ARTICLE IN PRESS Building and Environment 44 (2009) 633– 642

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Building and Environment journal homepage: www.elsevier.com/locate/buildenv

Modelling of hysteresis influence on mass transfer in building materials Jerzy Kwiatkowski a,b,, Monika Woloszyn a,b, Jean-Jacques Roux a,b a b

CETHIL, UMR5008, CNRS, INSA-Lyon, Universite de Lyon, Universite Lyon 1, F-69621 Villeurbanne, France INSA Lyon, bat. Sadi Carnot, 69621 Villeurbanne Cedex, France

a r t i c l e in fo

abstract

Article history: Received 11 January 2008 Received in revised form 30 April 2008 Accepted 8 May 2008

The processes of mass transfer in the material influence not only the conditions within the material but also inside the connected air spaces. A new module for precise representation of mass transfer in materials in contact with the indoor air, called Humi-mur, was elaborated and validated in this work. It allows for the precise representation of sorption isotherm and vapour permeability dependence on relative humidity. Also the sorption curve hysteresis has been implemented. The new module was then applied to estimate the sensitivity of the results to uncertainty in measured material properties and the impact of hysteresis effect. Reasonable estimation of experimental uncertainty resulted in the deviation of approximately 6% in the calculated results. Hysteresis quite strongly influences the dynamic behaviour of materials. Concerning hysteresis in the sorption isotherm, we showed that the average of the adsorption and desorption equations is a reasonable approximation of mean behaviour for coarse calculation. In case when precise results of the relative humidity (absolute humidity) are needed, the hysteresis effect should be taken into account. & 2008 Elsevier Ltd. All rights reserved.

Keywords: Hysteresis Sorption Mass transfer Humidity Modelling Sensitivity

1. Introduction Relative humidity is one of the most important parameters influencing perceived indoor air quality and human comfort. Moisture can also initiate microbiological growth at the surface of building envelope. The material that absorbs and desorbs water vapour can be used to moderate the amplitude of indoor relative humidity and therefore to participate in the improvement of the indoor air quality and energy saving [1,2]. Mass transfer in the hygroscopic materials, even if it is taken into whole-building simulation programmes, is simplified. Neglecting water vapour transport between air and the material, or simplifications in mass flows inside the material can lead to serious errors in estimating the indoor air humidity. Therefore a new module, Humi-mur, for calculations of mass flow exchanged between indoor air and the material is developed in this work. The final objective is to integrate this module into a whole-building simulation tool. Humi-mur allows for the precise representation of the sorption isotherm and vapour permeability dependence on relative humidity. Also the sorption curve hysteresis has been implemented in the mass transfer model, and the impact of this phenomenon on

 Corresponding author at: CETHIL, UMR5008, CNRS, INSA-Lyon, Universite de Lyon, Universite Lyon 1, F-69621 Villeurbanne, France. Tel.: +33 472 437 191; fax: +33 472 438 811. E-mail address: [email protected] (J. Kwiatkowski).

0360-1323/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2008.05.006

the mass uptake and hygric condition in the material has been investigated.

2. Modelling of mass transfer For the last 15–20 years, many computer-based tools for heat, air and moisture (HAM) transfer simulation in building elements have been developed around the world. Hens [3] presented 37 models while the Canada Mortgage and Housing Corporation (CMHC) listed 45 computerized hygrothermal modelling tools [4]. The models can be divided into several types taking into consideration different parameters, i.e., transfer dimension: one, two or three, or the type of transfer: heat and moisture, heat and air or all three components. A classification in order of overall complexity has been presented in [3], and nine different types have been found. Most of the codes can be used by their own developers but are difficult to work with for other researchers. However, most of them are not available to the public outside the organization where they were developed. There are only few codes that are available to interested users. Here some of them are shortly described. WUFI is a two-dimensional (2-D), heat and moisture transfer tool that allows for the calculation of the hygrothermal behaviour of multi-layer building components exposed to natural climate. The tool requires standard material properties and moisture storage and liquid transport functions. It can use measured weather data (including driving rain and solar radiation) in order

