Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 15.6.4 - Numerical Simulation of n-Heptane Spray Auto-Ignition
ALL VOLUMES CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00102023/00387
 Material Information
Title: 15.6.4 - Numerical Simulation of n-Heptane Spray Auto-Ignition Reactive Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Bouali, Z.
Pera, C.
Reveillon, J.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: auto-ignition
negative temperature coefficient (NTC)
preferential segregation
n-heptane
 Notes
Abstract: This paper investigates evaporating liquid fuel influence on the autoignition of n-heptane/air mixtures over a wide range of conditions encountered in internal combustion engines. For this purpose, droplet evaporation source terms and semi-detailed chemistry are simultaneously solved considering two types of configurations. The first one is a homogeneous constant-pressure reactor where the effects of diffusion and stratification can be neglected. The second type of simulation deals with evaporating droplet segregation impact. Consequently, the configuration is not homogeneous anymore so diffusion and stratification effects must be considered. Semi-detailed chemistry (29 species and 52 reactions) is introduced to account for specific kinetics behaviour in the Negative Temperature Coefficient (NTC) region. The impact of mass and heat source terms due to evaporation is put forward. The specificity of two-phase flow auto-ignition is the competition between the fuel vapour availability and the evaporation-induced temperature fall. Droplet evaporation time restricts the gaseous local fuel/air equivalence ratio and consequently the kinetics runaway. Temperature reduction due to evaporation may either reduce or enhance chemical reactivity depending on the location of the auto-ignition reaction inside or outside the NTC region.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00387
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1564-Bouali-ICMF2010.pdf

Full Text



7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Numerical Simulation of n-Heptane Spray Auto-ignition


Z. Bouali* i, C. Pera* and J. Reveilloni

Department of Engine CFD and Simulation, IFP, Rueil-Malmaison, 92852, France
SCORIA, University of Rouen, Saint-Etienne du Rouvray, 76801, France

zakaria.bouali~ifp.fr, cecile.pera~ifp.fr and julien.reveillon~coria.fr

Keywords: Auto-ignition; Negative Temperature Coefficient (NTC); Preferential Segregation; n-heptane




Abstract

This paper investigates evaporating liquid fuel influence on the autoignition of n-heptane/air mixtures over a wide
range of conditions encountered in internal combustion engines. For this purpose, droplet evaporation source terms
and semi-detailed chemistry are simultaneously solved considering two types of configurations. The first one is a
homogeneous constant-pressure reactor where the effects of diffusion and \Iluslilk~.elisl I can be neglected. The second
type of simulation deals with evaporating droplet segregation impact. Consequently, the configuration is not homo-
geneous anymore so diffusion and \Ilus li.lk~lilsl effects must be considered. Semi-detailed chemistry (29 species and
52 reactions) is introduced to account for specific kinetics behaviour in the Negative Temperature Coefficient (NTC)
region. The impact of mass and heat source terms due to evaporation is put forward. The specificity of two-phase flow
auto-ignition is the competition between the fuel vapour availability and the evaporation-induced temperature fall.
Droplet evaporation time restricts the gaseous local fuellair equivalence ratio and consequently the kinetics runaway.
Temperature reduction due to evaporation may either reduce or enhance chemical reactivity depending on the location
of the auto-ignition reaction inside or outside the NTC region.


Introduction

During the last decades, combustion chamber model-
ing has been extensively developed thanks to progresses
made in the understanding of the various physical phe-
nomena interacting in engines from the liquid fuel in-
jection, down to combustion processes and gas ex-
haust. However, to optimize environmental and eco-
nomical outputs of the considered systems, model accu-
racy needs to be unceasingly improved. Numerous phe-
nomena are interacting within the chamber. These intri-
cated couplings directly define the engine performances
as well as the pollutant emissions. So, understanding
even better controlling auto-ignition process is crucial
for improving the energy efficiency of internal combus-
tion engines and for aiming at near-zero pollutant emis-
sions.
After the primary atomization process occurring close
to the injector outlet, secondary atomization generates
dispersed droplets small enough to undergo the turbu-
lent velocity fluctuations of the carrier phase. This
spray evaporates according to the local gaseous prop-
erties (temperature, pressure, vapor fuel concentration).
During the last decades, the more and more stringent
emission regulations have lead to the development of


