Study of the Hygrothermal Behavior of Wood Fiber Insulation Subjected to Non-Isothermal Loading

applied sciences

Article Study of the Hygrothermal Behavior of Wood Fiber Insulation Subjected to Non-Isothermal Loading

Zakaria Slimani 1, Abdelkrim Trabelsi 1,* , Joseph Virgone 1 and Roberto Zanetti Freire 2

1 Univ Lyon, CNRS, INSA-Lyon, Université Claude Bernard Lyon 1, CETHIL UMR5008, F-69621 Villeurbanne, France; [email protected] (Z.S.); [email protected] (J.V.) 2 Industrial and Systems Engineering Graduate Program (PPGEPS), Polytechnic School (EP), Pontiﬁcal Catholic University of Parana (PUCPR), Rua Imaculada Conceição 1555, Curitiba 80215-901, Brazil; [email protected] * Correspondence: [email protected]; Tel.: +33-472-438-489

Received: 10 May 2019; Accepted: 3 June 2019; Published: 9 June 2019

Abstract: Building envelopes are constantly subjected to temperature and moisture gradients. This loading induces a complex response, particularly for highly hygroscopic insulating materials. Latent effects can no longer be neglected for these materials in which heat and moisture transfers are strongly coupled. The purpose of this article is to analyze the behavior of a wood fiber insulation subjected to non-isothermal loading under a vapor concentration gradient. An experimental setup and a mathematical model of hygrothermal transfer were developed to analyze the behavior of the wall. The mathematical model describes the main physical phenomena involved, notably water vapor adsorption and the dependence of thermophysical properties in state variables. The experimental setup developed allows studying a wall under controlled conditions. The temperature and relative humidity profiles within the wall were measured. The evolution of the profiles with time suggests that the adsorption of the water vapor occurs together with the redistribution of liquid water within the envelope. The comparison of the experimental results with the numerical model shows good agreement although the prediction can be improved during the transient phase. The comparisons of these results with a purely diffusive thermal transfer model show the limits of the latter and permit quantifying the latent effects on the total heat transfer.

Keywords: heat and mass transfers; hygrothermal coupling; wood ﬁber insulation; water vapor adsorption; latent eﬀects

1. Introduction The construction sector represents a considerable source of energy saving and greenhouse gas reduction [1]. Thermal regulation is constantly evolving and increasingly reduces energy consumption [2]. Therefore, a type of building is emerging characterized by strong thermal insulation intended to limit losses through the envelope. Under these conditions, large heat fluxes by conduction are considerably reduced but it is no longer possible, to neglect latent effects, especially for strongly hygroscopic materials. Furthermore, we are witnessing renewed interest in low-energy impact materials and especially for plant-based materials such as wood and its derivatives whose strongly hygroscopic nature is known. This interest can also be explained by the moisture buffer effect of this type of material on the hygrothermal behavior of buildings [3–5]. The literature includes several analyses of the behavior of plant-based materials, assemblies, and structures which propose experimental data to validate numerical models of Heat, Air and Moisture (HAM) transfer. Roels et al. [6] studied the response of several assemblies composed of wood wool cement board. Experimental results focused on water content discussion. They showed that the theory

Appl. Sci. 2019, 9, 2359; doi:10.3390/app9112359 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 2359 2 of 12 of Philip and de Vries [7] gave satisfactory results for simulating wetting–drying. Talukdar et al. [8,9] presented a very complete study on a dataset for benchmarking 1D transient heat and moisture transfer models of spruce plywood and cellulose insulation in two parts. The first presented their experimental setup and its calibration, while the second presented experimental, numerical, and analytical results that could be used for benchmarking. Teasdale-St-Hilaire et al. [10] focused on wood-frame wall assemblies wetted by simulated wind-driven rain infiltration. The analysis mainly dealt with the distribution of water content in the wood during drying. Li et al. [11] presented extensive data from a laboratory experimental program in which full-scale wall panels were used for model validation. The latter focused only on water content in a 2D configuration. Piot et al. [12] developed an experimental wooden frame house to provide data for the validation of numerical models for whole building heat, air, and moisture transport. They highlighted the importance of temperature-driven moisture diffusion in the case of exterior hygroscopic paneling. Desta et al. [13] presented experimental data on heat, air, and moisture transfer through a full-scale lightweight building envelope wall under real atmospheric boundary conditions. It was found that if the walls were sufficiently airtight the amount of accumulated moisture in the winter season was limited and dried out in the summer for the given configuration. For the same wall type, Langmans et al. [14] performed exeprimental and numerical study to analyse the hygrothermal consequences of using an exterior air barrier. They highlighted buoyancy effects for high walls (above 2 m). Rafidiarison et al. [15] presented a dataset for validating 1D heat and mass transfer models within building walls with hygroscopic materials. They showed that moisture accumulation was observed in the layer close to the plaster for the wall without Oriented Strand Board (OSB). Latif et al. [16] carried out an in situ experiment on a full-scale timber frame test building to study the hygrothermal performance of wood-hemp composite insulation in timber frame wall panels with and without a vapor barrier. They observed a very low impact on the U-value for the stresses studied. In the present article, in addition to study the evolution of the water content in a strongly hygroscopic material and proposing data to validate transfer models, we propose a detailed analysis of latent effects in a wood fiber insulation material subjected to non-isothermal conditions under a vapor concentration gradient through experiments and numerical modeling. For the experiment, we opted for a test under laboratory conditions on a wall at intermediate scale between the material-scale and full-scale experiments. The objective is to integrate heterogeneities exceeding the size of samples for the experiments at the material-scale, limiting edge effects and overcoming difficulties of implementation and interpretation linked to full-scale experiments under real conditions. Numerically, we opted for a fine-scale model with heat and moisture (HM) coupling and a purely diffusive thermal transfer model in order to compare them with the experimental observations and to calculate the latent effects and their importance. This work was performed in the framework of the ANR HYGRO-BAT project [17] which aims to propose a methodology to improve hygrothermal design for buildings and was completed in the framework of the COOPER-CEMIRA project intended to estimate the latent effects in very hygroscopic materials.

