COMBUSTION SIMULATION IN A SPARK IGNITION ENGINE … · COMBUSTION SIMULATION IN A SPARK IGNITION...

COMBUSTION SIMULATION IN A SPARK IGNITION ENGINECYLINDER: EFFECTS OF AIR-FUEL RATIO ON THE

COMBUSTION DURATION

by

Nureddin DINLER * and Nuri YUCEL

De part ment of Me chan i cal En gi neer ing, Fac ulty of En gi neer ing, Gazi Uni ver sity,Maltepe/An kara, Tur key

Orig i nal sci en tific pa perUDC: 621.43.019:519.876.5

DOI: 10.2298/TSCI10041001D

Com bus tion is an im por tant sub ject of in ter nal com bus tion en gine stud ies. To re -duce the air pol lu tion from in ter nal com bus tion en gines and to in crease the en gineper for mance, it is re quired to in crease com bus tion ef fi ciency. In this study, ef fectsof air/fuel ra tio were in ves ti gated nu mer i cally. An axisymmetrical in ter nal com bus -tion en gine was mod eled in or der to sim u late in-cyl in der en gine flow and com bus -tion. Two di men sional tran sient con ti nu ity, mo men tum, tur bu lence, en ergy, andcom bus tion equa tions were solved. The k-e tur bu lence model was em ployed. Thefuel mass frac tion trans port equa tion was used for mod el ing of the com bus tion. Forthis pur pose a com pu ta tional fluid dy nam ics code was de vel oped by us ing the fi nitevol ume method with FORTRAN pro gram ming code. The mov ing mesh was uti lizedto sim u late the pis ton mo tion. The de vel oped code sim u lates four strokes of en ginecon tin u ously. In the case of lam i nar flow com bus tion, Arrhenius type com bus tionequa tions were em ployed. In the case of tur bu lent flow com bus tion, eddy break-upmodel was em ployed. Re sults were given for rich, stoichiometric, and lean mix tures in con tour graphs. Con tour graphs showed that lean mix ture (l = 1.1) has lon gercom bus tion du ra tion.

Key words: internal combustion engines, finite volume method, combustionmodeling

In tro duc tion

World’s en ergy de mand is met mostly with com bus tion tech nol o gies. In spite of al ter -na tive tech nol o gies of en ergy pro duc tion for power plants, there is no al ter na tive for trans por ta -tion. Re search ers also work on al ter na tive tech nol o gies, like fuel cell, for trans por ta tion sec tor.

In ter nal com bus tion en gines are ma jor sources of ur ban air pol lu tion [1, 2]. Com bus -tion phe nom ena in in ter nal com bus tion en gines are to be in ves ti gated in de tail. The most im por -tant pro cess on in ter nal com bus tion en gines is com bus tion pro cess, and one of the im por tantparts of en gine mod el ing is com bus tion mod el ing [3]. Nu mer i cal meth ods are cheaper than ex -per i men tal meth ods. Nu mer i cal meth ods are used to es ti mate the pa ram e ters, that can not be

Dinler, N., et al.: Combustion Simulation in a Spark Ignition Engine Cylinder: Effects of ...

THERMAL SCIENCE: Year 2010, Vol. 14, No. 4, pp. 1001-1012 1001

* Corresponding author; e-mail: [email protected]

mea sured or hard to mea sure, eas ily [4]. In ter nal com bus tion en gine mod el ing is one of the keyel e ments of de sign ing new en gines. In ter nal com bus tion en gine con cept was first de signed by J.de Hautefeuille in 1676, and then de vel oped by Ch. Huygens and M. Pupin [5]; fur ther more, de -vel oped by other re search ers and de vel op ment of in ter nal com bus tion en gines still con tin ues.

