Gilles Parent

Giacomo Erez

Anthony Collin

Mathieu Suzanne

Aurélien Thiry-Muller

Mathieu Weber

Eddie Faure

Pascal Boulet

Spectral radiation emitted by kerosene pool res

Keywords: radiative heat transfer, pool re, multi-scale, opacimetry, spectrometry

We present an equivalent medium model that considers emission from the ame volume to compute spectral radiation intensities. This is considered a more detailed description than common radiation models used in re safety applications, which often treat the ame as a grey emitting surface. Given its importance in re radiation, the present study focuses on emission by soot. The required parameters for the model are an equivalent absorption coecient, and an equivalent temperature. They were determined using two independent measurements, namely multispectral opacimetry, and infrared spectrometry. Results are presented for kerosene pool res (widths from 30 cm to 250 cm). It is shown that the equivalent temperature can be considered independent of ame size, and thus an intrinsic parameter of the fuel.

These results also make clear that radiation emitted from the ame is not grey, and can only be considered black for very large ames (i.e. wider than 1.75 m for present tests).

Introduction

Characterising radiative heat ux emitted by a re is of primary importance because it is the main heat source involved in vaporisation or pyrolysis of the fuel (for ames suciently large, i.e. wider than approx. 0.2 m [START_REF] Babrauskas | Estimating large pool re burning rates[END_REF]). Mass loss rate (MLR) and consequently heat release rate (HRR) are then driven by radiative heat ux. More generally, radiation is also a major parameter controlling re spread [START_REF] Fernandez-Pello | Controlling Mechanisms of Flame Spread[END_REF] and propagation to distant combustible targets.

Flames studied in re science are turbulent diusion ames, with fast and large spatial variations of species (combustion gases and soot) concentrations and temperature. A comprehensive description of such ames is out of reach experimentally and numerically, and is not necessary because time and space averaged heat uxes are sucient to compute the energy received by the fuel. Simplications are thus made, and in re science ame radiation is often assumed to be emitted by an equivalent grey surface (solid ame model) with a ux density equal to Φ = σ B T 4 .

(1)

In this expression two quantities have to be determined, namely the ame temperature T and the ame emissivity (σ B is the Stefan-Boltzmann constant). The ame temperature can be measured using thermocouples, but attention Email address: gilles.parent@univ-lorraine.fr (Gilles Parent) must be paid to account for heat losses (mainly radiative), otherwise the temperature can be largely underestimated.

An example of such correction is given in [START_REF] Silvani | Fire spread experiments in the eld: Temperature and heat uxes measurements[END_REF]. Regarding the ame emissivity, several approaches have been developed, as described in a recent and comprehensive review by Raj et al. [START_REF] Raj | A rened methodology to determine the spatial and temporal variation in the emissivity of diusion ames[END_REF]. The experimental methodologies listed in their work can be summarised into four main classes. The rst one is based on a simple heat balance at the surface of the combustible proposed by Babrauskas [START_REF] Babrauskas | Estimating large pool re burning rates[END_REF]. In this approach, ame emissivity is simply related to the MLR of the pool re. It is noted that this emissivity is then a mean emissivity of the ame seen from the combustible surface. The second one is based on the radiative heat uxes measured by uxmeters around the re [57]. By using radiative view factors the heat ux emitted by the ame can be estimated. In this way a global emissivity for the ame is obtained. The third one relies on ame transmittance measurements. Indeed, the ame emissivity can be related to its transmittance T by the relation = 1-T . In these methods, one [811] or several [4, 6, 12 15] heaters are put behind the ame, and an infrared camera looks at this/these heater(s) through the ame. In [START_REF] Raj | A rened methodology to determine the spatial and temporal variation in the emissivity of diusion ames[END_REF] and [START_REF] Raj | Measurement of geometric and radiative properties of heptane pool res[END_REF], 40 electrically heated strips were used, allowing to compute temperature and emissivity maps of the ame.

The last class of methods is related to two-colours pyrometry [START_REF] Zhou | Experimental investigations on visualization of three-dimensional temperature distributions in a large-scale pulverized-coal-red boiler furnace[END_REF], multicolour pyrometry, or even to hyperspectral imaging [START_REF] Liu | Measurement of distributions of temperature and wavelength-dependent emissivity of a laminar diusion ame using hyper-spectral imaging technique[END_REF]. In these methods, both emissivity and temperature are theoretically obtained at the same time.

Regarding two-colours pyrometry, a grey emissivity (same Preprint submitted to Fire Saf. J.

2nd July 2019

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

emissivity for both wavelengths) is assumed, which is not true for a ame as will be shown in the present paper.

Assessing the error due to this approximation is dicult.

Except multicolour pyrometry and hyperspectral imaging, all the techniques mentioned before assume that the ame is grey, or give a grey equivalent ame emissivity. But it is known that, in the general case, radiative ame properties are not grey. This is particularly true for small ame thicknesses (e.g. < 0.20 m as cited in [START_REF] Àgueda | Experimental study of the emissivity of ames resulting from the combustion of forest fuels[END_REF]), for which radiation comes predominantly from combustion gases that emit in precise wavelength ranges, and not at all in other ranges. For intermediate size ames, soot becomes a signicant, or even predominant, contributor to the emission [START_REF] Sibulkin | Estimates of the Eect of Flame Size on Radiation from Fires[END_REF]. The spectral dependence of the absorption coecient κ(λ) for soot (and then the spectral emission coecient by virtue of Kirchho principle) are generally described by the Rayleigh theory which states that κ(λ) = 6πE(m)f v /λ. In this relation, f v is the soot volumetric fraction, λ the wavelength, and E(m) a function of the so-called optical parameter m (see Appendix A).

As an approximation, κ(λ) is often described by a simpler expression [START_REF] Modest | Radiative Properties of Particulate Media[END_REF] κ

(λ) = Cf v λ α , (2)
where α is a coecient dependent on the fuel type.

When the ame width e increases, its optical thickness τ (λ) = κ(λ)e increases as well. Ultimately, the ame becomes opaque, and thus emits like a blackbody. According to data available in the literature, the required ame thickness to reach this limit is equal to several meters. For hydrocarbons pool res, this size is in the order of 3 m [START_REF] Steinhaus | Large-scale pool res[END_REF].

For forest fuels, authors report ame emissivities close to that of a blackbody (i.e. 0.90) for re widths greater than 2 m to 4.8 m [START_REF] Àgueda | Experimental study of the emissivity of ames resulting from the combustion of forest fuels[END_REF].

For combustible materials with (almost) wavelengthindependent absorption, a grey description of the radiation emitted by the ame is a satisfactory approach to assess heat transfer from the ame to the combustible. But many fuels, including alcohols [START_REF] Wakatsuki | Eects of fuel absorption on radiative heat transfer in methanol pool res[END_REF], hydrocarbons [START_REF] Suo-Anttila | Characterization of thermal radiation spectra in 2m pool res[END_REF][START_REF] Sikanen | Modeling and simulation of liquid pool res with in-depth radiation absorption and heat transfer[END_REF] and polymers [START_REF] Linteris | Absorption and reection of infrared radiation by polymers in re-like environments[END_REF][START_REF] Boulet | Optical and radiative properties of clear PMMA samples exposed to a radiant heat ux[END_REF], actually behave as highly nongrey materials with some transparent, semi-transparent and opaque spectral windows. Particularly several of these fuels are perfectly transparent in visible and near-infrared ranges, and opaque in mid-infrared and beyond. This results in dierences depending on the radiation source.

As an example, it was shown in [START_REF] Boulet | Optical and radiative properties of clear PMMA samples exposed to a radiant heat ux[END_REF] that absorption by PMMA changes when exposed to a re propagation apparatus (FPA), which has a high level of radiation in visible and near-infrared ranges, or a cone calorimeter, which emits mainly in mid-infrared. The same applies when considering radiation from res. Indeed, given the emissive properties of soot (see Equation 2), the emissivity of a ame is expected to be higher at visible and near-infrared wavelengths, where the materials mentioned before are almost transparent. This illustrates the importance of a spectral description of ame radiation to correctly model absorption by this kind of materials.

