M Asli

E Sassine
email: emilio.sassine@gmail.com

F Brachelet

E Antczak

Thermal and hygroscopic study of hemp concrete in real ambient conditions

Keywords: Hemp concrete, MBV, Thermal conductivity, Water vapor sorption, Numerical simulation, Heat and Mass Transfer, experimental facility, sensitivity analysis

Most building materials, and more particularly bio-based materials, are subject to hygrothermal transfers in the environment in which they are disposed. These transfers depend on their thermophysical characteristics as well as the ambient humidity and temperature conditions. In such environment, and despite these variations, the material must be able to ensure in a sustainable manner, the functions for which it was implemented (thermal, mechanical, acoustic ...). Among these materials, hemp concrete, which is a bio-based material, is widely considered in building construction for its superior thermal and hygroscopic performance. The hygrothermal modelling of such materials in real conditions is essential for a better understanding of buildings' energy performances. Several works targeted the numerical hygrothermal modelling of hemp concrete; however most of them are done in controlled laboratory conditions, which may be different from the real buildings scenarios. In this paper, heat and mass transfer are investigated both numerically and experimentally in real conditions. The hygrothermal properties of hemp concrete were first determined through laboratory experiments; then, an experimental wall segment made of hemp concrete was instrumented in real ambient conditions in order to validate the Philip and De Vries model describing heat and mass transfer. The comparison of the numerical results to the experimental data leads to interesting results regarding local temperature and relative humidity variations. Moreover, numerical investigation of the moisture buffer values of hemp concrete was performed and the results were validated by bibliographic data. The hemp concrete was found to be a very interesting potential hygrothermal regulation material in terms of thermal conductivity, decrement factor, time lag, and humidity regulation.

INTRODUCTION

The scientific community carried out several work in order to demonstrate the thermal and hygroscopic efficiency of bio-based material compared to classical insulation materials, and the advantages they offer in terms of energy needs [1], environmental impact [2], indoor air quality, durability [3], [START_REF] Delannoy | Durability of hemp concretes exposed to accelerated environmental aging[END_REF], [START_REF] Benmahiddine | Experimental investigation on the influence of immersion/drying cycles on the hygrothermal and mechanical properties of hemp concrete[END_REF], and thermal comfort [START_REF] Holopainen | Comfort assessment in the context of sustainable buildings: Comparison of simplified and detailed human thermal sensation methods[END_REF].

Hemp concrete is one of the most famous bio-based materials, it offers an ecological alternative solution with advantageous thermal properties [START_REF] Limam | Experimental thermal characterization of bio-based materials (Aleppo Pine wood, cork and their composites) for building insulation[END_REF], [START_REF] Vololonirina | Characterization of hygrothermal properties of woodbased products -Impact of moisture content and temperature[END_REF], [START_REF] Tuzcu | Hygro-Thermal Properties of Sheep Wool Insulation[END_REF] and moisture buffering capacity [10], [START_REF] Palumbo | Determination of hygrothermal parameters of experimental and commercial bio-based insulation materials[END_REF], with a low life cycle impact compared to similar products [START_REF] Bories | Development of porous fired clay bricks with bio-based additives: Study of the environmental impacts by Life Cycle Assessment (LCA)[END_REF]. Numerous authors investigated the hygrothermal properties of hemp concrete. Elfordy et al. [13] assessed the impact of hemp concrete density on its thermal and mechanical properties. Collet Furthermore, the positive effect of hemp concrete on building energy consumption was demonstrated in several works [14], [START_REF] Shea | Hygrothermal performance of an experimental hemp-lime building[END_REF], [START_REF] Ngo | Design a soil concrete as a new building material -Effect of clay and hemp proportions[END_REF], [START_REF] Jami | A review of the properties of hemp concrete for green building applications[END_REF]. Besides its impact on the energy consumption, the humidity in the building envelope can also lead to problems related to materials' durability and internal mold risks [START_REF] Viitanen | Moisture and Bio-deterioration Risk of Building Materials and Structures[END_REF], [START_REF] Arundel | Indirect Health Effects of Relative Humidity in Indoor Environments[END_REF]. For these reasons, it is essential to be able to precisely quantify heat and moisture transfers phenomena within construction building materials.

In the literature, numerous works deal with simultaneous heat and mass transfer within porous media.

Several experiments assessing the hygrothermal behavior of bio-based materials such as wood fiber materials [21], [START_REF] Geving | Laboratory Investigations of Moisture Conditions in Wood Frame Walls with Wood Fiber Insulation[END_REF], hemp concrete [10], [START_REF] Tran Le | Transient hygrothermal behaviour of a hemp concrete building envelope[END_REF], [START_REF] Maalouf | Study of hygrothermal behaviour of a hemp concrete building envelope under summer conditions in France[END_REF], [START_REF] Rahim | Experimental investigation of hygrothermal behavior of two bio-based building envelopes[END_REF] were performed at different scales (material sample, wall, and building). These experimental methods allow the assessment of water content, temperature, and relative humidity within the investigated media subjected to controlled boundary conditions and the results were used to validate the numerical models describing heat and mass transfer [START_REF] Lelievre | Hygrothermal behavior of bio-based building materials including hysteresis effects: Experimental and numerical analyses[END_REF], [START_REF] Maalouf | Study of hygrothermal behaviour of a hemp concrete building envelope under summer conditions in France[END_REF]. Generally, good agreement is found between the numerical and measured data.

Nevertheless, in most of the cases, the experiment is held in controlled temperature and relative humidity conditions and may not reflect accurately the hygrothermal behavior in real uncontrolled conditions where the simultaneous heat and mass transfer phenomena are more complex.

In this work, heat and mass transfer phenomena within hemp concrete submitted to real ambient conditions are studied through numerical and experimental approaches. In the numerical work, the model of Philip and De Vries [25] is adopted (section 2). The input parameters of the model are experimentally determined with respect to the temperature and moisture content (section 3). A comparison between the experimental and numerical data as well as a sensitivity study are presented in (section 4), aiming at evaluating the results accuracy of the model. The last part is dedicated to the investigation of the moisture buffering capacity of hemp concrete (section 5); in this part the humidity regulation properties of hemp concrete are demonstrated and validated with respect to data founded in the bibliography.

MATHEMATICAL MODEL

The energy and mass balances equations derived from the energy and mass conservation principles, are applied under the following assumption:

 The mass transfer takes place through the material's openings;  The material is assumed to be continuous, homogeneous and no chemical reaction occurs;

 Local thermodynamic equilibrium is assumed at every point of the material;  The effect of gravity is considered negligible  The total gas pressure is considered to be constant and equal to the atmospheric pressure; Where θ is the water content and is expressed [kg.kg -1 ], T is the temperature [°C], DT [m 2 .s -1 K -1 ], and Dθ [m 2 .s -1 ] are respectively, the mass transport coefficients associated to temperature and moisture content gradient. ρ0 is the dry density, Lv is the latent heat of vaporization is set at 2500 KJ.kg -1 , ρl represents the water density 1000 kg.m -3 , and Cpm is the specific heat and is calculated as the average specific heat of solid matrix and liquid phase:


𝐶 𝑝𝑚 = 𝐶 𝑝0 + 𝐶 𝑝𝑙 𝜌 𝑙 𝜌 0 𝜃 (3)
λ is the equivalent thermal conductivity of the material and it is a function of moisture content. DT,v and Dθ,v are the vapor phase transport coefficients associated with temperature and moisture content gradient, respectively.

The associated boundary conditions are given by the equations (4) and [START_REF] Benmahiddine | Experimental investigation on the influence of immersion/drying cycles on the hygrothermal and mechanical properties of hemp concrete[END_REF], the index of the external and internal sides, respectively (x = 0, x = L).

-𝜆 𝛻𝑇 -𝜌 𝑙 𝐿 𝑣 𝐷 𝑇,𝑣 𝛻𝑇 + 𝜌 𝑙 𝐿 𝑣 𝐷 𝜃,𝑣 𝛻𝜃 = ℎ 𝑇,L,0 (𝑇 𝑎,𝑒,𝑖 -𝑇 𝑠,𝑒,𝑖 ) + 𝜌 𝑙 𝐿 𝑣 (𝜌𝑣 𝑎,𝑒,𝑖 -𝜌𝑣 𝑠,𝑒,𝑖 ) + 𝜑 𝑟𝑎𝑑,𝑒,𝑖 [START_REF] Delannoy | Durability of hemp concretes exposed to accelerated environmental aging[END_REF] Where hT,L,0 is the convective heat transfer coefficient from external and internal sides, ρv,e,i is the air density, and φrad,e,i is a radiation term which is assumed negligible in our study.

The subscripts "e" and "I" correspond to external and internal sides respectively, and "a" and "s" correspond to air and solid surface neighboring environments respectively. 𝜌 𝑙 (

Where ℎ 𝑚,𝑒,𝑖 is the convective mass coefficients. To be closer to the reality, boundary conditions must be more realistic, otherwise the boundary conditions most relate the microscopic material properties with externals ambient variations. For this purpose, the temperature and relative humidity are measured during the test at the wall interface.