2. Materials and Methods

2.1. Material The biosourced material studied in this article is a wood fiber insulation. It can be used for the thermal insulation of different parts of a building (floor/wall, internal/external insulation, etc.). It takes the form of rigid panels to facilitate its assembly on the building site. It also has good phonic insulation properties regarding impact and airborne noises. Its hygrothermal characteristics result from the synthesis of contributions from different laboratories achieved in the framework of the HYGRO-BAT project [17,18]. Several experimental approaches were compared and concluded on reliable values for properties for which the variances observed were quite admissible in view of the uncertainties found for the measures performed. For example, the water vapor adsorption isotherm presented in Figure1 Appl. Sci. 2019, 9, 2359 3 of 12

Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 12 and Table1 is the synthesis of results obtained from three di ﬀerent methods: gravimetric (standard EN ISOgravimetric 12571 [19 (standard]), volumetric, EN ISO and 12571 dynamic. [19]), Tablevolumetric,2 summarizes and dynamic. the main Table hygrothermal 2 summarizes properties the main of thehygrothermal material studied. properties of the material studied.

Figure 1. Mean adsorption isotherm for wood fiber ﬁber insulation.

Table 1. Mass water content as a function of relative humidity expressing sorption–desorption curves Table 1. Mass water content as a function of relative humidity expressing sorption–desorption curves of wood ﬁber insulation at 20 C. of wood fiber insulation at 20 ◦°C.

RH RH(%) (%) 0 0 15 15 22.5 22.5 30 30 43 43 45 45 60 60 66 66 75 75 90 90 93 93 97 97 USorptionUSorption 0.000.00 3.103.10 4.10 4.10 4.88 4.88 6.06 6.06 6.25 6.25 8.08 8.08 9.14 9.14 11.27 11.27 16.70 18.1418.14 20.2620.26

UDesorptionUDesorption 0.000.00 3.603.60 4.74 4.74 5.61 5.61 6.81 6.81 6.99 6.99 8.73 8.73 9.74 9.74 11.79 11.79 17.15 18.5818.58 20.7020.70

UMeanUMean 0.000.00 3.353.35 4.42 4.42 5.25 5.25 6.43 6.43 6.62 6.62 8.40 8.40 9.44 9.44 11.53 11.53 16.92 18.3618.36 20.4820.48 SD SD - - 0.86 0.86 0.86 0.86 0.87 0.87 0.89 0.89 0.89 0.89 0.93 0.93 0.94 0.94 0.96 0.96 0.970.97 0.980.98 0.980.98 RH:RH relative: relative humidity humidity (%) (%) and and 𝑈U:: mass mass waterwater content content (%). (%).SD SD: Standard: Standard Deviation. Deviation

This materialmaterial has has a higha high moisture mois storageture storage capacity capacity with thermal with conductivitythermal conductivity strongly dependent strongly ondependent water content on water and content temperature. and temp Thiserature. can lead This tocan variations lead to variations of 12% in of the 12% hygroscopic in the hygroscopic domain, contrarydomain, tocontrary only slightly to only hygroscopic slightly hygroscopic materials such mate asrials concrete such [20as]. concrete In addition, [20]. this In materialaddition, has this a meanmaterial vapor has resistancea mean vapor coeffi resistancecient of 2.73 coefficient which indicates of 2.73 which that water indicates vapor that crosses water this vapor material crosses easily. this material easily. Table 2. Hygrothermal properties of the wood fiber insulation. Table 2. Hygrothermal properties of the wood fiber insulation. Hygrothermal Property (unit) Value Hygrothermal Property (unit) Value Apparent density (kg/m3) 146 Apparent density (kg/m3) 146 Porosity (%) 90–99 WaterPorosity vapor resistance(%) coefficients (-) 2.73 90–99 Water vapor resistance coefficients (-) 2.73 3 Thermal conductivity (W/(m K)) (38 + 0.28 U + 0.108 T) 10− · · · · Thermal conductivitySpecific heat (W/(m·K)) (J/(kg K)) 1103.1(38+0.28∙𝑈+0.108∙𝑇)∙10+ 11.271 T Specific heat (J/(kg·K)) · 1103.1 +· 11.271 ∙ 𝑇 U: mass water content (%) and T : Temperature (◦C). 𝑈: mass water content (%) and 𝑇: Temperature (°C). These hygrothermal properties are the inputs of our heat and moisture transfer model for which any attemptThese hygrothermal at identification properties is ruled are out the when inputs comparing of our heat the and experimental moisture transfer measures. model for which any attempt at identification is ruled out when comparing the experimental measures. 2.2. Experimental Setup 2.2. Experimental Setup The experimental setup proposed permits studying the behavior of a multilayer wall of 1 m2 underThe diff experimentalerent hygrothermal setup loadingsproposed [ 21permits,22]. It stud is designedying the to behavior provide experimentalof a multilayer observations wall of 1 m in orderunder to:different hygrothermal loadings [21,22]. It is designed to provide experimental observations in order to: Better understand the hygrothermal phenomena involved during the transfer. • • Obtain Better su ffiunderstandcient data the to validate hygrothermal or build phen predictiveomena Heat,involved Air during and Moisture the transfer. transfer models. • • CharacterizeObtain sufficient transport data properties to validate at theor build wall scale.predictive Heat, Air and Moisture transfer • models. • Characterize transport properties at the wall scale.

