Numerical Study on the Characteristics of Vaporization, Ignition, and Turbulent Combustion Processes in Dimethyl Ether (DME)-Fueled Engine Conditions

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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 Kwan-Soo 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 Kwan-Soo Lee
Department of Mechanical Engineering,Hanyang UniVersity,17,Haengdang-Dong,Sungdong-Ku,
Seoul 133-791,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 n-heptane 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,high-pressure 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 high-pressure,combustion processes,
ignition characteristics of homogeneous mixtures and spray jets,flame structure,and turbulence-chemistry
interaction in the n-heptane and DME-fueled 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 compression-ignition engines.The thermal
efficiency of a DME-powered diesel engine is comparable to that
of diesel fuel operation,and soot-free 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 fuel-air mixing
processes.Although DME burns well in the combustion systems
of direct-injection (DI) diesel engines at light and medium loads
and all speeds,the combustion efficiency of DME-fueled 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
1-5
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 constant-volume 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 low-pressure 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,Haengdang-Dong,Sungdong-
Ku,Seoul 133-791,Korea.Telephone:+82-2-2220-0428.Fax:+82-2-2297-
3432.E-mail:ymkim@hanyang.ac.kr.
(1) Arcoumanis,C.The second European auto-oil programme (AOLII).
European Commission,2000;Vol.2,Alternative Fuels for Transportation.
(2) Sorenson,S.C.;Glensvig,M.;Abata,D.Di-methyl 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 di-methyl ether injected by a DI diesel injector.
Proceedings of the Fourth International Symposium COMODIA,1998;pp
537-542.
(4) Kajitani,S.;Chen,Z.;Oguma,M.;Konno,M.A study of low
compression-ratio di-methyl 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 1999-01-3600.
(6) Teng,H.;McCandless,J.C.;Schneyer,J.B.Thermo-chemical
characteristics of di-methyl ethersAn alternative fuel for compression-
ignition engines.2001 SAE Paper 2001-01-0154.
(7) Golovitchev,V.I.;Nordin,N.;Chomiak,J.Neat di-methyl 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 299-306.
(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 DME-fueled 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,auto-ignition of fuel vapor,and turbulence-chemistry
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 high-pressure spray
combustion processes.The modeling of the droplet vaporization
process under high-pressure conditions requires to take into account
the additionally complex effects such as the real gas behavior,the
variation of thermophysical properties,the non-ideality of the latent
heat of evaporation,and the non-ideal phase equilibriumincluding
the solubility of the ambient gas inside the droplet.So far,most
spray combustion models are based on the low-pressure model
similar to the vaporization routine of the KIVA code.
10
However,
the low-pressure vaporization model unrealistically predicts the
vaporization process in the high-pressure 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 high-pressure
vaporization,mixing,and combustion processes encountered in
liquid-fueled propulsion systems.
The fuel vapor auto-ignition also considerably influences the
characteristics of the spray combustion.The spray ignition
process is often simulated by the Shell ignition model,
12-14
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 turbulence-chemistry interaction based on
the detailed chemistry.Hence,auto-ignition,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 time-dependent
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 direct-injection
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 high-pressure environment,the present study
employs the KH-RT breakup model,
19
the stochastic droplet
tracking model,
10
the collision model,
20
the high-pressure
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 high-pressure 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 high-pressure
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 high-temperature
auto-ignition,fuel decomposition,and fuel oxidation.
This improved spray combustion model has been applied to
simulate the spray dynamics,vaporization,auto-ignition,and
combustion process in n-heptane- and DME-fueled 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
n-heptane 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 high-pressure
conditions,combustion processes,ignition characteristics of
homogeneous mixtures and spray jets,flame structure,and
turbulence-chemistry interaction in n-heptane- and DME-fueled
diesel-like 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,LA-11560-MS.
(11) Yang,V.Modeling of supercritical vaporization,mixing,and
combustion processes in liquid-fueled 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 auto-ignition 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.Three-dimensional modeling of
NO
x
and soot formation in DI-diesel engines using detailed chemistry based
on the interactive flamelet approach.1996,SAE Paper 962057.
(16) Barths,H.;Antoni,C.;Peters,N.Three-dimensional simulation of
pollutant formation in a DI-diesel 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,LA-9069T.
(21) Yu,Y.W.;Kim,S.K.;Kim,Y.M.Numerical modeling for
autoignition and combustion processes of fuel spays in high-pressure
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 high-pressure
environment using the multiple-RIF 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,auto-ignition,and turbulence-chemistry interaction.In this
study,all submodels for these important physical processes are
implemented in the multidimensional Eulerian-Lagrangian for-
mulation.The gas-phase equation is written in an Eulerian
coordinate,whereas the liquid-phase is presented in Lagrangian
coordinates.The two-way 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
high-pressure vaporization model,standard k-ε 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 subgrid-scale
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 gas-phase
velocity field.If the gas-phase 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 droplet-eddy
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.High-Pressure Vaporization Model.To account for the
high-pressure vaporization processes in context with the compre-
hensive spray combustion modeling,the present high-pressure
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 quasi-equilibriumstate.(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