The relationships that relate transport coefficients of mass with transport coefficients of vapor and liquid phase are:

𝐷 𝑇 = 𝐷 𝑇,𝑙 + 𝐷 𝑇,𝑣 [m 2 .s -1 K -1 ] (6)
𝐷 𝜃 = 𝐷 𝜃,𝑙 + 𝐷 𝜃,𝑣 [m 2 .s -1 ] (7)
The diffusion coefficients are the most important factors used in the mathematical model, while the use of the experimental ways is required, so a great attention is paid to these coefficients. For this purpose the vapor diffusion coefficients are determined according to Zeknoun et al [START_REF] Zaknoune | Identification of the Liquid and Vapour Transport Parameters of an Ecological Building Material in Its Early Stages[END_REF], and Maalouf et al [START_REF] Maalouf | Study of hygrothermal behaviour of a hemp concrete building envelope under summer conditions in France[END_REF].

The transport coefficients associated with moisture gradient are related to water vapor permeability δ0 and the specific hygroscopic capacity ξ, which is the slope of sorption curve:

𝐷 𝜃 = 𝛿 0 𝑃 𝑣,𝑠 𝜌 0 1 𝜉 (8)
𝛿 0 = 𝛿 𝑎 𝜇 (9)
Where δ a is the vapour permeability to air and it is equal to 2.10 -10 kg.m -1 .s -1 .Pa -1 , μ is the water vapor resistance factor.

Vapor and liquid transport coefficients under a temperature gradient are given by the relations:

𝐷 𝑇,𝑣 = 𝛿 0 𝜑 𝜌 𝑙 𝑑𝑃 𝑣,𝑠 𝑑𝑇 (10)
𝐷 𝜃,𝑙 = 𝑃 𝑣𝑠 .𝛿 𝑝 𝜉 𝜑 ( 1 µ * (𝜑) - 1 µ 0 ) (11)
µ* (ϕ) is the coefficient of water vapor resistance measured at high relative humidity, µ0 is the coefficient of water vapor resistance corresponding to the beginning of the capillary condensation.

MATERIAL CHARACTERIZATION

The studied hemp concrete sample is shown is Fig. 1, it is a 20 cm x 30 cm x 60 cm block and manufactured by CHANVRIBLOC (La Mure, France) [START_REF]Béton de Chanvre[END_REF]. shows the manufactured hemp concrete block.

Fig.1 Block of hemp concrete

In order to guarantee the accuracy of the input parameters in the model, the material properties were measured in the laboratory.

The thermal conductivity was measured according to standard NF EN 12664 [32] under transient conditions on a sample of 400x400 mm, using fluxmeter of size 250x250mm. First, the sample is dried in a climatic chamber at 50°C and medium ventilation for a long duration in order to ensure that the humidity has been completely evacuated. The sample was weighed several times in order to check its stability by making sure that weight does not vary more than ± 2% of its mass. Afterwards, the same sample was moistened at different water content levels and weighed in the same way and the conductivity test is repeated by following the same protocol. In this way the curve in Fig. 2 was drawn,

showing the evolution of the measured thermal conductivity of hemp concrete versus its water content.

A dry thermal conductivity value of 0.07 W.m -1 .K -1 is computed.

By using the same protocol, the heat fluxes were explored in order to determine the volumetric heat (ρc) as a function of the water content. The dry specific heat (cp,s) was first determined, and then the evolution of volumetric heat capacity (ρc) versus the water content is investigated and reported in Fig. 3. The main sorption isotherms were determined at 23°C using a climatic chamber in order to reproduce relative humidity. Fig. 4 shows the experimental results obtained for the main adsorption and desorption isotherms of hemp concrete. The sorption desorption curves were determined according to the ISO 12571 standard [33], the test consists of placing samples in a climatic chamber under controlled conditions T and W, we vary the relative humidity between 0 and 100% while keeping the temperature constant, for at each relative humidity step the samples are weighed, and so the water content is determined for each relative humidity step. The experimental data are fitted with a GAB model [34], [START_REF] Von | The Dynamical Character of Adsorption[END_REF], which assumes a mono and multi-layer moisture adsorption at the pore surface. The GAB model is considered to be among the most efficient for this purpose and can be used to approximate the experimental data for water activity up to 0.9 presented in the form:

Fig.2 Thermal conductivity of hemp concrete versus water content

w = C. θ m . K. RH (1 -K. RH). (1 -K. RH + K. C. RH) (12)
Where θm, C and K are the fitting coefficients (-). In the studied case, θm = 0.034, C = 165.64 and K = 0.834 for the main adsorption curve and θm = 0.042, C = 275.54 and K = 0.78 for the main desorption curve. The measurements and fitted curves for the adsorption and desorption isotherms of hemp concrete are shown in Fig. 4.:

Fig.4 Main adsorption and desorption isotherms of hemp concrete: measurements and fitted curves.

The water vapor permeability is a hygrothermal parameter correlated to the water vapor resistance μ, where µ was carried out according to standard NF EN ISO 12572 [36]. The test is based on the cup method to determine the water vapor resistance of materials under isothermal conditions. This test consists in imposing a permanent and unidirectional vapor pressure gradient on a sample of given thickness. The vapor pressure gradient is obtained by placing a saline solution on the underside of the sample to reproduce HRint. A saturated solution of sodium hydroxide (NaOH) was used in order to obtain a very low relative humidity (0% -2%) inside the cup. The effectiveness of this solution was tested beforehand by placing it in a sealed cup with a humidity sensor; very satisfactory results were obtained where the relative humidity did not exceed the 2%. The used cups are made of glass and are therefore watertight, in order to comply with the device described in the standard on the one hand, and to avoid corrosion on the other hand. The sealant used is paraffin because it is impermeable to water vapor and does not undergo any chemical or physical transformation during the test.

The assembly consisting of the material to be tested and the cup + saline solution system is placed in a climatic chamber regulated in temperature and humidity where the external environment HRext is reproduced. Since the behavior of hemp concrete is studied in real conditions, where the relative humidity varies between 0% and 100%, then the resistance to water vapor diffusion was investigated in this range to make the modeling as accurate as possible. Unfortunately, while studying the resistance to water vapor diffusion between 0-100%, it was found that working at high relative humidity > 85% leads to condensation phenomena which may distort the results. For that, the results were presented for RH varying between 0% and 80%. in real renovation applications, the projected thicknesses varies between 6 and 10 cm.

The sample was cut carefully with a jigsaw fixed on a table, the saw is connected to a mechanical arm for a better precision (one millimeter). The cut block was stored under laboratory conditions with an average temperature of 20°C and a relative humidity of 50% RH before inserting it within the wall.

The experiments were performed in the laboratory, where the sample (wall segment) was placed integrated to wall inside the ventilation opening as shown in Fig. 6. The sample was stored at 23°C and RH 50% for 15 days to get constant and known initial conditions.

Additionally, all the sample lateral surfaces were insulated with silicone to ensure 1D heat and moisture transfer within the sample. The temperature and relative humidity were recorded at different positions within the wall segment (Fig. 6). A particular care was accorded to the sensors installation on the faces and within the sample where three holes were perforated inside the wall segment every 20 mm, for positioning the temperature and humidity sensors. Indeed, due to the sample thickness, using less sensors would lead to less precision while using more sensors would lead to measurement bulk. The authors found that the optimal solution would be to put a sensor every 20 mm in order to have the minimum influence between the sensors. Two additional sensors were used for evaluating the boundary conditions. The impact of sensors position accuracy will be investigated by sensitivity analysis, considering the heterogeneity of the material, this approach is necessary.

The five thermocouples with a diameter d = 0.2 mm and five humidity sensors HIH-4000 with a dimension (4.17 x 8.59 mm) used for this purpose (Fig. 7), present many advantages such as having long-term stability and being individually calibrated; their accuracy is evaluated by the supplier (± 3.5%

for humidity and ± 0.02 °C for temperature).

The data recorded through a data acquisition system GL820 [39] connected to all the sensors, and the monitoring lasted two month with a time step of five minutes (300 s).

Boundary conditions

The experimentation on the wall segment of hemp concrete lasted almost two months, between July 13, 2016 and September 08, 2016. Fig. 8 and Fig. 9 show the measured relative humidity and temperature variations within ambient air at the boundaries of the sample. The external air relative humidity and temperature are found to present a cyclic variation, the mean values recorded for RH is 73.90 % ± 25 % and 20.19°C ± 10°C. The indoor conditions were found to be more stable with mean values of 21.55 °C for the temperature and 58.80 % for the relative humidity.

The solar effect was neglected in the modeling due to the orientation of the studied wall segment, which was completely oriented to the North. Other orientations will be the subject of future research work where the solar heat flux effect may be more important; in this case another term will be added to the equation model in order to refine the simulation and get more precision. Two segments of 5 days each were chosen to ensure a clear display of data.

