefficient for ith term and jth speciesvolume or velocityworkdistancenon-dimensional length (xjXrer)molar fraction of 'it.h speciesl'"f,'r(lIH'" 1(1l\g(,hnon-d imonaioun.l Lime [afcl(tf,l'l'I,d]vis.-osit.y cootficiont,(Tank n.nglnlt.icuiaun vurin.hlo _! + 1(I. - 1)/:211 'Rii-uiann v.uiu.hlo A - [(I. ,- I )/:2J I'stoir-hiomot.ric coefficientill('I'('llH'nt or Ctu u-rr-nu-n t of' Y,densitywal! slu-m- si I'('ssequivuh-ncc rn,t ioviscosit y

pTI/1

o st,a.gnati

I1

r:1

S

re.e,t

ylee,1S;:0

.It

A model for spark ignition engine with intake and exhaust systems 99

half the total mass emissions comes from each peak. At present, the modelsimulations for both nitric oxide and hydrocarbon emissions neglect theinteraction of the gas dynamics in the intake and exhaust system with thecylinder conditions. Since it would a,ppear that control of exhaust emissionscan he at.tempted through the desigll of the intake and exhaust system, it isclear that a suitable model to simulate t.}wl'e svstoms is desirable. In this papera model is presented for a single cylinder four-stroke spark ignition engine. Ina second paper the model is applied to a crankcase scavenged two-strokeengine." The power cycle will be first described followed by the gas exchangeprocess. Nitric oxide emissions only will he examined. The model will becompared with experimental results.

PO'YER CYCLE MODEL

A number of power cycle models have been suggested. That of Lavoie et al.' isgenerally recognized as giving the closest approximation to the combustion process in lotspark ignition engine. However, t ho model depends either on a known pressure-timediagram or a semi-empirical burning law which would also include the ignition delay.Lavoie et al:" considered a temperature gradient in the cylinder related to the burning rate.In this paper we propose to use the chemical react ion equations suggested by Lavoie butthe cylinder volume is restricted to two zones, a burnt and an unburnt zone. The twozones are separated by the flame front. Furthermore, we propose to use a simple methodfor predicting the ignition time for the commencement. of combustion. With these twomodifications to Lavoie's method we avoid the empirical burning law and simplify thecomputational procedure. However, the new method introduces a new variable, namely,the flame propagation speed. It is to be hoped that introduction of this variable mayenable a more rigorous prediction of the combustion process than a burning law.

Since the rates of the energy producing reactions in the burned gas zone are so fastthat the burned gases are close to thermodynamic equilibrium, we assume that the pressureu.ru] j,

100 H. S. BEKSON, w. J. D. ANNAND and P. C. BARuARspeed increases with increasing turbulence. Until recently it was held that the increase offlame speed was duo to the wrinlding of the flame front (which increases its a1'ea)l1 incombination with enhancement of heat a.nd muss transfer rates, and the turbulent propa-gation speed 1tt would be expressed as a simple function of the larninar propagationspeed 11./ and the r.m.s. turbulent velocity It'. This has been found to be true only for Iowintensity of turbulence, '\'hen u' becomes comparable with u/ it appears that the flamefront is broken up and replaced by a much th ickor zone containing small volumes ofunburned , burning and burned. material stirred together by turbulence. Sokolik et aU2and Chomiak+' have presented some experimental evidence for this. Howe and Shipman-"have proposed an elaborate statistical model charact.criz.ing the burning zone as sphericalparcels of unburned gas dispersed through burned gas with burning at periphery of theparcels, At the moment, there is no precise relation between turbulent and laminarflame speeds for t.urbulence of high intensity.

In their computer simulation work, Phillips and Orman" reviewed a number oftheories for laminar flame propagation and t.hoir final choice was for the thermal theory ofMallard and Le Chatelior.!" Bailey" at.temptod to use the Mallard and Le Chatelierexpression for his work on combust ion limit at.ions ut' gaseous fuels in reciprocating engines.However, some difficulty was encountered relating to the adjustment of temperatures.This was attributed to the exclusion of a pressure term in the expression. Kuehl-" usedmeasurements made on a fif,t burnt'!' to develop an empirical expression for propane-airmixture which correlated experimental flame speed data over a wide range of pressuresand temperatures, This was successfully used by Bailey Y Kuehl's expression for Iaminarflame speed u/ in a propane air mixture is

_ [ 1087 x 10r. ] -0,09876u/ - ((lO'ITb) + (900/7',,))H38 p ,

whoro 'I;" '/',,1\1'0 th" (. is the eqnivalencc ratio.

(1 )

(2)

fn,.nwle)f12

14

al

ofofer3S.

3S.

od3.11'

.ar

(1)

isisvillbu

(2)

i of'ontitaltheno

HI1'('

vmc

.uneplusmeaposemate

A model for spark ignit.ion engine with intake and exhaust systems 101

An energy balance is made and tp adjusted until the specific internal energy of theproducts = the specific internal enArgy of the reactants, and tp determined. The flamespeed (Ut) is calculated from equations (1) and (2) where Tb = tp and Tu = tm The volumeof the burnt mixturo I'~is given by

where r = u,(6ex/360n) is the radius of the flame front from the spark plug, 6ex is theangle increment and n is the engine speed, rev/see.