Spectral characterisations of large ames were reported only in a few papers. Suo-Anttila et al. [START_REF] Suo-Anttila | Characterization of thermal radiation spectra in 2m pool res[END_REF] gathered emission spectra of radiation from 2 m diameter pool res, for several liquid fuels. Spectral range was between 1.3 and 4.8 µm. In their work, emission spectra were recorded through a sight tube allowing to measure downwards radiation, from the ame to the combustible. The tube tip height was varied from a few centimetres up to 1 m above the fuel surface. Combustion gases were the primary emitters for ethanol res, while soot dominated for an ethanol/toluene mixture, JP-8, and heptane. For these three fuels, radiation was attenuated in the lower region of the ame due to absorption by H 2 O, CO 2 , fuel vapour, and soot. In [START_REF] Parent | Measurement of infrared radiation emitted by the ame of a vegetation re[END_REF], emission spectra of small wood res (tray size 50 × 50 cm 2 ) showed that emitted radiation was located in precise spectral ranges typical of combustion gases radiation. Soot emission levels were very low for such ame size. In [START_REF] Boulet | Experimental Investigation of Radiation Emitted by Optically Thin to Optically Thick Wildland Flames[END_REF], larger wood res (from 0.5 m up to 4 m wide)

were investigated. For the largest re sizes, a high emission level coming from soot was observed, but the ame was still not black. Assuming an opaque ame ( = 1)

for the largest re size and the smallest wavelengths (for which κ is the greatest according Equation 2), a temperature close to 1400 K was obtained. Still for the largest re size, the emissivity was found to be only 0.5 at wavelengths near 10 µm, showing the highly non-grey behaviour of ame emissivity. Spectral measurements performed on large scale kerosene pool res were reported in [START_REF] Erez | Flame properties of large kerosene res[END_REF]. The present paper is an extension of this study with more results provided and an extended analysis.

As stated in the introduction, a fully resolved charac-

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
cessary, but can be analytical, as it will be shown.

In a rst step, we studied kerosene pool res, and measurements were performed along a horizontal line of sight, ten to twenty centimetres above the pool. This height was chosen because the thickness of the ame is easier to determine there (width nearly equal to the pool size). Complementary work will have to be done to see if there is a signicant sensitivity of the equivalent medium parameters with the position and the orientation of the emitted radiation. Ideally, this model could be accurate enough to allow calculation of radiative heat uxes received everywhere in space given only the ame geometry.

Experimentally, the radiation coming from the ame was measured by a Fourier transform infrared (FTIR) spectrometer in the spectral range 800 cm =1 to 6000 cm =1 (i.e.

12.5 µm to 1.67 µm). This radiation is the result of the emission by combustion gases and soot along the line of sight of the spectrometer. Along this path, concentration of species and temperature inside the ame are highly heterogeneous, and vary quickly due to the highly turbulent nature of the ame. As said above, an equivalent homogeneous and isothermal medium was considered instead of these actual properties. In such a medium, the resolution of the radiative transfer equation (RTE) that describes the evolution of the spectral radiant intensity I λ (s) along the curvilinear coordinate s is analytical [START_REF] Modest | Radiative Properties of Particulate Media[END_REF] (soot scattering being neglected as discussed in Appendix A). At the exit point of a medium of thickness e, the intensity is given by

I λ (s = e) = (1 -T (λ))I bb λ (T ) = (1 -exp (-κ(λ)e)) I bb λ (T ), (3)
where I bb λ (T ) stands for the blackbody intensity at a temperature T [START_REF] Modest | Radiative Properties of Particulate Media[END_REF], and T (λ) for the ame transmittance. The latter is related to the ame width e and absorption coecient κ(λ) by the Beer-Lambert law: T (λ) = exp (-κ(λ)e). At this stage, the radiation intensity is still dependent on two quantities: the equivalent ame temperature T and the ame transmittance T (λ). This is similar to the usual surface ame model in Equation 1, where temperature and ame emissivity were needed. Two independent measurements should thus be performed. In this work, emission spectra were gathered along with transmittance values, determined by using several laser beams crossing the ame. Laser wavelengths were chosen outside gases absorption bands, so only soot absorption, and consequently emission, was studied.

Experimental setup

Overview

Two test sites were used to conduct the experiments, depending on the re size. The rst was a former aircraft hangar (approx. 300 × 50 × 17 m 3 , length × width × height, see Figure 1), gracefully lent by Groupe ADP (Orly, France).

It easily accommodated the largest res so they could be In addition to the need to modulate the beams, a second point has to be taken into account: due to refractive index gradients inside the ame, beam deviation is observed (mirage eect). The distance between the emitter and the receiver being equal to several meters, this deviation can reach several centimetres. This is why the light was collected using a 20 cm diameter o-axis parabolic mirror, and focused at the entry of a 150 mm diameter integrating sphere with a 38 mm diameter entry port (see right side in Figure 2). The light coming from all wavelengths was mixed in the integrating sphere: optical band-pass lters were thus used to measure the signal at each wavelength.

The light sources were laser diodes, as they are available for many wavelengths, and because they are small enough to be integrated in a compact device. All the laser diodes were thermally stabilised thanks to thermoelectric coolers (TEC), insuring a very stable emission level. Thus, transmission through the ame can be simply calculated by dividing the light intensity during the tests, I(t), by the initial intensity, I(t = 0), measured at the beginning of the experiments. We checked that the signal does not suer any time drift which could arise from the stability of the laser source or the response of the detectors. This stability is visible in Figure 4 where the signal comes back

1 Peak intensity around 16 W • m =2 • sr =1 • nm =1
for a blackbody at temperature 1000 • C, and 700 W • m =2 • sr =1 • nm =1 for a tung- sten halogen source (assuming T = 2700 K and emissivity around 0.5 for tungsten).

2 Assuming a 5 × 10 =4 sr =1 solid angle and in a 10 nm spectral bandwidth, power is 0.8 mW for a 10 × 10 cm 2 blackbody, and 20 µW for a 100 W tungsten halogen lamp (assuming a 10 mm 2 emitting surface). Based on this approach, two setups were developed.

The rst one involved 4 visible and near-infrared wavelengths: 410 nm, 520 nm, 785 nm and 1650 nm. Silicon photodetectors were used for the rst three wavelengths, and an InGaAs photodetector was used for the 1650 nm wavelength. The integrating sphere was a Spectralon ® sphere suitable for visible and near-infrared wavelengths, up to 2500 nm. The second one involved 4 near-infrared wavelengths: 785 nm, 1650 nm, 2300 nm and 3800 nm. A PbS detector was used for the 2300 nm wavelength, and an InSb detector for the 3800 nm. The integrating sphere was an Infragold ® sphere. All the chosen wavelengths are loc- ated outside absorption bands of combustion gases so that only soot can signicantly absorb at these wavelengths.

Measurements were made approximately 10 or 20 cm above the pan (for small or large res respectively) for the sake of simplicity. Indeed at these heights the ame thickness can be considered equal to the pan diameter. Having a line of sight close to the pool surface could have been a problem because it is likely to cross a fuel-rich atmosphere [29, p. 131], which increases even further the ame inhomogeneity (species and temperature), both in time and space.

However, it will be shown that this did not aect the results: the measurements presented here allowed to model the emitted radiation as the emission of an equivalent homogeneous isothermal medium. Photographs of a setup are given in Figure 3.

Emission spectrometry

For all tests, spectral radiative intensities were measured using a Fourier transform infrared (FTIR) emission spectrometer (Matrix ® spectrometer by Bruker ® ), from 800 cm =1 to 6000 cm =1 (i.e. 12.5 µm to 1.67 µm). sorption coecients (see Section 3.1) and Equation 3to compute soot equivalent temperatures T (see Section 3.2).

