Roda Bounaceur
email: roda.bounaceur@ensic.inpl-nancy.fr

Pierre-Alexandre A Glaude
email: pierre-alexandre.glaude@ensic.inpl-nancy.fr

René Fournet
email: rene.fournet@ensic.inpl-nancy.fr

Frédérique Battin-Leclerc
email: frederique.battin-leclerc@ensic.inpl-nancy.fr

S Jay

A Pires Da Cruz

A Pires

D A Cruz
email: cruz@ifp.fr

Kinetic modelling of a surrogate diesel fuel applied to 3D auto-ignition in HCCI engines

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Engines running on HCCI combustion mode (Homogeneous Charge Compression Ignition) have the potential to provide both diesel-like efficiencies and extremely low emissions. HCCI engines rely on a lean combustion process (in excess of air), resulting in a reduction of both particulate matter and nitric oxide (NOx) emissions; the latter are directly related to the creation of tropospheric ozone in urban areas. Fundamentally, the reason for these beneficial effect is that, in a HCCI engine, there is not any region with either fuel rich conditions (that would lead to the generation of particulate matter) or stoichiometric conditions (which would yield high temperature and NOx emissions). These advantages are obtained under optimal working conditions of the engine. In order to warrant such optimal conditions and to further develop HCCI engines, it is important to predict the auto-ignition delay of the homogenous mixture during the compression cycle and to model the formation of pollutants according to the fuel composition [START_REF] Aceves | A Multizone Simulation of HCCI Combustion and Emissions[END_REF].

Diesel fuel can potentially be directly used in HCCI engines. Therefore, it is of particular interest to model its auto-ignition characteristics in conditions close to those of diesel engines. However, commercial diesel fuels contain more then 1000 different molecules and their composition is not completely well known. It is then necessary to define a model diesel fuel which would be composed of molecules capable of representing the most important classes of organic compounds present in such a fuel. We have chosen to study a mixture including n-decane as a model molecule of paraffins and α-methylnaphthalene to represent polyaromatic compounds. This hydrocarbon mixture has already been used by other authors [START_REF] Pitsch | Reduced kinetics of multicomponent fuels to describe the auto-ignition, flame propagation and post flame oxidation of gasoline and diesel fuels[END_REF][START_REF] Pfahl | Self-ignition of diesel-engine model fuels at high pressures[END_REF][START_REF] Barths | Computational fluid dynamics modelling of non-premixed combustion in direct injection diesel engines[END_REF] as a surrogate model for diesel fuel.

The chemistry of hydrocarbon oxidation is very complex and detailed kinetic mechanisms based on elementary steps are a useful way to describe the complex chemical phenomena over the wide range of temperature, pressure and equivalence ratio observed in engines.

The aims of our work were to write a detailed kinetic model for the oxidation and auto-ignition of n-decane and α-methylnaphthalene mixtures, to validate it using laboratory experimental data from the literature and to apply the model to real engine CFD 3D computations. Kinetic mechanism development is described in the first part of this paper. The second part focusses on mechanism validation against experimental laboratory data. The kinetic model is then applied to 3D conventional diesel and HCCI engine simulations. The coupling approach between the detailed chemical mechanism and the engine combustion CFD model is described in the third part of the paper which also presents the CFD simulations and results compared to experimental engine data.

DETAILED KINETIC MECHANISM FOR THE OXIDATION OF n-DECANE AND

α-METHYLNAPHTHALENE MIXTURES

The mechanism for the oxidation of n-decane/α-methylnaphthalene mixtures includes the mechanism for n-decane automatically generated by EXGAS-ALKANE software as described by [START_REF] Buda | Progress towards a unified detailed kinetic model for the autoignition of alkanes from C 4 to C 10 between 600 and 1200 K[END_REF] 1 , a new mechanism for the oxidation of α-methylnaphthalene and the crossed 1 EXGAS-ALKANES software automatically generates detailed kinetic mechanisms for the oxidation of linear and branched alkanes and is freely available for academic researchers (valérie.warth@ensic.inpl-nancy.fr).

reactions involved by the interactions between the two fuels. The mechanism for n-decane has been designed to reproduce the low and high temperature oxidation, i.e. the additions of alkyl radicals to oxygen molecules have been taken into account.

Mechanism for the oxidation of α-methylnaphthalene

Few simulations of the oxidation of α-methylnaphthalene are described in the literature: a detailed kinetic mechanism was proposed by [START_REF] Pitsch | Detailed kinetic mechanism for ignition and oxidation of α-methylnaphthalene[END_REF] and computations of the overall fuel decay in a flow reactor were presented by [START_REF] Shaddix | Analysis of fuel decay in high-temperature oxidation of 1-methylnaphtlalene[END_REF] The present paper proposes a new mechanism based on the recent models by [START_REF] Costa | Experimental and modelling study of the oxidation of benzene[END_REF] for the oxidation of benzene and by [START_REF] Bounaceur | Experimental and modeling study of the oxidation of toluene[END_REF] for the oxidation of toluene. The α-methylnaphthalene mechanism includes three parts:

♦ The mechanisms for the oxidation of toluene (193 reactions) and benzene (132 reactions) presented in previous papers [START_REF] Costa | Experimental and modelling study of the oxidation of benzene[END_REF], Bounaceur et al., 2005) which include the C 0 -C 6 reaction base (709 reactions), first proposed by [START_REF] Fournet | Experimental and modeling study of the oxidation of acetylene, propyne, allene and 1,3-butadiene[END_REF]updated by Belmekki et al. in 2003. In this reaction base, most C 0 -C 2 and some C 3 -C 4 pressure-dependent rate constants (i.e. unimolecular decompositions, combinations, beta-scissions and additions) follow the formalism proposed by [START_REF] Troe | Fall-off curves of unimolecular reaction[END_REF] and efficiency coefficients have been included.