For initiat.ion of combust.ionF, is set equal to 0001~~and the angle (6ex)deIIlY calculatedfrom the above expression, 1f the time from the nominal spark angle is less than (6ex)delaythe mixture is consi.lcrcd not to have been burnt and the compression process carries onfor the next timo increment

102 g. s. BEl'SON, \V. J. D. ANl\AND and P. C. BAllUAH

and

;;0 that the total internal energy is then

,..,'Irp ('. ICqllililJ/'alio!L oJ 1)/'('88111'('This step is assumed to bo an ad ia.bat ir constu nt. vol umo prO(;('SK. The total intorna.l

energy is(10)

Balancing the t.otal int.ornu.l energy before and after step C

(11)

which, after rearrangement, becomes

m C t' (tm, - 1) = '/Ill' (.'CP

t'p' h- ~t~").nI'1 t:1I/ l1l /.'", \ '

1)1

(12)

As before

(~) ,k",-J "".

JJ(13)

andI". = (p")(kP-J)II.'P,~p" .

(14)

(1 fi)

Combining equations (12), (14) and (15) and letting

and

we haveo - 1 = A (1 - EO'), (16)

which can be solved for 0 by an iterative technique.

THERMODY='J AMIC:::;

Eqn'il-ib1'i-mn thermodspiam i~8The following species are considered to be present in the product in the cylinder and

in the exhaust gases. They are referred to by the number in brackets appearing againsttheir names.

(1) H20, (2) H2, (3) OH, (4-) H, (5) N2, (6) NO,

(7) N, (8) CO~. (9) CO. (10) O2, (11) 0, (12) AR.

Argon is separated off from atmospheric nit.roger. in order to determine the NO concen-tration. The composition is calcu lated in terms of molar fractions of these species denotedby Xi' 'I'ho [\1('1 is writ tr-n ItS C"" Hl\y Oox. and one mole of the total products arises fromet moles of fuel plus (l/cp) t.irncs t.he st.oichiomot.ric quant.ity of air (cp = equivaJence ratio).

(tl)

(9)

6)

nd1St

en-ted'0111

io).

A model for spark ignition engine with intake and exhaust systems 103

The equilibrium distribution of these species can bo fully described by the following

(1) ~H2----+ 11,

(2) ~()2 0,

( :l) ~~2 )- i\",

(-I) 2HzCJ 2H2 + O2,

(5) H/J-----+ OH +~H2'(iI) ('02 + H2 ----'? J-I/) +CO,

(7) H2O+1N2 H2+NO.

(17)

(I H)

(In)

(20)

(~l )

(22)

TIU'l.;p rcuctions H.n'l t lu- same HS those used bv Vic-khmd et al."The equilibrium constant K p for the stoichiomet.ric reaction between the substances

.I.B,C,D,

"Hit bp cx presse.l as!"

(24)

where v is t.he stoichiometric coefficient X is the molar fraction and p is the total pressure.Using this expression of equilibrium const.an ts for reactions given in equations (17)-(23),

c-an be written respectively as

(I) ]{~, = J(p) X4NX2, (25)(2) u; = J(p) XllNXlO, (26)(:1) ]{v, = J(p) .Y,NXo (27)

U) 1\v, = }I.\ 1\1//)2, (~l:i)(5) K; = ,/(p) X3/(b JXJ, (29)(6) J\", = /).\ 9/X 8' (30)(7) J\", = ,'(p) X o/(/J JX 5)' Pi)

whereb = X1/X2

The equilibrium constants (]{p) for these reactions are given by!"

In K. - [I( v,,(T) ) _ I ( v,,(T) ) ] _ t:.HoP - Rm,)] T react Rmol T prod Rmo] T .

The specific Gibbs Iunction is given by the expression

g(J.') = a (l-.lnT)-b 1'-S!.T2_~T3_~'1'4_klllllol T Y (I 2 :3 4. Url'

(32)

(:33)

where ay, by. eg, d,p e" and kg are constants, the values of which can be obtained fromref. (HI).

We have 1:3 unknowns, the 12 species fractions and the total number of mols, so weneed 6 more equations for the solution. Onc of these is

(8) IX; = 1.

The remainder are the atomic mass balances for argon, carbon, hydrogen, oxygen andnitrogen.

The method of solution of equa.t.ions (17)-(34) is outlined in Appendix 1.

BASIC RATE KINETICS

The following basi rea.et.ion i,,; considorcd :

KrA+H-~ C+D,

J...~ iI(35)

104 R. S. BENSON, \V. J. D. ANNAND and P. C. BAIWAH

where I(, and Kt> represent forward and backward rate constants. Using

(A)/(A), = C~, (B)/(ll), = {J, (0)/(0), = y, (D)/(D), = 8,where the suffix e represents oquil ibrium, for the considered reaction, then for

t lu- ron\'HnJ mt.f' = 1\,(.4) (In = rx{J](,(A)" (fJ)"

the reverse rate = Kb(O) (D) = y8Kb(0), (D),.At. equilibrium tho forwu n l ra.to is equal to the reverse rate,

unu

Therefore,](t(A), (E), = ](b(O), (D), = R,.

the net rate = 1\/V-J.) (E) - 1\.b(O) (D) = (rx{3-y8) R,.

x o KI~ETrCS

]t, is now recognized that. the formation of NO in an engine combustion chamber is anon-equilibrium llIofesl>.In an earlier work Newha.I120assumed t.hat the initial conditionsfor t.ho expansion calculation are given by ohornical equilibrium distribution of speciescorresponding to 11 combination of temperature and pressure representative of the enginesubsequent to flame propagation. 'I'ho assumption is based on two facts, firstly, thepressure and temperature at the initial stage of expansion are at a maxima and the reactionrates are at a. maxima, secondly, owing to the kinemat ics of the engine mechanism thepiston velocit.y and hence the expansion rate is very low at the beginning of the expansionstroke.