F
are calculated from

F
)2πr
s
F
g
D
g
Sh* ln(1 +B
M
) (5)

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 11-18.
DME-Fueled 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
}
dV-R
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 Peng-Robinson 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
turbulence-chemistry 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
-

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
-

j
Z
˜
) )

∂x
j
(
µ
t
σ
Z
∂Z
˜
∂x
j
)
+F
-
ω

v
(23)

∂t
(F
-
Z
˜
′′
2
) +

∂x
j
(F
-

j
Z
˜
′′
2
) )

∂x
j
(
µ
t
σ
Z′′
2
∂Z
˜
′′
2
∂x
j
)
+

t
σ
Z′′
2

2
Z
˜
∂x
j
2
-
F
-


+2(F
-

˜
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
-

˜
v
≈ F
-
Z
s
ω
v
˜
)

p
Z
s
p

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 small-scale
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
-

j
Z
˜
Z
j
ini
) )

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

0
1
Z
ini
ω

v|Z
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.;McGraw-Hill: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
(Z-Z
˜
)
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
n-Heptane Droplet.Previously,the present high-pressure
vaporization model
21
was validated against experimental data
26,27
for the evaporation process of a freely falling n-heptane 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 high-pressure evaporation model,
the low-pressure evaporation model based on the infinite
conductivity model and Clausius-Clapeyron equation for phase
equilibriumwas unable to account for the high-pressure 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 high-pressure 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
high-pressure vaporization model has been applied to simulate
the vaporization characteristics of DME and n-heptane 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 n-heptane 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 web-bulb temperatures
for n-heptane and DME droplet at the given ambient condition
(41 bar and 723 K) are 470 and 330 K,respectively.When
temperature is increased,the wet-bulb temperature and the
vaporization rate increase and the droplet lifetime decreases for
both fuels.In comparison to n-heptane,DME has a much higher
vaporization rate and a much lower wet-bulb temperature.As
shown in Figure 1,n-heptane has a much slower heat-up process
and takes a much longer time to reach the wet-bulb 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 n-heptane.
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 heat-up period.On
the other hand,the n-heptane droplet slowly reaches the thermal
equilibrium and the heat transfer into the droplet is partially
used to evaporate the droplet during the relatively long heat-up
period.
Figure 2 shows the effect of pressure on the droplet
evaporation for n-heptane 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-
97-GT-151.
(27) Stengele,J.;Prommersberger,K.;Willmann,M.;Wittig,S.
Experimental and theoretical study of one- and two-component 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 n-heptane and DME at different temperatures.
DME-Fueled 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 n-heptane and DME droplets have a much larger subcooling
effect,which increases evaporation,while they have a much
higher wet-bulb 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 n-heptane 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 n-heptane,the vaporization
characteristics of DME are more sensitive to the initial relative
velocity,which has a much higher vaporization rate and a much
lower wet-bulb 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 n-heptane.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 vapor-pressure state.Numerical results also
indicate that the wet-bulb 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 n-heptane 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 auto-ignition,mixing field,scalar dissipa-
tion rate,turbulence-chemistry interaction,and pollutant forma-
tion in the turbulent spray combustion of high-speed direct-
injection diesel engines.
3.2.Auto-ignition Characteristics of Homogeneous
DME and n-Heptane Mixtures.The present n-heptane/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 auto-ignition
Figure 2.Temporal evolutions of the evaporation rate and droplet surface temperature of n-heptane and DME at different pressures.
Figure 3.Temporal evolutions of the evaporation rate and droplet surface temperature of n-heptane and DME at different initial relative velocities.
F Energy & Fuels,Vol.xxx,No.xx,XXXX Yu et al.
delay times of homogeneous n-heptane/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 auto-ignition
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 auto-ignition 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 auto-ignition delay times
of the homogeneous DME/air mixture are compared to mea-
surements
32
performed at the high-pressure 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 n-heptane
and DME homogeneous mixture in the low- and high-pressure
conditions,four temperatures (700,800,900,and 1000 K),and
the unitary equivalent ratio.In comparison to the n-heptane
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 n-heptane mixture has a much
stronger NTC behavior,especially at the lower pressure
condition.
3.3.Comparison of Auto-ignition and Combustion
Characteristics for n-Heptane and DME Sprays.Next,the
present approach has been applied to simulate the auto-ignition
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 high-pressure 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 non-uniform 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 well-specified 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 auto-ignition
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 high-pressure non-premixed n-heptane autoignition in counterflow.
Combust.Flame 2004,137,320–339
.
(29) Ciezki,H.K.;Adomeit,G.Shock-tube investigation of self-ignition
of n-heptane-air 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 auto-ignition