Results

The MLR for large scale experiments (e.g. Figure 1 in [START_REF] Erez | Flame properties of large kerosene res[END_REF]) was very stable except at the very beginning and end of the re. It showed some uctuations for the small scale experiments because they were carried out with a thiner layer of kerosene and no water. Even so, transmittance and emission measurements always varied around a stable value for the main part of the tests (see Figure 4 for opacimetry), considered here as the steady phase. These results are discussed hereafter.

Opacimetry

The opacimetry setup allowed to measure transmittance T (λ i , t) across the ame at various wavelengths λ i .

A typical timeplot is shown in Figure 4 transmission for these re sizes could be lower than the measured values (i.e. larger optical thickness), and actual slopes could thus be higher.

Flame extinction coecient

As seen in Figure 4, transmittance uctuates signicantly with time due to the turbulent nature of the ames investigated here. Transmission levels also vary a little from one test to another, because experimental conditions cannot be exactly the same for each test. For these reasons, time-resolved analyses of the transmission were performed, in order to obtain mean and standard deviation values of the results for each test.

FTIR spectra are usually presented as functions of wavenumber 3 , generally expressed in cm =1 , which is the inverse of the wavelength (σ = 1/λ). For this reason wavenumbers will be used instead of wavelengths in the following.

Moreover, the power law mentioned earlier to describe the spectral dependence of κ(λ) (see Equation 2) and τ (λ) (see Section 3.1.1) is rewritten as

τ (σ) = β(σ) = β 0 σ σ 0 α , (5)
where β 0 is the extinction coecient at a reference wavenumber σ 0 (here σ 0 = 4000 cm -1 was chosen, i.e. λ 0 = 2.5 µm). This allows to use the dimensionless term σ/σ 0 , which is preferable with the non-integer exponent α. Optical thickness was divided by the geometrical thickness of the ame, assumed to be equal to the pan size (as measurements were performed near the base of the ame) in order to obtain an equivalent extinction coecient β(σ).

For each test, the extinction coecient was tted with the model in Equation 5. In this way, time variations of β 0 and α were obtained. Means and standard deviations of β 0 and α are represented in Figure 6. The extinction coefcient β 0 is around 1.74 m -1 for ame thicknesses from 30 cm to 70 cm. For wider ames, β 0 increases to 2.1 m =1

for the 100 cm thick ame, and to 3.1 m -1 for the 175 and 250 cm thick ames. Such an increase could be expected as the soot volume fraction is likely to increase for large ames. Even so, variations of the extinction coecient are small for ames thinner or equal to 70 cm, and remain moderate for thicker ames. This is an interesting feature which is a benet of the ame volume model over a surface model. Indeed, for the latter, emissivity (e.g. in Equation 1) has to be strongly dependent on the ame thickness. Regarding the exponent α, it is around 1.12 for tests with a width less than or equal to 70 cm. Above this size, the exponent decreases, as already seen in Figure 5.

Whether these smaller values of α have a physical meaning or not is not determined yet (as discussed for the slope α in Section 3.1.1).

Spectrometry

An example of emission spectra is shown in Figure 7 for a 50 cm wide ame. =1 . Yet, such a time resolved charac- terisation of the emitted radiation was not the goal of the present work. We focused instead on averaged data. In a rst step, analyses were performed on spectra averaged over all the ame steady phase (see Section 3.2.1). Later, complementary investigations were conducted on instantaneous spectra (see Section 3.2.2) in order to check if data (i.e. extinction coecient and equivalent temperature) extracted from averaged spectra give similar results than averaged data calculated from instantaneous spectra.

Mean spectra

Considering the emission of radiation by a homogeneous and isothermal equivalent medium, as proposed in the introduction, the intensity is given by

I σ (s = e) = (1 -exp (-κ(σ)e)) I bb σ (T ). ( see
Combining Equations 3 and 6 thus gives

I σ (s = e) = 1 -exp -β 0 σ σ 0 α e I bb σ (T ). ( 7
)
This model is a three-parameter model: β 0 , α and T have to be determined. The exponent α was found to be almost constant for ames thinner or equal to 70 cm (see Figure 6(b)), and it decreases for larger ames. Whether

or not this variation has a physical meaning still has to be investigated (see discussion in Section 3.1.1), but ignoring it for the present study is considered a reasonable approximation. Indeed, as the re gets wider (e increases in Equation 3), the ame becomes optically thicker and its emission tends towards that of a blackbody (exp (-κ(σ)e) → 0 =⇒ I σ (s = e) → I bb σ (T )). In this limit, the radiation intensity I σ thus becomes insensitive to the variations of the absorption coecient or the parameters used to compute it. For this reason, a constant α was deemed acceptable. A slight correction was made to the value presented earlier (in Section 3.1.2, where α = 1.12), because it was determined over the whole range of wavelengths used for opacimetry (i.e. 410 nm to 3800 nm), and not only for the infrared range. It is observed in Figure 5 that the agreement between the modelled mean extinction coecient and the measured values is poorer for infrared wavelengths. In order to use Equation 6 in conjunction with spectrometry measurements (performed from 2000 nm to 12 500 nm), a new t was performed using only infrared values, resulting in α = 1.07. Regarding β 0 (extinction coecient at the reference wavenumber σ 0 = 4000 cm -1 ), it was shown in Section 3.1.2 that β 0 is almost independent of ame thickness (see Figure 6 wavenumbers below 2500 cm =1 ). This could show a limit of the power law used to describe spectral variations of the absorption coecient (e.g. Equation 2or Equation 6).

Indeed, this model was considered valid over the entire spectral range investigated here, but there is no experimental validation for large wavelengths. It is worth mentioning that, although the results of the model may resemble blackbody curves, only very thick ames can indeed be computed using Planck's law, with emissivities close to unity. All other ames cannot be modelled as blackbodies or grey bodies, that is using constant (non-wavelengthdependent) emissivities. A given grey body could describe the data for short wavelengths but not large ones, and another one could do the opposite, but no grey body can describe the radiation intensity over the entire spectrum, and thus the spectral energy distribution.

The temperature identied for the various tests at different sizes is shown in Figure 9. The average temperature is 1208 K. Although values uctuate around this mean, no clear trend can be linked to ame thickness. This temperature can thus be considered an intrinsic characteristic of kerosene ames.

Instantaneous spectra

As seen in Figure 7, emission spectra show some large variations with time as a consequence of the pulsation and the turbulence of the ame. These changes are undoubtedly due to variations of both the optical thickness to the measurement process. Indeed, the laser beams are not perfectly coaxial, and so they do not follow exactly the same path inside the ame. This means that part of the transmittance dierence between two wavelengths is in fact due to spatial variation of the extinction coecient, and not to a spectral variation. Keeping a constant value for α is therefore considered to be a reasonable assumption. On the contrary, time variations of β 0 are very likely due to large changes of soot concentration in space and time. Time and space variations of temperature are also certain. To summarise, ts of instantaneous spectra were performed with the model in Equation 7, with two free parameters (β 0 and T ), and α being xed to 1.07.

This two-parameter adjustment was performed only for ame thicknesses less than or equal to 100 cm. This is because for larger res, and for the spectral range in which the adjustment is made, the emitted radiation approaches that of a blackbody, and thus the model becomes insensitive to the extinction coecient (or to the exponent α as discussed in Section 3.2.1). Therefore, for the 175 and In addition to kerosene, other fuels (wood, heptane, diesel and polyurethane foam) are being investigated. The optical properties presented here will also be used in conjuction with ame geometry measurements to model radiation, and compare the results to the heat uxes recorded during the tests.

