1、472 1 Indoor Humidity Modeling and Evaluation of Condensation on Franck Lucas, Ph.D. Interior Surfaces ABSTRACT In tropical humid climates, moisture and condensation on walls lead to significant damage of buildings. The purpose of this article is to present a numerical model to improve the predictio
2、n of internal humidity in buildings. Thermal simula- tion codes usually evaluate moisture due only to airflow trans- fers. The model presented takes into account the moisture transfers between walls and air inside a zone. It allows a fore- cast of the quantities of liquid condensed on a surface. An
3、experimental comparison is presented to appreciate the improvement of the model. INTRODUCTION The design of buildings is confronted with many contra- dictory requirements. These requirements appear in the phys- ical, physiological, economic, sociological, and ecological concepts implied. Managing th
4、ese contradictions has lead to a new global approach to design. The purpose of the concept of sustainable buildings is to evaluate the total performance of a construction. Concerning building thermal design, increasing user claims, in terms of comfort, go against energy and envi- ronmental requireme
5、nts. Many tests carried out on envelope design in tropical climates, especially in French overseas departments, have allowed the emergence of regulations to improve the comfort of buildings, avoiding air conditioning. Nevertheless, it appears that the design must be adapted to some local climatic sp
6、ecificity. Thus, highlands and coasts of tropical areas are characterized by appreciably different climates. The studies undertaken until now show that the main problems concerning building design in the highlands are linked to the high humid- Frederick Miranville, Ph.D. ity. These problems are visi
7、ble: proliferation of mold, damage of surface coatings due to condensation phenomena, and streaming of condensation. Pathologies observed concern the comfort and the health of occupants and the permanence of buildings. In some cases, on windows, for example, conden- sation is acceptable as long as t
8、he quantities of condensed water are small enough to avoid streaming. To fight all disor- ders related to condensation, the design of buildings must be adapted accordingly. It is a precondition to any recourse to active heating or dehumidification systems. It is thus neces- sary to develop specific
9、tools in order to help designers to improve construction quality in the highlands of tropical areas. To meet the requirements of the French thermal regulation, these tools must require dynamic simulation codes. In this context, this study proposes to present models related to the behavior of buildin
10、gs faced with humidity problems. The first objective is to provide a design tool used during the prepara- tory project to improve building conception. The second objective is to help researchers study moisture transfer and condensation potential within walls. This tool therefore needs to be simplifi
11、ed and with a reduced number of parameters in order to be compatible with information available at the beginning of a building project. The second objective imposes a development of a specific model to precisely characterize the behavior of the building envelope. The assessment of the hydrous exchan
12、ges between various walls of a zone and the air will enable the determina- tion of the relative humidity within the wall. The objective of this model is to evaluate the potential risk of condensation or mold appearance on building envelope. _ F. Lucas is an assistant professor and a researcher and E
13、 Miranville is a researcher in the Civil Engineering Department and at the Laboratoire de Gnie Industriel, Universit de La Runion, Reunion Island, France. 300 02004 ASHRAE. MODELING REVIEW Vapor transfer through walls is a major concern for build- ing designers. In 1959, Glaser (1 959) worked out on
14、e of the first procedures to evaluate vapor flows through walls. The dew point method, or the Kiepper method (ASHRAE 2001), was then established to evaluate the risks of water vapor condensation inside walls. As underlined by Galbraith (Galbraith and McLean 1993), these methods, based on the Fick la
15、w, are intended to study walls in steady conditions. This approach assumed that the transfers occur only in vapor phase and that liquid transfers are not considered. The vapor pressure is the potential of the diffusion. The advantage of this method is that its implementation is simple and does not r
16、equire numerical tools. However, the steady-state method does not consider water quantities stored in the material nor the time- constants of the phenomena. More precise dynamic models have recently been elaborated, considering interactions between liquid, vapor, and solid phases. They are based on
17、the study of porous media. This phenomenological approach consists of expressing transport equations of mass in porous media in the same way as equations of heat difision. As mentioned earlier, mass transport occurs in liquid and vapor phase. In the vapor phase, two gradients intervene simulta- neou
