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Article
Numerical Study on the Characteristics of Vaporization,
Ignition, and Turbulent Combustion Processes in
Dimethyl Ether (DME)Fueled Engine Conditions
Yongwook Yu, Sungmo Kang, Yongmo Kim, and KwanSoo Lee
Energy Fuels, Article ASAP DOI: 10.1021/ef8002119
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Numerical Study on the Characteristics of Vaporization,Ignition,
and Turbulent Combustion Processes in Dimethyl Ether
(DME)Fueled Engine Conditions
Yongwook Yu,Sungmo Kang,Yongmo Kim,* and KwanSoo Lee
Department of Mechanical Engineering,Hanyang UniVersity,17,HaengdangDong,SungdongKu,
Seoul 133791,Korea
ReceiVed March 24,2008.ReVised Manuscript ReceiVed July 23,2008
Among oxygenated fuels,the simplest ether fuel,dimethyl ether (DME),is often regarded as the next
generation fuel because of its superior soot emission characteristics.However,DME has distinctly different
spray combustion characteristics fromthe conventional hydrocarbon liquid diesel fuels in terms of evaporation,
ignition,high vapor pressure,cetane number,oxygenate ingredient,heat release rate,liquid density,etc.In the
present study,to understand the overall spray combustion characteristics of DME fuel as well as to identify
the distinctive differences of DME combustion processes compared to conventional hydrocarbon liquid fuels,
the sequence of the comparative analysis has been systematically made for DME and nheptane liquid fuels.
To realistically represent the physical processes involved in the spray combustion,this study employs the
hybrid breakup model,the stochastic droplet tracking model,collision model,highpressure evaporation model,
and transient ﬂamelet model with detailed chemistry.On the basis of numerical results,the detailed discussions
are made in terms of the evaporation characteristics of a single droplet at highpressure,combustion processes,
ignition characteristics of homogeneous mixtures and spray jets,ﬂame structure,and turbulencechemistry
interaction in the nheptane and DMEfueled spray combustion processes.
1.Introduction
Among oxygenated fuels,the simplest ether fuel,dimethyl ether
(DME),has been attracting much attention as a clean alternative
fuel for diesel engines.The cetane number of DME is high enough
to operate conventional compressionignition engines.The thermal
efﬁciency of a DMEpowered diesel engine is comparable to that
of diesel fuel operation,and sootfree combustion can be achieved
without any extra modiﬁcations.However,because DME has
distinctly different spray combustion characteristics fromconven
tional hydrocarbon liquid diesel fuels in terms of evaporation,
ignition,vapor pressure,cetane number,oxygenate ingredient,heat
release rate,and liquid density,the application of DME in diesel
engines creates many problems associated with the fuelair mixing
processes.Although DME burns well in the combustion systems
of directinjection (DI) diesel engines at light and medium loads
and all speeds,the combustion efﬁciency of DMEfueled diesel
engines with insufﬁcient mixing could be deteriorated at high loads
and high speeds.In this respect,more research is needed for spray
dynamics,vaporization,ignition,and turbulent combustion pro
cesses of DME fuel.
There have been experimental
15
and analytical
6
studies to
understand the characteristics of the DME spray combustions
as well as to optimally design the DME injection and combus
tion systems.The numerical modelings for the DME spray
combustion processes are relatively rare because of the lack of
reliable and fully informative experimental data as well as the
shortcomings of the combustion model to realistically simulate
the DME spray combustion processes.Golovitchev et al.
7,8
performed numerical simulations of DME spray combustion.
The predictive capability of their spray combustion model was
validated against experimental data in terms of liquid and vapor
penetration and ignition in a constantvolume chamber.Very
recently,Kimet al.
9
numerically and experimentally investigated
the characteristics of the turbulent combustion processes of DME
sprays.Numerical simulation of spray development and ignition
process of DME sprays was performed using a transient ﬂamelet
model together with the lowpressure vaporization model and
the reduced chemical kinetic mechanism.The numerical results
agreed reasonably well with the experimental data.However,
there is still a lot of room to improve the physical submodels
* To whom correspondence should be addressed:Department of Me
chanical Engineering,Hanyang University,17,HaengdangDong,Sungdong
Ku,Seoul 133791,Korea.Telephone:+82222200428.Fax:+8222297
3432.Email:ymkim@hanyang.ac.kr.
(1) Arcoumanis,C.The second European autooil programme (AOLII).
European Commission,2000;Vol.2,Alternative Fuels for Transportation.
(2) Sorenson,S.C.;Glensvig,M.;Abata,D.Dimethyl ether in the diesel
fuel injection systems.1998;SAE Paper 981159.
(3) Wakai,K.;Nishida,K.;Yoshizaki,T.;Hiroyasu,H.Spray and
ignition characteristics of dimethyl ether injected by a DI diesel injector.
Proceedings of the Fourth International Symposium COMODIA,1998;pp
537542.
(4) Kajitani,S.;Chen,Z.;Oguma,M.;Konno,M.A study of low
compressionratio dimethyl ether diesel engines.Int.J.Engine Res.2002,
2,1–11
.
(5) Wakai,K.;Nishida,K.;Yoshizaki,T.;Hiroyasu,H.Ignition delays
of DME and diesel fuel sprays injected by a DI diesel injector.1999,SAE
Paper 1999013600.
(6) Teng,H.;McCandless,J.C.;Schneyer,J.B.Thermochemical
characteristics of dimethyl ethersAn alternative fuel for compression
ignition engines.2001 SAE Paper 2001010154.
(7) Golovitchev,V.I.;Nordin,N.;Chomiak,J.Neat dimethyl ether:
Is it really diesel fuel of promise?1998,SAE Paper 982537.
(8) Golovitchev,V.I.;Nordin,N.;Chomiak,J.;Nishida,N.;Wakai,K.
Evaluation of ignition quality of DME at diesel engine conditions.
Proceedings of the Fourth International Conference of Internal Combustion
Engines 99 (ICE99):Experiments and Modeling,1999;pp 299306.
(9) Kim,Y.;Lim,J.;Min,K.A study of the dimethyl ether spray
characteristics and ignition delay.Int.J.Engine Res.2007,8,337–346
.
Energy & Fuels XXXX,xxx,A
10.1021/ef8002119 CCC:$40.75 XXXX American Chemical Society
to realistically predict the physically complex DME spray
combustion processes.
In general,the comprehensive modeling of the spray combustion
in DMEfueled combustion engines requires physical submodels
for the complex physical processes,such as the atomization of the
liquid fuel,the evaporation of the fuel droplets,the mixing of fuel
and air,autoignition of fuel vapor,and turbulencechemistry
interaction.Among these physical processes,vaporization is one
of the dominant mechanisms in DME spray combustion.Because
the pressure level during the combustion process of the compression
ignition engines is usually higher than the critical pressure of the
liquid hydrocarbon fuels,the reliable droplet vaporization model
is an essential element to realistically predict the highpressure spray
combustion processes.The modeling of the droplet vaporization
process under highpressure conditions requires to take into account
