Mariam Abdo

Hassan Flity

Lucas Terrei

André Zoulalian

Rabah Mehaddi

Pierre Girods

Yann Rogaume

An alternative wood pyrolysis model based on TGA and cone calorimeter tests

Keywords: Wood, Pyrolysis, Thermogravimetric analysis, Kinetic, Cone calorimeter, Modelling

Understanding the process of pyrolysis is crucial to achieve continuous progress in the efficient use of wood as a fuel source in various applications. In the literature, a wide range of kinetic models for wood pyrolysis has been introduced, varying from simpler to more complex and predictive. Some of these models are mathematical, with the sole objective of fitting the experimental results. The others are physical models that describe the underlying chemical processes involved in wood thermal degradation, but they tend to be more complex and time-consuming. In our study, a compromise between these two categories of models was established. A new physical and simple kinetic model of wood thermal degradation was proposed. This model was validated using a multi-scale approach. At micro scale, the thermal degradation of wood was studied using thermogravimetric analysis (TGA). TGA experiments were conducted with two wood species, beech and spruce, in an inert atmosphere at five different heating rates. Based on the latter analysis, our kinetic model of wood thermal degradation was established. Its associated kinetic parameters were determined by fitting the experimental mass loss and mass loss rate data. Good agreement was achieved between the experimental and numerical results. At bench scale, tests were performed in a controlled atmosphere chamber placed in front of a cone calorimeter. The thermal degradation of wood was studied at two heat fluxes in an inert atmosphere obtained by a constant argon injection. The kinetic model developed at the micro scale was implemented into a one-dimensional pyrolysis model, taking into account both thermal and mass transfer phenomena within the wood. The validity of the 1D pyrolysis model was established by comparing the numerical results with the mass loss, mass loss rate, and temperature profile measured during cone calorimeter tests.

Introduction

Biomass is currently the world's largest renewable energy source, providing a scalable, flexible and, in many instances, the only reliable source of energy [START_REF]Wood Energy in the ECE Region: Data, Trends and Outlook in Europe, the Commonwealth of Independent States and North America, UN[END_REF]. The term "biomass" commonly refers to all organic materials derived from plants, with wood being the primary type. For many years, wood has been employed WOOD K GAS+CHAR [START_REF] Shafizadeh | Thermal Deterioration of Wood[END_REF].

mainly to cook food, heat space and satisfy the construction needs of buildings, works of art and furniture [START_REF] Simo-Tagne | Experimental modelling of a solar dryer for wood fuel in epinal (france)[END_REF].

Today, the sustainable production of heat and energy from wood is at the centre of scientific and industrial interest. Actually, the proper use of wood energy as a substitute for fossil fuels can have a particular impact on climate change by reducing the net release of carbon into the atmosphere [START_REF]Wood Energy in the ECE Region: Data, Trends and Outlook in Europe, the Commonwealth of Independent States and North America, UN[END_REF] through sequestration in biomass and long-lived products. On the other hand, wood energy can also have an economic advantage by satisfying the growing demand for energy. The question is, how can wood energy be used sustainably to achieve these benefits?

For this purpose, research has aimed to characterise the pyrolysis, gasification and combustion of wood in order to design efficient and environmentally sustainable units. However, an accurate study of these techniques requires a global understanding of their fundamental processes, especially the primary pyrolysis phase. Pyrolysis, the thermal degradation of wood, is a potentially useful thermochemical conversion process.

It is considered not only as an independent process for the production of bio-oil and biochar, but also as a first step of the gasification and combustion processes [START_REF] Koufopanos | Kinetic modelling of the pyrolysis of biomass and biomass components[END_REF]. Therefore, knowledge of the wood pyrolysis behaviour, especially as a function of wood sample size, provides the quantitative basis for a general rigorous modelling approach applicable to any wood application in any scale [START_REF] Di Blasi | Modeling of Transport Phenomena and Kinetics of Biomass Pyrolysis[END_REF][START_REF] Chan | Modelling and experimental verification of physical and chemical processes during pyrolysis of a large biomass particle[END_REF].

Many researchers have studied the thermal degradation behaviour of wood using thermogravimetric analysis (TGA). At this scale, small particles are used to ensure the absence of internal heat and mass transfer.

The results obtained from TGA tests are used to determine reaction mechanisms and kinetic data of wood pyrolysis. In the literature, numerous kinetic schemes for wood pyrolysis have been carried out. Many authors [START_REF] Tang | Effect of Inorganic Salts on Pyrolysis of Wood, Alpha-cellulose, and Lignin Determined by Dynamic Thermogravimetry[END_REF][START_REF] Thurner | Kinetic investigation of wood pyrolysis[END_REF][START_REF] Wagenaar | Pyrolysis of biomass in the rotating cone reactor: modelling and experimental justification[END_REF] have considered a one-step global reaction that converts wood to volatile products and char without a detailed description, as shown in Fig . 1. Other authors such as Caballero et al. [START_REF] Caballero | Pyrolysis kinetics of almond shells and olive stones considering their organic fractions[END_REF] and Thunman et al. [START_REF] Thunman | Combustion of wood particles-a particle model for eulerian calculations[END_REF] have used kinetic schemes with independent competitive reactions. These schemes follow the proposal of Shafizadeh-Chin [START_REF] Shafizadeh | Thermal Deterioration of Wood[END_REF] shown in Fig. 2.

Multi-stage mechanisms were also used in the literature [START_REF] Ward | Experimental weight loss kinetics of wood pyrolysis under vacuum[END_REF][START_REF] Miller | A Generalized Biomass Pyrolysis Model Based on Superimposed Cellulose, Hemicelluloseand Liqnin Kinetics[END_REF][START_REF] Branca | Kinetics of the isothermal degradation of wood in the temperature range 528-708 K[END_REF][START_REF] Branca | Global interinsic kinetics of wood oxidation[END_REF], suggesting the presence of intermediate components as shown in Fig. 3. Furthermore, there are many authors who consider that the description

Nomenclature α abs

Average absorptivity [-] ∆h Reaction heat [J ⋅ kg -1 ]

λ Thermal conductivity [W ⋅ m -1 ⋅ K -1 ]
q " e External heat flux per unit area [kW ⋅ m -2 ]

q " loss Heat losses per unit area [kW ⋅ m -2 ]

Q " r sum of reaction heat [kW ⋅ m -2 ⋅ K -1 ] ρ Density [kg ⋅ m -3 ] σ Stefan-Boltzman constant [W ⋅ m -2 ⋅ K -4 ] ε Emissivity [-] K reaction rate [s -1 ] K 0 Pre-exponential factor [s -1 ] m 0 Initial mass [Kg] Cp Thermal capacity [J ⋅ kg -1 ⋅ K -1 ] E Activation energy [kJ ⋅ mol -1 ] h Thermal convective coefficient [W ⋅ m -2 ] L Thickness of the sample [m] R Universal gas constant [J ⋅ mol -1 ⋅ K -1 ] T Temperature [K] t Time [s]
x Distance from the exposed surface [m] of wood pyrolysis with only one component is not accurate enough. For instance [START_REF] Radmanesh | A unified lumped approach in kinetic modeling of biomass pyrolysis[END_REF][START_REF] Wang | Tg study on pyrolysis of biomass and its three components under syngas[END_REF][START_REF] Grønli | Thermogravimetric Analysis and Devolatilization Kinetics of Wood[END_REF][START_REF] Branca | Critical evaluation of global mechanisms of wood devolatilization[END_REF][START_REF] Sharma | Kinetic modeling and simulation: Pyrolysis of jatropha residue de-oiled cake[END_REF][START_REF] Barneto | Simulation of the thermogravimetry analysis of three non-wood pulps[END_REF] assumed that the wood pyrolysis is the sum of its main components: cellulose, hemicellulose and lignin. This reaction scheme, shown in Fig. 4, can be applied to a variety of wood species, as the content of cellulose, hemicellulose and lignin varies from one type of wood to another. A major disadvantage of this reaction scheme is that it neglects the interactions between the different components and ignores the influence of minerals. Table 1 summarises the main mechanisms of wood/biomass pyrolysis in the literature. A wide variation in the kinetic parameters can be observed in the literature. At a first glance, it appears that the degradation reactions of lignocellulosic material are more commonly assumed to be first-order reactions. The activation energy of the one-component reaction presents widely variable values, roughly comprised between 44 and 243 kJ ⋅ mol -1 . Likewise, the activation energies vary between 86 and 147 kJ ⋅ mol -1 for hemicellulose, 193 and 236 kJ ⋅ mol -1 for cellulose, and 46-181 kJ ⋅ mol -1 for lignin. This variation may be due to the large variability of the biomass resource, the operating conditions and the mathematical treatment of the experimental data. The variation observed in this context may also be ascribed to the compensation effect of Arrhenius parameters. Changes in the activation energy (E a ) could be partly or entirely offset by adjustments in the pre-exponential factor or reaction order, and conversely [START_REF] Gong | A review on flaming ignition of solid combustibles: Pyrolysis kinetics, experimental methods and modelling[END_REF][START_REF] Shi | A method for addressing compensation effect in determining kinetics of biomass pyrolysis[END_REF]. For coarse or "thermally thick" wood samples, the internal gradients cannot be neglected. In this case, the chemistry of thermal decomposition is influenced by heat and mass transfer effects. It is therefore necessary to take into account in the modelling process the complex nature of wood, the coupling between chemical kinetics, heat transfer and mass transfer that takes place during the pyrolysis process of solid samples. Many efforts, both experimental and theoretical [START_REF] Haberle | Numerical models for thermochemical degradation of thermally thick woody biomass, and their application in domestic wood heating appliances and grate furnaces[END_REF][START_REF] Diblasi | Modeling chemical and physical processes of wood and biomass pyrolysis[END_REF][START_REF] Groenli | A theoretical and experimental study of the thermal degradation of biomass[END_REF][START_REF] Bilbao | Modelling of the pyrolysis of wet wood[END_REF], have been carried out to better understand the complex mechanisms interacting in the thermal degradation of thermally thick wood samples. Among all these researchers, many authors have studied the thermal degradation of wood at the cone calorimeter scale. Most of these studies have been carried out in an oxidative atmosphere [START_REF] Sadhukhan | Modelling and experimental studies on pyrolysis of biomass particles[END_REF][START_REF] Chan | Modelling and experimental verification of physical and chemical processes during pyrolysis of a large biomass particle[END_REF][START_REF] Fateh | Multi-scale modeling of the thermal decomposition of fire retardant plywood[END_REF][START_REF] Papari | A review on the pyrolysis of woody biomass to bio-oil: Focus on kinetic models[END_REF][START_REF] Colombiano | Numerical analysis of the characteristics of the decomposition zone of a burning wood sample under cone calorimeter and evaluation of the limiting process[END_REF][START_REF] Moghtaderi | An Integral Model for the Transient Pyrolysis of Solid Materials[END_REF][START_REF] Masmoudi | 2-D Modeling of thermo-kinetics coupled with heat and mass transfer in the reduction zone of a fixed bed downdraft biomass gasifier[END_REF][START_REF] Anca-Couce | Single large wood log conversion in a stove: Experiments and modelling[END_REF]. Under these conditions, oxidation reactions involving the gases (flame) and carbon (smouldering) increase the complexity of the problem. Therefore, it is necessary to limit these reactions and pay attention to pyrolysis by working in an inert atmosphere. Whereas, the study of wood degradation at the cone calorimeter in an inert atmosphere has been a subject of few prior investigations. In this area, the experimental study of 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] has for many years been the basis of numerous numerical works to develop a pyrolysis model. This study provides experimental data on mass loss rates and information on the in-depth temperatures for two heat fluxes: 25 and 40 kW⋅m -2 . Swann et al. [START_REF] Swann | Controlled atmosphere pyrolysis apparatus ii (capa ii): A new tool for analysis of pyrolysis of charring and intumescent polymers[END_REF], on the other hand, has developed a new apparatus, Controlled Atmosphere Pyrolysis Apparatus II, which facilitates the collection of data on mass loss rate, temperature, and sample shape for materials exposed to radiant heating in a controlled atmosphere. However, this apparatus has not been applied in the study of wood pyrolysis. Lautenberger and Fernandez-Pello [START_REF] Lautenberger | Generalized pyrolysis model for combustible solids[END_REF], Jia et al. [START_REF] Jia | Numerical simulation of the mass loss process in pyrolizing char materials[END_REF] and Richter et al. [START_REF] Richter | A multiscale model of wood pyrolysis in fire to study the roles of chemistry and heat transfer at the mesoscale[END_REF] used data from 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] to validate their thermal pyrolysis model.