ARTICLE IN PRESS J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

to investigate the behaviour of the component under realistic weather conditions. This model can be used for calculating the drying time of the component with trapped construction moisture, the risk of condensation, the influence of driving rain or the hygrothermal performance of roofs and walls under different parameters, i.e. in different climate zones [5–7]. MOIST is a one-dimensional (1-D) programme predicting heat and moisture transfer in building envelope. The programme allows investigating the effect of various parameters on moisture accumulation within layers of the construction. It can be used as well for calculation of the surface relative humidity in order to analyse the possibility of mould growth. The MOIST model can also be used to analyse the effect of moisture on heat transfer [8]. 1-D HAM is a 1-D tool calculating HAM transfers in multilayered wall components. The transport of moisture is by diffusion and convection and no liquid water transport is represented. Heat transfer consists of convection, conduction and latent heat. The hourly values of external conditions are used as a climatic data [9]. MATCH is a 1-D, heat and moisture transfer tool to calculate the hygrothermal behaviour of composite building structures. In this programme the hygroscopic capacity of building materials is considered. Moisture is transferred by diffusion and convection in the vapour phase. In this model, the hysteresis effect between absorption and desorption is included [10–12]. LATENITE-VTT is an enhanced version of the original LATENITE, 2-D, heat and moisture transfer tool. It can be used not only to solve the transport in the building envelope but also to calculate the interaction between the building structure and the indoor air by solving the whole-building energy and mass balance [13]. The presented models are just a sample of a large group of HAM simulation programs. But they are representative of the problems existing codes can solve. However, models cannot simulate real-world situations without reliable data. Most of the programs require a large amount of experimental data and boundary conditions, such as material properties, outdoor climatic data, indoor condition or initial conditions [14]. All of those parameters are changing in time. For climatic data, indoor and initial condition it is obvious but even material properties are not fixed values. It has been proved that two most important hygric properties of material, vapour permeability and sorption isotherm, have significant influence on the hygrothermal behaviour of building components [15,16]. Thus it is very important to have good experimental data of material properties. The vapour permeability describes the moisture transport property of the material. Permeability is not a constant value but it is a function of relative humidity. This property is often expressed as the vapour resistance factor: the ratio of vapour permeability of the material to vapour permeability of the stagnant air. For each relative humidity level, there will be equilibrium in water content in the material. This dependence is known as the sorption isotherm of the material. An example of sorption and desorption isotherm curves for different materials is presented in Fig. 1. The differences in the sorption curves for different materials are due to micro-structural properties, such as specific surface area, pore-size distribution, and total porosity. During drying, less of water is released from the material than water trapped during humidification. Therefore, desorption and adsorption curves are not identical. The shape of curves is similar but the desorption isotherm has higher values of water content than the adsorption isotherm for the same value of relative humidity. This phenomenon is called hysteresis [18]. Modelling of the hysteresis effect is not so simple because the nature of this process is not known very well. Nevertheless, some

0.3 Concrete sorption Concrete desorption

0.25

Brick sorption

Water content [kg/kg]

634

Brick desorption

0.2

Wood sorption Wood desorption

0.15

0.1

0.05

0 0

10

20

30

40 60 50 70 Relative humidity [%]

80

90

100

Fig. 1. General shape of the sorption/desorption isotherm for different materials (based on [17]).

ways on how to model this phenomenon were presented by researchers. Mualem [19] presented a model based on the inkbottle concept, and Pedersen [11,12] described hysteresis by an empirical approach using the weighted values of the capacity. Some other models has been developed for porous materials, i.e. [20–22] or [23]. Unfortunately, only two of the 37 HAM models specified by Hens [3] consider the sorption isotherm hysteresis effect. Those two models are MATCH and CHEoH. All other codes accept that the sorption hysteresis exists but assuming that its influence on the hygrothermal behaviour of the material is marginal. However, it is anticipated that in the whole-building perspective, the situation can be different. Indeed, the sorption process depends not only on material properties but also on varying indoor conditions. Indoor air humidity is also strongly influenced by sorption processes in materials in contact with the indoor air. To investigate these effects, there is a need for a whole-building simulation tool, including comprehensive modelling of moisture transfers in materials, hysteresis among others. Therefore the objective of this work is to introduce a comprehensive moisture transfer module, and to integrate it into a whole-building simulation tool. The first steps of this project, namely elaboration, validation and testing of this mass transfer module, are presented in the following. Also the implementation of the mass transfer module in a whole-building simulation tool together with an example of application is discussed at the end of this paper.

3. Model description The Humi-mur programme was elaborated in order to simulate isothermal water vapour transfer between air and the material and the moisture flow inside the material. The simulations are performed using the control volume method (CVM) with a 1-D model and a first-order explicit time scheme. In the material, the mass conservation (1) was used as the main equation in the model qwj ¼ rg j  Gj qt

(1)

where wj (kg/m3) is the mass content, gj (kg/m2 s) is the density of the mass flux and Gj (kg/m3 s) is the source of the humidity of the component j. The mass transfer consists of three components: water vapour transfer, liquid water transport and ice formation.

ARTICLE IN PRESS J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

Humi-mur represents materials in contact with the indoor air, where the temperature is in general above zero, so the ice formation is neglected. Also, in general only a thin layer of the envelope is active for moisture buffering effect, which is of interest here. Such a thin layer in modern highly insulated envelopes can be considered isothermal. At the surface of the material, the equation of convective mass transfer (2) was used as the boundary condition: mcon ¼ bpsat ðfext  fsurf Þ

(2)

2

where mcon (kg/m s) is density of the convective mass flux, b (s/m) is the convective mass transfer coefficient, fext and fsurf (dimensionless) are ambient air relative humidity and relative humidity at the surface of the material. Assuming that the mass transport is 1-D in the x direction and isothermal, and the relative humidity is used as the driving potential, Eq. (1) reads:   qf q qf rx ¼ ðDl rx þ pvsat dÞ (3) qt qx qx where r (kg/m3) is the dry density of the material, x (kg/kg) is the moisture capacity (derivative of the sorption isotherm), Dl (m2/s) is the liquid diffusivity, pvsat (Pa) is the saturation pressure, d (kg/Pa m s) is the vapour permeability, f (dimensionless) is the relative humidity, t (s) is the time and x (m) is the thickness. The moisture capacity and the vapour permeability are functions of relative humidity. 3.1. Methodology of the calculations The material properties, namely dry density, equation of the sorption isotherm w ¼ f1(f), equation of moisture capacity x ¼ f2(f) ¼ qw/qf (the first derivative of sorption isotherm) and equation of vapour permeability d ¼ f3(f), are the requested data. Then the parameters of the calculation (temperature and convective mass transfer coefficient, thickness of the material, and also the number of layers and the time step) must be given. The initial profile of relative humidity in the material is required as well. The calculations are then executed as follows:

 Using the sorption isotherm the initial moisture content is calculated for each layer and at the surface of the material.

