Moisture buffering capacity of heavy timber structures directly exposed to an indoor climate: a numerical study

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1 Building and Environment 4 (25) Moisture buffering capacity of heavy timber structures directly exposed to an indoor climate: a numerical study Stéphane Hameury Department of Civil and Architectural Engineering, Division of Building Materials, KTH The Royal Institute of Technology, SE-1 44 Stockholm, Sweden Received 23 September 24; received in revised form 14 October 24; accepted 18 October 24 Abstract This paper introduces a hygrothermal model accounting for the moisture and heat transport in a massive wood envelope directly exposed to an indoor climate. A better knowledge of the passive interaction between an indoor climate and a heavy timber structure could lead to presenting an alternative to high air exchange rate, and to increasing the thermal comfort of the inhabitants. So far, the model is developed as a stand-alone application with a finite difference method, and is written in a Neutral Model Format, enabling a later implementation in a modular environment for indoor climate energy calculations, called IDA ICE. A numerical simulation is provided to depict the buffering capacity of a massive timber structure as a function of the air exchange rate and the effective wood wall area. r 24 Elsevier Ltd. All rights reserved. Keywords: Massive wood wall; Moisture transport; Heat transport; Indoor climate; Moisture buffering capacity 1. Introduction The emergence of massive wood layers in floor and wall components presents a rather new significant alternative in the market of building materials for medium-rise timber constructions in Sweden. This emergence is in its beginning and one has to be cautious during its development phase to avoid severe defects in the product. Indeed, the building industry has to deal more and more with energy efficiency and healthy indoor air climate and a massive wood building does not waive this principle. The significance of indoor climate to the health of the inhabitants has become evident and much more attention is nowadays paid to improving the indoor air quality. A literature survey shows that humans are best suited to and feel most comfortable at certain humidity and temperatures [1 3]. Therefore, there is a growing interest nowadays in exploiting the moisture and heat buffering effect of building materials address: stephane.hameury@byv.kth.se (S. Hameury). as a passive system to dampen the indoor fluctuations of humidity and temperature. The moisture buffering capacity is investigated further in this paper even though it is recalled that the model is also valid for studies on the heat buffering capacity of massive wood walls. The concept of moisture buffering capacity may be regarded as the ability of hygroscopic materials such as wood to moderate the daily or seasonal humidity variations of the indoor environment [4] and even the ability to moderate a sudden step change of an indoor moisture level. The accumulation of moisture in a wood wall with large surface area directly exposed to the indoor climate and without any particular coatings is thought to present an effective moisture capacity important enough to interact with the indoor climate, especially in a dwelling house where the ventilation rate is often less important than in an office building. In comparison with other building materials, wood has a low heat conductivity which prevents the heat from penetrating into the structure but also infers a limiting factor for heat storage purposes. However, since wood is a hygroscopic /$ - see front matter r 24 Elsevier Ltd. All rights reserved. doi:1.116/j.buildenv

2 S. Hameury / Building and Environment 4 (25) Nomenclature A surface (m 2 ) c p wood specific heat capacity (J kg 1 K 1 ) c pa air specific heat capacity (J kg 1 K 1 ) D t wood transverse moisture diffusion coefficient (m 2 s 1 ) G wall moisture flow via the wall surfaces (kg s 1 ) G ventilation moisture flow via the ventilation (kg s 1 ) G source moisture flow from indoor sources (kg s 1 ) G m wood specific gravity (kg kg 1 ) H m latent heat of moisture in wood (J kg 1 ) H v latent heat of evaporation (J kg 1 ) h T heat convection coefficient (W m 2 K 1 ) h v mass convection coefficient (m s 1 ) n ventilation rate (h 1 ) NMF neutral model format p wood porosity P s saturated vapour pressure (Pa) R universal gas constant r buffering effect ratio S surface emission factor T temperature (K) T i indoor temperature (K) T o outdoor temperature (K) T s surface temperature (K) u wood moisture content (kg kg 1 ) u eq equivalent indoor moisture content (kg kg 1 ) u initial wood moisture content (kg kg 1 ) u s surface wood moisture content (kg kg 1 ) V volume (m 3 ) v i indoor water vapour concentration (kg m 3 ) v o outdoor water vapour concentration (kg m 3 ) Greek letters DH s differential heat of sorption in wood (J kg 1 ) l wood heat conductivity (W m 1 K 1 ) r wood density (kg m 3 ) r a air density (kg m 3 ) r o oven-dried wood density (kg m 3 ) r w water density (kg m 3 ) j relative humidity (%) material, it has the capacity to pump, store and release moisture to the surroundings. The moisture captured in the material thus contributes to increase the basic heat storage capacity of dry wood. In regards to that, wood can be considered as a good compromise between insulation, heat storage and energy efficiency purposes [5]. This interesting issue has been the starting point to make use of the wood ability as an insulating and buffering material. An attempt has been made to directly measure the moisture and heat buffering capacity of a massive wood envelope at the Vetenskapsstaden building in Stockholm, Sweden [5 7]. Numerous researches have focused on the dynamical behaviour of such heavy timber constructions taking into consideration the thermal mass behaviour of the structure [8,9]. It has already been pointed out that further research should now focus on the relationship between heat and moisture response of massive wood buildings exposed to an indoor environment [9] and a literature survey shows experimental and numerical attempts to determine the moisture performances of building materials exposed to an indoor climate [1 12]. The hygrothermal behaviour of the building in a dynamical perspective is thus an important issue in the development of sustainable massive wood building. The hygrothermal performances of a building envelope may be characterised by defining and quantifying the effective heat and moisture storage capacity of a massive wood wall under real conditions to assess the impact on the thermal comfort of such structures exposed to an indoor climate, as well as the energy recovering possibilities. The effect of the moisture transport in a porous medium on the heat flowing through it, has already been shown to be of importance [13]. It has been pointed out in [13], that a model which ignores moisture, gives rise to an overestimation of the heat conduction peaks load and an underestimation of the yearly heat fluxthrough the structures. One of the main tasks for this project is therefore to consider the interaction between wood, heat and moisture in various forms since building envelopes are normally subjected to both thermal and moisture variations. To determine accurately the heat flow between an envelope and its surrounding, requires a simultaneous calculation of both sensible and latent heat. Furthermore, thermal comfort studies in indoor spaces imply taking into consideration the temperature fluctuations as well as the relative humidity fluctuations. In addition, the thermal and hygroscopic behaviour of a building component are closely interrelated. An increase in moisture content favours heat losses, and inversely, the thermal situation affects the moisture transport. Therefore, both processes have to be investigated together in their reciprocal interdependence. A theoretical basis for modelling the coupled transport phenomena in porous media was developed in the late 195s with the work of De Vries et al. [14], and later Luikov [15]. Models to calculate the combined heat and moisture transport through a porous medium by two governing partial differential equations using the moisture content and the temperature as driving potentials were presented. The transport coefficients in these models are nonlinear functions of the driving potentials.