multiple-injection strategies for direct injection Diesel
engines. These strategies widely allow reducing pol-
lutant emissions and noise levels but at the same time
imply for more complex combustion processes with lo-
cal auto-ignition spots that may occur within evapo-
rated spray. Even if auto-ignition is a widely studied
and reviewed phenomenon, either on the kinetics side
(Battin-Leclere (2008)) or on the turbulent combustion
side (Mastorakos I,** i'LII evaporating droplet fuel in-
fluence still raises numerous problems. Indeed, most
studies are devoted to purely gaseous mixtures and, con-
sequently, numerical (Stauch et al. (2006), Wang & Rut-
land (2005)) and experimental (Wang et al. (1996), Khan
et al. (2007)) literature on two-phase flow auto-ignition
is still scarce and only a few general trends are known.
The objective of the present paper is to analyse how
the mass and heat source terms from liquid evaporation
influence n-heptane auto-ignition process. In order to
analyse the key chemical paths, skeletal chemistry able
to reproduce NTC kinetics is used. The focus is on the
modification of local temperature and on the restricted
fuel availability resulting from droplet preferential seg-
regation due to the turbulent mixing.







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


where R is the ratio of the perfect gas constant with the
carrier phase molar mass.
Various source terms are present in the previous equa-
tions: LjF, Ljm and Lje are related to the chemical reac-
tion processes whereas m, vr and e result from a two-way
coupling between the carrier phase and the evaporating
spray. These last terms are detailed in a subsequent
part whereas the chemical reactions source terms are
obtained thanks to the coupling of the DNS-DPS with a
ChemkinB solver.
The sixth order Pad6 scheme from Lele (1992) has been
used to compute spatial derivatives of the gas phase
balance equations on a regular mesh. Time integration
of both spray and gas phase equations is carried out
through a third order explicit Runge-Kutta scheme with
a minimal data storage method (Wray (1990)). A third
order interpolation is employed when gaseous phase
properties must be determined at the droplet positions.


Numerics and configuration

The objective of this work is to point out the evap-
orating droplet preferential segregation effect on the
auto-ignition process. For this purpose, a Direct Numer-
ical Simulation (DNS) approach is used in the context
of Discrete Particle Simulation (DPS) leading to DNS-
DPS simulations for which numerics is detailed in the
following subsections.

Gas phase balance equations
The carrier phase is a compressible Newtonian fluid fol-
lowing the equation of state for a perfect gas. The in-
stantaneous balance equations describe the evolution of
mass p, momentum pu, total (except chemical) energy
et and species mass fraction. YF denotes the mass frac-
tion of gaseous fuel resulting from spray evaporation and
Ym stands for all other species. The following set of
balance equations are solved, where usual notations are
adonptd:


Continuity equation:


Lagrangian description of the dispersed phase
As described by Reeks (1991), it is possible to account
for many forces to characterize the droplet dynamics.
(1) Because of the high density ratio between liquid and
gas phases, only the drag force, which is prevalent, has
been selected. Moreover, several usual assumptions
have been used. Some of them are given in the follow-
ing, others may be found in Sirignano reference paper
(2)
' (Sirignano (1983)). First, the spray is dispersed and
each droplet is unaware of the existence of the others.
Any internal liquid circulation or droplet rotations are
neglected, an infinite heat conduction coefficient and a
weak load ratio is assumed. Therefore, liquid core tem-
perature remains uniform in every considered droplet
although it may vary as a function of time. The spray
is then composed of local sources of mass following
the saturation law of Clausius-Clapeyron and modifying
temperature, momentum and gaseous fuel topology, de-
(3) pending on the carrier phase temperature, pressure and
vapor mass fraction.


d put
8 8xt


& ,


Momentum equation:

8pui 8puit
8t 8xt


dlP dail
+ + v
8xyi 8xt a


i'(8 Butdz T z d


2 But
3(a: 8xt


Energy equation:

8pet 8 (pet +p)ut
81t 8xt


i3 iT
8xt x


+ aut+ pie, + e ,
8xi


Monocomponant fuel vapor equation:


Position and velocity
By denoting va and xa the velocity and position vectors
of every droplet k, the following relations:


8pYI; 8pYval
8 8xt


+pa, + m



8~l 8Ym u\ir~

~p~m


(u, (xk, t)

v ,


Other species equation:

8pYm dpYmug
81t 8xt


vrc)


are used to track their evolution throughout the compu-
tational domain. The vector u (xli, t) represents the gas
velocity at the droplet position xg. The right hand side


Equation of state for perfect gas:

P = pRT ,







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


interface thanks to the Clausius-Clapeyron relation:

d In(P )_ L,
~ (14)
dT RFT2
where RF is the specific gas constant in the gaseous fuel.
It leads to the following expression for the partial pres-
sure Pf of fuel vapor at the surface of the droplet:


term of equation (6) stands for a drag force applied to
the droplet and P is a kinetic relaxation time:


19 '


where as is the droplet diameter and p is the gas dy-
namic viscosity. Co 1 + Re2, /6 is a corrective
coefficient introduced to allow for the variation of the
drag factor according to the droplet Reynolds number
Reg p | u(xy ve) | ag/p.