 Vapour permeability, moisture capacity and the relative  

humidity values are updated for each time step and for each layer, depending on the calculated moisture content. Using the sorption isotherm and instantaneous ambient relative humidity, the moisture content in each layer is calculated for each time step. Finally the change of moisture content in the material, total mass uptake and mass flux between air and the material is computed.

As the results of simulation, the following data are obtained: profile of the relative humidity in time for each layer, profile of relative humidity in the material for each time step, profile of the mass absorbed/desorbed by the material. Some of the results are presented in the next section.

635

response’’ (http://www.kuleuven.be/bwf/projects/annex41). For the simulation the set of three superimposed boards of gypsum has been used. The total thickness of the specimen was equal to 37.5 (mm) and exposed for the vapour transfer area was equal to 0.1384 (m2). The experimental measurements and simulations were done for different variants: with or without the paint layer, and for different boundary conditions (changing the convective mass transfer coefficient b). In the test, the transient moisture transfer (TMT) facility was used. The facility was build to measure 1-D heat and mass transfer between air and a porous material. A small wind tunnel was used in order to develop steady airflow over the material surface. The air was preconditioned to the desired temperature and relative humidity in the climatic chamber and suck by a vacuum pump into a wind tunnel. The set of thermocouples and humidity sensors were placed in the specimen to measure the temperature and relative humidity profile in the material. The load sensors were used to measure moisture accumulation in the material. The sensors were placed in such way that any change in mass during the test corresponded to water vapour exchange between air and the specimen. Only one side of the sample was exposed to the ambient air with relative humidity varying according to a step change: preconditioning at initial humidity, then a 24-h step of higher value and then decrease till the initial value. The other five sides of the sample were insulated with a vapour-tight material; therefore moisture transfers can be considered as mono-dimensional. In Tables 1 and 2 the parameters for three cases discussed in the following are presented. The hygric properties (sorption isotherm and water vapour permeability) of the gypsum board are presented in Figs. 5 and 7 as reference curves. The material properties, and therefore the equations of the sorption isotherm and vapour permeability for the gypsum board, are the same for all simulations. Additionally, in Test 3 the equations of the sorption isotherm and water permeability of the paint layer have been used. The measured and calculated values of relative humidity in the set of gypsum boards were compared at the depths of 12.5 and 25.0 mm. Hereafter the results for the cases presented in Tables 1 and 2 are shown. In Figs. 2–4 the relative humidity profiles in the material at two depths are presented. The figures show that the shape of the simulated RH profiles in the material is in good agreement with the measured data; however, some differences can be seen. The differences are smaller in the first part of the calculation where

Table 1 Presented benchmark cases Parameter

Test 1/3/4

Thickness, l (mm) Density, r (kg/m3) Temp., T (1C) Time step (s) Time of calcu. (h) Step of RH (%)

37.5 690 23 60 48 30/72/30

Common parameters.

3.2. Validation of the model

Table 2 Presented benchmark cases

The comparison of Humi-mur results with the results from other models and with measurements was performed, in order to validate our approach. The simulations have been done according to the instructions of a benchmark case-Common Exercise 2 [24] of Subtask 2, from Annex 41 of International Energy Agency (ECBCS programme): ‘‘Whole-building heat, air and moisture

Parameter b (m/s) Paint layer Number of layers Changing parameters.

Test 1

Test 3 8

2.41 10 No 15

3.22  10 No 15

Test 4 8

2.41 108 Yes 16

ARTICLE IN PRESS 636

J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

Relative humidity [%]

Relative humidity profile for Test 1 75 70 65 60 55 50 45 40 35 30 25

Table 3 Mean deviation between calculated results and measured data

RH (%) x=12,5mm RH (%) x=25mm RH (%) x=12,5mm EXP. RH (%) x=25mm EXP.

0

6

12

18

24 Time [h]

30

36

42

Depth (mm)

Relative humidity [%]

Relative humidity profile for Test 3 RH (%) x=12,5mm RH (%) x=25mm RH (%) x=12,5mm EXP. RH (%) x=25mm EXP.

0

6

12

18

24

30

36

42

48

Time [h] Fig. 3. Calculated and measured relative humidity profiles in material at different depths, for test 3.

Relative humidity profile for Test 4

Relative humidity [%]

65

RH (%) x=12,5mm RH (%) x=25mm RH (%) x=12,5mm EXP. RH (%) x=25mm EXP.

60 55 50 45 40 35 30 0

6

12

18

24

30

36

42

Sorption (%)

Desorption (%)

Test 1 12.5 25

6.29 10.29

6.27 10.97

Test 2 12.5 25

6.42 10.92

10.37 17.59

Test 4 12.5 25

3.65 5.58

7.35 10.29

48

Fig. 2. Calculated and measured relative humidity profiles of the material at different depths, for test 1.

