7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Large Eddy Simulation of liquid atomization : From the resolved scales to subgrid
spray
J. Chesnel*t, J. Reveillont, T. Menard, A. Berlemontt and F.X. Demoulint
Renault SA, Direction des Technologies Avancees de l'Automobile
t University de RouenCORIA, CNRS UMR 6614, Avenue de l'universite, St Etienne du Rouvray, 76801, France
demoulin@coria.fr
Keywords: Large Eddy Simulation, Atomization, Turbulent Liquid Jet
Abstract
Liquid injection takes an important part in many physical processes, especially within internal combustion engine (ICE). Up
to know the Reynolds Averaged NavierStokes (RANS) approach has been widely used, both in Eulerian and Lagrangian
framework. Several works on atomization have been done in our team developing the ELSA model. However, LES of
atomization seems to be a necessarily step forward. In addition to standard LES method for turbulent flows, a special
attention is necessarily to represent the interface. Two limit cases have to be considered:
The liquid surface can be well captured with the available mesh size (or filter size) then the LES formulation
must recover the DNS methods used to track the interface (such as Level Set or VOF)
The liquid surface wrinkles size are smaller than the mesh size and the twophase LES formulation must recover
the LES used for spray where finally droplets are considered very small by comparison to the mesh size.
In this work we present a LES method for two phase flow that can recover these two limits. It is shown that the unresolved
SGS (Sub Grid Scale) term that appears in the phase function equation plays an important role, even if it is very small by
comparison to the resolved contribution. Application of this method to the atomization of a Diesel jet is presented. LES
results are then compared to a DNS data base.
Introduction
For many years research on atomization has been carried on
to improve the characteristic and the control of sprays. This
is particularly true as far as fuel injection is considered.
Because the finale combustion is directly dependant on the
characteristics of the spray, for instance to reduce pollutant
emission, a special attention has been spend on the design of
fuel injector. As a consequence for injector manufacturers
the time needed to develop a new injector has been reduced
and the requirements are more drastic. To face this
challenging task, numerical simulations of flow inside the
injector has been developed, see for instance (Macian, Payri
et al. 2003, Giannadakis, Gavaises et al. 2008). In the other
hand simulations of two phase flow with vaporisation and
combustion have been used extensively to improve internal
combustion engine (ICE) for many years (Amsden, Butler et
al. 1987). New models of atomisation able to represent the
dense zone at the exit of the injector (Lebas, Menard et al.
2009) have build a bridge between in injector flow
simulations and simulations of the whole combustion
process.
Since phenomena involved in this kind of applications are
very complex the direct numerical simulation (DNS) is still
out of reach. Thus, most of the studies devoted to injection
and combustion in ICE have been done in the Reynolds
average NavierStokes (RANS) context. Because the power
of computer has been growing fast, large eddy simulation
appears as a solution to benefit of the new computational
possibilities to improve the reliability of RANS simulation
and to explore new ways of using numerical simulation. The
LES approach initially developed for single non reactive
flows has been applied recently and successfully for ICE
engine (Vermorel, Richard et al. 2009). The possibility of
using LES for simulation inside the injector and potential
gains have just been explored (Payri, Tormos et al.).
Therefore a strong interest exits in prolonging the ability of
LES to deal with complex flows to the field of atomisation.
The present work is a step forward in this direction.
Nomenclature
surface normal vector
velocity component
velocity vector (ms1)
Greek letters
(01 liquid volume fraction
0 distance function (m)
K surface curvature (m 1)
P density (kgm3)
oa surface tension coefficient (Nm 1)
T, subgrid scale term for p(0
Subsripts
1
g
liquid
gas
Overview of LES for two phase flows
To address the problem of LES of atomisation it is useful to
overview the possible approach used in the context of LES
for two phase flows. LES is originally developed to deal
with turbulence in single phase flows. Here, two phase
flows are considered only as liquidgas flows. Compare to
single phase flows, the complexity is amplified mainly
because of three phenomena:
The presence of important density variations
requires a robust computational code.
