Irene Mustieles Marin

Déborah De Masi

Pier Lise-Marie Lacroix

Francesco Fazzini

Piet W N M Van Leeuwen

Juan M Asensio

Bruno Chaudret

Hydrodeoxygenation and Hydrogenolysis of Biomass-Based Materials Using FeNi Catalysts and Magnetic Induction

Bimetallic FeNi3 nanoparticles (NPs) enriched with Ni (FeNi3@Ni) have been used to perform the hydrodeoxygenation reaction (HDO) and cleavage of lignocellulose-derived products in solution using magnetic induction. The application of a high frequency magnetic field induces high temperatures at the surface of the NPs that drive the catalytic reaction. The activation of the C-O bond of several functional groups was studied. FeNi3@Ni NPs, which act both as catalysts and magnetic heating agents, catalyzed the total conversion of furfural and 5-hydroxymethyl furfural into respectively 2-methylfuran and 2,5-dimethylfuran under mild conditions (12 mol% catalyst, 3 bar H2, 49 mT). The oligomerization of cyclopentanone, derived from furfural, was also achieved to yield C10 and C15 oligocyclopentyl products. Under the same conditions, diphenyl and benzyl phenyl ether, used as model molecules of polymeric lignin, were cleaved at 86 % and 100 % conversion respectively, to yield a mixture of hydrogenolysis and hydrogenated products. This is explained by the presence of Ni at the surface of the NP that favors the hydrogenation of the aromatic rings. The short reaction times and simplicity of the experimental set-up highlight the advantages of the application of magnetic heating for difficult transformations in solution, here the catalytic treatment of biomass-derived molecules.

Introduction

The transformation of biomass residues into valuable chemicals is a timely and important research topic to anticipate the fossil resources shortage and develop new ways to access valuable carbon-based molecules. For this purpose, numerous processes have been developed to hydrolyze biomass, reduce it and depolymerize natural polymers such as cellulose or lignin. [1][2][3] One important process is hydrodeoxygenation (HDO) which has been extensively studied during the past few years. [4][5][6] For instance, furfural and 5-hydroxymethylfurfural (HMF), which are generated by the respective dehydration of C5 and C6 sugars in the acid hydrolysis of lignocellulose, yield 2-methylfuran (MF) and 2,5-dimethylfuran (DMF) as hydrodeoxygenation products, which are considered as promising biofuel candidates due to their high octane number and physicochemical properties. [7][8][9][10] This transformation has been studied with noble (Ru, Pd) [11][12][13][14] and non-noble (Cu, Co, Ni) [15][16][17][18] metal catalysts for which harsher conditions are required (temperatures up to 280 °C and pressures ranging from 10 to 50 bar). 5 It has been observed that the use of bimetallic catalysts may enhance the selectivity towards the HDO product. This is the case of the Ni/SiO2 catalyst reported by Sitthisa et al., for which the yield on MF increased from 1.4 % (at 51 % conversion) with only Ni as catalyst, to 39 % (at 96 % conversion) when a Ni-Fe alloy was used (5 wt% Ni-2 wt% Fe). 19 Thus, this group 19,20 as well as that of Lercher 21 have reported that FeNi alloys are able to reduce the kinetic barrier for C-O bond activation in HDO reactions. In addition, oligomerization of cyclopentanone, a product of furfural hydrogenation, 22 can be of interest for the production of high-density biofuels with applications in the aviation field. [23][24][25] As demonstrated by Wang et al., C15 and C20 hydrocarbons can be obtained by aldol condensation of this molecule. 23 Similarly, several studies have focused on the potential of lignin as the largest natural source of low-carbon aromatics. 26 Lignin is constituted by methoxy-phenol units linked mostly by strong ether bonds. 27 In this respect, di-aryl and alkyl-aryl ethers such as diphenyl ether (DPE) and benzyl phenyl ether (BPE) are commonly used as model substrates to investigate the catalytic cleavage of the polymer. These structures display the 4-O-5 and α-O-4 linkage features, widely present in lignin 28 with bond dissociation energies (BDE) ranging from 218 to 314 kJ mol -1 hence requiring harsh conditions to be cleaved. [START_REF] Luo | Comprehensive Handbook of Chemical Bond Energies[END_REF] The catalytic hydrogenolysis of these model molecules has been widely studied in homogeneous and heterogeneous catalysis here again with nickel-based catalysts.

Lercher et al. investigated the cleavage of alkyl-aryl and aryl-aryl ethers on silica-supported nickel NPs (4-8 nm) under mild conditions (120 °C, 6 bar of H2), yielding a mixture of aromatics and cycloalkanes. [START_REF] He | [END_REF] In an initially homogeneous system, Hartwig et al. reported total conversion of aromatic ethers to the corresponding monomers. 31 The practical difficulties linked to biomass transformation, especially the problems of heat and mass transfer, call for the search for new, less expensive and easy-to-implement catalytic systems.

In this respect, the use of magnetically heated catalysts present inside the reaction mixtures could be advantageous in terms of heat diffusion. Ferromagnetic nanoparticles (NPs) can produce heat when exposed to an alternating magnetic field working at high frequency. This technique has been mostly applied in biology for cancer therapy: the so-called magnetic hyperthermia. 32 More recently, magnetic heating has also been applied to activate catalytic reactions as it permits generating a rapid and localized rise of the temperature at the surface of the heating agents without the need to heat up the whole reactor. Several groups including ours, explored the magnetic activation of heterogeneous catalytic reactions in the gas phase such as the Fischer-Tropsch reaction, 33,34 CO2 hydrogenation, [35][36][37][38][39] methane reforming [40][41][42][43] or alkane dehydrogenation. 43 Magnetic heating has also been used in liquid phase reactions, but it was often limited to reactions taking place at moderate temperatures such as C-C coupling, 44 amide condensation, 45 and more recently hydrogenation of furfural. 46 In order to have access to higher temperatures, we investigated the design of hybrid materials in which the catalyst is in close contact with the heating agent, namely FeC NPs decorated with Ru NPs (FeC@Ru). 47 In this way, we were able to reach local high temperatures, well-above the mean temperature of the bulk solution and to perform the HDO of platform molecules under much lower pressures (3 bar H2) and low catalyst loadings (0.25-1 mol% Ru). 47 This experiment suffered however from two drawbacks: the use of a noble metal catalyst and the complex synthesis of the FeC@Ru nanoparticles. In order to prove the efficiency of the magnetic activation in solution, we turned to the FeNi system. Thus, FeNi3 NPs which display low magnetocrystalline anisotropy, catalyze the CO2 hydrogenation at lower magnetic field than previously reported materials, e.g. FeC 35 and FeCo NPs, 43 thus improving the energy efficiency of the process. 48 Furthermore, FeNi3

NPs are easily synthesized and can also be easily enriched with additional nickel leading to FeNi3@Ni NPs. Finally they are good candidates for HDO and ether cleavage reactions as mentioned above.

In this paper, we report the catalytic activity of FeNi3@Ni NPs in HDO in solution using magnetic heating. The cleavage of the C-O bond was achieved for a range of substrates under mild conditions and a catalyst loading of 12 mol%. HDO, oligomerization and cleavage of biomass-derived products were performed at low H2 pressure (3 bar) in the absence of any noble metal. These reactions evidence the interest of magnetically activated catalysis which allows one to perform difficult reactions using a simple set-up and low pressure, while high temperatures only build up at the surface of the nano-catalysts.

Experimental part

FeNi3@Ni NPs were prepared following the procedure recently reported by De Masi et al. and is described in the supplementary information. 48 These particles can be obtained by reduction of the organometallic precursors {Fe[N(SiMe3)2]2}2 and Ni[ i PrNC(CH3)N i Pr]2, under H2 in the presence of palmitic acid. As prepared, the particles possess a Fe-Ni core with a Fe-rich surface. A second reaction step serves to enrich the surface with additional nickel, leading to FeNi3@Ni NPs.

The NPs have been characterized by X-ray Diffraction (XRD), Transmission Electron Microscopy (TEM), High Resolution Transmission Electron Microscopy (HR-TEM) and Scanning Transmission

Microscopy-Energy Dispersive Analysis by X-Ray (STEM-EDX). The X-ray diffractograms only show the peaks of the fcc structure corresponding to FeNi3 and/or Ni. After catalysis no significant changes in the peaks position and linewidth were observed (see Figure 1). TEM analysis of the particles have also been performed before and after catalysis, namely furfural HDO, diphenyl ether hydrogenolysis and reaction with cyclopentanone. Representative examples of images obtained before and after reaction with cyclopentanone are shown on Figure 2. TEM analysis were performed on nanoparticles after 3 catalytic cycles. The particles display a mean size near 16 nm and no significant change in the size distribution is observed for TEM micrographs recorded after catalysis (see SI, Figure S1). However, as a general trend, a noticeable agglomeration of the NPs was observed after catalysis. Regarding the magnetic properties, these NPs are superparamagnetic at 300 K and display a magnetization at saturation value of 87 A•m 2 •kg -1 . The Specific Absorption Rate (SAR), a property related to the heating power of the NPs, measured at 93 kHz and 47 mT, was 350 W•g -1 (see SI, Figure S2). A brief description of the magnetic properties is presented in the Supporting Information.

The catalytic reactions were performed using a 3 cm wide and 2 cm high coil working at 300 kHz.

The magnetic field amplitude can be settled between 0 and 65 mT. A view of the set-up is presented on Figure S3. A typical catalytic procedure as well as an example of a GC-MS chromatogram is shown in the Supporting Information.

Results

Hydrodeoxygenation of acetophenone Scheme 1. Reaction pathway for acetophenone HDO and catalytic results obtained after three recycling cycles.

Preliminary studies for HDO were performed using acetophenone as a model substrate. Mesitylene was used as solvent because of its high boiling point (ca. 165 °C). Magnetic field amplitude of 49 mT was chosen for the reaction since it maximizes the SAR of FeNi3@Ni NPs (see Fig. S2). The HDO was performed using 12 mol% of catalyst and 3 bar of H2. When the magnetic field was applied, the NPs reorganized to form chains along the magnetic field direction (see Fig. S3) as previously observed by our group with FeC@Ru NPs. 47 In addition, solvent boiling could be observed in the vicinity of the NPs, while a temperature of 150-160 °C was determined on the Fisher-Porter bottle external walls using an IR camera.

After 3 hours, total conversion of acetophenone was achieved with a full selectivity for the expected HDO product, ethylbenzene. The recyclability of the NPs then was studied. After three cycles, the conversion decreased to 82 % and the selectivity for ethylbenzene dropped to 66 %. TEM images evidenced the agglomeration of the NPs after reaction (see Figure 2). This important morphology change leads to a reduction of both the catalytically active surface and the heating power, since the agglomerated NPs can no longer self-organize to form chains.

Hydrodeoxygenation of furfural

Scheme 2. Hydrodeoxygenation reaction of furfural and HMF. FL = furfural, HMF = 5-hydroxymethylfurfural, MF = 2-methylfuran, FA = furfuryl alcohol, DMF = 2,5-dimethylfuran, HMMF = 5-methyl-2-furfuryl alcohol.