In t.his quant.it at.ivo t.hcorotical unalysis rate expressions for 16 elementary chemicalreactions were combined to give la coupled noril inear differential equations representing13 chemical spocics. 'I'lu-so equations wero numerically integrated along with a coupledenergy equation start.ing at the initial point of expansion where the chemical specios weredetermined with equilibrium calculations. The time variations of the rate-controlledconcentrations of the species from their equilibrium concentrations were shown.

In the present paper no such assumption is used and the reaction kinetics of nitricoxide are applied from the start of combustion.

The rate kinetic model for NO is based on the theory developed by Lavoie et al?with some modifications.

The governing equations for the mechanism of NO formation are

( 1) N+NO ------" N2+O, Xlt = 31 X 1010x el-160fT); (36)..,....----_.(2) N+02 NO+O, ](21 = 64 X 106 x '1' x el-3125fT); (37)

(3) N+OH NO+H, 1(3[ = 42 X 1010; (38)

(4) H+N20 --~ N2+OH, X., = :30X 1010x el-5350fT); (39)(5) o + N20 :;:=----=::::. N 2 + O2, Kof = 32 X 1012x el-18,900fT); (40)(6) 0+N2O NO+NO, KGt = J(Sf; (41)(7) N2O+M N2+O+M, 1(71 = 1012x el-3O,500fT). (42)

The above rate constants are given in m3/kg mole per sec.At the temperatures and densities in an internal combustion engine it is a reasonable

first approximat ion to [1,8S1l11W that thc volume of t.he reaction zone is negligible and thatthe gas within it cyl inder consists of a burned fraction at thermal equilibrium plus anunburned fraction frozen at original condition. We will consider the process occurringin t.ho burned gaR behind the reaction zone only. The rates of energy producing reactionsin a flame are sufficiently fast l;l() t.hut. t lio burned gases are close to thermodynamicequilibrium. It can bo ussumod. therefore, that H and OH are at equilibrium concen-trations, and that 0 iHin equilibrium with 02' The rate equations for NO, Nand NzOcan then be developed. These are developed in Appendix Il; it is there shown that, the

is aionsciesginethet.ionthe

.sion

nicalit.ingrpledwereoUed

,it.ric

t al. 7

(36)

(37)

(38)

(39)

(40)

(41)

(42)

enable.d that.lus anrurr ingactions;rnamlC.oncen-ld N20nat the

A model for spark ignition engine with intake and exhaust systems 105

rate equation for NO is the most important and is given by

2.. ~ ((NO) J') = 9(1- 2) ( RI + R6 ) (43)Vdt 1 - O:e 1+O:e[1>\((1?2+R3)] 1+[R6((R4+R5+R7)]'

where O:c denotes (NO)((NO)e' R is the "one-way" equilibrium rate for the ith reaction,l' is the volume of burnt gat;; and the suffix e denotes the equilibrium condition. Thekinetic rates for Nand N20 formation are much faster, and may be assumed to equilibrateinstant.aneously, giving values for eN) and (N20). Along with (NO) determined byintegration of the rate equat.ion, a total nitrogen balance can be formed to yield (Nz) ateach instant..

'Ye now turn to the cycle calculation.

CYCLEThe cycle of events between air valve closing and exhaust valve opening comprises:(1) Compression stroke.(2) Ignition and propagation of flame front.(3) Expansion: (a) two zone; (b) full products.

(1) Compression strokeThe compression process st.arts at the j ral'P

106 R. S. BENSOJ:-;, \\". .r. D. ANNA:sn u.ncl P. C. B,\Hl.'AH(2) Lqnltion. and propaqtttion of jlurne [ront

\-rH have alrr-adv conside-red till' provess [01' usr-c-rtu.ining the ignition of the fucl-u.irmixture. Unce ignition has taken place we consider the flame to be propagated spherica.llyfrom the spark plug. The \OIU.IlH'S of the burnt and. unburnt regions are computed byr.ho methods described els('whnJ'(,.21 F(JI' t.h is 1HU'j>0::;C,a not.e must, be kept not only of theonflumed YOlUllH' agaill::;t t.he Ham!' rtul ius but al~o the flame front urea awl the Ham('contact :U'C'lt with r.ho cyl indi-r wa.l! and piston. \\-'hen the flame i", propagated and thozones set up by tl\l' mothods dl'sl'.ri be( I ('Hrlipr, t hr eaiellllLtion 1)J'()(('('d" in a stop-by-stopmannor using HlIIlgl1-Kllt,(a illtt'gnt-t ion,

(3a) E,l'p([l'Ision uith t uo Z01/f8'1'11(' major tt,;slln1l'titlIlS HI'(':(H,) the original l'ha,rgc- is htllllogelH'()(l>;:(b) the pressure ut any time is uniform throughout the cylinder:(c) till' volume orcupiod by t.lu- fla.mr- roar-t ion Z()(W is negligib!:(d) tlu: burned gas i" u.t full t.lH'\J)1tltlynami( "'1"ilibrilUll ex('('pt fr (lit' nitrog(,1I spcei('~;(e) the unburned gas is froze-n at its original coraposit ion :(f) both burned and unburn.-d gasps hav unifor-m loc-al "pt'cifi(' hont s ,(g) t lun- is 110 lu-n.t. t rn.nstr-:: hpt \\'('(,11 burru-d "IHt unburnc-d ZOllt'S.It can be SPC'1l that this mode! is cx trornc ly simplified but, t'x]wJ'it'Ill:E' shows that till'

assumptions arc \'ery we l l jnst ifiod.