the additionally complex effects such as the real gas behavior,the
variation of thermophysical properties,the nonideality of the latent
heat of evaporation,and the nonideal phase equilibriumincluding
the solubility of the ambient gas inside the droplet.So far,most
spray combustion models are based on the lowpressure model
similar to the vaporization routine of the KIVA code.
10
However,
the lowpressure vaporization model unrealistically predicts the
vaporization process in the highpressure environment.In this
respect,it is quite desirable to develop an improved vaporization
model that can be applicable to a wide range of operating pressures.
Recently,Yang
11
made a comprehensive review of highpressure
vaporization,mixing,and combustion processes encountered in
liquidfueled propulsion systems.
The fuel vapor autoignition also considerably inﬂuences the
characteristics of the spray combustion.The spray ignition
process is often simulated by the Shell ignition model,
1214
which is unable to include the turbulent effects on the ignition
process.Moreover,this Shell ignition model has the basic
shortcoming that the parameters must be tuned according to
the combustion conditions.To overcome these defects,Pitsch
et al.
15
suggested the representative interactive ﬂamelet (RIF)
model,which does not require the tuning of parameters and
can account for the turbulencechemistry interaction based on
the detailed chemistry.Hence,autoignition,partially premixed
burning,diffusive combustion,and pollutant formation need not
be modeled individually.These RIF calculations are made
interactively with the changes of ﬂow and mixing ﬁelds,which
are obtained by a CFD solver.Therefore,the timedependent
effects of ﬂow and mixing ﬁelds are accounted for in RIF
through appropriate modeling of the scalar dissipation rate.To
account for the spatial inhomogeneity of the scalar dissipation
rate in the nonstationary spray ﬂame ﬁeld of directinjection
diesel engines,Barths et al.
16
devised the multiple ﬂamelets
procedure.On the other hand,most of the previous works for
the simulation of turbulent spray combustion have neglected
the vaporization effects on turbulent spray combustion,except
the interphase vaporization source term in the mean mixture
fraction.However,the DNS results by Reveillon and Vervisch
17
revealed that the impact of vaporization sources on the small
scales of the turbulent fuel distribution signiﬁcantly modiﬁes
the ﬂuctuations of mixture fraction and subsequently the scalar
dissipation rate.Recently,Demoulin and Borghi
18
proposed the
new model to include these major effects of spray vaporization
on the mixture fraction ﬂuctuations and the PDF model.
To realistically represent the spray combustion processes
involved in the highpressure environment,the present study
employs the KHRT breakup model,
19
the stochastic droplet
tracking model,
10
the collision model,
20
the highpressure
evaporation model,
21
and the transient ﬂamelet model with
detailed chemistry.Moreover,to include the spray vaporization
effects on the mixture fraction ﬂuctuations and the PDF model,
the present study employs the model proposed by Demoulin
and Borghi.
18
The present highpressure evaporation model can
account for transient liquid heating,circulation effect inside the
droplet,forced convection,Stefan ﬂow effect,real gas effect,
and ambient gas solubility in the liquid droplets in highpressure
conditions.The coupling between complex chemistry and
turbulence is treated by employing the representative interactive
ﬂamelet (RIF) model.The spatial inhomogeneity of the scalar
dissipation rate is treated by the multiple RIF procedure.
16,22
The chemistries used in this study are based on the detailed
chemical mechanisms,which include low and hightemperature
autoignition,fuel decomposition,and fuel oxidation.
This improved spray combustion model has been applied to
simulate the spray dynamics,vaporization,autoignition,and
combustion process in nheptane and DMEfueled engine
conditions.In the present study,to understand the overall spray
combustion characteristics of DME fuel as well as to identify
the distinctive differences of DME combustion processes
compared to conventional hydrocarbon liquid fuels,the sequence
of the comparative analysis has been systematically made for
nheptane and DME liquid fuels.On the basis of numerical
results,the detailed discussions are also made in terms of the
evaporation characteristics of single droplet under highpressure
conditions,combustion processes,ignition characteristics of
homogeneous mixtures and spray jets,ﬂame structure,and
turbulencechemistry interaction in nheptane and DMEfueled
diesellike combustion conditions.
2.Physical and Numerical Models
The spray combustion involves complex physical processes,such
as the atomization of the liquid fuel,droplet breakup,droplet
(10) Amsden,A.A.;O’Rourke,P.J.;Butler,T.D.KIVAII:Acomputer
program for chemically reactive ﬂows with sprays.Los Alamos National
Laboratory Report,1989,LA11560MS.
(11) Yang,V.Modeling of supercritical vaporization,mixing,and
combustion processes in liquidfueled propulsion systems.Proceedings of
the 28th International Symposiumon Combustion,The Combustion Institute,
Pittsburgh,PA,2000.
(12) Halstead,M.P.;Kirsch,L.J.;Prothero,A.;Quinn,C.P.A
mathematical model for hydrocarbon autoignition at high pressures.Proc.
R.Soc.London,Ser.A 1975,346,515–538
.
(13) Kong,S.C.;Han,Z.;Reitz,R.D.The development and application
of a diesel ignition and combustion model for multidimensional engine
simulations.1995,SAE Paper 950278.
(14) Sazhina,E.M.;Sazhin,S.S.;Heikal,M.R.;Marooney,C.J.The
shell autoignition model:Applications to gasoline and diesel fuels.Fuel
1999,78,389–401
.
(15) Pitsch,H.;Barths,H.;Peters,N.Threedimensional modeling of
NO
x
and soot formation in DIdiesel engines using detailed chemistry based
on the interactive ﬂamelet approach.1996,SAE Paper 962057.
(16) Barths,H.;Antoni,C.;Peters,N.Threedimensional simulation of
pollutant formation in a DIdiesel engines using multiple interactive
ﬂamelets.1998,SAE Paper 982456.
(17) Reveillon,J.;Vervish,L.Spray vaporization in nonpremixed
turbulent combustion modeling:A single droplet model.Combust.Flame
2000,121,75–90
.
(18) Demoulin,F.X.;Borghi,R.Assumed PDF modeling of turbulent
spray combustion.Combust.Sci.Technol.2000,158,249–271
.
(19) Patterson,M.A.;Reitz,R.D.Modeling of the effects of fuel spray
characteristics on diesel engine combustion and emission.1998,SAE Paper
980131.
(20) O’Rourke,P.J.Collective drop effects on vaporing liquid sprays.
Los Alamos National Laboratory Report 1981,LA9069T.
(21) Yu,Y.W.;Kim,S.K.;Kim,Y.M.Numerical modeling for
autoignition and combustion processes of fuel spays in highpressure
environment.Combust.Sci.Technol.2001,168,85–112
.
(22) Kim,S.K.;Yu,Y.W.;Ahn,J.H.;Kim,Y.M.Numerical
investigation of the autoignition of turbulent gaseous jets in a highpressure
environment using the multipleRIF model.Fuel 2004,83,375–386
.
B Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
dispersion by turbulence,droplet collision,evaporation,turbulent