Nu mer ous stud ies could be found in the lit er a ture. Re search ers stud ied com bus tion us -ing the mod els in a range of sim ple ther mo dy namic mod els to com pli cated chem i cal ki neticmod els. Few of these stud ies are given be low. Ahmadi-Befrui et al. [6] stud ied two-di men sional in ter nal com bus tion en gine cyl in der. The au thors in ves ti gated in-cyl in der flow and com bus tion; in ad di tion, they com pared some pa ram e ters of in-cyl in der flow with ex per i men tal re sults.Bilgin [7] stud ied in take stroke flow of a two-di men sional in ter nal com bus tion en gine cyl in der.Bilgin used k-e model for tur bu lent flow and com pared his re sults with other re search ers’ stud -ies. Abd-Alla [8] stud ied spark ig ni tion en gine cy cle; in fact, Abd-Alla in ves ti gated the ef fectsof com pres sion ra tio, equiv a lence ra tio, spark ig ni tion tim ing, heat re lease rate, com bus tion du -ra tion, com bus tion ef fi ciency us ing ex per i men tal re sults from other re search ers, and ther mo dy -namic ex pres sions for ideal gas, and fric tion work for mu las. Abu-Orf et al. [9] de vel oped a newre ac tion model for pre mixed tur bu lent com bus tion in spark ig ni tion (SI) en gines. They com -pared their en gine cyl in der pres sure with other re search ers’ ex per i men tal and nu mer i cal data;fur ther more, ef fects of fuel type such as pro pane, isooctane, and meth ane, equiv a lence ra tio, and en gine speed on tur bu lent com bus tion in a SI en gine cyl in der was in ves ti gated by re search ers.Kodah et al. [3] mod eled com bus tion us ing Wiebe func tion. Their model was built on ther mo -dy namic prop er ties. They in ves ti gated the change of in-cyl in der pa ram e ters with re spect toin-cyl in der pres sure. El Tahry [10] adopted lam i nar flamelet model of other re search ers’. Hecom pared his com pu ta tional re sults with other re search ers’ ex per i men tal re sults. There weredis par i ties be tween re sults due to as sump tion of one-di men sional flamelet as sump tion.

Kong et al. [11] com pared ex per i men tal and nu mer i cal re sults of HCCI en gine us ingKIVA-3V and CHEMKIN im ple mented in KIVA-3V. They com pared nu mer i cal re sults of cyl -in der pres sure, HC and CO emis sions with mea sured data. Ac cord ing to their cal cu la tions nu -mer i cal model com bus tion re sults are not af fected with grid res o lu tion; i. e., struc ture of coarsemesh and fine mesh cal cu lated com bus tion with same level of ac cu racy. Emis sion cal cu la tion inpis ton-ring crev ice is re quired to be de ter mined. They con cluded that com bus tion and emis sionlev els of HCCI are more sen si tive to ini tial mix ture tem per a ture than wall tem per a tures. Thecom pu ta tional fluid dynamics (CFD) model re sults are con sis tent with cyl in der pres sure, heatre lease rate, and HC emis sions rates; how ever, CO emis sion level was un der pre dicted.

Ogink et al. [12] stud ied gas o line ho mo ge neous charge com pres sion ig ni tion en ginemod el ing. They com bined one di men sional gas dy nam ics pro gram AVL-BOOST en gine cy clesim u la tion code with sin gle-zone com bus tion model for fur ther en gine re search. They com -pared their re sults with a sin gle cyl in der test en gine. Their com bined code pre dicts fuel con -sump tion and in di cated mean ef fec tive pres sure over a range of 1-10% er rors. There are manystud ies in the lit er a ture to solve the flow in the cyl in der of an in ter nal com bus tion en gine likeHaworth et al. [13] and Jasak et al. [14]. Akkerman et al. [15] stud ied axisymmetrical two di -men sional SI en gine to in ves ti gate tur bu lent flow pro duced by pis ton mo tion. Also some otherstud ies deal with de tailed com bus tion mech a nisms like Soyhan et al. [16] and Kong [17].

In this study, ef fect of air-fuel ra tio on pre mixed fuel air mix ture com bus tion in anaxisymmetrical SI en gine cyl in der was in ves ti gated nu mer i cally; more over, ef fect of en ginespeed on com bus tion is stud ied.