A V 1 B K v1 K B B V 2 D K v2 K D D V 3 C K v3 K C K 1 =K v1 +K B ; K 2 =K v2 +K D ; K 3 =K v3 +K C
W ood ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ Lignin Cellulose Hemicellulose Gases + char Gases + char Gases + char K 1 K 2 K 3
Stoliarov et al. [START_REF] Stoliarov | Thermo-kinetic model of burning for pyrolyzing materials[END_REF] proposed a specific calculation code, Thermakin, to investigate the thermal degradation of polymer materials. This code allows the analysis of the decomposition of various types of materials in different dimensions, ranging from 0D to 2D. Terrei et al. [START_REF] Terrei | Experimental and numerical multi-scale study of spruce wood degradation under inert atmosphere[END_REF] have performed a new experimental setup allowing to study the wood thermal degradation at the cone calorimeter scale in an inert atmosphere. This study provides experimental data on mass loss rates and in-depth temperatures of spruce wood for three heat fluxes: 38, 49 and 59 kW ⋅ m -2 . These measurements were used to validate their one-dimensional pyrolysis model with GPYRO [START_REF] Terrei | Experimental and numerical multi-scale study of spruce wood degradation under inert atmosphere[END_REF]. More recently, Gong and Yang [START_REF] Gong | Pyrolysis and autoignition behaviors of oriented strand board under power-law radiation[END_REF] have published an exhaustive review regarding the pyrolysis of commonly used solid combustibles.

In summary, wood pyrolysis has been investigated using a multiscale approach in the literature. In this approach, relatively simplified schemes are preferred to avoid lengthy calculation times. Numerous kinetic models, ranging from simpler to more complex and predictive, have been introduced in previous studies. Some of these models are mathematical, with the sole objective of fitting the experimental results.

The others are physical models that describe the underlying chemical processes involved in wood thermal degradation, but they tend to be more complex and time-consuming. However, the ongoing challenge lies in formulating a simple kinetic model capable of accurately predicting mass loss and mass loss rate data while maintaining fidelity to the underlying chemical processes involved in wood thermal degradation. The present work addresses this challenge at the micro scale. At the bench scale, several wood pyrolysis models are available in the literature. However, the properties of these models are calibrated to fit the experimental data.

In most cases, the large number of unknown properties in the model and the limited amount of experimental data result in non-intrinsic properties. Therefore, when the experimental setup is changed or scaled up, the reliability of the model decreases. This aspect is the main focus of this paper at a larger scale.

A global multi-reaction kinetic model of wood thermal degradation was proposed. This model was inspired from a two stages, semi global multi reaction kinetic model established to study the carbonisation of olive wood [START_REF] Grioui | Thermogravimetric analysis and kinetics modeling of isothermal carbonization of olive wood in inert atmosphere[END_REF]. It divides the wood into three pseudo-components that are not considered to be the main components of wood: hemicellulose, cellulose and lignin. These pseudo-components degrade in a single step reaction, which allows a proper study of the kinetic aspects related to a variable temperature levels. The best set of the model kinetic parameters is then determined by an optimisation method. A comparison between numerical and experimental evolutions of the mass loss and the mass loss rate for the different heating rates obtained from TGA showed a good agreement. At larger scale, cone calorimeter tests were then carried out in an inert atmosphere at two heat fluxes (38 and 49 kW ⋅ m -2 ). Mass loss and in-depth temperatures at twelve different positions were measured. A 1D-pyrolysis model was developed by coupling the kinetic model with the mass and energy consevation equations. All the properties of the model were taken from literature or determined through experimental measurements, except for the thermal conductivity above 200 °C. This particular property was estimated by fitting the mass loss data obtained from cone calorimeter tests. To validate the model at this scale, an additional experiment was conducted using a different heat flux of 25 kW ⋅ m -2 , which was not used to optimize the model parameters. The latter model shows good efficiency in predicting the experimental results obtained from the cone calorimeter tests.

Study at the micro scale

This section presents the experimental and numerical studies conducted at the micro scale to evaluate the thermal degradation of wood in an inert atmosphere, with a primary focus on chemical aspects. Two wood species, beech and spruce, were used for the tests. These species have chemical compositions representative of the typical standards for the hardwood and softwood categories, respectively [START_REF] Branca | Global interinsic kinetics of wood oxidation[END_REF].

Thermogravimetric analysis

The degradation studies were performed using a STA 449 f3 Jupiter thermobalance in an inert atmosphere of nitrogen at a flow rate of 20 mL ⋅ min -1 . The tests were conducted using approximately 50 ± 3 mg of wood powder with a thickness of less than 0.1 mm. Before each test, the samples were dried at 105 °C for 24 hours to remove moisture. During the experiments, the sample was heated from the ambient temperature to 800 °C at five different heating rates of 5, 10, 20, 30 and 40 K ⋅ min -1 . The mass of the wood sample and the furnace temperature were continuously recorded. For each experiment, mass loss and normalised mass loss rate curves were plotted as a function of temperature. The mass loss represents the ratio of the sample weight (m) to the initial weight (m 0 ). The normalised mass loss rate curves were obtained numerically using the time derivative of the mass loss curves. In order to ensure good reproducibility of the experiments, at least two runs were carried out for each heating rate. Therefore, the reported experimental data correspond to the average of these tests, where the relative difference was less than 2 %.

Fig. 5a and Fig. 5b show the mass loss curves, for beech and spruce wood, respectively, under nitrogen atmosphere at five different heating rates 5, 10, 20, 30, 40 K ⋅ min -1 . As can be seen in Fig. 5, the evolution of mass loss for both woods is similar regardless the heating rate. Even if the beech and spruce samples were pre-dried, the mass loss curves show a minor decline in mass before reaching 150 °C. This decrease is attributed to the evaporation of bound water still present in the wood. It is important to note that oven drying at 105 °C can only remove free water and not bound water from the wood samples. Furthermore, about 70 % of the initial mass of beech and 65 % of the initial mass of spruce was found to be degraded between 240 and 400 °C, while 10 % of the initial mass of beech and 20 % of the initial mass of spruce was lost between 400

°C and 800 °C. The mass of the residue remaining at the end of the experiment was approximately 19 % and 21 % of the initial mass for beech and spruce, respectively. The analysis of Fig. 5 does not allow to clearly identify all the steps of the thermal degradation of beech and spruce wood under inert atmosphere. In this sense, Fig. 6a and Fig. 6b show the normalised mass loss rate curves, for beech and spruce wood respectively at five different heating rates 5, 10, 20, 30, 40 K ⋅ min -1 under nitrogen atmosphere. For both woods, it was noticed that the pyrolysis process is characterised by two regions: main devolatilization and continuous slight devolatilization. The main pyrolysis process develops from about 240 °C to 400 °C at low heating rates (5, 10 and 20 K ⋅ min -1 ) and 430 °C at high heating rates (30 and 40 K ⋅ min -1 ). In this region, there are two peaks: a peak of approximately 305 °C at low heating rate and 350 °C at high heating rates. This peak is mainly related to hemicellulose decomposition. Another peak was observed at a higher temperature around 345 °C for low heating rates and 380 °C for high heating rates and is essentially related to the cellulose decomposition. The continuous slight devolatilization region occurred above 430 °C. This region corresponds to the slow degradation of lignin, which decomposes in both regions without characteristic peaks [START_REF] Dhyani | A comprehensive review on the pyrolysis of lignocellulosic biomass[END_REF]. In order to quantify the effect of the heating rate on the degradation process characteristics of beech and spruce wood, the same parameters as those introduced by Gronli et al. [START_REF] Grønli | Thermogravimetric Analysis and Devolatilization Kinetics of Wood[END_REF] were evaluated and reported in Table 2. The initial degradation temperature T initial was considered to be the temperature at which the solid mass fraction is equal to 0.975. The parameter T f inal was obtained when the normalised mass loss rate curve represents an inflection point at a temperature of about 400 °C. The temperature of the first peak was defined as T shoulder . The temperature T peak was the temperature at which the maximum peak is reached.

The maximum normalised mass loss rate was called D max .

As the heating rate increased from 5 K⋅min -1 to 40 K⋅min -1 for beech and spruce wood, all the characteristic temperatures (T initial , T f inal , T shoulder , T peak ) became successively higher especially T shoulder and T peak , as shown in Table 2. The whole decomposition process was shifted towards higher temperatures and the normalised mass loss rate increases. The shift of the normalised mass loss rate curves at higher temperature is clearly shown, for example, by the normalised mass loss rate curves of beech wood for 5 and 40 K ⋅ min -1 reported in Fig. 7. The maximum normalised mass loss rate D max showed an increasing trend up to about 0.39 min -1 for both species as the corresponding temperature increased from 342 °C to 380 °C for beech and from 350 °C to 392 °C for spruce wood. This can be interpreted on the basis of heat transfer limitations.

Indeed, at a low heating rate, the sample has more time to establish a uniform temperature within it. On the other hand, at a high heating rate, the sample has less time to establish a uniform temperature within it: heat transfer within the sample takes time, and the temperature at the core of the wood is not exactly the same as that of the reactor. In such a case, the kinetic aspect competes with the heat exchange aspect within the sample [START_REF] Slopiecka | Thermogravimetric analysis and kinetic study of poplar wood pyrolysis[END_REF]. Therefore, the low heating rate results were used to evaluate the kinetic parameters for a proposed model. In this case, the temperature gradients in the samples are smaller and the process is controlled by the kinetics.

The mass loss and normalised mass loss rate curves for beech and spruce wood at the heating rate of 5 K ⋅ min -1 are shown in Fig. 8a and Fig. 8b, respectively. It can be seen that the evolution of mass loss is similar for both woods and they differ only in the mass of the residue remaining at the end of the experiment.