♦ A primary mechanism (Fig. 1) containing 95 reactions, in which only α-methylnaphthalene and oxygen are considered as molecular reactants. The reaction pathways consuming α-methylnaphthalene are: the unimolecular initiations giving H-atoms and phenylbenzyl radicals and naphthyl and methyl radicals, the bimolecular initiations with oxygen molecules abstracting a methyl side hydrogen atom; the ipso-additions (addition of an atom to an aromatic ring leading to the abstraction of another atom or of a radical) of H-atoms producing naphthalene and methyl radicals; the ipso-additions of O-atoms forming methylnaphtoxy radicals and H-atoms; the additions of OH radicals leading to methylnaphthols and H-atoms; the metatheses by H-abstraction. As in the case of toluene, the abstractions of hydrogen atoms were considered from the methyl side, but also from the rings. [START_REF] Pitsch | Detailed kinetic mechanism for ignition and oxidation of α-methylnaphthalene[END_REF] did not consider the additions of atoms or radicals, neither the abstractions of H-atoms from the rings. The related rate constants are derived from those proposed for toluene [START_REF] Bounaceur | Experimental and modeling study of the oxidation of toluene[END_REF]. The reactions of resonance stabilized phenylbenzyl radicals are close to those of toluene: the decomposition by formation of a C 5 ring (here, by formation of indenyl radicals and acetylene), the reactions with oxygen molecules to give naphthaldehyde and the combinations with H and O-atoms, OH, HO 2 and methyl and phenylbenzyl radicals are taken into account. Products obtained by combination are methyl naphthalene, naphthaldehyde, methylhydroxy naphthalene, methylhydroperoxy naphthalene, which immediately decomposes by breaking of the O-OH bond, ethylnaphthalene and bi-1-methylnaphtyl, respectively. Two differences were nevertheless made in order to obtain satisfactory simulations: the formation of peroxy radicals was not considered and the recombination with HO 2 radicals led to the direct formation of naphthaldehyde or naphtyl radicals with the rate constants proposed by [START_REF] Emdee | A kinetic model for the oxidation of toluene near 1200 K[END_REF] for a similar reaction in the case of toluene. Naphthyl radicals and the radicals obtained by H-abstractions from the rings react similarly to phenyl radicals, i.e. mainly by reactions with oxygen molecules to give naphthoxy or methylnaphthoxy radicals and by combinations with H and O-atoms, OH, HO 2 and methyl radicals. In the case of naphthyl radicals, we have also considered the addition to acetylene to form acenaphthalene as proposed by [START_REF] Pitsch | Detailed kinetic mechanism for ignition and oxidation of α-methylnaphthalene[END_REF]. The reactions of naphthoxy and methylnaphthoxy radicals are directly derived from those of cresoxy radicals, i.e. CO eliminations with rearrangement and terminations with H-atoms. The reactions of resonance stabilized indenyl radicals are inspired from those of cyclopentadienyl radicals: the combinations with H-atoms to give indene or with OH radicals to produce indenol, the self recombinations and the reactions with oxygen atoms or molecules involving the opening of the C 5 ring by elimination of CO or CO 2 .

♦ A secondary mechanism including 152 reactions, in which the reactants are the polycyclic molecular products formed by the primary mechanism, i.e. indene, methylindene, naphthalene, dimethylnaphthalenes, α-ethylnaphthalene, acenaphthalene, bi-indenyl, bi-1-methylnaphtyl, indenol, naphthols, α-naphthaldehyde, methylnaphthols, α-methylhydroxy naphthalene, naphthalenediones and methylnaphthalenediones (see fig. 1). The different involved isomers are not differentiated. The secondary mechanism of a polycyclic molecule has been written based on the reactions of the analogous monocyclic parent proposed for modelling the oxidation of benzene [START_REF] Costa | Experimental and modelling study of the oxidation of benzene[END_REF] and toluene [START_REF] Bounaceur | Experimental and modeling study of the oxidation of toluene[END_REF]. For instance, the reactions of naphthalene are derived from those of benzene and those of naphthaldehyde from benzaldehyde and both compounds lead mainly to the formation of naphthyl radicals.

Specific heat, heat of formation and entropy of the molecules or radicals have been calculated using software THERGAS [START_REF] Muller | A computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF], based on the group and bond additivity methods proposed by [START_REF] Benson | Thermochemical Kinetics[END_REF]. As simulations showed an important sensitivity to thermodynamic data, the heats of formation of some biaromatic species (naphthalene, α-methylnaphthalene, naphthols (taken as that of 1-naphthol), indene, acenaphthalene and indenyl, naphthyl, phenylbenzyl and naphthoxy radicals) for which the presence of two aromatic cycles increases the uncertainty in the group additivity estimation, have been taken from the values computed by [START_REF] Richter | Formation of polycyclic aromatic hydrocarbons and their radicals in a nearly sooting premixed benzene flame[END_REF] using density functional theory.

Crossed reactions in n-decane/α-methylnaphthalene mixtures

While previous studies have shown that crossed reactions have negligible effect on the oxidation of mixtures of two alkanes [START_REF] Glaude | Modeling of the oxidation of mixtures of primary references fuels[END_REF] or even of an alkane and toluene [START_REF] Klotz | Modeling of the combustion of toluene-butane blends[END_REF],

we have considered here the crossed reaction which can be involved by the presence of important amounts of resonance stabilized phenylbenzyl radicals and which could enhance the inhibiting effect of α-methylnaphthalene only induced by an action on the common pool of free radicals. Two types of possible crossed reactions have been taken into account :

Metatheses involving the abstraction by a phenylbenzyl radical of a hydrogen atom from n-decane. Phenylbenzyl radicals can be involved in the following reversible metatheses with n-decane and lead to the formation of the 5 isomers of decyl radicals:

♦ + C 10 H 22 + C 10 H 21
The combination of phenylbenzyl and decyl radicals. Phenylbenzyl radicals can also combine with each of the 5 isomers of decyl radicals:

♦ + C 10 H 21 CH 2 C 10 H 21
Similar types of crossed reactions have been considered for mixtures containing n-butane and toluene and have allowed autoignition delay times obtained in a shock tube to be modelled satisfactorily.

VALIDATION OF THE DETAILED KINETIC MECHANISM USING LABORATORY

EXPERIMENTS

The mechanism for the oxidation of pure α-methylnaphthalene has first been validated and only then simulations have been performed for mixtures of α-methylnaphthalene and n-decane. The global mixture mechanism involves 2834 reactions and 530 species among which 1282 reactions and 189 species belong to the α-methylnaphthalene mechanism. Simulations have been performed using software components from the CHEMKIN II library (Kee et al., 1993). In all graphical representations in this section, symbols correspond to experimental data and lines represent the numerical simulations.