Spark plug

Total volume 0 VPressure = P

Fro. 2. Cornbust ion zouc shape.

Consider-ing Fig, 2, the total internal energy for the system is

(5~)

The first law of thermodynamics is

dQ dV clWda = do: + "'J;; , (53)

dVdo:

(.,)-1-)

and

53Therefore, equation (52) becomes

(. . elm,.", C dl",. ,dl" cl V dQ/l'v-Il''')-I-+III",v -1-+nl),C"-I +P-[---l{(Y 111

lr('.ally

!:"'~

~~:iv-::~

A model for spark ignilion engine wit h intake and exhaust systems 107

cl]' cH;" .n;-=--+-,dex dex dex

(56)

.nd difl"!'t'ntiating t ho r-quation ofstan- (pi'= milT),~ = (~_~) istoll andl.Lm

I{ = Cv", fkmm 0'7

The piston speed Vpistoll and cylinder bore D ar used f1R the parameters in the Reynoldsnumber expressions.

108 R. S. BE~soN, W. J. D. AN~AND and P. C. BARuAH

The pressure changes dp/c1excan be obtained directly from equation (63) since all theterms arc known. The temperature changes dt",/dex and dtp/dex can then be dircct lyevaluated from equations (61) and (62). respectively.

This completes the calculation for the two zone expansion for the time ex QCA. Wethen calculate the new variables x at the next. time step by the Rungo-Kut.ta methodusing the general expression

d.i't'n+1 = -r"+-l C:.a:lex

where :V is any variable, the suffix n + 1 is the new time stop and t:;ex IS the time stepincrement, in crank angle.

Time stepIn the Runge-Kutta method the crank angle increment C:.ex is the parameter which

decides the accuracy of solution and the computing time. If C:.ex is large the results will beinaccurate and if it is too small, t.liocomputing time will be higher. To make a compromise,a test was developed to maintain the right level of accuracy while adjusting the value of C:.o:.In this method all the varia.blcs (except the variables heat transfer and work output)during the expansion stroke arc tostcd to sco if the increment of any of them during atime stop (C:.ex) has d()('I'clt,wd by Jll

hx.t)aissI:e,oe

ed,toly,to,'C'.

.gle:1 a

.aryiics.

able'mal'mallong11,

rtion

oasic

(66)

A model for spark ignition engine with intake and exhaust systems 109

Momentum:211 811 1op F' 0-+'1t-;;-+--;;-+' = ,ct (.1: P (,.l;

where F' is wall friction defined by

(67)

F' = ~~~J) 2 III I

I j 711)anc = -1-2''2'pn

The first law of thormodynamics (encrgy equation) is

qpP d.l; = [(pF d.r) (Cv '1'+U;2)] + :v [(puF) (Cv '1'+~+ '1;2)] dx,where q represents rate of heat transfer per unit. time and per unit mass of fluid.

Using continuity and momentum equations and simplifying, the energy equation isobtained in the form

(68)

o (; 0 8(k-l) p(q+u.F') = f +u ",p -a2 (!+u ,f).ot uX cA uX (69)

The heat transfer rate q may either be through the walls or be the result of longitudinalheat conduction, In the event of a chemical reaction with change of state these will berepresented by It heat addition equal in magnitude to the constant volume heat of reactionof the actual process."

The equations of continuity, energy and momentum are solved by the method oncharacteristics. For the continuity, energy and momentum equations this gives the .!following charucteriet.ica: '()

dxdt = u a (characterist.ice) (70)

anddzdt = u (path lines),

Combining the continuity, energy and momentwn equations with the characteristicswe obtain

dp du (4j U31.1,) a2 pu dF 4j pau2 udtpadt-(k-l)p q+D2GZi +-yj'dxD-2-fUj=O,

which is the compatibility condition along dxfdt = u a.Combining the continuity, energy and momentum equations with path lines, we

obtain

(72)

dp 2 dp (41 u2 U)dt-a dt-(k-l)p q+1t D2GZi = 0,

which is the compability condition along dxfdt = u:Defining the Riernann variablea= as

.:\=A+lc-1U,2

(73)

fJ=A_k-12

and

A=.:\+fJ. 2'

u = .:\-fJk-l'

we have the characteristic solutions in the Iorm :Direction condition:

clX _ U AdZ - + ' (74)

110 R. i::l.BE.'>SON, W. J. D. ANNAND and P. C. BAHUAH

Compatibil ity condition:

d,\ = _"-1 Al.j ~dZ"".1 (L..j,,_~~ 2!-Y:reIU2:2 F dS ".-1" :2 lJ I /..,' I

(IT) , (k-l)2 qX'r'" 1 I'x 1-(1\-1)- dZ+---,--

i)

3)

9)25

.uccal

for

iontedt.hcthethebedmal

-nalt hr-Lt.he

A model for spark ignition engine with intake and exhaust systems III

Considering a path line, Fig. 3, the pressure and temperature are calculated from theexpressions

. _ (1I+f3)2kl(h-ll .Ji - .) 4 Prel,

~. a(80)

(81)

From Jl and T t,hp quilibrium composit.ion is calculated from equations (17) to (34)using the same met.hocl as in tho l'yliwlel' a.lcu la.t.ions, and from the equilibrium values of(~O), .. (N)" (N20)c the kinet ica lly controlled amounts of NO, Nand N20 are evaluatedas ill t he cylinder culoulat.ious from cquat ion (:\6) to (43). In practice, the equilibriumcalculut.ions and the rate alcula.t ions a ro ol'g[l,nized as subroutines which can be enteredeit.hei-from the cyl inrler or the pipe ca.iculat ions. "re now have all the species, the pressureand temporat.urc : we call calculate, therefore. the ratio of the specific heats, k, in thefollowing manner.