The normalised mass loss rate of beech shows a clear shoulder peak in the first stage of the normalised mass loss rate curve at around 300 °C, which is not obviously noticeable in the normalised mass loss rate curve of spruce, possibly due to its lower hemicellulose content compared to beech [START_REF] Grønli | Thermogravimetric Analysis and Devolatilization Kinetics of Wood[END_REF]. However, the differences in the corresponding degradation characteristics for beech and spruce at different heating rates are not exceedingly large. The characteristic parameters are quantitatively similar for both cases at different heating rates, as shown in Table 2. It is therefore worth looking for a common pyrolysis mechanism.

Kinetic model

As mentioned in the introduction, several kinetic models for the thermal degradation of wood have been proposed in the literature. Some describe the pyrolysis of wood in terms of a single component, while others recommend dividing the wood into three components corresponding to the main components of wood (hemicellulose, cellulose and lignin). Models of these two categories have advantages and drawbacks: more or less complex, more or less predictive. However, the thermal degradation of wood cannot be considered as a reflection of the sum of the thermal responses of its main components, since some inorganic components catalyse the conversion process in an unpredictable variety of ways [START_REF] Blasi | Heat, momentum and mass transport through a shrinking biomass particle exposed to thermal radiation[END_REF][START_REF] Maschio | Pyrolysis, a promising route for biomass utilization[END_REF]. Furthermore, the interaction between the main components cannot be neglected, as shown by Hosoya et al. [START_REF] Hosoya | Cellulose-hemicellulose and cellulose-lignin interactions in wood pyrolysis at gasification temperature[END_REF].

Based on the experimental results and on previous works, it was proposed to develop a global multi-reaction kinetic model of wood degradation in order to properly follow the kinetic aspects related to the variable temperature levels received by the sample. The model developed here is inspired from a two-stages, semi global multi-reaction kinetic model established to study the carbonisation of olive wood [START_REF] Grioui | Thermogravimetric analysis and kinetics modeling of isothermal carbonization of olive wood in inert atmosphere[END_REF] and then used to study the isothermal degradation of wood panel and of its components [START_REF] Girods | Thermal removal of nitrogen species from wood waste containing urea formaldehyde and melamine formaldehyde resins[END_REF].

In the proposed model, wood is divided into three pseudo-components A 1 , A 2 and A 3 . These pseudo solids cannot be assimilated to the main components, which are cellulose, hemicellulose and lignin. Each pseudocomponent corresponds to a specific kinetic law and a mass fraction α 1 , α 2 and α 3 , respectively of the initial solid. A 1 , A 2 and A 3 degrade in a single stage reaction to give gas products G 1 , G 2 and G 3 , respectively, and a non-degradable solid residue C 2 and C 3 . It is worth mentioning that there is no chemical difference between C 2 and C 3 . At low temperatures (T ≤ 300°C) only the degradation of A 1 occurs and the product is gaseous. Above this temperature, the transformation of the two pseudo-components A 2 and A 3 begins, giving gaseous products G 2 and G 3 and non-degradable solids C 2 and C 3 respectively. The proposed kinetic scheme is as follows:

A 1 (First pseudo component) k1 → G 1 (Gas) A 2 (Second pseudo component) k2 → G 2 (Gas) + γ 2 .C 2 (Solid) A 3 (Third pseudo component) k3 → G 3 (Gas) + γ 3 .C 3 (Solid)
γ 2 and γ 3 correspond to the mass fractions of solid produced by the components A 2 and A 3 respectively.

K i is the rate coefficient which follows an Arrehiuns-type law (K i =K 0i .exp(-E i /RT)). Assuming that the kinetics of the three reactions are described by first order laws, the mass balance of the solid and slightly volatile A 1 , A 2 , A 3 , C 2 and C 3 , can be respectively written as:

dm A1 dt = -K 1 .m A1 ( 1
)
dm A2 dt = -K 2 .m A2 ( 2
)
dm A3 dt = -K 3 .m A3 ( 3
)
dm C2 dt = γ 2 .K 2 .m A2 ( 4
)
dm C3 dt = γ 3 .K 3 .m A3 (5)
The total mass of the sample at the time t, is then described by m(t), which is:

m(t) = m A1 (t) + m A2 (t) + m A3 (t) + m C2 (t) + m C3 (t) (6)
The analytical resolution of the balance equations leads to the following equation:

m(t) m 0 = γ 2 .α 2 + γ 3 .α 3 + α 1 .exp(-K 1 .t) + α 2 .(1 -γ 2 ).exp(-K 2 .t) + α 3 .(1 -γ 3 ).exp(-K 3 .t) (7)
Eq. 7 shows that the calculated mass of the sample according to this model during the thermal degradation in an inert atmosphere depends on 11 kinetic and stoichiometric parameters (α

1 , α 2 , α 3 , E 1 , E 2 , E 3 , K 01 ,
K 02 , K 03 , γ 2 and γ 3 ). These parameters must be estimated as they cannot be measured or determined experimentally. In practice, the least squares method was used to find the set of parameters that minimises the total error E r1 (Eq. 8) and E r2 (Eq. 9) between the numerical and experimental mass loss and mass loss rate respectively:

E r1 = X ∑ i=1 (m num (i) -m exp (i)) 2 (8)
E r2 = X ∑ i=1 (mlr num (i) -mlr exp (i)) 2 (9)
Where m num and m exp are respectively the numerical and experimental mass loss of the samples, mlr num and mlr exp are respectively the numerical and experimental normalised mass loss rate of the samples, and X is the number of experimental points. The Levenberg-Marquardt algorithm was used in the optimisation. Initially, the kinetic parameters provided by Grioui et al. [START_REF] Grioui | Thermogravimetric analysis and kinetics modeling of isothermal carbonization of olive wood in inert atmosphere[END_REF] were utilized as a set of initial values for the estimation based on E r2 (Eq. 9). The resulting kinetic parameters were then used as initial values to minimize E r1 (Eq. 8). This iterative process was repeated multiple times to obtain the optimal set of kinetic parameters that effectively fit the mass loss and mass loss rate curves simultaneously. To avoid heat and mass transfer limitations, the optimization process excluded the use of high heating rates (30 and 40 K ⋅ min -1 ). Instead, the optimization was performed for the slow heating rates: 5, 10, and 20 K ⋅ min -1 simultaneously. Indeed, employing the parameter estimation procedure on multiple experiments conducted under diverse conditions, such as various heating rates, while utilizing the same kinetic model and parameters, helped to circumvent the compensation effect [START_REF] Branca | Global interinsic kinetics of wood oxidation[END_REF]. The values of the kinetic parameters, obtained for beech and spruce wood, and the deviations between numerical and experimental are listed in Table 3.

The order of the reactions was kept constant and equal to one (n=1). The introduction of higher order reactions in this model provides an excellent description of the experimental results. This was not done in accordance with the hypothesis that the reaction rate depends only on the amount of reactant present in the reactor [START_REF] Chornet | Compensation effect in the thermal decomposition of cellulosic materials[END_REF]. The other parameters were estimated with constraints to ensure a successive degradation of the three components in the following order: A 1 , then A 2 , and finally A 3 . The degradation of the first component, leading to the formation of gases, precedes that of the second and third components which lead to the formation of gases and char.

Details about the dynamics of the different pseudo-components and a comparison between predicted and measured mass loss and normalised mass loss rate at the three heating rates: 5, 10 and 20 K ⋅ min -1 for beech and spruce wood are shown in Fig. 9 and Fig. 10, respectively. In the case of beech, the reaction of the first pseudo-component A 1 , which was completely converted to gas, started at 250 °C and was completed at 300 °C approximately. The maximum mass loss rate of A 1 occurred between 290 °C and 320 °C depending on the heating rate. As the heating rate is higher, the maximum mass loss rate occured at a higher temperature as shown in the section 2.1. The decomposition of the second pseudo-component A 2 , which leads to the formation of gas and non-degradable solid C 2 , started at about 300 °C and was completed at about 400 °C.

The maximum mass loss rate of A 2 was proceeded between 340 °C and 370 °C. The final pseudo-component, A 3 , initiated its degradation into gas and C 3 at approximately 420°C and concluded around 650°C. The maximum mass loss rate of A 3 was between 500 °C and 600 °C. The char was completely obtained at about 650 °C. For spruce, the decomposition of the first pseudo-component A 1 started at about 230 °C and was completed at 300 °C. The maximum mass loss rate of A 1 rate occurred between 320 °C and 340 °C depending on the heating rate. The decomposition of the second pseudo-component A 2 started at about 300 °C and was accomplished at about 400 °C. The maximum mass loss rate of A 2 was attained between 350 °C and 370 °C.

The last pseudo-component A 3 initiated to degrade at about 400 °C and was achieved at about 650 °C with a maximum mass loss rate between 500 °C and 600 °C. The char was fully formed at about 650 °C. As can be seen, the simulated mass loss and the normalised mass loss rate for both species show a good agreement with the experimental results for different heating rates. The performance of the kinetic mechanism was evaluated using the Normative Root Mean Squared Error (NRMSE), between the experimental and predicted mass loss, characterised by the following variable:

N RM SE(%) = √ ∑ X i=1 (mnum(i)-mexp(i)) 2 X max i=1...X m exp (i) -min i=1...X m exp (i) ⋅ 100 (10)
For beech the total deviation for the mass loss curve is about 1.06, 1.4 and 2.7 % for 5, 10 and 20 K ⋅ min -1 respectively, leading to an average NRMSE of 1.72 %. For spruce, the overall deviation for the mass loss curve is about 1.26, 1.27 and 2.1 % for 5, 10 and 20 K ⋅ min -1 respectively, giving an average NRMSE of 1.21 %. For both species, the fit of the model to the experimental mass loss and mass loss rate curves was very good from the ambient temperature to 400 °C. At temperatures above 400 °C, there is a slight discrepancy between the experimental and simulated curves. This can be attributed to a delayed degradation of the third pseudo-component. In addition, at higher temperatures, many reactions are likely to dominate which are not described in detail in this model and which cause the discrepancy. The maximum peak of the mass loss rate is slightly underestimated. This can be attributed to the presence of heat transfer phenomena and the experimental procedures. In any case, the prediction by the present model is considered encouraging in terms of the validity of the model itself.

To validate the kinetic parameters obtained through optimisation, these parameters were employed to predict mass loss and mass loss rates at elevated heating rates of 30 and 40 K ⋅ min -1 . Despite these two heating rates not being incorporated into the optimization process, the model demonstrates its efficacy in predicting experimental mass loss and normalised mass loss rates for beech and spruce wood, as shown in Fig. 11 and Fig. 12, respectively. Indeed, the NRMSE for beech is 3.3 % at 30 K ⋅ min -1 and 3.5 % at 40

K ⋅ min -1 .
For spruce, it is 2.7 % at 30 K ⋅ min -1 and 3.1 % at 40 K ⋅ min -1 .

Study at the bench scale

The objective of this section is to describe the thermal degradation of spruce and beech wood during the cone calorimeter experiments under inert atmosphere. First, the experiments performed at the cone calorimeter scale are briefly described. Then, the numerical model of pyrolysis at the cone calorimeter scale is presented.