A compatibility between the simulated and measured data in terms of kinetic evolution is observed; the simulated and measured curves present similar trends.

The observation of the three graphs shows that the accuracy of the relative humidity is related to the position inside the sample; the local variation of relative humidity at 2 cm present some difference in terms of amplitude, while a higher accuracy is recorded at a depth of 6 cm. The decrease in accuracy close to the indoor side may be justified by the precision of the boundary conditions logged for the inner side. The decrement factors and time lags were evaluated from the humidity curves and expressed in (hh:mm) and (%) for time las and decrement factors respectively. By definition, the term 'decrement factor' refers to the amount by which conditions are moderated by a building element. In other terms, when a temperature (or humidity) peak reaches the outer surface of a building element, the decrement factor represents the amount by which this peak is reduced by the time it reaches the inner surface.

The average decrement values at 2cm, 4cm and 6 cm were respectively: 14%, 20% and 24% and the average time lag values were 2h45min, 3h22min and 5h15min. agreement in all the remaining cases. Better agreement was found at x = 4 cm (Fig. 16) and at x = 6 cm (Fig. 17) than close to the surface x = 2cm. This slight difference can be caused by the heterogeneity of the material, the uncertainty on the physical properties of the material during the characterization campaign, and the sensor's position and accuracy. Furthermore, the hysteresis effects also present a major factor of discrepancy [41], [START_REF] Moissette | Influence of hysteresis on the transient hygrothermal response of a hemp concrete wall[END_REF], [START_REF] Alioua | Investigation on heat and moisture transfer in bio-based building wall with consideration of the hysteresis effect[END_REF], [START_REF] Reuge | Hygrothermal effects and moisture kinetics in a bio-based multi-layered wall: Experimental and numerical studies[END_REF]. Fig. 18 shows the decrement factors (%) and the time lags of temperature. The decrement factors are evaluated, the results are respectively 7% for a thickness of 2 cm, 11.42% for 4cm, and 14.46% for 6 cm. Concerning the time lags the following vales are founded: 1h08, 1h48, 2h23 for 2cm, 4cm and 6cm of thickness. The time lags can be calculated for any material by the formulation (Eq.13).

𝑇𝑖𝑚𝑒_𝑙𝑎𝑔𝑠 = 𝑃 2 𝜋 √ 𝜋 𝜌 𝐶 𝜆 𝑃 𝑒 (13)
Where e (m) is the material thickness, P is the cycle of temperature variation (hour), ρ is the material density (kg.m -3 ), λ (W.m -1 .K -1 ) and C (J.kg -1 .K -1 ) are the thermal conductivity and specific heat respectively. The calculated and experimentally evaluated time lags are plotted in Fig. 18. Because of some practical uncertainty in the experimental results, and the assumptions in the theoretical method, the comparison results have some acceptable differences. Furthermore, the comparison of time lags values of hemp concrete with those founded in the bibliography [45] for a wall of 5cm made of concrete (01:08), polyurethane (00:07), and gypsum (00:53), proves that hemp concrete is more efficient in terms of thermal inertia compared to other conventional materials. The sensitivity of the sensors was validated by a calibration and balancing test in our laboratory before starting the experimentation and measurement phase. This step was carried out according to the following protocol: the humidity and temperature sensors were placed in the climatic chamber, the interior conditions of the chamber were varied in several ranges and different configurations, isothermal, relative humidity cycles, etc... The aim of these measurements was to validate the data provided by the sensors using the climatic chamber as reference. In conclusion, the accuracy of the sensors has been widely verified and validated.

To explore the origin of differences observed between the simulated and the measured data, a sensitivity analysis related to the sensors' positions is performed in order to quantify the impact induced by the uncertainty of positions on the local relative humidity and temperature variations. The results presented in Fig. 19 and Fig. 20 show that a positional offset of only 5 mm induces differences of 4% for the relative humidity and 0.97 °C for the temperature. In view of the material heterogeneity and the difficulty of precisely the sensors, the impact of those two parameters justify the slight differences observed between simulated and measured data. Furthermore, the sensitivity analysis must be wider and take into account other parameters as materials properties (thermal conductivity, sorption isotherm…).

MOISTURE BUFFER INVESTIGATION

The Moisture Buffer Value (MBV) characterizes the ability of a material, or a multilayer component, to moderate the air humidity variations. The Japanese Industrial Standard (JIS), the Draft International Standard (DIS) and the Nordtest protocol (NT) all define similar methods based on measurements of mass change of a sample subjected to cyclic variations of relative humidity. In this study, we propose a numerical investigation of hemp concrete subjected to the Nordtest protocol conditions.

The goal of the MBV measurements is to participate in the enrichment of knowledge around hemp concrete, by comparing the behavior of the hemp concrete with respect to the cyclic humidity variations and to determine its ability to moderate these variations. The behavior of hemp concrete is compared to the behavior of other classic materials such as normal concrete, bricks, and glass wool.

The sample conditioned to a specific RH and sealed at all but its normally exposed sides, is alternatingly exposed to a high and a low ambient RH for predefined intervals of time. The sample moisture mass evolution is recorded, and the (MBV) [kg.m -2 .%RH -1 ] is calculated by: Sample thickness [cm] 10

𝑀𝐵𝑉 = 𝑚 𝑚𝑎𝑥 -𝑚 𝑚𝑖𝑛 𝐴 . (𝑅𝐻 ℎ𝑖𝑔ℎ -𝑅𝐻 𝑙𝑜𝑤 ) (14
Ten cycles have been simulated and the MBV is determined based on the results for the last day. The specimen was supposed to be at least 10 cm thick in order to avoid the moisture penetration depth effect for daily humidity variations. The predicted moisture content evolution is presented in Fig. The determined MBV values of hemp concrete classifies the material under the category of good or even excellent humidity regulator regarding the classification of Nordtest Project (Fig. 22). Moreover, the comparison of these values with those given in the Nordtest Project shows that the hemp concrete is a

The hygrothermal performance of hemp concrete was demonstrated in the real building conditions in this study; however, other tests must be conducted in multilayer common case walls to investigate its potential integration as building layer element in real scenarios.

After comparing the ability of hemp concrete to moderate the ambient conditions and investigating its thermal characteristics with respect to conventional building materials such as rock wool and glass wool, the hemp concrete can be considered as an efficient bio-based material in building envelope.

In the future up-coming studies, a more complete investigation will be carried out for hemp concrete in a multi-layered wall with different configurations, in order to identify the interaction of hemp concrete with other materials and to put forward its performances in a more comprehensive context.

  et al. [10] determined experimentally the Moisture Buffer Value (MBV) of hemp concrete. Tran et al. [14] studied the impact of transient hygrothermal behavior of hemp concrete in building envelopes [14]. Lelievre et al. [15] investigated the hygrothermal behavior at different scales (sample and wall) and under various controlled conditions.

  No air transfer occurs;  Liquid mass transfers under thermal gradients are neglected. Several models based on the previous assumption principles were provided by Luikov [26], Whitaker [27], Philip and De Vries [25], and adapted to building materials [28], [29]. The model of Philip and De Vries [25] is considered in this work for predicting the hygrothermal behavior of hemp concrete. This model considers that the moisture transport occurs under two phases (liquid and vapor); the vapor phase moves under a gradient of partial vapor pressure while the water phase moves under capillarity. The model of Philip and De Vries is represented by Equations (1) and (2) describing mass and heat transfers respectively:

Fig. 3

 3 Fig.3 Volumetric heat of hemp concrete versus water content

Fig. 5

 5 Fig. 5 shows the principle of this test. The vapor flow is deduced from the variation in mass of the sample-cup assembly as a function of time.

Fig. 5

 5 Fig.5 Schematic view of the cup method

Fig. 6

 6 Fig.6 Diagram of the experimental device.

Fig. 7

 7 Fig.7 Themocouple (a) and humidity sensor HIH-4000 (b)

Fig. 8 4 . 3

 843 Fig.8 Measured relative humidity in the ambient air

Fig. 10 (Fig. 13

 1013 Fig.10 (a-b) Measured and simulated relative humidity inside the sample at x = 2cm

  Fig. 14 presents the histogram of relative humidity decrement factors and time lags for the hemp concrete sample. The results show that the decrement factor and the time lag increase with to the thickness, which is usually observed for insulation material.