The hydrodeoxygenation of furfural under magnetic heating was studied as a function of H2 pressure, magnetic field and catalyst loading in mesitylene. After 1 hour in the presence of 3 bar of H2, 12 mol% of catalyst and a magnetic field amplitude of 49 mT (reference experiment, see Scheme

2), 64 % of furfural was converted leading to a 51 % yield of furfuryl alcohol (FA) and 13% of methylfuran (MF). As in the case of acetophenone, the pressure increase in the Fisher-Porter bottle was of only 0.2 bar during the reaction.

 Influence of the pressure (Table 1, entries 2 and 3):

The reaction was performed for 1 hour at variable pressure while maintaining the catalyst loading (12 mol%) and the magnetic field amplitude constant (49 mT). By increasing the H2 pressure from 1 to 5 bar, the furfural conversion varied from 42 to 74 %. Furfuryl alcohol and methylfuran were the only reaction products. Indeed, even at high pressure, no hydrogenation of the aromatic ring was observed. FA was the major product obtained independently of the pressure.  Influence of the magnetic field (Table 1, entries 4 and 5):

Entry

To determine the influence of the magnetic field on the catalytic process the reactions were carried out for 1 hour at 33 mT, 49 mT and 60 mT magnetic field amplitudes. FA remained as the main product with similar selectivities in all the three cases. Regarding the conversion, it decreased from 64 to 49 % when reducing the magnetic field from 49 to 33 mT. However, it barely changed when the reaction was conducted at 60 mT (60 %). This may be due to the fact that the FeNi3@Ni NPs SAR value significantly increases between 33 and 49 mT (190 vs 350 W•g -1 Fig. S2), but then saturates at high field. These results evidence the key importance played by the NPs heating power in the catalytic process.

 Influence of the catalyst loading (Table 1, entries 6 and 7):

The influence of the catalyst loading was also investigated by using lower (6 mol%) and higher (24 mol%) amounts of catalyst compared to the 12% used in the reference conditions. A drastic increase of the furfural conversion from 10 to 64 % was observed when the catalyst loading was doubled from 6 to 12 mol%. Increasing the catalyst loading up to 24 mol% led to 79 % conversion.

The improvement is thus less drastic but a higher selectivity for MF was observed, which is explained by the increase of temperature due to a higher SAR caused by the formation of larger/longer chains. 49,50 These studies show that 12 mol% of catalyst loading, 3 bar of H2 and a magnetic field of 49 mT are the best compromise between good conversion, mild conditions and catalytic loading, and therefore these were kept for further investigations.

 Reaction profile of furfural:

The HDO of furfural was further investigated at different reaction times under the optimized catalytic conditions. The reaction profile is shown on Figure 4. The conversion of furfural occurred very fast. After 3 hours, furfural was almost totally converted into FA and MF, with 61 and 36 % yield, respectively. At short reaction times, the major product was FA, which was further converted to MF (see For the sake of comparison, the HDO of furfural was also studied with FeNi3@Ni but using conventional heating (oil bath, 180 °C). After 3 hours of reaction in refluxing mesitylene under 3

bar of H2 at initial room temperature (4 bars at 180°C), the conversion reached 60 % but with a selectivity of only 8 % for MF (see Table 1). The difference with magnetic heating will also be examined in the discussion section.

Hydrodeoxygenation of hydroxymethylfurfural

The HDO of HMF was monitored at different times using the same catalytic conditions as previously described (Figure 5).

Oligomerization of cyclopentanone

Cyclopentanone oligomerization may lead to the formation of polycycloalkanes, which are promising molecules for fuel applications due to their high densities. 23,24 The proposed mechanism involves aldol condensation followed by HDO. We investigated the performance of our catalytic system in this reaction in order to get further insight into the reactivity of FeNi3 NPs towards the activation of C-O bonds. After 3 h under standard conditions, 80 % of the cyclopentanone was converted into cyclopentanol (see Figure 6). Total conversion was achieved after 8 h to yield a mixture of dimeric and trimeric products, while no cyclopentanol was observed. Cyclopentyl cyclopentane was the main product, 79 %, along with small amounts of dimers 2-cyclopentyl cyclopentanone (7 %), 1-cyclopentyl cyclopentene (8 %), and the trimer 1,3-dicyclopentylcyclopentane (6 %). When the reaction was run for 16 h, all the unsaturated dimers (B and C) were consumed and the final mixture was composed of 72 % of cyclopentylcyclopentane and 28 % of 1,3-dicyclopentylcyclopentane. The presence of cyclopentanol as the first reaction product is in contradiction with the proposed aldolisation mechanism. It is therefore more likely that the first step proceeds through cyclopentanol dehydration leading to a reactive cyclopentene.

Cleavage of diphenyl ether and benzyl phenyl ether

The cleavage of benzyl phenyl ether and diphenyl ether, two of the most common lignin model molecules, was investigated using the optimized conditions and FeNi3@Ni NPs as catalyst. In this case decane was the solvent of choice for analytical reasons, as it displays a high boiling point (174 °C). Figure 7 shows the conversion of diphenyl ether and the product distribution at 1, 2, 5, 8 and 15 hours. After this time no further evolution of the reaction was observed. 4). No phenol was observed at any time, suggesting that it is rapidly hydrogenated into cyclohexanol (see Scheme 3). Cyclohexane was also formed in minor amounts during the reaction as a result of the slow hydrogenation of benzene. Its yield increased with time and reached 26 % at the end of the reaction. Small amounts of cyclohexyl phenyl ether (CPE) were also observed resulting from the partial hydrogenation of diphenyl ether. [START_REF] He | [END_REF]51 The yield of CPE reached a maximum of 6 % after 5 hours and did not experience further variation.

For the sake of the interpretation, the reactivity of phenol and cyclohexyl phenyl ether were investigated in two control experiments under the standard conditions using 1 mmol of phenol or CPE instead of DPE. After 5 hours of reaction, all the phenol was converted to cyclohexanol, while CPE did not react at all. The effect of hydrogen pressure and magnetic field amplitude were investigated in the cleavage of DPE after 5 hours of reaction. The results are shown in Table 5 and Figure 8. When the H2 pressure was increased from 1 to 3 bar, the conversion notably increased from 36 to 64 %. However, when further increasing the H2 pressure to 5 bar, a small decrease of the conversion from 64 to 55 % was observed. Regarding the product distribution, a larger amount of the hydrogenated products cyclohexane and cyclohexyl phenyl ether was observed as a result of the higher hydrogen pressures, but benzene and cyclohexanol still remained as the main products. The change in the magnetic field amplitude, usually translated into a change of the catalyst surface temperature, did not have an influence on the product distribution. When increasing the field from 33 to 49 mT, the conversion increased from 36 to 64 %, but then slightly decreased to 59 % at 60 mT. A similar effect was observed when using furfural as substrate and this is explained by the difference on the SAR measured at 33 and 49 mT. The small decrease observed at 60 mT might be caused by the sintering of the NPs due to the high magnetic field amplitude applied. Table 5. Conversion and product selectivities obtained for the cleavage of DPE at different pressures and magnetic field amplitude. Conditions: 1 mmol of substrate, 12 mol% of catalyst, 5 hours of reaction and 5 mL of decane. *The temperature used was 170 °C.

The activity of FeNi3@Ni was also studied using conventional heating (oil bath, 170 °C) instead of magnetic heating. The conversion only reached 18 % at 5 h and the main products were benzene and cyclohexanol (see Table 5). As in previous experiments, no phenol was detected.

The cleavage of benzyl phenyl ether was investigated using magnetic heating under the optimized conditions. The reaction is faster than that of DPE and all the substrate was consumed after 5 hours (see Figure 9 and Table 6). From the beginning of the reaction the main products were toluene and cyclohexanol, in proportions which remained mostly constant (about 50 %) during the reaction. This indicates that the cleavage proceeds in this case via direct hydrogenolysis of the benzylic PhCH2-O bond. As observed with DPE, no phenol was detected in the reaction mixture due to its fast hydrogenation At the end of the reaction the yields of toluene and cyclohexanol were close to 90 %, while the yield of the side-product cyclohexyl benzyl ether was only 2%. No methylcyclohexane was observed as a result of toluene hydrogenation. Nevertheless, some traces of benzene were detected at 5 h of reaction, likely as the result of phenol hydrogenolysis.

Scheme 4. Proposed reaction pathway for the cleavage of benzyl phenyl ether and yields obtained at 5 h (total conversion).

Using conventional heating, FeNi3@Ni NPs converted 94 % of the substrate (see Table 6). The main products were toluene and cyclohexanol with yields of 76 and 61 % respectively. Cyclohexyl benzyl ether could only be detected at low concentrations.

Recyclability of the catalyst

The recyclability of the NPs was studied for three of the substrates herein studied, namely furfural, cyclopentanone and diphenyl ether. Three reactions of 3 hours each were performed using the same batch of catalyst. Once the reaction was completed, the NPs were decanted with a magnet and the solution was removed and the reaction charged again with a new substrate and internal standard under inert atmosphere. Even though the NPs were decanted and easily separated from the solution, some NPs were dissolved during the reaction and some of them are also lost during solution removal, so catalyst charges are not comparable during recycling experiments. At the end of the three reactions (for all the three substrates), only 4 mg of the 10 initial mg could be isolated. Table 7. Conversion and yields obtained in the HDO of furfural at different times. Conditions: 1 mmol substrate, 49 mT, 3 bar H2, initial 12 mol% of catalyst, 3 hours of reaction and 5 mL of mesitylene.

We reported 97 % conversion of furfural with 61% furfuryl alcohol and 36% of MF. In this precise experiment, the initial conversion is lower (see Table 7). However, after 2 recycles the conversion increases slightly and the selectivity towards MF increases spectacularly. Taking into account that we have less and less NPs in the Fisher-Porter bottle, these results show that the performance of our catalyst increases upon recycling. Table 8. Conversion and selectivity obtained for the oligomerization of cyclopentanone in the recyclability tests. Conditions: 1 mmol substrate, initial 12 mol% catalyst, 3 bar H2, 49 mT, 3 hours of reaction and 5 mL of mesitylene.

The conversion is similar to what has been observed with other batches of NPs and the selectivity is the same (see Table 8). Both conversion and selectivity are maintained after recycling. The conversion obtained at the first reaction is coherent with other batches, as is the selectivity (see Table 9). After reusing the NPs, the conversion initially decreases but the selectivity is maintained.

These experiments are surprising since recycling improves the catalysis in the case of furfural, remains stable in the case of cyclopentanone and leads to a decrease of the conversion in the case of diphenyl ether.

Discussion

Overall, FeNi3@Ni NPs have been shown to be very active in the magnetically-induced HDO catalysis in solution. Reactions normally carried out at high temperature and pressure can be achieved in apparent mild conditions. In fact, these transformations are made possible by an overheating of the surface of the nano-catalyst which leads to local harsh conditions involving temperatures well above the boiling point of the solvent and possible pressure build up.