Another key aspect that could not be addressed so far is ame inhomogeneity: complementary tests could be performed to produce radiative maps of ames, as done before [START_REF] Sudheer | Measurement of Flame Emissivity of Hydrocarbon Pool Fires[END_REF][START_REF] Raj | Measurement of geometric and radiative properties of heptane pool res[END_REF][START_REF] Markstein | Scanning-radiometer measurements of the radiance distribution in PMMA pool res[END_REF] but with the multispectral approach presented here (e.g. [START_REF] Suo-Anttila | Characterization of thermal radiation spectra in 2m pool res[END_REF]). A rst step would be to conduct the measurements presented here (i.e. opacimetry and emission spectrometry) along the ame centerline at various heights. These additional data would also conrm if the line of sight used in the present study can be considered representative of the ame volume that is being modelled [START_REF] Dupuy | Thermal infrared emissiontransmission measurements in ames from a cylindrical forest fuel burner[END_REF][START_REF] Suo-Anttila | Characterization of thermal radiation spectra in 2m pool res[END_REF].

To conclude, the model presented here oers an analytical formulation to account for the spectral dependence of soot radiation, and thus provides a more detailed description of ames while being computationally ecient. As the key parameters appear to be independent of ame size, only a few tests would be required to determine their values and produce a database for several fuels. An example of end application is to provide a detailed description of heat transfers for re spread models, meant to predict fullscale burning behaviour based on small-scale tests.

Declarations of interest

None.

is once again acknowledged for providing the test site. The technical sta at LEMTA is thanked for designing and building measuring devices and other equipment.

Appendix A. Assessment of soot scattering

This appendix is meant to explain why soot scattering in the infrared was neglected, allowing to consider that the absorption coecient κ(λ) is nearly equal to the measured extinction coecient β(λ).

Soot particles are recognised for years to be pseudofractal aggregates of primary carbonaceous spherical particles.

The number of primary particles follows the law [START_REF] Sorensen | Light Scattering by Fractal Aggregates: A Review[END_REF] N

= k f R g d p D f , (A.1)
where d p is the diameter of primary particles, R g the gyration radius, D f the fractal dimension and k f the prefactor parameter of the aggregate. The Rayleigh Debye Gans theory for Fractal Aggregates (RDG-FA) is nowadays the most used theory to describe the interaction between light and soot. The review by Sorensen [START_REF] Sorensen | Light Scattering by Fractal Aggregates: A Review[END_REF] presents in details soot properties and the RDG-FA.

According to this theory, the absorption cross section is given by σ abs = N 4πk R 3 p E(m), , m being the complex optical index of soot, and g(kR g ) the total scattering form factor.

As pointed out by Krishnan et al. [START_REF] Krishnan | Extinction and Scattering Properties of Soot Emitted From Buoyant Turbulent Diusion Flames[END_REF], the ratio ρ sa between scattering and absorption is given by ρ sa = 2 3 N (kR p ) 3 g(kR g ) F (m) E(m) .

(A.4)

As a consequence, the bigger the aggregate (large N ), the higher ρ sa . Regarding spectral variations, ρ sa is proportional to (kR p ) 3 = 8π 3 (R p /λ 3 ). Thus, the smaller the particle or the larger the wavelength, the lower the scattering/absorption ratio. The last parameter is the Regarding the present work, infrared spectra begin at 1.67 µm, and the main wavelength range is beyond 2 µm.

For this wavelength, the maximum value of ρ sa is equal to 0.15, for benzene soot [START_REF] Krishnan | Extinction and Scattering Properties of Soot Emitted From Buoyant Turbulent Diusion Flames[END_REF]. The parameter used to quantify scattering is usually the single scattering albedo ω = σ sca /σ ext = σ sca /(σ sca + σ abs ) which is related to ρ sa to produce small size soot). As ρ sa is linearly related to N , a decrease in soot size leads to a decrease in scattering. Soot morphology of in-re and overre 2-meter wide JP-8 kerosene pool res was studied by Jensen et al. [START_REF] Jensens | Measurement of Soot Morphology, Chemistry, and Optical Properties in the Visible and Near-Infrared Spectrum in the Flame Zone and Overre Region of Large Jp-8 Pool Fires[END_REF]. Reported primary particles diameters are in the range 57 nm74 nm and gyration radii between 239 and 340 nm. Corresponding primary particle number N calculated by Equation A.1 are in the range 5595, which is signicantly smaller than the values determined in the paper by Krishnan et al. and implies consequently less scattering. Regarding primary particles, Huang et al. [START_REF] Huang | Experimental investigation on the morphology of soot aggregates from the burning of typical solid and liquid fuels[END_REF] recently reported primary particle diameter of kerosene soot (sampled in and over the ame of a small pool pan) in the range 50 nm to 60 nm, which is somewhat smaller than the values of Jensen et al.

As a conclusion, the highest reported scattering albedo for the infrared spectral range under consideration in the present work, that is wavelengths higher than 2 µm, is ω = 0.15 [START_REF] Krishnan | Extinction and Scattering Properties of Soot Emitted From Buoyant Turbulent Diusion Flames[END_REF]. The value for in-re kerosene soot is likely to be signicantly smaller, owing to smaller soot aggregates sizes and albedos reported in other works [3436].

Moreover the albedo, and thus scattering, decrease very fast with increasing wavelengths. This is why scattering by soot particles was neglected in the infrared spectral range considered here.

Figure 1 :

 1 Figure 1: View of a 6 m 2 kerosene pool re in Orly. The opacimetry setup (behind brick walls) can be seen to the left and right of the re.

  to its original value at the end of the experiment.

Figure 2 :

 2 Figure 2: Elements of the opacimetry setup.

  The spectrometer was calibrated with a cavity blackbody (Mikron ® model M330EU) at 1200 • C. Measurements were performed at the same height as opacimetry ones (i.e. 10 or 20 cm above the pan), to provide comparable data. Spectral radiation intensities will be used in conjunction with ab-M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT (a) Laser sources (note the green one bouncing o the chopper). (b) O-axis parabolic mirror, integrating sphere and detectors.

Figure 3 :

 3 Figure 3: Opacimetry setup: (a) emission, (b) detection.

Figure 4 :

 4 Figure 4: Spectral ame transmittance (log scale) for a 70 cm wide pan at four wavelengths in visible and near-infrared ranges.

4 )Figure 5 :

 45 Figure 5: Mean optical thickness as a function of wavelength for various re sizes, in log-log base 2 scale.

4

  Acquisition time of the full interferogram allowing the 4 cm =1 resolution. Information required for a 100 cm =1 resolution allowing a good enough spectrum outside gases emission wavelength bands is contained in less than 5 ms around the interferogram center-burst.

  cm -70 cm)=1.12 (b) Exponent α.

Figure 6 :

 6 Figure 6: Parameters of Equation 5 for all re sizes (several repeats for the smaller ones).

Figure 7 :

 7 Figure 7: Examples of instantaneous spectra for a 50 cm wide ame.

3 )

 3 As already discussed, I σ depends on κ(σ) and T . For the infrared wavelengths involved here, soot scattering can be considered negligible, as explained in Appendix A. Thus the absorption coecient κ(σ) is equal to the extinction coecient β(σ) previously determined through opacimetry measurements. As averaged spectra are considered, a mean absorption coecient is used. It was shown in Section 3.1.2 that the extinction coecient, and thus the absorption

Figure 8 :

 8 Figure 8: Mean emission spectra for all re sizes, and the adjustments using the one-parameter model (i.e. Equation 7 with α and β 0 xed).

Figure 9 :

 9 Figure 9: Identied temperatures from adjustments made on mean spectra using the one-parameter model (i.e. Equation 7 with α and β 0 xed).

Figure 10 :

 10 Figure 10: Temperature T and extinction coecient β 0 identied from adjustments on instantaneous spectra using the twoparameter model (i.e. Equation 7 with α xed). Flame thickness equal to 50 cm.

Figure 11 :Figure 12 :

 1112 Figure 11: Parameters of Equation 7 for all re sizes (several repeats for the smaller ones).

Funding:

  This work was supported by the Laboratoire Central de la Préfecture de Police and the Laboratoire Énergies et Mécanique, Théorique et Appliquée (UMR 7563, Université de Lorraine/CNRS).