Validation of the α-methylnaphthalene oxidation mechanism

The oxidation of α-methylnaphthalene has been experimentally investigated in several types of reactors in a temperature range varying from 800 K to 1500 K and a pressure range from 1 bar to 13 bar. [START_REF] Pfahl | Self-ignition of diesel-relevant hydrocarbon-air mixtures under engine conditions[END_REF] have measured auto-ignition delay times for α-methylnaphthalene in a shock tube at temperatures from 900 K to 1500 K, a pressure of 13 bar and a stoichiometric mixture in air

(1.6 % hydrocarbon). Figure 2 shows that our simulations reproduce well these experimental data. [START_REF] Shaddix | Oxydation of 1-methylnaphtalene[END_REF][START_REF] Shaddix | Analysis of fuel decay in high-temperature oxidation of 1-methylnaphtlalene[END_REF] have studied the oxidation of α-methylnaphthalene in a flow reactor at 1170 K, atmospheric pressure, for mixtures containing around 0.1% hydrocarbon with nitrogen as bath gas. Globally, there is an acceptable agreement between our calculations and the measurements for the three studied equivalence ratios, 0.6, 1 and 1.5: The consumption of α-methylnaphthalene (Fig. 3a) is very well reproduced by the model; the formation of naphthalene (Fig. 3b) is also well reproduced although the agreement is not as good as for the α-methylnaphthalene; the consumption of oxygen and the production of carbon monoxide, naphthaldehyde and naphthols (Fig. 3c) are in agreement with experimental measurements for an equivalence ratio of 0.6. [START_REF] Marchal | Etude de la contribution des familles chimiques constitutives des gazoles à la formation de polluants non réglementés[END_REF] has studied the oxidation of α-methylnaphthalene in a jet stirred reactor between 800 K and 1150 K, at 10 bar, a residence time of 0.5 s, for a stoichiometric mixture containing 0.111% hydrocarbon with nitrogen as bath gas. The agreement is here also acceptable, as shown in Fig. 4 for the consumption of α-methylnaphthalene and oxygen and the formation of carbon monoxide and carbon dioxide (Fig. 4a), methane, benzene, toluene and naphthalene (Fig. 4b). The orders of magnitude for product formation are well reproduced, but the maxima are obtained for temperatures around 40 K higher than in experiments.

Validations of the mechanism for the oxidation of n-decane/α-methylnaphthalene mixtures

No gas-phase study of the oxidation n-decane/α-methylnaphthalene mixtures was found in the literature, but [START_REF] Moriue | Effects of dilution by aromatic hydrocarbons on staged ignition behavior of n-decane droplets[END_REF] have studied the auto-ignition of these mixtures in a pressurized chamber at 3 bar in which a suspended droplet was suddenly brought to a temperature from 600 K to 750 K. Diagnostics carried out with a Michelson interferometer detected cool-flame, as well as hot flame appearance. The purpose of the current validation is not to propose an accurate physical model of these experiments, but to roughly reproduce the qualitative trends observed by using our detailed chemical mechanism. We have then simulated this system as an adiabatic well-mixed reactor containing, after an induction time due to vaporization (τ vap (T)), a gas phase stoichiometric fuel/air mixture. In the real reactor, there is a concentration gradient which develops around the droplet when it vaporizes that is not reproduced by simulations. Nevertheless, it can be assumed that the appearance of cool flame and hot ignition will be triggered by the most reactive zone in which the composition is probably not far from stoichiometry. For each studied temperature (T), the vaporization induction time is deduced from a comparison between the experimental ignition delay time for cool flame appearance (τ cf exp. (T)) and the time simulated assuming gas-phase conditions (τ cf. sim gas-phase (T)) in the case of pure n-decane:

τ vap (T) = τ cf exp. (T) -τ cf sim gas-phase (T).

Since the pure n-decane model has been validated independently for real gas-phase experiments [START_REF] Buda | Progress towards a unified detailed kinetic model for the autoignition of alkanes from C 4 to C 10 between 600 and 1200 K[END_REF], τ cf. sim gas-phase (T) can be taken as a baseline. For n-decane/α-methylnaphthalene mixtures, the same τ vap (T) is used for all compositions and the simulated (τ cf sim (T)) ignition delay time for cool flame appearance is then :

τ cf sim (T) = τ vap (T) + τ cf sim gas-phase (T).

Fig. 5a shows a comparison between experimental and simulated ignition delay times for cool flame appearance for mixtures containing different fractions of α-methylnaphthalene. In spite of the strong assumptions made here, the agreement in terms of auto-ignition delays as a function of temperature is good for the mixture containing 40% α-methylnaphthalene, but deteriorates with higher contents of this component, for which the reactivity is overestimated by simulations. This is probably due to the difference in volatility between n-decane (normal boiling point = 447.3 K) and α-methylnaphthalene (normal boiling point = 517.9 K), inducing a higher content of n-decane in the gas-phase than in the liquid phase. Fig. 5b shows a comparison between experiments and simulations for the time between cool flame and hot-flame appearance. Our model qualitatively reproduces the inhibiting effect of the addition of α-methylnaphthalene, but the simulated effect is more marked for mixtures containing from 0 to 40 % aromatic compounds than in experiments.

This is also probably due to the difference in volatility between both hydrocarbons not taken into account by the numerical simulations. These validations should be regarded as a very primary approximation showing that the crossed reactions considered are not meaningless, but further work is needed when new experimental data in a gas-phase reactor is available.

APPLICATION OF THE DETAILED KINETIC MECHANISM TO ENGINE 3D

SIMULATIONS

Delay sensitivity analysis in engine conditions

In the absence of more realistic diesel fuel models, n-heptane has been widely used in past studies as a surrogate diesel fuel [START_REF] Pires Da Cruz | Detailed chemistry-based auto-ignition model including low temperature phenomena applied to 3D engine calculations[END_REF], Curran et al., 1998-1, Curran et al., 1998-2, Embouazza et al., 2003[START_REF] Da | Three-Dimensional modeling of self-ignition in HCCI and conventional diesel engines[END_REF]. Detailed kinetic models for the auto-ignition and oxidation of n-heptane have been available for a number of years. It is therefore interesting to compare the auto-ignition behavior of n-heptane against n-decane and α-methylnaphthalene mixtures in engine thermodynamic conditions. In this study, we have first compared the relative deviations between the main ignition delays for pure n-heptane and a mixture of 70 % volumetric n-decane and 30 % α-methylnaphthalene (hereafter named Z=70 mixture, where Z is the percentage of α-methylnaphthalene in the mixture). According to [START_REF] Pitsch | Reduced kinetics of multicomponent fuels to describe the auto-ignition, flame propagation and post flame oxidation of gasoline and diesel fuels[END_REF], the 70/30 proportion is the one which best represents the behavior of the diesel fuel. The n-heptane mechanism was generated by the same algorithm as the one for n-decane. Both are issued from the EXGAS software.

Auto-ignition delays with both mechanisms can be calculated in an adiabatic, homogeneous reactor at constant pressure along the thermodynamic conditions that one may expect to find in a real engine. The differences between the delays of these two fuels can then be represented by plotting the relative deviations between the two mechanisms in an initial temperature versus initial pressure (T 0 ,p 0 ) space for different compositions distributed along all possible conditions that we have tested. The initial temperature T 0 and the initial pressure p 0 were varied (T 0 OE [600 K-1500 K] with a 10 K step and p 0 OE {1,1.5,2,2.5,3,4,6,8 MPa} respectively). The mixture composition expressed in terms of the global equivalence ratio φ (φ OE[0.3-0.5-0.7-1.0-1.5-3.0]) and dilution gas fraction relative to air composed of 21 % O 2 and 79 % N 2 (X res OE[0%-30%-60%-80%-90%]) was also varied.

