Full Leng h A icle
Analysis o he combus ion speed in a spa k igni ion engine uelled wi h
hyd ogen and gasoline blends a di e en ai uel a ios
Ped o Gabana
a,*
, Blanca Gim´
enez
a
, Jos´
e Ma ín He e os
b
, A hanasios Tsolakis
b
a
Depa men o Ene gy and Fluid Mechanics Enginee ing, Uni e si y o Valladolid, Paseo del Cauce 59, E-47011 Valladolid, Spain
b
Depa men o Mechanical Enginee ing, Uni e si y o Bi mingham. Edgbas on, Bi mingham, B15 2TT, UK
ARTICLE INFO
Keywo ds:
Hyd ogen-Gasoline combus ion
Quasi-dimensional combus ion diagnosis
Tu bulen combus ion speed
P emixed combus ion
Combus ion speed analysis
Expansion speed
ABSTRACT
The use o hyd ogen in in e nal combus ion engines is a p omising solu ion o he deca bonisa ion o he
anspo sec o . The cu en ansi ion scena io is ma ked by he una ailabili y and s o age challenges o
hyd ogen. Dual uel combus ion o hyd ogen and gasoline in cu en spa k igni ion engines is a easible solu ion
in he sho and medium e m as i can imp o e engine e iciency, educe pollu an emissions and con ibu e
signi ican ly in ank o wheel deca bonisa ion wi hou majo engine modi ica ion. Howe e , new esea ch is
needed o unde s and how he inco po a ion o hyd ogen a ec s exis ing engines o e ec i ely implemen
gasoline-hyd ogen dual uel op ion. Unde s anding he impac o hyd ogen on he combus ion p ocess (e.g.
combus ion speed) will guide and op imize he ope a ion o engines unde dual uel combus ion condi ions.
In his wo k, a comme cial gasoline di ec injec ion engine has been modi ied o ope a e wi h gasoline-
hyd ogen uels. The expe imen s ha e been ca ied ou a a ious ai – uel a ios anging om s oichiome ic
o lean combus ion condi ions a cons an engine speed and o que. A each one o he 14 expe imen al poin s,
200-cycle in-cylinde p essu e aces we e eco ded and p ocessed wi h a quasi-dimensional diagnos ic model
and a combus ion speed analysis was hen ca ied ou . I has been unde s ood ha hyd ogen mainly educes he
du a ion o he i s combus ion phase. Hyd ogen also enables o inc ease ai excess a ios (lean in uel com-
bus ion) wi hou signi ican ly inc easing combus ion du a ion.
Fu he mo e, a co ela ion is p oposed o p edic combus ion speed as a unc ion o he uel and ai mix u e
p ope ies. This co ela ion can be inco po a ed o calcula e combus ion du a ion in p edic i e models o engines
ope a ing unde di e en uel mix u es and di e en geome ies o he combus ion chambe wi h pen - oo
cylinde head and la pis on head.
1. In oduc ion
The anspo sec o is inc easingly mo ing owa ds deca bonisa ion.
This sec o is la gely sus ained by he use o ossil uels ha a e bu ned
in gas u bines o in e nal combus ion engines (ICEs) o ob ain me-
chanical ene gy. Wi hin he anspo sec o , ICEs a e he mos wide-
sp ead p opulsion sys ems because hey can wo k in a wide ange o
ope a ing condi ions. On he o he hand, he lowe he ca bon con en o
uels, he lowe he CO2 emissions in ela ion o he ene gy p oduced in
hei combus ion [1]. As hyd ogen has no ca bon a oms in i s compo-
si ion, i does no gene a e CO2 du ing combus ion. The e o e, hyd ogen
is p esen ed as an al e na i e o ossil uels, since i s use as a uel in
engines means he educ ion o CO2 [2], CO, unbu ned hyd oca bons
and soo emissions [3].
The use o syn he ic uels p oduced om enewable ene gy is a way
o mo e away om he use o ossil uels in ICEs. H2 can be p oduced
om enewable elec ici y wi h ze o CO2 equi alen emissions [3].
Hyd ogen in he mobili y sec o is majo ly used in wo ways. The i s
one is he use o hyd ogen in uel cells [3,4]. The second op ion is he use
o hyd ogen in he mal engines [3,5]. Wi hin he ecip oca ing he mal
engines, he use o hyd ogen in comp ession igni ion engines (CIE) has
he disad an age ha he au oigni ion empe a u e o hyd ogen is
highe han hose o con en ional uels [5]. In spa k igni ion engines
(SIE), he use o pu e H2 as uel enables he use o high ai – uel a ios
and high le els o esidual gas concen a ions. The highe he ai – uel
a io o esidual gas concen a ions, he lowe he in-cylinde empe -
a u e du ing he combus ion p ocess. The lowe he combus ion
* Co esponding au ho .
E-mail add esses: [email p o ec ed] (P. Gabana), [email p o ec ed] (B. Gim´
enez), [email p o ec ed] (J. Ma ín He e os), [email p o ec ed]
(A. Tsolakis).
Con en s lis s a ailable a ScienceDi ec
Fuel
jou nal homepage: www.else ie .com/loca e/ uel
h ps://doi.o g/10.1016/j. uel.2024.133563
Recei ed 18 Augus 2024; Recei ed in e ised o m 11 Oc obe 2024; Accep ed 25 Oc obe 2024
Fuel 381 (2025) 133563
A ailable online 3 No embe 2024
0016-2361/© 2024 The Au ho s. Published by Else ie L d. This is an open access a icle unde he CC BY license (
h p://c ea i ecommons.o g/licenses/by/4.0/ ).
empe a u e, he lowe he NOx emissions. Pe o mance imp o emen s
ha e also been obse ed as epo ed by Kapus e al. [6]. Howe e , he
implemen a ion o hyd ogen p esen s se e al challenges, some o he
mos impo an ones a e s o age and a ailabili y [2,7].