Heating and evaporation
The heating and evaporation of every droplet in the flow
may be described through a normalized quantity Bi,
namely the "mass transfer number". Be is the normal-
ized flux of gaseous fuel between the droplet surface,
where the fuel mass fraction takes the value Y,", and the
surrounding gas at the droplet position, where the fuel
mass fraction is YF (xk). It may be written:




By solving the mass and energy balance equations at the
surface of a vaporizing droplet (Kuo (1986)), the follow-
ing relations for the surface and the temperature evolu-
tion of every "k" droplet are found:


P" = Pr, exp R
a I (


1
Tref


where Prey and Trey are two reference parameters. A
fuel boiling temperature Tref corresponding to a refer-
ence pressure Prey has been introduced. T( is the gas
temperature at the droplet surface. Within each droplet,
the droplet temperature Te is spatially uniform. Thus,
it is equal to the temperature of the gas at the interface
Tk Ti-
The gaseous fuel mass fraction at the surface of the
droplet may be determined with:


I))'


i~=(1 ~(P(xrc)P,"


where P(xa) is the gaseous pressure at droplet position
xg. W and WF are the molecular weights of the con-
sidered mixture and fuel, respectively. Once the gaseous
fuel mass fraction at the droplet surface Y," is known, the
varying number Be is determined by introducing rela-
tion (16) into equation (9). Consequently, equations (10)
and (11), describing the evolution of droplet surface and
temperature, are closed.

Eulerian/Lagrangian coupling
The source terms rk2, v and e: in equations (1, 2, 3)
are modifying the gaseous phase mass, momentum and
temperature, respectively, owing to a distribution of the
Lagrangian quantities on the Eulerian grid. Every La-
grangian source has to be distributed over the Eule-
rian nodes by adding the volumic contributions from
droplets. A particle-source-in-cell (PSI-cell) method
(Crowe et al. (1977)) is used. The mass, momentum
and energy source terms are instantaneously distributed
in the cells surrounding the considered droplets propor-
tionally to the inverse of the distance between the cell
and the droplet introducing a weak numerical dispersion,
Indeed, in real spray flows, this distribution is not instan-
taneous and further assumptions are needed to perform
simulations. To address this issue, the droplets could
be fully resolved but it would limit the simulations to a
few of them (Lacas & Calimez (2000)). Another solu-
tion would be to introduce a diffusion delay between the
droplet and the surrounding nodes. However, in the case
of reacting flows, some of the evaporated fuel would not
directly interact with the local flames. This procedure is


pa)

1(~ ( i;


B L,C


characteristic relaxation times appear. They are defined
by:


Sc Pa a ~
4She p In(1 Brc)
Pr Os, By
6Nuc C, p In(1 +Bc)


Normalized gas and liquid heat capacities are denoted
C, and Cd, respectively. L, is the latent heat of evapo-
ration. In the present set of equations, the properties of
the liquid phase are constant. Sc and Pr are the Schmidt
and Prandtl numbers, respectively. She and Nu, are the
convective Sherwood and Nusselt numbers, respectively.
They are both equal to 2 in a quiescent atmosphere, but a
correction has to be applied in a convective environment.
In this context, empirical expressions (Kuo (1986)) may
be used.
One of the most accurate model to describe the evap-
oration process is to consider a phase equilibrium at the







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


not really satisfactory but this stumblingblock remains
an open task for the time being.
For every Eulerian node, a control volume 1/ is de-
fined by the mid-distance between the neighbor nodes.
If an isotropic Cartesian grid is considered (A = x4 1 -
x4 a, a, az), then 1/ A a. The mass source
term applied to any Eulerian node n is denoted mt"):


y -ak di(17)


where C, is the sum over all the droplets affecting the
node n. a is the distribution coefficient of the k
droplet source term on the node n. Considering all the
nodes affected by the droplet k, it is necessary to have
(n) )
during the Lagrangian/Eulerian coupling. In fact, ak
is the portion of the control volume of the node n mnter-
secting the control volume of the droplet k:


and it may be developed as

e( ) = -Cap
d~4


3


Te B LV/C, Te
P ) 4a)


This last equation details how energy fluxes reaching
the droplet surface are distributed (evaporation and liq-
uid core heating) and the loss of energy due to the loss
of liquid mass.