The initial molar composition for the detailed kinetics computations (X fuel , Xo 2 , X D , where X D is the molar fraction of dilution gases) was determined as follows : One can note that, in this system, X res is seen as the amount of non-reactive species (N 2 , CO 2 , H 2 O, Ar,…) in excess relative to the amount of N 2 present in air. In some cases, one needs to be careful that the definition adopted here matches the definition of X res used for experimental results.

An example of the results obtained is plotted in Fig. 6a for φ = 1 and X res = 0%.

The differences essentially depend on the initial temperature. Pressure effects are small.

Nevertheless, the same deviation between two distinct pressures will result in a more important difference between the delays when the pressure is low (for instance, p < 3 MPa) since the auto-ignition delay is longer in such conditions. The discrepancies between the two fuels are pressure independent and are essentially located in a medium temperature range, between 750 K and 900 K (cool flame region). Deviations between delays for both fuels can be significant and reach 100 % for these conditions. Above 1000 K, differences fall below 10 %. These results are confirmed by the classical delay plots as a function of pressure and inverse of the temperature (see Fig. 6b). One may then expect that the good prediction of the auto-ignition delays like those obtained by [START_REF] Réveille | Contribution of 3D CFD tools to the development and understanding of diesel engines : improving today's engines and designing tomorrow's power units[END_REF] in engine 3D simulations with pure n-heptane at high temperature will not be affected. When low temperature mechanisms are involved, some strong effects can be observed by choosing the n-decane/α-methylnaphthalene mixture.

Coupling approach with the 3D combustion model ECFM3Z of [START_REF] Benkenida | The 3-Zones Extended Coherent Flame Model (ECFM3Z) for computing premixed/diffusion combustion[END_REF] In practical applications, especially for new low emission combustion concepts such as HCCI engines, the cool flame heat release C 1 ∆h, where C 1 is the fuel fraction consumed by the cool flame and ∆h is the enthalpy difference due to combustion, significantly contributes to the total heat release. Such strategies imply that the mixture is nearly homogeneous at an early time in the engine cycle so that its temperature is not high enough to trigger fast auto-ignition. Bypassing the cool flame mechanism by considering a single delay τ HT without the early heat release C 1 ∆h may imply an erroneous calculation of the main auto-ignition. As shown by Pires da Cruz ( 2004), the heat released during the cool flame period (during t L t τ Τ ΗΤ < < in Fig. 7) significantly modifies the thermodynamic conditions (pressure and temperature increase). Consequently, the chemical reactions after the delay τ LT must be described accurately.

The TKI (Tabulated Kinetic Ignition) auto-ignition model of Colin et al. ( 2005) is briefly summarized here. It relies on tabulated auto-ignition quantities issued from detailed chemistry calculations. The auto-ignition database can be generated by the Senkin code [START_REF] Lutz | Senkin: A Fortran program for predicting homogeneous gas phase chemical kinetics with sensitivity analysis[END_REF] which is part of the Chemkin package [START_REF] Kee | Chemkin II. A fortran chemical kinetics package for the analysis of gas-phase chemical kinetics[END_REF]. Databases have been built for the same set of thermodynamic conditions (T 0 ,p 0 ,φ 0 ,X res 0 ) as used in Pires da Cruz ( 2004) at constant pressure and using the model fuels described in this work (n-heptane and the Z=70 mixture).

The following parameters are determined through post-processing of the complex chemistry simulations (see Fig. 7) and then tabulated in the databases:

• Cool flame ignition delay τ LT when present. It corresponds to the maximum temperature versus time derivative during the cool flame ignition period.

• Cool flame heat release C 1 . Even if in some cases the cool flame heat release is not fast, it is always modeled as a step. If a cool flame is not present, C 1 = 0 and the main auto-ignition process is directly computed using chemical progress rates c ω & , where c is a progress variable between 0 and 1 based on the temperature evolution.

• Chemical progress rate The TKI auto-ignition model was implemented in the IFP-C3D engine code. Auto-ignition information is retrieved from the databases through linear interpolation along the local thermodynamic conditions met in a computational cell. This model allows computation of the autoignition processes in both low and high temperature conditions. It was validated against Senkin detailed chemistry calculations performed on a constant volume configuration and on a perfectly homogeneous rapid compression machine system. The results presented on Fig. 8 show that the TKI model is capable of reproducing the auto-ignition behavior of the Z=70 mixture when compared to detailed chemistry calculations for conditions typical of HCCI engines (φ=0.7, EGR=0 and 30%, engine speed of 1200 rpm…).

Engine 3D simulations

Engine computations with the IFP-C3D code were performed using thermodynamic properties of a diesel fuel and kinetic results of either pure n-heptane or the mixture Z=70. The computed cases are 3D sector geometries operating on conditions shown in Table 1. 3D temperature fields corresponding to both conditions on Table 1 are plotted in Fig. 9. One can see that the onset of auto-ignition is different between the two cases. In Fig. 9a, the conventional part load temperature field shows that auto-ignition occurs in a narrow region. Reaction rates in this case are high. In Fig. 9b, the HCCI engine computation features a smoother heat release and the auto-ignition region spreads over a wide area with cooler conditions. The temperature fields in Fig. 9 clearly show the differences between the conventional diesel engine and the HCCI operating conditions in terms of the homogeneity of the mixture at the onset of auto-ignition. The lower temperature field in HCCI conditions strongly justify the particular attention dedicated to cool flames description included in the surrogate fuel kinetic modeling and in the engine auto-ignition 3D model exposed previously.

Figure 10a compares the experimental pressure curve of a partial load, diluted (EGR=30%), direct injection diesel engine with the pressure curves computed with n-heptane and with the Z=70 mixture fuel. Only small differences were observed on the auto-ignition and remaining combustion processes between experimental and modeling results using both model fuels.

Figure 10b corresponds to a HCCI (EGR = 50%) split injection engine. Again, in these conditions, the n-heptane and the Z=70 mixture mechanisms predict the same auto-ignition delay. However, the pressure rise after ignition is slower with the Z=70 model indicating a lower heat release rate when n-decane and α-methylnaphthalene kinetic properties are considered. It is important to note that the mixing process plays a significant role in the auto-ignition prediction which may explain why the initial delay and cool flame heat release is not so well positioned for both n-heptane and n-decane/α-methylnaphthalene kinetics. It can be deduced from these results that the simulations are more sensitive to the kinetics in HCCI conditions where the auto-ignition delays are usually longer when compared to conventional diesel. The use of detailed kinetics is essential in those conditions insofar as large deviations between delays and reaction rates are observed between the two fuels.