Cone calorimeter experiments

As a detailed description of the experimental apparatus has been reported by Terrei et al. [START_REF] Terrei | Experimental and numerical multi-scale study of spruce wood degradation under inert atmosphere[END_REF], only a brief description of the experimental setup is given here. The tests were performed in front of a cone calorimeter oriented vertically. During the tests, the sample was placed in a stainless-steel chamber specifically designed to study the wood thermal degradation under a controlled atmosphere. A sapphire window placed on the front face of the chamber allows the heat flux from the cone to pass through. The chamber was inerted by a continuous injection of argon at a flow rate of 10 L ⋅ min -1 . A Testo 350 gas analyser was used to determine the oxygen concentration. A test was started when the concentration of oxygen in the chamber stabilised at around 3 %. This concentration was always less than 6 % during the tests. For each test, the wood sample was placed in a specific sample holder made of low density calcium silicate plates to limit the thermal interactions with the edges and to ensure a 1-D heat transfer. The rear surface of sample is exposed to free gas flow. The sample and its holder were then inserted into the chamber via the rear face, which consists of a sliding door. Fig. 13 shows the experimental setup. The mass loss of the sample was measured using a load cell with a precision of 0.1 g. The in-depth temperatures were measured using twelve thin wire thermocouples embedded in the wood samples. Ten thermocouples were placed every 2 mm from 2 to 20 mm depth from the exposed surface, one at a 30 mm depth and one at a 40 mm depth. Tests were conducted at heat fluxes of 38 and 49 kW ⋅ m -2 for 10 minutes. The samples used in the tests were square wood samples of 100 × 100 × 50 mm 3 , dried at 105 °C for 48 hours prior to each test to remove moisture. The initial mass of the samples tested was 180 ± 12 g and 300 ± 16 g for spruce and beech respectively. Terrei et al. [START_REF] Terrei | In-depth wood temperature measurement using embedded thin wire thermocouples in cone calorimeter tests[END_REF] have already performed the tests only for spruce wood. In this study, the experimental data on spruce wood are identical to those presented in the study of Terrei et al. [START_REF] Terrei | In-depth wood temperature measurement using embedded thin wire thermocouples in cone calorimeter tests[END_REF]. On the other hand, tests were carried out using beech wood samples, with a few technical modifications. In these experiments, the flow rate of argon was 12 L ⋅ min -1 instead of 10 L ⋅ min -1 to ensure an oxygen concentration less than 3% throughout all the tests, and then to limit char oxidation as much as possible. In addition, a load cell with a precison of 0.01 g was used in order to provide a more reliable mass loss and mass loss rate. It is important to note that a single test was conducted on a spruce wood sample using a purging flow rate of 12 L ⋅ min

Modeling of the cone calorimeter experiments

In the literature, many software have been used to simulate the degradation of wood at bench scale, like GPYRO, FDS and FireFoam. Previous works [START_REF] Valencia | Experimental and numerical investigation of the thermal decomposition of materials at three scales: application to polyether polyurethane foam used in upholstered furniture[END_REF][START_REF] Fateh | Multi-scale modeling of the thermal decomposition of fire retardant plywood[END_REF] have shown the inadequacy of FDS to numerically simulate cone calorimeter tests with kinetic parameters calculated from TGA data. Otherwise, many authors [START_REF] Lautenberger | Generalized pyrolysis model for combustible solids[END_REF][START_REF] Richter | A multiscale model of wood pyrolysis in fire to study the roles of chemistry and heat transfer at the mesoscale[END_REF] have shown that GPYRO is able to well predict the thermal degradation behaviour of wood well.

However, in GPYRO, the evolution laws of the model thermal properties are imposed. Regarding FireFoam, it is less commonly used in the literature compared to other software. In this paper, the modelling has been written in MATLAB ® environment, in order to develop a model with a good knowledge of the assumptions and a good control of the evolution laws of all the properties. The modelling must focus on phenomena that can predict what happens inside the sample, such as heat transfer, mass transfer, chemical reactions, as well as the change in its thermophysical properties (conductivity, specific heat). The developed scheme and its associated kinetic parameter, validated at TGA scale, were used as input data to simulate the thermal decomposition of the spruce and beech wood at the cone calorimeter scale. The following assumptions were made in the pyrolysis model:

1. The heat transfer was considered to be one dimensional since the wood sample seemed to degrade uniformly from the exposed side.

2. The heat and mass transfer between the solid and gas phases were neglected.

3. The thermo-physical properties of the three pseudo-components A 1 , A 2 , and A 3 were equivalent to those of dry wood.

4. The dimensions and shape of the wood sample remained constant and cracks and shrinkage were neglected.

5. The heat of the three chemical reactions was supposed to be the same and was taken from the literature [START_REF] Grioui | Thermochemical modeling of isothermal carbonization of thick wood particle -Effect of reactor temperature and wood particle size[END_REF].

Based on the above assumptions, the energy conservation equation for pyrolysis of the dry wood is described as:

∂ ∂t [T (ρ s C ps )] = ∂ ∂x (λ s ∂T ∂x ) + Q " r ( 11
)
where: Q " r is the sum of reaction heat of the three pyrolysis reactions, as follows

Q " r = k 1 α 1 ρ A1 ∆h 1 + k 2 α 2 ρ A2 ∆h 2 + k 3 α 3 ρ A3 ∆h 3 . (12)
Here, ρ s is the bulk density described as the sum of the constituents (A 1 , A 2 and A 3 ) and products (C 2 and C 3 ) densities as:

ρ s = α 1 ρ A1 + α 2 (ρ A2 + ρ C2 ) + α 3 (ρ A3 + ρ C3 ) (13)
where, C ps and λ s are respectively the thermal capacity and conductivity of the wood sample.

For the resolution of Eq. 11, it was assumed that at t=0, T=T 0 , and that at t > 0, on the exposed side of the sample (x=0), the heat balance for the control volume with thickness (∆ x ) is as follows:

∂ ∂t [T (ρ s C ps )] | x=0 = (α abs q " e -q " loss1 -λ s ∂T ∂x ) /∆ x + Q " r ( 14
)
where q " loss1 is the heat balance of the control volume defined by: Moreover, for t> 0, at the back surface (x=L) another heat balance for the control volume with a thikness of (∆ x ) is established:

q " loss1 = σε (T 4 s -T 4 0 ) + h (T s -T 0 ) (15)
∂ ∂t [T (ρ s C ps )] | x=L = (λ s ∂T ∂x -q " loss2 ) /∆ x + Q " r ( 16
)
where q " loss2 is the heat losses by radiation and convection from the back surface and characterized by the following relation:

q " loss2 = σε (T 4 b -T 4 0 ) + h (T b -T 0 ) (17)
During wood pyrolysis, its thermo-physical properties such as thermal conductivity, specific heat, and density, change. The density of the sample was easily measured and then the variation in sample density was calculated by the model. The average initial density of the virgin spruce and beech samples was found to be 360 and 600 kg ⋅ m -3 respectively. In contrast, it was difficult to obtain the variation of the thermal properties of wood (thermal conductivity and specific heat) over large temperature ranges (> 200 °C). In fact, above 200 °C, the properties of the original material are subjected to a large accompanying chemical reactions, and there are practical difficulties in determining material properties. Therefore, a wide range of different thermo-physical properties of wood were used in the literature. In addition, there is no clear trend in how the thermophysical properties vary in the modelling. Therefore, it was suggested that they should be chosen in such a way that the modelling results fit the experimental data well [START_REF] Haberle | Numerical models for thermochemical degradation of thermally thick woody biomass, and their application in domestic wood heating appliances and grate furnaces[END_REF].

Fig. 14 shows the variations of the specific heat capacity of wood and char as a function of temperature reported in the literature. In most previous modelling studies, the heat capacity of wood and char were modelled as a linear function of temperature. In our case, the specific heat capacity of wood (C p wood ) and char (C p char ) was supposed to vary according to the relations of Wenzl et al. [START_REF] Wenzl | The chemical technology of wood[END_REF] and Anca-Couce et al.

[56] respectively. The specific heat capacity of the wood sample was then assumed to vary linearly between wood and char depending on the conversion factor η, the ratio between the current and initial density

(C ps = (1 -η) ⋅ C p wood + η ⋅ C p char ).
It is worth mentionning that the choice of the specific heat of wood and char are not the most sensitive parameters affecting the accuracy of the model, as reported by Haberle [START_REF] Haberle | Numerical models for thermochemical degradation of thermally thick woody biomass, and their application in domestic wood heating appliances and grate furnaces[END_REF].

For thermal conductivity, Di Blasi [START_REF] Diblasi | Modeling chemical and physical processes of wood and biomass pyrolysis[END_REF] in their extensive review on the modelling of chemical and physical processes of wood and biomass pyrolysis reported that among the wood properties, this property causes the highest sensitivity of the model predictions. In the literature, thermal conductivity was assumed to be mainly temperature dependent [START_REF] Harada | Thermal constants of wood during the heating process measured with the laser flash method[END_REF][START_REF] Suleiman | Thermal conductivity and diffusivity of wood[END_REF]. In the present study, the thermal conductivity used was defined as follows:

1. Below 200 °C: the thermal conductivity of dry spruce and beech wood was measured in the laboratory using the hot wire method and was found to be 0.102 and 0.138 W ⋅ m -1 ⋅ K -1 respectively [START_REF] Flity | Thermal conductivity parallel and perpendicular to fibers direction and thermal capacity measurements of eight wood species up to 160 °c[END_REF].

2. Above 200 °C: the thermal conductivity of spruce and beech was assumed to vary as a function of temperature as follows:

λ spruce = 0.102 + a ⋅ (T -473) 2 + b ⋅ (T -473) (18)
λ beech = 0.138 + c ⋅ (T -473) 2 + d ⋅ (T -473) (19)
Where a, b, c and d are four constants to be estimated. An inverse method was applied to the mass loss measurements obtained from the cone calorimeter tests at 38 and 49 kW ⋅ m -2 simultaneously using this model. The Levenberg-Marquardt algorithm was used to minimise the following objective function:

E r = X ∑ i=1 (m num (i) -m exp (i)) 2 (20)
Table 4 gives the thermal conductivity obtained by optimisation and the other properties used in the model.

Fig. 15 shows the thermal conductivity of spruce and beech wood from the current study side by side with the available thermal conductivity from previous studies. For both species, the thermal conductivity increases with temperature, which is quite logical. The thermal conductivity of beech is higher than that of spruce, which is quite satisfactory taking into account the difference in density between the two species. Fig. 15 also shows the large discrepancies in the thermal conductivity values used in the literature. Moreover, the emissivity of the wood surface was measured by Terrei et al. [START_REF] Terrei | Experimental and numerical multi-scale study of spruce wood degradation under inert atmosphere[END_REF] and found to be 0.83.

The value for the convective coefficient of the solid surface was taken as 10 W ⋅ m -2 ⋅ K -1 [START_REF] Spearpoint | Predicting the piloted ignition of wood in the cone calorimeter using an integral model -effect of species, grain orientation and heat flux[END_REF]. The heat and mass conservation equations were numerically solved using a finite volume method written in a MATLAB ® code. The model allows the calculation of the temperature distributions within the sample, the mass loss and the mass loss rate per unit area (MLRPUA).

Results and discussion

This section presents the experimental and numerical results obtained at the cone calorimeter scale. Fig. 16 and Fig. 17 show the comparison between experimental and numerical temperatures at different depths within spruce and beech wood samples respectively during their decomposition in front of the cone calorimeter at 38 and 49 kW ⋅ m -2 . It can be noticed that the experimental and predicted in-depth temperatures are in good agreement for both species and heat fluxes. Although, the temperature predictions at depth (i.e. from 8 mm) were better than those near the surface. For 38 kW ⋅ m -2 , it can be seen that the calculated temperatures close to the surface for both species fit well the experimental data below 400 °C. Above this temperature, the simulation tends to underestimate the experimental evolution of near-surface temperatures.