The surface that separates the two phases is the
place of jump for several quantities such as the
density, the viscosity and the pressure.
The surface tension force appears as an additional
force inside the flow that requires a good
representation of the interface geometry, to be
reliably estimated.
To address this complexity in the context of LES two main
approaches have been proposed.
The first one applies to twophase flows where a continuous
carrier phase and a discrete phase can be defined (CDLES).
As for RANS approach, in LES this simplified
representation of the spray can be useful for many problems.
It consists to assume that the liquid part is only composed
by spherical droplets that are mainly isolated from each
other. Then, the flow inside the droplet does not need to be
computed integrally. They can be considered at a subgrid
scale level as a set of particles that are characterized by a
reduce number of parameters such as position, velocity and
diameter. Of course, an important effort on modelling may
be require to describe the evolution of the spray and its
interaction with the carrier phase (Squires and Simonin
2006, Apte, Gorokhovski et al. 2003, Apte, Mahesh et al.
2009). However, this formulation can be analysed thanks to
DNS simulations based on a similar description of the spray,
for phenomenon as complex as the effect of preferential
concentration on the vaporisation process (Reveillon and
Demoulin 2007).
At the opposite when no discrete phase can be defined both
phases have to be considered continuously this the
continuouscontinuous LES of two phase flows (CCLES).
In this case the flow is resolved for both phases and special
numerical methods have been developed to describe the
interface. In the first step the flow is supposed to be
completely resolved like in DNS. Numerical methods
dedicated to liquid gas flows with an interface include front
tracking methods (Unverdi and Tryggvason 1992), boundary
integral methods (Oguz and Prosperetti 1990),
volumeoffluid methods (Hirt and Nichols 1981), level set
methods (Sussman, Fatemi et al. 1998). Each method has
his own advantages and drawbacks, the last development in
this fields proposed to combine different numerical
approaches. The resulting approaches are able to simulate
completely complex flows such as the atomisation of a
highspeed liquid jet (Menard, Tanguy et al. 2007).
However their extension to LES simulation is not straight
forward expect in a special case where the interface
wrinkles are resolved at the LES filter size. This is the case
for instance of waves in oceans. The characteristic size of
waves can be one order of magnitude bigger, or even more,
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
than the smallest sizes of the turbulent structures in the air.
In this case the LES modelling concerns only the dynamic
of each phase from each side of the interface. For such
methods, generally, a modelling of the subgrid stress tensor
is applied for the velocity very similarly than those used for
single phase flows (Lubin, Vincent et al. 2006). Because the
interface geometry is resolved at the LES filter level, the
treatment of the interface is done like in DNS, though
special modifications have been proposed to the
Smagorinsky model to represent the turbulence decay close
to the interface (Reboux, Sagaut et al. 2006).
In the case of atomization it is expected to use CCLES
approach with a filter size allowing the interface scales to be
resolved close to the injector exit. This is necessary to
capture the first instabilities that promote the breakup of the
jet. However, most of the injectors produce shortly a dilute
spray with very small droplets. The interface resolved
CCLES approach would be far to consuming in term of
computational resources. Indeed, once the spray is formed
such an approach would be comparable to a DNS approach
which is unaffordable because the droplet size decrease as
large scales of the flow increase following the expansion of
the spray. Once the spray is formed the appropriate
numerical approach should be the CDLES that considers
the spray at a subgrid level. Thus, the challenge, as far as
LES of atomisation is concerned, is to proposed a method
that include CCLES and CDLES approaches and able to
represent the transition between both approaches in a
realistic way.