A new detailed kinetic mechanism has been proposed to model the oxidation of α-methylnaphthalene and n-decane/α-methylnaphthalene mixtures. The mechanism for α-methylnaphthalene is derived from recent mechanisms for the oxidation of benzene and toluene and has been successfully validated using experimental results obtained in a shock tube, in a flow reactor and in a jet-stirred reactor. The mechanism for the mixture can qualitatively reproduce the evolution of the cool flame and auto-ignition times observed when introducing a fuel droplet in a heated pressurized chamber.

The n-decane/α-methylnaphthalene mixture kinetic model developed in this study as well as an available n-heptane auto-ignition mechanism were applied to both conventional diesel and HCCI engine 3D simulations. The kinetic mechanisms were not directly coupled with the 3D CFD engine code but rather used a priori in the construction of auto-ignition delays and reaction rate databases covering a broad range of thermodynamic conditions typical of internal combustion engines. The engine simulation results show that both fuels behave well in predicting auto-ignition delays and reproducing the experimental pressure throughout the engine cycles. This explains why, from a used as model fuels. However, in HCCI engine conditions, important differences were observed in the reaction rate after ignition. Since pollutant emissions from engines are mostly generated during the high temperature combustion phase, it is important during this period to have a correct estimation of the reaction rate. Therefore, a surrogate diesel fuel with kinetic properties closer to a real diesel (including alkanes, aromatics and eventually other components) should perform better than a single component fuel such as n-heptane.

FIGURE CAPTIONS

Figure 1: Primary mechanism of the oxidation of α-methylnaphthalene. The bicyclic primary products are written in bold.

Figure 2: Auto-ignition of α-methylnaphthalene in a shock tube [START_REF] Pfahl | Self-ignition of diesel-relevant hydrocarbon-air mixtures under engine conditions[END_REF].

Figure 3: Oxidation of α-methylnaphthalene in a flow reactor [START_REF] Shaddix | Oxydation of 1-methylnaphtalene[END_REF][START_REF] Shaddix | Analysis of fuel decay in high-temperature oxidation of 1-methylnaphtlalene[END_REF] Figure 4: Oxidation of α-methylnaphthalene in a jet-stirred reactor [START_REF] Marchal | Etude de la contribution des familles chimiques constitutives des gazoles à la formation de polluants non réglementés[END_REF].

  c ω & . The time derivative of the progress variable c is stored for discrete values of this quantity. An adequate refinement is needed in the low temperature region. This corresponds to small values of c. Different number and combinations of these points have been tested. Sufficient accuracy was obtained with 7 points between c = 0.025 and c = 0.3. For c > 0.3, the reaction is always very fast and c ω & becomes sufficiently high to promote auto-ignition.

  Figure3: Oxidation of α-methylnaphthalene in a flow reactor[START_REF] Shaddix | Oxydation of 1-methylnaphtalene[END_REF][START_REF] Shaddix | Analysis of fuel decay in high-temperature oxidation of 1-methylnaphtlalene[END_REF]): (a) mole fraction of α-methylnaphthalene, (b) mole fraction of naphthalene and (c) mole fraction of oxygenated compounds for an equivalence ratio of 0.6. The initial hydrocarbon mole fractions used for simulations were 1100 ppm at Φ 0.6 (a time shift of 20 ms has been considered) and 950 ppm at Φ = 1 and Φ = 1.5 (no time shift, but T sim = 1190 K).

Figure 5 :

 5 Figure 5: Auto-ignition of n-decane/α-methylnaphthalene mixtures in a pressurized chamber with

Figure 6 :

 6 Figure 6: Comparisons of the n-heptane and the n-decane/ α-methylnaphthalene mixture delays as a function of 1000/T. (a) Relative deviations (in %) between the delays of the two fuels, (b) pure n-heptane delay curves (symbols) and n-decane/ α-methylnaphthalene delay curves (solid lines).

Figure 7 :

 7 Figure 7: Coupling approach between detailed kinetics and 3D combustion model. Right : Model schematic using a double tabulated delay (τ LT , τ HT ) and cool flame consumption C 1 . Left :

Figure 8 :

 8 Figure 8: Comparison of temperature profiles obtained with the TKI 3D auto-ignition model (long dashed line) and with detailed chemistry computations (solid line) for the Z=70 mixture. φ = 0.7, X res = 0 % and 30%. Engine speed is 1200 rpm and at ca = -180, T 0 = 550 K, p 0 = 0.4 MPa.

Figure 9 :

 9 Figure 9: Engine 3D simulations. Temperature field mesh) in the combustion chamber at the

Figure 10 :

 10 Figure 10: Engine 3D simulations. Comparison of the pressure evolutions using n-heptane and

  FIGURE 2

  FIGURE 10

Table 1 : Engine test cases: 3D simulations main parameters.

 1

	Simulation parameters	Part load (1 injection)	HCCI (split injection)
		(related to fig. 9a)	(related to fig. 9b)
	BMEP 2	0.37 MPa	0.5 MPa
	RPM 3	1640	1500
	EGR 4 rate	31 %	50 %
	Compression ratio	17.8	14
	Injection start	6 ca BTDC 5	9 ca and -11 ca BTDC
	Injection duration	8 ca	3.79 ca and 3.54 ca
	Injection pressure	96 MPa	140 MPa
	2 Brake Mean Effective Pressure
	3 Rotations Per Minute
	4 Exhaust Gas Recirculation
	5 Before Top Dead Center

ABSTRACT

The prediction of auto-ignition delay times in HCCI engines has risen interest on detailed chemical models. This paper described a validated kinetic mechanism for the oxidation of a model Diesel fuel (n-decane and α-methylnaphthalene). The 3D model for the description of low and high temperature auto-ignition in engines is presented. The behavior of the model fuel is compared with that of n-heptane. Simulations show that the 3D model coupled with the kinetic mechanism can reproduce experimental HCCI and Diesel engine results and that the modeling of auto-ignition in the cool flame region is essential in HCCI conditions. Keywords : Diesel fuels, n-decane, α-methylnaphthalene, auto-ignition, HCCI engines.

Authors :

Roda Bounaceur : PhD in chemical engineering ( 2001


Alexandre Mouradian

Véronique Vèque

Dissemination Strategies in Realistic V2V Highway Networks: the Madrid Trace Case

Keywords: VANETs, Dissemination, Performance Evaluation

Multi-hop message dissemination in vehicular networks has been largely studied in the past decade. It notably allows to push information to the drivers concerning hazards that they will encounter ahead on the road such as, for instance, traffic jams, ice patches, etc. It could thus reduce the number of car crashes. During the dissemination of the information, each node have to decide if it will forward a received packet or not. In the literature, many forwarding strategies have been proposed, but they are usually evaluated by simulation with simple mobility models. In this paper, we investigate the performance of several dissemination schemes on the Madrid Highway vehicular mobility trace. This trace is a realistic micro-mobility model representing 10 km portions of two highways around the city of Madrid. The main result of this paper is to show that a carry-and-forward version of farthest node dissemination strategy is a very promising scheme under realistic highway traffic conditions, because this scheme increases the number of receivers and distance covered by the packet at a very low cost in terms of traffic overhead and algorithmic complexity.