In contrast, the simulation predicts very well the temperature evaluation in large depths. For tests at 49 kW ⋅ m -2 , the simulation tends to slightly overestimate the experimental near-surface temperatures below 500 °C for both species. Beyond this value, the simulation underestimates the experimental data. As for 38 kW ⋅ m -2 , the model predicts very well the temperature evolution from 8 mm. In general, the numerical results are in good agreement with the experimental results for low temperatures (< 350 °C). For higher temperatures, and especially near to the exposed surface, there is some bias. This bias mainly caused by the low accuracy of measurements during the conversion of wood into char. As the wood undergoes pyrolysis and transforms into char, its porosity increases, leading to decreased thermal contact between the material and the thermocouple. Additionally, the ignorance of the effects of the volume shrinkage and cracks in this model could also be another source of the bias. However, the numerical temperatures were quite satisfactory. for spruce and beech wood respectively. It can be noticed that there is a good agreement between the calculated and the experimental results for both species, whatever the heat flux.

The performance of the model was evaluated by calculating the NRMSE (Eq. 10), between the experimental and predicted mass loss. For spruce wood, the NRMSE is 1.5 and 3.8 % for 38 and 49 kW ⋅ m -2 respectively.

For beech wood, the NRMSE is 3.2 and 0.7 % for 38 and 49 kW ⋅ m -2 respectively. Regarding the MLRPUA for both species, the numerical and experimental results are in good agreement for the quasi steady state.

However, the numerical peak of the MLRPUA is overestimated at the beginning, especially for spruce. This bias may be due to an initial overestimation of temperatures from the near-surface thickness. To summarize, the model predict well the temperature profiles inside wood, the mass loss and the mass loss rate at the scale of the cone calorimeter. An additional experiment was conducted using a different heat flux of 25 kW ⋅ m -2

with samples of spruce and beech wood. The results of this experiment were not used for optimising the model parameters. Instead, they were employed for model validation. The purpose of this experiment was to verify the predictive capability of the model and assess its performance when applied to conditions beyond those used for parameter optimisation. Fig. 20 shows the efficiency of the model in predicting mass loss and MLRPUA obtained from the experiments conducted at 25 kW ⋅ m -2 for spruce and beech wood. For spruce, the NRMSE is 4.9 %, while for beech, it is 2.2 %. So, despite the results under a heat flux of 25 kW ⋅ m -2 not being utilised for optimising the model parameters, the model demonstrates its efficiency in predicting experimental mass loss and normalised mass loss rates for beech and spruce wood under this flux.

These results validate the kinetic model developped at the micro scale in this study and show that the multi-scale approach is appropriate to model the wood pyrolysis at large scales.

Conclusion

In this work, the thermal degradation of beech and spruce wood has been investigated throughout the multi-scale approach. At the micro scale, the thermal degradation of spruce and beech wood was studied using a thermogravimetric analyser at five heating rates (5, 10, 20, 30 and 40 K ⋅ min -1 ) under an inert atmosphere. The results led to a suggested wood thermal degradation mechanism with global multi-reactions.

The associated kinetic parameters for both species were calculated by using the least squares method. The results showed efficient predictions in agreement with experimental mass loss and mass loss rate for different heating rates. At the bench scale, the model was completed by adding a heat and mass transfer model to the kinetic mechanism. At this scale, the model was validated by comparing the predicted results with those obtained from cone calorimeter tests. These tests were performed in a specific chamber, which was designed to perform tests in an inert atmosphere. The wood samples (beech and spruce) were exposed to three heat fluxes [START_REF] Diblasi | Modeling chemical and physical processes of wood and biomass pyrolysis[END_REF][START_REF] Jia | Numerical simulation of the mass loss process in pyrolizing char materials[END_REF] and 49 kW ⋅ m -2 ) for 600 s. The results predicted by the model were in good agreement with the experimental measurements. Our perspective for the model developed in this study is to couple it

Figure 1 :Figure 2 :

 12 Figure 1: One step global reaction mechanism.

Figure 3 :

 3 Figure 3: Multi-stage pyrolysis mechanisms proposed by Di Blasi and Branca [14] (A is the wood, B and D are intermediate components).

Figure 4 :

 4 Figure 4: Independent parallel reactions model.

3

 3

Figure 5 :

 5 Figure 5: Normalised mass loss of beech and spruce wood in nitrogen atmosphere at five heating rates with TGA.

Figure 6 :

 6 Figure 6: Normalised mass loss rate of beech and spruce wood in nitrogen atmosphere at five heating rate with TGA.

Figure 7 :

 7 Figure 7: Normalised mass loss rate of beech with characteristic temperature for rates of 5 and 40 K ⋅ min -1 .

  (a) Normalised mass loss (b) Normalised mass loss rate

Figure 8 :

 8 Figure 8: Mass loss and normalised mass loss rate curves of beech and spruce under a heating rate of 5 K ⋅ min -1 .

(a) 5 K ⋅ min - 1 (b) 5 K

 515 ⋅ min -1 (c) 10 K ⋅ min -1 (d) 10 K ⋅ min -1 (e) 20 K ⋅ min -1 (f) 20 K ⋅ min -1

Figure 9 :

 9 Figure 9: Comparison between the experimental and the numerical mass loss and normalised mass loss rate curves for beech wood at 5, 10 and 20 K ⋅ min -1 .

Figure 10 :

 10 Figure 10: Comparison between the experimental and the numerical mass loss and normalised mass loss rate curves for spruce wood at 5, 10 and 20 K ⋅ min -1 .

(a) 30 K

 30 ⋅ min -1 (b) 30 K ⋅ min -1 (c) 40 K ⋅ min -1 (d) 40 K ⋅ min -1

Figure 11 :

 11 Figure 11: Comparison between the experimental and the numerical mass loss and normalised mass loss rate curves for beech wood at 30 and 40 K ⋅ min -1 .

(a) 30 K

 30 ⋅ min -1 (b) 30 K ⋅ min -1 (c) 40 K ⋅ min -1 (d) 40 K ⋅ min -1

Figure 12 :

 12 Figure 12: Comparison between the experimental and the numerical mass loss and normalised mass loss rate curves for spruce wood at 30 and 40 K ⋅ min -1 .

- 1 .Figure 13 :

 113 Figure 13: (a) Back and (b) front side of the experimental setup [41].

  (a) Wood[START_REF] Koch | Specific heat of ovendry spruce pine wood and bark[END_REF][START_REF] Wenzl | The chemical technology of wood[END_REF][START_REF] Simpson | Physical properties and moisture relations of wood[END_REF][START_REF] Harada | Thermal constants of wood during the heating process measured with the laser flash method[END_REF][START_REF] Gupta | Specific heat and thermal conductivity of softwood bark and softwood char particles☠†[END_REF][START_REF] Parker | Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity[END_REF] (b) Char[START_REF] Koufopanos | Kinetic modelling of the pyrolysis of biomass and biomass components[END_REF][START_REF] Anca-Couce | Numerical analysis of a biomass pyrolysis particle model: Solution method optimized for the coupling to reactor models[END_REF][START_REF] Sadhukhan | Modelling of pyrolysis of large wood particles[END_REF][START_REF] Blasi | Physico-chemical processes occurring inside a degrading two-dimensional anisotropic porous medium[END_REF][START_REF] Grønli | Mathematical model for wood pyrolysiscomparison of experimental measurements with model predictions[END_REF]

Figure 14 :

 14 Figure 14: Specific heat capacities of wood and char available in literature.

Figure 15 :

 15 Figure 15: Thermal conductivity as a function of the temperature [69, 70, 71, 72, 73, 74].

Fig. 18 and

 18 Fig. 18 and Fig. 19 present the comparison between the mass loss and the Mass Loss Rate Per unit Area (MLRPUA) as a function of the time obtained by the model and those obtained from experiments performed at 38 and 49 kW ⋅ m -2 for spruce and beech wood respectively. It can be noticed that there is a

(a) 38

 38 kW ⋅ m -2 (b) 49 kW ⋅ m -2

Figure 16 :

 16 Figure 16: Comparison between the experimental and the numerical in-depth temperatures of spruce wood for 38 and 49 kW ⋅ m -2 heat fluxes.

(a) 38

 38 kW ⋅ m -2 (b) 49 kW ⋅ m -2

Figure 17 :

 17 Figure 17: Comparison between the experimental and the numerical in-depth temperatures of beech wood for 38 and 49 kW ⋅ m -2 heat fluxes.

(a) 38

 38 kW ⋅ m -2 (b) 38 kW ⋅ m -2 (c) 49 kW ⋅ m -2 (d) 49 kW ⋅ m -2

Figure 18 :

 18 Figure 18: Comparison between the experimental and the numerical mass loss and MLRPUA for spruce wood for 38 and 49 kW ⋅ m -2 heat fluxes.

(a) 38

 38 kW ⋅ m -2 (b) 38 kW ⋅ m -2 (c) 49 kW ⋅ m -2 (d) 49 kW ⋅ m -2

Figure 19 :

 19 Figure 19: Comparison between the experimental and the numerical mass loss and MLRPUA for beech wood for 38 and 49 kW ⋅ m -2 heat fluxes.

Figure 20 :

 20 Figure 20: Comparison between the experimental and the numerical mass loss and MLRPUA for spruce and beech wood for 25 kW ⋅ m -2 heat flux.