75 70 65 60 55 50 45 40 35 30 25

Deviation

48

Time [h]

butes to higher differences. The higher error for the deeper layer can be influenced by uncertainty in the material properties. It is obvious that material properties are characterised with experimental uncertainty and in calculation the impact is more significant for the deeper layers. The differences between experimental measurements and calculation are not so high and quite good agreement can be seen. For all cases, a good agreement with the results from others codes has also been found [24]. It must be noticed that for most of the codes the results of simulations are almost the same but quite different from the experimental measurements. None of the numerical model gave exactly the same results as the measurements. One of the reasons might be that some of the moisture transport phenomena in the porous material were not taken into consideration.

4. Sensitivity study In order to check the influence of some of the material properties and of the calculation parameters on model results, a sensitivity study was performed for two thicknesses of sample 37.5 and 150.0 mm. Two of the material properties (sorption isotherm and vapour permeability) and two of the calculation parameters (time step and number of layers) were taken into consideration. Each parameter has been changed to a lower and a higher value and compared with the original ‘‘reference’’ results for corresponding thickness. Test 1 from Table 1 was taken as the reference case for samples of 37.5 mm. Finally, eight additional cases were simulated for each thickness. For each additional case only one parameter/material property was changed, the others were kept constant. The comparison of results between each variant and the reference case was made by checking the relative humidity profiles at depths of 12.5 and 25.0 mm for the 37.5 mm specimen and at depths of 50.0 and 100.0 mm for the four-times thicker material.

Fig. 4. Calculated and measured relative humidity profiles in material at different depths, for test 4.

4.1. Influence of numbers of layers and time step the moisture was absorbed by the material and higher in the second part where moisture was desorbed out of the material. Also, smaller differences can be noticed for the depth of 12.5 mm and higher for the deeper layer. The mean values of relative error for each case and process are presented in Table 3. The higher values of the error in desorption are connected with the hysteresis phenomenon. At the beginning of calculation, the RH condition in the material is uniform for simulation and measurement. But when the desorption process starts, the difference between the RH condition in the sample in the calculation and the measurement already exists, which contri-

The reference number of layers (15, see Table 1) was increased to 18 and decreased to 12 (for the 150-mm-thick sample 48, 60 and 72 layers were tested). The time step has been changed from the reference value of 60–120 and 30 s. The calculation showed that none of those changes influenced the simulation result for either the thinner or the thicker material. The relative error for the highest value of the RH profile (after 24 h) on the depth of 12.5/50.0 and 25.0/100.0 (mm) is presented in Tables 3 and 4. All calculations for the 12, 15 and 18 layers gave very similar results. The difference was less than 0.1%, showing good precision

ARTICLE IN PRESS J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

Table 4 Sensitivity of relative humidity calculations for different number of layers and time step for 37.5 mm thick sample Parameter

Number of layers

Time step (s)

Value

Deviation (depth 12.5 mm) (%)

Deviation (depth 25.0 mm) (%)

12 18

0.01 0.05

0.01 0.09

30 120

0.01 0.65

0.02 1.14

637

isotherm influence vapour transfer and mass accumulation in the material. The uncertainty on the vapour permeability presented as water vapour resistance factor is shown in Fig. 7. The upper and lower curves were established from the standard deviation in the cited above round robin test as proposed by James et al. [24]. The results of relative humidity profile calculation for all three variants are presented in Fig. 8.

Relative humidity profile at depth 12,5 mm 75 0.0200

0.0140

Relative humidity [%]

Water content [kg/kg]

0.0160

Test1 - reference

70

0.0180 sorption (-) sorption (+) reference sorption

0.0120 0.0100 0.0080

Sorption Adjusted (+)

65

Sorption Adjusted (-)

60 55 50 45 40 35

0.0060

30

0.0040

25 0

6

12

18

0.0020 0.0000 0.00

24

30

36

42

48

Time [h] 0.20

0.40

0.60

0.80

1.00

Relative humidity [-]

Fig. 6. Relative humidity profile at depth 12.5 mm for sorption isotherm uncertainty.

Fig. 5. Uncertainty on the sorption isotherm.

Water vapour resistance factor [-]

of numerical computations. Also, the difference was negligible for the results computed with 30 and 60 s time steps. However, for the 120 s time step the difference increased to approximately 1%. For validation purposes and the following sensitivity studies, a 15layer mesh and a 60 s time step were used, which ensures correct precision. Also the difference is more significant for deeper layers for the thinner material. For the 150-mm-thick sample, the divergence problem occurs in the simulation with 72 layers (60 s time step) and in the simulation with 120 s time step (60 layers). Therefore the results for numerical calculation in these cases cannot be obtained. In the first situation (with 72 layers), the layers were too thin. In the second situation (with the 120 s time step), the time step was too long. The divergence problem occurs deeper in the material, so for the 37.5-mm-thick material this problem did not appear.

14.00 12.00 10.00 8.00 6.00

reference mi

4.00

mi (-) mi (+)

2.00 0.00

0.20

0.60 0.40 Relative humidity [-]

0.80

1.00

Fig. 7. Uncertainty on vapour permeability.