I. INTRODUCTION

Vehicular communications are an important part of Intelligent Transport Systems (ITS) which are now in their standardization phase. Among others, ETSI and ISO have defined a basic set of distributed applications [START_REF]Intelligent Transport Systems (ITS)[END_REF] to be provided by intelligent vehicles and management systems. They have several targets: Public Safety, Traffic Efficiency Management, Traveler Information Support and Comfort of driver and passengers but also, Air pollution emission measurement and reduction, Electric Vehicle Itinerary Planning, Law enforcement and Broadband services. These applications can be distinguished according to their communication type either Vehicle-to-Vehicle (V2V) or Vehicle-to-Infrastructure (V2I), their Quality of Service (QoS), and their delivery requirements such as broadcasting, unicasting or geocasting. In this work, we focus on applications which rely on V2V and information dissemination. Active road safety applications, cooperative traffic efficiency and some cooperative local services fall in this category. We are especially interested in the dissemination of Decentralized Environmental Notification Message (DENM), as defined in [START_REF]Intelligent Transport Systems (ITS)[END_REF], in order to alert road users of hazardous events in an Area of Interest. For these types of applications, simple link-level broadcasting is not enough, but multi-hop dissemination is needed. With multi-hop dissemination, the source of the information broadcasts a message to its neighbors, each node receiving the message decides to forward it in its vicinity or not according to the dissemination algorithm.

The process should stop when the message reaches the limit of the Area of Interest. In this paper, we focus on the different forwarding or relaying strategies proposed in the literature. A forwarding strategy is defined as the actions taken by a node when it receives a dissemination message. The simplest flooding algorithm which allows each node to relay a received packet to all its neighbors provoke the broadcast storm problem [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF]. Many criteria have thus been proposed in the literature in order to reduce the number of packet copies and thus the contention in the network. Dissemination algorithms have been largely studied in the literature [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF] [3] [START_REF] Villas | Drive: An efficient and robust data dissemination protocol for highway and urban vehicular ad hoc networks[END_REF], but most of the time the studies are limited to simulations with low fidelity traffic models. In this work, in order to evaluate dissemination strategies, we use a realistic micro-mobility trace: the Madrid Highway trace [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF].

The main forwarding strategies proposed in the literature are introduced in sections II and III. Then we provide the simulation setup in Section IV. Using the Madrid Highway trace, we focus on the simulation of generic forwarding strategies instead of their various implementations. In Section V, we discuss the simulation results. We detail the global performance of the schemes in terms of number of receptions, traveled distance, replication and contention of the disseminated message. We also look at the timing dynamics of the schemes in order to evaluate their timeliness and thus their ability to be employed for road safety applications. Section VI concludes and provides future works.

II. RELATED WORK

Message dissemination in vehicular networks has been a subject of great interest in the past decade. Dissemination schemes are envisioned to be part of Intelligent Transport Systems (ITS) in order to push various information about the road network to the drivers [START_REF] Hartenstein | VANET: vehicular applications and inter-networking technologies[END_REF]. In this paper we focus on multi-hop dissemination and especially forwarding strategies. The numerous proposed protocols can be classified into the following categories according to how the forwarding decision is made: location-based [START_REF] Chiasserini | Smart broadcast of warning messages in vehicular ad hoc networks[END_REF] [8] [START_REF] Panichpapiboon | Irresponsible forwarding[END_REF] [10] [START_REF] Villas | Drive: An efficient and robust data dissemination protocol for highway and urban vehicular ad hoc networks[END_REF], probability-based [7] [11] [12] [13] [START_REF] Panichpapiboon | Irresponsible forwarding[END_REF], density-based [START_REF] Tseng | A vehicledensity-based forwarding scheme for emergency message broadcasts in vanets[END_REF]. These strategies are detailed in Section III.

Even if performance studies have been provided in order to evaluate these dissemination schemes [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF] [4], they do not focus on the dissemination strategy principles but rather on specific implementations. Moreover the evaluation is performed on mobility traces which are built from scratch for the simulation purpose. For instance, the authors of [START_REF] Villas | Drive: An efficient and robust data dissemination protocol for highway and urban vehicular ad hoc networks[END_REF] use a highway and a grid scenario where the mobility pattern of the vehicle is not detailed. In [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF], the authors also use a highway scenario with vehicle traffic generated from a simulation tool according to well-known vehicular traffic patterns (free flow, car following, jam), but not from real data. In this work we go a step further by considering a realistic highway mobility pattern constructed from real world data [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF] while evaluating generic dissemination strategies.

III. DISSEMINATION ALGORITHMS

In this section, we present the schemes which are evaluated in the remainder of the paper. These generic dissemination strategies: Blind Flooding, Probabilistic Flooding, Densitybased Flooding, Farthest node Flooding, Probabilistic Farthest node Flooding and carry-and-forward are taken from various sources of the literature such as [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF] and [START_REF] Chaqfeh | A survey on data dissemination in vehicular ad hoc networks[END_REF] for instance. Nevertheless, in this paper, we do not investigate the performance of cluster-based schemes because, as shown in [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF] this kind of dissemination algorithms does not perform very well for vehicle densities above 40 vehicle/km. In the Madrid trace we are seldom under this density [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF].

The behavior of a dissemination scheme is defined by the actions taken upon a packet reception. In the remainder of this section, we thus describe these actions for all the considered schemes.

A. Blind Flooding

Blind flooding (BF) is the simplest scheme: upon reception, a node checks if it has already received this packet. If not, it broadcasts it. In the other case, it silently discards it. BF is the most reliable scheme since the message is broadcasted by all the nodes. Nevertheless, it induces a huge amount of redundancy. As messages are transmitted multiple times in the same areas of the network, it causes congestion and collisions which can delay some message deliveries. Nonetheless, BF is a reference dissemination scheme to which others can be compared. The only information needed in the packet is an ID so that the nodes can decide if they have already seen the packet or not.

B. Probabilistic Flooding

For Probabilistic Flooding (PF), the nodes act the same as for BF except that they forward the packet (only if it is the first time it is received) with probability p and discard it with probability 1p. Depending on the value of p, this scheme can drastically reduce the number of redundant transmissions. Nevertheless, there is no guaranty that the network is fully flooded on convergence of the algorithm. Once again, the only information needed in the packet is an ID.