Table 1 :

 1 Summary of one-component and multi-component mechanisms of lignocellulosic material pyrolysis.

	Reaction mechanism	Author (Ref.)	Biomass	Experimental system	Size/mass Reaction order Kinetic constants: E (kJ ⋅ mol -1 ), A (s -1 )
	Fig.1	Tang et al. [6]	Ponderosa Pine	Dynamic TGA 325-350 °C	20-100 mg	1	K= 6.5× 10 6 exp (226/RT)
	Fig.1	Thurner and Mann [7]	Oak	Isothermal tube furnace 300-400 °C	650 µg	1	K=2.47× 10 6 exp (106.5/RT)
	Fig.1	Wagenear et al. [8]	Pine	Isothermal TGA 380 °C	100-125 µg	1	K=1.4× 10 10 exp (150/RT)
						1.58	kG=1.27× 10 13 exp (163.4/RT)
	Fig.2	Font et al. [9]	Olive stones	Dynamic TGA 2, 10 and 25 K ⋅ min -1	3-4 mg	0.667	kL= 4.3× 10 13 exp (194.6/RT)
						7.21	kC=6.59× 10 16 exp (188.1/RT)
						1	kG=1.3× 10 8 exp (140/RT)
	Fig.2	Thunman et al. [10]	Pine	Pyrex reactor	-	1	kL= 2.0× 10 8 exp (133/RT)
						1	kC=1.08× 10 7 exp (121/RT)
						1	k1=9.6× 10 8 exp (186.73/RT)
	Fig.3	Wared and Braslaw [12]	Lignin	Isothermal TGA 300 °C	0.25mm	1	k2= 1.57× 10 16 exp (205.9/RT)
						1	k3=1.13× 10 17 exp (240/RT)
						1	k1=2.8× 10 19 exp (242.4/RT)
	Fig.3	Miller and Bellan [13]	Cellulose	Isothermal tube furnace 300-450 °C	≤ 80 µg	1	k2= 3.28× 10 14 exp (196.5/RT)
						1	k3=1.3× 10 10 exp (150.5/RT)
						1	k1= 2.7× 10 4 exp (76.2/RT)
	Fig.3 k2=5.9× 10 Fig.4 Di blasi and Branca [14] Beech Isothermal tube furnace 300-450 °C ≤ 80 µg 1 Branca et al. [19] Beech 1 kHemicellulose= 2.527× 10 11 exp (147/RT) Dynamic TGA 5, 20, 80 K ⋅ min -1 from the 20 mg 1 kCellulose=1.379× 10 14 exp (193/RT) initial temperature to 500 °C 1 kLignin=2.202× 10 12 exp (181/RT)
	Fig.4	Barneto et al. [21]	Rice straw pulp	Dynamic TGA 5, 10, 20 K ⋅ min -1 from the initial temperature to 500°C	10-100 mg	1 1 1	kHemicellulose= 2.19× 10 5 exp (86/RT) kCellulose=1.17× 10 15 exp (206/RT) kLignin=8.97× 10 2 exp (62/RT)

9 exp (142.8/RT) 1 k3=9.97 exp (43.8/RT) Fig.3 Di blasi and Branca [15] Beech Dynamic TGA 5, 10, 20, 40 K ⋅ min -1 from the initial temperature to 500 °C 5 mg 1 k1= 6.29× 10 7 exp (106/RT) 1 k2=8.6× 10 17 exp (226/RT) 1 k3=7.83× 10 6 exp (114/RT) 1.54 k3=1.10× 10 12 exp (183/RT) Fig.4 Gronli et al. [18] Birch Dynamic TGA 5 K ⋅ min -1 from the initial temperature to 500 °C 5 mg 1 kHemicellulose= 7.96× 10 2 exp (100/RT) 1 kCellulose=4.06× 10 7 exp (236/RT) 1 kLignin=1.8 exp (46/RT)

Table 2 :

 2 Degradation characteristics parameters under different heating rate of beech and spruce wood.Sample Heating rate (K ⋅ min -1 ) T initial (°C) T f inal (°C) T shoulder (°C) T peak (°C) D max (min -1 )

		5	240	371	296	342	0.06
		10	249	387	300	357	0.11
	Beech	20	256	397	320	368	0.2
		30	263	412	331	374	0.29
		40	269	420	337	380	0.39
		5	234	380	317	350	0.06
		10	250	390	325	363	0.12
	Spruce	20	260	407	342	376	0.2
		30	271	424	346	382	0.29
		40	277	430	350	392	0.4

Table 3 :

 3 Kinetic parameters estimated for the thermal degradation of beech and spruce wood.

	Sample Reaction E (kJ ⋅ mol -1 ) K 0i (1/s)	α	γ	Mean NRMSE (%)
		(1)	116	3.4 × 10 8	0.2	-
	Beech	(2)	155	5.52 × 10 10 0.55 0.08	1.72
		(3)	80	2.37 × 10 2 0.25 0.63
		(1)	105	2.1 × 10 7	0.16	-
	Spruce	(2)	172	1.3 × 10 12	0.6 0.15	1.21
		(3)	76.5	2.52 × 10 2 0.24 0.56

Table 4 :

 4 Values and correlations of thermophysical parameters used in the model. >200 °C, λ spruce = 0.102 + 1.2 ⋅ 10 -6 (T -473) 2 + 3.7 ⋅ 10 -9 (T -473) Optimised T<200 °C, λ beech = 0.138 Measured T >200 °C, λ beech = 0.138 + 1.06 ⋅ 10 -6 (T -473) 2 + 6.42 ⋅ 10 -9 (T -473) Optimised

	Property	Correlation/Value	Ref.
		T<200 °C, λ spruce = 0.102	Measured
	Thermal conductivity (W ⋅ m -1 ⋅ K -1 ) T Specific heat (J ⋅ kg -1 ⋅ K -1 )	C pwood = 1112 + 4.85 ⋅ (T -273) C pchar = 808.9 + 0.93 ⋅ (T -273)	[55] [56]
	Density (kg ⋅ m -3 )	ρ spruce =360 ρ beech =600	Measured Measured
	Emissivity	ε=0.83	[41]
	Convective coefficient (W ⋅ m -2 ⋅ K -1 )	h=10	[57]
	Absorptivity	α abs = ε = 0.83	[41]
	Reaction heat (kJ ⋅ kg -1 )	∆h i = -100	[54]


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

Virginie Tihay-Felicelli

Guillaume Gerandi

Frédéric Morandini

Paul-Antoine Santoni

Experimental study of the large scale flammability of wood cladding at the wildland-urban interface

Keywords: WUI fire, wood cladding, fire spread, safety distance

The aim of this work is to improve the understanding of the fire behaviour of building materials used in the wildland urban interface at a large scale. To this end, wood cladding was exposed to the heat flux from the burning of a cistus hedge ignited by a spreading fire front in a fuel bed of excelsior litter. Six experiments were performed with different configurations: hedge/cladding distance, cistus bulk density, hedge length. During the experiments, the assessment of the cladding ignition was observed by camera. Wind direction and velocity were measured continuously since the tests were conducted outdoors and wind is a significant driver of flame spread. Heat fluxes and temperatures were also measured in order to compare the intensity of the thermal aggression on the cladding coming from the burning hedge. When the distance between the hedge and the cladding was 3 m, the wood did not ignite even when the wind was in the direction of propagation towards the cladding. In these cases, the maximum heat flux was 18 kW.m -2 . This value did not allow the ignition of the wood cladding. When the distance was reduced, the ignition of the cladding depended on the wind direction. When the cladding was ignited, the heat fluxes from the burning hedge could exceed 100 kW.m -2 .

Introduction

Wildland-Urban Interface (WUI) fires are a recurring issue around the world due to the high number of destroyed dwellings [START_REF] Cohen | The wildland-urban interface fire problem: A consequence of the fire exclusion paradigm[END_REF][START_REF] Caton | Review of pathways for building fire spread in the wildland urban interface part i: exposure conditions[END_REF]. A statistical study shows that the best way for homeowners to reduce the risk of these fires is through preparation and active defence. In 1 fact, an unprepared home is 10 times more likely to be affected by a fire [START_REF] Price | Comprehensive examination of the determinants of damage to houses in two wildfires in eastern australia in 2013[END_REF]. As a result, Australia and the United States have established recommendations on the vulnerability of building materials to wildfire, such as minimum water supply, or defensible space around dwellings [START_REF] Association | NFPA 1140 standard for reducing structure ignition hazards from wildland fire[END_REF]. These guidelines were determined through post-fire investigations in which houses were exposed to wildfires [START_REF] Cohen | Home destruction examination: Grass valley fire, lake arrowhead, california[END_REF][START_REF] Maranghides | A case study of a community affected by the witch and guejito fires: Report# 2: Evaluating the effects of hazard mitigation actions on structure ignitions[END_REF]. In Australia, regulations for fire prevention in the WUI are set out in AS 3959-2018 which sets Bushfire Attack Levels (BAL) based on vegetation and ground topography [START_REF] Weir | As 3959: Construction of buildings in bushfire-prone areas: Standards australia[END_REF]. In the United States, recommendations concerning the distance between the house and the vegetation vary from state to state, with a minimum distance of 1.5 m in California (and now expanding to other regions) [START_REF] Cohen | The wildland-urban interface fire problem: A consequence of the fire exclusion paradigm[END_REF]. This distance is still under discussion with stakeholders. As for the other recommendations for distances beyond 1.5 m, these are rather vague. On the other hand, in Europe, regulations are limited despite the large number of fires that occur there [START_REF] Ganteaume | What causes large fires in southern france[END_REF][START_REF] Ganteaume | A review of the main driving factors of forest fire ignition over europe[END_REF] and the presence of materials that can be damaged by a wildfire in the WUI [START_REF] Xanthopoulos | Factors affecting the vulnerability of houses to wildland fire in the mediterranean region[END_REF][START_REF] Manzello | Enabling the study of structure vulnerabilities to ignition from wind driven firebrand showers: A summary of experimental results[END_REF]. Some countries have their own rules about the distance between hedges and house walls. It can be 2 m in Portugal or Italy, or three times the height of the vegetation in France, with a minimum distance of 3 m. These different distances observed around the world therefore show that there is no consensus on the minimum safety distances to be specified in the forest fire / bushfire prone areas.

The Mediterranean, Australian and Californian are regions where forest fires are significant and destroy homes every year. These fires can in some cases be caused by the spread of fire from one house to a second [START_REF] Himoto | A field experiment on fire spread within a group of model houses[END_REF][START_REF] Yuan | Characteristics and mechanism of fire spread between full-scale wooden houses from internal fires[END_REF] or one material to another. Among the materials that can be a vector for the fire spread, cladding, is a key element as it can propagate a surface fire to the most vulnerable points of a building, including openings, roofs or vents. With the popularity of bio-based materials in buildings, wood has become a commonly used material for walls, whether in new construction or renovation. It is therefore important to study how wood reacts to the effects of vegetation fire, as this material can spread fire to weak points such as the under-eave or windows, vents, etc. Studies of the fire behavior of cladding are varied, ranging from the material scale with cone calorimeter tests [START_REF] Nguyen | Assessing the combustibility of claddings: A comparative study of the modified cone calorimeter method and cylindrical furnace test[END_REF][START_REF] Mclaggan | Flammability trends for a comprehensive array of cladding materials[END_REF] to the large scale with a fire escaping from a compartment vent [START_REF] Oleszkiewicz | Fire exposure to exterior walls and flame spread on combustible cladding[END_REF]. Nevertheless, these types of experiments are different from the conditions that may be encountered during a WUI fire. With regard to the coupling between wildland fires and building materials, studies are limited and the most widely used study of wooden walls subjected to a representative fire ignition in a WUI is that of Cohen et al. [START_REF] Cohen | Relating flame radiation to home ignition using modeling and experimental crown fires[END_REF]. Cohen et al. observed that the walls ignited but were self-extinguished at the same time as the crown fire for the distances tested between the walls and the forest. Grishin et al. [START_REF] Grishin | A field experiment on grass fire effects on wooden constructions and peat layer ignition[END_REF] observed through field experiments that a wooden structure did not ignite during a wildfire when the distance of the fire from the structure was 5 m, as the temperature and heat flux data remained low. The radiation threshold for ignition of external building elements containing wood such as cladding is estimated at 12.5 kW.m -2 according to [START_REF] Leonard | Building and land-use planning research after the 7th february victorian bushfires: preliminary findings[END_REF].

To the best our knowledge, there are no other large scale outdoor experiments that have studied the effect of a vegetation fire on a wood cladding.

The aim of this work is to study the fire behaviour of a large scale wood cladding exposed to the combustion of a hedge in order to contribute to the knowledge base of the distance between the vegetation and the constructions. For this, six experiments were carried out with burning hedges to investigate the impact of the fire on the cladding by assessing the influence of the wind and that of the distance between the hedge and the cladding.