4.2. Sensitivity to material data

Relative humidity profile at depth 12,5 mm

The material properties for gypsum board (sorption isotherm with its uncertainty and permeability with its uncertainty) for the sensitivity study were taken from [24]. The uncertainty on the sorption isotherm is shown in Fig. 5. In all simulations relative humidity was higher than 30% (see Table 1); therefore the point at 33% RH was assumed to be fixed and the uncertainty in the sorption isotherm was investigated only above this point. The uncertainty was described by the standard deviation on the slope of the sorption isotherm, as measured in the ‘‘Round Robin Test’’ from Annex 41 project [24]. The comparison of the calculation results of relative humidity at depth 12.5 mm for the upper (sorption (+)), lower (sorption ()) and reference (reference sorption) curves is presented in Fig. 6. Similar results were obtained for the relative humidity profile at depth 25.0 mm. They show that the changes in the sorption

Relative humidity [%]

75 70 65

Test1 - reference

60 55

Permeability Adjusted (-)

Permeability Adjusted (+)

50 45 40 35 30 25

0

6

12

18

24

30

36

42

48

Time [h] Fig. 8. Relative humidity profile at depth 12.5 mm for vapour permeability uncertainty.

ARTICLE IN PRESS J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

A similar chart was obtained for the relative humidity profile at depth 25.0 mm. The changes of the vapour permeability influence also the vapour transfer and its accumulation in the material. Hereafter, in Table 6 the relative deviation for the highest value of the RH profile (after 24 h) at depths of 12.5 and 25.0 mm is presented. The same analysis has been done for the thicker material, and the deviations of relative humidity at depths of 50.0 and 100.0 mm are presented in Table 7. Again, the errors are bigger and deeper in the thinner material, but this time, for the thicker sample the deviations are lower and deeper in the material. For both thicknesses of the material in the simulation with lower values of water vapour permeability than in the reference case, the problem with divergence occur. It might be connected with a too long time step and too thin layers used in the numerical simulations. Some uncertainty is always associated with the experimental characterization of materials. The variations used in the sensitivity study above seem reasonable approximation of experimental uncertainty. Therefore it must be remembered that the calculated values are also within a limit of several percent; here about 6% as shown in the results in the table above.

5. Modelling hysteresis of the sorption isotherm Sorption hysteresis influences the water vapour transport in the material. To describe the effect of hysteresis, the empirical model proposed by Pedersen [11] in MATCH software was used in Humi-mur. Eq. (4) is used for desorption and Eq. (5) is used in the case of adsorption xd;h ¼

xa;h ¼

ðu  ua ÞA xd þ Bðu  ud ÞA xa ðud  ua ÞA Bðu  ua ÞA xd þ ðu  ud ÞA xa ðud  ua ÞA

(4)

(5)

where ua and ud are moisture contents in kg/kg, xa and xd are the moisture capacities (kg/kg) of, respectively, adsorption and desorption isotherms for a given relative humidity, and u is the actual moisture content in kg/kg. Computed moisture capacity xd,h or xa,h is used in Eq. (3). The function (4) is used for desorption if in the previous two time steps the water content was decreasing, the function (5) is used for adsorption if in the previous two time steps the water content was increasing. Pedersen proposed the values of A and B coefficients as follows: A ¼ 2 and B ¼ 0.1. Although, like the other researchers showed [21,25], it is better to fit those coefficients for each material. For fitting the experimental data, primary sorption and desorption isotherm and secondary sorption or desorption isotherm are needed. 5.1. Setting A and B coefficient The coefficients A and B from Eqs. (4) and (5) were chosen using experimental data of primary adsorption and desorption isotherm and secondary desorption isotherm, as plotted in Fig. 9. Finally, coefficient A was found to be equal to 1.6 and B to 0.68. Those values were used in Eqs. (4) and (5), implemented in Humimur, for simulations of mass flow in the material with the effect of hysteresis. Even if the values of A and B coefficients fit well the experimental data, the fully empirical procedure of selection is not satisfactory from the theoretical point of view. It is still a present challenge to enhance understanding and modelling of

0.0180 0.0160 Water content [kg/kg]

638

0.0140 0.0120

desorption 79.5-33% adsorption desorption

0.0100 0.0080 0.0060 0.0040 0.0020 0.0000 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Relative humidity [-]

Fig. 9. Curves of primary sorption and desorption isotherms, and second desorption isotherm from [24].

hysteresis. It seems interesting to exploit micro-structural properties, such as pore-size distribution. 5.2. Simulations and results In this part of the paper the results of mass flow calculation for the model with the hysteresis effect are presented. The simulations were done for gypsum board from Test 1 (Table 1), with thickness of the sample l ¼ 12.5 mm, number of layers z ¼ 5, time step ¼ 60 s, and period of calculation ¼ 360 h. The boundary condition, ambient relative humidity, was described by a sinusoidal function with a 24-h period, oscillating between 30% and 50%. The initial relative humidity in the material was equal to 40%. In Fig. 10, water content in the middle layer of the material is plotted. The darker line describes the process of change in water content when at the beginning the desorption process appears. The lighter line depicts the process starting with adsorption. A large difference can be seen during several initial cycles between the two situations. However, after several cycles (approximately 12 here), the material water content is predictably at the same level in both situations. Additional simulations of the mass flow in the material were performed with different levels of relative humidity: for the first 7 days it was varying sinusoidaly between 55% and 45% and for the next week between 50% and 40%. Fig. 11 shows that moisture content in the material, as expected, is situated in between the curves of adsorption and desorption, and the shape of the curve is similar to previous results from the literature [12].

