Jean-Louis Consalvi

Fengshan Liu

M Kashif

G Legros

Numerical study of soot formation in laminar coflow methane/air diffusion flames doped by n-heptane/toluene and isooctane/toluene blends

Keywords: Laminar coflow diffusion flame, Gasoline Surrogate, Toluene reference fuels, PAH-based soot model, Synergistic effects

The laminar coflow nitrogen-diluted methane/air diffusion flames doped with a small amount of n-heptane/toluene and iso-octane/toluene binary mixtures, investigated experimentally by Kashif et al. [Combust. Flame 162 (2015) 1840-18476], were simulated numerically by using a detailed reaction mechanism and a sectional polycyclic aromatic hydrocarbon (PAH)-based soot model. The numerical model provides results in reasonable qualitative agreement with the experimental data by using the same chemical mechanism, the same soot model, and the same set of constants employed successfully in a previous study to model the effects of nheptane/iso-octane doping, demonstrating that this overall model is promising to model soot formation in gasoline flames. Soot production is enhanced monotonically with increasing the toluene content in either the n-heptane/toluene or iso-octane/toluene doping fuel mixture. The increase in benzene and pyrene production displays a non-monotonic and synergistic response to the increase in toluene content. These numerical results are consistent with available experimental results as far as the trends in the effects of increasing the toluene content are concerned. Model results show that the dominant pathways responsible for the synergistic effects on benzene and pyrene production are respectively C 6 H 5 CH 3 (n-heptane) + H ↔ A1 (benzene) + CH 3 and A3-(C 14 H 9 ) + C 2 H 2 ↔ A4 (pyrene) + H.

Introduction

Emissions of soot produced during incomplete combustion from various combustion systems, such as internal combustion engines and biomass burning, into the atmosphere have become a serious environment and health concern worldwide [START_REF] Bond | Bounding the role of black carbon in the climate system: A scientific assessment[END_REF][START_REF] Krzyzanowski | Health effects of transport-related air pollution[END_REF]. The transportation sector is largely responsible for black carbon emissions in developed countries and most of the on-road vehicles are powered by gasoline engines. The newly developed gasoline direct injection (GDI) engines offer better fuel economy by about 5 to 15% as compared to the traditional port fuel injection (PFI) gasoline engines, which helps lower CO 2 emissions. Unfortunately, GDI engines emit much more soot due to the stratified combustion mode in such engines. It is therefore desirable to understand the effects of various physical and chemical factors on soot formation to reduce soot emissions. Although it is important to investigate the effects of these factors on soot emissions from GDI engines, it is challenging to isolate the influence of a particular factor, such as fuel chemistry, on soot formation, as the high sensitivity of soot emissions from a GDI engine to various engine parameters can mask the effect of this particular factor on soot formation. In order to circumvent this drawback, well-controlled laminar diffusion flames have been often used [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF][START_REF] Witkowski | Evaluation of the sooting properties of real fuels and their commonly used surrogates in a laminar co-flow diffusion flame[END_REF][START_REF] Kashif | Sooting tendencies of primary reference fuels in atmospheric laminar diffusion flames burning into vitiated air[END_REF][START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF][START_REF] Khosousi | Experimental and numerical study of soot formation in laminar coflow diffusion flames of gasoline/ethanol blends[END_REF].

Gasoline consists of hundreds of aliphatic and aromatic hydrocarbon species. In order to make CFD analysis of gasoline engine performance and pollutants emissions tractable, it is necessary to develop surrogate fuel models, i.e., a simple mixture of few hydrocarbon compounds formulated in such a way that it has similar physical, chemical, and combustion characteristics as the real fuel. The primary constituents of gasoline are n-heptane (nC 7 H 16 ), iso-octane (iC 8 H 18 ) and toluene (C 6 H 5 CH 3 ) [START_REF] Pitz | Development of an experimental database and chemical kinetic models for surrogate gasoline fuels[END_REF]. The binary mixtures of n-heptane and isooctane are referred to as the primary reference fuels (PRF) for octane ratings. A binary mixture of n-heptane and iso-octane corresponds to a particular octane number or octane rating. Most gasoline surrogates are composed of toluene (C 6 H 5 CH 3 ), iso-octane (i-C 8 H 18 ), and n-heptane (C 7 H 16 ), also known as toluene reference fuels (TRFs) [START_REF] Pitz | Development of an experimental database and chemical kinetic models for surrogate gasoline fuels[END_REF][START_REF] Gauthier | Shock tube determination of ignition delay times in full-blend and surrogate fuel mixtures[END_REF][START_REF] Andrae | Autoignition of toluene reference fuels at high pressures modeled with detailed chemical kinetics[END_REF][START_REF] Morgan | Mapping surrogate gasoline compositions into RON/MON space[END_REF][START_REF] Blanquart | Chemical mechanism for high temperature combustion of engine relevant fuels with emphasis on soot precursors[END_REF]. This has motivated the development of full and skeletal kinetic mechanisms for gasoline surrogates involving polycyclic aromatic hydrocarbons (PAHs), which are a prerequisite to model soot production [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF][START_REF] Blanquart | Chemical mechanism for high temperature combustion of engine relevant fuels with emphasis on soot precursors[END_REF][START_REF] Marchal | Modelling of aromatics and soot formation from large fuel molecules[END_REF][START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF].

Several experimental studies based on well-controlled laminar diffusion flames and aiming to understand soot formation in gasoline surrogates were reported. The sooting tendencies of gasoline, diesel, jet-A fuels and their surrogates were experimentally investigated in a laminar coflow heated methane/air diffusion flame at atmospheric pressure by doping methane with a small amount of vaporized liquid fuels (2200-2300 ppm) [START_REF] Witkowski | Evaluation of the sooting properties of real fuels and their commonly used surrogates in a laminar co-flow diffusion flame[END_REF]. Kashif et al. conducted similar experiments to characterize the fuel sooting propensity of binary mixtures of n-heptane and iso-octane, n-heptane and toluene, and iso-octane and toluene [START_REF] Kashif | Sooting tendencies of primary reference fuels in atmospheric laminar diffusion flames burning into vitiated air[END_REF][START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF]. They considered laminar CH 4 /air coflow diffusion flames doped with these vaporized binary mixtures. The sooting tendency of these binary mixtures was determined by considering the Yield Sooting Indices (YSI) based on n-hexane and benzene. The soot production tendency of PRF was found to increase linearly with the volume fraction of iso-octane [START_REF] Kashif | Sooting tendencies of primary reference fuels in atmospheric laminar diffusion flames burning into vitiated air[END_REF]. In contrast, the sooting tendency of n-heptane/toluene and iso-octane/toluene mixtures was found to increase in a non-linear and monotonic fashion with the toluene mole fraction [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF]. In other words, the peak soot volume fraction in these binary mixture doped flames was found to be higher than that from a simple linear-per-volume model. In addition, the experimental data showed a larger degree of non-linear behavior in iso-octane/toluene mixtures than that in n-heptane/toluene mixtures [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF].

The non-linear variation of the peak soot volume fraction with toluene content in the binary mixtures is consistent with the experimental study of Choi et al. [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF] conducted in nheptane/toluene and iso-octane/toluene mixtures in soot formation/soot oxidation counterflow diffusion flames. Moreover, the experimental results of Choi et al. [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF] showed that there exists a synergistic effect in PAH production in these mixtures, especially in iso-octane/toluene mixture, but not in soot formation. The synergistic effect is defined in a consistent manner with previous studies on soot and PAH formation and refers to the case when a mixture fuel (containing two hydrocarbons) can produce more PAH and/or soot as compared to the individual pure fuels [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF][START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF][START_REF] Hwang | Synergistic effect of ethylene-propane mixture on soot formation in laminar diffusion flames[END_REF][START_REF] Lee | Synergistic effect on soot formation in counterflow diffusion flames of ethylene-propane mixtures with benzene addition[END_REF][START_REF] Yoon | Synergistic effect of mixing dimethyl ether with methane, ethane, propane, and ethylene fuels on polycyclic aromatic hydrocarbon and soot formation[END_REF][START_REF] Joo | Sooting limit in counterflow diffusion flames of ethylene/propane fuels and implication to threshold soot index[END_REF].This study intends to gain fundamental understanding into the effects of fuel chemistry of a TRF gasoline surrogate on soot formation. In particular, the focus is on the chemical kinetic interactions between iso-octane and toluene and between nheptane and toluene with respect to PAH and soot formation. This study is complementary to the previous studies [START_REF] Kashif | Sooting tendencies of primary reference fuels in atmospheric laminar diffusion flames burning into vitiated air[END_REF][START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF], where soot formation in laminar coflow methane/air diffusion flames doped with iso-octane and n-heptane blends was conducted experimentally and numerically, to gain a more comprehensive understanding of soot formation in diffusion flames fueled with binary mixtures of TRF components.

Experiments

The laminar coflow diffusion flames studied experimentally by Kashif and coworkers [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF] are simulated. In these experiments, measurements of soot volume fraction distribution were conducted in laminar coflow nitrogen-diluted methane diffusion flames doped with binary mixtures of either n-heptane and toluene or iso-octane and toluene at atmospheric pressure.