18、sly: the gradient of concentration and the variation in temperature. Liquid transfers depend on capillary forces, and the gradient involved is the difference of capillary pressure inside the pores. The choice of the potentials is essential in equation formulation. Galbraith et al. (1997) relies on t
19、he ther- modynamics of irreversible phenomena to show that the couples temperature/relative humidity or temperature/vapor pressure are the real potentials ofmoisture transfers. However, many authors use potentials derived from the relative humidity and vapor pressure obtained thanks to thermodynamic
20、 laws. These derived potentials often introduce discontinuities at the borders of the material. In general, the potentials must be chosen while keeping in mind the necessity to validate the models. Thus, a significant criterion is the accessibility of potentials by measurement. The most common formu
21、lations in literature use the couple temperature/water content of mate- rial. The mass balance equation of water is The two coefficients DT and Dx characterize water trans- fers in liquid and vapor phase due to temperature and water content gradient and are given by: Philip and DeVries (1957) propos
22、e expressions allowing the determination of the values of these exchange coefficients according to the characteristics of material such as porosity, tortuosity, density, and relative humidity of air. A simpler formulation is usually used. It relies on global coefficients to define transfers in porou
23、s media. The mass balance is written using the water content X in the following way : with The flux density p is then given by (4) To complete the problem, the following heat balance equation should be considered: This theoretical description of mass transfer in porous media thus reveals complex phe
24、nomena, which intervene simultaneously (example: transfers in vapor and liquid phase) or in a consecutive way (adsorption and capillary condensa- tion) (Philip et al. 1957). These phenomena are particularly difficult to evaluate in the case of buildings where materials are very different and whose p
25、roperties are often unknown. To describe the building envelope, the physicist is then confronted with the choice of the numerical values of the parameters. In addition, it is important to recall that the objec- tive of building thermal simulation codes is the evolution of the air inside the zone rat
26、her than the evolution of internal characteristics of envelope materials. Building thermal simulation codes are generally based on the phenomenological equations and, more particularly, the Fick law. This expresses the flux density transported accord- ing to a gradient of potential and a coefficient
27、 characteristic of the material. As Kohonen (1 989) underlines it, it is then neces- sary to be aware of the mechanisms of transport taken into account in the coefficients used. It is then possible to distin- guish various models: models that take into account transfers in the vapor and in the liqui
28、d phase separately, such as Galbraith?s model (Galbraith et al. 1993). models that simultaneously take into account the two transfers by a coefficient of effective diffusivity such as that introduced by Philip et al. (1957) or by neglecting the liquid transfers when the water content of materials is
29、 weak (Budaiwi et al. 1999). Kerrestecioglu develops two models, one based on the ?evaporation and conden- sation? theory and the other on the ?effective depth? of penetration (Kerrestecioglu et al. 1990; Kerestecioglu et a1.1990). To be quoted are the models of Yik (1991) and El Diasty et al. (1993
30、). ASH RAE Transactions: Research 301 To represent the behavior of materials inside a zone, glo- bal models are also used. These lumped parameter mod- els represent the whole material reacting with air moisture by a single fictitious volume called “buffer” (Duforestel and Dalicieux 1994; Plathner an
31、d Litter 1998; TRNSYS 1997). MODEL DEVELOPMENT A comprehensive study of building thermal design must be combined with the problem of comfort and maintenance of the frame. In tropical climates, it is necessary to develop specific tools to provide a response to troubles involved in moisture in buildin
32、gs. The purpose of the developed model is, thus, to evaluate the impact of moisture on walls and the poten- tial risk of condensation. In the highland of tropical climates, most of the buildings do not have air conditioning. Indoor conditions are not controlled and, therefore, inside tempera- ture a
33、nd humidity are free floating. In these conditions, vapor transfers through walls are small and the direction of these transfers is reversed during the day. Therefore, the model assumes that there is no vapor transfer through the walls. The model will study the case of hygroscopic walls first and th