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Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 12 To achieve this, the wall studied was placed between two compartments with a volume of To achieve this, the wall studied was placed between two compartments with a volume of 0.5 0.5 1 1 m3 whose role was to maintain the desired thermal and moisture loadings (see Figure2). 11× m× whose role was to maintain the desired thermal and moisture loadings (see Figure 2). The The humidity of compartment 1 was regulated using a Saturated Salt Solution (SSS), while its humidity of compartment 1 was regulated using a Saturated Salt Solution (SSS), while its temperature temperature was regulated by fluid–air exchangers linked to a circulation cryostat. Compartment was regulated by fluid–air exchangers linked to a circulation cryostat. Compartment 2 had two 2 had two operating modes with natural and forced convection. The first mode was obtained with operating modes with natural and forced convection. The first mode was obtained with humidity humidity regulation using the SSS and temperature regulation with a climatic chamber in remote mode. regulation using the SSS and temperature regulation with a climatic chamber in remote mode. The The second mode was obtained directly with the climatic chamber that pulsed treated air parallel to second mode was obtained directly with the climatic chamber that pulsed treated air parallel to the the wall studied at a controlled flowrate. Using the SSS for regulation permits measuring the vapor wall studied at a controlled flowrate. Using the SSS for regulation permits measuring the vapor flowrate exchanged between the air in the compartments and the wall, by monitoring the evolution of flowrate exchanged between the air in the compartments and the wall, by monitoring the evolution the mass of SSS as a function of time. Fans were installed to homogenize the temperature and humidity of the mass of SSS as a function of time. Fans were installed to homogenize the temperature and in each compartment. Heating and cooling powers of regulation systems were sufficiently large to humidity in each compartment. Heating and cooling powers of regulation systems were sufficiently quickly reach the desired temperature. The vapour stream obtained by the SSS were limited. The mass large to quickly reach the desired temperature. The vapour stream obtained by the SSS were limited. of the used SSS (both compartments were equipped with an adapted balance) for relative humidity The mass of the used SSS (both compartments were equipped with an adapted balance) for relative control was about 2.5 kg and its exchange surface area was about 0.46 0.3 m2. humidity control was about 2.5 kg and its exchange surface area was about× 0.46 × 0.3 m².

Air exit (to the climatic chamber) Internal parts Salt Solution + balance External parts (mass monitoring)

Tested wall Compartment 1

Compartment 2

Heat exchanger (to thermal bath)

Air entrance Compartment insulation (from climatic chamber) (a) (b)

Figure 2. Experimental test bench: ( (aa)) image; image; ( (bb)) sketch. sketch.

The compartments were were composed of two elements, an internal box and an external box that served asas aa thermal thermal guard. guard. They They were were made made of stainless of stainless steel with steel airtight with airt weldsight controlled welds controlled by penetrant by penetranttesting. Since testing. the two Since compartments the two compartments were regulated were differently, regulated their differently, designs and their compositions designs wereand compositionsdifferent. Compartment were different. 1 simulating Compartment the internal1 simula atmosphereting the internal was atmosphere composed fromwas composed the exterior from to thethe interiorexterior ofto thethe outer interior box, of of the a rigid outer layer box, of of insulation a rigid layer 60-mm of thick;insulation two countercurrent60-mm thick; heattwo countercurrentexchangers (for heat more exchangers homogenous (for more temperature homoge innous the temperature thermal guard) in the linked thermal to a guard) cryostat linked and anto ainternal cryostat box and with an internal a volume box of with0.5 m a3 volumeproviding of 0.5 an exchangem providing surface an exchange of 1 m2 with surface the wallof 1 m studied. with theCompartment wall studied. 2 simulating Compartment the exterior 2 simulating atmosphere the wasexterior composed, atmosphere from the was exterior composed, to the interior,from the of exteriora thin multilayer to the interior, thermo-reflective of a thin multilayer insulation; ther a rigidmo-reflective insulation 80insulation; mm thick; a anrigid external insulation box linked 80 mm to thick;a climatic an external chamber box by insulatedlinked to ventilationa climatic chamber ducts and by the insulated internal ventilation box. ducts and the internal box. Temperature, relative humidity and differential pressure sensors were installed in the two compartmentsTemperature, to continuously relative humidity measure and the differential loading applied pressure to the sensors wall studied. were Thermo-hygrometersinstalled in the two compartmentswere also installed to continuously on the surface measure and at thethe core loading of the applied wall, at ditoff erentthe wall positions, studied. to obtainThermo- the hygrometersresponse of the were wall also to theinstalled loading. on the The surface data were and acquiredat the core every of the minute. wall, at Technical different details positions, for the to obtainwhole datathe response acquisition of the system wall installed,to the loading. calibration The data of the were sensors, acquired installation, every minute. and qualification Technical details of the forexperimental the whole set-up data (airtightness,acquisition system regulation, installed, test protocol) calibration are presentedof the sensors, in [21,22 installation,]. Table3 gives and a qualificationsummary of theof the hygrothermal experimental operating set-up domain(airtightn ofess, the experimentalregulation, test setup protocol) and the are uncertainties presented onin [21,22].both temperature Table 3 gives and a relative summary humidity of the ashygrothermal a function of operating the type ofdomain sensor. of the experimental setup and the uncertainties on both temperature and relative humidity as a function of the type of sensor.