The use o dual uel (hyd ogen and gasoline) is p esen ed as a sho -
e m and medium- e m al e na i e o educe CO2 emissions by uni o
ene gy p oduced [8,9] wi hou majo engine modi ica ions. P e ious
wo ks ha e s udied how he addi ion o hyd ogen o gasoline a ec s
engine ope a ion [9–11]. Like engines unning only wi h hyd ogen, he
dual combus ion o hyd ogen and gasoline in SIE allows NOx emissions
educ ions by ope a ing he engine a highe ai – uel a io [12]. When
hyd ogen is added o gasoline, highe combus ion speeds a e ob ained
compa ed o hose ob ained when he engine ope a es only wi h gaso-
line [13]. I also enables he ai – uel a io [12] and esidual gas con-
cen a ions o be inc eased while main aining a s able engine ope a ion.
Ve hels e al. [5] poin ed ou ha mo e s udies o hyd ogen com-
bus ion unde engine condi ions we e equi ed. Un il now, he lack o
his ype o s udies is pa icula ly no iceable o he case o hyd ogen-
gasoline spa k igni ion engines. The me hodology used o s udy he
combus ion p ocess cha ac e is ics in hyd ogen-gasoline blends can be
used in he combus ion analysis o hyd ogen blends wi h o he enew-
able uels and unde o he di e en engine ope a ing condi ions. Going
beyond, s udying combus ion speed pe mi s de e mine he he mo- luid-
mechanic esponsible on how he combus ion p ocesses ake place
un eiling new knowledge o unde s and he impac o uels on com-
bus ion cha ac e is ics.
Applying he modynamic diagnos ic models o in-cylinde p essu e
aces calcula es he amoun o ene gy eleased in a ce ain angula
iming. The a e a which ene gy is eleased is a consequence o he
p oduc o he combus ion speed and he lame on a ea. To calcula e
he combus ion speed om hea elease a e, i is necessa y o use a
geome ical model o de e mine lame on a ea [14].
The combus ion speed calcula ed wi h bo h he modynamic and
geome ical models can be co ela ed wi h he mo- luid-mechanical
a iables inside he combus ion chambe (lamina combus ion speed,
u bulence in ensi y, in eg al leng h scale, lame on hickness,
expansion speed and lame on pe ime e ).
This knowledge ansla ed in o a co ela ion can be used o p edic
in-cylinde p essu e om he he mo- luid-mechanical a iables in he
combus ion chambe . Fo his pu pose, he combus ion speed ob ained
wi h he co ela ion is used as inpu o he he modynamic and geo-
me ic models.
This wo k s udies he e ec s on combus ion speed o subs i u ing
pa o he gasoline uel wi h H2 in a comme cial spa k igni ion engine.
Fo his pu pose, a blend o gasoline and e hanol is expe imen ally
in es iga ed as he e e ence/baseline uel being pa ially eplaced by
H2. The in-cylinde p essu e eco ds a e ob ained and p ocessed wi hin
a wo-zone he modynamic diagnos ic model [14]. The esul s o he
Nomencla u e
Va iables
AA ea (m2)
clTu bulence dissipa ion cons an ( − )
cpSpeci ic hea (J/kg/K)
c Tu bulence p oduc ion cons an ( − )
DiMass di usi i y o species iin he mix u e (kg/m2)
HpHea powe (J/kg)
k u bulen lux ene gy (J)
KMean lux ene gy (J)
kδlFlame on hickness mul iplica ion e m ( − )
LMa ks ein leng h (m)
LLeng h scale (m)
Lee E ec i e Lewis ( − )
mMass (kg)
pP essu e (Pa)
PTu bulence p oduc ion e m ( − )
P Flame on pe ime e (m)
˙
QHea ans e (J/s)
RRadius (m)
SCombus ion speed (m/s)
TTempe a u e (K)
uʹTu bulence in ensi y (m/s)
VVolume (m3)
Ac onyms
BMEP B ake Mean E ec i e P essu e (ba )
CA C ank Angle (◦)
CIE C omp ession Igni ion Engine
CoV Coe icien o Va ia ion
EVC Exhaus al e closing
EVO Exhaus al e opening
FSR Flame speed a io
GGasoline
H2 Hyd ogen
ICE In e nal Combus ion Engine
IVC In ake al e closing
Ac onyms (con .)
IVO In ake al e opening
MGasoline hyd ogen mix u e es s
MFB Mass ac ion bu ned
NG Na u al Gas
SIE Spa k Igni ion Engine
SoI S a o combus ion
G eek le e s
α
Angle (◦)
α
uThe mal di usi i y unbu ned p oduc s (m2/s)
βZel’do ich numbe ( − )
γspeci ic hea s a io ( − )
δFlame on hickness (m)
λAi uel equi alence a io ( − )
λTThe mal conduc i i y (J/(m s K))
ρ
Densi y (kg/m3)
σ
Densi y a io ( − )
ω
Ampli ude g ow h a e ( − )
Subsc ip s
bBu ned
dDiagnos ic
eExpansion
Flame on
iIn eg al
kKolmogo o
lLamina
max Maximum
pPis on
pu Unbu ned p oduc s in con ac wi h he pis on
e Re e ence
es Residual gas concen a ion
Tu bulen
uUnbu ned
wWoschni
P. Gabana e al. Fuel 381 (2025) 133563
2
he modynamic model a e ed in o a newly de eloped geome ical
model o pen oo cylinde head combus ion chambe which is de ined
by 6 pa ame e s enabling o adap he model o cylinde heads wi h
di e en angle be ween al es, bo es and in e sec ion wi h he engine
head gaske . The ou pu s o he geome ical model a e used o p edic
combus ion speed as a unc ion o he p ope ies o he uel–ai mix u es
by using a new me hodology, unde pinned by Gim´
enez e al. [14] (NG
and H2 blends in a He on pis on op combus ion chambe ). A new
me hodology o calcula ing and i ing he co ela ion o he combus-
ion speed has been p oposed. This wo k demons a es ha he newly
p oposed co ela ion can be used o p edic he combus ion cha ac e -
is ics o di e en ai – uel a ios and new uels (e.g. gasoline-hyd ogen
blends), which could be ex ended o a a ie y o spa k igni ion com-
bus ion chambe geome ies.