1002 THERMAL SCIENCE: Year 2010, Vol. 14, No. 4, pp. 1001-1012

Prob lem def i ni tion and for mu la tion

The con fig u ra tion of the cyl in der with its ports isshown in fig. 1. The cyl in der is axisymmetric and in let and ex haust valves are lo cated at the cyl in der axis. Inor der to ob tain flow field and com bus tion char ac ter is -tics, the en sem ble-av er aged dif fer en tial form of con ti -nu ity, mo men tum, enthalpy, stan dard k-e and chem i -cal re ac tion equa tions are solved with ap pro pri atebound ary con di tions. Tur bu lent com bus tion is sim u -lated by eddy break-up model. All these equa tionswere used to de velop FORTRAN code to sim u late thecom plete en gine cy cle. Code starts with in take stroke,then fol lowed by com pres sion, ex pan sion (work ing),and ex haust strokes, re spec tively.

Con ti nu ity equa tion

Con ti nu ity equa tion for 2-D un steady flow incylinderical co-or di nates are given as:

¶

¶

¶

¶

¶

¶

r r r

t

u

z r

r u

r+ + =

( ) )z r(10 (1)

Mo men tum equa tions

Mo men tum equa tions for two axes sep a rately can be given as:

– r-axis ra dial mo men tum equa tion

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ) )r r rm

u

t

u u

z r

r u u

r z

u

zr z r r r

effr( (

+ + =æ

èç

ö1

ø÷ +

æ

èç

ö

ø÷ +

1

r rr

u

rS

¶

¶

¶

¶meff

r (2)

SP

r

u

rS t

r= - - +¶

¶meff

r

2(3)

Sz

u

r r rr

u

r

utr z r=

æ

èç

ö

ø÷ +

æ

èç

ö

ø÷ -

¶

¶

¶

¶

¶

¶

¶

¶m m meff eff eff

1 r

r rk

2

2

3- Ñ× +

¶

¶( )m reff V

r(4)

Ñ× = +rV

1

r

ru

r

u

zr z¶

¶

¶

¶

( )(5)

– z-axis mo men tum equa tion

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( ) ( )r r rm

u

t

u u

z r

r u u

r z

u

zz z z r z

effz+ + =

æ

èç

ö1

ø÷ +

æ

èç

ö

ø÷ +

1

r rr

u

rSeff

z¶

¶

¶

¶m (6)



Figure 1. Schematically description ofpiston-cylinder assembly of the problem

SP

zS t

z= - +¶

¶(7)

Sz

u

z r rr

u

z ztz =

æ

èç

ö

ø÷ +

æ

èç

ö

ø÷ -

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶m meff

zeff

r1 2

3( )m reff VÑ× +

rk (8)

m m meff t= + (9)

m re

mt = Ck 2

(10)

Tur bu lence equa tions

For tur bu lence mod el ing, k-e two equa tion tur bu lence model was cho sen:

– trans port equa tion of tur bu lent ki netic en ergy, k:

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( ) ( )r r r m

s

k

t

u k

z r

r u k

r z

k

z+ + =

æ

èçç

ö

ø

z r eff

k

1÷÷ +

æ

èçç

ö

ø÷÷ +

1

r rr

k

rS

¶

¶

¶

¶

m

seff

kk (11)

S G kk eff V V= - Ñ× + Ñ× -2

3( )m r re

r r(12)

– trans port equa tion of tur bu lence ki netic en ergy dis si pa tion rate, e:

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( ) ( )re r e r e m

s

e

et

u

z r

r u

r z z+ + =

æ

èçç

ö

ø

z r eff1÷÷ +

æ

èçç

ö

ø÷÷ +

1

r rr

rS

¶

¶

¶

¶

m

s

e

ee

eff (13)

Sk

C G Ce

ere= -( )1 2 (14)

Gu

r

u

z

u

z

u

zt= +

æ

èç

ö

ø÷ +

æ

èç

ö

ø÷ +

æ

èç

ö

ø÷m mt

z r z r¶

¶

¶

¶

¶

¶

¶

¶

2 2

2

2 2

+æ

èç

ö

ø÷

é

ë

êê

ù

û

úú

u

rr (15)

The con stants are: C1 = 1.44, C2 = 1.92, Cm = 0.09, sk = 1.00, and se = 1.30.