C. Density-based Flooding

With Density-based Flooding (DF), the selection of the forwarder is based on the degree of the nodes. The packet is forwarded by the node with the highest degree in the neighborhood of the sender. It can be implemented in two ways: [START_REF]Intelligent Transport Systems (ITS)[END_REF] neighbor nodes exchange their degrees using hello messages and the dissemination message is sent only to the neighbor with the highest degree, or (2) the message is broadcasted, the receivers initialize a timer which is inversely proportional to their degrees and the first node whose timer expires forwards the packet. The idea behind this scheme is that it is better to use the more connected nodes as forwarders since they will disseminate information to more nodes. We will see that this scheme does not perform very well in practice, at least in the Madrid trace case.

D. Farthest node Flooding

The Farthest node Flooding (FF) scheme is similar to the density-based in the sense that only one node is selected as a forwarder: the farthest from the sender. In this case as well, the two previously mentioned implementations are possible (for the timer-based implementation, the timer is function of the distance from the sender). Choosing the farthest node to forward the packet allows to cover rapidly a long distance in the flooding direction while keeping the traffic low. It is considered as the best dissemination scheme available [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF] as will be confirmed in the case of the Madrid trace in Section V. To implement this scheme, the nodes have to know their position and direction (which is a standard requirement in VANETs [START_REF] Hartenstein | VANET: vehicular applications and inter-networking technologies[END_REF]).

E. Probabilistic Farthest node Flooding

Probabilistic Farthest node Flooding (PFF) is a mix between the probabilistic and farthest node scheme. In this configuration, the nodes compute their probability of retransmitting the packet according to their distance to the sender. The farther from the emitter the node is, the higher the probability to retransmit.

F. Carry-and-Forward Flooding

The basic carry-and-forward scheme [START_REF] Wu | Mddv: a mobility-centric data dissemination algorithm for vehicular networks[END_REF] [START_REF] Zhao | Vadd: Vehicle-assisted data delivery in vehicular ad hoc networks[END_REF] consists in keeping the packet in memory when no neighbors are available and forwarding it as soon as it is possible (when a neighbor is available). It aims at solving the partitioned network problem that can appear in case of low vehicular traffic. It can be adapted to any of the previously described forwarding policies. In this paper, we propose to adapt this scheme to FF: a node with no farther neighbor in the flooding direction has to wait until one appears and then it can forward the packet.

For all these schemes, providing that the nodes know their locations and directions, the flooding range can be easily limited by adding the position of the first emitter in the packet and discarding it if the forwarding node is more than Xm away from the first node. Moreover, a dissemination direction can also be defined by setting it in the message.

IV. SIMULATION SETUP

In this section, we describe the mobility trace, the simulator and the metrics used in order to realize the performance evaluation of the schemes presented in the previous section.

A. The Madrid trace

The Madrid Highway trace [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF] is a set of realistic micromobility traces for portions of two Madrid highways: the A6 and the M40. These traces give the position and speed of the nodes at each second during 1800s, over a 10 km The traces are generated from traffic count data collected from induction loop sensors. The original dataset includes: the timestamp of the vehicle crossing the loop, the speed of the vehicle and the lane (both A6 and M40 have three lanes). From this original dataset, the trace itself is generated using a microscopic vehicular mobility simulator developed by the authors of [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF] which is based on state of the art carfollowing and lane-changing models. The resulting trace is a text file in which each line presents the following information: [time(s), nodeID, x(m), y(m), speed(km/h)].

B. The simulator

In order to evaluate the dissemination schemes on the Madrid traces, we developed our own lightweight simulator. The main reason why we did not use a classic discrete event simulator (NS2, Omnet++, etc) is that the number of nodes in the trace is too large to be handled by such simulators with the full network stack modeled. The tool we developed allows to evaluate the performance of the previously presented generic dissemination strategies on large scale traces. It performs the following tasks for each second of the trace:

1) parse the trace file and build its graph representation; 2) execute the algorithm on the graph: neighbors exchange messages according to the evaluated algorithm.

During the first step, the graph is a simple geometric graph where nodes are considered neighbors if they are separated by less than a given range. Concerning the results presented in this paper, the range is 150m, it is considered as a realistic value according to [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF]. For the second step, one of the dissemination algorithm presented in Section III is executed on the graph. As the graph changes only every seconds and a message can be sent more rapidly with the standard MAC and physical layers [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF], we choose to perform several steps of the algorithm on the same graph. In our case we choose to perform 5 steps of the algorithm during one second. For most of the presented algorithms, a step executed by a node consists in broadcasting a message to its neighbors. We thus consider that the MAC and Physical layers delays are of 200ms. When the algorithm converges (meaning that no more packets are scheduled to be sent), the simulator terminates. The outputs consist in several result metrics which are described in the next subsection.

In this paper, the considered simulation scenario is the following: at a given time, a node at the center of the highway portion is chosen to be the source of the information to disseminate. We choose dissemination start times as i × 200s with i ∈ 1, ..., 8. In each simulation run presented in this paper, one source disseminates one information message.

C. The considered metrics

In order to compare the different protocols, we use the following metrics:

1) the number of receivers of the packet which allows to evaluate the delivery efficiency of the protocols; 2) the number of packet copies received which allows to indicate the level of redundancy of each protocol;

3) the maximum contention which is the maximum number of contending packets in the neighborhood of a node (the maximum is taken over all the nodes and the duration of the simulation), and allows to evaluate how much the MAC layer is stressed; 4) the backward distance traveled by the packet which indicates the ability of the protocol to diffuse the information in space.

We compute forward distance as well but we only present backward distance in the paper as the results are very similar.

V. RESULTS AND DISCUSSIONS

In this section, we present and discuss the results obtained from the simulator. Two types of results are shown: first the metrics once the algorithms have converged, and then the temporal dynamics of the metrics until the algorithms converge. Finally we compare the results to the Carry-and-Forward version of Farthest Node dissemination to determine the usefulness to let the vehicles carry information.

A. Memory-less algorithms performance

In this section, we are interested only in memoryless algorithms (without Carry-and-Forward).

1) General Performance:

The first thing we have to notice on the graphs of Fig. 1 is the large standard deviation bars. They account for the large variety of situations that can occur in the traces: when the packet is sent, depending whether the network is fully connected or on the contrary very sparse, the algorithms will behave very differently. As the results of [START_REF] Gramaglia | Vehicular networks on two madrid highways[END_REF] suggest, there is a large variability in the situations encountered over time, even for one single trace scenario. This variability of situations has to be taken care of by the dissemination protocols.