(A. 2 )

 2 whereas the scattering cross section is given byσ sca = N 2 8π 3 k 4 R 6 p F (m) g(kR g ), (A.3) where R p = d p /2, k = 2π/λ, E(m) = Im m 2 -1 m 2 +1 , F (m) = m 2 -1 m 2 +1 2

F

  (m)/E(m) ratio. Krishnan et al. report measurements of this parameter by several groups as well as their own, up to infrared wavelengths. The spectral trend of this ratio is a clear increase with wavelength. Overall, spectral variations of ρ sa are a competition between the decrease with λ due to the (kR p ) 3 term and an increase due to the F (m)/E(m) ratio. Because of the cubic dependence, the rst factor ends up always winning. Using measured soot morphologies and inferred soot optical indices, Krishnan et al. calculate estimates of ρ sa ratios for various fuels as a function of wavelength from visible to infrared. Kerosene soot is not referenced in this paper. A maximum, between 0.35 and 0.7 depending on the fuel, is observed at a wavelength around 500 nm. Beyond this maximum, ρ sa decreases rapidly.

  ω = ρ sa /(1 + ρ sa ). Thus, a ratio ρ sa = 0.15 corresponds to a 0.13 albedo, whereas the ρ sa maximum values (between 0.35 and 0.7) correspond to albedos between 0.26 and 0.41 respectively. Bond and Bergstrom[START_REF] Bond | Light Absorption by Carbonaceous Particles: An Investigative Review[END_REF] report albedos determined by various groups to be in the range 0.150.29, with most values below 0.2, for wavelengths in the range 514 nm to 633 nm, which is signicantly smaller than the values measured and estimated by Krishnan et al. Moreover, the measurements of Krishnan et al. were performed overre, whereas ours are performed in-re, and even near the pool surface. Krishnan et al. reported that in-re soot particles are signicantly smaller (N in the range 3080) than overre soot (N in the range 420550, excluding n-heptane [N = 260], known

Acknowledgements

The authors would like to thank the sta of the Fire Engineering division at LCPP for performing the large scale tests, and more widely all personnel of the Préfecture de Police who helped setting them up. Groupe ADP


Lucas Terrei
email: lucas.terrei@univ-lorraine.fr

Zoubir Acem

Véronique Georges

Paul Lardet

Pascal Boulet

Gilles Parent

Experimental tools applied to ignition study of spruce wood under cone calorimeter

Keywords: Ignition of wood, cone calorimeter, surface temperature, IR thermography

A study of wood ignition was performed using a dedicated experimental setup including a cone calorimeter. This setup mainly includes a non-intrusive metrology by infrared camera, enabling an accurate surface temperature measurement and a fast visible camera (3000 fps), used to observe the "auto" ignition location. The study was carried out in vertical orientation only. Fast visible camera pictures showed three types of ignition: auto-ignition close to the exposed surface, auto-ignition far from the exposed surface and ignition piloted by the cone coil. Ignition occurred only above 45 kW.m -2 . Besides, for low heat fluxes, no ignition occurred but it was possible to observe a transition between pyrolysis solely, without combustion, and smoldering combustion for a sample surface temperature around 400 • C.

INTRODUCTION

For fire safety concerns in construction domain, study of fire behavior and flame propagation in wood structures is relevant, owing to wood flammability. Overall, wood structures can exhibit a good performance under fire conditions thanks to the charring behaviour that results in a slow in-depth heat propagation and, under specific conditions, an ability to self-extinguish [START_REF] Emberley | Self-extinction of timber[END_REF][START_REF] Emberley | Critical heat flux and mass loss rate for extinction of flaming combustion of timber[END_REF]. A recent review performed by Bartlett et al. [3] presents the state of the art on burning behaviour of wood for structural applications. In particular, this review reports factors influencing the wood degradation with regards to material properties itself (including pyrolysis, moisture transport, charring), system properties (like sample orientation for instance) and thermal exposure (including ignition and extinction). It appears that numerous parameters are involved in the burning process of timber, underlining the complexity for real tall buildings application. Among all these parameters, the present work aims at studying the ignition phenomenon in cone calorimeter tests, and more precisely auto-ignition, i.e. ignition without any external source of energy inducing ignition when pyrolysis gases form a flammable mixture with air (ignition piloted by a spark or a pilot flame). Ignition criteria were widely studied for many years and a state of the art was proposed by Babrauskas [START_REF] Babrauskas | Ignition of wood: a review of the state of the art[END_REF]. Most of the studies were conducted in piloted mode, looking for the conditions for which pyrolysis produces enough gas to allow and maintain flaming combustion, whatever the cause of ignition. Results obtained with piloted ignition are less scattered than without, because ignition will occur as soon as pyrolysis gases and air are in good proportion. That is why piloted ignition occurs at lower heat fluxes and surface temperatures as compared to the case when the ignition is not piloted. Concerning the heat flux, the piloted ignition occurs for flux in 10-15 kW.m -2 range whereas auto-ignition occurs in 25-33 kW.m -2 range for a horizontal sample orientation [START_REF] Bartlett | A review of factors affecting the burning behaviour of wood for application to tall timber construction[END_REF]. For vertical orientation, higher fluxes are necessary to ignite wood samples (28 kW.m -2 for piloted ignition and 63-79 kW.m -2 for auto-ignition,

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according to Hottel and Wilkes work's [START_REF] Hottel | Wood flammability under various conditions of irradiation[END_REF]). Moreover, for identical applied heat flux, times-to-ignition are always shorter in the horizontal orientation [START_REF] Bartlett | A review of factors affecting the burning behaviour of wood for application to tall timber construction[END_REF][START_REF] Tsai | Orientation effect on cone calorimeter test results to assess fire hazard of materials[END_REF][START_REF] Shields | The effects of geometry and ignition mode on ignition times obtained using a cone calorimeter and iso ignitability apparatus[END_REF]. Bartlett et al. [START_REF] Bartlett | A review of factors affecting the burning behaviour of wood for application to tall timber construction[END_REF] suggested that it could be explained both by an increase of sample convective cooling and by pyrolysis gases dilution in vertical orientation. Nevertheless, in real fire situations, there are many cases where flammable products are subjected to high radiative fluxes but where no external "ignition" source (like a flame) is present near the exposed material. It becomes consequently relevant to study when and where the spontaneous ignition can occur. In previous studies, ignition criteria were studied with regards to critical heat flux necessary to achieve auto-ignition and to surface temperature at ignition [START_REF] Babrauskas | Ignition of wood: a review of the state of the art[END_REF][START_REF] Boonmee | Glowing ignition of wood: the onset of surface combustion[END_REF][START_REF] Shi | Experimental study of woods under external heat flux by autoignition[END_REF]. Nevertheless, in existing works, some aspects are poor or less addressed, in particular the two following points:

• The first one concerns the ignition location. Indeed, one wonders if ignition occurs in the core of air/pyrolysis gases mixture, or at sample surface, or even near the cone calorimeter hot coil. In this last case, ignition can be considered to be piloted by the coil, and then not to be a true spontaneous ignition. Crémona [START_REF] Cremona | Caractérisation expérimentale et numérique des scenarii de feu impliquant un conduit de fumée d'appareils de combustion bois[END_REF] pointed out that this type of ignition can happen for the cone calorimeter oriented horizontally. In the second case, ignition is piloted by the sample surface, but this ignition is not due to an external cause and ignition can still be considered to be spontaneous. Such an ignition driven by the sample hot surface was reported by Kashiwagi et al. [START_REF] Kashiwagi | Effects of external radiant flux and ambient oxygen concentration on nonflaming gasification rates and evolved products of white pine[END_REF]. Boonmee and Quintiere [START_REF] Boonmee | Glowing ignition of wood: the onset of surface combustion[END_REF] highlighted that two kinds of ignition occur in vertical orientation when using a cone calorimeter: a flaming ignition for high heat fluxes and a glowing ignition for low heat fluxes. In that work, glowing ignition term was used when ignition comes from the surface at very long time, while flaming ignition term was used when ignition occurs at short time in the core of combustion gases.