Wall func tions ap plied to near wall flow are given in de tail in Versteeg et al. [18].

En ergy equa tion

To tal enthalpy is used for cal cu lat ing the en ergy equa tion. En ergy equa tion is given as:

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( ) ( )r r r m

s

h

t

u h

z r

r u h

r z

h

z+ + =

æ

èçç

ö

ø

z r t

n, t

1÷÷ +

æ

èçç

ö

ø÷÷ +

1

r rr

h

r

P

t

¶

¶

¶

¶

¶

¶

m

st

n, t

(16)

– total enthalpy

h C T u u k m hj j= + + + +p r z

1

22 2( ) S (17)

m jall j

=å 1 (18)



Chem i cal re ac tion equa tion

Chem i cal equa tion is given for hy dro car bon fu els:

C H O CO H On m + +æ

èç

ö

ø÷ + +

æ

èç

ö

ø÷ ® + +n

mn

mN n

m

43 76

4 23 762 2 2 2. . n

m+

æ

èç

ö

ø÷

42N (19)

Chem i cal re ac tion trans port equa tion is used as:

¶

¶

¶

¶

¶

¶

¶

¶

¶

¶

( ) ( ) ( )r r r m

s

m

t

u m

z r

r u m

r z

m

zf z f r f t

f, t

f+ + =æ

è

1çç

ö

ø÷÷ +

æ

èçç

ö

ø÷÷ -

1

r rr

m

rR

¶

¶

¶

¶

m

st

f, t

ff (20)

Dur ing the so lu tion of chem i cal re ac tion equa tion the source term Rf is de pend on flowcon di tions. For lam i nar flow com bus tion, the re ac tion rate is kinetically con trolled andArrhenius type source term is used:

R m mE

Tf

afb

oxc

R=

-æ

èç

ö

ø÷r exp (21)

where E/R = 1.84·104 K.In this study the model con stants are taken as:

a = 1.59252 + 1.54482exp(–0.0055N)b = 1.0c = 1.6

For tur bu lent flow com bus tion, eddy break-up model is used. The re ac tion rate of fuelis taken as the small est value of tur bu lent dis si pa tion rates of fuel, ox y gen, and prod ucts:

- =R C mk

fu R fre

(22)

- =R Cm

s kox R

oxre

(23)

- = ¢+

R Cm

s kpr R

prr

e

1(24)

Equa tion of state

Equa tion of state is used as sup ple men tary equa tion:

P = rRT (25)

Bound ary and ini tial con di tions

Bound ary and ini tial con di tions that used in or der to solve the equa tions are given be -low. Bound ary con di tions dur ing in take stroke are di vided into parts. At the cyl in der head hastwo parts; first one is the valve gap for in let pro cess, sec ond one is the walls of cyl in der head.Fuel mass frac tion in the fuel/air mix ture change ac cord ing to the mix ture is rich, stoichiometric,



and lean mix ture. On the pis ton head, which lim its com bus tion cham ber, ve loc ity of the work ing fluid is equal to ve loc ity of the pis ton. On the walls of the com bus tion cham ber wall bound arycon di tions are used, due to ge om e try on the symmery axis, sym met ric bound ary con di tions areused.

At the cyl in der head (z = 0) (dur ing the in take stroke):

u u u u

T T k u

z z in r r in

in in z

in

K lin

= =

= = =

=

- -

300 0000

0164

2.

.e 30035

1 5k

B

m f

inat the valve inlet.

.