Fig. 14

 14 Fig.14 Decrement factors and time lags evaluated for different thicknesses of hemp concrete

Fig. 15 (Fig. 17

 1517 Fig.15 (a-b) Measured and simulated temperature inside the sample at x = 2cm

  Fig.17(a-b) Measured and simulated temperature inside the sample at x = 6cm

Fig. 18

 18 Fig.18 Decrement factor and time lags evaluated for different thicknesses of hemp concrete

Fig. 19

 19 Fig.19 Influence of sensors positions on the local relative humidity.

)

  Where mmax and mmin [kg.m-2 ] are the sample's maximum and minimum moisture mass, obtained in the final stable cycle, A [m -2 ] is the exposed surface of the element's sample, and RHhigh and RHlow [%] are the high/low Relative humidity levels imposed during the test.The results of the simulated MBV are obtained by simulation with a numerical model for moisture transfer [46] . All simulations are isothermal with temperatures constant at 23 °C. The model is presented by Eq.15, and the associated boundary conditions is expressed by the Eq.16. ∂𝑤 𝜕𝑡 = ∇( 𝛿 𝑝 (𝑃 𝑣 )∇𝑃 𝑣 ) (15) 𝐺 𝑠 = β( 𝑃 𝑣𝑖 -𝑃 𝑣𝑖 ) (16) with w [kg.m -3 ] the moisture content, t [s] the time, δp [s] the water vapor permeability, pv [Pa] the vapor pressure, Gs [kg.m -2 .s -1 ] the vapor exchange flux, β [s.m -1 ] the surface mass transfer coefficient, and p Pvi, Pvs [Pa] the interior/surface partial vapor pressure. The Nordtest protocol and the input parameters used in the simulation are reported in

  . The surface transfer coefficient values varied between 1.10 -8 s.m -1 and 3.10 -6 s.m -1 . Tab. 2 gives an overview of the calculated MBV's of hemp concrete for the different surface transfer coefficients.

Fig. 21

 21 Fig.21 Simulated moisture content evolution

Table 1 -

 1 Summary data for the water vapor permeability test

	Material	Boundary	Exposed area	Thickness	μ0 [-]	μ*
		conditions	(m x m)	(m)
	Hemp	RH : 0% -80%	0,175 x 0,175	0.04	10	3.72
	concrete	T : 23°C
	The value found from this experimental protocol for hemp concrete is µ* = 3.72; this value is very close
	to that found by F. Collet et al [10].

INVESTIGATION OF THE SAMPLE IN REAL WEATHER CONDITIONS 4.1 Experimental setup

  In order to evaluate the hygrothermal behavior of hemp concrete under real ambient conditions, a wall segment made of hemp concrete was instrumented and submitted to uncontrolled ambient temperature and relative humidity.The sample of hemp concrete had already been investigated in previous studies [14][START_REF] Colinart | Experimental and numerical analysis of the transient hygrothermal behavior of multilayered hemp concrete wall[END_REF] [38] under controlled conditions; however, in the present study, the sample behavior under moderate changes of relative humidity and temperature inside a room/building is tested.The tested sample has a large open surface (300×300 mm 2 ) and a thickness of 80 mm which is thicker than the moisture penetration depth calculated for such a material[START_REF] Collet | Experimental investigation of moisture buffering capacity of sprayed hemp concrete[END_REF]. A smaller thickness causes measurement errors, while the large thicknesses of this material will not be representative of the reality;

Table 2 .Table 2 -

 22 MBV Simulation parameters

	Protocol Nordtest	Values
	RH levels (high/low) [%]	75/33

much better hygroscopic regulator than cellular concrete (MBV = 1.04 kg.m -2 .%RH -1 ), plaster (MBV = 0.64 kg.m -2 .%RH -1 ) and cement concrete (MBV = 0.38 kg.m -2 .%RH ).

Fig.22 Nordtest classification of MBV Project [36]

CONCLUSION

Although more efforts are still needed to learn more about its hygrothermal behavior. For this purpose, an experimental study was performed in real weather conditions by instrumenting a hemp concrete wall segment with temperature and humidity sensors at its both exposed faces and from inside. The wall segment was exposed to outside weather conditions from one side and to laboratory indoor conditions from the other side. The material's thermophysical properties were first evaluated experimentally and then used as input parameters in the numerical adopted model describing heat and mass transfer.

The numerical results were in a good agreement with the experimental measurements. Generally, the local variations of temperature and relative humidity were modeled with high accuracy over the wall thickness; a slight difference between the simulated and measured data was observed at a depth of 2cm. For this reason, a sensitivity analysis was carried out to quantify the impact on sensors positions uncertainty.

To study the efficiency of hemp concrete in regulating the ambient humidity, a numerical investigation of the Moisture Buffer Value was performed for the extreme high/low values of surface film coefficients.

From those results and according the Nordtest classification, the hemp concrete can be classified between good and excellent humidity regulator materials. One can conclude that, even if the hemp concrete presents a thermal conductivity higher than other conventional insulation materials, its strong humidity regulation potential as well as dynamic hygrothermal performance (time lag and decrement factor) make it a favored choice to be integrated in energy efficient building envelopes.


M Asli

E Sassine
email: emilio.sassine@gmail.com

F Brachelet

E Antczak

Hygrothermal behavior of wood fiber insulation, numerical and experimental approach

Keywords: Wood fiber, hygrothermal behavior, experimental and numerical study, isotherm of sorption, thermal conductivity

Many new insulation materials are being developed and thermally tested aiming at understanding and improving their insulation characteristics in order to improve the energy performance of new and existing buildings. Bio-sourced materials appear among the new insulation solutions presenting the advantage of being able to save energy on one hand and having a low environmental impact on the other. The wood fiber material is one of the most successful natural insulation materials being recently used in building constructions. It presents many advantages besides its insulation performance; due to its density, it stores moisture thereby improving the indoor air quality; it is also an excellent acoustic insulator because it has a natural tendency to absorb and reduce sounds.

In order to evaluate its effectiveness in building applications, this study analyzes the hygrothermal modelling and performance of the wood fiber insulation in building applications by adopting two approaches:

-A numerical approach using a mathematical model that describes heat and mass transfer within the wood fiber material being considered as porous media. The hygrothermal characteristics of the wood fiber material are first determined experimentally for this purpose, namely the thermal conductivity, the heat capacity, and the isotherms of sorption and desorption.

-An experimental approach is carried out in controlled and uncontrolled ambiance conditions in order to validate the numerical model.

A 50 cm x 50 cm wood fiber sample having an 8 cm thickness is tested for this purpose. A very high accordance is observed between the measured and modelled results for both the temperature and the relative humidity evolutions within the sample at x=2cm and x=4cm with a mean difference ΔT ̅̅̅̅ of

Introduction

Nowadays, human activities are causing the depletion of natural resources and significant climate changes impacting the environment through the increasing occurrence of natural disasters such as floods, hurricanes, drought, and heatwaves…etc. In order to deal with these issues, the international community is seriously concerned trying to reduce the greenhouse gas emissions (GHG) by 2050 across the globe [1], [START_REF]Convention-cadre sur les changements climatiques[END_REF]. While developing countries are unable to meet the highly fixed objectives, the industrialized countries are in turn making a special effort to divide by four their GHG in less than fifty years without compromising a sustainable development of their societies.

The building sector is particularly involved in such commitments. In France, as in many other countries, the building sector is the largest energy consumer among all economic sectors with about 43% of the global consumed energy (1.1 ton oil equivalent per year per capita according to the ADEME [3]).

Moreover, the buildings produce over 120 million tons of carbon dioxide and greenhouse gases representing nearly a quarter of national emissions [4]. Furthermore, the cost of energy bills alone accounts for 30% of the household budget; and these figures are expected to increase due to the decrease of fossil fuel availability in the coming years [START_REF]Oil price developments: drivers, economic consequences and policy responses[END_REF]. Substantial efforts are thus required for improving the energy performance of both new construction and existing buildings [START_REF] Thomsen | Energy consumption and indoor climate in a residential building before and after comprehensive energy retrofitting[END_REF]. These efforts will not only reduce the energy cost, but also improve the well-being of residents by improving the indoor thermal comfort; as well as providing employment opportunities in the building sector [START_REF] Holopainen | Comfort assessment in the context of sustainable buildings: Comparison of simplified and detailed human thermal sensation methods[END_REF].

The choice of building materials is just as important as good design and quality construction. They have a significant impact on the energy bill [8], [START_REF] Khadiran | Advanced energy storage materials for building applications and their thermal performance characterization: A review[END_REF]. However, the energy required for their production, transportation, implementation and recycling should be taken into consideration. It is therefore wise to look for the usage of natural materials having equivalent performance and reduced environmental impact compared to those produced by chemical processes.

Bio-based materials are by definition the materials made from plant biomass resources or animal origins. They now cover a wide range of products and are used in many applications in the building and construction field such as bricks [START_REF] Bories | Development of porous fired clay bricks with bio-based additives: Study of the environmental impacts by Life Cycle Assessment (LCA), Construction and Building Materials[END_REF], insulations (wool plant or animal fibers, recycled textiles, cellulose wadding, straw bales, etc.), mortars and concretes (hemp concrete, wood, flax, etc.) [START_REF] Bennai | Experimental characterization of thermal and hygric properties of hemp concrete with consideration of the material age evolution[END_REF], [START_REF] Chennouf | Hygrothermal characterization of a new bio-based construction material: Concrete reinforced with date palm fibers[END_REF], and panels (particles or plant fibers, compressed straw, etc.) [START_REF] Kočí | Interior thermal insulation systems based on wood fiberboards: experimental analysis and computational assessment of hygrothermal and energy performance in the Central European climate[END_REF], [START_REF] Li | Modelling the hygrothermal behaviour of cement-bonded wood composite panels as permanent formwork[END_REF].