The oxidizer is pure air. The composition of the binary mixture is identified by the volume fraction of toluene, X tol , which is varied between 0 (pure n-heptane or iso-octane) and 1 (pure toluene). The burner consists of two concentric steel tubes of 11 mm (for fuel) and 102-mm (for oxidizer) inner diameter, respectively. The carrier gas, with a composition of 50% methane/50% nitrogen by volume, and the dopant (binary mixtures of n-heptane/toluene or iso-octane/toluene) flow through the central fuel tube and their volumetric flow rates are kept at 400 cm 3 /min and 10.13 cm 3 /min (at 20°C and 1 atm), respectively. This leads to a mole fraction of the vaporized binary fuel mixture of 2.47×10 -2 in the fuel stream. The fuel line is maintained at about 423 K to prevent the condensation of the dopant.

The distribution of soot volume fraction was measured by a 2D light extinction measurement (LEM) technique at 645 nm. The value of the soot absorption refractive index function, E(m), corrected to take into account the contribution of scattering ( ( ) ( )

m E sa α + 1
, where α sa is the relative contribution of scattering to extinction) is taken equal to 0.28 for n-heptane and isooctane and 0.308 for toluene [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF]. For binary mixtures of n-heptane/toluene and isooctane/toluene, this value is assumed to vary linearly with X tol . It should be pointed out that varying the refraction index from 0.28 to 0.308 as X tol varies from 0 to 1 modifies the measurements of soot volume fraction by only about 10 % which significantly less than the experimental uncertainty related to the value of E(m) itself. Further details of the experimental setup and soot measurements using the LEM technique can be found in [START_REF] Kashif | Sooting tendencies of primary reference fuels in atmospheric laminar diffusion flames burning into vitiated air[END_REF][START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF].

Numerical model

The governing equations and the solution method have been given in previous studies [START_REF] Khosousi | Experimental and numerical study of soot formation in laminar coflow diffusion flames of gasoline/ethanol blends[END_REF][START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF][START_REF] Zhang | Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model[END_REF] and will be described only briefly. The numerical model solves the conservation equations for mass, momentum, gas-phase species mass fraction, and energy in the low Mach number formulation and in axisymmetric coordinates by using a finite volume method and the SIMPLE algorithm. Additional transport equations for sectional soot aggregate and primary particle number densities are solved to describe the soot particle dynamics [START_REF] Khosousi | Experimental and numerical study of soot formation in laminar coflow diffusion flames of gasoline/ethanol blends[END_REF]. The divergence of the radiative flux was computed by the discrete ordinate method coupled to a statistical narrow-band-correlated k-based wide-band model for properties of CO, CO 2 , and [START_REF] Liu | An efficient approach for the implementation of the SNB based correlated-k method and its evaluation[END_REF]. The spectral absorption coefficient of soot was obtained by Rayleigh's theory.

H 2 O
The reaction mechanism was assembled by merging the PAH formation and growth submechanism developed at DLR [START_REF] Slavinskaya | A modelling study of aromatic soot precursors formation in laminar methane and ethane flames[END_REF][START_REF] Dworkin | Application of an enhanced PAH growth model to soot formation in laminar coflow ethylene/air diffusion flame[END_REF] to the non-PAH part of a shortened version of the mechanism developed by Raj et al. [START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF] for gasoline surrogate fuel involving mixtures of nheptane, iso-octane, and toluene. The shortened version of Raj et al. mechanism was described in [START_REF] Consalvi | Numerical study of the effects of pressure on soot formation in laminar coflow n-heptane/air diffusion flames between 1 and 10 atm[END_REF] and the assembled hybrid mechanism for gasoline surrogate based on the DLR PAH sub-mechanism and the shortened Raj et al. non-PAH mechanism was described in detail in [START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF]. The final mechanism consists of 175 chemical species and 1175 reactions. The validation of this mechanism has been documented by Raj et al. [START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF]. The replacement of the original PAH sub-mechanism of Raj et al. [START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF] by that of DLR is not expected to alter its performance in flame modelling other than concentrations of PAHs, which are in general very low.

The fixed sectional soot model has been used and described in several previous studies, e.g. [START_REF] Zhang | Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model[END_REF]. The range of soot aggregate mass is divided into a number of discrete sections, each with a prescribed representative mass [START_REF] Zhang | Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model[END_REF]. In each section, all the soot aggregates are assumed to be identical and to be comprised of equally sized spherical primary particles and to have a fractal dimension of 1.8. The evolution of each section is governed by two transport equations for the number densities of soot aggregate and primary particle [START_REF] Zhang | Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model[END_REF]. The incipient soot particles are assumed to be spherical and belong to the first section. As in previous studies [START_REF] Khosousi | Experimental and numerical study of soot formation in laminar coflow diffusion flames of gasoline/ethanol blends[END_REF][START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF][START_REF] Zhang | Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model[END_REF][START_REF] Liu | An efficient approach for the implementation of the SNB based correlated-k method and its evaluation[END_REF], 35 sections were used with a spacing factor of 2.35. Coagulation terms are calculated using the same method given in Ref. [START_REF] Wen | Detailed kinetic modeling of carbonaceous nanoparticle inception and surface growth during the pyrolysis of C6H6 behind shock waves[END_REF]. The soot kinetics model is based on the work of Appel et al. [START_REF] Appel | Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons[END_REF]. Soot inception is assumed to be the result of collision of two pyrene molecules (A4). All the A4-A4 collision leads to the formation of a soot particle. Surface growth and oxidation are assumed to follow the HACA mechanism, with the model parameters taken as those prescribed in the original version [START_REF] Appel | Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons[END_REF], except the steric factor α.

Based on our recent study using the same assembled hybrid gasoline surrogate mechanism for modelling soot formation in laminar coflow methane/air diffusion flames doped with isooctane and n-heptane blends [START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF], the same steric factor of α = 0.1 was also used in the present calculations. Soot surface growth through PAH surface condensation was also taken into account and modelled as the condensation of A4 molecules colliding with soot aggregates [START_REF] Appel | Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons[END_REF]. A PAH condensation efficiency is introduced and assumed to be 0.5 [START_REF] Zhang | Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model[END_REF].

It should be pointed out that the sub-models for gas-phase chemistry and soot production and the set of model parameters are all the same as those considered in Ref. [START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF]. They were found to provide a reasonably good description of soot production in laminar coflow diffusion flames of methane doped with different blends of n-heptane and iso-octane. As a consequence, the present study presents additional more challenging cases in the validation of these models for predicting soot production in methane doped flames with other binary TRF components involving toluene.

Numerical calculations were performed according to the experimental conditions of Kashif et al. [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF] in a domain of 9.82 cm (z) × 4.71cm (r) using 210 (z) × 88 (r) control volumes. A nonuniform mesh was used with a resolution of 0.01 cm in the r-direction and 0.01375 cm in the z-direction near the burner exit. At the fuel inlet a parabolic velocity profile was considered with a mean stream velocity of 7.19 cm/s. At the oxidizer stream, the inlet temperature was set at 293 K and a uniform velocity of 12.32 cm/s was assigned.

Results and discussion

Figure 1 compares the computed temperature distributions in the n-heptane/toluene doped flames of different X tol . A similar behavior is also observed for iso-octane/toluene doped flames. Increasing the toluene percentage in the binary n-heptane/toluene or iso-octane/toluene doping mixture has only a minor effect on the total carbon flow rate, the carbon-to-hydrogen ratio, or the oxidizer-to-fuel mass ratio. As a consequence, the peak flame temperature, which occurs in the annular region low in the flame around z = 2 cm, and the stoichiometric flame height, defined as the axial location of the maximum temperature, are only slightly decreased and increased, respectively, as more toluene is added to the nheptane/toluene blend. The residence times of a fluid parcel to reach a given height in these flames are therefore expected to be nearly the same. Although the peak flame temperature is only slightly lowered (by 11 K), the temperatures in the centerline region around the flame tip are actually significantly reduced with increasing X tol from 0.2 to 0.8. This is explained by the enhanced radiative heat loss associated with the increase in soot loading with increasing X tol shown below. The distributions of computed soot volume fraction are compared with those of experimental measurement in both the n-heptane/toluene doped and iso-octane/toluene doped flames in Fig.