Enter species trompr evious time steo

Z+LZ /r--III

LZ I

Interpolote speciesatAandB

A\-~----- ,-I

P,'T'B

Boundary BoundaryI

~~~Aa, '"

[NO] Along po+hune

Z

II_____ -.-l __

P,TIS rate controlled

1

112 R. S. BENSON, \'1. J. D. ANNAND and P. C. BAJWAH

(a.) Cyl-inder boundaryIn this case when there is outflow from tho cylinder into the pipe the pipe end boundary

species are filled in with the cylinder species. If there is inflow from the pipe into thecylinder the boundary species are obtained by the int.orpolat.ion of the inside and outsidepath lines at the pipe end.

(b) Junction boundaryThe junction boundary uses a constant pressure pcrfoct mixing model. The principle

applied here is that only the boundary species flowing into the junction will participatein mixing (Fig. 4). The resultant mixture species will be entered for the pipe ends whereflow is moving away from the junction. The pipe ends, where flow is into the junction,will retain t heir own incoming species.

- ve flow adjustoutgoing species

FIG, 4. Junction boundary with species.

The flow direction and the mass flow parameters are obtained using the conventionalexpressions. Using suffix nn to denote a pipe end at the junction, we can write:

Velocity parameter:

Mass flow parameter:(88)

w - (,.\. -) t ) r".!!..Fn rr - 1Illln '''01l.,11I A 2 l1n

nn(89)

Considering positive flows only, represented by W~" (Fig. 4), we write the averageconcentration for species i

(90)

For pipe ends having negative flow(X;)nn = (Xdav (91)

A similar procedure will be applied for NO, Rand k. The equilibrium and rate equationsare not included in the junct.ion boundary.

(c) Nozzle and open end boundaryIn this boundary when flow is going out, of the pipe into the ambient condition the

species at the pipe end are obtained by the interpolation of the outside and inside pathlines existing at the pipe end. When there is inflow into the pipe the values from theprevious time step are used, to fix the pipe end species at the current time step. This isan approximation, in actual practice a slight amount of ambient species may enter into thepipe. However, it is expected that mass blown back will be small and this approximationwill have negligible effect, on the prediction of NO. EoI' engines with excessive back flowthe calculation will have to be modified to allow for the mixing of air and gas.

To obtain the integrated mass flow for any gas ;'( we use the expression

X - Im{X,) (92)- Im 'where Xi is the mass/mass concentration and. rn is the total mass flow rate,

,al

3S)

30)

90)

(1)

.ons

theraththe

.is is,the.tionflow

(92)

A model for spark i(!nilion engine wit.h intake and exhaust systems 11:\

CylinrlcTIn this model wo assume that the composition of the products of combustion are frozen

.tt release (e.v.o) arul rcmain so during tlw gas exchange process in the cylinder. When thegases are in the pipes the residence time will be longer than in the cylinder and theequilibrium and rate equations 0.1'(' used. The value of le in the cylinder will depend,therefore, on the tcmperat uro in the c.ylin

114 R. s. BENSON, \N. J. D. ANNAND and P. C. BARUAH

T1H'1l whether the flow is choked or nut. t.lu- l'l'l's:;lll'e ratio (p,,/pJ is determined fromeither (07) or (05). TI1(\ entropy Aa, is now evaluated from (98) and compared with thec-st.imutc-d va.lue of /1 "e-t.' I f the two agree within the accurar-y required, then the calcu-lation is l'()}llpll'l ('; i i' not, t.lun tilt' c'al('liln,(ioll is l'l 'Jl' ,,"t,od w iIh a.not.hor est imn.t.o (If A"unt.il t.lio required l1l'l'uJ'Ul'Y is obt.a.inr-d.

Lnjlou', FoJ' inflov,: In' assumo that t hc Hovv i" isr-nt rop i to t h throat and that t.hot hruut jll'l'SSlIJ'C i" ('l]u,),1 10 the ('.vlindl'r PI'!'>'slll,('. 'I'Iio boru u lu.ry ond it iona al'(' IlO\V1'l'j>l'C'sc'lltl'dby till' expression

o

for subsonie flow where

A* _ /\""1 {Jirl.r)Ck-11/2kout - _,.1

/1\ Pc .

It, is not, us uu.l to huvo r-ho kr-d inflow t.Ju'ollgh it \.;\.1\'(', From the vah ros of]J.., Aill and A.,we can determine A~" Equation (l01) is t.hen so lvcd for A * and then A~lIt whence Aout isfully determined.

Cylinder tlierniodijnamics

The combustion products, suffix 'jJ, are oonsidi-red t.o have a fixed composition at release,Cl.V.O. This remains constunt until the air valve opens, a.v.o., when the air-fuel mixtureenters the cylinder. The air-fuel mixture mixes with the products uiithout chemicalreaction to give the final products. suffix g.

The molecular weight of the fuel ail' mixt.nre '11/ "'m' and the products m UJ" are obtainedfrom the expression (85). The specific heats at constant volume for the air fuel mixtureC,.", and 1110 products 0"" arc. ol it.a.inod frorn .-xprossion (S4). Now