Chemistry validation

,i is the chemical source term for species i computed by
the kinetics solver and Lje is the chemical heat release
computed as the sum of individual species 36 times
their formation enthalpy. Lji are computed with the
ChemkinB solver using the n-heptane kinetics of Patel
et al. (2004). This semi-detailed mechanism involves 29
species and 52 reactions and has already been success-
fully compared to other reference complex chemistries
Patel et al. (2004). To illustrate its accuracy to reproduce
temperature sensitivity, especially in the NTC region in
which the reactivity decrease with temperature, we have
compared Patel mechanism Patel et al. (2004) simula-
tion results to recent measurements of Vanhove et al.
(2006) (Fig. 1).
la fig. 1 shows good agreement between the simulation
results and the experimental data.
1nn


where x *" and xasi are the coordinates along the ius
direction of the node n and the droplet k, respectively.
This approach is generally used as far as dispersed par-
ticles are considered. (Crowe et al. (1998),Schroll et al.
(2009)).
The mass of the considered k droplet in the neighbor-
hood of the node is me = pd-.7~ /6 and, using equa-
tions (10) and (17), one may write:


: : i~iftc~l :~i~)
r,


80

~60
3
~ 40
4


Similarly, the following relation:


- (n) 1 (s) dmave
v -a
7 di


700 800
Temperature To (K)


900 1000


leads to the expression of the momentum source term:


Figure 1: Auto-ignition delays of a stoichiometric n-
heptane/air mixture for pressure around 4bar. Symbols:
measurements from Vanhove et al. (2006); line: Patel
mechanism Patel et al. (2004) simulation results.


Results and discussions

OD configuration
To study spray influence on the auto-ignition process, a
basic configuration has been selected: a homogeneous
reactor containing a monodispersed spray. The liquid
fuel evaporates in air which pressure and temperature


s) Tr1 (n) ,
v ~n= -p Q*



(2u(xd, t) -v V
3 ( )


vr,
4 a)


The energy variation of the gaseous flow induced by the
droplets inside the volume 1/ may be written:

r:(n) 1 ) m= (22)


(u ( )
7 e1 4












are initially prescribed. It relates to a constant-presure
combustion process without any convection or diffusion
effect in order to provide two-phase flow reference ho-
mogeneous cases.
A key parameter in a reactive mixture of hot air and
spray is the ratio between the fuel initially introduced
as liquid droplet and the air content within the reactor.
It is quantified as the global fuellair equivalence ratio.
In order to control the spray evaporation dynamics, the
influence of fuellair equivalence ratio is studied through
droplet density variation maintaining initial droplet di-
ameter to To be representative of automotive engine conditions,
the initial droplet temperature is To = 300K and ini-
tial gaseous pressure is P<3 = 10batr. Three groups of
simulation with various global equivalence ratio (4 =
0.6; 1.0; 2.0) were simulated. Large variations of initial
gaseous temperature To from 650K to 1300K are inves-
tigated to illustrate the role of evaporating droplets in the
NTC auto-ignition process.
103 t


102

E
1

;i;j
a


10
600


800 1000 1200
Temperature To (K)


1400


7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


NTC region, initial observed for gaseous auto-ignition
(Fig. 1), is also largely modified due to evaporating liq-
uid presence. Unlike gaseous observation, NTC tem-
perature range becomes dependent on global fuel/air
equivalence ratio as far as two-phase flow auto-ignition
is considered. Moreover, NTC temperature range moves
towards higher temperatures for larger global fuel/air
equivalence ratios. These trends are linked to the com-
petition between evaporation and reactivity that both
depend on gas temperature and gaseous fuel to air ratio.
The shift of the NTC domain involves critical modifi-
cation on the auto-ignition process. For instance, for
To = 900K (Fig. 4-Middle), gaseous temperature de-
creasing due to droplet evaporation supports the system
reactivity. In that case (Fig. 4-Middle), the global equiv-
alence ratio 4 = 2 auto-ignites before weaker equiva-
lence ratio. This phenomenon can occur in the NTC
region where the reactivity decreases with temperature



COOlillC effeCt









A B C

Temperature To

Figure 3: Chemistry zones and potential transitions in-
volving NTC due to cooling effect. Zones 24 and C
correspond to low and high temperature chemistries, re-
spectively. Zone B is the NTC chemistry domain. Cool-
ing effect allows to define three transitions near the NTC
region (zone B)