mixing,autoignition,and turbulencechemistry interaction.In this
study,all submodels for these important physical processes are
implemented in the multidimensional EulerianLagrangian for
mulation.The gasphase equation is written in an Eulerian
coordinate,whereas the liquidphase is presented in Lagrangian
coordinates.The twoway coupling between the two phases is
described by the interphase source terms that represent the rate of
momentum and mass and heat transfer.The physical models used
in the present study include the hybrid droplet breakup model,
19
stochastic droplet tracking technique,
10
O’Rourke’s droplet collision
model,
20
highpressure vaporization model,standard kε turbulent
model,and transient ﬂamelet model.
15,21
All of these physical
models for the spray dynamics are implemented in the KIVA II
code.
10
The atomization process occurs on time and length scales too
short to be resolved with practical computational grid sizes and
time steps.Thus,atomization should be modeled as a subgridscale
process.To account for the liquid atomization and droplet breakup,
the hybrid droplet breakup model
19
has been employed.This
breakup model is based on the assumption that atomization and
drop breakup are indistinguishable processes within a dense spray
near the nozzle exit.Accordingly,atomization is prescribed by
injecting drops that have a characteristic size equal to the nozzle
exit diameter.In the stochastic droplet tracking approach,
10
to
account for the droplet dispersion by turbulence,the instantaneous
velocity components are obtained by adding stochastically generated
turbulent ﬂuctuating velocity components to the mean gasphase
velocity ﬁeld.If the gasphase turbulence is assumed to be isotropic,
the randomturbulent ﬂuctuating velocity components are assumed
to have a Gaussian probability distribution with the standard
deviation based on the turbulent kinetic energy.The dropleteddy
interaction time is assumed to be the minimum of either the eddy
lifetime or the droplet transit time to cross the eddy.In the drop
collision model,
20
the probability distributions governing the number
and outcomes of the collisions between two drops are sampled
randomly in consistency with the stochastic particle tracking
method.
Among the physical submodels adopted in this study,the high
pressure vaporization model and the transient ﬂamelet model are
precisely described below.
2.1.HighPressure Vaporization Model.To account for the
highpressure vaporization processes in context with the compre
hensive spray combustion modeling,the present highpressure
vaporization model is based on the following assumptions:(1) The
fuel droplet is assumed to be a continuum of perfect sphere.(2)
The gas phase is assumed to be spherically symmetric using a
modiﬁed relation based on the ﬁlmtheory to account for the effect
of convection.(3) The liquid phase is also assumed to be spherically
symmetric.(4) The interface between the liquid and gas phases is
calculated by the condition of phase equilibrium.(5) The gas phase
is assumed by the quasiequilibriumstate.(6) The
1
/
3
lawis adopted
to calculate the average properties of the gas phase,and properties
of the liquid phase are accounted for by the spatial and time
variance.(7) The ambient pressure is constant.(8) There is no
radiation effect.(9) Dufour effect and viscous dissipation are
neglected.
To calculate the heat and mass ﬂux between the droplet and gas
ﬁeld,a ﬁlm correction presented by Abramzon and Sirignano
23
is
chosen.The convective effects on heat and mass transfer of the
droplet evaporation are determined by
Nu* )2 +
(Nu
0
2)
F(B
T
)
(1)
Sh* )2 +
(Sh
0
2)
F(B
M
)
(2)
where Nu is the Nusselt number and Sh is the Sherwood number.
B
M
and B
T
are the Spalding numbers of mass and heat transfer.
The subscript “0” and the superscript “/” denote nonvaporizing
and vaporizing spheres,respectively.The Stefan ﬂowresulting from
mass transfer increases the ﬁlm thickness.Abramzon and Sirig
nano
23
suggest that the variation of ﬁlmthickness has the following
relationship with Spalding transfer number,B
F(B) )(1 +B)
0.7
ln(1 +B)
B
(3)
The convective heat or mass transfer between a solid nonva
porizing spherical particle and a ﬂuid ﬂow are calculated from the
correlation of Ranz and Marshall.
Nu
0
)2.0 +0.6Re
1/2
Pr
1/3
Sh
0
)2.0 +0.6Re
1/2
Sc
1/3
(4)
Here,Re,Pr,and Sc denote the Reynolds number,Prandtl number,
and Schmidt number,respectively.The thermophysical properties
used in the above equations are obtained in the ﬁlmby the
1
/
3
rule,
but the gas density of the Reynolds number is calculated from the
free stream conditions.Using ﬁlm theory,the mass transfer rates
m˙
F
are calculated from
m˙
F
)2πr
s
F
g
D
g
Sh* ln(1 +B
M
) (5)
m˙
F
)2πr
s
K
g
C
pg
Nu* ln(1 +B
T
) (6)
Here,r
s
,F
g
,D
g
,K
g
,and C
pg
denote droplet radius,gas density,
diffusion coefﬁcient,thermal conductivity,and speciﬁc heat of the
gas phase,respectively.Subscripts “s” and “g” represent the values
of the droplet surface and gas ﬁlm,respectively.B
M
and B
T
are the
Spalding number of mass and heat transfer,deﬁned as below
B
M
)
Y
Fs
Y
F∞
1 Y
Fs
(7)
B
T
)
C
pg
(T
∞
T
s
)
L(p,T
s
) +Q
L
/m˙
F
(8)
Here,Y
Fs
and Y
F∞
represent the mass fraction of fuel vapor at the
droplet surface and ambient,respectively,and L(p,T
s
) denotes the
latent heat of vaporization.Q
L
,the heat transferred into the droplet,
is deﬁned as below
Q
L
)4πr
s
(
K
dT
dr
)
s
(9)
Combining eqs 5 and 6,the following relationship between the
Spalding number of mass and heat transfer is obtained:
B
T
)(1 +B
M
)
φ
1 (10)
where φ)
C
pF
F
g
D
g
K
g
Sh*
Nu*
In the liquid vaporization model,
24
it is important to calculate
the physical properties accurately at both the vapor and liquid phase
of each species.Internal circulation arising from shear force must
be considered when the relative velocity exists between the droplet
surface and the nearby gas.To include the internal circulation effect,
the effective conductivity model is introduced by Abramzon and
Sirignano.
23
In the present study,the properties of each species at
both the vapor and liquid phase are calculated as a function of the
temperature and pressure.The appropriate mixing rules are also
used for calculations of mixture properties.
25
Thermodynamic equilibrium at the droplet surface requires that
the fugacities of each species in the gas phase be equal to its
fugacities in the liquid phase.Thermodynamic equilibrium condi
tions at the droplet interface are given by
(23) Abramzon,B.;Sirignano,W.A.Approximate theory of a single
droplet vaporization in a convective ﬁeld:Effects of variable properties,
Stefan ﬂow and transient liquid heating.Proceedings of Second ASME
JSME Thermal Engineering Joint Conference,1987;Vol.1,pp 1118.
DMEFueled Engine Conditions Energy & Fuels,Vol.xxx,No.xx,XXXX C
T
v
)T
l
;p
v
)p
l
;f
i
v
)f
i
l
(11)
where subscript v represents the vapor phase and subscript l
represents the liquid phase.
The fugacities of each species in the gaseous and liquid phases
are calculated from
R
u
T ln
(
f
i
X
i
P
)
)
∫
V
∞
{
(
∂p
∂n
i
)
T,V,n
i