2. Me hodology
2.1. Expe imen al se up
The engine s udied is a spa k igni ion Gasoline Di ec Injec ion En-
gine. The engine speci ica ions a e p esen ed in Table 1.
The o iginal engine has been modi ied o add H2 in he in ake pipe o
he engine. The H2 low a e was measu ed wi h a H2 olume ic low
me e (Pla on NG se ies VA GTF-2AHD wi h a ange o 2–44 L/min
1.013 ba 20 ◦C). Thus, a mix u e o ai and hyd ogen is in oduced in o
he cylinde . The gasoline is supplied di ec ly in o he cylinde . Com-
bus ion da a was measu ed and logged in one cylinde using an AVL
piezo-elec ic in-cylinde p essu e ansduce , a cha ge ampli ie (AVL
FlexIFEM) and a Baume (720 pulse pe e olu ion) magne ic c ank
angle encode . The p essu e da a ha e been eco ded each 0.1 c ank
angle in e al using an AVL Indicom sys em. A schema ic diag am o he
expe imen al se up is shown in Fig. 1.
2.2. Expe imen al me hodology
Table 2 shows an o e iew o he es plan o he engine ope a ing
poin s. Two uels ha e been used, gasoline and e hanol E10 (G) and he
same uel being eplaced by hyd ogen a 10 % by mass and 87.3 % by
olume (M). The uel–ai a io was also modi ied om s oichiome ic o
λ=1.2 in Gand o λ=2 in M. All expe imen s ha e been ca ied ou
keeping he engine speed a 2000 pm and he b ake o que a 40 Nm.
The spa k iming is se in o de o ha e a mass ac ion bu ned o 50
% (CA50) in a c ank angle (CA) o be ween 3 and 4◦a e op dead cen e
as in p e ious wo ks [12]. A each expe imen al poin , 200 cycles ha e
been eco ded and p ocessed.
The uel low has been uned o achie e he a ge e ec i e o que
(40 Nm). By inc easing ai – uel equi alence a io (λ), he in ake p essu e
has been g adually inc eased o in oduce he ai o H2/ai mix u e
(depending on he case) equi ed o achie e he λ alue speci ied.
Consequen ly, he maximum engine p essu e is inc eased. The amoun
o ene gy in oduced in o he engine pe cycle is simila in all
expe imen al poin s. As λinc eases, less uel is in oduced, his is
because he indica ed e iciency inc eases wi h λ.
2.3. Da a p ocessing
The me hodology ollowed du ing he diagnos ic p ocess is sum-
ma ised in he ollowing s eps:
1. Da a il e ing using an adap i e il e based on Sa i zky-Golay
polynomials [15] o ob ain a con inuous and de i able p essu e
signal a each cycle.
2. De e mina ion o p essu e and angle o se s, comp ession a io (10.8)
and hea ans e coe icien (0.9). Fo his, a me hodology based on
gene ic algo i hms is used, as s a ed by Reyes e al. [16]. Excep o
he p essu e o se , which is chosen o each cycle, he es o he
a iables ake he same alue in all expe imen al condi ions.
3. P ocessing o he il e ed p essu e da a wi h a wo-zone diagnos ic
he modynamic model [14,17]. The he modynamic diagnos ic
model allows calcula ing he bu ned mass a e, dmb/d , om dp/d
ob ained p ocessing p essu e da a. Mo e in o ma ion abou he
he modynamic model is a ailable in Mendeley da a sec ion.
4. P ocessing o he esul ing da a o bu ned p oduc s olume wi h a
geome ic model ha enables calcula ing lame on adius (R ) and
lame on a ea (A ). The lame on a ea is combined wi h dmb/d
o calcula e he combus ion speed (Sd) Eq. (1).
dmb
d =SdA
ρ
u(1)
5. A e age combus ion speed calcula ion o each lame on posi ion
in a popula ion o 200 cycles. A cycle a e aged combus ion speed
esul is ob ained o each es poin and lame on posi ion inside
he combus ion chambe . The esul s a e independen o he c ank
angle a which hey ake place and dependen on he posi ion in he
combus ion chambe .
3. Geome ic model
Based on he olume o mass bu ned, which is he esul o he
he modynamic model, he idea is o de e mine he adius o he sphe e
cen ed on he spa k plug in e sec ing wi h combus ion chambe walls
and he la pis on. The combus ion chambe is de ined by he 6 pa-
ame e s. Once he adius o he sphe e has been de e mined, he nex
objec i e o he model is o calcula e he a ea o he sphe e con ained in
he combus ion chambe . This a ea is he one used in Eq. (1). Fo his
pu pose, he combus ion chambe in he cylinde head is assumed o be
delimi ed by (Fig. 2):
- Two inclined and symme ic planes o ming he angle
α
, he in e -
sec ion ho izon al line o he wo planes is loca ed a a dis ance Z
om he spa k plug.
- A hal -angle cone
α
Cwi h a base a he cylinde head gaske ha ing a
diame e equal o he Bo e.
- Two e ical planes a a dis ance Yp om he cylinde axis.
- A ho izon al plane a a dis ance Z o e he spa k plug.
- The plane o he cylinde head gaske is a a dis ance Zc om he
spa k plug.
The combus ion chambe olume below he cylinde head gaske is
delimi ed by:
- Cylinde head gaske plane.
- The cylinde o diame e 2 Rp.
- The pis on plane loca ed a a dis ance Xp om he cylinde head
gaske .
Table 1
Engine geome ic speci ica ions.