3 142 ARTICLE IN PRESS S. Hameury / Building and Environment 4 (25) At this time, it was hardly possible to solve the equations and predict the hygrothermal performance of building materials and structures for practical situations. Nowadays, new modular simulation environments like IDA-Indoor Climate and Energy, called IDA ICE 3. [16], allow a high flexibility in the use of numerical tools. Attempt to predict the indoor temperature and humidity conditions in a whole building perspective, taking into account the hygrothermal interaction between the indoor climate and the building envelope is a real challenge, which has shown an appreciable increase of interest among the building research society [4,17] and the building practitioners in the building industry. In this paper, the modelling of the hygrothermal performance of a massive wood structure directly exposed to an indoor climate is investigated to enable further studies on a whole massive wood building configuration. This paper presents the basis of the modelling of a massive wood wall in the IDA modular simulation environment. Numerous work on wood material and mechanism of moisture transport in wood has been covered by Siau [18]. The governing equations for heat and moisture transfer, specific to wood are adapted from [18,19], and have been incorporated in the numerical model developed in this project. A first part of this paper briefly describes the simulation environment IDA, which has been chosen for the modelling, as well as the reasons which have governed this choice. A second step briefly depicts the governing equations for moisture and heat transport in wood. A third step exposes the determination and validation of the wood properties emphasising its latent heat of sorption. Indeed, the input data in the numerical investigations reveal to be of first importance for the accuracy of the results. The last section of the present paper presents a numerical investigation of the moisture buffering capacity of a massive wood wall, making use of the model as a stand-alone application. 2. Method 2.1. Modular simulation environment IDA Heat and moisture transfer studies for a massive wood envelope, in order to predict the indoor climate and energy consumption, is made possible by numerical modelling against the time-consuming field experiments. Numerous simulation tools of heat and moisture transfer are already commercially available. To only cite a few, 1D-HAM is a basic simulation tool developed jointly between the Chalmers University of Technology in Gothenburg, Sweden and the Building Technology Group, Massachusetts Institute of Technology in Cambridge, USA. The transient simulation program MATCH has been developed at the Thermal Insulation Laboratory of the Technical University of Denmark, and the more advanced WUFI simulation tool has been developed at the Fraunhofer Institute for Building Physics in Holzkirchen, Germany. These hygrothermal programs have been compared in [2]. They all differed in the heat and moisture transfer equations used to describe the hygrothermal state of the building envelopes and they also handle the material properties differently. Furthermore, 1D-HAM does not take into account the variability of the material properties, which is a drawback when the boundary conditions fluctuate a lot in magnitude during the simulation time. Recently, new simulation tools have been released in the market with a modular environment enabling to add its own sub-model. Along this project, the modular simulation environment IDA previously developed for indoor climate and energy calculations has been used. It has been developed by the division of Building Service Engineering at the Royal Institute of Technology, Stockholm, and the ITM Swedish Institute of Applied Mathematics. The environment is divided into three distinctive parts to allow better flexibility. The core of IDA is the differential-algebraic solver based on implicit integration methods with a variable time step, controlled by error estimation. The time step can vary from seconds up to hours depending on the fluctuations in the system. This enables to optimise the time running of the simulation without losing the accuracy. The modelling is conducted in the IDA environment through a Neutral Model Format (NMF), which is a toolindependent modelling language. The NMF language describes models in a simple way and then translates them into a FORTRAN code to be readable by the solver. A complete description of the NMF can be found in the NMF handbook [21]. This format enables researchers to develop compatible models for a specific problem and changes in the models can be easily done. This gives also the opportunity to build models compatible with the IDA Indoor Climate and Energy environment, a particular application of IDA, and to implement it into a whole building system for further simulations. The third part of IDA is the model where new systems can be graphically created before simulation. It is the front-end of the IDA simulation environment. Simulation tools as IDA ICE offer a possibility for long-term performances assessments of massive wood envelopes. A one-dimensional approach of heat and mass transfer through massive wood wall component can be successfully used since heat and moisture flows can be described with sufficient accuracy. However, the actual wall model implemented in IDA ICE only takes into account the thermal mass and not its hygroscopic ability. Particularly, making use of massive wood structures, this ability is thought to be of consequence