Transition from the low to the high temperature chem-
istry appears for well-defined initial conditions defining
three zones (Fig. 3): low (zone 24) and high (zone C)
temperature domains and NTC chemistry region (or in-
termediate temperature) in between (zone B). For two-
phase flow cases, in addition to pure low and high tem-
perature chemistry, three types of transition involving
NTC are possible (Fig. 3) because of gas temperature re-
duction due to droplet evaporation: (1) for initial air tem-
peratures just above gaseous NTC range (low To within
zone C, Fig. 3), cooling effect implies transient gas tem-
peratures within the NTC domain (zone B, Fig. 3); (2)


Figure 2: Auto-ignition delays of a homogeneous dis-
tributed monodisperse spray of n-heptane evaporating
within a hot air mixture for various global fuel/air equiv-
alence ratios. (circles 0.6; triangles 1.0;
crosses = 2)

First, unlike purely gaseous case, the auto-ignition de-
lay does not strictly decrease when global fuel/air equiv-
alence ratio increases. The evaporation dynamics may
even lead to a reverse evolution as shown in Fig. 2. For
example, considering To = 1200K, auto-ignition oc-
curs earlier at = 0.6 than at 4 = 2 (see also Fig.
4-left). Indeed, the larger temperature diminution due
to evaporation at 4 = 2 overcompensates the higher
mixture reactivity observed for richer mixtures in purely
gaseous conditions. This shorter auto-ignition delay for
leaner cases is coherent with observations of Wolff et al.
(1998).







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


0 2000



Eime (ms)


10001 5 0 2

Eime (ms)


Figure 4: Gas temperature of a homogeneously distributed monodisperse spray of n-heptane wihin hot air mixture
for various global fuellair equivalence ratios. (circles 9 = 0.6; triangles 9 = 1.0; crosses 9 = 2) and various initial
gaseous temperature To (Left: 1200K, Middle: 000K, Right: 750K


for To in the upper part of the gaseous NTC range (high
To within region B, Fig. 3), temperature decreases due
to evaporation but still lies within the NTC range (zone
B, Fig. 3); (3) for To in the lower part of the gaseous
NTC range (low To within zone B, Fig. 3), temperature
reduction is large enough to exit from the NTC domain
(zone 24, Fig. 3).
For the first and the second cases, cooling effect leads
to an increase of the reactivity, hence an earlier auto-
ignition. Conversely, for the third case, the cooling
effect leads to a reactivity decrease, hence a later auto-
ignition.

2D configuration
As underlined in the introduction, all the simula-
tions are carried out on a two-dimensional square do-
main although the evaporation process is kept three-
dimensional. This would correspond to a thin slice of
a 3D field with regularly spaced droplets in the third
direction. A two-dimensional square domain of 7.8
mm is considered thanks to a uniform mesh (129 x
129 points). Both directions are periodic. Similarly
to the homogeneously distributed spray configuration,
monodispersed n-heptane droplets are evaporating in a
hot air gas at the pressure 10batr. The initial droplet
temperature and diameter are 300K and 7pm, respec-
tively. Three cases were simulated varying the initial
gas temperature To considering a low, an intermediate
and high temperature in regard to auto-ignition process:
750K, 000K and 1200K. The average over the domain
simulation of the global equivalence ratio after complete
droplet evaporation is 9 0.6 but because droplet are
not homogeneously distributed, spatial variations are
observed dealing with local fuel/air equivalence ratio.

The generation of clouds of droplets with a prescribed
cloud characteristic size and cloud density is based on
the spectral procedure described by Reveillon (2005).
Nevertheless, some details concerning the control of


the droplet preferential segregation are given here since
it is the basis of the present configuration of extended
spray auto-ignition reactor. First, it is necessary to de-
fine two probability density functions (PDF): one for the
droplet diameter ( and the other P(E) is the PDF of the local particle den-
sity E(x) defined as the number of droplets per unit of
volume. P( tal or analytical shape (Log-Normal, Roslin-Rammler,
..., (Crowe et al. (1998))). In the present work we are
considering a monodispersed spray and consequently
P( the PDF of the spray density P(E) allows us to generate
various initial topology of droplet clouds introduced by
a ,9-function (Press et al. (1992)). Thanks to this pro-
cedure, the mean spray density E and the initial droplet
diameter set the global equivalence ratio of the system
while the density variance E2 in the ,9-function used for
the PDF of the density controls the local droplet segre-
gation S, = E2/E(1 E) inside the clouds. If S, 1 a
maximum segregation level is chosen but if S, 0 the
droplets are uniformly and randomly distributed in the
domain. An example of droplet cloud distribution with
an intermediate droplet segregation is shown on Fig. 5.
Different droplet cloud distribution have been generated
in order to investigate droplet segregation influence on
spray auto-ignition. Nevertheless, in order to focus in
this paper on the NTC chemistry modification, only one
initial particle distribution is used. It corresponds to
the field shown on Fig. 5. To point out the complexity
of the NTC chemistry, various initial gas temperature,
To, have used to illustrate qualitative spray auto-ignition
modes. Three test cases are presented here correspond-
ing to a low (750K region 4 in Fig. 3), an intermediate
(900K region B in Fig. 3) and a high initial gas tem-
perature (1200K region C in Fig. 3). For all cases,
the auto-ignition is observed after the complete droplet
evaporation. Nevertheless, the auto-ignition spots are
correlated with the initial droplet cloud distribution.