2. The experimental data (top plots in Fig. 2) show that, in both binary mixtures, the increase in the percentage of toluene in the mixture leads to a monotonic increase in the peak soot volume fraction i.e., in soot production. However, there is no synergistic effect in soot formation in these binary mixture doped flames. In addition, for a given value of X tol the isooctane/toluene doped flames, top right plots in Fig. 2, produce more soot than the nheptane/toluene doped flames, top left plots in Fig. 2. The higher soot volume fractions in the iso-octane/toluene doped flames are somewhat expected, since the sooting propensity of isooctane is known to be higher than that of n-heptane [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF][START_REF] Kashif | Sooting tendencies of primary reference fuels in atmospheric laminar diffusion flames burning into vitiated air[END_REF][START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF].The experimental results of Kashif et al. [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF] obtained in laminar co-flow diffusion flames, shown in the top panels of Fig. 2, are consistent with those of Choi et al. [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF] obtained in counterflow diffusion flames. The experimental soot volume fractions also suggest that the luminous flame height behaves differently from the stoichiometric flame height as X tol is increased. The increase in the luminous flame height with increasing X tol is related to the increase in soot loading, which requires more time to be fully oxidized. Overall, the trends in the numerical results shown in the bottom panels of Fig. 2 agree qualitatively well with the experiments, i.e., the peak soot concentration increases with increasing X tol and is higher in iso-octane/toluene doped flames than in n-heptane/toluene doped ones. The predicted "luminous flame" height increases also with X tol , though the rate of increase seems to be lower than that observed experimentally. The main deficiency in the predicted soot volume fraction distributions lies in the significant underestimation in the centreline region of the upper portion of the flames, which has been frequently observed in previous numerical studies of soot formation in laminar coflow diffusion flames [START_REF] Khosousi | Experimental and numerical study of soot formation in laminar coflow diffusion flames of gasoline/ethanol blends[END_REF][START_REF] Consalvi | Numerical study of soot formation in laminar coflow diffusion flames of methane doped with primary reference fuels[END_REF]. The predicted peak soot volume fraction occurs in the annular region of the flame wing, regardless of the toluene content in the doping mixture. On the other hand, The variation of the peak soot volume fraction with X tol is plotted in Fig. 3a. As mentioned previously, f S,max , increases monotonically with X tol in both the n-heptane/toluene and isooctane/toluene doped flames. The experimental variations are clearly non-linear. It appears that adding toluene to n-heptane or iso-octane produces more soot than expected from the simple linear-by-volume model [START_REF] Kashif | Sooting propensities of some gasoline surrogate fuels: combined effects of fuel blending and air vitiation[END_REF]. The computed f S,max follows a similar trend to the experiments, increasing monotonically with X tol and exhibiting a similar non-linear behaviour, albeit the overall variation with X tol is somewhat less significant than that of measurements, Fig. 3(a). A metric is defined to quantify the degree of non-linearity based on the relative departure from the linear behaviour, E r , between the actual values, φ a , and the values expected from the linear-by-volume model, φ l ( ( ) [ ]

) 0 ( ) 0 ( ) 1 ( = + × = - = = tol a tol tol a tol a tol l X X X X X φ φ φ φ ): ∑ = = - = 8 . 0 2 . 0 ) ( ) ( ) ( tol tol X X tol a tol l tol a r X X X E φ φ φ (1)
where φ is any quantity of interest, such as soot volume fraction or soot surface growth rate. E r is positive when the actual quantity is higher than the value from the linear-by-volume model, i.e., ( ) ( ) tol l tol a X X φ φ

>

. The larger the value of E r is, the stronger the non-linearity in φ is. The determination of E r in the case of the experimental data of peak soot volume fraction

shows that the non-linearity is stronger in iso-octane/toluene doped flames (E r = 1.07) than that in n-heptane/toluene doped flames (E r = 0.59). However, the predicted soot volume fractions show that the non-linearity of the peak soot volume fraction in the n-heptane/toluene doped flames (E r = 0.63) is higher than that in the iso-octane/toluene doped flames (E r = 0.37). It is noticed that this disagreement between the model and experiments merely reflects the fact that the predicted peak soot volume fraction in n-heptane/toluene doped flames has a larger departure from the linear increase with X tol than that in iso-octane/toluene doped flames shown in Fig. 3(a), while the opposite is true in the measurements. The departure from the linear variation with X tol , i.e., non-linearity, is a higher-order effect. What is much more important is the fact that the model correctly predicts the main features of the results shown in Fig. 3(a): the peak soot volume fractions increase with increasing X tol and are higher in isooctane/toluene doped flames than those in n-heptane/toluene doped flames, in agreement with the experimental measurements.

Although there are deficiencies in the current PAH/soot models, as reveled in the mismatch between the modeled and measured peak soot volume fraction locations and the different degrees of non-linearity in the peak soot volume fraction with respect to X tol variation, it is believed that the model is still capable of identifying the dominant pathways responsible for the enhanced production in PAH and soot with increasing X tol based on the overall qualitative agreement between the predicted and measured soot volume fractions shown in Figs. 2 and 3(a).

The mechanisms responsible of the synergistic effects are analysed at the locations where soot nucleation, PAH condensation, and surface growth through HACA rates peak. It is recognized that these peak soot formation rates occur at different locations in a given flame and even differ from those in the experiments. However, such analysis is followed as a convenient way to identify the main mechanisms responsible for the non-linear responses of soot nucleation and surface growth through HACA and PAH condensation. The maximum rates for inception, nucl ω ! , and PAH condensation, cond ω ! , occur along the flame centreline; however, the peak for surface growth by C 2 H 2 addition through HACA, SG ω ! , appears along the flame wing. The maximum rates for inception, PAH condensation, and surface growth through HACA are plotted in Figs. 3(b), 3(c) and 3(d), respectively. Model results show that the HACA surface growth process dominates the mass growth of soot particles. Figures 3(c)and 3(d) show that the peak HACA surface growth rates are approximately an order of magnitude higher than the peak PAH condensation rates, which are in turn higher than the peak inception rates, shown in Fig. 3(b), by a factor of about 3 to 4. The three soot formation rates are lower in the pure nheptane or pure iso-octane (X tol = 0) doped flames than those in the pure toluene (X tol = 1) doped ones. Between these two limits they increase monotonically with X tol , with the exception of the peak nucleation rate in iso-octane/toluene doped flames, which exhibits a synergistic effect and reaches a maximum at X tol = 0.6, Fig. 3(b). In addition, all the soot formation rates display a non-linear relationship with X tol This suggests that all the three modes of soot mass growth, especially the HACA surface growth which contributes for most of the soot production, are likely responsible for the non-linear behaviour of f S,max shown in Fig. 3(a).

The temperatures, T, were found to remain nearly constant at the locations where soot reaction rates peak as X tol increases. As a consequence, temperature plays a negligible role in how these soot formation rates vary with the toluene content in the binary doping fuel mixtures. In addition, the pathways responsible for the non-linear behaviour of soot formation rates were found to be the same in both n-heptane/toluene and iso-octane/toluene doped flames. As a consequence, to facilitate the understanding of results shown in Figs. 3(b), 3(c), and 3(d), the following discussion will be focused on only one blend (either nhepthane/toluene or iso-octane/toluene).

In this study soot nucleation is modelled by the collision between two pyrene molecules [25, 26] [26]:

[ ] T A nucl 2 4 ∝ ω ! (2)
where [A 4 ] is the molar concentration of pyrene. The variation of [A 4 ] at the location of the peak nucleation rate with X tol is also displayed in Fig. 3(b) in the iso-octane/toluene doped flames. It is evident the molar concentration of A 4 displays a synergistic effect with respect to increase in X tol and peaks at X tol = 0.6, which explains why nucl ω ! in iso-octane/toluene doped flames also peaks at X tol = 0.6.

The soot mass growth by PAH condensation is modelled by the collision between soot particles and pyrene molecules. As a consequence, it depends in a nonlinear fashion on temperature, pyrene concentration, and soot particle size. Figure 3(c) shows the variation of both [A 4 ] and the soot surface area density, A S , with X tol at the locations where the PAH condensation rates peak in n-heptane/toluene doped flames. Once again, [A 4 ] exhibits a synergistic effect and peaks at X tol = 0.2, Fig. 3(c),though [A 4 ] does not vary significantly with X tol at the location of peak PAH condensation rates. Clearly, the increase in the PAH condensation rate of soot growth with increasing X tol results from an increase in both [A 4 ] and A S . On the other hand, the soot surface area density A S increases almost linearly with X tol due to enhancement in both the soot number density, N, and the surface area per soot particle, A Sp , i.e., a direct consequence of increased soot loading as more toluene is added to the fuel mixture. The non-linear effects have been found to be more pronounced in cond ω ! (E r = 0.62 from Eq. ( 1)) than in [A 4 ] (E r = 0.44). At this point, it is useful to point out that the predicted synergistic effects in PAH concentration (here A 4 ), but not in soot volume fraction, and the stronger synergistic effect of A 4 in iso-octane/toluene doped flames than that in nheptane/toluene ones, are consistent with the findings of Choi et al. [START_REF] Choi | Soot formation characteristics of gasoline surrogate fuels in counterflow diffusion flames[END_REF] in their experimental investigation of counterflow diffusion flames. Such qualitative agreement supports the notion that the present reaction mechanism and soot model are capable of capturing the overall influence of toluene content in binary doping fuel mixtures of n-heptane/toluene and isooctane/toluene on PAH and soot formation.

The soot surface growth is modelled using the HACA mechanism [START_REF] Appel | Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons[END_REF]:

[ ] Csoot S SG A H C k χ ω 2 2 4 ∝ ! (3)
where k 4 is only a function of temperature [START_REF] Appel | Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons[END_REF]. [C 2 H 2 ] and χ Csoot are the molar concentration of acetylene and the number of de-hydrogenated sites per unit soot surface area (cm 2 ), given by:

( )

] [ ] [ ] [ ] [ ] [ ] [ 2 5 2 2 4 2 2 2 1 2 1 O H C O H H H Csoot OH H Csoot X k X k X k X k X k X k + + + + = - - - χ χ (4)
where [X i ] represents the molar concentration of species i. The expressions of the reaction rate constant k i can be found in Ref. [START_REF] Appel | Kinetic modeling of soot formation with detailed chemistry and physics: laminar premixed flames of C2 hydrocarbons[END_REF]. Model predictions have shown that [C 2 H 2 ] is almost constant at the locations of the peak HACA surface growth rate at different X tol . The nonlinear relationship followed by the maximum value of SG ω ! as a function of X tol can then only be due to A S and/or χ Csoot . Their variations with X tol at the location where SG ω ! is maximum are plotted in Fig. 3(d) in n-heptane/toluene doped flames. The soot surface area density A S increases monotonically and in a non-linear manner with X tol . On the other hand, χ Csoot decreases nearly linearly with X tol due primarily to a decrease in H radicals (not shown). It was found that the non-linearity in the product A S × χ Csoot (E r = 0.60) is slightly stronger than that in A S (E r = 0.51).