4 S. Hameury / Building and Environment 4 (25) on the global response of the structure with the surroundings. It has been one of the reasons which have stimulated the development of a new specific wall model in IDA ICE for the application of massive wood structures. This model incorporates the moisture diffusion process through a wood structure, as well as the latent heat of moisture. The parameters of the wood material are also optimised with the concern for better accuracy in the results. The numerical model developed in this paper is built up from a finite difference solution method. The massive wood structure is divided into finite control volume, where the space discretization is based upon a two-way expansion scheme and the first cell at the inner wood surface is fixed at 1 mm The governing equations The heat and mass transfer equations governing the transport process are briefly described in this section. The temperature T and moisture content u have been chosen, respectively, as heat and moisture transport potentials. The choice in moisture content as a moisture transport potential has been considered, even though the model encounters some difficulties of discontinuities at the boundary conditions. This choice was made since moisture content is the most commonly employed moisture potential in the wood material science to characterise the moisture state of wood. The governing Eq. (1) for heat transfer through a massive wood layer is assumed to follow the second law of Fourier and the latent heat of moisture is introduced as well: rc p qt qt ¼ q qx l qt qx þ qu qt r wg m H m ; (1) where x is the distance along the direction flow (m), t is the time (s), r is the wood density (kg m 3 ) function of the moisture content u, c p is the specific heat capacity of wood (J kg 1 K 1 ) function of temperature and moisture content u (kg kg 1 ), T is the Kelvin temperature, l the wood thermal conductivity (W m 1 K 1 ) expressed as a function of temperature and moisture content u, r w is the water density (kg m 3 ), G m, is the wood specific gravity (kg kg 1 ), and H m is the latent heat of moisture in wood (J kg 1 ). The specific gravity of wood, G m is by definition the ratio of the oven-dry mass of wood to the mass of water displaced by the bulk specimen at a given moisture content u [19]. The local moisture content u in the wood material is expressed as the weight of water present in the wood divided by the weight of oven-dry wood substance. The complication for describing moisture movement and penetration pattern in porous media, stems among other from the non linearity of the moisture diffusion process. Indeed, the most significant moisture transport for our purpose, and supposing no extreme situations with capillary water transport, is known as a diffusion transport including water vapour diffusion and boundwater diffusion in wood. The moisture diffusion process resulting from the random motion of water molecules may be described on a macroscopic scale assuming a Fickian approach, which stipulates that moisture flows under the influence of its spatial gradient. It will be recalled latter that there are some evidences which show that wood material does not strictly follow the Fickian model, especially at high relative humidity. In a Fickian approach, the modelling is based on the Fick s equation for the moisture flow, the sorption isotherm for the moisture content and the mass conservation equation. The diffusion coefficient in the moisture flow equation depends on the moisture state and the temperature. The governing equation for unsteady-state isothermal moisture transfer through a massive wood wall is given as the Fick s second law (2) in one dimension qu D tðt; uþ qu ; (2) qx where D t depicts the transverse wood moisture diffusion coefficient (m 2 s 1 ) based on the moisture concentration in wood. The moisture transport equation through the massive wood wall structure is not extensively described in this paper but the reader is referred to [18,19] for further information. To close the moisture transfer system of equations, the phase equilibrium equation for wood material has to be given. Moisture in wood can be identified in three basic forms, i.e. as bound or hygroscopic water held in the cell walls, as free or capillary water held in the cell cavities, and as water vapour in the cell cavities and in the pit chambers. Bound-water is hydrogen bonded to the hydroxyl group of amorphous cellulose, hemicelluloses and to a lesser extent lignin. Moisture properties of wood in use, i.e. after drying, are estimated in the hygroscopic moisture range, that is, under the fibre saturation point u f. The term fibre saturation point of wood was originally coined by Tiemann [22] and is defined as the moisture content of the wood at which no free liquid water appears in the lumen and the cell wall is saturated with bound water. Equilibrium in moisture content is reached when wood neither gains nor loses moisture from the surrounding atmosphere. It is a function of both relative humidity and to some extent temperature. The Hailwood Horrobin theory [23] has been adopted here as a first approximation of the sorption isotherm curve of wood material with the coefficient given by Simpson [24]. Eq. (3) states the relationship between the moisture content u in wood at a given temperature and relative humidity. It fits the sorption isotherm curve of most wood materials. u ¼ 18 W K 1 K 2 j 1 þ K 1 K 2 j þ K 2 j ; (3) 1 K 2 j

5 144 ARTICLE IN PRESS S. Hameury / Building and Environment 4 (25) Moisture Content [%] where j is the relative humidity (%). W, K 1 and K 2 are function of the temperature u (1C): W ¼ 223:4 þ :6942u þ :1853u 2 ; K 1 ¼ 4:737 þ :4773u :512u 2 ; K 2 ¼ :759 þ :1695u :5638u 2 : Generally speaking, there is a phenomenon of sorption hysteresis between the adsorption and the desorption curves. Therefore the Hailwood Horrobin equation only presents an average of the isotherm sorption curve, as can be seen in Fig. 1. The hysteresis effect has not been taken into account in the first step of the modelling Wood properties Equilibrium Moisture Content 1ºC 2ºC 3ºC 4ºC 5ºC Fig. 1. Equilibrium moisture content of wood at various temperatures versus the relative humidity. Another point to be carefully evaluated is the material properties of wood, which are introduced in the model as fixed parameters or variables. These values are crucial to provide reliable results without losing accuracy. The wood species retained during the analyses has been Scots pine (Pinus sylvestris), since it is the most common species provided in a massive wood wall in Sweden. The material properties have to be chosen in a way to limit the uncertainties in the input data. It has been pointed out in a previous work on the effective thermal capacity of massive wood structures [8] that the values of the wood properties given by the Swedish building code has to be taken cautiously. Since the code focuses on steadystate heat-loss calculations through the building envelopes, the