Bo e x S oke 84 x 90 mm
Numbe o cylinde s 3
Numbe o Val es 12
Displacemen 1497 cm
3
Comp ession Ra io 11:1
IVO 20 CAD
IVC −88 CAD
EVO 92 CAD
EVC 0 CAD
Inle al e peak li 10 mm
Exhaus al e peak li 9 mm
To al C ank/Pis on o se 9.6 mm
P. Gabana e al. Fuel 381 (2025) 133563
3
The olume co e ed by he sphe e o adius R is calcula ed om
ho izon al planes a di e en dis ances Z om he spa k plug. The in-
e sec ions o hese planes wi h he combus ion chambe esul in a
geome y o s adiums de ined by wo pa allel lines and a ci cle cen ed
on he spa k plug. The in e sec ion o he plane wi h he sphe e olume
has he same geome y unless he sphe e does no in e sec in ha plane
wi h he cylinde head, hen i is a ci cle. The bu ned p oduc s olume
ou side he cylinde head co esponds o he in e sec ion o a sphe e o
adius R wi h he plane o he pis on and cylinde . Full geome ic model
desc ip ion is a ailable in Mendeley da a sec ion.
In Fig. 2 wo side iews wi h he pa ame e s cha ac e izing he
model a e shown. The loo plane shows a ho izon al plane loca ed a a
dis ance Z om he spa k plug.
Fig. 3 shows an image o he bu ned olume a a ce ain pis on po-
si ion and o a ce ain lame on adius. Fig. 3 has been ob ained wi h
Au odesk In en o so wa e. This so wa e has been used o alida e he
geome ic model.
4. Combus ion p ope ies
4.1. Un il his sec ion, he me hodology o p ocessing he expe imen al
da a o calcula e he combus ion speed (Sd) has been p esen ed. These
esul s and hei analysis a e p esen ed in sec ion 5.1. The inal objec i e o
his wo k, as men ioned in he in oduc ion, is o p edic combus ion speeds
(S ) om he he mo- luid-mechanical a iables inside he combus ion
chambe . This sec ion explains how o calcula e he a iables (lamina
combus ion speed, esidual exhaus gases concen a ion, u bulence
in ensi y and lame p ope ies) dependen on he condi ions in he
combus ion chambe necessa y o i he co ela ion o he combus ion
speed (S ) in sec ion 5.2.Lamina combus ion speed
Hyd ogen-gasoline mix u es lamina combus ion speed (Sl) de e -
mina ion has been p e iously add essed in he li e a u e [18,19]. The
lamina combus ion speed depends on he p essu e and empe a u e
condi ions and on he mix u e composi ion, de e mined by he p opo -
ion o hyd ogen in he uel, he ai excess a io (λ) and mass ac ion o
combus ion p oduc s Y es. The exp ession p oposed by [19] has been
used as Eq. (2), which is alid o he engine ope a ing condi ions.
Fig. 1. Expe imen al acili y schema ic diag am.
Table 2
Cha ac e is ics o he 14 es poin s analysed a Me =40Nm, n =2000 pm, BMEP =3.35 ba .
Name λ˙
m (kg/h) ˙
ma(kg/h) SoI (◦CA) pIVC(ba ) pmax(ba ) Indica ed e iciency (%) Y es(%mass)
G1 1.0 0.785 11.614 –32.4 1.01 29.51 34.9 19.9
G1.1 1.1 0.760 12.369 −35.9 0.95 29.49 36.4 18.9
G1.2 1.2 0.760 13.481 −41.2 1.01 29.87 36.5 18.4
M1 1.0 0.638 10.833 −20.3 1.02 28.87 34.9 21.7
M1.1 1.1 0.657 12.283 −21.1 1.11 30.09 35.8 20.7
M1.2 1.2 0.634 12.942 −21.7 1.12 30.04 36.9 21.2
M1.3 1.3 0.623 13.784 –23.6 1.17 30.67 37.7 21.2
M1.4 1.4 0.612 14.580 −25.2 1.21 30.90 38.5 21.2
M1.5 1.5 0.602 15.389 −26.5 1.24 31.57 39.2 21.2
M1.6 1.6 0.610 16.605 −28.5 1.28 32.00 39.7 21.2
M1.7 1.7 0.593 17.172 −28.5 1.30 31.66 40.2 21.2
M1.8 1.8 0.588 18.040 –33.1 1.37 33.18 40.5 21.1
M1.9 1.9 0.585 18.945 −36.2 1.40 33.30 40.7 20.7
M2 2.0 0.586 19.984 −41.4 1.45 34.54 41.1 20.6
P. Gabana e al. Fuel 381 (2025) 133563
4
Sl=Sl0(Tu
T e )
α
T(p
p e )βp
(1−2.1Y es)(2)
Whe e Tu(K) is he unbu ned p oduc s empe a u e, p(ba ) is he
p essu e, and he e e ence empe a u e and p essu e a e espec i ely
298 K and 1 ba . Sl0,
α
Tand βpcan be calcula ed acco ding o he
exp ession p oposed in [19]. These h ee pa ame e s depend on he
hyd ogen olume ac ion in he in ake gas and λ.
Eq. (2) p o ides lamina combus ion speed (Sl) dependen on he
combus ion chambe condi ions.
Expe imen s a low p essu es and empe a u es show ha he com-
bus ion speeds o e hanol and iso-oc ane a e simila [20]. Simula ions
o he calcula ion o he lamina combus ion speed o gasoline-e hanol
blends a high p essu es and empe a u es show ha he p esence o
e hanol in gasoline has li le in luence on he lamina combus ion speed
compa ed o p essu e, empe a u e, uel ai a io and eci cula ed
exhaus gases [21]. Fo his eason, he lamina combus ion speed has
been conside ed o be simila o a mix u e o iso-oc ane and hyd ogen;
howe e , he lame p ope ies in sec ion 4.4 ha e been calcula ed
conside ing he composi ion o he mix u e.