The results discussed above reveal how a variation in the toluene content in the binary doping fuel mixture affects the soot formation processes. Figure 4 shows the maximum molar concentrations of benzene (A 1 ), naphthalene (A 2 ), phenanthrene (A 3 ), and pyrene (A 4 ) as a function of X tol in the iso-octane/toluene doped flames. The same trends can also be observed for those in the n-heptane/toluene doped flames. It is clear that the concentration of A 4 displays a synergistic effect and peaks at X tol = 0. The variation of the reaction rates of all the reactions leading to the production of A 1 , A 2 , A 3 , and A 4 as a function of X tol has been analyzed. The following reaction

3 1 8 7 CH A H H C + ↔ + (R0)
was found to be responsible for the synergistic effects for A 1 shown in Fig. 4. Fig. 5(a) shows the maximum normalized reaction rate in the case of the iso-octane/toluene doped flames as a function of X tol as well as the corresponding normalized molar concentrations for the species involved in this reaction (R0). The same behaviour also occurs in the n-heptane/toluene flames. As X tol increases, the molar concentration of toluene (C 7 H 8 ) increases monotonically, whereas that of H decreases monotonically. These opposite evolutions are consistent with those reported by Raj et al. [START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF] for the soot formation and soot formation/oxidation laminar counterflow diffusion flames and are responsible for the synergistic effects observed for A 1 .

The maximum reaction rate of R0 displays a synergistic effect and peaks at X tol = 0.8, Fig.

5(a).

The formation of A 2 is dominated by the following three reactions:

2C 5 H 5 ↔ A 2 + 2H (R1) A 2 -+ H ↔ A 2 (R2) C 10 H 9 + H ↔ A 2 +H 2 (R3)
The last reaction, R3, was found to exhibit a strong synergistic effect. The production of A 3 is mainly due to the following reactions: Normalized reaction rates and species concentrations for the main reactions responsible for the production of: (a) A 1 , (b) A 2 , (c) A 3 , and (d) A 4 . These results are for the iso-octane/toluene doped flames.

A 2 R 5 (biphenyl) + C 2 H 2 → A 3 (R4) A 2 + C 4 H 2 → A 3 (R5) A 3 -+ H ↔ A 3 (R6)

Concluding remarks

Axisymmetric laminar coflow nitrogen-diluted methane diffusion flames doped with binary mixtures of n-heptane/toluene and iso-octane/toluene were simulated using a fairly detailed reaction mechanism for gasoline surrogate and a PAH-based sectional soot model to gain insights into the influence of toluene content on soot formation. The following conclusions can be drawn:

(1) The numerical model predicts that the peak soot volume fractions in both the nheptane/toluene and iso-octane/toluene doped flames increase with increasing the toluene content in these binary doping mixtures and more soot is produced in iso-octane/toluene doped flames. These results are in qualitative agreement with experimental measurements and were obtained by using the same chemical mechanism, the same soot model, and the same set of soot model constants used in a previous study to model soot formation in n-heptane/isooctane doped methane diffusion flames. This model performs fairly consistent in modelling soot formation in laminar methane diffusion flames doped with any two components of the toluene reference fuels for gasoline surrogate using the hybrid reaction mechanism.

(2) The model is capable of reproducing the experimentally observed phenomena of the nonlinear increase in soot formation and the synergistic effects in benzene and pyrene production with increasing the toluene content in both the n-heptane/toluene and iso-octane/toluene doped laminar methane diffusion flames.

(

Figure 1 .

 1 Figure 1. Distributions of temperature (in K) in n-heptane/toluene doped flames for different

Figure 2 .

 2 Figure 2. Measured (top row) and computed (bottom row) distributions of soot volume

ωωωFigure 3 .

 3 Figure 3. Variations of the peak soot volume fraction and other soot related quantities with X tol : (a) the measured and predicted peak soot volume fraction, (b) the computed peak nucleation rate and A4 molar concentration, (c) the computed peak condensation rate, A4 molar concentration, and soot surface area density, and (d) the computed peak HACA surface growth rates, soot surface area density, and the number of de-hydrogenated sites.

6 .

 6 It should be pointed out that the variation of the maximum [A 4 ], Fig 4, is consistent with that observed at the location of the peak nucleation rate shown in Fig. 3(b). The variations of A 1 and A 4 concentrations with X tol display a synergistic effect, but not those of A 2 and A 3 , in qualitative agreement with the experimental observations of Choi et al. made in soot formation and soot formation oxidation counterflow diffusion flames [3].

Figure 4 .

 4 Figure 4. Variations of the peak molar concentrations of A 1 , A 2 , A 3 , and A 4 with X tol in isooctane/toluene doped flames.

Figures 5 (Figure 5 .

 55 Figures 5(b), 5(c) and5(d) show the variation of the maximum normalized reaction rates of R3, R5 and R7 and the corresponding molar concentrations of the species involved in these reactions with X tol for the iso-octane/toluene doped flames. The results show that, consistently with the findings of Raj et al.[START_REF] Raj | A reaction mechanism for gasoline surrogate fuels for large polycyclic aromatic hydrocarbons[END_REF], the synergistic effects are likely to occur in the reactions in which the concentrations of the two reactants evolve oppositely with X tol , see R0 and R7 for example. It is interesting to point out that A 2 does not display a synergistic effect, Fig.4, even though there is a strong synergistic effect in the reaction rate R3 shown in Fig.5(b).

)( 4 ) 8 1 3 CFigure 1 .

 4831 Figure 1. Distributions of temperature in n-heptane/toluene doped flames for different X tol .

Figure 2 .

 2 Figure 2. Measured (top row) and computed (bottom row) distributions of soot volume

Figure 3 .

 3 Figure 3. Variations of the peak soot volume fractions and other soot related quantities with

Figure 4 .

 4 Figure 4. Variations of the peak molar concentration of A 1 , A 2 , A 3 , and A 4 with X tol in iso-

Figure 5 .

 5 Figure 5. Normalized reaction rates and species concentration for the reactions responsible of


Khanh-Hung H Tran
email: khtran@u-paris10.fr

P Guibert

Céline Morin

Jérôme Bonnety

Stoyan Pounkin

Guillaume Legros

Temperature measurements in a rapid compression machine using anisole planar laser-induced fluorescence

Keywords: temperature measurement, planar laser-induced fluorescence, rapid compression machine, particle image velocimetry, anisole, temperature heterogeneities