• The second one concerns the sample surface temperature at ignition. Indeed, in many works, this temperature is measured by thermocouples. Yet, such a measurement is subjected to several causes of inaccuracy because a good thermocouple/surface thermal contact is difficult to achieve, since thermocouple is both subjected to the air/pyrolysis gases flow and exposed to the radiative heat flux coming from the cone. Some papers reported surface temperatures measured thanks to pyrometers [START_REF] Boonmee | Glowing ignition of wood: the onset of surface combustion[END_REF][START_REF] Fangrat | Surface temperature at ignition of wooden based slabs[END_REF] which more likely measure a "true" surface temperature. These measurements are always higher (between 400 and 600 • C) than temperatures measured with thermocouples (between 250 and 400 • C) [START_REF] Bartlett | A review of factors affecting the burning behaviour of wood for application to tall timber construction[END_REF].

In the following, study of wood auto-ignition is addressed regarding: i) if it occurs either in gases or near the sample surface, and in which proportion; ii) if false spontaneous ignition (ignition piloted by the coil) can occur or not when using a cone calorimeter. A contactless measurement using an infrared camera was implemented in order to obtain a reliable surface temperature. The studied material was spruce laminated wood (glulam) which is a recomposition of solid wood for large scale structural applications. This material is elaborated by gluing together, in the wood grain direction, purged laminated wood. The obtained glulam can be considered like solid wood if wood layers and glue are correctly chosen [START_REF] Grexa | Flammability parameters of wood tested on a cone calorimeter[END_REF][START_REF] Frangi | Experimental analysis of cross-laminated timber panels in fire[END_REF]. In some cases, the glulam can experience delamination. This is an important issue because the delamination can lead to a further increase of sample degradation or even a re-ignition of wood [START_REF] Crielaard | Selfextinguishment of cross-laminated timber[END_REF] which can penalize the use of glulam for structural purposes. In cone calorimeter tests, as small size samples are tightened in sample holder, the delamination is generally not observed. The basic composition of the setup included a vertically oriented cone calorimeter and a precision scale used to record mass loss during tests. A fast visible camera was used for catching the ignition location during tests. Some tests were performed with a sapphire window put between sample and cone calorimeter coil in order to avoid a possible contribution of the cone coil on wood auto-ignition. An infrared camera was used to observe the radiation emitted from wood samples surface during thermal degradation experiments. Infrared images were post-processed involving a subtraction method between successive images, to withdraw high incident flux from the cone calorimeter partly reflected by the sample. Then, an identification step was implemented linking the rise in intensity between two time steps with the increase of sample surface temperature [START_REF] Acem | Surface temperature of carbon composite samples during thermal degradation[END_REF].

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MATERIALS AND METHODS

Samples and cone calorimeter

Figure 1 presents the experimental setup. This configuration allows applying the heat flux and measuring both mass loss with a scale (Mass Loss Rate Per Unit Area (MLRPUA) deduced) and surface temperature with the infrared camera which looks to the sample through the cone hole.

Figure 1: Experimental setup (In this photograph the sample was not put in the sample holder in order to see the cone aperture. The infrared camera looks to the sample through this aperture).

The selected glulam material was made with two layers of spruce wood with a 25 mm thickness, glued with melamine-urea-formaldehyde (MUF). Sample sizes were 100×100 mm with a 50 mm thickness. The sample average density was about 480 kg.m -3 , given for an average moisture content around 9 %. As specified in the standard ISO 5660-1, samples were wrapped with two layers of aluminum foil, except their top side exposed to the radiative flux. The distance between sample and heater was 25 mm. Samples were exposed vertically to the radiative heat flux between 15 and 85 kW.m -2 during one hour. The radiative heat flux emitted by the cone was controlled before each test thanks to a Schmidt-Boelter fluxmeter (Medtherm). The heat flux was considered correct when value was ± 0.5 kW.m -2 from the desired flux.

Ignition location by fast visible camera

A fast visible camera (Photron APX-RS) was used in order to study the ignition location. The camera was set to 3000 frames per second, which allowed recording 1.3 seconds in its buffer. An example of recorded pictures obtained during ignition is presented in figure 2.

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As can be seen in figure 2, ignition phenomenon is very fast and occurs for this test far from the exposed surface. Indeed, it is seen in the picture at t= 0.003 s, that the fire point is located within the gas phase far from exposed surface. Once ignition occurred, the flame spread all over the flammable mixture in about 0.1 s (see picture at t= 0.133 s). The fast visible camera is very useful for determining the ignition type. A specific study linking time-to-ignition to ignition type and exposed heat fluxes will be presented and discussed below.

Surface temperature measured by infrared camera

Surface temperatures are usually measured using thermocouples. However, these measurements are punctual and could be affected by the heat sink along the thermocouple wire or the bad contact between thermocouple and sample. This contact seems all the more difficult to maintain because wood is degrading during the test, producing char and cracks [START_REF] Urbas | Surface temperature measurements on burning materials using an infrared pyrometer: accounting for emissivity and reflection of external radiation[END_REF]. For the present work, a multispectral infrared camera (Orion SC7000 by FLIR) was used for measuring the surface temperature of samples during tests. This non-intrusive measurement allows studying temperature field evolution on a large surface while avoiding contact problems. During infrared measurements, the flame between the infrared camera and the sample surface can lead to mismeasurement of temperature. Some studies showed that emission by flames is predominant in specific wavelengths where major combustion gases (CO 2 and H 2 O) can emit [START_REF] Parent | Measurement of infrared radiation emitted by the flame of a vegetation fire[END_REF]. Outside these bands, only soot can emit, and since the optical thickness of flames involved in cone calorimeter experiments is very small, the flame can be considered as almost transparent outside gas emission bands [START_REF] Acem | Surface temperature of carbon composite samples during thermal degradation[END_REF]. The camera had a filter wheel to select desired wavelengths. The selected wavelength was 3.9 µm (2564 cm -1 ), which is outside emission bands of combustion gases. Such a measurement method was already successfully performed by authors' group on other materials [START_REF] Acem | Surface temperature of carbon composite samples during thermal degradation[END_REF]. Once the camera signal is acquired, it is converted to a spectral intensity, thanks to a preliminary calibration of the camera involving a blackbody, and the temperature is calculated using the inversion of Planck's law. The emissivity for wood was studied in [START_REF] Boulet | On the influence of the sample absorptivity when studying the thermal degradation of materials[END_REF]. It is shown that the wood emissivity at 2564 cm -1 is close to 0.9 and that it does not vary more than ± 5 % around this value when the wood deteriorates under a heat flux. According to Chaos [START_REF] Chaos | Spectral aspects of bench-scale flammability testing: application to hardwood pyrolysis[END_REF], a misestimate of the emissivity in the 0.8-1 range can lead to an error of 8 % in the surface temperature. Figure 3 shows the temperature field obtained for two different tests (20 and 55 kW.m -2 ) at 120 s exposure. The white circle corresponds to the studied area, where the mean surface temperature was calculated. For the test at 55 kW.m -2 , we can observe that emission of flame is actually negligle (i.e. not visible in the IR image) at the selected wavelength (3.9 µm). The temperature field at surface is quite homogenous, except for the temperature estimated into cracks (in yellow).