0 1 200

Time (ms)







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


creases from around 850K (because of the droplet evap-
oration) to around 950 corresponding to a cool flame
heat release. Then, the main auto-ignition process oc-
curs in the center of the clouds, spreading from the inside
to the edge of the initial droplet cluster. This behaviour
is very different from the high temperature case. For
To = 900K, the system is within the region B (NTC
domain) in (Fig. 3): the reactivity is supported as the
temperature is lower. Consequently, because of the cool-
ing effect leading to lower temperature inside the initial
droplet cloud, the main auto-ignition occurs in the center
of the clusters. For the intermediate temperature config-
uration, the first auto-ignition delay (cool flame) is con-
trolled by the fuel availability. Nevertheless the main
auto-ignition occurs in the core of the cluster supported
by the lower temperature.
The low initial gas temperature (To = 750K) config-
uration corresponds to region A in Fig. 3 outside the
NTC region. In this region, the higher the tempera-
ture, the faster the auto-ignition. Consequently, as for
the high temperature case (To = 1200K), first auto-
ignition spots occur near the edge of the initial droplet
clouds (Fig. 8). But, contrary to high temperature case,
the reaction process involves a two-step chemistry auto-
ignition. During this cool flame, the temperature is able
to spread from the periphery to the inside of the initial
clouds leading to the auto-ignition runaway inside the
initial droplet cluster (Fig. 8). Because of low gas tem-
perature, the auto-ignition delay is very long allowing to
'propagate' the cool flame phenomenon from the edge
to the core of the clouds. In the center of the initial
droplet cluster the heat fluxes are dampened and sup-
port the main auto-ignition runaway leading to the main
auto-ignition is the center of the initial droplet clouds.
Three auto-ignition modes have been pointed out, in the
presence of evaporated fuel spray, the initial gas temper-
ature modifies not only the chemistry path (cool flame
and auto-ignition runaway) but also the observed auto-
ignition patterns. To illustrate droplet segregation influ-
ence on the auto-ignition process, global system auto-
ignition is plotted for the three configurations in Fig.
9. In order to focus on droplet segregation effect, seg-
regated configurations are compared on Fig. 9 to their
alter-ego initial droplet homogeneous distribution. As
shown on Fig. 9, the global auto-ignition of the system
can be promote or slow down by the droplet segrega-
tion. Because n-heptane kinetics define chemical paths,
namely the presence or not of a cool flames, the two-step
auto-ignitions are conserved even if droplet segregations
are considered (To 750K and 900K). Nevertheless,
initial gas temperature coupled with droplet segregation
is able to modify dramatically the auto-ignition process.


Three behaviours can be distinguished depending on the
initial gas temperature.
For high initial gas temperature (To = 1200K), the
auto-ignition starts at the periphery of the regions (Fig.
6) where droplet clusters were initially left. Because
of high temperature, the auto-ignition process presents
only one main step (no cool flame is observed). There-
after, the reaction is spreading from the external cloud
side toward the initial inner cluster region (Fig. 6). The
case (To = 1200K) is within region C in Fig. 3, outside
the NTC domain in which the auto-ignition is supported
by the increasing of temperature. Because of the cooling
effect due to droplet evaporation, the local gas tempera-
ture before the auto-ignition becomes lower in the core
of the droplet clusters. On the contrary, near the edge
of the droplet clouds, the gas temperature is higher that
increases the reactivity. Consequently, the beginning of
the auto-ignition occurs around the initial position of the
droplet clusters.