Introduction

The present study describes temperature measurements in a rapid compression machine (RCM) using anisole as tracer for PLIF technique. This device is well suited to the study of combustion processes under similar conditions to those experienced in an IC engine, enabling the measurements of fuel ignition delays and the validation of kinetics mechanisms [START_REF] Minetti | A rapid compression machine investigation of oxidation and auto-ignition of n-heptane measurements and modelling[END_REF], [START_REF] Donovan | Demonstration of a free-piston rapid compression facility for the study of high temperature combustion phenomena[END_REF] . It is thus essential to characterize the RCM temperature fields, using a non-intrusive optical technique such as PLIF. Clarkson et al. [START_REF] Clarkson | Temperature fields during the development of combustion in a Rapid Combustion Machine[END_REF] used PLIF to measure temperature fields in an RCM, with an acetone tracer under non-reactive conditions, and with DTBP (di-tert-butyl peroxide) decomposition, which forms acetone under reactive conditions. As their measurements were not calibrated, no quantitative data was reported. These authors observed a spatially non-uniform temperature field following compression, with a cold core. This consequence may affect chemical development and ignition delay measurements. The measurement of temperature distributions in an RCM using acetone PLIF, at different times along compression, was proposed by Mittal and Sung [START_REF] Mittal | Aerodynamics inside a Rapid Compression Machine[END_REF] (2006). Thurber et al. [START_REF] Thurber | Temperature imaging with single and dual wavelength acetone planar laser-induced fluorescence[END_REF] inferred temperature fields from the fluorescence signal by accounting for absorption phenomena and temperature effects. In-cylinder temperature imaging was also applied to the study of an IC engine, using toluene fluorescence at a single excitation wavelength and twocolour detection [START_REF] Luong | Toluene laser-induced fluorescence for in-cylinder temperature imaging in internal combustion engines[END_REF] , and using 3-pentanone [START_REF] Modica | 3-Pentanone LIF at elevated temperatures and pressures: measurements and modeling[END_REF], [START_REF] Rothamer | Simultaneous imaging of exhaust gas residuals and temperature during HCCI combustion[END_REF]. Löffler et al. [START_REF] Löffler | Acetone laser-induced fluorescence behavior for the simultaneous quantification of temperature and residual gas distribution in fired sparkignition engines[END_REF] used acetone with the dual excitation wavelength technique, at 308/277 nm and 308/248 nm. Similar approaches have been described in the literature. Strozzi et al. [START_REF] Strozzi | Characterization of a two-dimensional temperature field within a rapide compression machine using a toluene planar laser-induced fluorescence imaging technique[END_REF] used PLIF to characterize a two-dimensional temperature field in an RCM, with a single-excitation, two-colour detection technique, relying on the temperature dependence of toluene fluorescence established by Koban et al. [START_REF] Koban | Absorption and fluorescence of toluene vapor at elevated temperatures[END_REF], at atmospheric pressure and for the temperature range 300-950 K. These authors obtained temperature fields that clearly revealed a distorted structure, in particular at the boundary between the hot and cold zones. In-cylinder temperature imaging using a shock tube or spray has also been applied to the study of IC engines. Kaiser et al. [START_REF] Kaiser | Thermal stratification in an internal combustion engine due to wall heat transfer measured by laser-induced fluorescence[END_REF] studied the LIF imaging of toluene at an excitation wavelength of 248 nm, to determine the spatial fluctuations of gas temperature in an optically accessible engine. These fluctuations are due to wall heat-transfer during the compression stroke in a homogeneous mixture. Löffler et al. [START_REF] Löffler | Acetone laser-induced fluorescence behavior for the simultaneous quantification of temperature and residual gas distribution in fired sparkignition engines[END_REF] presented calibration results from acetone fluorescence signal intensities in nitrogen, air, and an exhaust gas-air mixture, at temperatures ranging from 298 to 748 K and pressures ranging from 0.02 to 2 MPa, using 308 nm and 248 nm excitation wavelengths. From this data, inferred from single-shot images, temperature and exhaust gas concentrations in a spark ignition engine were accurately determined. The computed accuracy of the calibration data was 5.6%, and 3.2% for the signal measured under single wavelength excitation and for the signal ratio, respectively. The uncertainties in the measurements, made with an exhaust gas recirculation / air mixture, were slightly higher, as a consequence of small uncertainties in the mixing ratio: the errors were 6.9% and 5.1% for single wavelength excitation, and for the signal ratio, respectively. Yoo et al. [START_REF] Yoo | Planar laser-induced fluorescence imaging in shock tube flows[END_REF] used the PLIF technique to image temperature fields close to the walls of a shock tube. Two types of near-wall flow were considered: the sidewall thermal boundary layer behind an incident shock wave, and the end-wall thermal boundary layer behind a reflected shock wave. These thin layers were imaged at a high spatial resolution (15µm/pixel), using fused silica walls and near-UV bandpass filters to accurately measure the fluorescence signals with minimal interference from scattering and reflection effects at the wall surfaces. Nitrogen, hydrogen or argon gases were premixed with 1-12% toluene, with the LIF tracer. The measured pressures and temperatures ranged between 0.01 and 0.8 bar, and 293 and 600 K, respectively. The temperature field measurements were found to be in good agreement with the theoretical values calculated using 2-D laminar boundary layer and 1-D heat diffusion equations, respectively. In addition, PLIF images were taken at various times, behind incident and reflected shock waves, in order to observe the development of the sidewall and end-wall layers, respectively. This demonstrated that this diagnostic strategy can be used to accurately measure temperatures at distances as close as 60 µm to the wall. The temperature measurement accuracy within the sidewall boundary layer is approximately ± 5K. Cundy et al. [START_REF] Cundy | Gas-phase toluene LIF temperature imaging near surfaces at 10 kHz[END_REF] developed a high-speed transient temperature measurement technique using high-speed toluene LIF. They used single wavelength excitation at 266 nm, combined with detection within two spectral regions, yielding a calibrated, temperature-dependent signal ratio at temperatures between 373 and 873 K. These experiments were carried out in a wellstabilized heated nitrogen jet, to avoid signal reduction due to collisional quenching by oxygen.

Although the sensitivity of the diagnostics suggested that the accuracy should increase with increasing temperature, the fluorescence signal decreased strongly, and the associated noise levels were higher with increasing temperature, such that the error actually increased. The one standard deviation errors were computed as ± 8 and ± 25 K, at 373 K and 773 K, respectively.

The selection of the tracer is a crucial parameter of the LIF implementation. Among the potential tracers, small aromatic molecules, such as toluene (Luong, Koban, & Schulz, Novel strategies for imaging temperature distribution using toluene LIF, 2006) and naphthalene (Kaiser & Long, Quantitative planar laser-induced fluorescence of naphtalenes as fuel tracers, 2005), (Hirasawa, Kaneba, Kamata, Muraoka, & Nakamura, 2007), are attractive [START_REF] Schulz | Tracer-LIF diagnostics: quantitative measurements of fuel concentration, temperature and fuel/air ratio in pratical combustion systems[END_REF] due to their high-fluorescence quantum yield (FQY). However, anisole can be a potential candidate for use as fluorescent tracer for gas-phase imaging diagnostics. Due especially to its high FQY, its large absorption crosssection, and its Stokes shift, anisole can deliver a signal intensity up to 100 times stronger than conventional tracers such as toluene. This makes anisole a novel tracer alternative.

In the present study, quantitative temperature imaging was conducted in an RCM for the first time using the single excitation two-colour detection technique based on anisole fluorescence, including a prior calibration process over the range of experimental conditions met in the RCM. The experimental facilities and the image processing procedures are first outlined. A selection of 2D temperature fields are then combined with the velocity fields measured inside the combustion chamber to highlight the key role of the hydrodynamic features on the thermal conditions met in a RCM.

Experimental set-up

PLIF Model overview

The planar laser-induced fluorescence (PLIF) technique is well suited to this type of measurement, due to its sensitivity and ability to provide two-dimensional measurements with a high spatial resolution. The global expression governing the fluorescence signal S f depends on terms that quantify the sensitivity of the signal to the pressure, temperature, composition of the gas mixture, optical matching of the absorption cross-section, and fluorescence quantum yield [START_REF] Thurber | Temperature imaging with single and dual wavelength acetone planar laser-induced fluorescence[END_REF]:

f o p t c E X P S dV ( , T) ( , T, P, X) hc kT ⎡ ⎤ = η σ λ Φ λ ⎢ ⎥ ⎣ ⎦ λ ( 1
)
where E is the laser fluence, (hc/λ) is the energy of a photon at the excitation wavelength λ, η opt is the overall efficiency of the collection optics, k is the Boltzmann constant, and dV c is the collection volume. The terms characterizing the tracer are σ, its molecular absorption crosssection, and Φ, its fluorescence quantum yield. The tracer mole fraction X, total pressure P, and temperature T define the experimental thermodynamic conditions.

In the case of a gaseous single phase, as described in the present study, three different LIF-based temperature measurement techniques can be used. The first of these is a single-excitation, single colour detection approach. It requires a homogeneous distribution of a tracer together with the use of a known reference temperature inside the volume probed. The second technique, referred to as single-excitation, two-colour detection, provides with temperature measurements in the case of an inhomogeneous tracer distribution. Finally, the third technique involves the use of a dualexcitation wavelength and two-colour detection. The latter approach allows both concentration and temperature values to be measured. The selection of one of the above techniques is driven by the thermodynamic quantities to be studied, depending on the selected tracer and the specific experimental conditions. In the current study, the single-excitation, two-colour detection technique was chosen, since it allows the temperature to be measured in a non-homogeneous seeded flow, provided the pressure is known.

In the general case, the function ratio S f * of the fluorescence signals detected in the two spectral bands Δλ 1 and Δλ 2 is expressed by:

𝑆 ! * = ! ! ! !"# ! ! ! !"#$%"! ! ! ,! ! !"#$%"! ! ! ,!,!,! !" ! !!"!! ! !"#! ! ! ! !"# ! ! ! !"#$%"! ! ! ,! ! !"#$%"! ! ! ,!,!,! !" ! !!"!! ! !"#! (2)
The sensitivity of this ratio depends on the selected spectral wavelength bands Δλ 1 and Δλ 2 , and on the selected temperature measurement technique. In the case of the single-excitation, twocolour detection technique under inhomogeneous conditions, the expression S f * can be simplified at a given pressure, as follows:

𝑆 ! * = ! !"#! ! !,! ! !,!,!,! !" ! !!"!! ! !"#! ! !"#! ! !,! ! !,!,!,! !" ! !!"!! ! !"#! = ! ! !! ! (!,!) ! ! !! ! (!,!) ∝ ! !! ! ! ! !! ! ! = 𝑓(𝑇) (3)

Anisole fluorescence calibration set-up

The fluorescence of a vapour phase anisole (C 6 H 5 OCH 3 ), isooctane (C 8 H 18 ) blend was investigated in an optically accessible, high pressure, high temperature (HP-HT) chamber (cf. Figure 1), over temperature and pressure ranges of 473-823 K and 0.2-4 MPa, respectively, using a 266 nm excitation wavelength. The HP-HT chamber is a cylinder (height H= 200 mm, external diameter Ø ext = 170 mm, internal diameter Ø int = 70 mm, inner volume V in = 7.6969 × 10 -4 m 3 ), heated and maintained at constant temperature by eight 230 W electrical resistances. A system comprising three thermocouples (accuracy: ± 2.3 K) located inside the cell allows the temperature to be regulated, and ensures the cell temperature homogeneity. The maximum operating pressure and temperature of the HP-HT chamber are 5 MPa and 873 K, respectively. 1 mL (accuracy: ± 1%) of a liquid fuel/tracer mixture is injected into the chamber, via a syringe / capillary tube system, and is then vaporized by means of a vacuum pump as the (temperature-dependent) tracer vapour pressure is reached (anisole vapour pressure of 1360 Pa at 293 K). The experimental chamber is pressurized with different bath gases (Ar, N 2 , CO 2 , air and gas mixtures) via the admission circuit, which is equipped with pressure sensors (accuracy ± 1%) and valves.