Notwithstanding these harsh conditions produced at the nano-scale, only a slight overpressure in the reactor is produced and the reactions are completed despite the relatively low pressure (3 bar).

A strong temperature gradient must be present to dissipate the heat produced by the nanoparticles.

In this respect, furfural and HMF can be selectively converted into their respective HDO products under 3 bar of H2 and using low loadings of catalyst. Furthermore, the Ni-decorated FeNi3 NPs turned out to be more selective than other FeNi alloys previously reported, for which decarbonylated side-products were also produced during the reaction. 19 Resasco et al.

demonstrated that an η 2 (C-O) adsorption of the carbonyl group into the FeNi alloy catalyst surface was responsible for the selectivity towards MF. 19 This coordination is favored by the presence of oxophilic Fe sites in the FeNi catalyst which weaken the coordinated C-O bonds. The absence of decarbonylated products in the HDO of furfural and HMF may be indicative of a greater stabilization of the η 2 (C-O) intermediate by the FeNi3@Ni NPs which, thanks to the high temperatures reached by magnetic induction, promotes the C-O cleavage over C-C cleavage. In addition, no ring hydrogenation products were detected in any case, not even when the pressure was increased to 5 bar (Table 1, entry 3). It has previously been observed in the literature for conventional heating reactions that upon increasing hydrogen pressure the catalyst surface is saturated with hydrogen species, which hinders substrate coordination and thus decreases conversion. [START_REF] He | [END_REF]51 The pressures used here are fairly low, therefore the conversion keeps on increasing with the H2 pressure, presumably because the NP surface is not saturated in hydrogen species.

Scheme 5. Reaction pathway for furfural HDO.

The reaction profile of furfural conversion evidences the presence of the alcohol as intermediate and demonstrates that the reaction occurs in two steps (see Scheme 5). C-O bond cleavage, which possesses a higher activation energy, is slower than hydrogenation.

The conversion of HMF occurs faster than that of furfural, probably thanks to a better interaction with the catalyst surface favored by the additional hydroxyl group. At short reaction times HMMF was the main product followed by DMF while bis(hydroxymethyl)furan (BHMF) was not observed (see Scheme 6). The absence of the bis(hydroxymethyl) intermediate (BHMF) differs from the observations by the teams of Wang 52,53 and Hoyos, 54 who reported the formation of BHMF as intermediate of HMF to HMMF at low temperature at the beginning of the reaction when employing

Ni-based catalysts. The absence of BHMF does not allow us to determine the reaction mechanism, which can occur through hydrogenation/hydrogenolysis of the carbonyl group with BHMF as intermediate, or hydrogenolysis of the hydroxyl group followed by hydrogenation of the aldehyde, which, in turn, would afford 5-methylfurfural as reaction intermediate. The conditions employed here in the transformation of both furfural and HMF appear notably milder than those generally reported in the literature. 5 FeNi3@Ni NPs, acting both as catalyst and magnetic heating agent, may allow the HDO reaction to occur selectively at low pressures. Scheme 6. Reaction pathway for hydroxymethylfurfural HDO.

This was demonstrated by comparing heating (oil bath) and magnetically induced catalysis of furfural. After 3 hours of reaction at 180 °C and 3 bar of H2 pressure the conversion reached 60 % with a selectivity of only 8 % for the MF, while the conversion reached 97 % with a 37% selectivity for MF when the reaction was magnetically heated (49 mT) under the same reaction conditions (see Table 1). This is a good indication of the presence of local temperatures above the boiling point of the solvent in the case of the magnetic heating. In addition, higher overpressure (1 bar) was observed when conventional heating was used. In the presence of the magnetic coil, only a small increase of the pressure of 0.1-0.2 bar over the initial 3 bar was observed. The results obtained for these two reactions are similar to those reported previously for FeC@Ru NPs, 47 but here they were obtained at lower magnetic field and hence lower energy consumption.

FeNi3@Ni NPs were also demonstrated to be active in reactions not previously tested in magnetically activated catalysis such as the deoxygenating oligomerization of cyclopentanone, which was totally converted after 8 hours with a high selectivity for the C10 and C15 products after 16 h. The synthesis of C10 and C20 polycycloalkanes obtained by condensation of cyclopentanone has been investigated by Zhang and co-workers under solvent-free conditions and in the presence of hydrogen. 23,24 However, in that case, the presence of a base as well as a high H2 pressure (60 bars) was necessary. Here, total conversion of cyclopentanone to C10 and C15 olligocycloalkanes was obtained in a one-pot one-step synthesis without the presence of any base. Furthermore, the magnetic heating approach permits this oligomerization to take place at only 3 bar of H2 pressure, rendering the process much more accessible.

Magnetically induced catalysis was further proven to be effective in the cleavage of aryl-aryl and aryl-alkyl ethers, even though no total conversion was obtained in the case of DPE. A maximum conversion of 86 % was obtained at 15h for the latter, while BPE was totally converted at 5h. This difference is due to the lower bond dissociation energy of the C-O bond in the BPE (218 KJ mol -1 vs 314 KJ mol -1 for DPE). [START_REF] Luo | Comprehensive Handbook of Chemical Bond Energies[END_REF] In the case of DPE, the cleavage occurs via direct hydrogenolysis of the aryl C-O bond, while in BPE the aliphatic PhCH2-O bond is hydrogenolyzed (see Schemes 3 and 4). The phenol generated in the cleavage is directly hydrogenated into cyclohexanol and was not observed at any time of the reaction. This was confirmed by an independent experiment in which phenol was completely hydrogenated into cyclohexanol after 5 h using the same reaction conditions. On the other hand, benzene (in the case of diphenyl ether) was hydrogenated at lower rates, and toluene catalyst turns out to be very low and therefore, other cleavage routes prevail. 19 As the reaction evolves, other substrates such as phenol can cover the catalyst surface impeding the partial hydrogenation of the aryl ether. The conversion of DPE stopped after 15 hours of reaction perhaps as a result of sintering of the catalyst.

The comparison with conventional heating was studied for both substrates at short reaction times (5 h) at 170 °C. Taking into account the overpressure produced by classical heating, the pressure charged on the FP was 2.2 bar of H2, which rose to 3.2 bar once the reaction was placed in the oil bath. This way the pressure conditions were equal between conventional and magnetically induced heating (3.2 bar during the reaction). Conventional heating worked positively in the case of BPE, for which after 5 h a 94 % of the product was consumed compared to the 100 % conversion obtained using the magnetic coil (see Table 6). However, in the case of DPE only an 18 % conversion was obtained with conventional heating, compared to a 64 % obtained by magnetic heating (see Table 5). As DPE possesses higher bond dissociation energy than BPE, its conversion in both instances is lower. The difference in reactivity between both species under conventional and magnetic heating points to a much higher temperature at the surface of the catalyst than that of the mean solution in the case of magnetic heating.

Finally, the recycling experiments seem contradictory since in some cases (furfural, cyclopentanone) little or no deactivation is observed. In these cases, the NPs mean size does not seem much affected by the magnetic heating although some agglomeration is observed. The decrease in the catalytic properties in the case of diphenyl ether can be due to two factors: i) the decrease of the catalytically active surface and ii) a decrease of the heating power of the particles.

We have previously demonstrated the effect of the NPs organization into macroscopic needles on one side and of the formation of shapeless agglomerates on the other, which leads in the first case to a strong heating power and in the second one to virtually no heating. 49 The higher solubility of the particles in mesitylene may allow them to move freely and organize in the magnetic field leading to an improved heating power (see the improvement of catalysis for furfural) while the particles in decane are less soluble and more agglomerated which could explain a reduced heating power. Nevertheless, we show here that recycling is possible and that magnetic heating does not lead to a rapid deactivation of the catalysts through coalescence of the NPs.

Concluding remarks

In summary, herein we report a new methodology for the valorization of biomass-derived molecules using magnetically induced catalysis and the easily accessible FeNi3@Ni NPs. Magnetic heating induces the performance of these difficult reactions thanks to the local heating of nanocatalysts above the boiling point of the solvent. This approach enables the cleavage of C-O bonds of different functional groups such as ketones, aldehydes and aryl ethers, in spite of their high BDEs, and the reaction leads to high selectivity for the HDO products of furfural derivatives. The magnetic characteristics of the catalyst enables activation at lower magnetic field amplitudes than those reported previously, 47 rendering the catalytic process more energetically efficient. Moreover, the high abundance and low cost of Fe and Ni make this catalyst promising for scale-up purposes.

The combination of magnetic heating which only requires a simple set-up and low pressures, and the catalytic properties of FeNi3@Ni NPs lead to catalytic performances so far typically obtained under harsher conditions or using noble metals. Magnetic heating of nano-catalysts in solution may therefore develop as a powerful and energy efficient new tool for the transformation of organic matter.

Figure 1 .

 1 Figure 1. X-ray diffractograms of FeNi3@Ni NPs before (purple line) and after (black line) hydrogenolysis of diphenyl ether.

Figure 2 .

 2 Figure 2. TEM images of FeNi3@Ni NPs before (top) and after three catalytic runs with cyclopentanone (bottom).

Figure 3 .

 3 Figure 3. HR-TEM image (A) and STEM-EDX results obtained on FeNi3@Ni NPs and evidencing the presence of Ni (B), Fe (C) and Ni-Fe superposition (D).

Figure 4 .

 4 Figure 4. Furfural conversion and products yield as a function of the time. Conditions: 1 mmol substrate, 49 mT, 3 bar H2, 12 mol% of catalyst, and 5 mL of mesitylene.

Figure 6 .

 6 Figure 6. Oligomerization of cyclopentanone and product selectivities at 3, 8 and 16 hours. Conditions: 1 mmol substrate, 49 mT, 3 bar H2, 12 mol% of catalyst, and 5 mL of mesitylene.

Figure 7 .

 7 Figure 7. Conversion and products yield of DPE cleavage as a function of the time. Conditions: 1 mmol substrate, 12 mol% catalyst, 3 bar H2, 49 mT, and 5 mL of decane. CyOH = cyclohexanol, CPE = cyclohexyl phenyl ether.

Figure 8 .

 8 Figure 8. Conversion and yields obtained for the cleavage of DPE a) as a function of the pressure; and b) as a function of the magnetic field amplitude. Conditions: 1 mmol of substrate, 12 mol% of catalyst, 5 hours of reaction, 5 mL of decane, 49 mT for a), and 3 bar H2 for b).

Figure 9 .

 9 Figure 9. Conversion and product yields of BPE cleavage as a function of the time. Conditions: 1 mmol substrate, 12 mol% catalyst, 3 bar H2, 49 mT, 5 mL of decane.

Table 9 .

 9 Conversion and yields obtained for the cleavage of DPE in the recyclability tests. Conditions: 1 mmol substrate, initial 12 mol% catalyst, 3 bar H2, 49 mT, 3 hours of reaction and 5 mL of decane. CyOH = cyclohexanol, Cy = cyclohexane, CPE = cyclohexyl phenyl ether.