æ

èçç

ö

ø÷÷

ü

ý

ïïï

þ

ïïï

mf = 0.0608 for l = 0.9 rich mixture

mf = 0.055 for l = 1.0 stoichiometric mixture

mf = 0.0503 for l = 1.1 lean mixture

u u k

Tm

z

z r

fKon the walls o

= = = =

= =

ü

ýï

þï

0 0 0 0

450 0

, , ,

,

e¶

¶

f the cylinder

On the pis ton face (z = zpis ton)

uz = Upis(t), ur = 0, k = 0, e = 0, T = Tpis = 450 K, ¶

¶

m

zf = 0

On the cyl in der sur face (r = R)

uz = 0, ur = 0, k = 0 , e = 0, T = 450 K, ¶

¶

m

rf = 0

At the sym me try axis (r = 0)¶

¶

u

rur

z = =0 0,

¶

¶

¶

¶

¶

¶

¶

¶

k

r r

T

r

m

r= = = =0 0 0 0, , ,

e f

Ini tial con di tions (t = 0)

uz = 0, ur = 0, k = 0, e = 0, T = Tinitial = 300 K

mf = 0.0

Re cip ro cat ing mo tion of pis ton is mod eled by us ing mov ing mesh tech nique. All equa -tions were con verted ac cord ing to con ver sion equa tion of mov ing mesh [7, 19]:

x =z

z tpis ( )Nu mer i cal so lu tion pro ce dure

The gov ern ing equa tions sub ject to rel e vant bound ary con di tions were solved nu mer i -cally us ing fi nite-vol ume method. The up wind tech nique was em ployed to discretize the con -



vec tive terms. All discretization steps were given in [20]. A CFD code has been de vel oped byus ing the SIMPLE al go rithm [21] in FORTRAN pro gram ming lan guage. In or der to ob tain a so -lu tion in de pend ent of the grid dis tri bu tion, grid sen si tiv ity tests were per formed by trac ing thecyl in der pres sure against crank an gle (CA) as it was done by Watkins et al. [22]. It is found thatthe so lu tion be comes al most in de pend ent with 50 uni form grids in x-di rec tion and 30 uni formgrids in the r-di rec tion. All mo men tum, en ergy and chem i cal re ac tion equa tions are cou pled andsolved to gether. The de vel oped CFD code sim u lates four strokes of en gine cy cle in clud ing flowmo tion and com bus tion.

Re sults and dis cus sion

In this study com bus tion in an ide al ized ho mo ge neous charge SI en gine is an a lyzednu mer i cally. It is as sumed that spark plug and in let/ex haust valves are lo cated at the cen ter lineof cyl in der. Com pu ta tions are per formed for three dif fer ent air fuel ra tios, for com pres sion ra tioof 10:1 and in let valve an gle of 60°. En gine speed is set to N = 24 rpm and N = 2400 rpm, whichcor re sponds to lam i nar and tur bu lent flow con di tions, re spec tively. Cyl in der bore D = 0.1 m,stroke L = 0.09 m and di am e ter of in let/ex haust valve d = 0.05 m are cho sen. Meth ane is used asa fuel. In case of lam i nar com bus tion, Arrhenius type com bus tion equa tions were em ployed. Incase of tur bu lent com bus tion, eddy break-up model was used.

Ig ni tion tim ing is an im por tant pa ram e ter for SI en gine com bus tion. Ig ni tion tim ing ad -vance (ITA), is cal cu lated by the fol low ing equa tion which is sug gested by the au thors:

ITA = 6.83635 + 12.282[1 – exp(–0.00087 N)]

Com bus tion is started as sum ing the 70 per cent of fuel con sumed at the ig ni tion time inthe re gion around the spark plug. This re gion cor re sponds to the com pu ta tion cells of (1 to 3 ́ 1to 10) (r ́ x). The flame de vel ops from the ig ni tion points in a nearly hemi spher i cal re gion and it reaches to the pis ton sur face. Then the flame front prop a gates in the ra dial di rec tion.