material properties, like the wood properties, are estimated in a safety way, preferring for instance a higher thermal conductivity value rather than a more true value. The Swedish Building Code values leads thus to an over-estimation of the calculated effective heat capacity under dynamical processes. Moreover, a literature survey presents deviations in the values for the wood properties [18-19,25 29]. The moisture content has a large impact for instance on the moisture diffusion coefficient and the specific heat capacity. Both properties increase with moisture content, and tend to raise the effective heat and moisture capacity. It is, however, pointed out in [19] that the temperature effect on both thermal conductivity and specific heat capacity of wood are essentially equal so that they counterbalance each other in the heat balance differential Eq. (1). So far, it has been decided to fixthe wood thermal conductivity coefficient to the constant.11w m 1 K 1, since the moisture dependence is not so critical. Furthermore, the wood-specific heat capacity c p is expressed in (4) and valid between.5 and.24 kg kg 1 moisture content u [19]: 1176 þ 5859u 83:7 c p ðuþ ¼ : (4) 1 þ u The limitation seems acceptable since a massive wood structure exposed to an indoor climate remains mostly in this range. The wood specific heat capacity varies mostly between 132 and 16 J kg 1 K 1 in the assumed range of moisture content expressed in percentage and encountered in a cold climate indoor environment, i.e. between 5% and 12%. The transverse moisture diffusion coefficient D t (m 2 s 1 ) in wood depends on the local moisture content and the temperature. The wood anatomy reveals that nearly 94% of the bulk of softwood is made of longitudinal tracheids. Considered as the principal component of conifer woods, a mathematical modelling of the hygroscopic moisture movement through the tracheids can be envisaged. Stamm [3] first explained the moisture movement in the wood cells in the hygroscopic range with an electrical analogue model to simulate moisture movement. This analogue model has been the basis for the theory developed by Siau [19]. According to Siau [19], the transverse moisture diffusion coefficient in wood D t can be expressed with sufficient accuracy between 5% and 15% moisture content by the square root of the wood porosity a, and the transverse bound-water diffusion coefficient of the cell wall D bt (m 2 s 1 ). The transverse water vapour diffusion in the lumen is neglected, since the diffusion in the cell walls completely governed the mechanism of moisture transport at low moisture content in wood. The transverse bound-water diffusion D bt is fitted in the Arrhenius equation introducing the activation energy of bound water diffusion in the cell wall of the wood material as a linear expression of the moisture content. Eq. (5) depicts the final expression of the wood transverse moisture diffusion coefficient: D t ðt; uþ ¼ expð u=RTÞ : (5) ð1 pþð1 p 1=2 Þ

6 S. Hameury / Building and Environment 4 (25) Fig. 2. Wood transverse moisture diffusion coefficient (m 2 s 1 ) based on the moisture concentration in wood. The determination of the wood porosity is also a function of the moisture content and the wood specific gravity pðuþ ¼1 G u ðuþð:653 þ uþ: (6) According to [29], the specific gravity of wood is defined in (7) on the basis of the wood oven-dry density r o (kg m 3 ), the water density r w, and the moisture content u: r G m ðuþ ¼ o r w ð1 þ r o uþ : (7) The transverse moisture diffusion coefficient D t has been reported in Fig. 2 for the range of temperature and moisture content of wood exposed to an indoor climate. As can be seen in Fig. 2, the wood transverse moisture diffusion coefficient exposed to an indoor climate is expected to vary mostly between and m 2 s 1 based on the moisture concentration in wood. The dry density of Scots pine is fixed constant to 43 kg m 3, and it is the only wood property parameter provided to the model with the heat conductivity coefficient. The density of Scots pine is then calculated in (8) from its specific gravity and moisture content, and the water density rðuþ ¼G m r w ð1 þ uþ: (8) 2.4. Latent heat of sorption The migration of moisture through the wood layer of the building envelope generates heat due to the conversion of latent heat when moisture is absorbed or desorbed by the wood cell walls. This process leads to an increase or decrease of the wood temperature. The magnitude of the latent heat fluxcan be in certain cases of the same order as the sensible heat transfer, resulting in a more important heat gain than if the model does not take into account this phenomenon. Moreover, the wood and water system is known to have a large heat of sorption. The total heat energy in the massive wood wall model is then expressed as the amount of sensible heat and latent heat. Latent heat is the amount of heat required to bring about a change of state in a substance without any fluctuation in temperature. It is well known that sorbed water in a porous medium has a lower vapour pressure than ordinary liquid water. Its enthalpy is lower or more negative than the enthalpy of liquid water by the differential heat of sorption DH s. This means that more energy is needed for a sorbed water molecule to escape and evaporate compared to a liquid water molecule. When condensation occurs from a vapour phase to a liquid phase, heat is released at a rate of 251 kj kg 1 of vapour condensing at 1C. This is the latent heat of vaporization of water H v and is defined a constant in the IDA ICE environment. However, the latent heat of vaporization of water decreases from to kj kg 1, over the range of temperature 1 3 1C usually experienced in an indoor climate. During the project, the constant value kj kg 1 has been chosen corresponding to a temperature of 2 1C. As it has been pointed out previously, the enthalpy of sorbed water is less than the one of liquid water, and the differential heat of sorption has to be added at the latent heat of vaporization of water to achieve the latent heat of sorption of bound water in the cell walls of wood material. The differential heat of sorption in wood may be calculated approximately from the empirical Eq. (9) adapted from [28]: DH S ðuþ ¼1: expð 14uÞ: (9) The latent