and the numbe-r of mols

R = HIII"i.1nw

Ii ; =JI"lItli

(10:2)'lJ1w}I

1))/11n.: (103)'11/111111

c = (}I'iII + It Ill' (104)})/IIC = O"J)+H,p (105)JlI'

~\III

'}}I('/II

(106)III Will

X,,=Ul(.-nll'm

(107)1}J1.W}J

where ?ne is the total mass in t.he cyl inclcr and 1ll,. is t.ho mass of air-fuel mixture. Thetotal IIln.SR ill the r-vlindcr 11/, = '11/ i" giv('1l ill' '"

" (J)u

'Htlly = Xm 1nll:m + ~\{'P ','11v = 'IncThe "l)('cific hoat s 'Lt, constant. Pl'l'>"SIll'l' Hlld \'(1;11111(' will be

(10] )

(108)

(109)

(110)

I)

o 'is

SE',uecal

ledllre

103)

104)

105)

106)

(l07)

The

(108)

(109)

(110)

A model for spark ignition engine wit.h intake and exhaust systems 115

and viscosityz . _ (..{Ym Z('oeffm ,,rnl'/'m + X.pZ('oetTp J11'ltr):.JI.-oellq - (); m ,I'll/Will + ....y p \hn wp) ,

/.L == Zl'oett'j/ X 110.645, (112)

(Ill)

Spocific heat. ratio:( 113)

The mass flows into and out, of t l: (,.ylilld('l'(dlll";(le< an. l dm,,fde

116 R. S. BENsoN, W. ,T. D. ANNANDand P. C. BARuAH

If the model is to give a good simulation of the engine under test the number ofestimated variables in the input data should be a minimum. The flame factor ff is oneunknown, which must be based on previous experience. However, to reduce the computa-tional time a good ost.imat.c of the rosiduuls will help. It should be pointed out that thecalculation wi ll automatically adjust. the i-csiduuls. In order to test how sensitive the

Sampling station//@

Cylinder

/ CDJunction

"'-. Mixing chamberReceiver

Pipe No. Length Diameter(m) (m)

I 0219 0044IT 0[27 0044ID 0600 0044

FIG. 5. Four-stroke cycle engine configuration.

60r-------------------------,

E::t 30-'""0xo.~...z

Fraction residual

004---007-_._-Flome factor: 40

14Air fuel ratio

FIG. 6. Effect of fraction residual on nitric oxide prediction.

prediction of NO is to the residuals a number of power cycles were calculated withthe flame factor set at 40 based on the previous work of Bailey-? on the same engine. Theresults are shown in Fig. 6. It is quite clear that the peak NO is strongly influenced bythe residuals. This is not unexpected since NO formation rate is dependent on themaximum temperature and this is influenced by the internal energy of the inert gases.The greater the quantity of inert gases the lower the temperature rise during combustion.

The flame factor ff of 40 was based on Bailey's work-? which did not include waveaction calculations. We therefore carried out a number of calculations to establish the

)fle11.-

nehe

I with3. Theced by)Il thegases.ustion.3 waveish the

A model for spark ignition enginc with intake and exhaust systems 117

influence of this factor on the NO prediction when wave action is included and the backpl'C'>ismein the receiver set to the experimental value. The initial value of the residualswas selected at 0055 and.u set at 3,0, 3'15, 3'5 and 40. The calculation was carried outfor some 8 consecutive cycles (16 revolutions) for each value of if. A typical result isshown in Fig, 7. It. will be seen that the residuals soon settle to a constant value and at the

-

!-----

-

~ -,

-I

V -I

--- -I I I I I I

-2 3 4 6

'"025!0 nE~2490 -'"

0Q)

CL

4200'OE20.~ 0.

.:.1000

~ low temperatures.

Details of the calculation (Fig. 11) show trends which have been reported by otherworkers. This gives confidence in the modelling. The trend of flame speed with air fuelratio (Fig. 9) agrees with a number of published resulte.P The increase in flame radiuswith time (Fig. l1(a)) agrees with results given by Bailey?" and Iinuma.s" The variationof flame speed with angle (Fig. l1(b)) agrees with test results of Iinuma.P'' The predictionof maximum NO and its relationship to the time for freezing (Fig. l1(c)) agrees well withthe work of Lavoie et al.'

9

118 R. S. BENSON, W. J. D. ANNAND and P. C. BARUAH

The method is now being extended to four-cylinder four-stroke engines and to two-stroke crankcase compression engines. It is hoped to report later on the four-cylinderwork, the results from the first stage of the crankcase compression engines are given inanother paper."

Equivalence ratio = 09Computed points' 0,6,0

"Q

Ea.a.

__ --- 6-__ 6-6..----1\--

-0

'"'"~Q)

EG: 90L---=--3LO----.....J3-.5-----4L.;.OFlame factor

FIG. 8. Influence of flame factor.

e::>...~IDa.EIDI-

",I0

Ea.a.

o .;Q) :2~ "E 013 o-0 L+-

11 III ZQ)a.'"IIIE.'2u,

Air fuel ratio

a.EID...

II

IIIII -- [NO] ComputedI ExperimentII Flame factor 3'15

o:eQ)a.

FIG. 9. Influence of air-fuel ratio.

