Des simulations de l'auto-allumage par compression sont réalisées dans une configuration de Machine à Compression Rapide (MCR). Dans un premier temps, des résultats de simulations aux grandes échelles sont comparés avec des mesures expérimentales. Ensuite, la DNS de cette MCR est utilisée pour analyser les mécanismes contrôlant les noyaux précurseurs de l'allumage. Il est montré que les fluctuations locales de compression, quantifiées par l'historique de la divergence du champ de vitesse, ont un effet dominant sur l'allumage

DOMINGO, Pascale

LODIER, Guillaume

VERVISCH, Luc

I-Revues

20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
Etude de l’initiation et de la propagation de
l’auto-inflammation dans un milieu pre´sentant des
inhomoge´ne´ite´s de tempe´rature
Guillaume Lodiera,b, Pascale Domingoa, Luc Vervischa
a. CORIA-CNRS et INSA de Rouen, Technopole du Madrillet, 76801 Saint-Etienne-du-Rouvray, France
b. RENAULT - Technocentre 1, avenue du Golf 78288 Guyancourt cedex, France
Re´sume´ :
Cette e´tude se focalise sur le phe´nome`ne d’auto-allumage caracte´rise´ par une initiation spontane´e
de la combustion suite a` une forte compression. Des simulations nume´riques sont re´alise´es dans une
configuration de Machine a` Compression Rapide (MCR). Dans un premier temps, les re´sultats de
simulations aux grandes e´chelles d’un e´coulement inerte sont compare´s a` des mesures expe´rimentales.
Ensuite, la simulation directe bidimensionnelle d’un e´coulement re´actif dans cette MCR est utilise´e
pour analyser les me´canismes controˆlant la formation des noyaux pre´curseurs de l’allumage. Trois
sce´nari d’interaction entre les champs thermochimique et ae´rodynamique sont ainsi mis en e´vidence.
Abstract :
The processes involved in autoignition phenomenon, which is characterised by a spontaneous ini-
tiation of the combustion as a result of a strong compression, are investigated in the present study.
Numerical simulation of a flow generated by a Rapid Compression Machine (RCM) are performed.
First, results of a Large Eddy Simulation of an inert flow are compared with those of an experiment.
Then, the two-dimensional Direct Numerical simulation of a reactive flow is used to look into the me-
chanisms controlling the selection of the precursor nuclei of autoignition. Three interactions between
aerodynamic- and thermochemical-field are highlighted.
Mots clefs : Autoignition ; Simulation Nume´rique Directe ; Machine a` Compression
Rapide
1 Introduction
Carmakers have to meet increasingly stringent emission norms. Thus, technological breakthrough
must be imagined and for this purpose, it is necessary to have a deep insight into the highly unsteady
behavior of turbulent flames in an engine, specifically the auto-ignition phase, which depends on
strongly non-linear phenomena, must be fully under control. Some important issues still need to
be examined concerning the genesis of ignition kernels after a rapid compression, often referred as
‘hot spots’ as temperature plays a first order role in the initiation of combustion, as well as their
interactions once one, or some of them, begin to develop. In the following, it is shown that at least
three mechanisms enter the coupling between the aerodynamic fields and thermochemistry in the
formation of reactive kernels. First, the pressure decrease at the center of the turbulent structures
leads to lower reactivity of the medium. Second, this effect is counterbalanced by the fact that the
fluid trapped in the core of these vortices is thermally insulated from the rest of the flow, thus
avoiding thermal leakage if temperature at the vortex core allows for primary ignition. Third, local
compressibility effects, which intensity is measured by the divergence of the velocity field, on the
other hand locally increase the reactivity.
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
2 Three-dimensional Large Eddy Simulation of the RCM
The fully compressible finite volume SiTCom (Simulating Turbulent Combustion) LES & DNS code
is used [6]. The flow inside the combustion chamber of the RCM experimentally studied in [3] is
first simulated when a non-reactive mixture is admitted. The combustion chamber is a cylinder of
diameter 4 cm and of length 4.4 cm represented in SiTCom with immersed boundaries. The LES
filter is ∆ = 0.24 mm with a 4 million mesh. The effect of the piston in the compression is mimicked
using a mean velocity inlet profile < U(t, r, θ) >, which is assumed axisymmetric and self-similar in
time :
< U(t, r, θ) >= Un(t) p(r) (1)
where Un(t) is the average normal velocity of the flow at the inlet and p(r) is the spatial shape of
the inlet profile. On the top of this profile, turbulence is added [4] according to the grid properties
located at the inlet of the cylinder. Un(t) can be expressed as a function of the speed and the position
of the piston reported from the experiment :
Un(t) =
D2ccLcc
D2pL
∗ +D2p(xp(t)− x∗) +D2ccLcc
(
Dp
Dcc
)2
x˙p(t) (2)
where Dcc and Lcc are the diameter and the height of the combustion chamber, L∗ is an estimation