This study investigates the hygrothermal performance wood fiber materials. These products are manufactured on the basis of shredder softwood falls and present considerable environmental advantages, because they use wood being a natural and renewable resource that can be obtained from recycling the wastes from the timber industry.

The wood fiber materials can be found in various forms: Panels with a density of 40 kg.m -3 known as semi-rigid wood fiber panels. These are usually elastic, flexible and easily adaptable. They are generally used as interior insulation. The timber fiberboards panels are rigid with medium or high density (between 60 and 280 kg.m -3 or more), are mainly used in roof insulation and outside wall insulation. The wood fiber bulk material has a density of 35 kg.m -3 and is collected just after the shredding step; it can be blown or projected by inside. They can also be mixed with clay or concrete as innovative insulation material [START_REF] Bennai | Experimental characterization of thermal and hygric properties of hemp concrete with consideration of the material age evolution[END_REF] [START_REF] Taoukil | Moisture content influence on the thermal conductivity and diffusivity of wood-concrete composite[END_REF].

The use of bio-based material in building insulation is not limited to its advantageous thermal performance, but also to its sensitivity to moisture, in other words its ability to absorb and desorb water vapor in real weather conditions [START_REF] Rafidiarison | Dataset for validating 1-D heat and mass transfer models within building walls with hygroscopic materials[END_REF]. Indeed, in new construction or in existing buildings' rehabilitation, the moisture can be present in the walls under several forms such as: water vapor coming from inside, capillary water rise, exposure to weather conditions, etc… Moreover, by their nature, the bio-based materials are quite sensitive to the water and water vapor presence [17], [START_REF] Mourad | Analyse et caractérisation du comportement hygrothermique de parois agro-sourcées à l'échelle 1: expérimentation et modélisation[END_REF], which obviously impacts their durability and thermal performance.

In industrialized countries, the implementation of bio-based materials in building construction is recent and is still limited. Even though these studies present interesting findings for understanding the thermal behavior of wood fiberboards, the importance of mass transfer in these porous materials was not taken into consideration.

Many

Among the studies dealing with heat and mass coupling in wood fibers, Mvondo et al. [21], studied the influence of water content and the direction of the fibers on thermophysical properties for three tropical wood species by determining experimentally the thermal conductivity and volumetric heat capacity in the longitudinal, radial and tangential directions of the different samples for different moisture contents.

The study presents interesting results helping to understand the relation between thermal and hydric properties in fibrous materials. Latif et al. [START_REF] Latifa | An experimental investigation into the comparative hygrothermal performance of wall panels incorporating wood fibre, mineral wool and hemp-lime[END_REF] compared Mineral Wool, Wood Fiber and an assembly of wood fiber and hemp-lime panels having identical U-values in a large dual environmental chamber under identical controlled conditions. It was observed that the wood fiber and hemp-lime assembly panel showed the highest heat storing and releasing capability as well as the highest moisture dampening ability which can be useful in mitigating overheating of dwellings and reducing interstitial condensation. The effect of adding inorganic adsorbents was studied by Nguyen et al. [23] who found that they lead to a decrease in the thermal conductivity and an improvement in the moisture buffering of the insulation boards.

In this same approach, this work aims to study the wood fiber insulation, by analyzing its transient hygrothermal behavior and evaluating these intrinsic characteristics, which are temperature and moisture functions. For this reason, the present study is made of two parts:

-First, an adapted behavior pattern to predict the hygrothermal behavior of wood fibers is proposed using a mathematical model based on Philip and De Vries model [START_REF] Rafidiarison | Dataset for validating 1-D heat and mass transfer models within building walls with hygroscopic materials[END_REF]. A thermophysical characterization study is performed according to the standards for determining the material thermophysical properties.

-Then, the numerical model is validated through experimental results on a wood fiber wall submitted to controlled and uncontrolled ambient solicitations.

A comparative study of the decrement factor and time lags is also provided, and a comprehensive sensitivity analysis is presented in order to evaluate the results and the accuracy of the model. The first one is based on the homogenization of the porous media at microscopic and macroscopic scale. The porous media that is highly heterogeneous at microscopic scale is represented as a homogeneous and continuous media. The heat and mass conservation is written to describe the particle movement, then the variable states are averaged over the entire volume of the domain.

Numerical heat and mass coupled model

Whitaker [START_REF] Whitaker | Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying[END_REF], Samson [27] and Maghous [START_REF] Maghous | A model for in situ grouting with account for particle filtration[END_REF] are examples of works using this approach. It allows a better understanding and modelling of the complex phenomena that occur simultaneously at the pore scale, for example the water and the water vapor diffusion.

The second approach consists on phenomenological modelling, inspired by the works of Phillipe De The following assumptions are considered:

-The solid matrix is considered homogeneous, continuous and non-deformable.

-The medium volume equals at least a representative elementary volume (REV).

-The thermodynamic equilibrium is established between the different material components.

-Total gas pressure is constant, equal to the atmospheric pressure.

The model of Philip and De Vries

Where T and θ are the temperature and water content respectively ρ0 is the solid matrix density Lv is the latent vaporization heat ρl is the water density Cpm is the specific heat calculated as the average specific heat of solid matrix and liquid phase.

λ* is the equivalent thermal conductivity of the porous media and it is a function of temperature and moisture content DT,v and Dθ,v are the vapor phase transport coefficients associated with temperature and moisture content gradient respectively

The mass transfer balance equation is given by:

∂𝜃 𝜕𝑡 = ∂ 𝜕𝑥 ( 𝐷 𝜃 ∂𝜃 𝜕𝑥 ) + ∂ 𝜕𝑥 ( 𝐷 𝑇 ∂𝑇 𝜕𝑥 ) (2)
DT and Dθ are, respectively, the mass transport coefficients associated with temperature and moisture content gradient.

Boundary conditions

The air velocity sensors may induce relatively high uncertainty measurements, especially at the exterior side of the wall where the ambient conditions may be very disturbed. The convective heat and mass transfer at the air-porous material interfaces [31] may generate some uncertainties in the numerical modelling; imposed temperature and relative humidity on the internal and external wall sides were thus considered as boundary conditions for the numerical model (Dirichlet type boundary conditions).

The relative humidity and temperature sensors were placed at the internal and external faces of the wall, and the Dirichlet type boundary conditions can be written as:

𝑇 𝑠ex𝑡,𝑡 = T 𝑒𝑥𝑡 , 𝑇 𝑠in𝑡,𝑡 = T 𝑖𝑛𝑡 (3)
𝐻𝑅 𝑠𝑒𝑥𝑡,𝑡 = HR 𝑒𝑥𝑡 , 𝐻𝑅 𝑠𝑖𝑛𝑡,𝑡 = HR 𝑖𝑛𝑡 (4)

Where the indices "sext" and "sint", represent the temperature and humidity at the interior and exterior wall surfaces respectively, and "t" refers to the dynamics of the variables as a function of time.

To be closer to the reality, the temperature and relative humidity at the boundaries were measured during the tests.

Diffusion coefficients

The equations relating mass transport coefficients to vapor and liquid phase transport coefficients are:

DT = DT,l + DT,v m².s -1 .K -1 (5) Dθ = Dθ,l + Dθ,v m².s -1 (6)
The vapor diffusion coefficients were determined according to Zeknoun et al [START_REF] Zaknoune | Identification of the Liquid and Vapour Transport Parameters of an Ecological Building Material in Its Early Stages[END_REF], and Maalouf et al

[33].
The transport coefficients associated with moisture gradient are related to the water vapor permeability δ0 and the specific hygric capacity ξ, which is the slope of sorption curve:

𝐷 𝜃 = 𝛿 0 𝑃 𝑣,𝑠 𝜌 0 1 𝜉 (7)
𝛿 0 = 𝛿 𝑎 𝜇 (8)
Where δ a is the air vapor permeability and it is equal to 2.10 -10 kg.m -1 .s -1 .Pa -1 , and μ is the water vapor resistance factor.

Vapor transport coefficient under a temperature gradient is given by the relation:

𝐷 𝑇,𝑣 = 𝛿 0 𝜑 𝜌 𝑙 𝑑𝑃 𝑣,𝑠 𝑑𝑇 (9)

Numerical resolution

To solve the model of heat and mass transfer represented by Eq. (1) and Eq. ( 2), Comsol

Multiphysics® software [34] was used. The software is adapted to solve partial differential equations, based on the finite elements method (FEM) especially in Multiphysics problems where several coupled phenomena occur simultaneously. The specific boundary conditions of heat and mass flux represented in Eq. ( 3) and Eq. ( 4) have been implemented. Several simulations were done in order to determine the effect of the mesh on the accuracy of the results, and to be as confident as possible, it has been decided to tighten the mesh to the maximum so that the mesh length is 0.02mm with a 300s time step.