4.2. Residual exhaus gases
The esidual gases mass ac ions we e calcula ed by simula ing he
gas exchange p ocess wi h AVL BOOST so wa e. The same dis ibu ion
diag am as in he eal engine has been conside ed and he in ake
p essu e has been se o ob ain he same a e age mass low a e as he
measu ed mass low a e a each es poin . The esul s a e shown in
Table 2.
4.3. Tu bulence in ensi y
Tu bulence in ensi y (uʹ) is calcula ed using he simpli ied K-k model
[22] applied o a closed sys em. This model has as ini ial condi ions a
in ake al e closing ime an a e age kine ic ene gy o he mix u e KIVC
and a u bulen kine ic ene gy kICV dependen on uʹ. Ene gies e ol e
acco ding o he equa ions o he model Eq. (3).
dK
d = − P+K
˙
ρ
u
ρ
u
dk
d =P−m
ε
+k
˙
ρ
u
ρ
u
k=3
2muʹ2P=0.3307c
3
2
√K
clV
Ap
uʹ
ε
=uʹ3
clV
Ap
(3)
Whe e Pis he u bulen kine ic ene gy p oduc ion e m om he
a e age kine ic ene gy o he mix u e,
ε
is he u bulen kine ic ene gy
dissipa ion e m, Vis he combus ion chambe olume and Apis he
pis on a ea. Ini ial kine ic ene gies KIVC and kICV ha e been chosen o
ma ch hose ob ained wi h he gas exchange model de eloped in AVL
BOOST a he ins an o in ake al e closing.
The model has wo uning pa ame e s, c =0.6 which is a cons an
a ec ing u bulence p oduc ion and cl=0.3 a ec ing u bulence dissi-
pa ion. Bo h pa ame e s ha e been uned ollowing he AVL BOOST
guidelines so ha uʹa op dead cen e has alues be ween one and wo
imes he mean linea pis on speed.
4.4. Flame p ope ies
4.4.1. Lamina lame on hickness
The lamina lame on hickness (δl) is de ined using he di usion
scaling app oach.
δl=
α
u/Slas in [23,24]. The he mal di usi i y o he mix u e (
α
u) is
de ined as
α
u=λT/(
ρ
ucp)[25]. The p ocedu e p oposed by Ma hu e al.
[26] is ollowed o calcula e he he mal conduc i i y o he mix u e λT.
The cpo he mix u e has been calcula ed ollowing a mola ac ion
weigh ed o mula ion by calcula ing he cpo each species wi h he
co ela ions o NIST [27].
4.4.2. E ec o ins abili ies on lame on hickness
Ins abili ies cause an inc ease in lame on hickness which is
quan i ied by he pa ame e kδlin oduced in [14] Eq. (4).
kδl=exp(2
πω
DL −L
σ
(1+
ω
DL)(
σ
+
ω
DL)
σ
+ (
σ
+1)
ω
DL
4
π
2
LI)(4)
This e m includes hyd odynamic and he mo-di usi e ins abili ies. The
e m
ω
DL is only dependen on he densi y a io
σ
. Fu he mo e, Lis he
Ma ks ein numbe , which depends on he e ec i e Lewis, Zel’do ich
numbe and
σ
[28] Eq. (5).
L=δl[
σ
ln
σ
σ
−1+β(Lee −1)
2(
σ
−1)∫
σ
1
lnx
x−1dx ](5)
4.4.3. Zel’do ich numbe
Zel’do ich numbe is de ined as β= (Ea(T0
b−Tu))/(RT02
b). Whe e T0
b
is he adiaba ic lame empe a u e and Eais he ac i a ion ene gy. The
ac i a ion ene gy can be calcula ed acco ding o Eq. (6) [29].
Fig. 2. 1/4 cylinde head iews wi h one o he sec ion planes used o calcula e
he in e sec ion o he bu ned olume wi h he cylinde head.
Fig. 3. Au odesk In en o ep esen a ion showing he in e ac ion o he lame
on wi h he combus ion chambe walls.
P. Gabana e al. Fuel 381 (2025) 133563
5
Ea= − 2R⎡
⎢
⎢
⎢
⎣
∂
ln(
ρ
uSl)
∂
(1
T0
b)⎤
⎥
⎥
⎥
⎦p
(6)
4.4.4. E ec i e Lewis
E ec i e Lewis is de ined as Lee =
α
u/Di. The mass di usi i y (Di) is
a p ope y o a species in he mix u e calcula ed wi h he Blanc’s law
p esen ed in [25]. In his wo k bina y mass di usi i ies ha e been
calcula ed acco ding o [25].
Howe e , when he e a e mix u es o a ious uels, he e a e
di e en me hodologies o calcula e Lee . In [23] a ious me hodologies
o he calcula ion o he e ec i e Lewis o se e al hyd oca bon and
hyd ogen mix u es a e analysed. The e ec i e Lewis ha e been calcu-
la ed acco ding o he hea elease-based app oach Eq. (7) using he
esul s ob ained in [23] and he hyd ogen concen a ions in he expe -
imen al da a se o his wo k.
Lee =1+q1(Le1−1) + q2(Le2−1)
q1+q2
(7)
Whe e q1and q2co espond o he ene gy eleased by each uel in he
mix u e and Le1and Le2a e he Lewis numbe s o each uel species.
5. Resul s
5.1. The modynamic diagnos ic model esul s
F om he p essu e signal, mass ac ion bu ned (MFB) is calcula ed.
F om MFB, CA imings can be calcula ed. Fig. 4 (a) shows he a e age CA
iming om he s a o combus ion o MFB =0.1 and om MFB =0.1 o
MFB =0.9. CA imings a e calcula ed om mass ac ion bu ned (MFB)
and p essu e signal. CA0-90, CA0-10 and CA10-90 a e conside ed o
quan i y he du a ion o he o al combus ion p ocess, he i s phase o
combus ion and he main o second phase o combus ion, espec i ely.