R
u
T
V
}
dVR
u
T ln Z (12)
Here,R
u
,f
i
,X
i
,V,and Z represent the universal gas constant,the
fugacity of the ith species,the mole fraction of species i,the total
volume of the system,and the compressibility factor of the mixture,
respectively.
Deviation between the latent heat of vaporization for the pure
component and the enthalpy of vaporization of a gas mixture is
determined by employing the PengRobinson EOS.The energy
required for the phase change is given by
∆h )
∑
i
Y
i
l
H
j
i
(T,p,Y
i
v
) 
∑
i
Y
i
l
H
i,l
(T,p) (13)
Here,H
i,l
represents the enthalpy of the ith component at the liquid
phase.The partial enthalpy of ith component H
j
i
and its ideal gas
enthalpy H
i
0
are related through the following thermodynamic
relation:
(H
j
i
H
i
0
) )R
u
T
2
(
∂ ln f
i
∂T
)
(14)
2.2.Turbulent Combustion Model.In the present study,the
RIF model
15
has been employed to realistically simulate the
turbulencechemistry interaction in the spray combustion processes.
For convenience of presentation,brief descriptions are given below.
The governing equation of species and energy in laminar ﬂamelet
can be written by mixture fraction Z.
F
∂Y
i
∂t
)
F
2
∂
2
Y
i
∂Z
2
+m˙
i
(15)
∂T
∂t
)
2
1
c
p
∂
2
h
∂Z
2