of the dead-volume characteristic length, Dp is the piston diameter, xp the piston position, x∗ refers
to the dead-volume and x˙p is the piston-speed. With this expression, the time evolution of pressure
perfectly reproduces the experiment (Fig. 1).
Figure 1 – Time histories of pressure. Stars : experiment. Plus : LES, pressure averaged over the whole
domain.
Figure 2 – Fields of velocity magnitude at representative instants after top dead center. Top : PIV. Bottom :
LES.
Regarding the aerodynamic details, various p(r) distributions have been tested to compare LES
against Particle Image Velocimetry measurements. For some of the p(r) that have been tested, a
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
Figure 3 – Turbulent kinetic energy vs time. Symbols : PIV. Line : LES.
Kelvin-Helmholtz instability develops, which is not found in the experiment. To prevent it, the
Rayleigh criterion has to be satisfied and p(r) may not contain any inflection point. Second, the
levels of the velocity magnitude should be the reproduced (Fig. 2). Last, the turbulent kinetic energy
magnitude averaged over the median plane of the combustion chamber should also be representative
of the one obtained by PIV (see Fig. 3). This parametrization leads to p(r) expressed as an hyperbolic
tangent of the radius.
3 Two-dimensional Direct Numerical Simulation of the reactive
flow
To reduce the numerical effort allowing for DNS, the geometry of the combustion chamber has been
downsized four times in each direction, the mesh contains 530×514 cells of about 20 micron-meter.
The wall temperature is computed with a convection coefficient fixed at 40 W.m−1.K−1. Single-step
chemistry is used, two cases are considered keeping fixed the pre-exponential factor, but varying the
activation temperature so that ignition occurs at τ1 = 0.0283 s in case 1 and τ2 = 0.0329 s in case
2, when the top dead center is reached at τTDC = 0.0292 s. Admission turbulence intensity is higher
in case 1 (30%) than in case 2 (10%).
To analyze results, the temperature balance equation may be cast in :
DT
Dt
=
γ
ρCp
ω˙T
Term (1)
+
Term (2)
(1− γ)T∇ · u + γ
ρ
∇ · (ρDth∇T )
Term (3)
(3)
The first term is representative of chemistry effects, the second captures compressibility, the last is
molecular diffusion. For chemistry to be initiated at a given point, a local temperature rise (hot spot)
is needed. From Eq. 3, it is seen that compressibility (Term (2)) and diffusion of heat (Term (3))
compete. In a spatially weakly-varying temperature field, it is mainly compressibility that will first
controls ignition. Figure 4 is extracted from the computation of case 1, in the zone where combustion
starts. Here the fluid is pulled forward by two counterrotating vortices because of viscous shear effects.
While considering this process as being quasi-steady, streamlines merge with the trajectories of the
fluid particles. In the same way as an incompressible flow, the narrowing of the cross-sectional area
and the resulting streamlines constriction between the vortices generate the increase of the velocity
magnitude (see colors on the streamlines, where blue stands for 0 m/s and red, for the 20 m/s).
Differences between incompressible and compressible cases arise because of the confinement that
prevents the volumetric flow rate from being conserved : the compressible bulk velocity is less than
the incompressible one and ∇ · u is locally negative, meaning that Term (2) in Eq. 3 is positive and
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
reaches higher values (see the grey levels on Fig. 4). Consequently, this mechanism may participate
to the formation of primary hot spots.
Figure 4 – The value of the velocity magnitude, here only given on the streamlines, is increased between
the counterrotative vortices.
Aside from the strained zone, vortices core are found, which contribute to ignition according to two
counterbalancing mechanisms. Figure 5 is extracted from the computation of case 1 (on the top) and
2 (at the bottom). Colors in the left picture stand for the values of the Q-criterion making possible to
locate the turbulent structures, while grey levels represent the values of the temperature dissipation
rate χT = ρDth|∇T |2 that is here used to track the temperature inhomogeneities. In both cases, χT
wraps around the main rotating structures without penetrating them. Simultaneously, at the center
of the vortices, the pressure decreases according to the following equality :
Q =
1
2ρ
∆P (4)
The pictures at the center of Fig. 5 is an obvious illustration of this relationship between the velocity
(isocontour of the Q-criterion) and the pressure field (in grey levels).
In case 1 (Fig. 5-top), this pressure drop can be readily associated with a decrease of the chemical
source term magnitude. Indeed, the central vortex that stands for the lowest pressure in the domain
corresponds to a local minimum of heat release, hence combustion does not start within the vortex but