0 2 4 6
X (mm)


Figure 5: Initial dispersed Lagrangian spray with inter-
mediate droplet density segregation

For intermediate initial gas temperature (To 900K)
(Fig. 7), the reaction process is different from high tem-
perature concerning the first auto-ignition pattern but
also the chemistry path. Contrary to the previous exam-
ple (To 1200K) in which the reaction presents only
one auto-ignition delay, the case To 900K involves a
cool flame behaviour. The first auto-ignition pattern is
also different from the high temperature case in which
first auto-ignition spots are observed around the initial
droplet clouds. For the intermediate case (To 900K),
the beginning of the auto-ignition occurs simultaneously
inside the whole initial droplet clusters (Fig. 7) involv-
ing a cool flame reactivity: the local gas temperature in-









7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010



1000 1100 1200 1300 1400 1000 1500 2000 2500 1000 1500 2000 2500


01234567 01234567
X (mm) X (mm)
0 00 00 01 0 02 .6 0 .1





5 5

F4 F4


1 1'J L
0" 0

01234567 01234567
X (mm) X (mm)


01234567
X (mm)


0 1, i


1


01234567
X (mm)


Figure 6: Illustration of the auto-ignition patterns for high temperature case ( 3 = 1200K) for three sample times
(from left to right); top: gas temperature; bottom: n-heptane mass fraction. Please, note the difference in the tempera-
ture scale for left and middle pictures


850 900 950 1000 1050 1100 850 900 950 1000 1050 1100 1000 1500 2000 2500


0 ~L

0 12 34 5 67 0 123 4 5 67
X (mm) X (mm)
0 00 00 01 0 02 .6 0 .1


X (mm)
0 00 0 0 0 1



7/ -


1





X (mm)


X (mm)


X (mm)


Figure 7: Illustration of the auto-ignition patterns for high temperature case (T3 = 900K) for three sample times (from
left to right); top: gas temperature; bottom: n-heptane mass fraction. Please, note the difference in the temperature
scale for middle and right pictures









7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010



700 800 90 00 700 800 900 1000 700 800 900 1000


01234567
X (mm)
0 0.02 0.04 0.06 0.08 0 1






75





2 _1


01234567
X (mm)
1000 1500 2000 2500
















01234567
X (mm)



0 1)













01234567
X (mm)


01234567
X (mm)
0 0.02 0.04 0 06 0 08 0.1










~3(


2 4

01234567
X (mm)
1000 1500 2000 2500


01234567
X (mm)
0 00 00 01


01234567
X (mm)
0 00 00 01


01234567
X (mm)


01234567
X (mm)


Figure 8: Illustration of the auto-ignition patterns for high temperature case (To = 750K) for six sample times (from
left to right and top to bottom); first and third rows: gas temperature; second and forth rows: n-heptane mass fraction.
Please, note the difference in the temperature scale for the different pictures


01234567
X (mm)
0 0 02 0 04 0 06 0 08 0 1


1234567
X (mm)
1000 1500 2000 2500







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


droplet distribution was used as a reference configura-
tion. It pointed out the NTC region presence for inter-
mediate initial gas temperature. Then, the focus was on
the droplet segregation effect that can promote or slow
down the auto-ignition process of the system. Differ-
ent auto-ignition modes have been highlighted depend-
ing on the initial gas temperature (low 750K, interme-
diate 900K or high temperature 1200K). As well as the
chemical path (presence or not of a cool flame) modifi-
cation, auto-ignition patterns can be very different lead-
ing to auto-ignition near the edge or in the center of the
initial droplet cloud. These auto-ignition processes are
resulting from the competition between the fuel avail-
ability and the local gas temperature that will be investi-
gated in detail in future works to fill out complete turbulent
configurations.

References

Aggarwal S., A review of spray ignition phenomena:
present status and future research, Prog. Energy Com-
bust. Sci., vol. 24, pp. 565-600, 1998

Battin-Leclere F., Detailed chemical kinetic models for
the low-temperature combustion of hydrocarbons with
application to gasoline and diesel fuel surrogates, Prog.
Energy Combust. Sci., vol. 34, no. 4, pp. 440-498, 2008

Crowe C.T., Sharma M.P. and Stock D.E., The particle-
source in cell (psi cell) model for gas droplet flows, Jour-
nal of Fluids Engineering, pp. 325-332, 1977.

Crowe C., Sommerfeld M. and Tsuji Y., Multiphase
flows with droplets and particles, CRC Press, 1998

Khan Q., Baek S. and Ghassemi H., On the autoignition
and combustion characteristics of kerosene droplets at
elevated pressure and temperature, Combust. Sci. Tech.,
vol. 179, pp. 2437-2451, 1996

Kuo K.K., Principles of Combustion, John Wiley and
Sons, 1986

Lacas F. and Calimez X., Numerical simulation of
simultaneous breakup and ignition of droplets, Proc.
Combust. Inst., vol. 28, pp. 943-951, 2000

Lele S.K., Compact finite difference schemes with spec-
tral like resolution, J. Comput. Phys., vol. 103, pp. 16-
42, 1992.