DNS simulation of the atomisation
The proposed work concerns mainly the atomisation process
that is relevant for Diesel spray, but it has certainly
application for other injection devices. The main drawback
for this kind of atomisation is the lack of experimental data
in the vicinity of the injector tip. The high velocity and high
density variation in this zone prevent to use classical
measurement apparatus. In particular, the diffraction effect
is the main reason of failure for optical diagnostic. Even if
new measurement techniques have been developed (Leick,
Riedel et al. 2007, Blaisot and Yon 2005, Linne, Paciaroni
et al. 2006, Chaves, Kirmse et al. 2004), DNS simulation is
still a very interesting tools to explore the vicinity of the
liquid jet exit.
We use for this work a DNS code "ARCHER" developed at
the CORIA laboratory (Menard, Tanguy 2007, Tanguy and
Berlemont 2005). It has been used already to collect
statistical information in the dense zone of the spray where
nearly no experimental data are available. These simulations
are sufficiently predictive and quantitative to be used for
validation of modelling proposals (Lebas, Menard 2009).
The numerical method describes the interface motion
precisely, handles jump conditions at the interface without
artificial smoothing, and respect mass conservation.
Accordingly, the interface tracking is performed by a Level
Set method. The Ghost Fluid Method is used to capture
accurately sharp discontinuities. The Level Set and VOF
methods are coupled to ensure mass conservation. A
projection method is used to solve the incompressible
NavierStokes equations that are coupled to a transport
equation for level set and VOF functions.
Level Set methods are based on the transport of a
continuous function which describes the interface
between two phases (Sussman, Fatemi 1998, Sethian 1999).
This function is defined by the algebraic distance between
any point of the domain and the interface. The interface is
thus described by the 0 level of the Level Set function.
Solving a convection equation allows to determine the
evolution of the interface in a given velocity field V
(Sethian 1999):
+ V.Vb = 0 (1)
at
Particular attention must be paid to this transport equation.
Problems may arise when the level set method is developed:
a high velocity gradient can produce wide spreading and
stretching of the level sets, such that 0 no longer remains
a distance function. Thus, a redistancing algorithm
(Sussman, Fatemi 1998) is applied to keep 0 as the
algebraic distance to the interface.
To avoid singularities in the distance function field, a 5th
order WENO scheme has been used for convective terms
(Jiang and Shu 1996). Temporal derivatives are computed
with a third order Runge Kutta scheme.
One advantage of the Level Set method is its ability to
represent topological changes both in 2D or 3D geometry
quite naturally. Moreover, geometrical information on the
interface, such as normal vector n or curvature K, are
easily obtained through:
n= K()= Vn (2)
It is well known that numerical computation of equation (1)
and a resistance algorithm can generate mass loss in
underresolved regions. This is the main drawback of Level
Set methods. However, to improve mass conservation a
coupling between VOF and Level Set (Sussman and Puckett
2000) method has been performed.
Applying resolved interface CCLES method to the
atomisation
The resolved interface CCLES approach consists in using a
DNS approach with interface capturing ability in such
conditions that all scales of the velocity field are not
completely resolved but where all interface wrinkles are
resolved. A LES model is applied for the subgrid Reynolds
stress in order to represent the subgrid scale motion.
Applying such an approach for atomisation (Villiers,
Gosman et al. 2004) is appealing but rises some problems.
The front tracking methods need at less one mesh cell to
represent a liquid parcel. One quality of the numerical
method is to conserve the liquid mass, as a consequence the
method prevent any further breakup of the liquid parcels as
soon as their sizes become comparable to the mesh size.
This numerical artefact can be considered qualitatively as an
additional numerical surface tension force. When using this
method for atomisation the sizes of the droplets form during
the atomisation are numerically controlled. Such behaviour
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
is demonstrated on figure 1 where the DNS code ARCHER
is used to represent the atomisation of a Diesel jet. The inlet
diameter is D,=100/m The gas density is
Pg =25kg.m3
p, = 696kg.m .
a = 0.06N.m.