Figure 1: High pressure, high temperature chamber and optical assembly for spectrometer or 2 cameras setup

The optical system comprises a frequency-quadrupled, pulsed Nd:Yag laser (266 nm, 90 mJ/pulse at 10 Hz) for the fluorescence measurements. The laser beam is not focused, and has a diameter of 10 mm diameter and a pulse duration of 9 ns. The fluctuations in laser pulse duration are 3-4 ns, with an energy stability of ± 8%. The laser beam passes through the cell and is collected by a beam trap and a flux-meter, allowing the time-dependent fluctuations in laser energy and intensity to be determined. The fluorescence signal is collected at a 90° angle with respect to the incident beam, by a spectrometer (focal length: 500 mm, entrance slit width: 500 µm, diffraction grating: 150 grooves per mm, providing a resolution of 350 nm), equipped with an ICCD camera (1024 x 256 pixels², 16 bytes of dynamic range, 100 ns exposure time) and a UV lens (focal length = 78 mm, fratio = 3.8 and spectral resolution from 230 to 800 nm). Bandpass filters (Δλ 1 = 386 ± 11.5 nm and Δλ 2 = 292 ± 13.5 nm) are located in front of the measurement devices in order to calibrate the LIF temperature measurement. The laser intensity and pulse frequency are adjusted to 90 mJ/pulse and 10 Hz, in order to avoid saturation, and to remain within the fluorescence linearity regime. The fluorescence tracer concentration is adjusted to 360 µl of 1% anisole in an isooctane solution, corresponding to 2.58 10 16 molecule.cm -3 of anisole. This concentration makes re-absorption and self-quenching phenomena negligible.

Temperature measurement set-up

An experimental investigation of the turbulence effect on the combustion propagation in a rapid compression machine has been previously conducted in a RCM [START_REF] Guibert | An experimental investigation of the turbulence effect on the combustion propagation in a rapide compression machine[END_REF]. This machine can be separated into four main modules: the hydraulic system, a single piston moving inside a precompression chamber (diameter: 91.5 mm), the combustion chamber (diameter: 40 mm, height: 40 mm), and the acquisition and control system. Test gas mixtures are loaded into the precompression chamber, and then heated and maintained at 373 K by three resistors. The entire fast compression process is powered by the hydraulic system, which especially controls the final position of the piston and ensures that it is held without any rebound. The compression ratio is equal to 15, and the compression time is 29 ms. The stroke can be varied between 150 and 160 mm, and the piston can reach a velocity of 8 m.s -1 . The wall of the cylindrical combustion chamber is made of quartz glass, allowing extensive optical access. The optical system shown in Figure 2 comprises a frequency-quadrupled, pulsed Nd:YAG laser (266 nm, 110 mW, 7.6 mW/mm²). In the case of PLIF measurements in the RCM, two intensified ICCD cameras (with UV objectives and two bandpass filters centred at 292 nm and 386 nm), aligned perpendicularly to the laser beam (48 mm height, 0.2 mm thickness), are used to collect the fluorescence images. A computer connected to a delay generator is used to synchronize the laser pulse, the exposure of the ICCD cameras, the beginning of the compression cycle, and the image acquisition system.

Figure 2: Top view of the optical system for PLIF temperature measurements in the RCM.

Different bath gases are chosen in order to adjust the thermodynamic conditions at the end of compression : argon (Ar) and nitrogen (N 2 ) as inert gases, and carbon dioxide (CO 2 ) as a gas representing the exhaust gases recirculation in IC engines. Before compression, the mixture's temperature and pressure are 363 K and 0.35 bar, respectively. In order to characterize the temperature fields inside the RCM just before self-ignition, it was chosen to work with inert gases. The experimental conditions are equivalent to a reactive mixture (n-heptane C 7 H 16 , iso-octane C 8 H 18 , or hydrogen H 2 in air), in terms of pressure at the compression end, temporal variations of the pressure, and specific heat capacity. The experimental conditions are summarized in Table 1. As shown in Figure 3, there are only small differences in pressure variation for the two types of mixture (inert and reactive), up to the time of auto-ignition.

Results

Calibration of the single excitation two-colour detection technique

Faust et al. [START_REF] Faust | Photo-physical properties of anisole: temperature, pressure and bath gas composition dependence of fluorescence spectra and fluorescence lifetimes of toluene and naphtalene[END_REF] [21] compared the photo-physical properties of toluene, naphthalene, and anisole in terms of temperature, pressure, and bath gas composition dependencies of fluorescence spectra and lifetimes. These authors showed that, with 266 nm excitation the fluorescence spectrum of anisole at room temperature is red-shifted by 10-15 nm with respect to that of toluene. This allows the Rayleigh elastically scattered laser light to be discriminated from the fluorescence signal. As compared to the toluene characteristics, anisole exhibits a FQY that is 63% larger and an absorption cross section about 50 times higher. These features lead to significantly improve the fluorescence signal magnitude under identical conditions. Naphthalene can be used as an alternative to toluene [START_REF] Orain | Fluorescence spectroscopy of naphthalene at high temperatures and pressures : implications for fuel concentration measurements[END_REF]. However naphtalene is hampered by three factors, i.e., its very weak vapour pressure (0.024 mbar at 293 K) leading to low concentration in the gas-phase, therefore low LIF signal intensities at low temperature, its solid state at room temperature leading to a re-condensation at high pressure, and its carcinogenic properties restricting its application in flow and combustion studies at atmospheric pressure.

Anisole is a cheap, non-toxic, non-carcinogenic liquid with a vapour pressure of 3.6 mbar at room temperature. Actually, Faust and al. suggested that the anisole behaviour is suitable for quantitative imaging diagnostics of temperature and oxygen over a wide range of temperature and pressure.

Anisole was investigated by Tran et al. (Tran, Morin, Kühni, & Guibert, 2014) as a tracer due to the high sensitivity of the fluorescence signal to temperature, the redshift being an increasing function of temperature. Furthermore, anisole is shown to be soluble in primary fuels at comparable vapour pressures. The calibration curves reported by Tran et al. [START_REF] Tran | Fluorescence spectroscopy of anisole at elevated temperatures and pressures[END_REF] were obtained from LIF experiments carried out in the HP-HT cell. Different inert bath gases (argon, nitrogen, carbon dioxide, air and mixtures of these gases) were investigated over temperature and pressure ranging from 473 to 823 K, and from 0.2 to 4 MPa, respectively. For any given set of temperature and pressure conditions, the fluorescence signals were averaged over 900 emission spectra. Anisole exhibits a fluorescence emission band between 250-600 nm, with a peak centred at 296 nm, as shown in Figure 4. In nitrogen, the fluorescence intensity decreases strongly, by a factor of 50, when the temperature increases from 473 to 823 K at a pressure of 1.2 MPa, due to the highly non-radiative decay rate of its excited state at high temperatures. This observation further supports the selection of anisole as a tracer for LIF temperature measurements within the aforementioned temperature range. Furthermore, as shown in Figure 4, the redshift of 2 nm per 100 K observed in the vicinity of the fluorescence peak represents an advantage for the singleexcitation, two-colour detection technique using anisole LIF. Figure 5 presents the combined influence of temperature and pressure on anisole fluorescence quantum yield, when it is excited at 266 nm in nitrogen. The fluorescence signal globally decreases continuously with increasing pressure, at a given temperature. For the case of temperature measurements made using the single-excitation, two-colour detection technique, a specific study was focused on the technique's sensitivity, as a function of the selected spectral bands Δλ 1 and Δλ 2 (cf. Eq. ( 3)). The aim was to select the best pair of spectral bands, in order to achieve the strongest fluorescence signal ratio and signal-to-noise ratio (SNR). For the selected spectral pair, i.e. Δλ 1 = 374-399 nm and Δλ 2 = 300-325 nm, the fluorescence ratio increases by a factor of seven over the temperature range considered, and the SNR ratio of the integration spectral band Δλ 1 is 2.33 [START_REF] Tran | Fluorescence spectroscopy of anisole at elevated temperatures and pressures[END_REF]. The best commercial bandpass filters matching these values are centred at 292 nm, with a spectral width of 27 nm, and at 386 nm, with a spectral width of 23 nm, respectively. These filters were used in the optical collection system, for PLIF temperature measurements in the RCM (cf. Figure 1). As shown in Figure 6, the fluorescence signal ratio in nitrogen increases over the range of temperature studied, by factors of 11.4 and 15, at 0. The experimental fluorescence signal ratio correlations, inferred from measurements performed in three different bath gases (N 2 , CO 2 , Ar), are reported in Table 2. Due to the shape of the ratio as a function of temperature (see Fig. 6(a)), the ratio is expected to be driven by the following phenomenological trend: S f * = A(P) exp (B(P) T)

Considering the smooth evolution of the fluorescence signal ratio with temperature at any pressure (see Figure 6 (b)), the above expression is expected to deliver fair evaluations of the ratio for any set of temperature and pressure within the range of calibrating data without any further uncertainties. Above 900 K, the calibration procedure could not be conducted as the HT-HP chamber starts being damaged under thermal effect above this temperature. However, the extrapolation following Eq.() is also believed to be acceptable provided that the temperature measured does not exceed the anisole pyrolysis one. This pyrolysis temperature is estimated at about 1000 K in the HT-HP conditions, i.e. at long and static residence time of anisole. Indeed, Faust et al. [START_REF] Faust | Photo-physical properties of anisole: temperature, pressure and bath gas composition dependence of fluorescence spectra and fluorescence lifetimes of toluene and naphtalene[END_REF] observed that at temperatures beyond 1000 K significant pyrolysis may occur due to long residence time of the gas mixture in the vicinity of the heated walls.