The value settings of the parameters used in the numerical simulations are summarized in Tab. 1.

Tab 1.

Parameters value settings

Parameter

Adsorption and desorption of wood fiber

In this work, a series of characterization tests was established in our laboratory to guarantee the accuracy of the parameters used in the numerical model describing the hygrothermal behavior of wood fiber. Water vapor sorption is the process [39] that relates the water content inside the materials with the ambient relative humidity, for a given temperature. The porous materials with open porosity tend to fix the air humidity, which means the increase in air relative humidity leads to an increase of bulk density and vice versa. Generally, in order to classify the isothermal sorption of porous materials, the classification of the International Union of pure and Applied Chemistry (IUPAC) [40] is adopted. Note that the water content quantities at the sorption state differ from the quantities evaluated at the desorption [41].

Experimental setup

The water vapor sorption and desorption test was performed according to the discontinuous method described in the standard NF EN ISO 12571 [START_REF] Nf En | ISO 12571 Hygrothermal performance of building materials and products-Determination of hygroscopic sorption properties[END_REF]. The dynamic VDS test method was used where the ambient conditions are ensured by mechanical ventilation system. Three samples were tested for the wood fiber, which is the minimum required number by the standard NF EN ISO 12571 [START_REF] Nf En | ISO 12571 Hygrothermal performance of building materials and products-Determination of hygroscopic sorption properties[END_REF]. The three samples were placed inside a climatic chamber, where the climatic ambient conditions (temperature and relative humidity) were controlled. The wide range of temperature (-40°C to 60°C) and relative humidity (0% and 97%), allows reproducing the test conditions with high flexibility. The uncertainties in temperature and relative humidity were evaluated by the supplier at 0.5°C and 2% respectively. The water content was determined for successive stages of relative humidity (increasing then decreasing)

for a constant temperature 23°C (isothermal condition).

The samples were weighted until reaching the steady state; when a mass difference lower than 0.1% was reached after three successive weights in 24h, the equilibrium was considered to be reached, and the water content was calculated according to Eq. 10.

θ = m 0 -m m 0 ( 10
)
Where m0 is the mass of the sample in the dry state and m is the mass sample of the steady state.

Fig. 1 shows the kinetic sorption of wood fiber for different humidity stages [0%, 10%, 23%, 55%, 81%, 90% and 97%] for sorption and [97%, 90%, 81%, 55%, 23%, 10% and 0%] for desorption.

Figure 1-Kinetic sorption isotherm of wood fiber

Sorption Modelling

The purpose of the isotherm modelling is to have the water content curve spread out over the relative humidity range φ (1 to 100%

w = θ m + C. φ 1 + C. φ BET w = C. θ m . φ (1 -φ). (1 -φ + C. φ) GAB w = C. θ m . K. φ (1 -K. φ). (1 -K. φ + K. C. φ)
𝑤 is the water content of the material on a dry basis (kg water / kg dry solid) θm is the water content corresponding to the monolayer sorption for each model φ = (Pv/Ps) is the water activity Pv and Ps are respectively the vapor partial pressure and saturation pressure C and K are constants related to the temperature effect.

C = 𝑒𝑥𝑝 𝐸 𝑎 -𝐸 𝑚 𝑅.𝑇 K= 𝑒𝑥𝑝 𝐸 𝑙 -𝐸 𝑚 𝑅.𝑇
Ea is the heat of adsorption, El is heat liquefaction, and Em is binding energy.

The GAB model was compared to the obtained results of the water vapor sorption test since it covers a wide range of relative humidity (0.05 < φ < 0.95), while the other models cover a narrower range.

In order to obtain the different GAB model parameters, the least-square method was being implemented:

∑(w i -w exp,i ) = minimum (11)
wexp,i is the water content measured at the relative humidity i, and wi is water content calculated by the GAB model.

The relative error of linear regression can be calculated as: This type of curve is obtained for the micro-porous media and is in accordance with the nature of wood fiber. Furthermore, the sorption isotherm presents a hysteresis, which extends to the lower hygrometry.

𝐸 = 1 𝑛 ∑ abs (w i -w exp,i ) w exp,i n i=1 (12)
From this curve, three segments of the water content evolution can be observed, the test started from 0% of water content, which is the initial condition assumed (dry material). The first part at lower relative humidity φ < 23%, less than 5% of water content is recorded, only a monolayer is formed. The second part, 23% < φ < 80%, the water content presents a slight slope. The last part, at high hygroscopic region, 80 % < φ < 97 %, the moisture inside pores begins to form a water bridge, which is known as the condensation phenomenon. Tab. 3 summarizes the measurements of water content and their corresponding relative humidity, for both adsorption and desorption stages. The hysteresis is represented by the ratio between the average values obtained for adsorption and desorption (A/D).

Thermal characterization

Experimental method

Thermal characterization techniques were based on the study of the response of a sample material to a thermal loading. The guarded hot plate and heat flow meter methods according to the standard NF EN 822 [START_REF] Collet | Water vapor properties of two hemp wools manufactured with different treatments[END_REF] were used to measure thermal conductivity and specific heat of the tested material. This method was adopted due to its simplicity and its results' accuracy.

The experimental setup consists of maintaining a temperature difference ΔT between two parallel flat plates, a sample with known thickness (e=8cm) is positioned between them. The sample's area was selected higher than the flux sensor' area (15 cm x 15 cm) in order to prevent border heat loss effect.

Fig. 3 shows a schematic of the principle and the tested specimen.

Figure 3-Schematic of principle heat flow meter method

The thermal conductivity λ can calculated as follow:

𝜆 = 𝑒 . Ф 𝛥𝑇 ( 13
)
Where λ (W.m -1 .K -1 ) is the material's thermal conductivity, and Ф (W.m -²) is the measured heat flux.

Likewise, the specific heat was evaluated with the same device using different imposed thermal loads.

The sample was first submitted to a constant temperature until reaching a steady-state, then another constant temperature was applied until reaching a new steady-state. We assume that the sample goes from initial temperature Tinit to final temperature Tfin. Between these instances the sample stores an amount of energy Q (J.m -2 ); the heat capacity C (J.K -1 .m -2 ) is thus calculated as follows:

C = Q ΔT ( 14
)
Where ΔT = Tfin -Tinit, and 𝑄 = ∫ 𝛥Ф.

T 𝑓𝑖𝑛 T init

𝑑𝑇

The specific heat c (J.K -1 .Kg -1 ):

c = 𝐶 𝜌 . 𝐴. 𝑒 (15)
Where ρ and e are the material density and thickness respectively.

Experimental results

The thermal and hygroscopic characteristics of materials were tested in laboratory as described below.

The wood fiber material is first dried at constant temperature 100°C during 48h, then the thermal conductivity and heat capacity were measured. Afterwards, the sample was placed inside a climatic chamber and submitted to different relative humidity conditions. The water content was determined for each state and the thermal characteristics were measured for each corresponding water content. Fig. 4a represents the thermal conductivity evolution versus water content of wood fiber material. We observe a parabolic curve that represents the thermal conductivity evolution, where the lowest value corresponds to the dry thermal conductivity λ0 = 0.044 W.m -1 .K -1 . The measured λ0 is in accordance with the value founded by Vololonirina et all [START_REF] Vololonirina | Characterization of hygrothermal properties of wood based products -Impact of moisture content and temperature[END_REF]. However, the wet thermal conductivity reaches 0.063 W.m -1 .K -1 when the sample contains 20% of water content. The thermal conductivity presents a 43% growth compared to the initial measured value at the dry state, this shows the great influence of water content on the thermal behavior of wood fiber. The fitting curve relating the thermal conductivity of wood fiber to its water content is given by: λ wood fiber = 5E -05 (w 2 ) + 0.0002(w) + 0.0437 [START_REF] Rafidiarison | Dataset for validating 1-D heat and mass transfer models within building walls with hygroscopic materials[END_REF] The volumetric heat capacity of wood fiber (ρ.c) J.m -3 .K -1 as a function of water content was determined by the same method (Fig. 4b). The relationship between the volumetric heat of wood fiber and water content presents a linear shape and can be expressed as: 4 Controlled conditions test

Experimental setup

The wood fiber material sample was first exposed to controlled temperature and humidity boundary conditions inside the previously described climatic chamber. The sample has a 300mm x 300mm open section and is 80mm thick. To ensure a 1-D heat and mass transfer within tested sample, only the two large faces were exposed to the ambient conditions, the other faces being insulated with polyurethane and a vapor-tight material (silicone). A controller device was used to monitor the ambient temperature and relative humidity. Two other specimens with same configuration with different thicknesses 2mm and 4mm were also placed in the climatic chamber; these samples were weighted each time to assess the water content evolution with an accuracy of ± 0.01 g.