14

III

0-

.erin

a.E~.x:e'"0.

A model for spark ignition engine with intake and exhaust systems 119

2500

2480

1-0 12

Back pressure. bar

FIG. 10. Influence of back pressure.

AIE Eo u

(cl_-----'''12700 ~

c:.s+-ue-

\~.

\\\ \\ "-\

0 . "E . +-a. !"0 '"+- ., '1>tc- c.E E

c-'" "0 I-;: Two lone IJ..

c termination~0

---------705 720 15 30 45

Cronk angle, ATDC

!38EVO

360

Cronk ongle, ATDC

572Aye

FIG. 11. Performance prediction.

120 H. :-:;.BE:SSON, \Y. J. D. A:SNA:SDand P. C. BARUAH

CONCL USIONS

A comprehensive simulation model of 11 four-stroke cycle spark ignitionengine is presented. The model combines a full power cycle simulation withthe prediction of NO emissions with a comprehensive gas dynamic model forthe cylinder and ducts allowing for chemical reactions in the exhaust pipe.Calculations are presented comparing the predicted NO with test results froma. single cylinder cngine. It. is shown that good agreement is obtained betweenthe predicted and measured NO over an equivalence range of 08--11 when theflame speed is corrected at the equivuleucc (00) corresponding to the peak NO.The NO emission is sensitive to the residuals and the exhaust back pressureboth of which are automatically included in the overall simulation model.Further work is required to obtain a better quantitative understanding ofthe factors which influence the flame speed. In the meantime the selection ofan empirical factor jf which when multiplied by the Iarninar flame speed givesthe turbulent flame speed is suggested.

The program written from this simulatiou model call be used to assist inthe design of iutake and exhaust manifolds as well as to study many problemssuch as location of thermal reactors, catalytic devices, exhaust gas recirculatingvalves; effects of misfire and maldistribution of fuel-air mixture. Later paperson these applications will be presented as the research progresses.

Acknowledgements-The authors wish to acknowledge with thanks the assistance ofMr. 1. Milne who made available the results of his experiments on the National GasEngine, l\Ir. J. Nicholson for his assistance in the computing work and Dr. B. J. Tylerfor his advico on NO measurements.

The work has been carried out in both of the Mechanical Engineering Departments oft.ho Univorsity of Manchester and U.M.l.~.T. wit.h t.heir funds. It. is now boing sponsoredby t.ho t)"iOlll'tJ HO"O>tl'l'.h Council.

All tho calculat.ions were carried out. on tho V.M.R.C.C. C.D.C 7600 computers. Woacknowledge with thanks the assistance of the Director and his staff.

REFEHENCES

1. It. S. BEXSON, S.A.E. Auto. Engng Coruj., Detroit, Michigan, Paper No. 710173 (1973).2. H. S. BENS ON and P. C. BAIWAH, S.A.E. Combined Vehicle & Powerplant Meetings,

Chicago, Paper No. 730GG7 (1973).3. J. B. HEYWOOD, S. M. MATHEWS and B. OWEN, S. A. E. Paper No. 710011 (1971).4. J. B. HEYWOOD and J'. C. KEcR, EnviTOII. Se'i. Tech. 7,216 (1973).t!fl It. J. TABACZYNSKI, J. B. HEYWOOn and J. C. KECK, S.A.E. Paper No. 720112 (1972).\ '\a..>'1r n. S. BENSON, P. C. BAIWAH and B. WHELAN, 1. l.1ech. Engng.

~

(j.f.1''' 7 G. A. LAVOIE, J. B. HEYWOOD and J. C. Kacx, Combustion Sci. Tech. I, 313 (1970).\stI', . ,. C. W. VrCKLAND, F. M. STJtANOE, H. A. BELL and E. S. STARKMAN,S.A.E. 'Prams,

70, 785 (1!l(2).. 9. W. J. D. ANNAND, Froe. 1. Mech. E. 177,973 (1963).

10. D. B. SPALDING, P. L. STEPHENSON and H. G. 'I'AYLOR,Combustion Flame 17, 55 (1971).11. K. AKI'J.'A,i.. Chem, Engng 11, 739 (1971).12. A. S. SOKOLIIC,V. P. KARPov and E. S. SE:\1El,OV, Combustion, Explosion Shock Waves

3, a6 (1967). .13. J. CHOMIAK,Combustion Flame 15, 319 (1970j.14. N. M. HOWE and C. W. SHIPMAN, Tenth Si/mp. (Int.) on Combustion, p. 1139 (1964).15. H. A. PHILLIPS and P. L. ORMAN, Advances in Automobiie Enqineerinq, Vol. 4,

Pergamon Press, Oxford (19G6),16. E. MALLARD and H. Le CHATELIER., Annales de Mines 4, 274 (1883).

17.n IS.h 19.ir

20." ... 21.:n 22.m 23.

1e 24.

J. 25.26.re 27.e1. 2S.of 29.

of30.

Tes

in111S

ing.ers

) ofGas'yler

ts of01'00

Wo

973).'i1lg8,

,971 ).

1972).

1970).fral1s.

1971).

Waves

(1964).iT01. 4,

A model for spark ignition engine wit.h intake and exhaust systems 121

A. C. BAILEY, Ph.D. thesis, University of Manchester (1971).D. K. KUEHL, Eighth Symp. (Int.) on Combustion (1962).R. S. BENsoN, Acit-allced Enqineerinq Thermodynamics. Commonwealth and Inter-national Library.H. K. NEWHALL,TU'elfth Symp. (IlIt.) on Combustion (196S).W. J. D. ANNAND,.1.Mech. Ellgng Sci. 12, 146 (1970).R. S. BENsoN, R. D. GARGand D. VVOOLLATT,Int. J. mecli. Sci. 6, 117 (1964).R. S. BENSON.A. w. n.nd D. VVOOLIoN!"]', 1'roe. I. Mech. E. 184,276 (1969-70).H,. S. BENSON,Report. No. 1 for C.E.U.B., U.M.l.S.T. (1.970).R. S. BENSON,Lnt.. J. mech. Sci. 14, 635 (1972).K JENNY, Doctoral thesis, KT.H., Zurich (1949).R. S. BJ