(

  in the case of benzyl phenyl ether) was not hydrogenated at all. Hartwig et al. demonstrated that the use of an in situ-generated Ni catalyst in the presence of a base increases the selectivity for the aromatic products in the cleavage of benzyl phenyl ether. 31 In our case, the introduction of Fe likely increases the oxophilicity of the catalyst which favors the adsorption of phenol species facilitating the reduction of the aromatic ring. The small amounts of cyclohexane detected compared to cyclohexanol evidence the fact that the hydrogenation of the oxygenated product is preferred over the hydrogenation of benzene, due to the stronger interaction of the oxygen-containing molecule with the catalyst surface. The partial hydrogenated products, CPE and CBE, were present at low concentrations during all the reaction lifetime. Initially considered as a reaction intermediate in the C-O bond cleavage, the reactivity of CPE was investigated in a different experiment under the same reaction conditions. No conversion of CPE was observed after 5 hours of reaction indicating that CPE is not an intermediate but a side-product. This was also reported by Lercher et al. who observed that the rate of C-O bond cleavage of partially hydrogenated aryl ethers over a Ni-based

Table 1 .

 1 Conversion

			Catalyst			Yield (%)
		Pressure		Magnetic field	Conversion
			loading
		(bar)		(mT)	(%)	FA	MF
			(mol%)
	1(reference
		3	12	49	64	51	13
	reaction)
	2	1	12	49	42	37	5
	3	5	12	49	74	61	13
	4	3	12	33	49	42	7
	5	3	12	60	60	50	10
	6	3	6	49	10	9	1
	7	3	24	49	79	57	22
				*Conventional
	8	3	12		60	55	5
				heating

and partial yields obtained for the optimization of furfural HDO conditions. Conditions: 1 mmol of substrate, 5 mL of mesitylene, 1 hour of reaction. *The temperature used was 180 °C.

Table 2

 2

	products resulting from ring-hydrogenation, ring-opening or decarbonylation processes were
	observed.
			Conversion	Yield (%)
	Entry	Time (h)
			(%)	FA	MF
	1	0.5	28	24	4
	2	1	64	51	13
	3	3	97	61	36
	4	8	100	46	56
	5	16	100	0	100

). Thus, total selectivity for the final product was obtained after 15 hours of reaction. The reaction is highly selective and no side-

Table 2 .

 2 Conversion and yields obtained in the HDO of furfural at different times. Conditions: 1 mmol substrate, 49 mT, 3 bar H2, 12 mol% of catalyst, and 5 mL of mesitylene.

Table 3 .

 3 Hydroxymethylfurfural conversion and products yield as a function of the time. Conditions: 1 mmol substrate, 49 mT, 3 bar H2, 12 mol% of catalyst, and 5 mL of mesitylene.Similar to furfural, the conversion of HMF occurred very rapidly and was complete after 2 h leading to 5-methylfurfuryl alcohol (HMMF) and DMF with a 59 % and 41 % yield, respectively. At 8 hours, only 17 % yield of HMMF was observed, and at 16 hours total conversion into the HDO product DMF was achieved (see Table3). Conversion

	Conversion
	Yield DMF
	Yield HMMF

and yields in the HDO of HMF at different times. Conditions: 1 mmol substrate, 49 mT, 3 bar H2, 12 mol% of catalyst, and 5 mL of mesitylene.

Table 4 .

 4 Conversion and yields obtained for the cleavage of DPE. Conditions: 1 mmol substrate, 12 mol% catalyst, 3 bar H2, 49 mT, and 5 mL of decane. CyOH = cyclohexanol, Cy = cyclohexane, CPE = cyclohexyl phenyl ether.

		Time	Conversion		Yield (%)
	Entry
		(h)	(%)	Benzene CyOH	Cy	CPE
	1	1	23	13	21	2	2
	2	2	29	15	23	3	3
	3	5	64	47	48	12	6
	4	8	76	61	64	21	6
	5	15	86	62	74	26

Scheme 3. Proposed reaction pathway for the cleavage of diphenyl ether and yields obtained at 15 h (86 % conversion).

Toluene Conversion CBE Cyclohexanol into

  cyclohexanol (seeScheme 4). Traces of a high-weight product were detected during the course of the reaction, identified as cyclohexyl benzyl ether (CBE), which is formed by partial hydrogenation of BPE. As occurred with CPE, this product is present from the beginning of the reaction but does not evolve with time.

			Conversion		Yield (%)
	Entry	Time (h)
			(%)	Toluene	CyOH	CBE
	1	1	21	20	20	1
	2	2	56	52	42	1
	3	5	100	86	88	2
	4*	5	94	64	61	1

Table 6 .

 6 Conversion and yields obtained for the cleavage of BPE. Conditions: 1 mmol substrate, 12 mol% catalyst, 3 bar H2, 49 mT, and 5 mL of decane.*Using conventional heating, the temperature used was 170 °C.

Acknowledgements

The authors thank ERC Advanced Grant (MONACAT 2015-694159) and IDEX/Chaires d'attractivité de l'Université Fédérale de Toulouse Midi-Pyrénées for financial support.


Fatiha Nmira
email: fatiha.nmira@edf.fr

Li Ma
email: li.ma@edf.fr

Jean-Louis Consalvi
email: jean-louis.consalvi@univ-amu.fr

Influence of gas radiative property models on Large Eddy Simulation of 1 m methanol pool fires

Keywords: Large methanol pool fire, large eddy simulation, radiative heat transfer, gas radiative property models, angular discretization

The main objective of this work is to analyze the effects of gas radiative property models on the radiative outputs and flame structure in a 1 m diameter methanol pool fire. Large Eddy Simulation (LES) are run with the non-adiabatic steady laminar flamelet (SLF)/presumed filtered density function (FDF) model to close subgrid-scale (SGS) turbulence-chemistry and turbulence-radiation emission interactions. The radiative transfer equation (RTE) is solved using the Finite Volume Method (FVM) with different angular meshes, including uniform angular dicretizations comprising 16 (polar angle) × 24 (azimuthal angle) and 48 × 96 control angles and the FT n scheme with n up to 48. Four gas radiative property models, namely the Rank Correlated Full Spectrum k-distribution (RCFSK), the non-grey Weighted-Sum-of-Grey-Gases (WSGG), and two versions of the grey WSGG based on different evaluations of the mean path length are assessed. Model predictions with the RCFSK reproduce with fidelity the available experimental data in terms of

Introduction

Experimental studies evidenced that radiation is the dominant mode of heat transfer to fuel surface for scales larger than about 0.2-0.3 m [START_REF] De Ris | Fire radiation -A review[END_REF]. More quantitatively, Hamins et al. [START_REF] Hamins | Heat feedback to the fuel surface in pool fires[END_REF] reported that radiation contributes to the total heat feedback for 55 %, 80 %, and 96 % in the case of 0.3 m diameter methanol, heptane and toluene pool fires, respectively. This contribution generally increases with the fire size and the fuel sooting propensity [START_REF] Ditch | Dorofeev, Pool fires -An empirical correlation[END_REF].

Consequently, the development of LES-based fire simulators over the last 20 years raised naturally the issue of the radiation modelling for fire applications [START_REF] Xi | Fire dynamics simulation of a turbulent buoyant flame using a mixture-fractionbased combustion model[END_REF][START_REF] Wang | Large Eddy Simulation of fire plumes[END_REF][START_REF] Chen | Large Eddy Simulation of a medium-scale methanol pool fire using the extended eddy dissipation concept[END_REF][START_REF] Chen | Extension of the eddy dissipation concept and smoke point soot model to the LES frame for fire simulations[END_REF][START_REF] Chatterjee | Application of a subgrid soot radiation model in the numerical simulation of a heptane pool fire[END_REF][START_REF] Maragkos | Advances in modelling in CFD simulations of turbulent gaseous pool fires[END_REF][START_REF] Maragkos | Large eddy simulations of CH 4 fire plumes[END_REF][START_REF] Snegirev | On soot and radiation modeling in buoyant turbulent diffusion flames[END_REF][START_REF] Fraga | On the individual importance of temperature and concentration fluctuations in the turbulence-radiation interaction in pool fires[END_REF][START_REF] Maragkos | Towards predictive simulations of gaseous pool fires[END_REF][START_REF] Sikic | Non-grey radiative heat transfer modelling in LES-CFD simulated methanol pool fires[END_REF][START_REF] Wu | Detailed modeling of a small-scale turbulent pool fire[END_REF]. At the same time, the radiative heat transfer community reported significant progresses in the modelling of radiation in turbulent flames [START_REF] Modest | Radiative Heat Transfer in Turbulent Combustion Systems: Theory and Applications[END_REF]. This issue can be divided into three separate sub-problems, namely the RTE solver, the spectral dependence of radiating species, and the turbulence radiation interaction (TRI). Firstly, nowadays discrete ordinates methods (DOM) and finite volume method (FVM) are widely used as RTE solver mainly due to their compatibility with the discretization of the fluid dynamics equations, ease to code, fairly good accuracy, and often acceptable computational efficiency [START_REF] Coelho | Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media[END_REF]. Moreover, Monte Carlo techniques were also used in some recent simulations of flames (see [START_REF] Wu | Detailed modeling of a small-scale turbulent pool fire[END_REF][START_REF] Wang | Monte Carlo simulation of radiative heat transfer and turbulence interactions in methane/air jet flames[END_REF][START_REF] Gupta | Turbulence-radiation interactions in Large Eddy Simulations of luminous and nonluminous nonpremixed flames[END_REF][START_REF] Rodrigues | Analysis of radiative transfer in a turbulent sooting jet flame using a Monte Carlo method coupled to Large Eddy Simulation[END_REF]). Secondly, the absorption coefficient of the radiating combustion gases is strongly dependent on the wavenumber.