2
1
c
p
∑
k)1
N
h
k
∂
2
Y
k
∂Z
2

1
Fc
p
(
∑
k)1
N
h
k
ω
·
k

∂p
∂t
+ ∇q
rad
)
(16)
As spatial coordinates transform mixture fraction coordinates,
the scalar dissipation rate,,appeared in the above equations,can
be expressed as the molecular diffusion to a reciprocal of
characteristic time in the laminar ﬂamelet.
≡ 2D
(
∂Z
∂x
j
)
2
=
st
f(Z) )
st
Z
2
ln Z
Z
st
2
ln Z
st
(17)
The Eulerian particle ﬂamelet model (EPRM)
16
using the multiple
RIFs model is to handle the spatial inhomogeneity of the scalar
dissipation rate
Y
˜
k
(xb,t) )
∑
i)1
N
I
˜
i
(xb,t)
∫
0
1
Y
k
i
(Z,〈/Z〉
i
;t)P
˜
(Z;xb,t)dZ (18)
where I
˜
i
(xb,t) is the probability that the ith ﬂamelet is found in the
cell at location x at time t.An Eulerian transport equation for this
probability I
˜
i
(xb,t) can be derived.
∂
∂t
(F

I
˜
i
) +
∂
∂x
j
(F

u˜
j
I
˜
i
) )
∂
∂x
j
(
µ
eff
σ
I
∂I
˜
i
∂x
j
)
(19)
Y
k
i
in eq 18 is an unsteady solution for the ith RIF,and to obtain
the solution,the conditional scalar dissipation rate,〈/Z〉
i
,is
expressed by
〈/Z〉
i
)〈
∼
st
〉
i
f(Z) (20)
Here,the average conditional scalar dissipation rate for the ith RIF
in a given time is calculated as follows
〈
∼
st
〉
i
(t) )
∫
V
I
˜
i
F

〈
st
〉
3/2
P
˜
(Z
st
) dV
∫
V
I
˜
i
F

〈
st
〉
1/2
P
˜
(Z
st
) dV
(21)
where
〈
st
〉(xb,t) )
c
ε˜
k
˜
Z
˜
′′
2
∫
0
1
f(Z*)P
˜
(Z*) dZ*
(22)
To account for the vaporization effects on the turbulent spray
combustion,the present study adopts the model proposed by
Demoulin and Borghi.
18
The transport equation of the mixture
fraction variance is derived by using the PDF transport equation
for the mixture fraction.The equations for the mean mixture fraction
Z
˜
and its variance Z
˜
′′
2
coupled with the vaporization effects can be
written as follows:
∂
∂t
(F

Z
˜
) +
∂
∂x
j
(F

u˜
j
Z
˜
) )
∂
∂x
j
(
µ
t
σ
Z
∂Z
˜
∂x
j
)
+F

ω
∼
v
(23)
∂
∂t
(F

Z
˜
′′
2
) +
∂
∂x
j
(F

u˜
j
Z
˜
′′
2
) )
∂
∂x
j
(
µ
t
σ
Z′′
2
∂Z
˜
′′
2
∂x
j
)
+
2µ
t
σ
Z′′
2
∂
2
Z
˜
∂x
j
2

F

∼
+2(F

Zω
˜
V
F

Z
˜
ω
∼
v
) +F

Z
˜
2
ω
∼
v
F

Z
2
ω
v
˜
(24)
The last four additional source terms appearing in eq 24 account
for the vaporization effects on the mixture fraction variance.These
newcorrelations,to take into account the ﬂuctuation of equivalence
ratio because of vaporization,are in an unclosed form.By assuming
that the spray vaporization takes places only at the liquid surface,
Demoulin and Borghi
18
have proposed the model for these
correlations:
F