of n-heptane: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.Self-ignition of diesel-relevant
hydrocarbon-air mixtures under engine conditions.Proceedings of the 26th
International Symposium on Combustion,The Combustion Institute,
Pittsburgh,PA,1996;pp 781-789.
Figure 4.Calculated and measured (Ciezki et al.
29
and Minetti et al.
30
)
ignition delay times of homogeneous n-heptane/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
n-Heptane Mixtures
DME n-heptane
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
DME-Fueled 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 auto-ignition 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 auto-ignition.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 auto-ignition 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
n-heptane 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 8-10 show the instanta-
neous distribution of temperature,OH radical,and scalar
dissipation rate in the n-heptane and DME spray flame field.
The predicted ignition delay time (1.303 ms) of DME sprays is
much shorter than that of n-heptane sprays (1.602 ms).Thus,
the DME spray jet is ignited during the injection period,while
the n-heptane 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 auto-ignition 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 n-heptane spray jet
ignited after the completion of fuel injection,the auto-ignition
is initiated around the stoichiometric tail region of the n-heptane
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 n-heptane
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 n-heptane 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 n-heptane spray jet.These
distinctly different ignition characteristics of DME and n-heptane
sprays are closely related to evaporation characteristics,spray
behavior,and ignition delay time of the homogeneous mixture
for DME and n-heptane fuel.It is necessary to note that the
same injection condition of DME and n-heptane 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 n-heptane 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 auto-ignition of
n-heptane and DME spray jets injected at initial chamber
pressure and temperature of 4.1 MPa and 823 K,respectively.
In comparison to the n-heptane 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 non-equilibrium chemical reaction mostly occurs.These
results also suggest that the flame structure and pollutant
formation of the DME-fueled engines could be more sensitive
to the turbulence-chemistry interaction.At the early stage of
auto-ignition,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 fuel-lean and fuel-rich
side of the flame.These center peaks for the DME and n-heptane
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
n-heptane spray jet,the DME spray jet has a much broader hot-
temperature flame zone in the fuel-rich 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 fuel-rich 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 fuel-rich 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 fuel-rich region
can remarkably reduce the soot formation in the DME-fueled
diesel engines,compared to the conventional hydrocarbon-fueled
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
turbulence-chemistry interaction in the n-heptane and DME
spray combustion processes:(1) When temperature increases,
the vaporization rate and the droplet surface temperature increase
and the droplet lifetime decreases for n-heptane and DME liquid
droplets.In comparison to n-heptane,DME has a much higher
vaporization rate and a much lower wet-bulb 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.
n-Heptane has a much slower heat-up process and takes a much
longer time to reach the wet-bulb 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 auto-ignition in the transient spray field.
Figure 8.Instantaneous distribution patterns of the temperature distribution of n-heptane and DME spray flames.
DME-Fueled Engine Conditions Energy & Fuels,Vol.xxx,No.xx,XXXX I
pressure increased,the n-heptane and DME droplets have much
larger subcooling effects,which increases evaporation time,
while they have much higher wet-bulb 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 n-heptane 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 n-heptane and DME spray flames.
Figure 10.Instantaneous distribution patterns of the scalar dissipation rate of n-heptane 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 n-heptane.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 vapor-pressure state.These numerical results suggest
that these distinctly different evaporation characteristics of DME
droplets could greatly influence the auto-ignition,mixing field,
scalar dissipation rate,turbulence-chemistry interaction,and
pollutant formation in the turbulent spray combustion of high-
speed direct-injection diesel engines.(4) Numerical results
clearly indicate that the multiple RIF model together with the
present high-pressure vaporization model reasonably well predict
the ignition delay times for the DME spray jets in the diesel-
like environment.(5) For the DME spray jet-ignited during the
injection period,the auto-ignition 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 n-heptane
spray jet-ignited after the completion of fuel injection,the auto-
ignition is initiated around the stoichiometric tail region of the
n-heptane fuel vapor jet,where a certain low scalar dissipation
rate allows for the ignition.(6) In comparison to the n-heptane
spray jet,the DME spray jet has a much broader hot-temperature
flame zone in the fuel-rich 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 fuel-rich region.Moreover,in the
fuel-rich 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 n-heptane spray.
Figure 13.Time evolution of the temperature and mass fraction of
various species in the interactive flamelet for DME spray.
DME-Fueled 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 Eco-STAR 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
) Reynolds-averaged (density-unweighted) properties
ψ
˜
) Favre-averaged (density-weighted) 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.