In Figs. 1a,1b, 1c and 1d we monitor respectively the number of receivers, the number of received packet copies, the backward distance covered by the packet and the maximum contention for different scenarios and different schemes. We have to note that there are on average around 530 vehicles present on the simulated portion of the highway. First, we observe that BF and FF are the most efficient flooding algorithms in terms of number of receivers and distance covered by the packet, because they allow the packet to reach all the nodes of the connected component of the sender (as said, the variability in the results comes from the variability of the size of this connected component in the traces). Nevertheless, as can be observed on Figs. 1b and1d, BF induces more redundant receptions of the packet and the maximum contention is much higher. Although redundancy can be viewed as a good feature as it increases the reliability of the dissemination, it also causes congestion and collisions on the wireless medium. In the case of VANETs with a 802.11p MAC, high contention is really an issue [START_REF] Stanica | Broadcast communication in vehicular ad-hoc network safety applications[END_REF]. FF seems thus preferable in the context of vehicular networks.

Then, the probabilistic schemes have medium performance with PFF being better than PF-0.5 (it corresponds to the PF scheme described in Section III with p = 0.5): they are not as good as BF and FF in terms of number of received packets and covered distance, but induce less redundancy and maximum contention than BF. Regarding the PF scheme, we only consider p = 0.5 here. Nevertheless, we can note that, if p grows the PF scheme performance will converge toward the BF scheme performance.

Finally, concerning the density-based scheme DF, it performs not very well in terms of number of receivers and covered distance. This can be explained as follows: if the current forwarder (the highest degree neighbor of the previous forwarder) is close to the previous one, its neighbors may have already received the message from the previous forwarder, so the algorithm converges before flooding the entire connected component. In terms of redundancy, DF offers similar performances as FF.

These results thus show, as it was the case for previous studies with less realistic mobility setup [START_REF] Giang | Message dissemination in vanet: protocols and performances[END_REF], that FF is the best scheme for dissemination in vehicular networks. Interestingly, we observe that this result holds for all the 4 considered scenarios.

2) Timing Dynamics: In this section we compare the timing dynamics of the considered dissemination schemes. We are notably interested in the speed of the information dissemination which is a tremendously important parameter for road safety applications. We consider only the results for the A6-h11 scenario because of the limited available space, but the results for other scenarios are qualitatively similar.

First, we observe on Fig. 2 that all the algorithms converge before 10 seconds. This delay can appear very large for safety applications. Nevertheless, as depicted in Fig. 1c, most of the schemes are able to cover a distance of 500 meters in less than one second, which might be good enough in function of the target application [START_REF] Hartenstein | VANET: vehicular applications and inter-networking technologies[END_REF].

Figs. 2a and 2c are very similar as they depict respectively the number of receivers and the backward distance covered by the packet in function of time after its first emission. We observe in both cases, a linear growth followed by an inflection for all the schemes. We note that for the schemes with the best performance for these two metrics, the inflection is more delayed and thus the information flooded farther. Concerning the number of packet copies in Fig. 2b, the growth is similar as the number of receivers and backward distance, but the curves for the different schemes are separated earlier; FF and DF highly outperforming the other schemes. As for the maximum contention, concerning the BF, PF-0.5 and PFF the curves show a peak at the beginning of the dissemination because a lot of nodes have never received the packet and thus a lot of retransmissions happen, and then the number decreases with time. For the DF and FF schemes, there is a small peak of value 2 at the beginning as 2 neighbors of the first sender forward the packet (one for each direction) and then only one neighbor forwards it at each step.

We can conclude that during the first second (corresponding to 5 steps of the algorithm in our case), all the schemes have approximately the same performance in terms of dissemination (number of receivers and distance covered). Nevertheless, FF and DF induce less contention and on the long run FF outperforms DF for other metrics. In the previous subsection, we commented the performance of dissemination algorithms without memory. We concluded that FF is the best scheme as it allows to reach a maximum of nodes with a minimum of contention induced. In this subsection, we investigate the possibility to add carry-andforward capability to FF. The idea is to let nodes which have no neighbors farther in the dissemination direction to keep the packet until one appears. It notably allows nodes at the edges of a connected component to wait for components to merge and thus spread farther the information instead of letting the algorithm converge prematurely. In this case, the convergence of the algorithm can thus be decided with a delay since first emission or distance from first emitter criterion. Fig. 3 depicts the comparison of performance of the carryand-forward version of FF with the non carry-and-forward schemes. We let run the simulation for 200 seconds in this case. Since the non carry-and-forward schemes converge before 10 seconds, their performance then remains constant. On Fig. 3a and3c, we observe that the carry-and-forward version of FF dissemination performance is at least as good as the best scheme of non carry-and-forward schemes during the first 10 seconds. After 10 seconds the number of receivers, and even more the covered distance, continue to increase. At first rapidly and then an inflection occurs as the dissemination packet reaches the edge of the simulated portion of the highway. After that, the packet is still disseminated to vehicles which continue to appear in the simulated trace. Concerning the number of packet copies which can be seen in Fig. 3b, for the first 10 seconds, it is similar to the FF and DF schemes as expected. Nevertheless, it then grows linearly with time. This is due to nodes at the edges of connected components which will receive the packet several times when new nodes are added to the component. It is especially the case with this trace, because nodes appear slowly at the beginning of the portion of the simulated highway. Thus every time a node appears, it is farther from the current carrier of the packet and it triggers a new transmission. Finally, on Fig. 3d, we can observe that the maximum contention remains very low when using the carryand-forward version of FF. Even in this configuration where cars appear one by one at the edge of the simulated portion of the highway, the number of packet copies and contention remains acceptable. We thus conclude that the addition of carry-and-forward capabilities to the FF scheme is desirable as it increases the performance of the scheme at a very low cost in terms of redundancy and contention.

VI. CONCLUSION AND FUTURE WORKS

In this paper, we investigated the performance of several classic dissemination schemes. The performance evaluation is done in a realistic mobility context using the Madrid Highway trace. In order to make the simulations of the dissemination schemes on the traces scalable, we developed an adapted simulation tool. The results show that the FF scheme outperforms the others. Interestingly, the performance of the DF scheme which has been expected close to the FF is in fact much smaller. Finally we show the benefit of adding carry-andforward capabilities to the best performing scheme: FF. It allows to further improve its performance at a very marginal Fig. 3: Comparison with a carry-and-forward scheme cost in terms of network load. In the future, we consider taking into account cars traveling in the opposite direction in the performance evaluation. We also plan to evaluate several carryand-forward approaches using FF in a more complex mobility environment such as urban mobility.

Fig. 1 :

 1 Fig. 1: General performance

Fig. 2 :

 2 Fig. 2: Timing dynamics

  (a) Number of receivers of the packet (b) Number of received packet copies (c) Backward distance traveled by the packet (d) Maximum number of contenders in a neighborhood

The paper was submitted in a 6 pages version and accepted in a 3 pages version. This is the long version. The final version can be found at: http://ieeexplore.ieee.org/document/7461486/?arnumber=7461486&tag=1

ACKNOWLEDGMENT

The authors would like to thanks Mohamed Omar Mazouz and Riadh Tahri for their role in the development of the simulator.