Zω
˜
v
≈ F

Z
s
ω
v
˜
)
∑
p
Z
s
p
m˙
p
V
(25)
F

Z
2
ω
v
˜
≈ F

Z
s
2
ω
v
˜
)
∑
p
(Z
s
p
)
2
m
p
V
(26)
where the subscript “s” denotes the value at the liquid surface.These
additional source terms are mainly contributed to the production
of mixture fraction ﬂuctuations.In spray combustion processes,
these terms are contributed to increase the scalar dissipation rate
and the ignition delay time as well as to modify the smallscale
mixing processes and the spray structure.
Another important effect arising from vaporization is related to
the fact that the upper limit of the mixture fraction is not in unity
in spray combustion processes.Therefore,the upper limit (Z
ini
) of
the mixture has to be determined.Using the conditional PDF of
Z
ini
and mixture fraction equation,Demoulin and Borghi
18
derived
the following balance equation:
∂
∂t
(F

Z
˜
Z
j
ini
) +
∂
∂x
j
(F

u˜
j
Z
˜
Z
j
ini
) )
∂
∂x
j
(
µ
t
σ
Z
∂Z
˜
Z
j
ini
∂x
j
)
+
F

∫
0
1
Z
ini
ω
∼
vZ
ini
dZ
ini
(27)
(24) Kneer,R.;Schneider,M.;Noll,B.;Witting,S.Diffusion controlled
evaporation of a multicomponent droplet:Theoretical studies on the
importance of variable liquid properties.Int.J.Heat Mass Transfer 1993,
36 (9),2403–2415
.
(25) Reid,R.C.;Prausnitz,J.M.;Poling,B.E.The Properties of Gases
and Liquids,4th ed.;McGrawHill:New York,1987.
D Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
For a given position,therefore,the allowable space for mixture
fraction Z has to be automatically adjusted from 0 to Z
j
ini
.In the
present study,the pdf P
˜
(Z;xb,t) is employed and its shape has been
renormalized from the three constraints:
1 )
∫
0
Z
j
ini
P
˜
(Z)dZ,Z
˜
)
∫
0
Z
j
ini
ZP
˜
(Z) dZ,
Z
˜
′′
2
)
∫
0
Z
j
ini
(ZZ
˜
)
2
P
˜
(Z) dZ (28)
This modiﬁed upper limit of the mixture fraction also inﬂuences
the ignition delay and the spray combustion processes.A decrease
in the upper limit mixture fraction is contributed to increase in the
probability of combustion in a given mixture fraction interval and
to possibly decrease in the ignition delay time.
The mean species mass fractions are calculated by integrating
the ﬂamelet solution weighted with a presumed probability density
function:
Y
˜
i
(xb,t) )
∫
0
Z
j
ini
P
˜
(Z;xb,t)Y
i
(Z;t) dZ (29)
The calculation procedure of the RIF model is performed
interactively with the CFDsolver.During one time step of the main
CFDcode,the ﬂamelet equations are solved by the stiff ODE solver,
in which the time step is subdivided adaptively into subcycles to
resolve the much smaller chemical time scales.The detailed
numerical procedure for the RIF approach
15,16,22
and comprehensive
spray combustion model
10,21
including the RIF approach can be
found elsewhere.
3.Results and Discussion
3.1.Evaporation Characteristics of DME and
nHeptane Droplet.Previously,the present highpressure
vaporization model
21
was validated against experimental data
26,27
for the evaporation process of a freely falling nheptane droplet
at three ambient pressures (20,30,and 40 bar) and two gas
temperatures (550 and 650 K).Our previous numerical results
21
indicate that,compared to the highpressure evaporation model,
the lowpressure evaporation model based on the inﬁnite
conductivity model and ClausiusClapeyron equation for phase
equilibriumwas unable to account for the highpressure effects
including solubility and real gas effects.For all pressure levels
investigated,in terms of droplet size and droplet velocity,
numerical results
21
obtained by the highpressure evaporation
model favorably agreed with experimental data,while the low
pressure model considerably overpredicted the droplet lifetime.
To understand the vaporization process of DME fuel as well
as to identify the distinctive differences of the DME vaporization
process compared to conventional hydrocarbon liquid fuels,the
highpressure vaporization model has been applied to simulate
the vaporization characteristics of DME and nheptane liquid
fuels at a wide range of operating conditions.To simulate the
vaporization process of a single droplet,51 grids are used to
resolve the computational domain within the droplet.All
numerical calculations are stopped when the droplet radius
becomes 30% of the initial droplet radius.Figure 1 shows the
effects of temperature on the evaporation rate and droplet surface
temperature for nheptane and DME liquid droplet at three
ambient temperatures (T
∞
)723,823,and 923 K),the ambient
pressure,P
∞
) 41 bar,the initial interphase relative velocity,
U
d
) 10 m/s,the initial droplet diameter,D
d
) 50 µm,and the
initial droplet temperature,T
d
) 293 K.Numerical results
displayed in Figure 1 indicate that the webbulb temperatures
for nheptane and DME droplet at the given ambient condition
(41 bar and 723 K) are 470 and 330 K,respectively.When
temperature is increased,the wetbulb temperature and the
vaporization rate increase and the droplet lifetime decreases for
both fuels.In comparison to nheptane,DME has a much higher
vaporization rate and a much lower wetbulb temperature.As
shown in Figure 1,nheptane has a much slower heatup process
and takes a much longer time to reach the wetbulb temperature.
On the other hand,DME shows explosively high evaporation
characteristics during the initial stage.The peak evaporation
rate of DME is nearly 2.5 times higher than that of nheptane.
Numerical results also indicate that the higher ambient temper
ature results in a higher droplet surface temperature and wet
bulb temperature,higher vaporization rate,and shorter droplet
lifetime.In the case of DME,the droplet quickly reaches the
thermal equilibrium and heat transfer into the droplet is fully
used to evaporate the droplet after the short heatup period.On
the other hand,the nheptane droplet slowly reaches the thermal
equilibrium and the heat transfer into the droplet is partially
used to evaporate the droplet during the relatively long heatup
period.
Figure 2 shows the effect of pressure on the droplet
evaporation for nheptane and DME liquid droplets at three
ambient pressures (31,41,and 51 bar),the ambient temperature,
(26) Stengele,J.;Willmann,M.;Wittig,S.Experimental and theoretical
study of droplet vaporization in a high pressure environment.1997,ASME
97GT151.
(27) Stengele,J.;Prommersberger,K.;Willmann,M.;Wittig,S.
Experimental and theoretical study of one and twocomponent droplet
vaporization in a high pressure environment.Int.J.Heat Mass Transfer
1999,42,2683–2694
.
Figure 1.Temporal evolutions of the evaporation rate and droplet surface temperature of nheptane and DME at different temperatures.
DMEFueled Engine Conditions Energy & Fuels,Vol.xxx,No.xx,XXXX E
823 K,the initial interphase relative velocity,10 m/s,the initial
droplet diameter,50 µm,and the initial droplet temperature,
293 K.When the pressure increases,the vaporization rate and
the droplet surface temperature increase and the droplet lifetime
decreases for both fuels.When the ambient pressure is increased,
the nheptane and DME droplets have a much larger subcooling
effect,which increases evaporation,while they have a much
higher wetbulb temperature,which results in elevating the
vaporization rate.Because of these two competing effects,the
evaporation time of these liquid droplets is not quite sensitive
to the variation of the ambient pressure.
Figure 3 presents the effect of the initial relative velocity on
the droplet evaporation characteristics as well as the Nusselt
number and Sherwood number of DME and nheptane droplets
at the given ambient conditions (P
∞
) 41 bar,and T
∞
) 823
K) and the initial conditions (T