In or der to in ves ti gate the ef fect of air/fuel ra tio, ex cess air co ef fi cient l was cho senl = 0.9, 1.0, 1.1, which rep re sents the mix tures of rich, stoichiometric and lean, re spec tively.Air fuel mix ture en ters the cyl in der with given val ues as bound ary con di tion, then con cen tra -



Figure 2. Mass fraction of fuel at 343 °CA. Effect of excess air coefficient l: (a) l = 0.9, (b) l = 1.0, (c) l = 1.1; (compression ratio r = 10:1; engine speed N = 2400 rpm (color image see on our web site)

tion of fuel changes in the cyl in der. For the tur bu lent com bus tion mod el ing, en gine speed wascho sen 2400 rpm (figs. 2 and 3). Dur ing the in take stroke, con tours of mass frac tion of fuellook sim i lar but have dif fer ent val ues due to mix ture com po si tion. Af ter pis ton reaches BDC(bot tom dead cen ter), valve open ing closes and the air-fuel mix ture com pressed dur ing thecom pres sion stroke and ho mo ge neous mix ture frac tion ob tained (fig. 2). Af ter the ig ni tion,the flame de vel ops from the ig ni tion points in a nearly hemi spher i cal re gion and it reaches tothe pis ton sur face. Then the flame front prop a gates in the ra dial di rec tion. For the rich andstoichiometric mix tures com bus tion du ra tion is the same be cause the max i mum amount offuel that can be burned is the stoichiometric ra tio of that fuel. Ex cess fuel does not in volve inthe com bus tion. For lean mix ture, flame ve loc ity is lower than stoichiometric and rich mix -ture, com bus tion du ra tion is lon ger (figs. 3 and 4). The same trend was ob served in the re cent





study of Perini et al. [23] about com bus tion pro cess in SI en gines fu eled with hy dro gen, meth -ane, and hy dro gen-meth ane blends.

In fig. 5, mass frac tion of fuel con tours is given for the SI tim ing. Com bus tion du ra tion in lam i nar com bus tion is shorter in terms of the CA, be cause en gine speed is slower. When l in -creases com bus tion du ra tion also in creases in lam i nar com bus tion. The lon gest du ra tion is ob -tained for l = 1.1 (figs. 6 and 7). Ex per i men tal in ves ti ga tion on flame sta bil ity of hy dro ge natedmix ture was done by Hal ter et al. [24], it is ob served that for lam i nar com bus tion, burned gasMarkstein length, that is re lated to flame ve loc ity, in creases with de creas ing air/fuel ra tio. Thisob ser va tion is in agree ment with ob ser va tion of the nu mer i cal re sults of this study.



Figure 5. Mass fraction of fuel at 354.5 °CA. Effect of excess air coefficient l: (a) l = 0.9, (b) l = 1.0, (c) l = 1.1; (compression ratio r = 10:1; engine speed N = 24 rpm (color image see on our web site)

Figure 6. Mass fraction of fuel at 355.5 °CA. Effect of excess air coefficient l: (a) l = 0.9, (b) l = 1.0, (c) l = 1.1; (compression ratio r = 10:1; engine speed N = 24 rpm (color image see on our web site)

Con clu sions

The pur pose of this study is to in ves ti gate the ef fect of air/fuel ra tio on com bus tion du -ra tion. A 2-D CFD code was de vel oped for this pur pose. This code sim u lates over all en gine cy -cle – in take, com pres sion, ex pan sion, and ex haust strokes – with com bus tion. The au thors sug -gest ig ni tion tim ing ad vance (ITA) for mula to de ter mine the ITA ac cord ing to the codesim u la tions. In tur bu lent com bus tion eddy break-up model was used. Com bus tion du ra tions ofthe rich and stoichiometric mix tures are the same due to the max i mum amount of fuel that can be burned is the stoichiometric ra tio of that fuel. How ever, com bus tion du ra tion of the lean mix ture is lon ger than stoichiometric mix ture com bus tion du ra tion. In lam i nar flow con di tionsArrhenius type com bus tion model was used to model the com bus tion.