The addi ion o hyd ogen clea ly dec eases he du a ion o he com-
bus ion p ocess o he same ai o uel a io (Fig. 4 (a)). In G, he i s
phase o combus ion has a longe du a ion han he second phase. In M
he opposi e occu s (CA10-90 <CA0-10) o all λ alues lowe han 1.9.
Fo bo h cases (G and M), when λinc eases, he sha e o he i s phase o
combus ion wi h espec o he o al combus ion ime inc eases, in
ag eemen wi h he esul s o [30,31]. When compa ing he esul s o G
wi h M o λ alues be ween 1 and 1.2, i is concluded ha he addi ion
o hyd ogen o he uel leads o a educ ion in he i s phase o com-
bus ion (CA0-10) o be ween 40 % (λ=1) and 50 % (λ=1.2). Howe e ,
o he second phase o combus ion he educ ion anged om 8 % (λ=
1) o 16 % (λ=1.2). The e o e, he addi ion o hyd ogen o e all educed
he combus ion du a ion bu a ec ing mo e o he i s phase han he
second phase o combus ion.
CA0-10 is di ided in o CA0-1 and CA1-10, Fig. 4 (b). CA0-1 includes
he g ow h o he lame ke nel and he ansi ion o u bulen egime
[32]. CA0-1 is la ge han CA1-10 o all expe imen s. Bo h CA0-1 and
CA1-10 inc eased wi h λ o G and M uels, bu CA0-1 inc eased much
mo e han CA1-10. The e o e, mos o he inc ease in CA0-10 wi h
inc easing λis due o he inc ease in CA0-1.
Fig. 5 (a) shows Sd alues e sus R o 200 cycles o he G1.1 ex-
pe imen s. Compa ing he Sd esul s o each cycle o he same lame
adius enables o analyse he cycle- o-cycle luc ua ions and o de e -
mine he a e aged combus ion speed when he lame on passes
h ough a ce ain posi ion. Fig. 5 (b) shows he coe icien o a ia ion
(CoV) as a unc ion o lame on adius. The dispe sion o all adii
be ween 10 and 40 mm is be ween 9 % and 14 %. I should be no ed ha
all he expe imen s ha e been ca ied ou wi h he engine unning a he
same engine speed and, he e o e, he u bulence le els a e e y simila
o all expe imen s.
Fig. 6 (a) shows R as a unc ion o MFB a e aged o all expe imen al
condi ions. The mean MFB alue is also plo ed and highligh ed,
ob aining e y simila alues o all expe imen al condi ions. Fig. 6 (b)
shows he cycle a e aged combus ion speed (Sd) a he same lame on
posi ion (same R ) o 200 cycles a he 14 expe imen al condi ions. On
he bo om ho izon al axis an app oxima e alue o he mass ac ion
bu ned (MFB) is p esen ed.
The alues o lame on adii R <10 mm co espond o
MFB <1%. The combus ion speed alues in his zone (Fig. 6 (b)) a e no
eliable because he e is no enough esolu ion in he p essu e signal
de i a i e. Thus, i is no possible o ob ain eliable in o ma ion abou
he ke nel g ow h. The e o e, he esul s o Fig. 6 (b) a e analysed in
mo e de ail o lame on posi ions la ge han 10 mm whe e MFB >1
%.
In he R ange om 10 mm o 20 mm (CA1-10 app oxima ely) he Sd
o Ga e lowe han hose o M. A la ge in luence o λon Sd o λ alues
be ween 1 and 1.2 is no ob ained in ei he o he wo uels. In Mwhen
he alue o λexceeds 1.2, in he R ange be ween 15 and 20 mm, he
in luence o λis sligh ly app ecia ed, so ha Sddec eases when λin-
c eases. These ends a e shown in CA1-10 (Fig. 4 (b)). CA1-10 alues do
no signi ican ly a y wi h λ, being G alues la ge han hose ob ained
o M. Inc easing λin Mexpe imen s sligh ly inc eases CA1-10. This
combus ion phase akes place in an angula in e al be ween 6 and 9
c ank angle deg ees.
In he second phase o combus ion quan i ied by CA10-90 (app ox-
ima ely R >20 mm and R <40 mm), he in luence o λon Sd o bo h
Fig. 4. (a) Du a ion o he i s phase o combus ion (CA0-10), he second
phase o combus ion (CA10-90) and he o al combus ion du a ion (CA0-90) as
a unc ion o λ o Mand Gexpe imen s. (b) Values o CA0-1 and CA1-10 as a
unc ion o λ o Mand Gexpe imen s.
P. Gabana e al. Fuel 381 (2025) 133563
6
Mand Gis obse ed. In his second phase, combus ion speeds o G cease
o be lowe han hose o M.Sd ends a e e lec ed in he CA10-90 alues
in Fig. 4 (a), he highe he Sd he lowe he CA10-90 alues.
As combus ion e ol es, Sd alues o Gg ow as e han hose o M
esul s. The poin a which he lame on eaches he pis on, app oxi-
ma ely R =14 mm, is also obse ed. This poin is e y simila o all he
expe imen s, since he combus ion p ocess akes place a c ank angle
imes when he pis on is close o op dead cen e.
Fig. 6 (c) shows Slcycle a e aged a each expe imen as a unc ion o
R . Each Slhas been calcula ed wi h Eq. (2) as a unc ion o he he -
modynamic condi ions o he mix u e a each ins an . Sl alues inc ease
wi h dec easing λ. The addi ion o hyd ogen makes Sl alues wi h M
la ge han wi h G o he same λ alues. The di e ence ha exis s be-
ween Sl alues a e weakly e lec ed in Sdin he i s phase o combus-
ion R <20mm. In he second phase, Sl alues a e o de ed wi h λ, he
highe λ he lowe Sl. A R =30mm an inc ease in Sla ound 550 % is
e lec ed in an inc ease a ound 30 % in Sd. Tu bulence in luence in-
c eases s ongly wi h dec easing Sl.