Mastorakos E., Ignition of turbulent non-premixed
flames, Prog. Energy Combust. Sci., vol. 35, pp. 57-97,
2009

Patel A., Kong S.C. and Reitz R.D., Development and
Validation of a Reduced Reaction Mechanism for HCCI


4 6
Time (ms)


Figure 9: Average over the spatial domain of the
gas temperature for spray auto-ignition configurations.
Three initial gas temperature are compared (To =
750K, 900K and 1200K). Solid lines: initial homo-
geneous droplet distribution; dashed lines: segregated
configuration (Fig. 5)


For To = 750K, the slope of the cool flame is
smoother for the segregated case than for the homoge-
neous droplet distribution. This observation is related
to the first auto-ignition pattern illustrated previously
(Fig. 8): the cool flame begins near the edge of the
cloud and delays to come close the center of the clus-
ter. The global temperature system increasing in the cool
flame auto-ignition is lower than the alter-ego homo-
geneous droplet distribution and consequently the main
auto-ignition runaway is delayed.
For To 900K, the cool flame delay is very short
(around 0.3ms) and is slightly modified by the droplet
segregation. This very small gap is observed because the
cool flame auto-ignition occurs simultaneously inside
the whole cluster. Nevertheless, the main auto-ignition
delay is faster in the segregated configuration (around
3ms for the droplet segregated configuration versus 7ms
for the homogeneous one). This acceleration is boosted
by the NTC chemistry. As explained previously, in this
region (region B in Fig. 3) the reactivity is supported
by low temperature due to the cooling effect inside the
initial droplet clouds.


Conclusion

In order to characterize the geometrical aspect of the
spray dispersion, this work extended the homogeneous
reactor configuration to multiple droplet cloud distribu-
tion. This configuration allows accounting for droplet
segregation effect in addition to the fundamental ther-
modynamical properties. First to isolate droplet mass
and heat transfer source term influence, homogeneous







7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010


Stauch R., Lipp S. and Maas U., Detailed numerical sim-
ulations of the autoignition of single n-heptane droplets
in air, Combust. Flame, vol. 145, pp. 521-532, 2006

Vanhove G., Petit .G and Minetti R., Experimental study
of the kinetic interactions in the low-temperature au-
toignition of hydrocarbon binary mixtures and a surro-
gate fuel, Combust. Flame, vol. 145, pp. 521-532, 2006

Wang C., Shy K. and Lieu L., An experimental investi-
gation on the ignition delay of fuel droplets, Combust.
Sci. Tech., vol. 118, pp. 63-78, 1996

Wang Y. and Rutland C.J., Effects of temperature and
equivalence ratio on the ignition of n-heptane fuel spray
in turbulent flow, Proc. Combust. Inst., vol. 30, pp. 893-
900, 2005

Wolff M.C., Meis1 J., Koch R. and Wittig S., The in-
fluence of evaporation on the autoignition-delay of n-
heptane air mixtures under gas turbine conditions, Proc.
Combust. Inst., vol. 27, pp. 2025-2031, 1998

Wray A.A., Minimal storage time-advancement
schemes for spectral methods, Center for Turbulence
Research Report, Stanford University, 1990


Engine Simulations, SAE TECHNICAL PAPER SE-
RIES, 2004-01-0558, 2004.

Press W.H., Teukolsky S.A., Vetterling W.T. and Flan-
nery B.P., Numerical Recipies, Cambridge University
Press, 1992

Reeks M.W., On a kinetic equation for the transport of
particles in turbulent flows, Phys. Fluids, vol. 3, no. 3,
pp. 446-456, 1991.

Reveillon J., Numerical procedures to generate and vi-
sualize flow fields from analytical or experimental statis-
tics: turbulent velocity, fluctuating scalars and variable
density sprays, Journal of Flow Visualization and Image
Processing, Vol. 12, pp. 251-269, 2005

Schroll P., Wandel A.P., Cant R.S. and Mastorakos E.,
Direct numerical simulations of autoignition in turbulent
two-phase flows, Proceedings of the Combustion Insti-
tute, pp. 2275-2282, 2009

Sirignano W.A., Fuel droplet vaporization and spray
combustion theory, Prog. Energy Combust. Sci., Vol. 8,
pp. 291-322, 1983




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - Version 2.9.7 - mvs