The sample was instrumented with thermocouples and humidity sensors HIH-4000 to assess the temperature and relative humidity evolutions respectively. As shown in Fig. 5, the sensors were placed within the material thickness at different positions x = 0mm, 20mm, 40 mm and 80mm, and inside the climatic chamber in order to assess the relative humidity and temperature of the surrounding. The advantages of these sensors are their long-term stability and the fact of being individually calibrated, their accuracy is evaluated by the supplier to ± 3.5% for humidity and ± 0.02 °C for temperature. The data logging was done through a data acquisition system GL820 [51] connected to the sensors.

Figure 5-Schematic representation of experimental facility

Ambient conditions

The samples were first dried in a ventilated oven at 100°C in order to obtain the dry mass. They were next introduced inside the climatic chamber, where they were exposed to constant ambient conditions φ = 50% and T = 23°C for long periods. After 21 days, the samples of wood fiber were assumed to reach the steady state. The measured values were used in the modelling section as initial conditions.

Several test protocols of static solicitation have been performed inside the climatic chamber to identify precisely the relation between the temperature and relative humidity. The imposed measured ambient conditions of temperature and humidity for the three protocols are shown in Fig. 6.

Figure 6-Static solicitation of relative humidity and temperature

The first case study (first protocol) consisted in maintaining a constant temperature (T= 24°C), while varying φ from 50% to 75% for 4 days, then switching φ to 33% for other 4 days. Then the samples were submitted to T = 24°C and φ = 50% for 5 days, in order to reproduce the initial conditions before starting the second protocol.

The second case study consisted in maintaining a constant φ at 50% and switching the temperature from 24°C to 34°C, thus imposing a 10°C temperature gradient during 1 day.

In order to test the model's ability to predict the hygrothermal behavior, the 3 rd protocol was performed by coupling the ambient condition variations of the air temperature (from 24°C to 34°C), simultaneously with the humidity from (50% to 75%) during 1 day. The operation was repeated 2 times.

Experimental results

Fig. 7 -Fig. 9 show the experimental temperature and humidity measurements for the three protocols. In the first protocol, when switching the air relative humidity φ from 50% to 75%, the quasi steady state is reached after four days, for both sorption and desorption stages (Fig. 7b). The relative humidity within the sample started evolving gradually, where the evolution at the first 12 hours was more acute;

that can be explained by the monolayer adsorption phenomenon "Van der Waals forces", which is more important than the multilayer sorption forces. During the desorption phase, the evolution of relative humidity continued, however with less emphasis. The relative humidity φ at 2cm and at 4cm reached 70.38% and 65.74% respectively for the adsorption stages, and 31.76%, 29.89% for the desorption stages respectively. It can be shown that the fiber wood behavior during adsorption and desorption stages is not similar, this is due to the pores shape. Every relative humidity variation is accompanied of temperature fluctuation (Fig. 7a), this phenomenon is caused by the coupled effect of mass on heat transfer. The condensation around the thermocouples, is characterized by latent heat liberation and for this reason the temperature peaks at t=0 and t=4days are evaluated to be about +1.5°C for the sorption stage, and -3°C for the desorption.

In the second protocol, the air temperature increases from 24°C to 34°C; as expected the air temperature reaches the steady state after a very short time (about 20 minutes). The temperature profiles at 2cm and 4cm reach the steady-state thereafter, after about 1 hour (Fig. 8a). Concerning the relative humidity evolution during the second protocol (Fig. 8b), small peaks of relative humidity, φ: 50,92% and 47,99%, are registered at 2cm and 4cm respectively.

The third protocol is the closest to reality where temperature and relative humidity variations occur simultaneously. The air relative humidity and temperature measurements within the sample at 2cm and 4cm are shown in Fig. 9.

Comparison and discussion

The modelling was performed using COMSOL Multiphysics® in 2-D configuration with a mesh size of 1 mm and a time step of 300s; Dirichlet boundary conditions were adopted and the logged data at the interfaces were implemented in the model. The initial conditions were also taken from the measured values.

First protocol

The comparison between the modelled and measured relative humidity and temperature in the first protocol (Fig. 10), shows a good agreement between the experimental and the simulated data. A small difference is observed between the measured relative humidity and the modelled one in 2cm depth (Fig. 10b). The simulated temperature at 2cm and 4cm follows the temperature measured. The temperature peak is estimated to be 1.2°C and 1.5°C at 2cm and 4cm respectively during the sorption stage, and 2.5°C and 2.65°C during the desorption stage. The water content is evaluated during the test, where the samples inside the climatic chamber were weighted on a regular basis. The operation is done for the 1 st and the 3 rd protocols, and ignored for the 2 nd protocol (where the relative humidity was maintained constant). Fig. 11 represents the modelled and measured water content evolution within the sample. The measured water content starts from 7.4 kg/kg and 6.13 kg/kg at 2cm and 4cm respectively, which corresponds to the sorption curve of wood fiber (Fig. 2). The water content continues the evolution with the same way as the relative humidity, until reaching 10.15 kg/kg and 10.37 kg/kg at 2cm and 4 cm respectively. During desorption stage the water content decrease to 5.24 kg/kg and 5.09 kg/kg in four days. Hysteresis effect of 2.16 kg/kg and 1.04 kg/kg between the sorption and desorption stages at 2cm and 4cm are logged respectively.

Generally, a good agreement is observed between the modelled and the measured water content; the observed slight difference is due to the hysteresis effect, which has not been considered in the modelling part.

Figure 11-Measured and modelled Water content evolution at x = 2 and 4 cm (1 st protocol)

Second protocol

In the second test where a constant relative humidity of φ = 50% was maintained while varying the temperature, the heat transfer phenomena within the wood fiber was studied without accounting the humidity effect; this allows to check the accuracy of the thermal characteristics obtained in laboratory, namely the thermal conductivity and the specific heat of wood fiber. The simulated and measured temperatures for this configuration are shown in Fig. 12. The steady state is quickly reached within the wood fiber sample and the temperature profiles at 2cm and 4cm are very similar. A good agreement is recorded between the simulated and the measured temperatures, where average temperature differences ΔT of 0.08°C and 0.13°C are evaluated at 2cm and 4 cm respectively. The temperature evolution is predicted accurately over the entire thickness in terms of amplitude and time lags (Fig. 13a). Fig. 13b represents the numerical and experimental relative humidity evolutions within the sample at 2cm and 4cm respectively. As expected, the mass transfer process takes more time to reach the quasi steady state than the heat transfer process. A close difference between the modeled and the measured values at 2cm is noticed, while a higher difference is observed at 4cm. The relative humidity differences ΔRH at 2 cm during the transient phase and during quasi steady state are evaluated at 4% and 7% respectively, while at 4 cm the ΔRH was evaluated at 5% and 13%

respectively. This means that the relative humidity differences are larger than the sensor's uncertainty (3.5%), especially at 4 cm. These differences can be explained by sensors' sensitivities, sensors' position, humidity infiltrations, and the imperfect symmetric loads between T and φ at both faces of the samples, as well as the high heterogeneity of the media. and 15% at 2cm and 4 cm respectively. In order to reach more accuracy of water content evolution model within wood fiber, a hysteresis model will be the subject of the forthcoming studies.

5 Uncontrolled conditions test

Experimental setup and boundary conditions

After testing the hygrothermal behavior of the wood fiber material under controlled conditions in the laboratory, where different ambient conditions were generated inside a climatic chamber, the fiber wood sample was inserted in the laboratory wall, in the ventilation opening, as illustrated in Fig. 15.

The same sample was reused in order to keep the same material's properties, sensor's position and avoid all disturbances of initial water content. This study was done during the month of March.

Experimental and numerical results

The modelling of the hygrothermal behavior of fiber wood insulation in the real ambient conditions aims to predict the hygrothermal behavior in real complex conditions. The measured and modelled results obtained for this case study are represented in Fig. 17 and Fig. 18 showing the measured and modelled temperature and relative humidity evolutions within the sample at x =2cm and 4cm.

A very high accordance is observed between these profiles. Regarding the temperature evolution (Fig. 17); a perfect correspondence is found at x = 4cm where the mean difference ΔT ̅̅̅̅ is evaluated to 0,21°C, while ΔT ̅̅̅̅ is estimated to 1°C at x = 2cm.

The maximum recorded differences for the relative humidity are: 5,5% and 4,5% at x = 2cm and 4 cm respectively.

(a) (b) Promising result were found for relative humidity oscillations for the time lags (13h15 and 10h40) and the decrement factor (31,53% and 30,30%) at 2 cm and 4 cm (Fig. 19a).

The temperature results presented in Fig. 19b show that the time lag and decrement factor at 2 cm and 4 cm are respectively 02h55, 02h05, 11,45 % and 4,58%. These results are close to those presented by Rafidiarison et al [START_REF] Rafidiarison | Dataset for validating 1-D heat and mass transfer models within building walls with hygroscopic materials[END_REF] where they found a time lag of 3h00 for an 80 mm wood fiberboard sample having a 150 kg/m 3 density. The wood fiber insulation material can thus be considered as an efficient material in term of moderation against external solicitation.