heat of moisture is finally defined in H m ¼ H v þ DH S : (1) Fig. 3 shows the different levels of energy of moisture in wood. As can been seen, the differential heat of sorption increase with decrease in moisture content. A common way in the modelling of heat gain in a wall is to only consider the latent heat of vaporization of water. Fig. 3 shows, however, that for moisture content lying approximately between % and 2%, this assumption is not legitimate. The models usually developed for moisture transfer in porous media often assume two states, a water vapour phase, with vapour diffusion governed by a vapour pressure gradient, and a capillary phase, governed by capillary pressure gradient. The bound-water transport is often neglected. However, it has been pointed out in [28] that bound water diffusion through the cell walls of wood is the most important mechanism in the hygroscopic range. The bordered pits are often irreversibly aspirated during the kiln drying process decreasing the

7 146 ARTICLE IN PRESS S. Hameury / Building and Environment 4 (25) Energy level (kj/kg) relatively to liquid water Liquid water Ice -5-1 Water vapour Wood moisture content [%] accessibility of water vapour to diffuse through the tracheids Initial and boundary conditions The initial condition is given by a uniform moisture content profile through the width L of the massive wood layer t ¼! u ¼ u 8x 2½; LŠ: (11) The moisture and heat transfer between the surfaces of an exposed massive wood layer and the ambient air is governed by the boundary conditions (12) and (13): ¼ h T AðT S T i Þ; Surf Relative energy level of moisture in wood H v H s H m Bound water Fig. 3. Relative energy level of moisture in wood (adapted from Siau [19]). D t ¼ SAðu S u eq Þ; Surf where u eq is the equilibrium moisture content for wood in the ambient air, S (m s 1 ) is the mass convection coefficient, called sometimes the surface emission coefficient, and u S is the moisture content in wood at the surface. The surface emission coefficient is developed according to S ¼ 1 :18 P sh RTG m r ; (14) where P s is the saturated vapour pressure (Pa), and.18 kg mol 1 is the molecular weight of water vapour. The well-known analogy between heat and mass transfer is stated by the Lewis relation found in [31]. This analogy estimates the mass transfer coefficient based on the concentration in air potential from the thermal coefficient under the same conditions of temperature and velocity: h v h T ; (15) c pa r a where h v is the mass convection coefficient based on the concentration in the air (m s 1 ), h T is the coefficient of surface heat transfer (W m 2 K 1 ), c pa (J kg 1 K 1 )is the specific heat of air at constant pressure, and r a is the air density. The determination of the mass transfer from wooden surfaces by the Lewis relation has to be taken cautiously. The literature clearly indicates a mass transfer with wood much slower than the one predicted from the analogy between heat and mass transfer [32]. The wood material itself seems to present a resistance to evaporation at the surface. It has been argued that the sorption curve equation used in the modelling is perhaps incorrect, when not taking into account the hysteresis effect. A more reasonable reason is that thermodynamic equilibrium is assumed at the wood surface and this is certainly not correct. The low mass transfer below the fibre saturation point could be explained as a dynamic non-equilibrium between the water vapour of the air and the bound water of the wood surface Zone model A simple zone model assuming well-mixed air has been developed to investigate the interaction between the moisture fluctuations in an indoor climate and the moisture transport in a massive wood wall directly exposed to the indoor climate. This zone model has been developed here to make use of the wall model described previously as a stand-alone application before implementing it in the whole IDA ICE environment. The indoor and outdoor temperatures are supposed to be constant and a temperature gradient is built up through the massive wood wall. The link between the zone and the massive wood surface is explained by the heat and mass surface resistances. This is modelled by Eqs. (12) and (13), where the resistances for heat transfer at the surfaces, i.e. the inverse of h T, are chosen constant in normal building applications to.13 m 2 K 1 W 1 at the inner side of the wall and.4 m 2 K 1 W 1 at the outer side. The moisture balance in the zone is finally described by the conservation ¼ G ventilation þ G wall þ G source ; (16) where v i is the water vapour concentration in the indoor climate (kg m 3 ), V (m 3 ) is the zone volume, G ventilation is the moisture flow rate via the ventilation system, G wall is the moisture flow rate at the wall surface and G source is the moisture flow rate coming from the different indoor moisture sources, i.e. human breathing, plants, and cooking to cite only a few. The moisture flow rate via the

8 S. Hameury / Building and Environment 4 (25) ventilation system is defined by G ventilation ¼ n 36 Vðv o v i Þ; (17) where v o is the water vapour concentration in the outdoor (kg m 3 ), n is the air exchange rate commonly expressed as the renewal of the air in the zone based on an hourly basis (h 1 ). 3. Numerical results 3.1. Sudden moisture step change in the zone A first numerical simulation has been carried out to simulate the indoor moisture response to a sudden step change in the conservation Eq. (16). The room volume considered is m 3, and the overall wall surface is estimated to 4 m 2. The indoor temperature is considered constant at 2 1C and the relative humidity in the room is initially fixed to 6%, in equilibrium with the outdoor relative humidity. The simulation is launched with an outdoor temperature fixed to 5 1C and fresh air entering into the zone at the rate n and warmed up to 2 1C at 25% relative humidity. The moisture sources are supposed nonexistent. The results are depicted in Fig. 4 considering that the overall wall surfaces are open to moisture diffusion. The indoor relative humidity is shown as a function of time and air exchange rate. The dash lines show the case where moisture diffusion through the walls is inexistent. It is clearly seen that the massive wood wall contributes