6. Impact of hysteresis To demonstrate the influence of sorption hysteresis effect on water vapour transport in building materials, series of simulations of the 12.5-mm-thick gypsum board were performed. The same material and same boundary conditions were used with two models: with and without hysteresis effect. The convection mass transfer coefficient b and temperature were the same as those used in Test 1 (Tables 1 and 2), but the relative humidity in the air was changing sinusoidally between 45% and 55%. The calculations were made for four variants (see Fig. 12):

 Hysteresis: The model with hysteresis effect.  Adsorption: Model without the hysteresis effect. The dependency between the relative humidity and the water content is described by the adsorption isotherm.

ARTICLE IN PRESS J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

639

0.0060 0.0055

Water content [kg/kg]

0.0050 0.0045 0.0040 0.0035 0.0030

layer 3 desorption

0.0025

layer 3 adsorption

0.0020 0

24

48

72

96 120 144 168 192 216 240 264 288 312 336 360 Time [h]

Fig. 10. Moisture mass content at the depth of 6.25 mm.

 Desorption: Model without the hysteresis effect. The depen-

0.008 hysteresis

Water content [kg/kg]

0.007

sorption isotherm



desorption isotherm

0.006 0.005 0.004 0.003 0.002 0.25

0.35

0.45

0.55

0.65

Relative humidity [-] Fig. 11. Profile of water content at the depth of 6.25 mm, as a function of periodical changes of air relative humidity.

hysteresis adsorption desorption average

dency between the relative humidity and the water content is described by the desorption isotherm. Average: Model without the hysteresis effect. The dependency between the relative humidity and the water content is described by the average from adsorption and desorption isotherms.

In Fig. 15 the profiles of moisture content in the gypsum board after stabilization are presented. A significant difference can be seen between the model with hysteresis effect and the models using only adsorption or desorption equations. However, when the average curve between adsorption and desorption is used, the results can approximate correctly the behaviour with hysteresis effect. The results of simulations for the changing humidity conditions in the air (for the first week the relative humidity was changing from 45% to 55% and for the next week from 40% to 50%) are presented in Fig. 13. It can be seen that achieving the equilibrium state in the material takes approximately 1 week, in case of hysteresis. Here, significant differences in the level of moisture content between the model with hysteresis and all other variants can be seen. The effect of sorption hysteresis is more important in the case of strongly dynamic changes of the boundary relative humidity than in the case of steady-state conditions.

0.008

7. Practical use of the Humi-mur model

Water content [kg/kg]

0.007

7.1. Implementation in an energy performance simulation tool

0.006 0.005 0.004 0.003 0.002 240

252

264

276 Time [h]

288

300

312

Fig. 12. Moisture mass content in the gypsum board at the depth of 6.25 mm, for four calculation variants.

In order to demonstrate the practical use of the developed model, the first module of Humi-mur was implemented into a well-known building simulation tool called TRNSYS [26]. TRNSYS was designed to solve complex energy system problems but the variation of the indoor parameters like temperature or relative humidity can be also simulated. Thanks to the modular structure of the TRNSYS programme, the Humi-mur model was translated into FORTRAN and implemented in TRNSYS Studio as a new type responsible for the moisture buffering of the materials. Humi-mur calculates moisture flow exchanged between indoor air and moisture buffering materials. This moisture flow is also included in the water vapour mass balance of the indoor air, as shown in Fig. 14.

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hysteresis

0.008

adsorption desorption

Water content [kg/kg]

0.007

average

0.006

0.005

0.004

0.003

0.002 0

24

48

72

96

120

144

168 192 Time [h]

216

240

264

288

312

336

Fig. 13. Moisture mass content in the gypsum board at the depth of 6.25 mm, for four calculation variants, with changes in air relative humidity.

Fig. 14. Scheme of the Humi-mur implementation into the TRNSYS simulation tool.

It has been shown that the Humi-mur model implemented into TRNSYS environment allows to predict indoor relative humidity of the considered zone [27]. Also, the model of moisture buffering was used to examine the influence of materials water vapour storage on moulds growth risk on the internal wall surfaces. It was shown that materials that buffer water vapour can significantly decrease the risk of mould growth [28]. In order to check if hysteresis effect influences moisture buffering of the materials at the building level, some additional calculations in the TRNSYS programme have been performed. In the simulations two models have been used: the first without hysteresis and with average sorption isotherm, and the second with hysteresis of sorption curves. The calculations of indoor absolute humidity were made for a small room (2.5  3.5  2.6 m3) with the gypsum board (30 m2) as a buffering material. The considered room had two external walls and one window. It was assumed that the rest of the zone’s envelopes were adiabatic. Additional gains of heat and water vapour were also added. The periods with heat and humidity production were established each morning (from 6 to 8 a.m.), afternoon (from 12 to 14 p.m.) and evening (from 18 to 21 p.m.). Also a ventilation rate of 22.75 m3/h was assumed. The simulations were performed for 1 year, using weather file Warsaw (Poland). In order to avoid too low temperatures in the zone, the heating season with a constant temperature of 20 1C was set from the 1 October till 15 May. In the simulation the time step of 600 s was used for the model without hysteresis effect and of 72 s for the model with hysteresis effect. Hourly results were compared.