Sensitivity analysis

The slight observed differences between the experimental and numerical data in this study are principally due to the uncertainty of the sensors' position. Indeed, the installation of the sensors is very tricky; for this reason, a sensitivity study is presented below in order to quantify the sensors' position impact on the accuracy of the results.

The sensitivity study aims to evaluate the impact of the input parameters of the mathematical model describing the hygrothermal behavior of fiber wood. The approach is based on the determination of a sensitivity index, calculated as the relative deviation between the variation of output model functions compared to reference functions. The relative deviation is calculated according to the Eq. 18.

𝛿 𝑟 = |𝑥 𝑠𝑖𝑚 -𝑥 𝑟𝑒𝑓 | 𝑥 𝑟𝑒𝑓 x 100 (18)
In order to evaluate the uncertainty of the sensor's position, a variation of ±5mm within the sample at 4cm was considered.

Fig. 20 represents the sensitivity profiles computed using Eq. 18 for the temperature and the relative humidity, induced by a perturbation of ±5mm of the sensor's position in the middle of the sample. We observe that the average values of temperature profile are -2,93 % and -2,90 % of relative humidity.

According to these curves we can deduce that, for each 5mm uncertainty of the sensor's position, we obtain nearly 3% of errors between the simulated and measured data. , describing heat and mass transfer in porous media, was adopted for this bio-based material having a complex structure.

The water vapor sorption curve was first determined to know the studied material reaction against the micro-climatic conditions and represent the hygroscopic map of the material.

The thermophysical and hygroscopic properties were determined through experimental characterization methods according to the standards in order to simulate the material behavior in real conditions. An increasing thermal conductivity between 0.045 W.m -1 .K -1 and 0.06 W.m -1 .K -1 was found for a water content increasing from 2% to 18%. Similarly, the volumetric heat capacity had an increasing shape varying between 250 000 J.m -3 .K -1 and 350 000 J.m -3 .K -1 for the same water content range.

Then, a representative wood fiber sample was subjected to different ambient conditions and instrumented with thermocouples and humidity sensors. The numerical model of Philip and De Vries

[24] was implemented in Comsol Multiphysics® [34] using measured air temperature and air relative humidity at the interface as boundary conditions and compared to experimental measurements in controlled and uncontrolled ambiances.

Three controlled boundary scenarios were considered:

-In the first protocol, the transient relative humidity was studied by maintaining the temperature constant.

-In the second protocol, the relative humidity was maintained constant and the transient temperature was imposed.

-In the third protocol, a coupling of the air temperature and humidity ambient variations was studied.

A general good agreement was recorded between the simulated and the measured temperatures and relative humidity in the three protocols which validates the wood fiber behavior under controlled conditions.

The sample was then tested under uncontrolled conditions in order to predict the hygrothermal behavior of the wood fiber in real ambient conditions.

A very high accordance is observed between the measured and modelled results for both the temperature and the relative humidity evolutions within the sample with a maximum difference of less than 5,5% for the relative humidity, and a maximum difference of 0.21°C for the temperature profiles.

The obtained results highlight the coupling effect between the heat and mass transfer inside bio-based materials and allow the validation of the mathematical model describing heat and mass transfer within the wood fiber insulation material in stochastic real ambient conditions.

Both numerical and experimental approaches can be improved to predict the hygrothermal behavior of wood fiber with higher accuracy. More characterization series can be done, such as water vapor permeability determination or porosity analysis, to better understand the wood nature. The hysteresis models describing the isothermal of sorption and desorption is also foreseen in previous studies.

  research works investigated the thermal behavior of wood fiber construction materials. Troppova et al. [19], determined the thermal properties of medium density fiberboards with different thicknesses using a transient method. El-Sawalhi et al. [20], examined the structure and the thermal performance of natural fiber insulation materials through 3D tomographic imaging by measuring critical structural parameters like porosity, pore and fiber size distribution as well as local fiber orientation distribution.

2. 1

 1 Governing equationsSeveral models were carried out to investigate the coupled heat and mass transfer in porous media. The most popular ones are Philip and De Vries model [24] Whitaker [25] and Luikov [26]. Two approaches are generally used:

Vries [ 24 ]

 24 Luikov [26] Kunzel [29]. In this part the porous media is considered as continuous and homogeneous media, with equivalent properties, which allows to establish the heat and mass transfer equations from the thermodynamic principles. Most of these works are based on Fourier's heat conduction law, fluid mechanics Darcy law for fluid diffusion, and Fick's law for vapor diffusion [30].

[ 24 ]

 24 is taken as the basic model in this work for predicting the hygrothermal behavior of the wood fiber bio-based material. It takes into account moisture transport under two phases (liquid and vapor) and assumes that the vapor phase moves under a gradient of partial vapor pressure and the water phase moves under capillarity. With these considerations, the heat conservation equation becomes:

3

  Experimental characterization of wood fiberThe wood fiber materials hold very interesting properties related to their hygrothermal performance, represented by their low thermal conductivity [37] [38] and their high hygroscopic properties of humidity buffering [36]. Several works have been carried out to characterize wood fiber materials such as the work of Vololonirina and al. [36] studying the impact of moisture on the wood fiber product properties and the experimental study of Rafidiarison and al. [16] investigating the heat and mass transfer within the wood fiber insulation panels with different wall configurations and different boundary conditions.

Figure 2 -

 2 Figure 2-Adsorption and Desorption curve of wood fiber

Figure 4 -

 4 Figure 4-Thermal conductivity (a) and volumetric heat capacity (b) versus water content of wood fiberThe vapor permeability test (dry-wet cup [49]), requires a specific set-up and takes a long time to be performed adequately, for these reasons the water vapor permeability values of studied materials were taken from the literature [36] [50].

Figure 7 -Figure 8 -Figure 9 -

 789 Figure 7-Measured temperature (a) and relative humidity (b) evolution within sample (1st protocol)

Figure 10 -

 10 Figure 10-Measured and modelled Temperature (a) and Relative humidity (b) evolution at x = 2 and 4 cm (1st protocol)

Figure 12 -

 12 Figure 12-Measured and modelled temperature evolution at x= 2cm and 4 cm respectively (2 nd protocol)

Figure 13 -Figure 14 -

 1314 Figure 13-Measured and modelled Temperature (a) and Relative humidity (b) versus time at x = 2 and 4 cm (3rd protocol)

Fig. 14 presents

 14 Fig. 14 presents the mean moisture content evolution versus time. The sorption stage starts from 8.5 kg/kg which is in agreement with the sorption and desorption test results shown in Fig. 2. The differences observed between the measured and the modelled water content are evaluated to 10%

Figure 15 -Figure 16 -

 1516 Figure 15-Vertical cross section of the test under uncontrolled conditionsThe test of wood fiber under uncontrolled conditions lasted for two weeks; the external face was protected with a metal ventilation grid device preventing the rainwater infiltration disturbance. The measurements of ambient relative humidity and temperature at the interior and exterior interfaces of the sample are reported in Fig.16. The curves' continuity proves the proper installation of the sample within the wall, the airtightness, and the high stability of the sample's state. A more or less constant value of the internal ambient conditions is observed with an internal air temperature mean value of 16,81°C ± 0,67°C and an internal air relative humidity of 38,92% ± 2,5%. On the external side, a quasisinusoidal cyclic profile was observed for both temperature and humidity variations with a 24h repetition period. The maximum and minimum external temperature values were evaluated at 20°C and 5,4°C respectively while the external humidity grows until 92,02% and goes down to 42,36%.

Figure 17 -Figure 18 -

 1718 Figure 17-Measured and modelled Temperature evolution at x = 2 cm (a) and x = 4 cm (b)

Figure 19 -

 19 Figure 19-Mean time lags and decrement factor histogram for both relative humidity (a) and temperature (b) respectively

Figure 20 - 7 Conclusions

 207 Figure 20-Temperature and relative humidity evolution at different positions within sample 35mm, 40mm, 45mm

  The fitted parameters of the GAB model, namely the monomolecular water content θm, and the energy values (C and K) are given in Tab. 4. The obtained results present a big similarity with the work ofVololonirina and all [36] for the isotherm of sorption data.

				Ads	55.730	0.841	0.0500
		Wood Fiber		Des	26.800	0.788	0.0655
		Tab 3.	Water content versus relative humidity.
	RH %		0	10	23	58	81	90	97
		Ads	0	4.12	6.34	10.82	15.32	19.02	27.74
	Wood fiber	Des	0	4.81	6.93	12.27	17.11	22.09	27.74
		A/D		0.85	0.91	0.88	0.89	0.86	1
		Tab 4.	Fitted parameters for the GAB model
		Materials			C (-)	K (-)	θm (kg/kg)

Acknowledgment

This work is done as part of the project "Projet citoyen P2AR" financed by the region Nord Pas de Calais, France.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.