in the local compression zone bordering the high vorticity region. The opposite behavior is observed in
case 2 (Fig. 5-bottom), where it is rather the small temperature dissipation rate (therefore molecular
diffusion) that favor ignition within the vortex.
The difference in local flow properties promoting these various ignition behaviors relate to variability
of global quantities. First, it should be kept in mind that the turbulent intensity is higher in case
1 than in case 2. Second, autoignition in case 1 occurs earlier than in case 2, where turbulence has
already decayed. Implications of these two remarks regarding the global turbulent kinetic energy can
be observed in Fig. 6. This average behavior of the turbulent kinetic energy may be related to the
local vortices properties, where qualitative differences between case 1 and case 2 are quantified by
comparing the values of the Q-criterion and the pressure drop inside the central turbulent structures
in each case. In case 1, the Q-criterion is of the order of 1010 s−1 and the pressure drop, of the order
of 104 Pa. In case 2, both of them are dramatically reduced, that is to say, respectively to 108 s−1
and 103 Pa : the mechanism described by equation 4 is of weak importance compared to the thermal
insulation (lack of molecular diffusion within the core of the vortex) phenomenon which dominates
here in an obvious manner, then ignition occurs at the core of the vortex, while it is located in a
local compression zone in case 1.
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
Q & χT Q & Pressure Q & Term(1)
Figure 5 – Top : case 1. Bottom : case 2. Coupling mechanisms between the aerodynamic and the thermo-
chemical fields. From left to right : Q-criterion (in color) & temperature scalar disspation rate (in grey levels) ;
isocontour of Q-criterion (white line) & pressure (in grey levels) ; isocontour of Q-criterion (white line) & value
of term (1) (in grey levels)
Figure 6 – Bold line : velocity of the piston. Symbols : spatial average velocity fluctuation in the combustion
chamber. Case 1 : circles. Case 2 : squares.
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
4 Conclusion
Three-dimensional Large Eddy Simulation of a rapid compression machine was performed to cali-
brate DNS of the same flow problem, after downsizing its geometry. LES is used to parameterize
an inlet velocity profile, making it possible to obtain realistic time history of the quantities related
to thermodynamic and aerodynamic fields without having to simulate the full compression machine,
but only the combustion chamber. With these conditions, a two-dimensional DNS of a reactive flow
in the downsized combustion chamber has been conducted for two activation temperatures. Three
mechanisms coupling the aerodynamic to thermochemistry and promoting different scenarios for the
formation of very primary hot spots have been underlined :
1. local compression phenomena, tracked by the divergence of the velocity, increases the local
reactedness of the mixture ;
2. pressure drop at the vortex core diminishes the temperature and the chemical source as well ;
3. the fluid trapped in the vortex core may benefit from ‘thermal insulation’ from the rest of the
flow ; which can counterbalance the previous mechanism.
This study will be continued with three-dimensional DNS including multi-step chemistry in order to
account for vortex stretching in the third direction and for the impact of radical species dissociation.
Re´fe´rences
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grids in large eddy simulations. Computers and Fluids 33 (3), 375-404
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Finite-Difference Methods for Three-Dimensional Complex Flow Simulations. J. Comput. Phys.
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[3] Guibert P., Keromnes A. and Legros G. 2009 An Experimental Investigation of the Turbulence
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bustion 84, 79-95
[4] Klein M., Sadiki A. and Janicka J. 2003 A digital filter based generation of inflow data for
spatially developing direct numerical or large eddy simulations. Journal of Computational Physics
186, 652–665
[5] Iaccarino G. and Verzicco R. 2003 Immersed boundary technique for turbulent flow simulations.
Appl. Mech. Rev. 56 (3), 331-347
[6] Lodato G., Domingo P. and Vervisch L. 2008 Three-Dimensional boundary conditions for direct
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[7] Poinsot T. and Veynante D. 2005 Theoritical and Numerical Combustion. R. T. Edwards
[8] Veynante D. and Vervisch L. 2002 Turbulent Combustion Modeling. Progress in Energy and
Combustion Science 28 (3), 193-266
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Etude de l'initiation et de la propagation de l'auto-inflammation dans un milieu présentant des inhomogénéités de température

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Etude de l'initiation et de la propagation de l'auto-inflammation dans un milieu présentant des inhomogénéités de température

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