Ac knowl edg ment

This work was sup ported by the Sci en tific Re search Pro jects of Gazi Uni ver sity un derGrant 06/2006-02.




No men cla ture

a – model constant, [–]B – bore, [m]b – model constant, [–]C1 – turbulence model constant, [–]C2 – turbulence model constant, [–]CR – model constant, [–]

¢CR – model constant, [–]Cm – turbulence model constant, [–]c – model constant, [–]E – activation energy, [Jmol–1]Hj – formation enthalpy of jth component,

– [kJkg–1]

h – enthalpy [kJkg–1]k – turbulence kinetic energy, [m2s–2]M – molecular weight of gas, [kgkmol–1]mj – mass fraction of jth component of

– mixture, [kgkg–1]mf – mass fraction of fuel in air/fuel mixture,

– [kgkg–1]mox – mass fraction of oxygen in air/fuel

– mixture, [kgkg–1]mpr – mass fraction of products in mixture, [kgkg–1]P – pressure, [kPa]R – gas constant, [Jmol–1K–1]

Ref er ences

[1] Hey wood, J. B., In ter nal Com bus tion En gine Fun da men tals, McGraw-Hill, Sin ga pore, 1988[2] Pulkrabek, W. W., En gi neer ing Fun da men tals of the In ter nal Com bus tion En gine, Prentice Hall,

Engelwood Cliffs, N. J., USA, 1997[3] Kodah, Z. H., et al., Com bus tion in a Spark-Ig ni tion En gine, Ap plied En ergy, 66 (2000), 3, pp. 237-250[4] Eaton, A. M., et al., Com po nents, For mu la tions, So lu tions, Eval u a tion, and Ap pli ca tion of Com pre hen -

sive Com bus tion Mod els, Prog ress in En ergy and Com bus tion Sci ence, 25 (1999), 4, pp. 387-436[5] Borgman, G. L., Ragland, K. W., Com bus tion En gi neer ing, McGraw-Hill, In ter na tional edition, New

York, USA, 1998[6] Ahmadi-Befrui, B., et al., Mul ti di men sional Cal cu la tion of Com bus tion in an Ideal ised Ho mo ge neous

Charge En gine: A Prog ress Re port, SAE pa per 810151, 1981, pp. 636-651[7] Bilgin, A., Nu mer i cal Sim u la tion of the Cold Flow in an Axisymmetric Non-Com press ing En gine-Like

Ge om e try, In ter na tional Jour nal of En ergy Re search, 23 (1999), 10, pp. 899-908[8] Abd-Alla, G. H., Com puter Sim u la tion of a Four Stroke Spark Ig ni tion En gine, En ergy Con ver sion and

Man age ment, 43 (2002), 8, pp. 1043-1061[9] Abu-Orf, G. M., Cant, R. S., A Tur bu lent Re ac tion Rate Model for Pre mixed Tur bu lent Com bus tion in

Spark-Ig ni tion En gines, Com bus tion and Flame, 122 (2000), 3, pp. 233-252[10] El Tahry, S. H., Tur bu lent-Com bus tion Model for Ho mo ge neous Charge En gines, Com bus tion and

Flame, 79 (1990), 2, pp. 122-140[11] Kong, S. C., Reitz, R. D., Nu mer i cal Study of Pre mixed HCCI En gine Com bus tion and its Sen si tiv ity to

Com pu ta tional Mesh and Model Un cer tain ties, Combust. The ory Mod el ling, 7 (2003), 2, pp. 417-433[12] Ogink, R., Golovitchev, V., Gas o line HCCI Mod el ing: Com puter Pro gram Com bined De tailed Chem is try

and Gas Ex change Pro cesses, SAE pa per 2001-01-3614, 2001[13] Haworth, D. C., El Tahry, S. H., Prob a bil ity Den sity Func tion Ap proach for Mul ti di men sional Tur bu lent