to buffering a moisture step change and this is particularly the case when the ventilation rate drops. However, the buffering effect is not really impressive at ventilation rate between.8 and 1 h 1. It takes only around 2 h for the indoor relative humidity to drop half way at 1 h 1 ventilation rate and almost 4 h at.8 h 1. This is clearly shown in Fig. 5, where the time for half-drop of the Time [h] Fig. 4. Drop of the indoor relative humidity following a sudden step change as a function of the ventilation rate. Time [h] Time for half drop of the indoor relative humidity Active surface ratio Ventilation rate 1/h Ventilation rate.35/h indoor relative humidity is depicted as a function of the air exchange rate and the active surface ratio, where represents the case with the walls totally closed to moisture diffusion and 1 is the case where the entire wall surface interacts with the indoor climate. It is considered that no moisture diffusion occurs through the floor and the ceiling and the effect of the furniture is neglected. It can be seen that the response is not linear and that the buffering effect increases drastically with increasing active surface area. Fig. 5 clearly shows that if it is possible to decrease the ventilation rate, a massive wood structure should be effective in the buffering of an indoor climate to sudden moisture step changes since large amount of wood surface area are expected to be freely exposed to the indoor climate for this kind of construction Cyclic moisture pattern Ventilation rate.8/h Ventilation rate.25/h Ventilation rate.5/h Fig. 5. Time to half drop of the indoor relative humidity as a function of the active surface ratio and the ventilation rate. As previously defined the moisture buffering capacity of hygroscopic materials may also be regarded as the ability to dampen the cyclic indoor moisture variations. Different daily moisture source patterns have been considered. The zone depicts the main room of an apartment with a habitable surface of 34 m 2 at the Vetenskapsstaden multi-storied building located in Stockholm, Sweden. The geometry of the room considered is presented in Table 1 and the input data are provided Table 2. The input data corresponds to an average temperature and a relative humidity which mostly occur in the cold climate area as it is the case in Stockholm and are set up constant throughout this study. Table 1 shows that the wood wall surface area open to moisture diffusion corresponds to almost one-half of the total exposed surface area of the room. The initial conditions are set up to 5% indoor relative humidity

9 148 ARTICLE IN PRESS S. Hameury / Building and Environment 4 (25) Table 1 Surface areas (m 2 ) and net volume (m 3 ) of the zone Zone parameter Value Net floor area 14.4 Total wall area 29.7 Total surface area, A total 58.4 Exposed wood area, A 28 Ratio, A/A total.48 Indoor space volume, V 34.4 Table 2 Input data Parameters Winter season Summer season Outdoor temperature T o (1C) 2 Indoor temperature T i (1C) 2 2 Outdoor relative humidity j o (%) 8 7 and the massive wood wall is in equilibrium with the indoor temperature and relative humidity. The moisture source is modelled with step changes and a first scenario has been simulated considering a daily moisture pattern possible to be encountered in a bedroom where the indoor climate is subjected to periodic moisture release on two levels. During the night, moisture is release at a constant rate of 6 g h 1 and no moisture is released during the day. A second scenario has been applied assuming the same moisture source cycle but with increasing the moisture release during the night to a high rate of 12 g h 1. The simulation is launched and run until the system converges to a daily cycle of indoor relative humidity which does not diverge from one day to another. Fig. 6 depicts the results of the maximum and the minimum indoor relative humidity achieved during the daily moisture cycle for a moisture source release rate of 6 g h 1. The results are presented for the case of (a) a winter period (b) and a summer period. Fig. 7 presents similar results but for a rate of moisture source release of 12 g h 1 during the night. The results are shown as a function of the air exchange rate. The moisture buffering effect is depicted by the introduction of the ratio r defined by r ¼ Dj permeable Dj impermeable ; (18) where Dj depicts the difference between the maximum and minimum indoor relative humidity occurring during a daily period and at a specified ventilation rate, as shown Fig. 7a. Dj permeable depicts the case considering that a part of the overall indoor wall surface is permeable to moisture diffusion (dashed curves) and Dj impermeable depicts the case where the overall wall surface exposed to the indoor climate is closed to (a) (b) Winter Period / Moisture source = 6 g/h Max RH_permeable case Max RH_impermeable case Min RH_permeable case Min RH_impermeable case Summer Period / Moisture source = 6 g/h Max RH_permeable case Max RH_impermeable case r moisture diffusion (solid curves). Therefore the ratio r shows the contribution of an exposed massive wood wall surface to the indoor climate to dampen the indoor relative humidity at a defined ventilation rate and referring to the case where the whole wall surface is closed to the moisture diffusion. As can be seen in Fig. 6, the buffering capacity of massive wood directly exposed to an indoor climate becomes more impressive at low ventilation rate during the winter period. For instance, considering that 48% of the overall wall surface is provided with massive wood opened to moisture diffusion and that the ventilation rate is fixed to 1 h 1, the daily fluctuation of the indoor relative humidity is smoothened and the amplitude represents only 73% of the fluctuation which would have occurred if the whole indoor wall surface is assumed closed to moisture diffusion. The buffering effect increased relatively slowly with decreasing the ventilation rate until.5 h 1 and increased much more after this point. Furthermore, the response depicted by the ratio r shows a different shape during the summer period. The r Min RH_permeable case Min RH_impermeable case Fig. 6. Maximum and minimum indoor relative humidity achieved during (a) a winter daily period and (b) a summer daily period. The rate of moisture releases is set up to 6 g h 1 during the night Ratio r Ratio r