Table 3. Domain and measurement uncertainties.

Measurement Domain Uncertainty

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Table 3. Domain and measurement uncertainties.

Measurement Domain Uncertainty

Temperature (SHT75) 5–45 ◦C 0.17 ◦C Relative humidity (SHT75) 40–90% 2% Temperature (Pt100) 5–45 ◦C 0.15 ◦C Temperature (thermocouples) 5–45 ◦C 0.16 ◦C

2.3. Numerical Model The heat and moisture model developed was based on two conservation equations: energy and moisture (water in liquid and vapor form). The transfer potentials chosen are temperature T and vapor concentration ρv. The model presented is based on the works of Luikov [23] and on works developed more recently available in [24–29]. The general equation describing the transfer of humidity in a porous medium is given by Equation (1), that results from the sum of conservation equations of liquid water and water vapor with diﬀusion and capillarity as transfer phenomena expressed by the laws of Fick and Darcy, respectively: ! ∂ρm dif cap = → →J + →J (1) ∂t −∇· v l

dif cap m → → where ρ is the moisture content, J v is water vapor diffusion flux according to Fick’s law, and J l is liquid flow according to Darcy’s law. For building applications, global air movements are neglected in the case of very low air velocities and low variations of temperature and pressure found in practice [28]. The energy conservation equation (Equation (2)) was obtained from an enthalpy balance by explaining the enthalpies of different phases and elements composing the system. The hypothesis of local equilibrium was chosen with the consequence of equality of temperatures between the different phases and components:

" cap dif! # dif dif ∂T l → v→ → → → → → ρsc∗ + c J + c J T = J L J (2) p ∂t p l p v ·∇ −∇· q − vl∇· v

dif → where T is the temperature, ρs is the dry density, J q is diffusion heat flux according to Fourier’s law, Lvl is the specific latent heat for water and cp is the specific heat capacity. Exponents v, l, and * denote, respectively, vapor, liquid and effective state. Considering the moisture loading in the current study, mainly adsorption not exceeding 88% relative humidity (see Table4), capillary mouvment in the over hygroscopic range and hysterisis were not taken into account.

Table 4. Experimental conﬁgurations studied.

State Variable Interior Air Exterior Air

T(◦C) 19 5 RH (%) 55 88

The coupled heat and moisture transfer model obtained takes the form of a series of partial differential equations (PDE) that govern all the transfers. These non-linear and coupled PDE are resolved simultaneously using the COMSOL Multiphysics software based on the Finite Elements methods. We chose this environment since it can be used for modeling and resolving a wide range of engineering and research problems, mainly problems in PDE form. It is particularly well-adapted to solving Multiphysics problems in which several phenomena are studied simultaneously as in the case Appl. Sci. 2019, 9, 2359 6 of 12 of coupled HAM transfers. The use of such tools is justified because they are capable of solving this type of problem and allow the implementation of reliable and well-defined input data and the choice of meshing. It comprises several solvers adapted to a series of given problems.

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TheThe hygrothermal hygrothermal stresses stresses chosen chosen in the in theframework framework of this of study this study are presented are presented in Table in 4. Table These4. stressesThese stresses are applied are applied using the using setup the presented setup presented previously previously on a single-layer on a single-layer wood woodfiber insulating fiber insulating wall 8wall cm thick. 8 cm thick.A vapor A vapor concentration concentration gradient gradient and a and temperature a temperature gradient gradient are applied are applied on either on either side side of theof thewall. wall. ThisThis choice choice of of stresses stresses followed followed an an initial initial study study on on the the same same wall wall under under a a vapor vapor concentration concentration gradientgradient [22]. [22]. The The previous previous test test consisted consisted in in placing placing a awood wood fiber fiber wall wall between between two two atmospheres atmospheres regulatedregulated at at 20 20 °C◦C and and a a relative relative humidity humidity of of 50% 50% on on one one side side and and 70% 70% on on the the other. other. This This case case study study highlightedhighlighted the the eeffectsffects ofof moisturemoisture transfers transfers on on the the thermal thermal behavior behavior of the of wallthe wall when when the latent the latent effects effectsof heat of transfer heat transfer are dominant. are dominant. Thus, Thus, it was it possible was possible to show to show an increase an increase at the at core the ofcore the of wall the inwall the inregion the region of a degree. of a degree. However, However, this study this under study isothermal under isothermal conditions conditions did not lead did to not fully lead defining to fully the definingbehavior the of behavior the material of the and material validating and the validat modeling developed. the model Followingdeveloped. the Following same line, the the same choice line, of thestresses choice in thisof stresses study provides in this betterstudy understandingprovides better of theunderstanding hygrothermal of transfer the hygrothermal mechanisms involvedtransfer mechanismsand the graduated involved validation and the of graduated the model validation developed. of Indeed, the model the non-isothermaldeveloped. Indeed, case representsthe non- isothermalwinter type case stresses, represents critical winter from the type standpoint stresses, ofcrit moistureical from transfer the standpoint in the wall. of Itmoisture makes it transfer possible in to thetake wall. into It account makes theit possible impact of to the take water into content accoun oft the the impact wall on of its the thermophysical water content properties, of the wall and on thus its thermophysicalof the impact on properties, sensible heat and transfer. thus of the It also impact allowed on sensible evaluating heat thetransfer. contribution It also allowed of latent evaluating transfer in therelation contribution to sensible of latent transfer transfer when in the relation latter isto non-negligible. sensible transfer when the latter is non-negligible. 3. Results and Discussion 3. Results and Discussion The analysis of the hygrothermal behavior of the wood fiber insulation for the different stresses The analysis of the hygrothermal behavior of the wood fiber insulation for the different stresses presented was first done on the basis of the experimental results. The analysis mainly focuses on the presented was first done on the basis of the experimental results. The analysis mainly focuses on the contribution of moisture transfer on thermal transfer in the context of a strongly hygroscopic material. contribution of moisture transfer on thermal transfer in the context of a strongly hygroscopic material. We then compared these experimental results with the numerical results obtained from the model We then compared these experimental results with the numerical results obtained from the model developed. This comparison allowed us to perform a critical analysis on the capacity of the model to developed. This comparison allowed us to perform a critical analysis on the capacity of the model to mirror the behavior of the wall studied. To do this, the wall was subjected to moisture and thermal mirror the behavior of the wall studied. To do this, the wall was subjected to moisture and thermal stress on both sides with a variance in relative humidity of 33% and in temperature of 14 C. The system stress on both sides with a variance in relative humidity of 33% and in temperature ◦of 14 °C. The starts from an initial undisturbed hygrothermal state at 65% relative humidity and a temperature of system starts from an initial undisturbed hygrothermal state at 65% relative humidity and a 23 C. The results are presented for different positions as shown in Figure3. temperature◦ of 23 °C. The results are presented for different positions as shown in Figure 3.