Flow Cal cu la tions with Ap pli ca tion to On-Cyl in der Flows in Re cip ro cat ing En gines, AIAA Jour nal, 29(1991), 2, pp. 208-218

[14] Jasak, H., et al., Rapid CFD Sim u la tion of In ter nal Com bus tion En gines, SAE pa per 1999-01-1185, 1999, pp. 1964-1703

[15] Akkerman, V., Ivanov, M., Bychkov, V., Tur bu lent Flow Pro duced by Pis ton Mo tion in a Spark-Ig ni tionEn gine Flow, Tur bu lence and Com bus tion, 82 (2009), 3, pp. 317-337

[16] Soyhan, H. S., Mauss, F., Sorusbay, C., Chem i cal Ki netic Mod el ing of Com bus tion in In ter nal Com bus -tion En gines Us ing Re duced Chem is try, Com bus tion Sci ence and Tech nol ogy, 174 (2002), 11-12, pp.73-91

[17] Kong, S. C., A Study of Nat u ral Gas/DME Com bus tion in HCCI En gines Us ing CFD with De tailed Chem -i cal Ki net ics, Fuel, 86 (2007), 10-11, pp. 1483-1489

[18] Versteeg, H. K., Malalasekera, W., An In tro duc tion to Com pu ta tional Fluid Dy nam ics: The Fi nite Vol ume Method, Longman Sci en tific & Tech ni cal, Harlow, Essex, Eng land, 1995

[19] Farrashkhalvat, M., Miles, J. P., Ba sic Struc tured Grid Gen er a tion with an In tro duc tion to Un struc turedGrid Gen er a tion, Butterworth-Heinemann, Ox ford, Eng land, 2003



Rf – source term due to reaction, [kgm–3s–1]Rfu – turbulent dissipation rate of fuel,

– [kgm–3s–1]Rox – turbulent dissipation rate of oxygen,

– [kgm–3s–1]Rpr – turbulent dissipation rates of products,

– [kgm–3s–1]St – turbulent source term, [kgm–2s–2]s – stoichiometric oxygen value for unit

– mass of fuel, [–]T – temperature, [K]uz – z-axis (axial) velocity component, [ms–1]ur – r-axis (radial) velocity component, [ms–1]

Greek let ters

e – turbulent kinetic energy dissipation rate,– [m2s–3]

l – excess air coefficientmeff – effective viscosity of the fluid, [kgm–1s–1]mt – turbulent viscosity, [kgm–1s–1]r – density, [kgm–3]sk – turbulence model constantsn,t – turbulent Prandtl numberse – turbulence model constant

[20] Dinler, N., Nu mer i cal In ves ti ga tion of Flow and Com bus tion in a Spark Ig ni tion En gine Cyl in der, Ph. D.the sis, Gazi Uni ver sity, In sti tute of Sci ence and Tech nol ogy, 2006 (in Turk ish)

[21] Patankar, S.V., Nu mer i cal Heat Trans fer and Fluid Flow, Hemi sphere Pub lish ing Corp., New York, USA,1980

[22] Watkins, A. P., Li, S.-P., Cant, R. S., Pre mixed Com bus tion Mod el ling for Spark-Ig ni tion En gine Ap pli ca -tions, SAE pa per 961190, 1996

[23] Perini, F., Paltrinieri, F., Mattarelli, E., A Quasi-Di men sional Com bus tion Model for Per for mance andEmis sions of SI En gines Run ning on Hy dro gen-Meth ane Blends, Int. J. of Hy dro gen En ergy, 35 (2010),10, pp. 4687-4701

[24] Hal ter, F., Chauveau, C., Gökalp, I., Char ac ter iza tion of the Ef fects of Hy dro gen Ad di tion in Pre mixedMeth ane/Air Flames, Int. J. of Hy dro gen En ergy, 32 (2007), 13, pp. 2585-2592

Paper submitted: December 30, 2009Paper revised: January 26, 2010Paper accepted: May 18, 2010



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