10 S. Hameury / Building and Environment 4 (25) (a) (b) Winter Period / Moisture source = 12 g/h ϕ permeable ϕ impermeable Max RH_permeable case Min RH_permeable case Max RH_impermeable case Min RH_impermeable case Winter Period / Moisture source = 12 g/h Max RH_permeable case Min RH_permeable case Max RH_impermeable case Min RH_impermeable case Fig. 7. Maximum and minimum indoor relative humidity achieved during (a) a winter daily period and (b) a summer daily period. The rate of moisture released is set up to 12 g h 1 during the night. r Ratio r Ratio r (a) (b) Max Rh during the first daily cycle (Source = 6 g/h) Winter_permeable Winter_impermeable Summer_permeable Summer_impermeable Max Rh during the first daily cycle (Source = 12 g/h) Winter_permeable Winter_impermeable Summer_permeable Summer_impermeable Fig. 8. Response of the indoor relative humidity after the first day of calculation for a rate of moisture released fixed to (a) 6 g h 1 and (b) 12 g h 1 during the night. buffering effect is impressive even at high ventilation rate and the maximum relative humidity is much less. The fluctuations of the indoor relative humidity are damped as much as 52% at 1 h 1, compared with the case of the whole wall surface closed to moisture diffusion. The buffering effect seems to increase somewhat linearly with decreasing the ventilation rate. Even at ventilation rate as low as.5 h 1, it is surprising to see that the relative humidity does not cross the threshold of 1%, i.e. the indoor climate is not saturated in humidity if 48% of the wall surface is provided with massive wood. Comparing Figs. 6 and 7, it can also be depicted that the buffering capacity of the massive wood wall increased in effectiveness as the rate of moisture released is doubled. Fig. 8 depicts the results after the first day of simulation and it can be seen that the response of the indoor climate is initially at 5% relative humidity. Fig. 8 shows that the use of a water vapour permeable structure tends to increase the maximum indoor relative humidity during the winter season at higher ventilation rate. This tendency seems to be accentuated when the moisture source rate is lowered. Furthermore, a wall opened to the moisture diffusion seems to better withstand an increase of the moisture source rate during the winter season since the maximum indoor relative humidity remains acceptable at low ventilation rate compared to a wall closed to moisture diffusion. The same tendency can be depicted for the summer season. It may also be pointed out that the maximum relative humidity remains almost the same during the summer period whatever be the ventilation rate when the walls are opened to moisture diffusion. Since the diurnal moisture production in a living room is not periodic as it can be assumed for a bed room, a more complicated diurnal moisture production pattern has been derived (Fig. 9) for the assessment of the moisture buffering capacity of massive wood walls directly exposed to the indoor climate of a living room. The results are depicted Fig. 1 for the summer and the winter period. The dashed curves show the results where moisture transfer occurs between the massive wood wall and the indoor climate, and the filled curves show the results when assuming that the walls are

11 141 S. Hameury / Building and Environment 4 (25) Moisture Source rate per volume [g/m 3.h] Daily Moisture Source Fluctuations Time [h] Moisture Source rate [g/h] effect remains important even at high ventilation rate during the summer period but is less impressive during the winter period for usual ventilation rate occurring in dwellings. During the winter period and for ventilation rates from.8 h 1 and further, much less differences appear between a wall with impermeable coating and a massive wood wall opened to moisture diffusion. The fluctuations of the indoor relative humidity, making use of a massive wood wall surface, are damped by 2% at.8 h 1 air exchange rate and 13% at 1 h 1 air exchange rate, this compared to the case where the whole wall surface is assumed closed to moisture diffusion. Fig. 9. Diurnal moisture source pattern. 4. General discussion (a) (b) Winter Period r Max RH_permeable case Max RH_impermeable case r covered with a water vapour-tight surface layer closed to moisture diffusion. As can be seen Fig. 1, the massive wood wall surface exposed to the indoor climate contributes to buffering the indoor relative humidity especially at lower ventilation rate and during the summer period. The buffering Min RH_permeable case Min RH_impermeable case Max RH_permeable case Max RH_impermeable case Summer Period Min RH_permeable case Min RH_impermeable case Fig. 1. Maximum and minimum indoor relative humidity achieved during (a) a winter and (b) a summer daily period, as a function of the air exchange rate and for the moisture source pattern Fig. 9. Ratio r Ratio r Padfield [11] has shown that even if wood seems to have one of the most important volumetric moisture capacity compared to the common building materials, the low moisture diffusion of wood in the transverse direction inhibits a deeper penetration of moisture into the material. For this reason, the penetration depth of wood is not so impressive in its transversal direction, in the order of 1 mm for daily humidity cycles. This involves lower available water when wood is exposed to its transversal direction rather than in its longitudinal direction. But still, if we consider the case of a room with a low ventilation rate and a large surface area of wood exposed to the surrounding without any coatings, the buffering effect seems to play a significant role. Even if building materials such as gypsum board, cellular concrete and wool present higher available water, or effective moisture capacity, during a daily period, it should be recalled that these materials are commonly covered with coating or wallpapers and are seldom exposed directly to the indoor climate. In that way, their buffering capacities are barely activated due to the moisture diffusion resistance induced by this supplementary outer surface layer. Appreciably, the good aesthetic of wood enables to directly expose wood into the indoor climate of dwelling houses without any coating or painting. This presents obviously some advantages particularly when dealing with extremely short fluctuations of the indoor humidity level. The question on the ability of wood as a building material, in a massive construction perspective, to smoothening humidity and temperature variations of indoor spaces, remains, however, still open to discussion. A better understanding of the moisture transfer between the wood and indoor air interface should be necessary as the model assume an instantaneous equilibrium between the moisture content of the wood surface and the surrounding, which certainly overestimates the true variations and penetrations of moisture inside the wall. Equilibrium moisture content does not strictly exist in the uncontrolled atmosphere of