34、en the case of walls considered as nonhygroscopic. The dimensional analysis, which defines the Biot number by the expression below, can provide a criterion for the classification of the walls. The Biot number evaluates the relationship between mass transfer by diffusion and convective mass transfers
35、. Materials characterized by a high Bi (Bi O) can be considered as nonhygroscopic and exchanging little moisture with the air of the zone. Among building materials, glasses, metals, and certain coatings will be of this category. In the model, these surfaces will be taken into account only because th
36、ey consti- tute a support to surface condensation. All other materials interact with the air moisture and will be defined as hygro- scopic. The hydrous balance of the zone i, expressed in water mass, integrates exchanges between air and walls, as is seen in the following equation: (7) n= 1 n= I Qai
37、Clai +-+- I, I, + +hygroscopic walls i- 4nonhygroscopic walls This equation includes two terms representing the flux exchanged between air and Model of Hygroscopic Walls The model evaluates the mass exchanged between air and hygroscopic walls if the wall is dry (without surface conden- sation) and a
38、lso if there is a presence of condensation. The description of exchanges is proposed by analogy with the elec- tric difision according to Figure 1. The exchanges between air and hygroscopic walls must distinguish two different cases: humid and dry walls. The term of Equation 7 can be defined as foll
39、ows: Number of dry walls C +waii,ry,g - $hygroscopic wall - (8) g= 1 Number of humid walls + c +wall,cond,i i= I Case of a Dry Wall. ln order to simplifj the future inte- gration of this model in the building simulation code CODYRUN (Boyer 1993), the water content of the air is used as the potential
40、 for the mass exchanges. This choice supposes that the vapor behaves as a perfect gas and that the diffusion is isothermal. One can then pose, P, = ,Tp,w. (9) The flow exchanged between the air and dry walls (indexed g) corresponding to a vapor mass exchange is given by $wall,dry,g = hmSg(wwall,g- w
41、, and the evolution law of the water content of this wall is given by the differential equation, For dry walls, the liquid mass on the surface is null; there- fore, m1iq.g = 0 (12) Dry hygroscopic wail v- I t Tsuchiya 1980) agreed to establish that moisture exchanges affect only a reduced thickness
42、of the wall. The designation most often used is “the effective depth penetra- tion” or active thickness. This term is in fact a parameter, which allows an adjustment of the model to the material concerned. Assuming that for building thermal simulations, external conditions vary following a sinusoid,
43、 the active thickness of a material can then be evaluated by e, = E. For traditional building materials having a diffsivity of about lo- m2/s, the affected thickness calculated by this expression is a few millimeters. Tsuchiya (1 980) proposes an average thickness of humid material equal to 4 mm. Eq
44、uation 15 gives where where I El Diasty et al. 1993; Budaiwi et al. 1999; Thomas and Burch 1990; Sipes and Hosni 2000). Galbraith and McLean (1993) propose experimental investigations to determine vapor and liquid transport coefficients. Experimental procedures have also been worked out to study liq
45、uid transfers in concrete and wood (Lucas 2001). The hydrous problem is solved by iteration on the humid- ity ratio of internal air. EXPERIMENTAL SETUP AND TEST PROCEDURE Experiments are composed of measurements carried out on buildings having been damaged due to condensation phenomena (yellowish bl
46、ack spots, detachment of paint, etc.). The aim is first to identify the causes of the damage and then to validate the models. The study relates to a building located in the highlands of the French overseas department, Reunion Island, at “LEntre-Deux (400 m altitude). The site is char- acterized by a
47、 wet tropical climate. The majority of the instru- mented residences are uninhabited. The walls are made of 20 cm hollow blocks covered with painted mortar on both the outside and inside. The roof consists of a ceiling in plaster- boards of 1.2 cm, an air layer, a glass wool insulator, and a corruga
48、ted iron sheet. The experimental campaign was conducted during the end of the coldest period of the year corresponding to the southern winter. The most damaged rooms of the building were instru- mented in a precise way. Interior air characteristics (dry-bulb temperature, resultant temperature, relat
49、ive humidity) were recorded, as well as wall, floor, and ceiling surface tempera- tures (Figure 3). Because the main damages are located on the ceiling, the characteristics ofthe air layer inside the. ceiling and surface temperatures of various parts of the frame (Figure 4) were measured. Living rooms and bathrooms of some inhab- ited residences were instrumented by small autonomous sensors of air temperature and relative humidity (4000 points of measurements). In order to evaluate the climatic characteristics and to allow the numerical simulations, the site was equi