Materials and methods

The aim of this work is to investigate the fire reaction of wood cladding following the burning of a large scale cistus monspeliensis hedge. This Mediterranean species is present in a large part of the scrubland and garrigue, but is also used as an ornamental species.

Prior to this, 40 tests were performed using a cone calorimeter in order to assess the conditions leading to the ignition of the wood cladding in front of a controlled heat flux.

Wood cladding

The cladding used for the experiments was made of scotch pine with an average density of 350 kg.m -3 . The wooden slats purchased were 4 m long, 13 cm wide and 1.8 cm thick horizontal tongue and groove lap siding product.

Cone calorimeter experiments

A preliminary study was carried out using a cone calorimeter in order to determine the ignition conditions of wood cladding in terms of exposure time and heat flux. The wood samples used were pine, oven-dried at 105 • C for 24 hours. They were taken from the cladding boards and cut to a size of 10×10 cm 2 . For each test, the sample was wrapped in a double layer of aluminium and placed in a steel sample holder. The rear unexposed side was insulated with a ceramic wool and then with a ceramic plate, all held in place by the locking system. The samples were exposed to heat fluxes ranging from 15 to 45 kW.m -2 in a vertical orientation until ignition occurred or up to 25 min. The distance between the cone heater and the sample was 25 mm and a spark was used for pilot ignition. Shields et al. [START_REF] Shields | The effects of geometry and ignition mode on ignition times obtained using a cone calorimeter and iso ignitability apparatus[END_REF] showed that the ignition times were similar for flame and spark ignition using a vertical configuration of the cone calorimeter.

Large scale experiments

Six large scale tests were conducted outdoors in a flat, open area. The cistus hedge was ignited by flame propagation in a fuel bed of excelsior used as a surrogate for a herbaceous strata. This type of fuel bed is often used in laboratory experiments because it burns easily and without residue. In addition, the flame front produced when the excelsior wood wool is ignited is more homogeneous than with natural vegetation and is only intended to ignite the hedge. In the Mediterranean region, the cistus is a native species that is common on acidic soils in southern Europe. It is very specific in terms of its flammability, as it can have a very low moisture content in summer, which makes this species very deleterious if it is close to buildings in the WUI. This is the reason for the focus on this species. Cistus has been characterised on numerous occasions with laboratory scale tests [START_REF] Barboni | Aerosols and carbonaceous and nitrogenous compounds emitted during the combustion of dead shrubs according to twigs' diameter and combustion phases[END_REF][START_REF] Morandini | Experimental investigation of flammability and numerical study of combustion of shrub of rockrose under severe drought conditions[END_REF]. Figure 1 shows the detailed configuration of the experimental setup. The length L (Figure 1a) was related to that of the excelsior litter and the cistus hedge and varied from 2 to 4 m depending on the experiment (Table 1). The width of the litter was 2 m and the pine excelsior litter had a fuel load of 1 kg.m -2 and a moisture content around 5

% for all experiments. A cistus hedge was reconstructed with branches homogeneously placed in a welded mesh cages of 1 m 3 . The bulk density of the cistus was varied from 8 to 12 kg.m -3 in order to observe the influence on the ignitability of the cladding. For each experiment, the fuel bed of wooden wool was ignited along its entire length L using a butane burner.

The wood cladding was made of pine and was fixed to the cellular concrete with 28 mm thick pine cleats. Each plank was 10 cm high and 20 mm thick. The cladding was cut to obtain a section measuring into 100 cm×100 cm sections, i.e. 10 boards stacked vertically.

The cladding and the cellular concrete were mounted on a support in order to achieve a height of 95 cm for the lower part of the cladding. The cladding was centered on the hedge and the distance, d, between the hedge and the cladding was fixed at 2 or 3 m, depending on the experiment. The six tests were carried out on the same day in June, with the ambient temperature varying between 35 °C for test 1 to 40 °C for test 6. These temperature conditions were representative of the temperatures encountered in vegetation fires.

As the tests were conducted outdoors, the wind was uncontrolled and was a determining factor in the spread of the fire and therefore the likelihood of the wood cladding ignition.

Therefore, a standing anemometer was placed 15 m behind the cladding to continuously measure the direction and velocity of the wind. If the wind direction is 0°, then it is assumed that the wind is in the direction of propagation and perpendicular to the cladding. It is in this direction that the conditions are most favourable for the flame front to be tilted towards the cladding. It is also assumed that if the angle is greater than ± 45°, the wind direction is still in the propagation direction, but shifted to the right or to the left. Finally, if the wind direction is greater than ± 90°, it is in the opposite direction of fire spread. In this condition, it is very unlikely that the flame will hit the cladding.

For each test, temperatures and heat fluxes received by the cladding were measured. As shown in figure 1a, all the measurements were located to the right of the cladding. Eight K-type thermocouples were stapled on the cladding. Four were attached to the front side and four to the rear side at 15, 35, 55 and 65 cm from the base of the cladding and 10 cm to the right side. Grooves were made in the surface of the wood to match the diameter of the thermocouple (1 mm) so that they could be placed and stapled in place, ensuring contact between the tip of the thermocouple and the wood. Two pairs of heat flux gauges (by Medtherm) were placed at 1 and 1.5 m from the ground and 20 cm from the cladding.

For each pair, one measured the radiant heat flux (range [0-100] kW.m -2 ) and the other measured the total heat flux (range [0-200] kW.m -2 ). The water used to cool the fluxmeters was stored in a water chiller in order to maintain a constant temperature all day outdoor during the tests. Finally, two cameras were used to record the experiments: one from the side of and one from the front behind the pine wool. All the measurements were triggered simultaneously with a sampling rate of 1 Hz.

Results and discussion

3.1 Tests at material scale (using the cone calorimeter)

Table 2 shows the average ignition times calculated from three tests and the standard deviations as a function of heat flux. Times-to-ignition decreased with increasing heat flux. The standard deviation is higher for fluxes close to the critical heat flux. This is consistent with the literature [START_REF] Babrauskas | Ignition handbook-principles and applications to fire safety engineering, fire investigation, risk management and forensic science[END_REF][START_REF] Atreya | Effect of sample orientation on piloted ignition and flame spread[END_REF][START_REF] Hedayati | Effects of moisture content and heating condition on pyrolysis and combustion properties of structural fuels[END_REF]. This is due to the fact that close to the critical heat flux, ignition can be either caused by the embers on the surface of the wood or by the pilot. This resulted in considerable variability in ignition times. To achieve an ignition in less than one minute, the cladding had to be exposed to a heat flux higher than 25 kW.m -2 . Additional tests were carried out without a pilot to determine the critical heat flux for an auto-ignition. The cladding only spontaneously ignites at 45 kW.m -2 for times greater than 840 s. Ignition did not happen for each test at 45 kW.m -2 and never occurred at lower heat fluxes. These results are in good agreement with work investigating spontaneous ignition of wood in a vertical orientation [START_REF] Terrei | Experimental tools applied to ignition study of spruce wood under cone calorimeter[END_REF][START_REF] Boonmee | Glowing and flaming autoignition of wood[END_REF]. For auto-ignition to occur in less than 1 minute, the imposed heat flux must to be at least 55 kW.m -2 in vertical orientation [START_REF] Terrei | Experimental tools applied to ignition study of spruce wood under cone calorimeter[END_REF].

Tests at large scale

In each experiment, the flame spread in the wooden wool and then ignited the cistus hedge.

The fire then spread throughout the hedge, thermally attacking the wood cladding at different rates and intensities depending on the experimental conditions and the wind.

Figure 2 shows pictures of two tests corresponding to both hedge lengths of 2 and 4 m from the time of hedge ignition (t igh ). The wind direction and velocity are provided in each figure with an additional compass rose. Figure 2 shows the photographs of the different stages of combustion for tests 1 and 2, where the cistus bulk density and the distance from the cladding d were the same. Figure 3 shows the wind velocity and direction during the tests from the ignition of the cistus hedge. For each figure, the zone between the green dotted lines (±45°) represents the wind direction that will be in the direction of fire propagation towards the cladding. Between the green and red dotted lines, the wind will still be in the direction of spread, but will be shifted to the right or to the left of the cladding.

Tests

Hedge ignition (t igh ) t igh + 9 s t igh + 25 s t igh + 94 s The important variations in wind direction and velocity show the difficulty of conducting outdoor tests. The flame spread in the hedge for test 1 was very fast, with almost all of the cistus having burned 25 s after ignition. The shape of the flame front at t igh + 9 s and t igh + 25 s was inclined towards the wood cladding. This was mainly due to the wind direction during the test, which was close to the axis of propagation: on average ±0°with an average velocity of 1.8 m.s -1 during the first 30 seconds after ignition, when the flame front was most prominent. In test 2, the flame spread was slower, both because the wind was away from the axis of spread and because the average wind direction during the burning of the hedge in test 2 was ±54°at a speed of 1.9 m.s -1 . The time of flame residence in the hedge was 76 s and 96 s for tests 1 and 2 respectively. This difference is mainly due to the smaller size of the hedge in test 1. In general, the heat flux and temperature of the front face increase rapidly as the cistus ignites, reaching a peak value when the fire is fully developed. After the peak, heat flux and temperature decrease rapidly as the fire intensity decreased. In both tests, the radiative heat flux was very close to the total heat flux, showing that radiation was the dominant heat transfer and that the flame, did not reach the device. For test 1 with a 2 m long hedge, the maximum total heat flux was 12 kW.m -2 . For test 2 with a 4 m long hedge, the heat flux reached 17 kW.m -2 . Despite the less favourable wind direction for test 2, the heat flux received by the cladding was higher due to the length of the hedge and therefore a higher heat released. For both tests, the measured heat flux was in the range that allows the cladding to ignite on the cone calorimeter scale but the time was too short (less than 30 s) to allow the release of flammable gases. In fact, it has been shown on a laboratory scale that ignition was possible if the exposure to 15 kW.m -2 time was at least 370 s. On the other hand, for test 2, the heat fluxes and the temperatures increased with a time delay of 10 s compared to test 1. This difference may be due to the wind direction, which increased the propagation time. As for the heat fluxes, the maximum temperatures recorded during test 2 were higher than those of test 1: 140 and 110 °C respectively.