When the experimental (P, T) calibration data is processed to deliver the matrix, in which the Zaxis corresponds to the fluorescence ratio, it is then possible to determine the interpolated value of the fluorescence signal ratio at each mesh node of a PLIF image obtained in the RCM.

𝑆 ! * = ! ! !! ! (!,!) ! ! !! ! (!,!)
= 𝑓(𝑇) for anisole, at different pressures and using different bath gases. The chosen spectral bands are Δλ 1 = 386 ± 11.5 nm and Δλ 2 = 292 ± 13.5 nm. The uncertainty in the RCM temperature measurement is estimated to lie between 6.8% and 8.9% for the explored range of temperature and pressure, i.e., 473-823 K and 0.2-4 MPa. This uncertainty takes into account the errors in the HP-HT cell calibration measurements, as well as the RCM pressure measurements.

The parameter range over which this methodology can be applied is constrained by several phenomena. First, even if the spectral signal ratio has a significant value, the temperaturedependent fluorescence SNR must be sufficiently high. We arbitrarily set the detection limit at an SNR equal to 1.1 for the 386 nm filter, and 2.0 for the 292 nm filter. Another limitation is related to the anisole pyrolysis. In order to check that no anisole pyrolysis or photo-physical decomposition occurred during the experiments (especially at high temperatures), the anisole fluorescence spectrum was measured between 473 K and 823 K, over a long period of time. The magnitude and shape of the anisole fluorescence spectrum changed after approximately 10 minutes at the lowest temperature, and approximately 8 minutes at the highest temperature. The experimental process, starting with injection of the solution, and ending with the acquisition of data, does not exceed 3 min. Over this period of time, any change in the anisole fluorescence spectrum would have been observed. It can thus be concluded that there was no degradation of the anisole during the experiments. Further detailed discussion about the anisole thermal decomposition and its initial pyrolysis can be found in [START_REF] Scheer | Radical chemistry in the thermal decomposition of anisole and deuterated anisoles: an investigation of aromatic growth[END_REF], [START_REF] Pecullan | Pyrolysis and oxydation of anisole near 1000 K[END_REF].

Temperature distributions inside the RCM

Using the image processing steps, thermal fields were computed at different times between TDC and 40 ms after TDC, under different experimental conditions (cf. Table 1). Figure 7 shows the temperature maps and the associated histograms computed at TDC, TDC + 10 ms, and TDC + 30 ms. The inert mixture is here equivalent to the n-heptane reactive mixture (see case 1 in Table 1). The inert mixture is here equivalent to the n-heptane reactive mixture (charge of 180 mol/m 3 and equivalence ratio of 0.8 as reported in Table 1). The adiabatic temperature computed by the 0D model at TDC is T cal = 667 K.

TDC TDC + 10 ms TDC + 30 ms

The temperature fields can be seen to be inhomogeneous. At TDC, the hot zones (approximately 685 K) are located at the top of the chamber, and cool zones close to the walls exhibit temperatures ranged between 615 and 630 K. The kernels of the vortices located in both lower corners (see the velocity fields in Figure 10) can be observed, exhibiting temperatures ranging between 615 and 630 K. After TDC, the cold zones spread over from the lateral walls and from the bottom of the cylinder, amplifying the temperature heterogeneities. When the cold zones are conveyed towards the centre of the chamber, finger-like thermal heterogeneities propagate from the wall towards the centre. The temperature histograms also reflect these thermal heterogeneities. Over time, the probability density function (pdf) broadens and shifts towards lower temperatures. Moreover, the pdf peak at TDC is centred at 653 K. This is in agreement with the adiabatic temperature of 667 K calculated with the 0D multi-zone model that accounts for heat and mass transfer among RCM zones.

In Figure 8, the temperature field measurements correspond to an inert mixture that is equivalent to that of iso-octane (case 2, charge of 160 mol/m 3 and equivalence ratio of 0.6). It is important to note that the auto-ignition process is always initiated at the top of the combustion chamber, approximately 22 ms after TDC. Figure 8 shows that in this area the temperature field is nearly heterogeneous. This involves specific propagation of the combustion front, which depends on the local temperature gradient. TDC, (b) TDC + 10 ms, (c) TDC + 30 ms, The inert mixture is here equivalent to the iso-octane reactive mixture (charge of 160 mol/m 3 and equivalence ratio of 0.6 as reported in Table 1). The adiabatic temperature computed by the 0D model at TDC is T cal = 884 K.

The last experimental configuration, shown in Figure 9, corresponds to an inert mixture equivalent to a reactive hydrogen mixture (case3: charge of 160 mol/m 3 and equivalence ratio of 0.4). This condition corresponds to hydrogen auto-ignition 10 ms after TDC. The temperature fields and histograms are again represented at different times after TDC. Similar variations can be observed in the temperature field. The temporal evolution in temperature is also similar, with the cool zones propagating from the bottom to the top, and from the walls to the centre of the chamber. At TDC, the temperature field is highly homogeneous, two cooler kernels also appearing in the lower corners. At this time, the temperature distribution is very tight. The mean temperature then decreases with time due to the global cooling that is driven by the heat loss at the walls. This local heat transfer naturally leads to enhanced thermal heterogeneities. The TDC temperature histograms shown in Figure 8 and Figure 9 exhibit probability density function peaks of 0.34 and 0.38, centred at 894 K and 927 K, respectively. These temperature levels are in agreement with the adiabatic temperatures of 884 K and 926 K, respectively, calculated with the 0D model. The asymmetric feature of the distributions increases with time as a result of the predominant cooling processes at the cold walls of the combustion chamber. 1). The adiabatic temperature computed by the 0D model at TDC is T cal = 926 K.

The analysis of the spatio-temporal fluctuations of the temperature field is an important step towards the deep understanding of the auto-ignition phenomenon and the subsequent combustion processes. This is especially a key point when it comes to the identification of the actual discrepancies among different RCMs. Discriminating these discrepancies is ultimately crucial to the fair interpretation of the ignition delays. Under the various experimental conditions described here, we observe a highly non-uniform temperature field following the end of compression, characterised by two cold cores, which may affect the combustion process. In order to gain a better understanding of the temperature distribution inside the RCM, we focus on the interaction between gas flow induced by the inner geometry of the RCM, and piston motion. Velocity fields were measured by Particle Image Velocimetry (PIV). Following a similar setup as the one outlined in [START_REF] Guibert | An experimental investigation of the turbulence effect on the combustion propagation in a rapide compression machine[END_REF], the PIV diagnostics was performed in the RCM. The laser sheet was generated by a pulsed (10 Hz) Nd:Yag laser. A CCD camera equipped with a 60 mm lens was aligned perpendicular to the laser sheet to image the light scattered by the seeding particles. Micrometric, liquid Rhodorsil particles were used to seed the gas flow. PIV measurements were performed for an inert mixture equivalent to the n-heptane reactive mixture (charge of 180 mol/m 3 and equivalence ratio of 0.8). A pulse generator allowed the laser pulse to trigger the exposure of the frames. Figure 10 shows the temperature fields measured using LIF together with the velocity fields measured using PIV, at different times following the end of compression, i.e., TDC, TDC+10 ms, TDC+17 ms, and TDC+25 ms. Although the LIF and PIV measurements were not made simultaneously, the RCM acquisition system enables the sharp triggering of these measurements. Therefore both temperature and velocity measurements were conducted under identical experimental conditions. The maps presented in the following are averaged velocity fields, determined from 10 successive, instantaneous tests. At TDC, two vortices can be observed close to the walls in the lower corners. The velocity measured in the vortices ranges between 10 and 22 m/s. Both eddies grow and are conveyed due to the upward axial jet expelled after the piston stopped. The eddies then collide with the top end 25 ms after the end of compression. The global flow feature decreases rapidly, as a result of the unsteady flow. Comparing the evolution with time of the velocity and temperature fields, a strong correlation appears between the thermal and aerodynamic phenomena in the combustion chamber. Indeed, the locations of the vortices observed at TDC match those of the thermal kernels. As outlined by Guibert et al. [START_REF] Guibert | An experimental investigation of the turbulence effect on the combustion propagation in a rapide compression machine[END_REF], these vortices are formed due to gas pinching between the bottom of the cylinder and the piston head. These vortices convey cool gases from the walls towards the centre of the combustion chamber. The eddies then grow and propagate towards the upper combustion chamber, leading to cooling at the centre of the chamber. This aero-thermal interaction is well defined between 10 and 17 ms. When the eddies collapse due to the collision with the top end, cooling of the hottest area occurs 25 ms after the end of compression. At this time, it can be seen that some heat is transferred from the walls towards the centre of the chamber. The temperature distribution at TDC is especially influenced by the geometry of the RCM and the piston motion during the compression stroke. Indeed, while the piston is rising, gas is transferred from the compression chamber towards the smaller combustion chamber. With the ensuing increase in pressure, the gas temperature increases rapidly and homogenously until TDC. Then, due to the geometry of the piston head and the bottom of the cylinder, two aerodynamic vortices are formed due to gas pinching, as shown in Figure 11. The vortices are cooler than the bulk gas, as a consequence of the high surface to volume ratio of the pinched gas, which is cooled by convective heat transfer from the piston head and the wall at the bottom of the cylinder. Several authors have evidenced the temperature heterogeneities that exist in an RCM. Clarkson et al. [START_REF] Clarkson | Temperature fields during the development of combustion in a Rapid Combustion Machine[END_REF] also observed the presence of a roll-up vortex that collects cool gas from the walls and moves this gas across the cylinder head, pushing it forward into a plug at the centre. They also described a spatially non-uniform temperature field after compression, with a cold core affecting the potential chemical runaway in the combustion chamber. Recently, Mittal and Sung [START_REF] Mittal | Aerodynamics inside a Rapid Compression Machine[END_REF] used acetone PLIF to investigate the effects of aerodynamics on the measured properties inside an RCM. Their experiments especially highlighted the discrepancies associated with the use of a flat piston and a creviced one, under varying conditions. In agreement with the present study, Mittal and Sung observed that the flat piston design leads to significant mixing of the cold vortex with the hot core region, thereby promoting the coexistence of hot and cold regions inside the combustion chamber.