122 R. S. BENSON,\V. J. D. ANNAND and P. C. BARUAH

Falue of aWhen rp ~ 1'0,

13a = [en + 0'5hy + l'863(2en + 05hy - ox)!4>] exp (013T/1000)

and when rp < 10,13

a = [0'25hy+ 2'363(2ca+ 0'5hy-ox)Jrp + 0'50x] exp (0,131'/1000)

Value oj b

'When temperature 7' (in OK) > 3000

b = exp(10,3-(3'1-0'1710gP)7'/1000)and when 1'.,; 3000

b = exp ( - 9'0 + 0'5 log P + 30000/7').Adjust b for the following ease

BX = 20 - 9'0 log.p.If BX>35,

B = exp (exp (3'5) +0'25!og P)If BX.,;35,

B = exp [exp (20-9'0 log rp) +025 log P]If b B, then use

b = B,

where ea is the number of carbon atoms in the fuel, hy is the number of hydrogen atomsin the fuel, ox is the number of oxygen atoms in the fuel, .p is the equivalence ratio offuel (actual fuel-ail' ratio/theoretical fuel-air ratio), P is the pressure in atmospheres and7' is the temperature in OK.

Having fixed the values of a and b, X2 can be calculated by using the equilibriumconstants of equations (25) and (29) in equation (All) which will be

2bX2+2X2+K.b~X2+Ka~X2 = ax, (A21)

Then follow the calculat.ion of Xl> X3 and X . From (27) and (31) inserted in (AI3), wehave

whence Xs followed by Xs and X7 A combination of equations (30) and (AlO) gives

whence Xg, XD and XlO are evaluated from equation (28) and Xll from equation (26).Xl2 is given directly by equa.tion (A9). These values are now tested in equations (AS) and(A12), neither of which has so far been used. If they do not balance within a stipulatedaccuracy the calculations are repeated with new values of a and b adjusted by the Newton-Raphson method, in the following procedure.

Equation (AS) is written as

Equation (AI2) is written as

Xl +X3+ 2Xs +X6 + 2X10 +Xll +Xoer = --a.y

The right-hand sides of the above equations are functions of a and b only, therefore, wewrite

er = Pta, b),

es = G(a, b).

(AI4)

(AI5)

(A16)

(AI7)

(AIS)

(A19)

(A20)

(A22)

(A23)

(A24)

(A25)

(A26)

(A27)

i)

7)

8)

9)

0)

nsof~d

im

~I)

we

22)

23)

~6).mdtedm-

.24)

.25)

we

l26)

~27)

The required solution is obtained when

A model for spark ignition engine with intake and exhaust systems 123

er = 0,

es = O.

The solution starts with approximate values of er and es where

er = F(an, bn),

es = G(an, bn).

The new values of the variables are adjusted for the next step by

whereD.a _ er (G/ob) (es) -es (G/ob) (er)

- J(an, bn) ,

t,b = er - (%a) (er) t,a(%b) (er)

ande 0 0 0

J(a,,, bn) = oa (er) ob (es) - ob (er) oa (es).

(A28)

(A29)

(A30)

(A3I)

(A32)

(A33)

The above procedure will be repeated for new values of an+! and bn+! until the solutionwithin stipulated precision is obtained.

APPENDIX II

RATE FORMATION FOR NITRIC OXIDE

The rate formation for nitric oxide given by equation (43) is derived as follows.Let Kir denote the forward rate constant for the ith reaction, Kib the backward rate

constunt for t.he ith react.ion and R, the "one-way" equilibrium rate for the ith reaction.Thon

where the suffix e represents equilibrium and V is the volume of burned gas.

Calculation of (I/V) (d/dt) NO) V)From equation (36) the net rate is

-KI/N) (NO)+Klb(N2) (0) = -cx,{3, K1r(N), (NO),+K1b(N2), (0),.But

Klr(N). (NO), = K,b(N2). (0), = R"

so that the net rate becomes - ex,(3. RI +RI'Using the similar terms for equations (37), (38) and (41), involving NO, we finally have

I clTT rlt NO) V) = -ex.({3. RI +R2 +R3\- 2cx.R.) +Rl +j3,(Rz +Rs) + 2y, e;

Calculation of (I/V) (d/dt) N) V)Considering equations (36)-(38) and using similar procedure we have

~ ~ N) V) = -(3.(CY., RI +R2 +Rs) +R, +cxe(Rz +Rs).

(A34)

(A35)

,~ , _. " ,-......,. ~ -~ - -. - -- '" _ .'"Ir

, '. . )

Calculation oj (1/V) (d/dt) ((N20) V)Considering equations (39)-(42), we have

-VI~(("N20) F) = -y,(R4+R5+RS+R7)+R4+R,+a;R6+R7'Clt .

It has been found? t.hat the relaxation times for equation (A35) and equation (A:36)arc several orders of magnitude shorter than that of equation (A34). Therefore, steadystn,te Inl1y bo assumed for (N) and (N20) which moans tho right-hand sides of equations(A35) and (A36) can be set equal to zero.

Then from equation (A35)

(A36)

124 R. S. BENSON, W. J. D. ANNAND and P. C. BARUAH

fJ, = RL +cxe(R,z+Ra). cx.R,+l1z+Ra

(A37)

and from equation (A36)

R 4 +R 6 +a; Ro+R,y, = R4+R,+R6+B, .

Using these values of fJ. and y. in equation (A34) we have

~.:!.((NO)V)=2(1-CX;)( R, .+ R6 ),Velt l+cx,[Rd(RdRa)] 1+[Rs/(R4+R5+R7)]

which is the final rate equation for NO.

(A3S)

(A39)