U,= 79m.s'.
and the liquid density is
The surface tension coefficient is set to
The inlet liquid velocity is equal to
c
Figure 1: Numerical simulation of a Diesel injection for
three different mesh refinements, a1281281024
b64x64x512 c32x32x256
The figure 1 represents three instantaneous snapshot
obtained with the code ARCHER for three different mesh
refinements. The interface geometries are very different, as
expected the more the mesh is refined the smaller are the
liquid parcels. What is more surprising is that the mesh size
effect act not only on the smallest scales of the surface but
also on all scales of the surface. It may be due to the model
used for injecting a synthetic turbulence (Klein, Sadiki et al.
2003). Depending on the mesh cell size the spatial
behaviour of the turbulence can be affected. However,
increasing the mesh cell size has an effect very similar to an
increase of the surface tension coefficient.
The dependence of the result on the mesh refinement rises
two questions:
1. Is mesh convergence achieved in DNS?
2. Does that have an effect on mean behaviour of the
liquid jet?
Concerning the first question, the problem is that for liquid
gas flow the smallest sizes of the flow are not known in
contrary to single phase flows. There is no equivalent to the
Kolmogorov length scale. Because there is no diffusion of
the scalar (liquid concentration) even at small scales
(inviscid flows) the Batchelor scale is not defined. The
mechanism that prevents the existence of very small scales
is based on surface tension force. But it does act only for
strong curvatures. Thus liquid sheets can be very thin as
soon as their curvature remains small. Finally this
possibility to have very small dimension for the scalar field
as also an effect on the dynamic at small scales of the flow
because the density is linked to the scalar field.
To address the second question statistical results have been
extracted from the previous simulation.
DNS128
SD 2 DNS64
0.8
0.6 4
lv 's
0.4
0.2 "
0 5 10 15 20
z/D
Figure 2: Mean liquid volume fraction along the main axis
of injection obtained with DNS code ARCHER for three
different refinements. DNS128 (128x128x1024) DNS64
(64x64x512) DNS32 (32x32x256)
The mean liquid volume fraction obtained for three mesh
refinements is represented on figure 2. Clearly, different
mesh sizes lead to different liquid penetrations. For the less
refined mesh the numerical method introduces an
additional surface tension force that prevents the spray to
be atomized. As a consequence the liquid jet penetrates
further. It is interesting to test the resolved interface
CCLES. This is done here by adding a Smagorinsky
model to filtered velocity equations. The corresponding
results are represented on figure 3.
10
z/D
Figure 3: Mean liquid volume fraction along the main axis
of injection obtained with code ARCHER, LES simulation
corresponds to simulation with a Smagorinsky model for
velocity equation. DNS128 (same as figure 2) LES64
(64x64x512) LES32 (32x32x256)
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The effect of introducing a LES model for the velocity
equation does not bring a clear improvement. The liquid
penetrations remind strongly affected by the mesh size.
Partial conclusions at this point is that resolved surface
CCLES approaches are not sufficient to represent the
atomisation process; first because they do not lead to a
subgrid spray that can be described by a CDLES
approach; second even the initial behaviour of the spray is
affected by the mesh cell size.
A priori analysis of DNS to build a suitable LES of
atomisation
To improve LES modelling it is useful to analysis a filtered
field of a reference DNS simulation (Labourasse, Lacanette
et al. 2007, Chesnel, Reveillon et al. 2007). The filtered
liquid volume fraction equation can be written as:
0+
3t
ax,
ax,
Where the subgrid scale term is:
TO = Va (0 VaiP
Here the upper line refers to a filtered variable. Previous
studies, based on a priori analysis of a well resolved LES,
have shown that this subgrid term is negligible by
comparison of the other terms of the equation (3). But this a
priori analysis can only be used to evaluate an instantaneous
contribution. Even if this term is small instantaneously, its
cumulous effect all along the time may produce a visible
effect. To explore this possibility a Bardina model of the
subgrid scale term T has been used to compare with
resolved surface CCLES, for this later approach is set to
zero.
  

Figure 4: (a) comparison of isosurfaces (, =0.5 ; in
black the subgrid scale term T is neglected; in red T is
replaces by a model of Bardina. (b) isosurface of the
filtered liquid volume fraction with the latter modelling of
T,
The figure 4, demonstrates the effect of this subgrid term.