FigureFigure 3. 3. PositioningPositioning of of sensors sensors within within the the wall. wall.

3.1.3.1. Experimental Experimental Analysis Analysis TheThe regulation systemsystem setup setup provides provides very very stable stable boundary boundary conditions conditions with a standardwith a standard deviation deviationover the lastover 150 the h last not 150 exceeding hours not 0.75% exceeding in relative 0.75 humidity% in relative and humidity 0.14 ◦C in and temperature 0.14 °C in temperature (cf. Figure4). (cf.The Figure peaks 4). noticed The peaks correspond noticed to correspond disturbance to linkeddisturbance to the linked regeneration to the regeneration of the saturated of the salt saturated solution. salt solution.

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FigureFigureFigure 4. 4.4. Evolution EvolutionEvolution of ofof temperature temperaturetemperature and andand relative relativerelative humidity humidityhumidity at atat the thethe edges edgesedges of ofof thethethe wall.wall.wall.

TheseTheseThese stresses stressesstresses induce induceinduce a aa thermal thermalthermal and andand moisture moisturemoisture resp responserespresponseonseonse from fromfrom the thethe envelope, envelope,envelope, as asas shown shown shown in in in Figure Figure Figure 55. 5.5.. RegardingRegardingRegarding the thethe thermal thermalthermal behavior, behavior,behavior, wewewe observeobserveobserve thethethe developmentdevelopmentdevelopment of ofof aaa thermalthermalthermal gradientgradientgradient leadingleadingleading to toto ananan averageaverageaverage heat heatheatheat flux fluxfluxflux of ofofof5.8 5.8 5.85.8W W WWcalculated calculated calculatedcalculated over overoverover the thethethe last lastlastlast 50 50 h5050 of hourshourshours the test. ofofof thethe Thisthe test.test.test. flux ThisThisThis was fluxflux obtainedflux waswaswas obtainedfromobtainedobtained measures fromfromfrom measuresperformedmeasuresmeasures performed performedperformed with a flux with withwith meter a aa flux fluxflux installed meter metermeter on installed installedinstalled the surface on onon the thethe of surface thesurfacesurface wall. of ofof the thethe wall. wall.wall.

Figure 5. Evolution of temperature and relative humidity at diﬀerent depths of the wall. FigureFigureFigure 5. 5.5. Evolution EvolutionEvolution of ofof temperature temperaturetemperature and andand relative relativerelative humidity humidityhumidity at atat different differentdifferent depths depthsdepths of ofof the thethe wall. wall.wall.

TheThe concentration concentration of of water water vapor vapor in in the the airair occludingooccludingccluding the the porespores (Figure(Figure6 6),),6), calculated calculatedcalculated from fromfrom The concentration of water vapor in the air occluding the pores (Figure 6), calculated3 from temperature and relative humidity measures, evolves from an undisturbed state at 13.4 g/mto the temperaturetemperaturetemperature andandand relativerelativerelative humidityhumidityhumidity measures,measures,measures, evolvesevolvesevolves fromfromfrom ananan undisturbedundisturbedundisturbed statestatestate atatat 13.4 13.413.4 g/m g/mg/m to toto thethethe development of a vapor concentration gradient in steady state. This gradient induces a ﬂux of vapor developmentdevelopmentdevelopment of ofof a aa vapor vaporvapor concentration concentrationconcentration gradient gradientgradient in inin steady steadysteady state. state.state. This ThisThis gradient gradientgradient induces inducesinduces a aa flux fluxflux of ofof vapor vaporvapor through the inner side of the wall (55%, 19 ◦C) to the outer one (88%, 5 ◦C). throughthroughthrough the thethe inner innerinner side sideside of ofof the thethe wall wallwall (55%, (55%,(55%, 19 1919 °C) °C)°C) to toto the thethe outer outerouter one oneone (88%, (88%,(88%, 5 55 °C). °C).°C).