The modelling of gas radiative properties has benefited of the development of accurate high-temperature high-resolution spectroscopic databases such as HITEMP 2010 [START_REF] Rothman | HITEMP: the high-temperature molecular spectroscopic database[END_REF]. Line-by-Line (LBL) has then emerged as the reference for decoupled radiative heat transfer calculations and was combined to Monte Carlo techniques for coupled simulations [START_REF] Wang | Monte Carlo simulation of radiative heat transfer and turbulence interactions in methane/air jet flames[END_REF]. However, LBL/Monte Carlo calculations are limited to academic configurations. Alternative global gas property models were developed based on the k-distribution concept, such as the Full-Spectrum Correlated-k (FSCK) or the Spectral Line based Weighted-Sum-of-Grey-Gases (SLW). These models were found to provide a good compromise between accuracy and computational efficiency and to be adequate for engineering applications [START_REF] Denison | A spectral line based weighted-sum-of-graygases model for arbitrary RTE solvers[END_REF][START_REF] Denison | The spectral-line-based weighted-sum-ofgray-gases model in nonisothermal nonhomogeneous media[END_REF][START_REF] Denison | Development and application of an absorption line black-body distribution function for CO 2[END_REF][START_REF] Denison | The spectral-line weighted-sum-of-graygases model for H 2 O/CO 2 mixtures[END_REF][START_REF] Modest | The full spectrum correlated-k distribution for thermal radiation from molecular gas particulate mixtures[END_REF][START_REF] Cai | Improved full-spectrum k-distribution implementation for inhomogeneous media using a narrow-band database[END_REF][START_REF] Solovjov | The rank correlated SLW model of gas radiation in non-uniform media[END_REF][START_REF] Solovjov | The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model[END_REF]. Although having similar features with the Weighted-Sum-of-Grey-Gases (WSGG) model, these methods do not suffer from its limitation, namely its restriction to spatially constant absorption coefficients [START_REF] Modest | Radiative Heat Transfer in Turbulent Combustion Systems: Theory and Applications[END_REF]. FSCK/SLW models can be also applied to mixtures of gases and non-grey soot [START_REF] Modest | Assembly full spectrum k-distribution from a narrow band database: effects of mixing gases, gases and non-gray absorpting particles and non-gray scatters in non-gray enclosures[END_REF]. In addition, the development of lookup tables has significantly improved their computational efficiency [START_REF] Pearson | Efficient representation of the absorption line blackbody distribution function for H 2 O, CO 2 and CO at variable temperature, mole fraction, and total pressure[END_REF][START_REF] Wang | Improvement of full-spectrum kdistribution method using quadrature transformation[END_REF][START_REF] Wang | A full-spectrum k-distribution look-up table for radiative transfer in nonhomogeneous gaseous media[END_REF][START_REF] Wang | Full-spectrum k-distribution look-up table for nonhomogeneous gas soot mixtures[END_REF][START_REF] Wang | Efficient full-spectrum correlated-k distribution look-up table[END_REF][START_REF] Wang | Full-spectrum correlated-k-distribution look-up table for radiative transfer in nonhomogeneous participating media with gas-particle mixtures[END_REF].

Finally, TRI results from the highly non-linear coupling between turbulent fluctuations in temperature, composition, and radiative intensity [START_REF] Coelho | Numerical simulation of the interaction between turbulence and radiation in reactive flows[END_REF]. Accounting for TRI requires the modelling of two terms, namely absorption TRI and emission TRI. In LES, the contribution of turbulent fluctuations to TRI is decomposed into resolved-scale fluctuations and SGS fluctuations and only these latter require modelling. A consensus was reached that the SGS absorption TRI is negligible in both luminous and non-luminous flames [START_REF] Gupta | Turbulence-radiation interactions in Large Eddy Simulations of luminous and nonluminous nonpremixed flames[END_REF][START_REF] Coelho | Approximate solutions of the filtered radiative transfer equation in Large Eddy Simulations of turbulent reactive flows, Combust[END_REF][START_REF] Consalvi | On the modeling of the filtered radiative transfer equation in Large Eddy Simulations of lab-scale sooting turbulent diffusion flames[END_REF]. On the other hand, the importance of SGS emission TRI was found to depend on the filter size [START_REF] Coelho | Approximate solutions of the filtered radiative transfer equation in Large Eddy Simulations of turbulent reactive flows, Combust[END_REF][START_REF] Consalvi | On the modeling of the filtered radiative transfer equation in Large Eddy Simulations of lab-scale sooting turbulent diffusion flames[END_REF] and its modelling is strongly dependent on the turbulent combustion model. An appropriate way to model SGS emission TRI is to consider FDF approaches [START_REF] Gupta | Turbulence-radiation interactions in Large Eddy Simulations of luminous and nonluminous nonpremixed flames[END_REF][START_REF] Miranda | Study of turbulenceradiation interactions in Large Eddy Simulation of scaled Sandia flame D[END_REF][START_REF] Miranda | Large Eddy Simulation of a bluff-body stabilised nonpremixed flame with radiation heat transfer[END_REF].

One of the objectives of the fire simulators is to forecast the growth of fires at the scale of industrial fires. This introduces considerable challenges for the modelling of the physical processes involved and compromises between accuracy and computational resources have to be found. Consequently, less sophisticated radiation models were generally considered in most of the LES of fire plumes reported to date. These studies have mainly considered DOM and FVM as RTE solver [START_REF] Xi | Fire dynamics simulation of a turbulent buoyant flame using a mixture-fractionbased combustion model[END_REF][START_REF] Wang | Large Eddy Simulation of fire plumes[END_REF][START_REF] Chen | Large Eddy Simulation of a medium-scale methanol pool fire using the extended eddy dissipation concept[END_REF][START_REF] Chen | Extension of the eddy dissipation concept and smoke point soot model to the LES frame for fire simulations[END_REF][START_REF] Chatterjee | Application of a subgrid soot radiation model in the numerical simulation of a heptane pool fire[END_REF][START_REF] Maragkos | Advances in modelling in CFD simulations of turbulent gaseous pool fires[END_REF][START_REF] Maragkos | Large eddy simulations of CH 4 fire plumes[END_REF][START_REF] Snegirev | On soot and radiation modeling in buoyant turbulent diffusion flames[END_REF][START_REF] Fraga | On the individual importance of temperature and concentration fluctuations in the turbulence-radiation interaction in pool fires[END_REF][START_REF] Maragkos | Towards predictive simulations of gaseous pool fires[END_REF][START_REF] Sikic | Non-grey radiative heat transfer modelling in LES-CFD simulated methanol pool fires[END_REF]. Since the computational cost related to the solution of the RTE is relatively high, simplified radiative property models, assuming either an optically thin medium with the emission specified to reproduce the measured radiant fraction [START_REF] Xi | Fire dynamics simulation of a turbulent buoyant flame using a mixture-fractionbased combustion model[END_REF][START_REF] Wang | Large Eddy Simulation of fire plumes[END_REF][START_REF] Maragkos | Large eddy simulations of CH 4 fire plumes[END_REF] or a grey medium [6-8, 11, 13], were generally retained. Nevertheless, non-grey radiative property models, based on non-grey versions of the WSGG or box models [START_REF] Fraga | On the individual importance of temperature and concentration fluctuations in the turbulence-radiation interaction in pool fires[END_REF][START_REF] Sikic | Non-grey radiative heat transfer modelling in LES-CFD simulated methanol pool fires[END_REF],

were also applied in LES of medium-scale methanol and ethanol pool fires. Sivic et al. [START_REF] Sikic | Non-grey radiative heat transfer modelling in LES-CFD simulated methanol pool fires[END_REF] assessed several radiative property models, including grey and non-grey implementations of the WSGG and the exponential wide bandbased box model, to simulate 30 cm diameter methanol pool fires and recommended to use non-grey versions of the WSGG. On the other hand, LES of ethanol pool fires with diameters ranging from 0.5 m to 2 m demonstrated that SGS TRI contributes for a non-negligible part to radiative loss and its contribution increases significantly with the pool size [START_REF] Nmira | Turbulence-radiation interaction in Large Eddy Simulation of non-luminous pool fires[END_REF]. Neglecting it affects significantly the predictions of the fire plume structure and radiative heat flux even for medium-scale pool fires. Several other works [START_REF] Chatterjee | Application of a subgrid soot radiation model in the numerical simulation of a heptane pool fire[END_REF][START_REF] Snegirev | On soot and radiation modeling in buoyant turbulent diffusion flames[END_REF][START_REF] Sikic | Non-grey radiative heat transfer modelling in LES-CFD simulated methanol pool fires[END_REF] have extended the moment-based closure, proposed by Snegirev for RANS [START_REF] Snegirev | Statistical modeling of thermal radiation transfer in buoyant turbulent diffusion flames[END_REF], to model SGS emission TRI. This approach consists in approximating the filtered emission term by a Taylor series expansion and retaining only the lower-order moments. Nevertheless, moment-based methods introduce empirical adjustable coefficients that are generally tuned to match the experimental data [START_REF] Chatterjee | Application of a subgrid soot radiation model in the numerical simulation of a heptane pool fire[END_REF][START_REF] Snegirev | On soot and radiation modeling in buoyant turbulent diffusion flames[END_REF][START_REF] Sikic | Non-grey radiative heat transfer modelling in LES-CFD simulated methanol pool fires[END_REF]. Wu et al. presented DNS of a 7.1 cm heptane pool fire using a very fine description of radiative heat transfer [START_REF] Wu | Detailed modeling of a small-scale turbulent pool fire[END_REF]. In their work, radiation was modelled using the LBL/Photon Monte Carlo proposed by Wang et al. [START_REF] Wang | Monte Carlo simulation of radiative heat transfer and turbulence interactions in methane/air jet flames[END_REF], and the contributions of CO 2 , H 2 O, CO, CH 4 , C 2 H 4 and soot were taken into account.

The objective of the present study is twofold. The first aim is to validate the overall performance of a LES-based fire model to reproduce the structure of the 1 m methanol pool fire studied experimentally by Sung et al. [START_REF] Sung | The Thermal Character of a 1 m Methanol Pool Fire[END_REF].

The model includes a non-adiabatic SLF/presumed FDF model to close SGS turbulence-chemistry and turbulence-radiation emission interactions and the Rank Correlated Full Spectrum k-distribution (RCFSK) as spectral gas radiation model [START_REF] Solovjov | The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model[END_REF]. This fine description of gas radiation and SGS TRI in large-scale methanol pool fires constitutes the main originality of these simulations. The second aim is to assess the effects of angular discretization and radiative property models on radiative heat transfer. Four radiative property models, namely the RCFSK, the non-grey WSGG, and two versions of the grey WSGG based on different evaluations of the mean path length are considered. To the best of the authors knowledge, such a complete analysis of radiative property models on LES of large pool fires was not reported in the literature.

The article is organized as follows. The second section presents the numerical and physical models including the different radiation models. Numerical predictions and effects of the radiation models on flame structure and radiative outputs are discussed in Section 3. Finally Section 4 contains the concluding remarks drawn from the present work.

Numerical and physical models

Governing equations

The turbulent diffusion flame flow field is modelled by the Favre-Filtered conservation equations of mass, momentum, enthalpy, h, and mixture fraction, Z, as:

∂ ρ ∂t + ∂ ρũ i ∂x i = 0 (1)
∂ ρũ j ∂t + ∂ ρũ i ũj ∂x i = - ∂ p ∂x j + ∂ ∂x i (μ + µ t ) Sij + (ρ -ρ ∞ )g j (2)
∂ ρ Z ∂t + ∂ ρũ i Z ∂x i = ∂ ∂x i ρ( D + D t ) ∂ Z ∂x i (3)
∂ ρh ∂t + ∂ ρũ i h ∂x i = ∂ ∂x i ρ( D + D t ) ∂ h ∂x i -∇ • q R (4)
(•) and (•) represent filtered and density-weighted filtered quantities, respectively. ρ, u i , p, D, µ are the density, velocity vector components, u = (u, v, w), pressure, molecular diffusivity, and viscosity, respectively.