Conclusion

We presented a methodology based on the use of PLIF, to achieve quantitative temperature measurements in an RCM. This involves the development of calibration measurements in a HP-HT cell and image processing, depending on the experimental conditions used in the RCM. As a result of its spectroscopic characteristics and temperature sensitivity, anisole is shown to be an appropriate tracer for temperature measurements, based on the single excitation, two-colour detection technique. From the experiments carried out with an HP-HT cell, calibration fits were obtained over a large range of temperatures and pressures, i.e., 473 -823 K and 0.2 -4 MPa, respectively, and for three different gases, i.e., nitrogen, carbon dioxide, and argon. The temperature fields were inferred from the fluorescence images through the application of a correction and calibration procedure. An approach allowing quantitative measurements to be obtained was developed in this study. This is based on the normalization of images with respect to the laser energy, and corrections for the background contribution and the variations in the laser beam profile. The final image processing step consists in applying calibration fits. At different times after the end of the compression, temperature fields were measured for different inert mixtures whose compositions are adjusted to generate thermo-physical characteristics that are equivalent to those of reactive n-heptane, iso-octane, and hydrogen mixtures. The temperature field was found to be non-uniform. Hot and cold areas appeared as a result of recirculation in the chamber, convective heat transfer from the walls during compression and after TDC, compression of core gas, and flow motion towards the top end of the combustion chamber. Velocity fields were measured using PIV, in order to characterize the influence of gas flow on the spatial distribution of temperature. The comparison between velocity and temperature fields at identical times reveals a strong correlation between thermal and aerodynamic phenomena in the combustion chamber. As highlighted in the literature,, the variations in eddy structure and residual turbulence levels drive a combustion phenomenology depending mainly on two major parameters, i.e., local turbulence and the thermal gradient. Thus, the geometry of the RCM plays a first order role, influencing the conditions experienced by the mixture at the end of compression.

The main results of this study are that the PLIF technique is a highly useful tool for a large variety of practical situations, including those experienced in a confined, high pressure, high temperature combustion chamber. In the future, combustion systems will require a more detailed knowledge of thermodynamic and aerodynamic processes.

Severe conditions relevant to IC engines are considered here. The present paper clearly demonstrates the possibility of studying the evolution of thermal fields and associated temperature gradients. From the point of view of kinetics-related combustion this experimental characterization can bring useful information for the interpretation of RCM auto-ignition data. These observations could especially help explain the experimental discrepancies among the ignition delays measured in different RCMs, especially for mixtures exhibiting fairly short ignition delays. Heterogeneity (thermal and gas composition) together with turbulence play a significant role in the balance between auto-ignition process, front-like propagation, and potential transition to detonation.

Figure 4 :

 4 Figure 4: On the left, fluorescence spectra of anisole in carbon dioxide, at different temperatures and a constant pressure of 1.2 MPa (excitation wavelength: 266 nm). Each spectrum is normalized by the maximum value of the fluorescence signal at 473 K. On the right, influence of temperature on the redshift of the anisole fluorescence spectrum, in nitrogen at a pressure of 1.2 MPa. Each spectrum is normalized by the maximum value of its own fluorescence spectrum.

Figure 5 :

 5 Figure 5: Map of relative fluorescence quantum yield Φ measured with anisole in nitrogen (Φ is normalized by the reference value at 473 K and 0.2 MPa)

2 and 4 Figure 6 :

 46 Figure 6: (a) Variation of fluorescence signal ratios in nitrogen, as a function of temperature, for different values of pressure, corresponding to two spectral bands (Δλ 1 = 386 ± 11.5 nm and Δλ 2 = 292 ± 13.5 nm). (b) Fluorescence signal ratio calibration matrix vs. pressure and temperature.

Figure 7 :

 7 Figure7: Temperature fields, profiles and histograms at different times after the end of compression: (a) TDC, (b) TDC + 10 ms, (c) TDC + 30 ms. The inert mixture is here equivalent to the n-heptane reactive mixture (charge of 180 mol/m 3 and equivalence ratio of 0.8 as reported in Table1). The adiabatic temperature computed by the 0D model at TDC is T cal = 667 K.

Figure 8 :

 8 Figure8: Temperature fields and histograms at different times after the end of compression: (a) TDC, (b) TDC + 10 ms, (c) TDC + 30 ms, The inert mixture is here equivalent to the iso-octane reactive mixture (charge of 160 mol/m 3 and equivalence ratio of 0.6 as reported in Table1). The adiabatic temperature computed by the 0D model at TDC is T cal = 884 K.

Figure 9 :

 9 Figure 9: Temperature fields and histograms at different times after the end of compression: (a) TDC, (b) TDC + 10 ms, (c) TDC + 30 ms. The inert mixture is here equivalent to the H 2 reactive mixture (charge of 160 mol/m 3 and equivalence ratio of 0.4 as reported in Table1). The adiabatic temperature computed by the 0D model at TDC is T cal = 926 K.

Figure 10 :

 10 Figure 10: Temperature and velocity fields at different times after TDC. The inert mixture is here equivalent to the n-heptane reactive mixture (charge of 180 mol/m 3 and equivalence ratio of 0.8).

Figure 11 :

 11 Figure 11: Cross-section of the inner RCM geometry. The arrows represent the gas flow at successive times until the end of compression.

Table 1 :

 1 Temperature measurements are made at top dead centre (TDC), then at 10, 17, 25, 30 and 40 ms following TDC, as indicated by the red bars in Figure3. Molar fractions of reactive mixtures and their equivalent inert mixtures for temperature measurements using anisole (C 6 H 5 OCH

	Compound	Case1 : Molar concentration	Case 2 : Molar concentration	Case 3 : Molar concentration
		180 mol/m 3		160 mol/m 3	160 mol/m 3
		Molar		Molar fraction	Molar	Molar fraction	Molar	Molar fraction
		fraction of	of equivalent		fraction of	of equivalent	fraction of	of equivalent
		reactive			inert mixture		reactive	inert mixture	reactive	inert mixture
		mixture			(%)	mixture (%)		(%)	mixture (%)	(%)
		(%)
	C 8 H 18	0			0		9.62 10 -3		0	0	0
	C 7 H 16	1.42 10 -2			0		0		0	0	0
	H 2	0			0		0		0	9.33 10 -2	0
	O 2	1.96 10 -1			0		2.00 10 -1		0	1.17 10 -1	0
	N 2	2.37 10 -1			4.29 10 -1		1.11 10 -1	2.89 10 -1	2.37 10 -1	6.28 10 -2
	Ar	7.90 10 -2			1.34 10 -1		6.00 10 -1	6.92 10 -1	4.74 10 -1	9.16 10 -1
	CO 2	4.74 10 -1			4.19 10 -1		7.90 10 -2	1.00 10 -3	7.90 10 -2	1.00 10 -3
	C 6 H 5 OCH 3	0			1.81 10 -2		0	1.81 10 -2	0	1.81 10 -2
			3.5	x 10 6
					equivalent inert mixture C 7 H 16
			3		reactive mixture C 7 H 16 equivalent inert mixture C 8 H 18
			2.5		reactive mixture C 8 H 18 equivalent inert mixture H 2
		Pressure (Pa)	1.5 2		reactive mixture H 2
			1
						TDC
			0.5
			0.01 0	0.02	0.03	0.04	0.05	0.06	0.07	0.08
							Time (s)

3 ) PLIF in an RCM Figure 3: Pressure variations in the RCM combustion chamber for reactive and inert mixtures. The red bars indicate the times of temperature field measurements.

Table 2 :

 2 Experimental fluorescence signal ratio correlations:

Acknowledgements

This study was performed during the PhD thesis of K.H. Tran, and was supported by the FUI (French Fond Unique Interministériel) in the framework of the MODELESSAIS Pôles de Compétitivité MOVE'O project.