d
)293 K,and D
d
)50 µm).A
comparison is made for three initial droplet velocities:1,10,
and 100 m/s.As shown in Figure 3,the increase of the relative
velocity directly increases the convection between droplet and
atmosphere as well as shear stress exerted on the droplet surface
causing interior circulation in the droplet.When the initial
relative velocity is increased,the vaporization rate remarkably
increases and the droplet temperature quickly reaches the wet
bulb temperature.In comparison to nheptane,the vaporization
characteristics of DME are more sensitive to the initial relative
velocity,which has a much higher vaporization rate and a much
lower wetbulb temperature.In the case of the highest relative
velocity (100 m/s),the peak evaporation rate of DME is nearly
4.5 times higher than that of nheptane.This drastically high
evaporation rate of DME is mainly caused by the considerably
short heatup period and the substantially high heat and mass
transfer at the high vaporpressure state.Numerical results also
indicate that the wetbulb temperature is independent of the
interphase relative velocity.In general,the elevated interphase
velocity results in a much higher convective heat and mass
transfer between the droplet and the gaseous ﬂow ﬁeld as well
as enhanced internal circulation driven by Hill’s vortex inside
the droplet.In comparison to the nheptane droplet,these
numerical results clearly indicate that the vaporization rate of
the DME droplet is extremely sensitive to the interphase relative
velocity.These numerical results suggest that these distinctly
different evaporation characteristics of DME droplets could
greatly inﬂuence the autoignition,mixing ﬁeld,scalar dissipa
tion rate,turbulencechemistry interaction,and pollutant forma
tion in the turbulent spray combustion of highspeed direct
injection diesel engines.
3.2.Autoignition Characteristics of Homogeneous
DME and nHeptane Mixtures.The present nheptane/air
chemistry is based on the skeletal mechanism
28
of 43 chemical
species and 185 reactions,counting the forward and backward
reactions individually.In Figure 4,the predicted autoignition
Figure 2.Temporal evolutions of the evaporation rate and droplet surface temperature of nheptane and DME at different pressures.
Figure 3.Temporal evolutions of the evaporation rate and droplet surface temperature of nheptane and DME at different initial relative velocities.
F Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
delay times of homogeneous nheptane/air mixtures are com
pared to measurements performed at the shock tube
29
and the
rapid compression machines.
30
To check the accuracy of the
detailed chemical kinetics used in this study,the ignition delay
of homogeneous DME/air mixtures is calculated by the constant
volume homogeneous reactor model.In the autoignition
calculation,the ignition is deﬁned by the highest temperature
gradient that nearly coincides with the maximum CH concentra
tion.It can be clearly shown that the present chemistry model
has the capability of correctly predicting the negative temper
ature coefﬁcient (NTC) behavior arising from the nonlinearity
of the chemistry.Numerical and experimental results also
indicate that this (NTC) behavior is relatively strong at low
chamber pressure.In terms of the autoignition delay time,the
numerical results obtained in the present study agree well with
experimental data.The detailed chemistry
31
of 336 elementary
reaction steps and 78 chemical species is adopted for the DME/
air reaction.In Figure 5,the predicted autoignition delay times
of the homogeneous DME/air mixture are compared to mea
surements
32
performed at the highpressure shock tube.Mea
surements
32
were performed at a range of temperatures from
650 to 1300 K,the two pressures (13 and 40 bar),and the given
equivalent ratio (1.0).In these calculations,the ignition is
deﬁned by the highest temperature.Numerical results agree well
with experimental data for the wide range of temperatures (650
< T < 1300 K) at 40 bar.However,at 13 bar,there exist
noticeable deviations in the lower temperature conditions.Table
1 presents the predicted ignition delay times of the nheptane
and DME homogeneous mixture in the low and highpressure
conditions,four temperatures (700,800,900,and 1000 K),and
the unitary equivalent ratio.In comparison to the nheptane
mixture,the DME mixture yields a much shorter ignition delay
time.This trend is more apparent for the lower pressure case.
These listed data indicate that the nheptane mixture has a much
stronger NTC behavior,especially at the lower pressure
condition.
3.3.Comparison of Autoignition and Combustion
Characteristics for nHeptane and DME Sprays.Next,the
present approach has been applied to simulate the autoignition
and subsequent combustion processes of DME sprays.The
validation case has been chosen as measurements of Kim et
al.
9
at chamber pressure,2.1 MPa,and injection pressure,40
MPa.In this case example,the highpressure vaporization model
and the vaporization coupled RIF turbulent combustion model
are employed to predict the turbulent DME spray combustion
processes.A computational domain of 40 mm in radius and 90
mmin length is resolved by 60 radial and 80 axial computational
cells with a nonuniform mesh arrangement.The injection
velocity (235 m/s) of the DME liquid fuel was assumed to be
constant during the injection period.The nozzle diameter and
total injected mass are 0.22 mm and 6.9 mg,respectively.The
adiabatic condition is imposed at the wall.
Figure 6 presents the measured
9
and predicted ignition delay
times for the chamber pressure,2.1 MPa,and the injection
pressure,40 MPa.In this validation case,the predicted ignition
delay times agreed well with experimental data of Kim et al.,
9
which has relatively wellspeciﬁed initial conditions.At the
chamber pressure,2.1 MPa,and temperature,1132 K (1000/T
) 0.88),the predicted delay time (0.941 ms) is quite close to
experimental data (0.898 ms).However,at the relatively low
temperature conditions (T < 900 K),there exist certain
deviations with measurements.To illustrate the autoignition
process of the DME spray,the instantaneous DME spray jet
ﬂame ﬁelds for the initial chamber condition (2.1 MPa and 1132
K) and injection pressure,40 MPa,are plotted in Figure 7.In
this relatively short injection duration (0.64 ms) case,the auto
ignition occurs approximately at 0.94 ms after the completion
of liquid fuel injection.The ignition is initiated around the
(28) Liu,S.;Hewson,J.C.;Chen,J.H.;Pitsch,H.Effects of strain rate
on highpressure nonpremixed nheptane autoignition in counterﬂow.
Combust.Flame 2004,137,320–339
.
(29) Ciezki,H.K.;Adomeit,G.Shocktube investigation of selfignition
of nheptaneair mixtures under engine relevant conditions.Combust.Flame
1993,93,421–433
.
(30) Minetti,R.;Carlier,M.;Ribaucour,M.;Therssen,E.;Soche,L.R.
A rapid compression machine investigation of oxidation and autoignition
of nheptane:Measurement and modeling.Combust.Flame 1995,102,298–
309
.
(31) Lawrence Livermore National Laboratory (LLNL) site.https://
www.llnl.gov/.
(32) Pfahl,U.;Fieweger,K.;Adomeit,G.Selfignition of dieselrelevant
hydrocarbonair mixtures under engine conditions.Proceedings of the 26th
International Symposium on Combustion,The Combustion Institute,
Pittsburgh,PA,1996;pp 781789.
Figure 4.Calculated and measured (Ciezki et al.
29
and Minetti et al.
30
)
ignition delay times of homogeneous nheptane/air mixtures.
Figure 5.Predicted and measured
32
ignition delay times of homoge