The SGS momentum stress and scalar flux are computed using a dynamic Smagorinsky model and a dynamic eddy diffusivity model, respectively [START_REF] Moin | A dynamic subgrid-scale model for compressible turbulence and scalar transport[END_REF]:

τ sgs u i u j = -ρ( u i u j -ũi ũj ) ≈ 2µ t Sij (5)
τ sgs u i Z = -ρ( u i Z -ũi Z) ≈ ρD t ∂ Z ∂x i (6)
where µ t = C s ρ∆ 2 | S| is the turbulent eddy viscosity and

ρD t = C z ρ∆ 2 | S|
is the SGS diffusivity, with | S| = 2 Sij Sij being the norm of the resolved strain rate tensor, Sij , and ∆ the filter width. The coefficients C s and C z are calculated using the dynamic procedures according to Refs. [START_REF] Moin | A dynamic subgrid-scale model for compressible turbulence and scalar transport[END_REF][START_REF] Lilly | A proposed modification of the Germano subgrid-scale closure method[END_REF].

The Favre-filtered transport equations are solved by using the second-order iterative variable-density solver developed by Ma et al. [START_REF] Ma | Verification and validation of a variableâdensity solver for fire safety applications[END_REF] and implemented in the finite volume code Code_Saturne v5.0.9 [48]. The second-order Crank-Nicolson scheme is used for time advancement. The Total Variation Diminuishing (TVD) scheme is applied for convection in the mixture fraction transport to limit numerical oscillation whereas a second-order central difference scheme (CDS) is used for diffusion. For the momentum equation both convective and diffusive terms are discretized by using a second-order CDS.

Combustion model

The non-adiabatic SLF model is used to obtain the local thermochemical state relationship, φ f l , as a function of the mixture fraction, Z, the scalar dissipation rate, χ, and the enthalpy defect, X R = h -h ad , where h ad is the adiabatic enthalpy [START_REF] Carbonell | Flamelet mathematical models for non-premixed laminar combustion[END_REF]. The flamelet library was generated by solving the governing equations of counterflow diffusion flames in the physical space at a series of specified strain rates using the CHEMKIN code [START_REF] Lutz | OPPDIF: a FORTRAN program for computing opposed-flow diffusion flames[END_REF] and the full chemical kinetic mechanism developed by Li et al. [START_REF] Li | A comprehensive kinetic mechanism for CO, CH 2 O, and CH 3 OH combustion[END_REF]. The mixture fraction distributions are obtained by solving a transport equation for the mixture fraction, as suggested by Pitsch and Peters [START_REF] Pitsch | A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects[END_REF]. The Favre-filtered thermochemical quantities are then obtained from the state relationships by convolution with a presumed FDF:

φ = φ f l (Z, χ, X R ) P (Z, χ, X R )dZdχdX R (7)
Z, χ and X R are assumed to be statistically independent and the marginal FDFs are modelled by a β-distribution for Z and two δ-distributions for χ and X R :

P (Z, χ, X R ) = β(Z; Z, V Z )δ(χ -χ)δ(X R -XR ) (8)
where V Z is the SGS mixture fraction variance. All thermochemical quantities can then be expressed as a function of Z, V Z , χ, and XR [START_REF] Pierce | Progress-variable approach for Large Eddy Simulation of non-premixed turbulent combustion[END_REF].

Subgrid scalar variance and dissipation modelling

In this work, we consider a transport equation for the second moment of the mixture fraction Z 2 (STE) and the subgrid variance is then calculated from its definition [START_REF] Jiménez | Subgrid scale variance and dissipation of a scalar field in Large Eddy Simulations[END_REF],

V Z = Z 2 -Z2 : ∂ ρ Z 2 ∂t + ∂ ρũ i Z 2 ∂x i = ∂ ∂x i ρ( D + D t ) ∂ Z 2 ∂x i -ρ χ (9)
The remaining modelling step for STE concerns the filtered scalar dissipation rate, χ. Jiménez et al. [START_REF] Jiménez | Subgrid scale variance and dissipation of a scalar field in Large Eddy Simulations[END_REF] proposed to model the filtered scalar dissipation rate by relating the SGS scalar mixing time scale to the SGS turbulent time

scale. An equivalent SGS turbulent characteristic time τ is introduced as the ratio between SGS kinetic energy, κ sgs , and the filtered kinetic energy dissipation rate, ε. Given a proportionality between both time scales, the model for χ is derived as:

χ V Z = 1 τZ ≈ C τ = C ε κ sgs (10)
Therefore, the filtered scalar dissipation rate χ can be written as [START_REF] Jiménez | Subgrid scale variance and dissipation of a scalar field in Large Eddy Simulations[END_REF] with C I computed by a dynamic approach:

χ = D + D t C I ∆ 2 V Z (11)

Radiation modelling

Water vapour and carbon dioxide are considered as the only radiating species since our simulations showed that the contribution of carbon monoxide is negligible. For all the gas radiative property models, the line parameters of CO 2 and H 2 O are taken from HITEMP 2010 [START_REF] Rothman | HITEMP: the high-temperature molecular spectroscopic database[END_REF]. The filtered RTE can be written in a generic form as follows [START_REF] Modest | Radiative Heat Transfer in Turbulent Combustion Systems: Theory and Applications[END_REF]:

dI i ds + κ i I i = κ i a i I b ; i = 1, N g (12)
where I i , κ i , and I b are the radiative intensity, non-grey absorption coefficient, and blackbody intensity, respectively. N g and a i are the number of quadrature points and the stretching function for the RCFSK or the number of grey gases and the weight factor for the non-grey WSGG, respectively. For the grey models, only one RTE (N g = 1) has to be solved and the weight factor is set equal to 1.

The filtered absorption term, κ i I i , is closed by neglecting the SGS absorption TRI, leading to κ i I i ≈ κ i I i . This approximation was found to be valid in LES of non-luminous and luminous lab-and large-scale diffusion flames in which about 80% of the turbulent fluctuations are resolved [START_REF] Gupta | Turbulence-radiation interactions in Large Eddy Simulations of luminous and nonluminous nonpremixed flames[END_REF][START_REF] Coelho | Approximate solutions of the filtered radiative transfer equation in Large Eddy Simulations of turbulent reactive flows, Combust[END_REF][START_REF] Consalvi | On the modeling of the filtered radiative transfer equation in Large Eddy Simulations of lab-scale sooting turbulent diffusion flames[END_REF]. The absorption coefficient and the emission term depend only on temperature and mole fractions of CO 2 and H 2 O. Therefore, the filtering operation for these terms can be performed accurately by using the FDF approach [START_REF] Modest | Radiative Heat Transfer in Turbulent Combustion Systems: Theory and Applications[END_REF]:

κ i = ρ (κ i ) f l (Z, χ, χR ) ρ f l (Z, χ, χR ) β(Z; Z, V Z )dZ (13)
κ i a i I b = ρ (κ i a i I b ) f l (Z, χ, χR ) ρ f l (Z, χ, χR ) β(Z; Z, V Z )dZ (14)

RTE solver

The filtered RTE is solved by using the FVM [START_REF] Raithby | Finite-volume method for predicting a radiant heat transfer in enclosures with participating media[END_REF][START_REF] Chai | Patankar Finite volume method for radiation heat transfer[END_REF] with a uniform angular mesh of 384 (N θ × N φ = 16 × 24) control angles. The subscripts θ and φ represent the polar and azimutal angles, respectively. The selection of this angular discretization was based on the study of Jensen et al. [START_REF] Jensen | On various modeling approaches to radiative heat transfer in pool fires[END_REF] who suggested that, for uniform angular discretization, approximately 50 angles inside and 350 angles outside the fire are needed to adequately resolve radiation.

A frozen field analysis will be considered to investigate the angular mesh effects on the radiative outputs. In this analysis, instantaneous fields of filtered absorption coefficient (Eq. ( 13)) and emission term (Eq. ( 14)), computed with the uniform 16 × 24 angular mesh, are saved during the statistically stationary state. These fields are used to solve instantaneous RTE (Eq. ( 12))

with the other angular meshes over the statistically stationary state and, then, the resulting instantaneous radiative intensities are averaged to get the mean absorption term and radiative fluxes. The other angular meshes considered in the present study are, on the one hand, a three-time finer uniform angular mesh with 4608 (N θ × N φ = 48 × 96) control angles and, on the other hand, the non-uniform FT n angular discretizations [START_REF] Kim | A new angular discretization scheme of the finite volume method for 3-D radiative heat transfer in absorbing, emitting and anisotropically scattering media[END_REF]. In the FT n FVM, the polar angle, θ, is divided uniformly into an even number, n, while the azimuthal angle, φ, is uniformly divided into the numbers of the sequence of 4, 8, 12,...,2n -4, 2n, 2n, 2n -4,..., 8 and 4 in each level of the polar angle [START_REF] Kim | A new angular discretization scheme of the finite volume method for 3-D radiative heat transfer in absorbing, emitting and anisotropically scattering media[END_REF]. This results in n × (n + 2) control angles.

Using a frozen field analysis is justified by the fact that meshes finer than 16

× 24 were found to have no influence on the radiative heat transfer inside the flame and to change only the vertical distributions of radiative flux outside the flame. Refining the angular mesh further than 48 × 96 was found to have no effect on the vertical distributions of radiative flux outside the flame and this discretization will be used as reference.

RCFSK

The RCFSK model belongs to the family of the global k-distribution-based gas radiation models as the SLW or the classical FSCK. The RCFSK preserves the total emission and does not require any specification of a reference state [START_REF] Solovjov | The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model[END_REF]. In configurations relevant for combustion applications, the RCFSK was found to provide an overall very good agreement with reference LBL or Narrow Band calculations in both emission and absorption dominated problems [START_REF] Solovjov | The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model[END_REF][START_REF] Liu | Effects of the k-value solution schemes on radiation heat transfer modelling in oxy-fuel flames using the full-spectrum correlated k-distribution method[END_REF][START_REF] Consalvi | Assessment of engineering gas radiative property models in high pressure turbulent diffusion flames[END_REF]. Consequently, it will be used as reference in the present study.

Full spectrum (FS) cumulative k-g distribution function is defined as [START_REF] Modest | Radiative Heat Transfer in Turbulent Combustion Systems: Theory and Applications[END_REF][START_REF] Modest | The full spectrum correlated-k distribution for thermal radiation from molecular gas particulate mixtures[END_REF]:

g(k, φ, T p ) = ∞ 0 H[k -κ η (φ)]I bη (T p )dη I b (T p ) (15)
where and Riazzi [START_REF] Modest | Assembly full spectrum k-distribution from a narrow band database: effects of mixing gases, gases and non-gray absorpting particles and non-gray scatters in non-gray enclosures[END_REF], and a 10-point Gauss-Legendre quadrature scheme (N g = 10)

φ = {x CO 2 , x H 2 O , T } is
is used (see Eq. ( 12)). For each quadrature point, g i , the RCFSK scheme determines the absorption coefficient, κ i , and the stretching function, a i (T ),

by solving [START_REF] Solovjov | The rank correlated FSK model for prediction of gas radiation in non-uniform media, and its relationship to the rank correlated SLW model[END_REF]:

g(κ i , φ, T p ) = g i (16
)

a i (T ) = g[κ i , φ, T ] -g[κ i-1 , φ, T ] ∆g ; ∆g = g i -g i-1 (17)
The divergence of the radiative flux is then computed from the following equation:

∇ • q R = Ng i=1 4πκ i a i I b ∆g Q emi - Ng i=1 κ i G i ∆g Q abs (18)
where G i = 4π I i dΩ with Ω being the solid angle. As expected, predictions were found insensitive to the choice of T p . In the present simulations, T p was set equal to 1500 K.