The Flame Speed Ra io is de ined as FSR =Sd/Sl.Fig. 6 (d) shows
ln(FSR −1)cycle a e aged as a unc ion o R o all expe imen s. I is
obse ed ha FSR depends on R bu mo e on λ. The FSR end is
explained by he ac ha Sl a ies la gely wi h λwhile Sd akes alues in
he same o de o all λ alues. Acco ding o Gülde [33],FSR is p i-
ma ily dependen on he a io uʹ/Sl. The uʹ alue is e y simila a all
expe imen s since he engine speed is he same. The e o e, he a ia ion
o FSR be ween all expe imen s is due o he a ia ion o Sl.
Sd alues o di e en R a e shown as a unc ion o λ,Fig. 7. Fo λ
alues lowe han 1.2 and R ≤20mm in bo h Gand M he e is no clea
end wi h λ. Fo highe R alues, he end o Sdwhen inc easing λis as
expec ed om he end o Sl. In he case o Mwi h λ>1.2 he ends a e
dec easing wi h λa all R alues. The end o dec easing Sdwi h
inc easing λis la ge as R inc eases.
5.2. P edic ion o lame speed a io (FSR)
Gülde [33] p oposed a ela ionship be ween he u bulen (S ) and
he lamina combus ion speed (Sl) depending on uʹ/Sland Li/δl[28].
This ela ionship desc ibes he ee- ield combus ion beha iou , Eq. (8).
Fig. 5. (a) Sdas a unc ion o R o all cycles o G1.1. (b) Coe icien s o
a ia ion o Sdas a unc ion o R o all expe imen al poin s.
Fig. 6. (a)MFB cycle a e aged as a unc ion o R and in hicke line he
a e age o all expe imen al condi ions. (b) Sdcycle a e aged as a unc ion o R .
(c) Slcycle a e aged as a unc ion o R . (d) FSR o all expe imen s cycle
a e aged as a unc ion o R .
P. Gabana e al. Fuel 381 (2025) 133563
7
S
Sl
−1=k0(uʹ
Sl)a(Li
δl)b
(8)
Fo he case o in e nal combus ion engines, Gim´
enez e al. [14] p o-
posed a new co ela ion which conside s he e ec o ins abili ies
inc easing he appa en hickness o he lame on (δl) h ough a
lamina lame on hickness mul iplie kδl. Gim´
enez e al. [14] also
added a new e m o quan i y ha he low is con ined by he walls o he
ICE combus ion chambe (con ined combus ion). I was sugges ed ha
ha ing a con ined combus ion p oduces an addi ional u bulence ha is
aken in o accoun wi h a new e m called as he en ainmen eloci y
(Se), de ined as he speed o he eac an s close o he lame on . This
speed, close o he walls, p oduces shea s esses ha cause u he
u bulence. The amoun o u bulence ha is gene a ed and a ec s he
combus ion speed depends on he leng h o he in e sec ion be ween he
lame on and he combus ion chambe walls. In his wo k i is e e ed
o as he lame on pe ime e P .Conside ing Se he in ensi y o he new
u bulence gene a ed, he new co ela ion e m includes he ela ion
be ween he expansion speed Seand he lamina combus ion speed Sl
and also he in luence o he pe ime e o he lame on non-
dimensionalised wi h he in eg al scale LiEq. (9).
S
Sl
−1=a(uʹ
Sl)b(Li
δlkδl)c(SeP
SlLi)d
(9)
Acco ding o Gim´
enez e al. [14] i mean p ope ies o e he whole
combus ion chambe a e conside ed, Secan be calcula ed wi h Eq. (10).
Se=1
A [dV
d (Apu
Ap
−Vu
V)+Vu
˙
mbb ]+S ((γ−1)muHp
γpV )+(γ−1)
γpA (˙
Qw
Vu
V−
˙
Qu)(10)
The co ela ion p oposed by Gim´
enez e al. [14] has he d awback ha
Sedepends on S so i is no an explici exp ession. In his wo k, an
i e a i e new me hod o calcula e S is used. The me hod consis s o
making a hypo hesis o S and subs i u ing i in Eq. (10) o calcula e Se
and hen he new S wi h Eq. (9). The p ocess is epea ed i e a i ely un il
bo h S alues ma ch. In [14] he coe icien s we e i ed using mul i-
linea eg essions. Howe e , he cu en me hodology does no allow o
i he coe icien aand he exponen s b,cand d o he expe imen al da a
using he me hod p oposed in [14]. In his wo k, he coe icien s ha e
been i ed using a new op imisa ion me hod. The me hod is based on
using a gene ic algo i hm in eg a ed in Ma lab in which he unc ion o
be op imised is he mean squa e e o be ween Sdand he p edic ed
combus ion speed S . Fo 12 speci ic alues o he lame on adius
be ween 10 and 37 mm, he a e age alues o all a iables in ol ed in
he co ela ion ha e been calcula ed o e 200 cycles, esul ing in 12
di e en alues o all a iables a he 14 expe imen al condi ions. The
esul s om he i a e shown in Fig. 8.
Table 3 shows he co ela ion coe icien s ob ained in [14], he co-
e icien s ob ained in his wo k and he coe icien s o he i o he da a
om [14] using he me hodology o his wo k.
The exponen s o he co ela ion ob ained ollowing he new me h-
odology p oposed in his wo k, whe e Sedepends on S , a e e y simila
o he wo da a se s (cases 2 and 3). The e is a ema kable di e ence,
especially in he exponen o he hi d e m, d, when i is calcula ed wi h
he expe imen al alues o Sd(cases 1 and 3). The hi d e m is calcu-
la ed wi h S and i is he e m modi ied in he i e a i e p ocess.