Figure 6. Evolution of the water vapor concentration at different depths of the wall. FigureFigureFigure 6. 6.6. Evolution EvolutionEvolution of ofof the thethe water waterwater vapor vaporvapor concentration concentrationconcentration at atat different differentdifferent depths depthsdepths of ofof the thethe wall. wall.wall. Under the assumption of local equilibrium, the analysis of the relative humidity profile and the UnderUnder the the assumption assumption of of local local equilibrium, equilibrium, the the an analysisalysis of of the the relative relative humidity humidity profile profile and and the the waterUnder vapor the sorption assumption isotherm of permitslocal equilibrium, tracking back the toan thealysis water of the content relative profile humidity illustrated profile in Figureand the7. waterwater vapor vapor sorption sorption isotherm isotherm permits permits tracking tracking back back to to the the water water content content profile profile illustrated illustrated in in Figure Figure Itwater shows vapor the redistributionsorption isotherm of water permits in the tracking wall in back which to the water water shifts content from theprofile inner illustrated side of the in wallFigure to 7.7. It It shows shows the the redistribution redistribution of of water water in in the the wall wall in in which which water water shifts shifts from from the the inner inner side side of of the the wall wall the7. It outershows side. the redistribution Air looping from of water hot to in coldthe wall box in under which the water presented shifts thermalfrom the boundaryinner side conditionsof the wall toto the the outer outer side. side. Air Air looping looping from from hot hot to to cold cold bo boxx under under the the presented presented thermal thermal boundary boundary conditions conditions cannotto the outer occur side. due Air to thelooping low hightfrom hot of theto cold wall bo (1x m).under Given the presented the amount thermal of water boundary involved conditions and the cannotcannotcannot occuroccuroccur dueduedue tototo thethethe lowlowlow highthighthight ofofof thethethe wallwallwall (1(1(1 m).m).m). GivenGivenGiven thethethe amountamountamount ofofof waterwaterwater involvedinvolvedinvolved andandand thethethe directiondirectiondirection ofofof thethethe vaporvaporvapor fluxfluxflux (from(from(from thethethe internalinternalinternal sidesideside tototo thethethe externalexternalexternal side),side),side), ititit cancancan bebebe deduceddeduceddeduced thatthatthat thisthisthis

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Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 12 direction of the vapor ﬂux (from the internal side to the external side), it can be deduced that this shiftshift isis duedue toto thethe migrationmigration ofof waterwater inin liquidliquid andand vaporvapor formform fromfrom layerslayers locatedlocated inin thethe internalinternal sideside towardstowards thosethose locatedlocated inin thethe externalexternal side.side.

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shift is due to the migration of water in liquid and vapor form from layers located in the internal side towards those located in the external side.

FigureFigure 7. 7.ProfileProfile of of water water content content in in the the wall wall after after 1 1hour, h, 1 day,1 day, and and 1 week.1 week. 3.2. Comparison of Experimental Results with Numerical Codes 3.2. Comparison of Experimental Results with Numerical Codes We proceed in this part with the comparison of the results obtained using the experimental test We proceed in this part with the comparison of the results obtained using the experimental test bench under non-isothermal conditions and the results obtained from the numerical simulation of the bench under non-isothermal conditions and the results obtained from the numerical simulation of model developed. The boundary conditions chosen for the simulation were of Dirichlet type and were the model developed. The boundary conditions chosen for the simulation were of Dirichlet type and measured on the surface. were measured on the surface. Figure8 represents the comparison of numerical and experimental results of the evolution of Figure 7. Profile of water content in the wall after 1 hour, 1 day, and 1 week. temperature, relative humidity, and vapor concentration as a function of time for different positions. As3.2. we Comparison observed of in Experimental the isothermal Results case with [22 Numerical], the model Codes shows it can reproduce the experimental observation well. The largest variances were observed during the start-up phase. We proceed in this part with the comparison of the results obtained using the experimental test The temperature absolute deviation does not exceed 0.5 C which is quite acceptable. The deviations bench under non-isothermal conditions and the results obtained◦ from the numerical simulation of observed for relative humidity and for vapor concentration are more marked during the first hours the model developed. The boundary conditions chosen for the simulation were of Dirichlet type and and then fall until reaching a value lower than 2% after 25 h. were measured on the surface.

Figure 8. Comparison of measures: the model for temperature, relative humidity, and water vapor concentration at different positions in the wall.

Figure 8 represents the comparison of numerical and experimental results of the evolution of temperature, relative humidity, and vapor concentration as a function of time for different positions. As we observed in the isothermal case [22], the model shows it can reproduce the experimental observationFigureFigure 8. well. 8.Comparison Comparison The largest of of measures: measures: variances thethe were modelmodel observed for temper temperature, duringature, relativethe relative start-up humidity, humidity, phase. and and water water vapor vapor concentrationTheconcentration temperature at at di differentff erentabsolute positions positions deviation in in the the wall. wall.does not exceed 0.5 °C which is quite acceptable. The deviations observed for relative humidity and for vapor concentration are more marked during the first RegardinghoursFigure and 8 thenrepresents the heatfall until flux the (Figurereachingcomparison9), a wevalue of observednumerica lower thanl good and 2% experimental correlation after 25 h. between results of the the numerical evolution andof experimentaltemperature, results relative with humidity, a correlation and vapor coe fficoncentratiocient equaln as to a 0.9. function The dispersion of time for observeddifferent positions. is partially As we observed in the isothermal case [22], the model shows it can reproduce the experimental observation well. The largest variances were observed during the start-up phase. The temperature absolute deviation does not exceed 0.5 °C which is quite acceptable. The deviations observed for relative humidity and for vapor concentration are more marked during the first hours and then fall until reaching a value lower than 2% after 25 h.