7.2. Results and discussion In Fig. 15 the relative difference of water content of the indoor air between the models is presented. Although most of the time the difference is smaller than 5% and the mean difference equals 3.1%, it can be noticed that sometimes the difference reaches high values. It was calculated that for 23% of the time, the difference passes the limit of 5% and for 6% of the time is higher than 10%. The difference between results of the absolute humidity obtained using the model without hysteresis and with hysteresis can reach as much as 20%. The highest values of the difference were obtained when the absolute humidity in the zone had the highest or the lowest values. It was also noticed that for the maximum values of the zone absolute humidity, the model without hysteresis was decreasing water content in the air more significantly than the model with the hysteresis effect. Similar situations occurred for the minimum values of the zone absolute humidity. The model only with the average sorption curve was increasing the water content of the air more significantly than the model with hysteresis. This phenomenon shows that using in the calculation model only with the average sorption curve reduces the amplitude of indoor absolute humidity more than the more realistic model with hysteresis. Neglecting hysteresis in the sorption curve leads to overestimations of the moisture buffering capacity of materials. For some materials those differences will not provide significant errors but for others (such as wood) they may lead to underestimations of risk of condensation or of mould growth.

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641

Number of hours

10000

1000

100

10

1 7.5 2.5 12.5 17.5 22.5 Relative difference in water content between two models [%] Fig. 15. Relative difference in water content of the air between results obtained using the model without hysteresis and with hysteresis.

Table 5 Sensitivity of relative humidity calculations for different number of layers and time step for the 150 mm thick sample Parameter

Number of layers

Time step (s)

Value

Deviation (depth 50.0 mm)

Deviation (depth 100.0 mm)

48 72

0.01% Divergence

0.00% Divergence

30 120

0.01% Divergence

0.01% Divergence

Table 6 Sensitivity of relative humidity calculations for changes in sorption isotherm and vapour permeability for the 37.5 mm thick sample Property

Adjusted

Deviation (depth 12.5 mm)

Deviation (depth 25.0 mm)

Sorption isotherm

() (+)

3.50% 3.61%

6.15% 6.19%

Vapour permeability

() (+)

Divergence 2.70%

Divergence 4.94%

Table 7 Sensitivity of relative humidity calculations for changes in sorption isotherm and vapour permeability for the 150 mm thick sample Property

Adjusted

Deviation (depth 50.0 mm)

Deviation (depth 100.0 mm)

Sorption isotherm

() (+)

0.48% 12.11%

3.42% 10.67%

Vapour permeability

() (+)

Divergence 4.37%

Divergence 3.49%

8. Conclusions and perspectives A new module for the precise representation of mass transfer in materials in contact with indoor air, called Humi-mur, was elaborated and validated in this work. It was then applied to estimate the sensitivity of the results to uncertainty in measured material properties and the impact of hysteresis effect. Humi-mur

was also successfully implemented in a whole-building simulation code, TRNSYS. The new model allows considering several different materials, and for precise definition of properties for moisture transfer. Reasonable estimation of experimental uncertainty resulted in the deviation of approximately 6% in calculated results. It is important to know better the accuracy of predictions. The simulation tool cannot give results more precisely than the input data. Some kind of uncertainty or error-bar should then complement the simulation results. For some variation of parameters the divergence problems occur (see Tables 5–7). The difficulty in obtaining results from numerical calculation is related mainly with too long time step or too thin layer in the material. The stability of numerical simulation will be investigated in the near future. Concerning hysteresis in the sorption isotherm, we showed that using only one of the sorption isotherm equations (adsorption or desorption) leads to significant differences. More precise results were achieved if the average of the adsorption and desorption equations was used in the model. For less-precise calculations it appeared to be a reasonable approximation of mean behaviour. However, for strong variations in boundary conditions, it is not well suited. Indeed, convergence to some kind of quasi-permanent state is much slower if hysteresis is considered. This effect influences the dynamic behaviour of materials. It was also shown that in realistic conditions (a room under variable climate and hygrothermal loads), neglecting hysteresis leads to overestimation of moisture buffering properties of materials in contact with the indoor air. In some cases such overestimation may conduct to the underestimation of risks of mould growth and/or condensation. References [1] Padfield T. Humidity buffering of the indoor climate by absorbent walls [on line]. In: Proceedings of the fifth symposium on building physics in Nordic countries, vol. 2. Goteborg: Chalmers University of Technology; 1999. p. 637–44 Pdf available at: /http://www.padfield.org/tim/cfys/appx/ pubs.phpS. [2] Osanyintola OF, Simonson CJ. Moisture buffering capacity of hygroscopic building materials: experimental facilities and energy impact. Energy and Buildings 2006;38:1270–82. [3] Hens H. Final report, vol. 1, Task 1: modelling, IEA Annex 24. ACCO Leuven; 1996. [4] Canada Mortgage and Housing Corporation (CMHC). Review of hygrothermal models for building envelope retrofit analysis. Research highlights, technical series 03-128./http://www.cmhc-schl.gc.ca/publication/en/rh-pr/tech/03-128-e.htlmS. [5] Ku¨nzel HM. Simultaneous heat and moisture transport in building components. One- and two-dimensional calculation using simple parameters. IRB Verlag; 1995.