neous DME/air mixtures.
Table 1.Ignition Characteristics of Homogeneous DME and
nHeptane Mixtures
DME nheptane
temperature 13 bar 40 bar 13.2 bar 42 bar
700 K 3.067 ms 2.318 ms 5.436 ms 3.786 ms
800 K 1.518 ms 0.343 ms 2.093 ms 0.433 ms
900 K 1.518 ms 0.301 ms 4.389 ms 0.433 ms
1000 K 1.003 ms 0.208 ms 1.863 ms 0.456 ms
DMEFueled Engine Conditions Energy & Fuels,Vol.xxx,No.xx,XXXX G
stoichiometric tail region of the DME fuel vapor jet.In terms
of ignition site and delay time,these autoignition characteristics
are distinctly different fromthe relatively long injection duration
cases.During the injection period,ignition is almost impossible
near the stoichiometric tail region of the fuel vapor jet,mainly
because of the cooling effects of spray vaporization and the
considerably high scalar dissipation rate.However,after the
completion of liquid fuel injection,close to the stoichiometric
tail region of the fuel vapor jet,the scalar dissipation rate is
rapidly decreased and reaches a certain low level to allow for
the autoignition.This trend is clearly displayed in Figure 7.
On the other hand,it is quite possible that the relatively long
injection duration cases create the autoignition site around the
stoichiometric downstream region of the fuel vapor jet with a
sufﬁciently low scalar dissipation rate.
To compare the spray combustion characteristics of the
nheptane and DME fuels,numerical calculation is performed
using the same injection mass ﬂowrate (6 mg/1.4 ms),injection
velocity (225 m/s),the diameter of nozzle (0.2 mm),initial
chamber condition (P ) 4.1 MPa,and T ) 823 K),and the
injection duration (1.4 ms).Figures 810 show the instanta
neous distribution of temperature,OH radical,and scalar
dissipation rate in the nheptane and DME spray ﬂame ﬁeld.
The predicted ignition delay time (1.303 ms) of DME sprays is
much shorter than that of nheptane sprays (1.602 ms).Thus,
the DME spray jet is ignited during the injection period,while
the nheptane spray jet is ignited after the completion of fuel
injection.These different ignition delay times relative to the
injection duration result in the creation of the different ignition
sites.For the DME spray jet ignited during the injection period,
the autoignition occurs around the slightly rich downstream
region of the DME fuel vapor jet with a sufﬁciently low scalar
dissipation rate.On the other hand,for the nheptane spray jet
ignited after the completion of fuel injection,the autoignition
is initiated around the stoichiometric tail region of the nheptane
fuel vapor jet with a certain low scalar dissipation rate to allow
for the ignition.Because DME sprays have relatively short spray
penetration length and higher evaporation rate than nheptane
sprays,the DME spray ﬂame exists in the relatively upstream
region.Because of the high evaporation rate of DME fuel at
the initial injection stage,the scalar dissipation rate near the
injector is much higher than that of nheptane fuel.This trend
is clearly shown in Figure 11.In the initial injection period,
the maximum scalar dissipation rate for the DME spray jet is 7
times higher than that for the nheptane spray jet.These
distinctly different ignition characteristics of DME and nheptane
sprays are closely related to evaporation characteristics,spray
behavior,and ignition delay time of the homogeneous mixture
for DME and nheptane fuel.It is necessary to note that the
same injection condition of DME and nheptane sprays cannot
be arranged in an experiment or in real spray combustion
systems.Therefore,future works must include systematic
validations for the nonreacting,evaporating,and burning DME
and nheptane sprays with detailed and reliable injection
information.
Figures 12 and 13 present the time evolution of local ﬂame
structure in terms of temperature,mass fractions (fuel vapor,
O
2
,H
2
,OH,CO,and CO
2
) of the major and minor species,and
the consumption rates of the oxygen near autoignition of
nheptane and DME spray jets injected at initial chamber
pressure and temperature of 4.1 MPa and 823 K,respectively.
In comparison to the nheptane spray jet,the predicted proﬁles
of O
2
and fuel vapor in the mixture fraction space indicate that
the DME spray jet yields a much broader leakage zone,where
the nonequilibrium chemical reaction mostly occurs.These
results also suggest that the ﬂame structure and pollutant
formation of the DMEfueled engines could be more sensitive
to the turbulencechemistry interaction.At the early stage of
autoignition,the magnitude of the reaction rate decreases and
three peaks are formed.Thereafter,the center peak remains a
certain value,which is supported mainly by the diffusion ﬂame,
while two peaks propagate toward the fuellean and fuelrich
side of the ﬂame.These center peaks for the DME and nheptane
ignition processes lie on the slightly rich side.These complex
chemical reaction processes occur within a very short time
interval.In the overall ﬂame structure,compared to the
nheptane spray jet,the DME spray jet has a much broader hot
temperature ﬂame zone in the fuelrich side of the mixture
fraction space.This distinctly different structure of the DME
spray ﬂame could be mainly related to the characteristics of
the oxygenated fuels.The predicted proﬁles of oxygen mass
fraction,fuel mass fraction,and oxygen consumption rate for
both fuels clearly reﬂect this trend.In terms of the OH mass
fraction,DME yields a much broader distribution at the fuel
rich region.This distinctly broader OH distribution of the DME
ﬂame in the fuelrich region possibly plays a crucial role to
oxidate the soot particles in the actual spray ﬂame ﬁeld of the
DI diesel engines.Moreover,in the fuelrich region,DME
generates a much broader and higher hydrogen distribution,
which could greatly reduce the soot formation in the actual spray
ﬂames.These numerical results suggest that the distinctly
broader and higher OHand H
2
distribution in the fuelrich region
can remarkably reduce the soot formation in the DMEfueled
diesel engines,compared to the conventional hydrocarbonfueled
diesel engines.
4.Conclusions
On the basis of numerical results,the following conclusions
are drawn in terms of the evaporation characteristics of single
droplets,combustion processes,ignition characteristics of
homogeneous mixtures and spray jets,ﬂame structure,and
turbulencechemistry interaction in the nheptane and DME
spray combustion processes:(1) When temperature increases,
the vaporization rate and the droplet surface temperature increase
and the droplet lifetime decreases for nheptane and DME liquid
droplets.In comparison to nheptane,DME has a much higher
vaporization rate and a much lower wetbulb temperature.
Figure 6.Predicted and measured
9
ignition delay times of injected DME
spray at constant volume chamber.
H Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
nHeptane has a much slower heatup process and takes a much
longer time to reach the wetbulb temperature.On the other
hand,DME shows quite high evaporation characteristics during
the initial stage.(2) When the pressure increases,the vaporiza
tion rate and the droplet surface temperature increase and the
droplet lifetime decreases for both fuels.When the ambient
Figure 7.Instantaneous distribution patterns of temperature and droplets near autoignition in the transient spray ﬁeld.
Figure 8.Instantaneous distribution patterns of the temperature distribution of nheptane and DME spray ﬂames.
DMEFueled Engine Conditions Energy & Fuels,Vol.xxx,No.xx,XXXX I
pressure increased,the nheptane and DME droplets have much
larger subcooling effects,which increases evaporation time,
while they have much higher wetbulb temperature,which
results in elevating the vaporization rate.Because of these two
competing effects,the evaporation time of these liquid droplets
is not quite sensitive to the variation of the ambient pressure.
(3) In comparison to the nheptane droplet,the vaporization rate
of the DME droplet is extremely sensitive to the interphase
Figure 9.Instantaneous contours of the OH radical mass fraction of nheptane and DME spray ﬂames.
Figure 10.Instantaneous distribution patterns of the scalar dissipation rate of nheptane and DME spray ﬂames.
J Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
relative velocity.In the case of the highest relative velocity (100
m/s),the peak evaporation rate of DME is nearly 4.5 times
higher than that of nheptane.This drastically high evaporation
rate of DME is mainly caused by the considerably short heat
up period and the substantially high heat and mass transfer at
the high vaporpressure state.These numerical results suggest
that these distinctly different evaporation characteristics of DME
droplets could greatly inﬂuence the autoignition,mixing ﬁeld,
scalar dissipation rate,turbulencechemistry interaction,and
pollutant formation in the turbulent spray combustion of high
speed directinjection diesel engines.(4) Numerical results
clearly indicate that the multiple RIF model together with the
present highpressure vaporization model reasonably well predict
the ignition delay times for the DME spray jets in the diesel
like environment.(5) For the DME spray jetignited during the
injection period,the autoignition occurs around the slightly rich
downstreamregion of the DME fuel vapor jet with a sufﬁciently
low scalar dissipation rate.On the other hand,for the nheptane
spray jetignited after the completion of fuel injection,the auto
ignition is initiated around the stoichiometric tail region of the
nheptane fuel vapor jet,where a certain low scalar dissipation
rate allows for the ignition.(6) In comparison to the nheptane
spray jet,the DME spray jet has a much broader hottemperature
ﬂame zone in the fuelrich side of the mixture fraction space.
This distinctly different structure of the DME spray ﬂame could
be mainly related to the characteristics of the oxygenated fuels.
(7) In terms of the OH mass fraction,DME yields a much
broader distribution at the fuelrich region.Moreover,in the
fuelrich region,DME generates a much broader and higher
hydrogen distribution.This distinctly different OH and H
2
distribution in the DME ﬂame structure possibly plays a crucial
role to oxidate the soot particles in the actual spray ﬂame ﬁeld
of the DI diesel engines.
Figure 11.Temporal evolutions of the scalar dissipation rates and the
maximum temperatures.
Figure 12.Time evolutions of the temperature and mass fraction of
various species in the interactive ﬂamelet for nheptane spray.
Figure 13.Time evolution of the temperature and mass fraction of
various species in the interactive ﬂamelet for DME spray.
DMEFueled Engine Conditions Energy & Fuels,Vol.xxx,No.xx,XXXX K
Acknowledgment.This work was supported by the Center for
Environmentally Friendly Vehicle (CEFV) of the EcoSTAR project
from the Ministry of Environment (MOE),Republic of Korea.
Nomenclature
Roman Symbols
c
p
) speciﬁc heat of mixture at constant pressure
D
i
) diffusion coefﬁcient of species i
f ) fugacity
h and h
k
) enthalpy of mixture and species k
I
l
) probability to ﬁnd lth particle at a certain location and time
k ) turbulent kinetic energy
K ) thermal conductivity
L ) latent heat (enthalpy of vaporization)
p ) pressure
P ) probability density function
Q ) heat ﬂux
t ) time
T ) temperature
u
j
) Cartesian velocity component in x
j
direction
x
j
) Cartesian coordinates
Y
i
) mass fraction of species i
Z ) mixture fraction
Greek Symbols
) scalar dissipation rate
ε ) dissipation rate of turbulent kinetic energy
φ ) fugacity coefﬁcient
µ
eff
) effective viscosity
F ) density
ω˙
k
) chemical production rate of species k
Subscripts
d ) droplet condition
l ) liquid phase
s ) surface condition
v ) vapor phase
∞ ) conditions at inﬁnity of ambient
Superscripts
ψ
j
) Reynoldsaveraged (densityunweighted) properties
ψ
˜
) Favreaveraged (densityweighted) properties
ψ′ ) turbulent ﬂuctuating component
Nondimensional Numbers
Nu ) Nusselt number (hL/K)
Pr ) Prandtl number (µc
p
/λ)
Re ) Reynolds number (FuL/µ)
Sc ) Schmidt number (µ/FD)
Sh ) Sherwood number (hL/D)
EF8002119
L Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
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