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Surface temperature evolutions obtained from the IR camera and a sheathed K-type thermocouple (1 mm diameter) located at the surface center are plotted in Fig 4 . In a general way, surface temperature increases more or less quickly before reaching a plateau, near 800 • C for tests performed at 55 kW.m -2 , which is in good agreement with Shi and Chew [START_REF] Shi | Experimental study of woods under external heat flux by autoignition[END_REF]. At 1250 s, when the flame appears, a sudden increase of the surface temperature is observed for both types of measurement. Nevertheless this increase is low, about 20 K. Indeed, at cone calorimeter scale, the additional heat flux brought by the flame (q f ) is less than 1 kW.m -2 accordingly to a calculation based on Law's [START_REF] Law | Fire safety of external building elements[END_REF] work 1 . For the same reason, it will be shown later that the mass loss rate is almost unchanged when the flame appears. Until 1500 s, the temperature given by the thermocouple and the infrared camera are in pretty good agreement, even if the thermocouple underestimates the surface temperature by a few dozens of degrees, mainly when the temperature variation is fast, as a consequence of the thermal inertia of the thermocouple. The discrepancy between the two types of measurements increases for the largest times. Given that the sample surface burns, the contact between the thermocouple and the surface can no longer be ensured, resulting in a decrease of measured temperature. In addition, the thermocouple signal becomes more and more "noisy" since it is subjected to temperature variation of surrounding, caused by the turbulence of hot gases in the flame. Although widely used, we show here that the surface temperature measured by a thermocouple can lead to great uncertainty (fig. 4). For sake of accuracy, the surface temperature measurement by IR camera is preferable. This, of course, means that radiative properties have to be known, especially the sample emissivity, which may vary during the degradation process. A parametric study of sample emissivity was also done. Three values of emissivity (0.88, 0.90 and 0.95) were chosen in typical range of variation of wood emissivity during its thermal degradation, as reported by Boulet et al. [START_REF] Boulet | On the influence of the sample absorptivity when studying the thermal degradation of materials[END_REF]. For two tests performed at 20 and 55 kW.m -2 , the temperature variation due to the emissivity uncertainty is below 20 • C in the worst case, which is very reasonable. Moreover, figure 4 shows a decrease of temperature around 1500 s because the sample surface is degrading during test and the contact with thermocouple disappears. This phenomenon was already described in [START_REF] Tran | Burning rate of solid wood measured in a heat release rate calorimeter[END_REF]. Consequently, when the ignition occurs at long time, the thermocouple could not measure the surface temperature at ignition.

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Sapphire window

To avoid a possible ignition of pyrolysis gases by the hot cone calorimeter coil, a sapphire window, transparent in infrared range (up to 5 µm wavelength), was inserted between the cone and the sample. The window, with 20 cm diameter (equal to the cone external diameter) and 5 mm thickness was mounted on a thin steel support. As the mean transmittance of the window is around 60 %, the cone temperature has to be increased to obtain the desired heat flux. Consequently, tests were performed only at 45 and 55 kW.m -2 , because higher heat fluxes cannot be achieved with the sapphire window. The distance between sample and cone was set to 45 mm in order to ensure a good circulation of pyrolysis gases.

Mass loss measurements

As specified by the standard ISO 5660-1, a precision scale with a 0.1 g resolution was used for the mass loss measurement. As pointed out above, for some tests, the original cone calorimeter setup was modified to include a sapphire window between the cone coil and the sample. It might be asked whether the mass loss measurement is affected or not by this modification. Figure 5 shows mass loss rates per unit area (MLRPUA) evolutions for the two different configurations, with or without the sapphire window. Tests were performed at 55 kW.m -2 during one hour. Caption "Original" in legend stands for a test performed in the original configuration (i.e. without sapphire window and cone coil temperature at 800 • C) and caption "Sapphire" refer to tests carried out with the sapphire window (cone coil temperature at 950 • C). It appears that MLRPUA evolutions are very similar. It can be thus considered that tests with the sapphire window are carried out in similar conditions than without.

APPLICATION TO THE IGNITION STUDY OF GLULAM UN-DER CONE CALORIMETER

The setup was applied to the study of glulam degradation, especially the ignition type and the corresponding surface temperature at ignition. For each test, samples were exposed to the heat flux during one hour. After one-hour exposure, the heat flux was removed. Tests were carried out at different radiative heat fluxes, between 15 and 85 kW.m -2 in order to study flaming combustion or smoldering combustion. In the following, results are split in two parts focusing on flaming or smoldering combustion respectively.

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Study of flaming combustion

Type of ignition and time to ignition

As explained above, the time-to-ignition is defined as the moment when a flame appears. At this time, the surface temperature is often referred to the ignition temperature. However, it is difficult to explain conditions which lead to ignition. In this study, we planned to find out if the ignition always corresponds to a real auto-ignition as it is often claimed or if it can occur when pyrolysis gases encounter the hot cone coil. For that purpose, the ignition location was recorded by a fast camera. In our tests, in vertical orientation, ignition occurred when the sample was exposed to a heat flux above 45 kW.m -2 . Figures 2, 6 and 7 present fast visible camera pictures for tests performed at 55 and 75 kW.m -2 . Recorded pictures show three types of ignition: auto-ignition distant from the exposed surface (Fig. 2), auto-ignition close to the exposed surface (Fig. 6) and ignition piloted by the cone coil (Fig. 7). Statistics of ignition location (in percent) and time-to-ignition (t ig ) in seconds are gathered in Table 1 for tests performed at 45, 55, 75 and 85 kW.m -2 . For tests at 45 kW.m -2 , the ignition was not systematic and occurred always close to the exposed surface. Times-to-ignition were high (above 2790 s) and rather dispersed. Above 45 kW.m -2 , ignition occurred for each test and, as expected, increasing heat flux decreases time-to-ignition. For tests at 55 kW.m -2 , the ignition is located predominantly far from the exposed surface with a time-to-ignition lower than one minute. However, for two tests (over 31 performed), ignition happened close to the surface with a large time-to-ignition (1216 s and 1726 s). For the two highest heat fluxes, ignition could be piloted by the cone coil, especially due to the increasing temperature of coil. It also appears that the ignition location has not a significant impact on time-to-ignition even if this time is slightly shorter when the ignition is piloted by the coil. Given these first results, two kinds of behavior can be highlighted:

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• at low heat fluxes, ignition occurs close to the surface at a rather long time;

• at high heat fluxes, ignition occurs far from the exposed surface at a short time.

It seems obvious that the cone coil can affect ignition condition at high heat fluxes. Consequently, a sapphire window was put between sample and cone calorimeter to avoid pyrolysis gases to reach the cone coil. Table 2 presents corresponding statistics of ignition location and time-to-ignition. For each heat flux, ten films were recorded with the fast camera. At 45 kW.m -2 , results are comparable to tests performed without the sapphire window. Ignition was not systematic and times-to-ignition are long and dispersed, within the same range as for tests without window. On the contrary, at 55 kW.m -2 , results are different. Indeed, for tests without sapphire window, flaming occurred in a very short time and was mainly located far from the exposed surface. With the window, flaming origin is mainly located close to the exposed surface and ignition occurs at long times.

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Mass loss rate and surface temperature

Surface temperature was recorded for each tests. Figure 8 shows the surface temperature of samples measured with the IR camera when ignition occurred versus time-to-ignition for 91 experiments. Depending on heat fluxes, surface temperature at ignition laid within two intervals. For tests where the ignition occurred far from the surface (Fig. 2) or was piloted by the cone coil (Fig. 7), the surface temperature was found between 550 and 650 • C. These results are consistent with Fangrat [START_REF] Fangrat | Surface temperature at ignition of wooden based slabs[END_REF] and Boonmee [START_REF] Boonmee | Glowing ignition of wood: the onset of surface combustion[END_REF] who reported ignition temperatures (measured with a pyrometer) between 400 to 600 • C. For tests where the ignition is close to the exposed surface (fig. 6), the corresponding surface temperature range is between 710 and 820 • C. For glowing ignition, surface temperature at ignition for tests at 45 kW.m -2 are lower than those at 55 kW.m -2 even if times-to-ignition are longer. Indeed, in the steady state, surface temperature is close to the cone coil temperature. Consequently, for ignition In a general way MLRPUA first increases until a maximum. Then MLRPUA decreases, char layer formation increases, consequently the virgin wood receives lower heat flux, before reaching a constant or nearly constant value. MLRPUA and surface temperature increase are more pronounced for higher heat fluxes. However, for tests at 75 and 85 kW.m -2 , MLRPUA evolutions tend to a constant value around 6 g.m -2 s -1 . For glowing ignition (GI), at 45 and 55 kW.m -2 , surface temperature suddenly and slightly (about 25 • C) increases when the flame appears at 1750 s and 2950 s respectively. Glowing ignition occurs when surface temperature is constant, around 720 and 790 • C for 45 and 55 kW.m -2 respectively. This would mean that ignition at long times may occur for surface temperature higher than 700 • C. However, whatever the ignition location, no changes are observed in MLRPUA evolutions when the ignition occurred. It appears that the flame has not a significant impact on the sample degradation. Indeed, in the vertical orientation, the flame thickness is small and the additional heat flux provided by the flame is negligible compared to the heat flux coming from the cone. For the two lowest heat fluxes, heat flux removal induces a sudden decrease of the MLRPUA at 3600 s. For the two highest heat fluxes, MLRPUA decreases before the heat flux removal (at a time near 3200 s) corresponding to a total degradation of samples.