WSGG

The WSGG assumes that the total emissivity, , can be computed as follows [START_REF] Modest | Radiative Heat Transfer in Turbulent Combustion Systems: Theory and Applications[END_REF]:

= Ng i=1 a i (T )[1 -exp(-κ i L)] (19)
with

κ i = (x CO 2 + x H 2 O )p 0 κ p,i and a i = K k=0 b i,k T k (20)
L is the mean path length. In the present study, p 0 = 1 atm, N g = 4 and K = 4. The constant WSGG parameters, κ p,i and b i,k , derived in Ref. [START_REF] Coelho | WSGG correlations based on HITEMP2010 for gas mixtures of H 2 O and CO 2 in high total pressure conditions[END_REF] for x H 2 O /x CO 2 = 2, are used. These parameters were optimized to fit total emissivities determined from HITEMP 2010 [START_REF] Rothman | HITEMP: the high-temperature molecular spectroscopic database[END_REF] for a set of specified temperatures and optical path-lengths.

The non-grey WSGG solves 4 RTEs (N g = 4). For each RTE, κ i and a i are computed from Eq. ( 20). This approach will be referred to as WSGG-NG, hereafter. The divergence of the radiative flux is then determined as:

∇ • q R = Ng i=1 4πκ i a i I b Q emi - Ng i=1 κ i G i Q abs ; with G i = 4π I i dΩ (21)
The grey WSGG consists in determining a grey absorption coefficient, κ, from the WSGG emissivity (Eq. 19):

κ = - ln(1 -) L (22)
There is no theoretical procedure to determine L in Eqs. [START_REF] Gupta | Turbulence-radiation interactions in Large Eddy Simulations of luminous and nonluminous nonpremixed flames[END_REF] and [START_REF] Denison | A spectral line based weighted-sum-of-graygases model for arbitrary RTE solvers[END_REF]. Two approaches were considered in the literature. The first approach consists in using a cell-based mean path length whereas the second assumes a domain or flame-based mean path length. The two options are considered in the present study. The cell-based approach is referred to as WSGG-G-CB hereafter and, following the recommendation of Refs. [START_REF] Fraga | Evaluation of different gray gas formulations against line-by-line calculations in twoand three-dimensional configurations for participating media composed by CO 2 , H 2 O and soot[END_REF][START_REF] Mcgrattan | Mathematical model[END_REF], L is determined as five times the characteristic local grid size. On the other hand, the flamebased determination of L is arbitrary since it depends on the way to define the flame. In the present study, L = 4V /A, where V and A are the flame volume and surface, respectively. The flame shape is assumed to be a cone with a circular base of diameter equal to the pool diameter and a height defined by the iso-contour 600 K. This value was selected since it is expected to characterize the intermittent flame tip [START_REF] Mccaffrey | Purely Buoyant Diffusion Flames Some Experimental Results[END_REF]. Varying this temperature between 500 and 700 K was found to effect the radiant fraction by less than 1.5 %. This approach will be referred to as WSGG-G-FB, hereafter.

Results and discussions

Computational details

The 1 m diameter methanol pool fire investigated experimentally by Sung et al. [START_REF] Sung | The Thermal Character of a 1 m Methanol Pool Fire[END_REF] is considered for simulations. The burner was located 30 cm above the floor and the fuel lip height, defined as the fuel level below the burner rim, was maintained at 1 cm. The heat release rate (HRR, Qch ) was determined either from oxygen consumption calorimetry or from the measured mass burning rate assuming a complete combustion. As expected for methanol, both techniques were found to be consistent with a measured HRR of 256 kW. Fast Gardon-type total heat flux gauges (see Fig. 1) . Sung et al. [START_REF] Sung | The Thermal Character of a 1 m Methanol Pool Fire[END_REF] also deduced from their data the total radiative feedback, QR,S = A b q R,S dA (see Fig. 1). This quantity represents the incident radiative flux on the fuel surface integrated over the burner surface, A b . It was normalized by the HRR to provide χ R,S = QR,S / Qch . This latter set of data is completed by the local radiative feedback, q R,S , measured by Klassen and Gore [START_REF] Klassen | Structure and radiation properties of pool fires[END_REF].

Simulations are performed in a computational domain (x, y, z) of 9 × 9 × 7 m 3 (see Fig. 1). In the present study, z represents the vertical direction.

Consistently with the experimental configuration, the burner is located 30 cm above the floor and the fuel lip height is set equal to 1 cm. It was found necessary to respect these experimental features to reproduce adequately the pool dynamics. A non-uniform structured mesh with 8.01 million of cells is considered. The mesh is refined over the fuel surface with a cell size (∆x, All simulations were performed on the supercomputer Gaia of EDF R&D. This cluster is made of 1224 computer nodes and 42912 cores. Processor are Intel Xeon Gold 6140 CPU @ 2.30 GHz. The present LES were performed on 940 cores. Table 1 provides the CPU times for all the radiative models in one time step. A careful examination shows that CPU times for the different angular meshes and the different radiative property models increase almost linearly with number of control angles and the number of RTEs to be solved, respectively.

Quality of the LES

The ratio of resolved temperature variance, T 2 ReS = T 2 -T 2 , to the total temperature variance, T 2 = T 2 -T 2 , is considered to assess the quality of the present LES. Figure 2 shows radial profiles of this ratio at different heights above the burner covering the flaming region. It can be observed that more than 80 % of temperature variance is on the whole resolved by the present LES.

Comparison with available experimental data

In this section, the LES results obtained by the RCFSK/FVM (16 × 24) radiation model are compared with the experimental data. Figure 5a shows that the measured axial temperature fluctuation is of the order of 290 K very close to the burner and decreases down to 247 K at about z= 0.30 m. After this location, it increases with z to reach a peak of about 330 K at z= 0.8 m before decreasing as z is further increased. The numerical model captures well these trends. In particular, the peak location as well as the rates of increase and decrease are well reproduced. Figure 5 shows also that the experimental data exhibit pronounced M-shaped radial profiles close to the burner and transit progressively toward flatter profiles as z increases (see fig. 5b-f). The model captures also well these trends and provides predictions in overall good agreement with the experimental data. Nevertheless, it overestimates on the whole the temperature fluctuations. These discrepancies may be attributed, at least partially, to the measurements since previous experimental studies suggested that temperature fluctuations may be underestimated when measured by 50 µm thermocouples despite the use of compensation techniques [START_REF] Crauford | Experimental and numerical simulation of a buoyant fire[END_REF][START_REF] Weckman | Processing effects in simultaneous velocity and temperature measurements in an intermittent combusting flow[END_REF][START_REF] Weckman | Experimental investigation of the turbulence structure of medium-scale methanol pool fires[END_REF].

Table 2 reports the total emission, Qemi = V Q emi dV , the total absorption, Qabs = V Q abs dV , the ratio of Qabs to Qemi that represents the part of emission reabsorbed within the flame and can be used to quantify the flame optical thickness [START_REF] Nmira | Turbulence-radiation interaction in Large Eddy Simulation of non-luminous pool fires[END_REF], the radiant fraction, χ R = ( Qemi -Qabs )/ Qch , and χ R,S . These results show that about 59.8 % of emission is reabsorbed within the flame. The predicted χ R is 0.269 and overestimates the experimental one of 0.22 ± 16 % by about 22 %. The predicted χ R,S is 0.059, in closer agreement with the experimental data of 0.055 ± 21 %. The vertical, radial and feedback distributions of radiative flux are plotted in Fig. 6a-c. Let us start to analyze the results obtained with the 16×24 angular discretization. Predictions of the radiative flux in the downward direction outside the burner (see Fig. 6b) and the radiative feedback toward the fuel surface (see Fig. 6c) are in overall good agreement with the experimental data. Nevertheless, the model overpredicts the radiative flux at vicinity of the burner (see Fig. 6b) and underpredicts the radiative feedback by about 10% (see Fig. 6c). On the other hand, the vertical distribution of radiative flux exhibits clearly ray effects, especially for 0 ≤ z ≤ 1 m (see Fig. 6a).

Such effects are a major drawback of both DOM and FVM and are favored in optically thin medium [START_REF] Coelho | Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media[END_REF]. As a consequence, the present configuration is particularly sensitive to ray effetcts since radiation travels mainly a transparent medium before reaching the location r = 2.07 m where the vertical distribution is measured. The ray effects can be reduced by refining the angular mesh [START_REF] Coelho | Advances in the discrete ordinates and finite volume methods for the solution of radiative heat transfer problems in participating media[END_REF].

Radiation calculations were also performed by neglecting TRI with the 16

× 24 angular mesh. In these calculations, radiation is solved in decoupled manner by using time-averaged temperature and mole fractions of CO 2 and H 2 O obtained from the LES simulations. The total emission and the radiant fraction, obtained by neglecting TRI, were found to be Qemi,NoTRI =40 ×10 3 kW and χ R,N oT RI = 0.051, respectively. A comparison with the predictions reported in Table 2 shows that TRI represents about 80 % of the total emission and radiative loss. This high contribution agrees with the results reported in the literature for medium-scale non-luminous pool fires [START_REF] Fraga | On the individual importance of temperature and concentration fluctuations in the turbulence-radiation interaction in pool fires[END_REF][START_REF] Nmira | Turbulence-radiation interaction in Large Eddy Simulation of non-luminous pool fires[END_REF] and can be explained, on the one hand, by the rather low time-averaged temperature in pool fires and, on the other hand, by the high level of turbulence intensity due to the puffing process.

Effects of angular mesh

Results in Table 2 and Fig. 6a-c show that using the uniform 48 × 96 angular mesh instead of the uniform 16 × 24 angular discretization does not modify the predictions of Qabs , χ R and χ R,S as well as the radiative feedback toward the fuel surface (see Fig. 6c). In addition, this has almost imperceptible effects on the radial distribution of radiative flux along the plane of the burner rim (see Fig. 6b). In an opposite way, it improves significantly the vertical distribution of radiative flux by eliminating the ray effects (see Fig. 6a).

Table 3 and Fig. 6d-f investigate the effects of the FT n angular discretizations on both integrated and local radiative outputs. In agreement with the previous discussion, the results show clearly that the angular meshes affect only the vertical distribution of radiative flux outside the flame.

Figure 6d shows that significant ray effects are observed for FT 12 and FT 16 .