Even if this term is small and has negligible effect at the
beginning of the spray (zone 1), its cumulative effect
induced a clear difference depending on the model retained
for Z When this term is not neglected the isosurface
, = 0.5 does not represent the mean position of the
interface in zone 2 as it is the case in zone 1. As the spray is
transferred at the subgrid scale level this isosurface
corresponds only to a mean concentration of liquid and not
any more to an approximation of the liquid surface. In
contrary to the DNS approaches used in resolved interface
LES, the amount of liquid enclosed in the isosurface
9, =0.5 is not conserved. Indeed, the atomisation of the
liquid surface induces a flux of small liquid parcels out of
this isosurface. Similarly, gas inclusions go inside the
liquid zone. Conclusion of this section is that the transfer of
the liquid phase from a resolved interface area to a subgrid
spray is driven by this subgrid term Z .
First LES of atomisation
In this section we test a first LES model of atomisation
satisfying the requirement of a possible transition between
resolved interface CCLES and subgrid spray CDLES. The
model is based on the equation (3) where the subgrid term
T is not neglected and replace by a Bardina model.
Additionally a Smagorinsly model is used for velocity
equations similarly to previous LES simulation of figure 3.
Figure 5: Isosurfaces (, =0.5 at the beginning of the
injection. From top to bottom: DNS, resolved interface
CCLES ( TZ =0 ); LES of atomisation ( T,
approximated by a Bardina model)
The figure 5 shows the isosurfaces (, = 0.5 for a DNS
test case and the two LES approaches at the beginning of the
injection. As previously mentioned the resolved surface
CCLES prevent atomization of the liquid jet inducing a
greater liquid penetration. At the contrary the modeling
proposal of allow for a transition of the spray from the
resolved scale to the subgrid scale. The smooth contours
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
around the isosurface represent the filtered liquid volume
fraction in a cut plane passing through the middle of the jet.
The liquid volume fraction outside the isosurface
(1 = 0.5 corresponds to liquid parcels detached from the
main jet. This gives an encouraging qualitative result. To go
further statistic are extract from this latter LES simulation of
the atomisation to represent the profile of the mean liquid
volume fraction along the main axis, see figure 6.
10
z/D
Figure 6: Mean liquid volume fraction along the main axis
for the reference DNS case (DNS128) and the new LES of
atomisation
Comparisons of results presented in figure 3 and 6 show a
real improvement when applying the new LES models that
takes into account the subgrid term T It is now possible
to recover the axial profile of the mean liquid volume
fraction obtained with the most refined DNS despite the
lower mesh resolution. The apply model compare
favourably for a computational mesh reduced by a factor
height (New LES64) and even with mesh reduced by a
factor 64 (New LES32). With the present test case it is not
possible to go further because 10 mesh cells are at least
necessary to represent the injection profiles through the
diameter of the jet.
Conclusions
The present study proposed an original method to model the
atomisation in the context of an LES approach. The main
issue is the transfer of the spray from the resolved scale to
the subgrid scale. The modelling proposal consists in taking
into account of an additional subgrid term for the liquid
volume fraction that is generally neglected. This term
represents the effect of subgrid surface wrinkles that leads
to the atomisation of the liquid jet. The model is tested by
comparison to a refined DNS. Results are encouraging even
if the model needs more complete validations to be
definitely assessed. It is possible, for instance, that the
resolution of the reference DNS should not be high enough
to capture the smallest scales of the spray. However, the
interest of this LES approach is its ability to find similar
mean results with a smaller resolution. In a second step with
this approach, we will determine the characteristic length
scales of the subgrid liquid parcels. This information will
eventually be equivalent to a liquid droplet distribution of
diameter. This last step is underway thanks to a modelled
equation for the surface density equation. First results will
be shown during the oral presentation.
Acknowledgements
Authors want to thanks Renault for supporting this work.
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