Study of smoldering combustion (without flame)

The experimental setup was also used for tests at lower heat fluxes. During these tests, no flame appeared but the smoldering combustion phenomenon was observed. The smoldering combustion corresponds to the flameless degradation at low temperature. Three tests were performed during one hour for each heat flux. Figure 10 shows MLRPUA and surface temperature evolutions provided from IR camera images. For tests at 15 and 20 kW.m -2 , an increase of the MLRPUA is observed at 1100 s and 345 s respectively. This increase is also observed at same times for the temperature variation, around 380 • C and 410 • C respectively. This phenomenon corresponds to the beginning of the smoldering combustion that leads to an additional amount of energy release. The transition between pyrolysis to pyrolysis with smoldering combustion is more discernible for low heat fluxes (20 and 15 kW.m -2 ). Surface temperatures measured by Urbas et al. at 30 kW.m -2 with a pyrometer also showed a variation in this temperature range [START_REF] Urbas | Surface temperature measurements on burning materials using an infrared pyrometer: accounting for emissivity and reflection of external radiation[END_REF]. For tests at 35 kW.m -2 , transition between pyrolysis with and without smoldering combustion is hardly visible because MLRPUA and temperature increase are very fast. Finally, the sudden decrease of the MLRPUA at 3600 s stands for the heat flux removal and should not be confused with the total degradation of samples.

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CONCLUSION

A dedicated experimental setup was built up in order to improve the ignition study of wood under the cone calorimeter. A fast visible camera was used in order to determine the ignition location. Recorded pictures highlight that three types of ignition can occur in vertical orientation. For the highest heat fluxes (75 kW.m -2 and above), ignition times are short (less than 20 s). Ignition occurs in most cases far from the exposed surface in the core of combustion gases, less often near the cone coil and in a few cases close from the wood surface. For the lowest heat fluxes (55 kW.m -2 and below) auto-ignition occurs for a long exposure time and its location is close to the sample surface. When a sapphire window is added between the sample and the cone, time-to-ignition increases to very long time and ignition location is for very most cases close from the sample surface. The surface temperature was measured with an infrared camera. This temperature was determined using a bandpass optical filter to avoid the radiation emitted by the flame. The calculation was done by inverting Planck's law, fixing the emissivity. As a consequence of increase of temperature with time, the later ignition occurs, the higher the surface temperature is at this time. When ignition occurs far from the sample surface (in space between surface and cone, or close from cone coil), time-to-ignition is short (less than 45 s) and this surface temperature is in the range 500-650 • C. When the ignition location is close to the cone coil, ignition is "piloted" by the hot coil. When ignition occurs close from the sample surface, time-to-ignition is long (larger than 1200 s) and the average surface temperature is in 700-730 • C range for a 45 kW.m -2 heat flux and between 770 • C and 820 • C for 55 kW.m -2 . In this case, ignition is induced by a point hotter than mean surface temperature (generally near a surface crack). It was observed that the Mass Loss Rate is similar whatever a flame is present or not. This is a result of the negligible heat flux provided by the flame compared to the heat flux coming from the cone at this experiment scale, and especially for a cone in vertical orientation. Indeed, in this configuration,

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the flame has a small thickness, and is mainly located at the upper part of the sample. For heat fluxes lower than 45 kW.m -2 , there was no flame ignition. A transition from a pyrolysis regime without any combustion to a char combustion regime (also called smoldering combustion) was observed when the sample surface reaches a temperature between 380 • C and 410 • C. This transition is characterized by a sudden increase of the surface temperature due to an additional heat release by the char combustion. An increase of the MLRPUA is observed at the same time.

ACKNOWLEDGEMENT

Authors gratefully acknowledge Arbonis society for providing wood samples.

Figure 2 :

 2 Figure 2: Auto-ignition far from the exposed surface (flaming ignition) at 75 kW.m -2 .

Figure 3 :

 3 Figure 3: Temperature field in Kelvin and studied area (white circle) at 120 s for two different external heat fluxes (20 kW.m -2 (left) and 55 kW.m -2 (right)).

Figure 4 :

 4 Figure 4: Time evolution of the surface temperature for two different external heat fluxes (20 kW.m -2 (left) and 55 kW.m -2 (right)) calculated with the infrared camera for 3 values of emissivity and measured with a thermocouple located at the surface center.

Figure 5 :

 5 Figure 5: MLRPUA for tests with performed at 55 kW.m -2 in different configuration.

Figure 6 :

 6 Figure 6: Auto-ignition close from the exposed surface (glowing ignition) at 55 kW.m -2 .

Figure 7 :

 7 Figure 7: Ignition piloted by cone coil at 75 kW.m -2 .

Figure 8 :

 8 Figure 8: Surface temperature at ignition versus time-to-ignition.

  long time, surface temperature at ignition is lower when the heat flux is low.

Figure 9

 9 shows MLRPUA (left) and surface temperature (right) evolutions for tests between 45 to 85 kW.m -2 . For 45 and 55 kW.m -2 , two MLRPUA curves are plotted to describe the MLRPUA evolution when ignition location (flaming ignition: FI, glowing ignition: GI, no ignition: NI) and time-to-ignition are very different. Three tests were performed for each heat flux during one hour.

Figure 9 :

 9 Figure 9: MLRPUA and surface temperature for tests with sample ignition (45 to 85 kW.m -2 ).

Figure 10 :

 10 Figure 10: MLRPUA and surface temperature for tests without sample ignition (15, 20 and 35 kW.m -2 ).

oo

  and Authorship Conformation Form Please check the following as appropriate: o All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version. This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue. The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript o The following authors have affiliations with organizations with direct or indirect financial interest in the subject matter discussed in the manuscript:

Table 1 :

 1 Ignition origin and time-to-ignition in funciont of submitted heat flux.

		45 kW.m -2	55 kW.m -2	75 kW.m -2	85 kW.m -2
		10 films	31 films	28 films	26 films
		Tests	t ig (s)	Tests	t ig (s)	Tests t ig (s) Tests t ig (s)
	No ignition	60 %	-	-	-	-	-	-	-
	Auto-ignition far from the surface	-	-	87 %	25-43	78 % 11-17 70 % 10-13
	Auto-ignition close from the surface	40 % 2790-3400 6.5 % 1216-1726	-	-	-	-
	Ignition piloted by coil	-	-	6.5 %	33	22 % 9-13 30 % 8-11

Table 2 :

 2 Ignition location and time-to-ignition for tests performed with sapphire window.

		45 kW.m -2	55 kW.m -2
		Tests	t ig (s)	Tests	t ig (s)
	No ignition	40 %	-	-	-
	Auto-ignition far from the surface	-	-	10 %	55
	Auto-ignition close from the surface	60 % > 2500 90 % > 1200
	Ignition piloted by coil	-	-	-	-

The formula given by Law, q f = (1 -e 0.3t f )σTg = 0.3 kW.m -2 with Tg = 900 • C for a wood flame according to[START_REF] Wasan | Study of pyrolysis and upward flame spread on charring materials-part i: Experimental study[END_REF] and t f (flame thickness)= 1 cm. The same formula gives q f = 1 kW.m -2 for a flame temperature of 1300 • C, which is a very large ceiling value for Tg.