The

Effects of radiative property models

Table 4 shows that the WSGG-NG overestimates significantly both the total emission and the total absorption and, by a less extent, the ratio Qabs / Qemi , the radiant fraction, χ R , and the normalized radiative feedback to the fuel surface, χ R,S . In particular, these three latter quantities are moderately overestimated by about 8.07 %, 7.03% and 2.10 %, respectively. The WSGG-G-CB and WSGG-G-FB underestimate significantly both the total emission and the total absorption as well as Qabs / Qemi that is only of about 17.5% The WSGG-G-CB overpredicts χ R and χ R,S by 36.4% and 32.9%, respectively. On the other hand, as observed in previous studies involving decoupled radiative heat transfer calculations [START_REF] Fraga | On the individual importance of temperature and concentration fluctuations in the turbulence-radiation interaction in pool fires[END_REF][START_REF] Demarco | Assessment of radiative property models in non-gray sooting media[END_REF], the WSGG-G-FB provides better predictions of the radiative loss than the WSGG-G-CB. Nevertheless, discrepancies of the order of 18.2 % are still observed for χ R,S . lead to relative errors as compared to the RCFSK on the peak of vertical radiative flux (see Fig. 7a), on the radiative flux downward at r = 0.5 m (see Fig. 7b), and on the radiative feedback at the center of the fuel surface (see Fig. 7c), of 15.44 % and -22.05%, 18.95 % and -19.91%, and 40.2 % and -13.97 %, respectively.

The effects of the radiative property models on axial profiles of the mean emission term, mean absorption term, mean divergence of the radiative flux, and mean and rms temperature are investigated in Fig. 8. Consistently with the results in Table 4, the WSGG-NG overestimates significantly both local emission and absorption terms, but predicts a mean radiative source term in much better agreement with the RCSFK. However, the WSGG-NG produces noticeable discrepancies on the mean temperature, especially in the region located between z = 0 and z = 0.75 m. The peak of mean temperature is slightly shifted toward the fuel surface and its value is underpredicted by about 60 K as compared to the RCFSK. The WSGG-NG model leads also to a slight overprediction of the rms value of temperature fluctuations in this region with a peak value higher by about 20 K than that predicted with the RCFSK. The WSGG-G-CB overestimates substantially the radiative loss (see Fig. 8c). Consequently, it predicts mean temperature significantly lower than the RCFSK along the entire centreline (see Fig. 8d). Figure 8d shows that the peak value of mean temperature is lower by about 150 K than that computed with the RCFSK. A consequence of this underestimation of the temperature is that the buoyant forces are underestimated, producing in turn an underestimation of the temperature fluctuations as observed in Fig. 8e.

The WSGG-G-FB model provides a divergence of the radiative flux as well as mean and rms temperature comparable to those predicted by the WSGG-NG model. Nevertheless, it has to keep in mind that the WSGG-NG outperforms significantly the WSGG-G-FB in the prediction of the radiative flux (see Fig. 7).

Eventually, Fig. 3 shows that the gas radiative models have no effect on the prediction of the puffing frequency as well as on the first harmonic. 3. Whatever the definition of the mean path length, the grey WSGG models fails to reproduce the radiative structure of the fire plume, predicting an optically thin flame instead of an optically intermediate medium.

The WSGG-G-FB provides a better description of the radiative loss than the WSGG-G-CB. However, it leads to relative errors in the range 15-20 % on the radiative fluxes.

4. The non-grey WSGG model overestimates significantly both emission and absorption, but leads to predictions of the radiative loss and radiative flux within 10 % of the RCFSK. These results suggest that it can be a reasonable alternative for non-sooting pool fires.

  an array of thermodynamic variables affecting the spectral absorption coefficient, κ η , at the wavenumber η. H is the Heaviside function, k a given value of the absorption coefficient, and I bη (T p ) the spectral blackbody intensity at the Planck temperature T p . In the present study, mixed FS k-g distributions (for mixtures of H 2 O and CO 2 ) are constructed from HITEMP 2010[START_REF] Rothman | HITEMP: the high-temperature molecular spectroscopic database[END_REF] by using the procedure proposed by Modest

Fourier

  power spectrum of the time-varying flame height revealed a puffing frequency of 1.37 Hz and a first harmonic of 2.75 Hz. Temperature measurements were performed using 50 µm diameter Type S thermocouples and were corrected for thermal inertia effects. The compensation technique was based on an instantaneous time constant computed from the thermocouple bead geometry and an estimation of the flow conditions for the convective heat transfer. Vertical distribution, at a distance of 2.07 m from the pool axis, and radial distribution, along the plane of the burner rim outside the pool fires, of radiative flux were measured with wide-view angle, water-cooled,

  ∆y, ∆z) of 8.15 × 8.15 × 5 mm 3 . Outside the pan, ∆x and ∆y are stretched progressively towards the sides. In the vertical direction, ∆z = 5 mm is applied between the fuel surface (z = 0) and the burner rim (z = 1 cm). ∆z is then stretched from z = 0.01 m to z = 0.326 m to reach 1.58 cm. A uniform ∆z = 1.58 cm is then applied up to z = 1.8 m. Above z= 1.8 m, ∆z is stretched progressively.Typical outflow and entrainment boundary conditions are used for openboundaries at the outlet and sides, respectively. The fuel inlet temperature is set to the boiling temperature of methanol, i.e. 338 K. The inlet velocity is imposed to provide the specified HRR and both convective and diffusive mass and energy fluxes are accounted for. In the rest domain, the classical wall boundary condition is imposed.Simulations were run for 35 s and the time-averaged mean and root mean square values were collected over the last 20 s. The first 15 s of simulation were used to establish a statistically stationary flow. This latter time was selected to correspond to 10 flow-through times, t f = L d 0 dz/w(0, z) , based on the centreline velocity along the fire plume, w, and the length of the computational domain, L d[START_REF] Kemenov | Modelling effects of subgrid-scale mixture fraction variance in LES of a piloted diffusion flame[END_REF]. In addition, it corresponds to more than 20 puffing cycles based on the characteristic puffing frequency of the present pool fire of 1.37 Hz.

Figure

  Figure 3a shows the Power Spectrum Density (PSD) computed with a fast Fourier transform of the times series of the axial velocity along the axis at a height of 0.6 m. The model predicts a puffing frequency of 1.25 Hz and a first harmonic of 2.50 Hz in good accordance with the experimental ones of 1.37 Hz and 2.75 Hz, respectively.

Figure 4a shows the

  Figure4ashows the axial distribution of mean temperature. The experimental data exhibit the expected trends. The mean temperature increases with z close to the burner, reaches a plateau in the continuous flame and, then, decreases as z is further increased in the intermittent flame and in the

Figure 5

 5 Figure5displays the axial profile and the radial profiles at different heights of the rms values of temperature fluctuations. Figure5ashows that the mea-

FT 16 and 16 ×

 16 24 angular meshes have the same polar discretization and differ from the azimuthal discretization. These two angular meshes provide almost identical vertical distributions, showing that the discretization of the polar angle is mainly responsible for these ray effects. This can be explained by the statistically axisymmetric nature of the present fire plume. The FT 24 angular discretization mitigates the ray effects and predicts the peak of vertical flux within 7 % of the 48 × 96 angular mesh. However, relative errors as large as about 16 % are still observed at z = 1.2 m. Acceptable predictions of the vertical distribution of radiative flux are observed for the FT 32 angular discretization, which involves 1088 control angles. The FT 48 angular discretization provides the same vertical distribution of radiative flux as the uniform 48 × 96 angular mesh, but considers 2400 control angles instead of 4608.

and 9 . 2 %

 92 for the WSGG-G-CB and WSGG-G-FB, respectively, instead of 59.8% for the RCFSK. These results show that the grey models are not able to reproduce the radiative structure of the flame, predicting an optically-thin flame instead of an optically intermediate medium.

Figure 7

 7 Figure 7 illustrates the effects of the radiative property models on the radiative flux distributions. Predictions with the WSGG-NG agree well with the RCFSK. On the other hand, the WSGG-G-CB model overpredicts notably these fluxes whereas the WSGG-G-FB underpredicts them but by a less extent. Quantitatively, Fig. 7 shows that the WSGG-G-CB and WSGG-G-FB

  methanol pool fires have been exercised in order to investigate the effects of gas radiative property models on the radiative outputs and flame structure. The baseline radiation model involves the RCFSK coupled to the FVM with 16 × 24 control angles. Three other gas radiative property models, namely the WSGG-NG, the WSGG-G-CB and the WSGG-G-FB, are also considered. In addition, solutions obtained with other angular meshes, including the uniform 48 × 96 angular discretization and the FT n scheme with n up to 48, are assessed. The following conclusions can be drawn: 1. The present LES-based fire model involving the non-adiabatic/presumed FDF and RCFSK radiation model provides high fidelity predictions in terms of puffing frequency and first harmonic, mean and fluctuating temperatures, radiative feedback to the pool surface and radiative loss to the surrounding. 2. All radiative outputs at the exception of vertical distributions of radiative flux outside the flame can be accurately predicted with the FT 12 angular discretization. On the other hand, finer angular meshes, considering at least 32 segments to discretize the polar angle, are required to compute accurately the vertical distributions of radiative flux outside the flame.

Figure 1 :

 1 Figure 1: A shematic diagram of the computational domain and the locations of the radiative heat flux distributions.

Figure 2 :

 2 Figure 2: Radial evolution of resolved-part of temperature variance at different heights.

Figure 3 :=Figure 6 :

 36 Figure 3: Predicted Power Spectrum Density from axial velocity along the flame axis at z = 0.6 m

Table 1 :

 1 CPU times for different radiative property models and angular meshes.

	Model	Angular mesh CPU (s)
		16 × 24	247
		48 × 96	1333
		FT 12	200
	RCFSK	FT 16	216
		FT 24	282
		FT 32	375
		FT 48	636
	RCFSK	48 × 96	1333
	WSGG-NG	48 × 96	523
	WSGG-G-CB	48 × 96	241
	WSGG-G-FB	48 × 96	230

Table 2 :

 2 Model Angular mesh Qemi (kW) Qabs (kW) Qabs / Qemi χ R χ R,S Integrated flame radiative properties. Measured radiant fractions, χ

	RCFSK	16 × 24	172	102.6	0.598	0.269 0.059
	RCFSK	48 × 96	172	102.6	0.598	0.269 0.059

R , and fractional radiative heat feedback toward the fuel surface, χ R,S , were 0.22 ± 16 % and 0.055 ± 21 %, respectively

[START_REF] Sung | The Thermal Character of a 1 m Methanol Pool Fire[END_REF]

.

Table 3 :

 3 Effects of FT n FVM angular discretization on the integrated flame radiative properties. Values in parenthesis represent the relative errors in % of the current model as compared to the RCFSK/FVM 48 × 96. Results with FT n angular discretization higher than n = 16 are not reported since these angular meshes do not introduce any discrepancies on these quantities.

Table 4 :

 4 Effects of the gas radiative property models on the integrated flame radiative properties. Values in parenthesis represent the relative errors in % of the current model as compared to the RCFSK/FVM 48 × 96.

Acknowledgements

JLC wishes to express his gratitude to Electricité de France (EDF) for financial supports.