12 S. Hameury / Building and Environment 4 (25) a building indoor climate. Temperature and relative humidity change continuously and the wood material has not the time to achieve a surface moisture equilibrium during desorption or adsorption phase, which are very slow processes. Indeed, one shall recall that there are some evidences for wood to follow a non- Fickian behaviour [33] especially at high relative humidity, with a time-dependent moisture sorption as described in [34]. This retarded sorption in wood would have, as an effect, to decrease the real moisture buffer capacity of heavy timber constructions in comparison with the results presented in this paper. Furthermore, short-term fluctuations tend to influence only the wood surface because the mechanism of moisture transport in wood is really slow in comparison with the mechanism of heat transport. It could thus be envisaged to have recourse to the nuclear magnetic resonance (NMR) technique to further study the surface phenomenon between wood and an indoor climate [35]. Recent developments in nuclear magnetic resonance imaging of materials enable to measure the amount of free and bound water proton in wood with high resolution of the order of 1 25 mm and a field of view around 3 mm. Another step in the modelling presented in this paper should be to implement a non-isothermal model accounting for the modelling of an exterior massive wood wall, and taking into consideration the thermal diffusion, known as the Soret effect, neglected in this model. Implementation of the hysteresis present in the sorption isotherm of wood should be envisaged as well as the modelling of the retarded sorption in wood. 5. Conclusion In this paper, a one-dimensional finite difference model of a massive wood wall directly exposed to an indoor climate is investigated. The wood layer exposed to the indoor climate is divided into finite meshes where the wood material properties are expressed mostly in term of equations and only the oven-dried density needs to be given. Further research will follow this preliminary study by implementing the model in the modular simulation environment IDA ICE where the dynamic of a whole massive wood building may be investigated. The results so far may show that the buffering effect of massive wood wall is appreciable especially at the low ventilation rates, and increases greatly in effectiveness with sufficiently large surface area of wood layer directly exposed to an indoor climate and high indoor moisture loads. However, one should recall that the usual Fickian approach for moisture transport within wood material presents few shortcomings. The retarded or timedependent aspect of sorption in wood has been pointed out in several works [33,34] and this certainly means an actual moisture buffering effect less important than the one predicted in this paper. Further research envisaging the recourse to the innovating NMR approach should enable a better understanding of this phenomenon and might provide remedies to the modelling of the moisture transport in wood. Acknowledgements The author is indebted to Professor Ove So destro mat the Royal Institute of Technology, Stockholm, and to Dr. Per Sahlin at the Simulation Technology Group EQUA, Sundbyberg, for their fruitful discussions and comments. References [1] ANSI/ASHRAE standard 55. Thermal Environmental conditions for human occupancy. Atlanta: ASHREA; [2] Toftum J, Jorgensen AS, Fanger PO. Upper limits of air humidity for preventing warm respiratory discomfort. Energy and Buildings 1998;28: [3] Rodríguez E, Baalin a A, Molina M, Santaballa JA, Torres ER, Infante C. Relationship between humidity, temperature and biological pollution in domestic buildings in A Corun a (Spain). In: Proceedings of healthy buildings 2 conference, Helsinski, [4] NORDTEST. Workshop on moisture buffer capacity summary report. DTU: Department of Civil Engineering, Technical University of Denmark; 23. [5] Lundström T. Indoor Exposed massive wood, moisture and heat smoothening capacity. IBOIS 22:14 22 ( [6] Hameury S, Lundström T. Contribution of Indoor exposed massive wood to a good indoor climate: in situ measurement campaign. Energy and Buildings 24;36(3): [7] Hameury S. Heat and Moisture buffering capacity of massive wood construction. In: Proceedings of the eight world conference on timber engineering, Lahti, 24. [8] Nore n A, Akander J, Isfalt E, So derström O. The effect of thermal inertia on energy requirement in a swedish building results obtained with three calculation models. Internal Journal of Low Energy and Sustainable Buildings 1999;1 ( ce.kth.se/byte/leas). [9] Akander J. The effective heat capacity of three wood constructions theoretical and experimental assessments. Sweden: Division of Building Materials and Building Technology, Royal Institute of Technology; 22 TRYTA-BYMA 22:1 ISSN [1] Padfield T. Humidity buffering by absorbent materials in walls. The physic of the museum environment, 1999 ( [11] Padfield T. The role of absorbent building materials in moderating changes of relative humidity. PhD thesis, Department of Structural Engineering and Materials, The Technical University of Denmark, Series R, no. 54, [12] Simonson CJ, Salonvaara M, Ojanen T. Improving indoor climate and comfort with wooden structures. VTT publication 431. Finland: VTT Technical Research Centre of Finland; 21. [13] Mendes N, Winkelmann FC, Lamberts R, Philippi PC. Moisture effects on conduction loads. Energy and Buildings 22;1518: 1 14.