Appl. Sci. 2019, 9, 2359 9 of 12

Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 12 attributed to the tightness of the ﬂux meter to water vapor. This can disturb hygrothermal behavior locally which is not taken into account by the numerical model. The straight line of the linear regression does not go through the origin. This would be due to a systematic measurement error on the thermal ﬂux. Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 12

Figure 9. Comparison of heat flux from the fully coupled Heat and Moisture transfer model (HM) with the experimental heat flux.

Regarding the heat flux (Figure 9), we observed good correlation between the numerical and experimental results with a correlation coefficient equal to 0.9. The dispersion observed is partially attributed to the tightness of the flux meter to water vapor. This can disturb hygrothermal behavior Figure 9. Comparison of heat flux from the fully coupled Heat and Moisture transfer model (HM) with locallyFigure which 9. Comparison is not taken of heat into flux account from theby fullythe numericalcoupled H eatmodel. and MTheoisture straight transfer line model of the (HM linear) the experimental heat flux. regressionwith the experimentaldoes not go throughheat flux. the origin. This would be due to a systematic measurement error on the thermal flux. IfRegarding we analyze the temperature heat flux (Figure evolution 9), we in time observ at diedff erentgood positionscorrelation (Figure between5), then the itnumerical is di fficult and to assess theIf we contribution analyze temperature of heat di evolutionffusion and in time latent ate differentffects since positions these two(Figure physical 5), then phenomena it is difficult are experimentalto assess the results contribution with a of correlati heat diffusionon coefficient and latent equal effects to 0.9.since The these dispersion two physical observed phenomena is partially are concomitant. In order to quantify them and to highlight the latent effects on the total heat transfer, attributedconcomitant. to the In tightness order to ofquantify the flux them meter and to to wa highterlight vapor. the This latent can effects distur onb thehygrothermal total heat transfer, behavior we compared the experimental temperature measures with values obtained by different numerical locallywe compared which is the not experimental taken into temperatureaccount by themeasures numerical with valuesmodel. obtained The straight by different line of numerical the linear transfer models (see Figure 10). The first is a “non-linear Heat transfer model, purely Diffusive” named regressiontransfer modelsdoes not (see go throughFigure 10). the The origin. first Thisis a wo“non-linearuld be due Heat to atransfer systemat model,ic measurement purely Diffusive” error on HD where the thermal conductivity of the wall is a function of the water content and the second is the thenamed thermal HD flux. where the thermal conductivity of the wall is a function of the water content and the “fullysecondIf coupled we is analyze theH “fullyeat temperature and coupledMoisture H eatevolution transfer and Moisture model”in time transfer presentedat different model” in positions this presented article (Figure calledin this 5),HM article then. The called it deviationsis difficult HM. representto assessThe deviations the the contribution difference represent in of temperaturethe heat difference diffusion between in andtemp laerature thetent measurement effects between since the these and measurement the two model. physical and phenomenathe model. are concomitant. In order to quantify them and to highlight the latent effects on the total heat transfer, we compared the experimental temperature measures with values obtained by different numerical transfer models (see Figure 10). The first is a “non-linear Heat transfer model, purely Diffusive” named HD where the thermal conductivity of the wall is a function of the water content and the second is the “fully coupled Heat and Moisture transfer model” presented in this article called HM. The deviations represent the difference in temperature between the measurement and the model.

FigureFigure 10. 10.Comparison Comparison of of measures:measures: models for for different diﬀerent positions. positions.

DuringDuring the the first first hours, hours, it it can can be be seen seen thatthat inin reality, in comparison comparison to to the the purely purely diffusive diffusive model, model, thethe wall wall cooled cooled throughout throughout its its thickness, thickness, then then warmed warmed with with maximum maximum amplitudes amplitudes varying varying from from 1.5 1.5◦ C in the°C in cooling the cooling phase phase to 0.5 to◦C 0.5 in °C the in warming the warming phase. phas Thise. This dynamic dynamic is attributed is attributed to release to release of water of water from thefrom wall the (evaporation) wall (evaporation) then water then storagewater storage (condensation) (condensation) (see Figure(see Figure 11). 11). The The fall fall in temperature in temperature was morewas marked more marked at 4 cm fromat 4 cm the from inner the edge inner where edge the where withdrawal the withdrawal is highest. is These highest. results These corroborate results thosecorroborate obtained those in the obtainedFigure case of10. in theComparison the isotherm case of ofthe where measures: isothe anrm increase models where foran of increasedifferent temperature ofpositions. temperature in the region in the of region degrees wasof observed, degrees was attributed observed, to theattributed adsorption to the of adsorption water vapor of [22water]. We vapor also observed[22]. We also that, observed contrary that, to the purelycontraryDuring diffusive to the the model,first purely hours, the diffusive hygrothermalit can bemodel, seen that onethe hygrin succeeded reality,othermal in in comparison capturingone succeeded the to the transferin purelycapturing dynamics. diffusive the transfer model, thedynamics. wall cooled throughout its thickness, then warmed with maximum amplitudes varying from 1.5 °C in the cooling phase to 0.5 °C in the warming phase. This dynamic is attributed to release of water from the wall (evaporation) then water storage (condensation) (see Figure 11). The fall in temperature was more marked at 4 cm from the inner edge where the withdrawal is highest. These results corroborate those obtained in the case of the isotherm where an increase of temperature in the region of degrees was observed, attributed to the adsorption of water vapor [22]. We also observed that, contrary to the purely diffusive model, the hygrothermal one succeeded in capturing the transfer dynamics.