The es ima ion o uʹg ea ly a ec s he coe icien ao Eq. (9). The
alue o aob ained in case 2 is lowe han in case 3. In his wo k he
alues o uʹa op dead cen e di ided by he pis on mean linea eloci y
a e la ge han in [14]. An unde es ima ion o u’in [14] o an o e -
es ima ion in his wo k would jus i y he di e ences in he alue o a.
E en wi h e y di e en combus ion chambe geome ies (pen - oo
cylinde head s la cylinde head) he co ela ion exponen s ake e y
simila alues in cases 2 and 3.
Fig. 9 shows he Bo ghi-Pe e s diag am [34,35] and he loca ion o
he expe imen al condi ions o ou lame on posi ions (15, 22, 30
and 37 mm), unde wo lamina lame on hickness hypo hesis δland
δlkδl.
Th ee iso-FSR lines ha e been added (FSR =2, FSR =10 and FSR =
30) in o Fig. 9. These iso-FSR lines ha e been calcula ed by using he
exp ession o Gülde [33] co esponding o ee ield combus ion.
Conside ing δlas he lame on hickness, when λinc eases, as Sl
dec eases and uʹhas simila alues, he poin s mo e om he zone wi h
Lk>δl o he zone Lk<δlby changing he combus ion egime. The e-
o e, i i is assumed ha he lame on hickness is inc eased by he
ins abili y ( lame on hickness as δlkδl) he combus ion egime in all
expe imen al condi ions is in he hin eac ion zone ins ead o close o
Fig. 7. Sdas a unc ion o λ o di e en R .
Fig. 8. Expe imen al da a o ln(Sd /Sl −1) e sus alues ob ained om he
co ela ion. The plo includes12 lame on posi ions o Mand G.
P. Gabana e al. Fuel 381 (2025) 133563
8
he co uga ed lames zone.
I is obse ed ha he es poin s would be loca ed app oxima ely
be ween FSR =10 and FSR =30 [33] when he lame on hickness is
δl. I he in luence o ins abili ies in he lame on hickness (δlkδl) is
aken in o accoun , he poin s a e shi ed o he le wi h lowe FSR
alues.
5.3. Unde s anding he e ec o he co ela ion e ms on FSR p edic ion
Fi s and hi d e ms o Eq. (9) quan i y he ela ionship be ween he
u bulence in ensi y in he combus ion chambe and he lamina com-
bus ion speed. The u bulence in ensi y can be caused by he luid e-
loci y in he combus ion chambe o by he expansion o he eac ing
gases. The second e m e lec s he in luence o he a io o he cha -
ac e is ic u bulence dimension Li o he lame on hickness modi ied
by ins abili ies.
Fig. 10 shows he h ee combus ion e ms as a unc ion o he lame
on adius o all expe imen al condi ions. The end o uʹ/Slwi h R is
shown in igu e Fig. 10 (a). The end is always dec easing as R in-
c eases since he u bulence in ensi y dec eases wi h ime due o i s
dissipa ion and Slinc eases due o empe a u e inc ease. In Fig. 10 (c)
he end o he e m (SeP )/(SlLi)wi h R is shown. This e m is he one
ha p o ides he shape o S as a unc ion o R . As men ioned abo e,
his e m is a ibu ed o he u bulence gene a ed by he unbu ned gas
speed wi h espec o he combus ion chambe walls. The end wi h
espec o λis he same as uʹ/Sl, mainly due o he dec ease o Sl.
In i s and hi d e ms o Eq. (9), he ep esen a i e cu es o each λ
do no in e sec when changing R , so hey can ha dly explain he
di e en end when a ying he adius o Gand MFig. 4 (a). Fig. 10 (b)
shows ha Li/(δlkδl) e m does no main ain he same end agains R
o all λ alues. The alue o his e m is no o de ed as a unc ion o λ o
a ixed R as in he o he wo co ela ion e ms. Fo he same R alue,
he highes alues o his e m a e eached a λ alues o abou 1.5 in M.
The e m akes simila alues o λ=1 and o λ=2 in M o R alues
lowe han 20 mm. Subsequen ly, a alues o R >20mm he e m akes
la ge alues in M1 han in M2. G alues ha e ends wi h R simila o
hose in M1, bu wi h smalle alues. In M esul s, he highe he λ, he
highe he alue o he e m. The e olu ion o his e m wi h R can
explain he di e en beha iou o G esul s compa ed o M.
Fig. 11 shows p edic ed FSR as a unc ion o R o 4 es poin s, he
expe imen al FSR a e also plo ed. The p edic ed ends wi h uel ype, λ
and wi h R a e accep able especially in he cen al zone (R >10mm
and R <37mm). No hing can be s a ed abou he s a o combus ion
since he expe imen al esul s canno be calcula ed. Rega ding he end
o combus ion, he p edic ion does no dec ease a he same a e as he
expe imen al da a. In his zone he e ec s o quenching can be p opo -
ionally impo an wi h espec o he a e o uel being bu ned. In
p edic i e models whe e his co ela ion is used, i is necessa y o
comple e hem wi h ke nel g ow h and lame quenching models.
Table 3
Fi ing esul s wi h di e en da a and me hodology.
Case Da a Me hodology a b c d
1[14] [14] 0.114 0.86 0.29 0.4
2 This wo k This wo k 0.124 0.8 0.21 0.32
3[14] This wo k 0.21 0.85 0.26 0.31
Fig. 9. Bo ghi-Pe e s diag am and expe imen al esul s o 4 lame on po-
si ions. The e ec o conside ing he lame on hickness as δl(poin s on he
igh ) and as δlkδl(poin s on he le ) is shown.
Fig. 10. Cycle a e aged alues o he co ela ion e ms Eq. (9) as a unc ion o
R o all expe imen al condi ions. (a) uʹ/Sl. (b) Li/(δlkδl). (c) (SeP )/(SlLi).
P. Gabana e al. Fuel 381 (2025) 133563
9