Direction (°)

According to the two tests carried out, the distance of 3 m between the wood cladding and the hedge prevents the building material from igniting in such wind conditions. The cladding was always centered in relation to the hedge. The flame did not reach the cladding and the heat flux conditions did not allow the wood to ignite. On the other hand, the risk of ignition may increase if the exposure time is extended by a denser hedge that would burn for a longer period. The general description of the steps is similar to that given above. However, the pictures show that the spread of the fire and the thermal aggression on the cladding are different for each test. Ignition occurred only in test 3 because the flames reached the cladding. Figure 6 shows the wind direction and velocity during these tests. The wind direction during the first 20 s after ignition of the hedge is indeed close to 0°, resulting an inclination of the fire front towards the cladding. The cladding degraded, as indicated by the change in color and finally ignited (Fig. 7). However, the flame self-extinguished immediately as soon as the rate of burning of the hedge decreased. In tests 4 and 5, the flame front was slightly inclined towards the cladding or was vertical. This was due to the direction of the wind, which was between 45 and 90°during the first 30 s after the hedge was ignited. As a result, the flames did not reach the wood cladding. No ignition was observed and the cladding did not scorch, indicating that it did not undergo thermal degradation. These experiments show that under the same conditions, ignition of the cladding is possible as long as the average wind velocity is 1.3 m.s -1 and the direction is less than -20°to the cladding. On the other hand, even if the average wind velocity increases (1.8 m.s -1 for test 4 and 2.5 m.s -1 for test 5) but the direction is on average 50°to the axis of the cladding, then it will not ignite. The characteristics of the wind (velocity and direction) will therefore have a significant effect on the ignition of the cladding. However, these results should be treated with caution as these experiments only considered part of the cladding. The presence of a building can indeed induce air recirculation for strong winds, as shown by Hedayati et al.

and therefore influence the inclination of the flame and the ignition of the cladding [START_REF] Hedayati | Near-building noncombustible zone[END_REF]. In this test, the fire spread quickly, mainly because the wind direction was close to 0°and the wind velocity was slightly higher (about 2.5 m.s -1 ) than in the other tests. In addition, the increase in the bulk density of the vegetation contributed to the increase in fire dynamics compared to the other tests. As a result, the flame front reached and ignited the cladding. However, the burning of the cladding was not self-sustained as it extinguished as soon as the heat flux from the hedge decreases. Figure 10 shows the evolution of the wind direction and velocity during the test.

Conclusion

In order to better understand the fire risk in the WUI, large scale tests were carried out to assess the fire behaviour of wood cladding when exposed to the burning of a cistus hedge.

Firstly, material scale experiments were carried out on the wood cladding to quantify the time required to ignite the samples as a function of the applied heat flux. Secondly, a total of six tests were conducted by varying the distance hedge/cladding, bulk density of the cistus and the length of the hedge. Ignition of the cladding was only possible when the flame front touched the cladding. However, the configurations tested did not result in self-sustained burning of the cladding. At a distance of 3 m between the hedge and the cladding, no ignition of the cladding was observed. When the distance between the hedge and the cladding is reduced to 2 m, the cladding can be ignited but not systematically.

The direction of the wind will affect the flame front and therefore the intensity to which the cladding is exposed. However, if the wind direction is not towards the cladding, this latter will not ignite. When the cistus bulk density increases and the wind is in the propagation direction with a slightly higher velocity, cladding ignition is certain with total heat fluxes exceeding 100 kW.m -2 . It has been observed that the cladding extinguishes almost instantaneously as soon as the burning of the hedge decreases. The heat flux generated by the flame on the surface of the wood and the temperatures on the back side are not high enough to allow a self-sustaining combustion. Based on these results, it seems necessary to require a distance of more than 2 m between facades with wood cladding and a hedge of 1 m high. It is also important to ensure that no secondary fuel is present between the cladding and the hedge, as this could increase the burning duration of the cladding, leading to its self-sustaining combustion. In further works, it will be possible to vary the slope between the vegetation and the cladding and to add additional elements such as windows. A load cell will also be installed under the cistus hedge to measure the mass loss during the combustion.

[30] D. Drysdale, An introduction to fire dynamics. John wiley & sons, 2011.

Figure captions

Fig. 1 .

 1 Fig. 1. Experimental setup.

1 WV: 1 .Fig. 2 .

 112 Fig. 2. Pictures of the tests 1 and 2 with d = 3 m, ρ b = 8 kg.m -3 (WV: Wind Velocity, WD: Wind Direction).

Fig. 3 .

 3 Fig. 3. Direction and velocity of wind during the tests 1 and 2.

Figure 4

 4 Figure 4 compares the heat fluxes and the mean temperatures at the front face of the 197

Fig. 4 .

 4 Fig. 4. Heat flux and temperature measured for tests 1 and 2 after the cistus hedge ignition.

Figure 5

 5 Figure 5 shows pictures for tests 3, 4 and 5. The configuration of these three tests was the same, with d reduced to 2 m, compared to the previous experiments presented in Fig. 2.

Figure 8 Fig. 6 .

 86 Figure8shows the average cladding temperatures measured from the four thermocouples placed on the front side and the heat fluxes at 1 m height.

Fig. 7 .

 7 Fig. 7. Wood cladding after the test 3.

Fig. 8 .

 8 Fig. 8. Heat flux and temperature measured for tests 3, 4 and 5 after the cistus hedge ignition.

Fig. 10 .

 10 Fig. 10. Direction and velocity of wind during the test.

Figure 11 shows

 11 Figure11shows the heat fluxes at a height of 1 m and 1.5 m as well as the average 276

Fig. 11 .

 11 Fig. 11. Heat fluxes and temperatures measured for test 6 after the cistus hedge ignition.

Fig. 1

 1 Fig. 1 Experimental setup.

Fig. 2

 2 Fig. 2 Pictures of the tests 3, 4 and 5 with d = 3 m, ρ b = 8 kg.m -3 (WV: Wind Velocity, WD: Wind Direction).

Fig. 3

 3 Fig. 3 Direction and velocity of wind during the tests 1 and 2.

Fig. 4 Fig. 5

 45 Fig. 4 Heat flux and temperature measured for tests 1 and 2 after the cistus hedge ignition.Fig. 5 Pictures of the tests 3, 4 and 5 with d = 2 m, ρ b = 8 kg.m -3 , L = 4 m (WV: Wind Velocity, WD: Wind Direction).

Fig. 7

 7 Fig. 7 Wood cladding after the test 3.

Fig. 6

 6 Fig. 6 Direction and velocity of wind during the tests.

Fig. 8 Fig. 9

 89 Fig. 8 Heat flux and temperature measured for tests 3, 4 and 5 after the cistus hedge ignition. Fig. 9 Pictures of the test 6 with d = 2 m, ρ b = 12 kg.m -3 , L = 4 m (WV: Wind Velocity, WD: Wind Direction).

Fig. 10

 10 Fig. 10 Direction and velocity of wind during the test.

Fig. 11

 11 Fig. 11 Heat flux and temperature measured for tests 1 and 2 after the cistus hedge ignition.

Table 1 :

 1 Variation of the experimental parameters for each test (cistus/cladding distance (d), cistus bulk density (ρ b ), hedge length (L), hedge mass (m h ), excelsior mass (m e )).

	kg)

Tests d (m) ρ b (kg.m -3 ) L (m) m h (kg) m e (

Table 2 :

 2 Time-to-ignition (t ig ) according to the imposed heat flux.

	Heat flux (kW.m -2 ) 10	15 20 25 30 35 40 45
	Mean t ig (s)	1540 398 152 49 28 25 19 16
	Std t ig (s)	289 28 68 5 6 3 5 4

Acknowledgements

The authors would like to thank Antoine PIERI (research technician), Jean-Valère LORENZETTI and Bruno MARTINENT (PhD students), Anthony GRAZIANI (post-doctoral researcher), Erwan STACHOWIAK and Samuel JAWORSKI (interns), for their technical support during the test day.


An increasing number of high-rise building construction projects made largely of wood are either under study or under construction. A key issue for the construction of such buildings is the fire behavior of their structures. Indeed, when the wood is subjected to a high heat flux, it will degrade and it can self-ignite. The aim of the work is to experimentally study the degradation and the auto-ignition of the spruce wood used in buildings at two scales. The first one is at the cone calorimeter scale, commonly used in fire safety community, and the second one at a larger scale involving a one square meter radiant panel.

Study

Context and Objectives

Results: Mass Loss Rate, temperatures and t ig

Results: auto-ignition location

Conclusions

The tests were carried out with four radiant panels oriented vertically to form a radiant surface of approximately 1 m 2 . The aim of these tests was to expose spruce samples to heat fluxes equivalent to those studied at the cone heater scale, in order to observe the effect of the change in scale on wood degradation and auto-ignition. The measurements were MLRPUA with a load cell, surface temperature with an IR camera, in-depth temperature with embedded thermocouples, location and time of flame appearance with fast cameras and critical heat flux. The wooden panels measured 50 cm × 53 cm. The surface area is 26.5 times greater than that of the samples used for the cone tests (100 cm 2 for the cone compared to 2650 cm 2 for the radiant panels).  At a low heat flux, results at both scales are very similar.  For high heat fluxes, the MLRPUA and surface temperature are higher when the scale increases. These differences seem to be caused by both the presence of the flame, which provides an additional heat flux and also by the greater degradation at the side faces of the sample.  However, comparisons of the in-depth temperature show that the in-depth degradation is close between the two scales studied.  Tests carried out have shown that for the same imposed heat flux, the time to ignition is always shorter with the radiant panels than with the cone.  Regarding the auto-ignition location, the phenomena remain very similar for both scales.

o At 60 kW.m -2 , for both scales, the appearance of the flame far from the exposed surface, is initiated by a large concentration of pyrolysis gases (detected by the CO 2 filter) escaping from the surface of the sample. This quantity continuously increases in temperature, while mixing with the air as it rises. Once the temperature and mixing conditions are met, self-ignition occurs.

o At 38 kW.m -2 , the high-speed camera images show that the ignition occurring near the surface is initiated by a glowing wood splinter that reaches a temperature higher than the average surface temperature. At the panel scale with a 16 kW.m -2 heat flux, onset of smoldering combustion is observed at 22 min with the appearance of glowing zones that spread over the entire surface. It results in an increase in temperature and MLRPUA to a second plateau. For both scale, the phenomena are the same.

The evolution of the in-depth temperatures at 60 kW.m -2 is similar despite the change in scale. The maximum deviation is 50 °C in the temperature growth phase at 4 mm depth. This comparison supports the interpretations of the differences in surface temperatures (flame emission detected by the camera) as well as the MLRPUA between the two scales (edge effect on degradation). The location of the flame appearance was revealed using two fast cameras. One was in the visible (3000 fps) and the other in the infrared (4800 fps) with a 4.45 µm filter (hot CO 2 ) in order to better visualize the flame which emits in this wavelength. The figures below compare the ignition location at both scales for different values of the heat flux.

Fig. 7 .

 7 Fig. 7. Gases auto-ignition away from the exposed surface at the panel scale for 60 kW.m -2 .

Fig. 1 .

 1 Fig. 1. Wood sample exposed to 60 kW.m -2 .

Fig. 3 .Fig. 4 .

 34 Fig. 3. MLRPUA and surface temperature (a) and in-depth temperatures (b) for spruce wood exposed to 16kW.m -2 at the radiant panels and cone heater scales.

Fig. 2 .Fig. 5 .

 25 Fig. 2. Panel/sample distance (d) optimization (view factor method) to achieve a desired average heat flux on sample surface.

Fig. 6 .

 6 Fig. 6. Gases auto-ignition away from the exposed surface at the cone scale for 60 kW.m -2 .

Fig. 8 .

 8 Fig. 8. Gases ignition piloted by the glowing surface at the panel scale for 38 kW.m -2 .

of wood ignition and degradation at the medium scale and comparison with the cone scale s

  Université de Lorraine, INRAE, ERBE, F 88 000 Epinal, France

	Lucas TERREI 1 , Zoubir ACEM 1 , Yann ROGAUME 2 , Matthieu DEBAL 2 and Gilles PARENT 1
	a
	1 Université de Lorraine, CNRS, LEMTA, F-54000 Nancy, France
	2 LERMAB,

Table 1 .

 1 Number of tests and Time-to-auto-ignition (t ig ) according to the studied scale.