ARTICLE IN PRESS 642

J. Kwiatkowski et al. / Building and Environment 44 (2009) 633–642

[6] WUFI. PC-program for calculating coupled heat and moisture transfer in building components. /http://www.wufi.de/index_e.htlmS. [7] Holm A, Ku¨nzel HM. Two-dimensional transient heat and moisture simulations of rising damp with WUFI 2D. 12th international brick/block masonry conference, Madrid, 25–28 June 2000. [8] Burch DM, Chi J. MOIST. A PC program for predicting heat and moisture transfer in buildings envelopes. Release 3.0, 1997. [9] Hagentoft CE, Blomberg T. 1D-HAM. Coupled heat, air and moisture transfer in multi-layered wall structures. Manual with brief theory and an example, version 2.0, 2000. /http://www.buildingphysics.com/manuals/1dham.pdfS. [10] MATCH—Moisture and temperature calculation for constructions of hygroscopic materials, /http://www.match-box.dkS. [11] Pedersen CR. Combined heat and moisture transfer in building constructions. Ph.D. thesis. Report 214. Thermal Insulation Laboratory, Technical University of Denmark, 1990. [12] Pedersen CR. Transient calculation on moisture migration using a simplified description of hysteresis in the sorption isotherms. The second symposium on building physics in the Nordic Countries, Trondheim, 20–22 August 1990. [13] Geving S, Karagiozis A, Salonvaara M. Measurements and two-dimensional computer simulations of the hygrothermal performance of a wood frame wall. Journal of Thermal Insulation and Building Envelopes 1997;20(April 1):301–19. [14] Geving S. A systematic method for hygrothermal analysis of building constructions using computer models. In: Proceedings of the building simulation, vol. 2; 1997. p. 355–61. [15] Mukhopadhyaya P, Goudreau P, Kumaran MK, van Reenen D. Influence of material properties on the moisture response of an ideal stucco wall: results from hygrothermal simulation. In: Sixth Nordic Building Physics Symposium, Trondheim, Norway, 17–19 June 2002. [16] Salonvaara M, Karagiozis A, Holm A. Stochastic building envelope modeling—the influence of material properties. Performance of exterior envelopes of whole buildings VIII: integration of building envelopes, CD-ROM (2001), December 2–7 2001. 8pp. [17] Kumaran MK. Final Report, vol.3. Task 3: Material properties, Acco Leuven, 1996.

[18] Sereda PJ, Feldman RF. CBD-130.Wetting and drying of porous materials, 1970. [19] Mualem Y. A conceptual model of hysteresis. Water Resources Research 1974;10(3). [20] Time B. Studies on hygroscopic moisture transport in Norway spruce (Picea abies). Part 2: Modelling of transient moisture transport and hysteresis in wood. Holz Als Roh-und Werkstoff 2002;60(6). [21] Carmelit J, de Wit M, Jansen H. Hysteresis and moisture buffering of wood. In: Seventh Nordic symposium on building physics, Reykjavik, 12–15 June 2005. [22] Peralta PN. Modelling wood moisture sorption hysteresis using the independent-domain theory. Wood Fiber Science 1995;27:250–7. [23] Crausse P, Laurent JP, Perrin B. Influence des phenomenes d’hysteresis sur les proprietes hydriques de materiaux poreux: Comparaison de deux modeles de simulation du comportement thermohydrique de parois de batiment. Revenu Generale de Thermique 1996;35(410). [24] James C, Simonson CJ, Talukdar P. Annex 41 report for common exercise subtask 2, IEA annex 41, June 2007. 89pp. [25] Frandsen HL. Modelling of moisture transport in wood. Wood science and timber engineering, Paper no. 1, 2nd ed. Department of Building Technology and Structural Engineering, Aalborg University, March 2005. ISSN:1395-7953R0502. [26] Klein SA, Beckman WA, Mitchell JW, et al. TRNSYS 16, a transient system simulation program, Solar Energy Laboratory, University of Wisconsin, Madison, USA, 2004. [27] Kwiatkowski J, Feret K, Woloszyn M, Roux J-J. Predicting indoor relative humidity using building energy simulation tools. In: The sixth international conference on indoor air quality, ventilation & energy conservation in building, Sendai, Japan, 28–31 October 2007. [28] Kwiatkowski J, Woloszyn M, Roux J-J. The influence of material moisture buffering on moulds growth risk on the internal wall surfaces (Wplyw buforowania wilgoci przez materialy na ryzyko rozwoju plesni na powierzchni przegrod wewnetrznych), IX Polish conference ‘‘The problems of indoor air quality in Poland’’ (IX Ogolnopolska Konferencja ‘‘Problemy jakosci powietrza wewnetrznego w Polsce’’), Warsaw, Poland, 22–23 November 2007 [in polish].