Appl. Sci. 2019, 9, 2359 10 of 12 Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 12

Figure 11. Evolution of of water content calculated from the experimental data and the water vapor adsorption isotherm of the wood ﬁberfiber insulating material.material.

4. Conclusions Heat andand massmass transfers transfers in in highly highly hygroscopic hygroscopic materials materials are are coupled coupled with with an impactan impact on global on global heat fluxes.heat fluxes. This studyThis study performed performed showed showed these couplings these couplings experimentally experimentally and numerically and numerically for an insulating for an woodinsulating fiber wood material fiber under material non-isotherm under non-isothe conditions.rm We conditions. were able toWe highlight were able the followingto highlight points: the followingThe redistribution points: of water which took place as the heat gradient developed. The water migrated • •from The the redistribution warmest side of to water the coolest which side. took place as the heat gradient developed. The water Themigrated model from developed the warmest proved side e toffi cientthe coolest at reproducing side. hygrothermal behavior under • •non-isothermal The model developed stresses. proved efficient at reproducing hygrothermal behavior under non- Theisothermal variances betweenstresses. the measures—model were greater during the start-up phase. • •The The latent variances effects could between be detected the measures—model and highlighted we experimentallyre greater during and numerically the start-up by phase. comparison • •with The the latent purely effects diffusive could heat be model.detected and highlighted experimentally and numerically by comparison with the purely diffusive heat model. The next step to obtaining better understanding of the behavior of wood fiber insulating material The next step to obtaining better understanding of the behavior of wood fiber insulating material will consider the response of walls subject to dynamic stresses that include the effects of thermal and will consider the response of walls subject to dynamic stresses that include the effects of thermal and moisture inertia, in order to determine whether the variances between the measures and the model moisture inertia, in order to determine whether the variances between the measures and the model observed in the non-isotherm case propagate and increase. observed in the non-isotherm case propagate and increase.

Author Contributions: Conceptualization, methodology and and validation validation,, Z.S., Z.S., A.T. A.T. and J.V.; software, Z.S. and A.T.; formalformal analysisanalysis and and investigation, investigation, Z.S., Z.S., A.T., A.T., J.V. J.V. and and R.Z.F.; R.Z.F.; writing—original writing—original draft dr preparation,aft preparation, Z.S., Z.S., A.T. A.T. and J.V.; writing—review and editing, Z.S., A.T., J.V. and R.Z.F.; supervision and project administration, A.T. and J.V. and J.V.; writing—review and editing, Z.S., A.T., J.V. and R.Z.F.; supervision and project administration, A.T. Funding:and J.V. This research was funded by the Agence Nationale de Recherche (ANR), project HYGRO-BAT, ANR-10-HABISOL-005-01 and the Région Auvergne-Rhône-Alpes. Funding: This research was funded by the Agence Nationale de Recherche (ANR), project HYGRO-BAT, ANR- Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the study;10-HABISOL-005-01 in the collection, and analyses, the Région or interpretationAuvergne-Rhône-Alpes. of data; in the writing of the manuscript, or in the decision to publishConflicts the of results. Interest: The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to Referencespublish the results. 1. ADEME. Les Chiffres clés du Bâtiment Énergie—Environnement; ADEME: France, 2013. References 2. Décret n◦ 2010-1269 du 26 Octobre 2010 Relatif aux Caractéristiques Thermiques et à la Performance 1. ADEME.Énergétique Les desChiffres Constructions. clés du Bâtiment France. Énergie—Environnement 2010. ; ADEME: France, 2013. 3.2. DécretKuenzel, n° H.M.; 2010-1269 Holm, du A.; 26 Sedlbauer, Octobre K.;2010 Antretter, Relatif F.;aux Ellinger, Caractéristiques M. Moisture Thermiques Buffering E ffetect à of la Interior Performance Linings ÉnergétiqueMade from Wood des orConstructions. Wood Based Products France,; IBP2010. Report HTB-04/2004/e; Fraunhofer Institute of Building Physics: 3. Kuenzel,Holzkirchen, H.M.; Germany, Holm, A.; 2004. Sedlbauer, K.; Antretter, F.;Ellinger, M. Moisture Buffering Effect of Interior Linings 4. MadeRode, from C.; Mendes,Wood or Wood N.; Grau, Based K. ProductsEvaluation; IBP of Report Moisture HTB-04/2004/e; Buffer Effects byFraunhofe Performingr Institute Whole-Building of Building Simulations Physics:; ASHRAEHolzkirchen, Transactions: Germany, Nashville,2004. TN, USA, 2004; pp. 783–794. 5.4. Rode,Hameury, C.; Mendes, S. Moisture N.; Grau, buffering K. Evaluation capacity ofof Moisture heavy timber Buffer structures Effects by Performing directly exposed Whole-Building to an indoor Simulations climate:; AASHRAE numerical Transactions: study. Build. Nashv Environ.ille, TN,2005 USA,, 40, 1400–1412. 2004; pp. 783–794. [CrossRef ] 5. Hameury, S. Moisture buffering capacity of heavy timber structures directly exposed to an indoor climate: A numerical study. Build. Environ. 2005, 40, 1400–1412.

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