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Eleventh International IBPSA Conference Glasgow, Scotland July 27-30, 2009 FINITE ELEMENT MODELLING OF COUPLED HEAT AND MOISTURE TRANSFER IN TYPICAL EARTH-SHELTERED BUILDING ENVELOPE Xibin Ma1, Baoyi Cheng1, Jinfeng Mao1, Wenjie Liu2, Dongyi Zi1 1 Engineering Institution of Engineering Corps, PLA University of Science and Technology Nanjing, 210007, P.R. China, xibinma@gmail.com 2 Investigation and Design Institute of Guangzhou Military Region Air Force Guangzhou, 510052, P.R. China, newlewin@gmail.com irreversible thermodynamics to describe the ABSTRACT interactions of the forces and fluxes involved. A It is necessary to do research on the heat and mechanistic approach based on physical models of moisture transfer in the earth-sheltered building for the phenomenological processes that occur in the soil getting a better underground environment. Based on was established by Philips and De Vries (Philip et al., Philips and De Vries’ and Zhang’s theory (Philip et 1957; De Vries, 1958). Whitaker (Whitaker, 1973; al., 1957; Zhang et al., 2006), this paper establishes a Whitaker, 1977; Whitaker, 1980) averaged the detailed 2-D transient mathematical model to transport equation on a representative elementary understand the heat and moisture transfer exactly in volume (REV) at the continuum level and obtained the earth-sheltered building envelope and the the governing equations in a higher level. This surrounding soils. A general FEM (Finite Element modelling method overcomes the modelling Method) software is adopted to solve the highly difficulty that porous media are heterogeneous. But nonlinear governing equations. The numerical the transport coefficients of the model can not be get simulation showed that the existence of waterproof easily without the complex experiments. These layer makes the temperature field continuous and the models have been adopted widely by many moisture field discontinuous. The results may afford researchers (Deru, 2001; Lu, 2002; Lu, 2002; Janssen the basis of heat and moisture load calculation for the et al., 2004; Qin et al., 2006). According to the earth-sheltered building. models of Philip, De Vries, Luikov and Whitaker, Liu (Liu et al., 1995; Liu et al., 1998) developed the INTRODUCTION multiphysics-phase change-diffuse model recently With the development of economy and society, the which based on the Navier-Stokes equation. This underground space is explored widely in China to model has seven field variables. Besides, there are enlarge the urban space (Carmody et al., 1982; Tong, more models established by the researchers 2005; Qian et al., 2007). However, moisture is one of worldwide (Thomas, 1987; Pedersen, 1990; the most important factors limiting an earth-sheltered Matsumoto et al., 1997; Mendes et al., 2002; dos building’s service life. Moisture damage has been Santos et al., 2006; Tariku et al., 2006). identified as one of the main reasons for building Compared to the heat and moisture research in the envelope deterioration. More recently recognized are ground buildings, the literature referred to earth- the potential serious health hazards of mould and sheltered building is limited. Ogura analysed the heat other organisms which flourish in buildings and and moisture behaviour in underground space by constructions with excessive moisture (Geving, quasilinearized method (Ogura et al., 1999). Zhang 1997). Therefore, it is necessary to do research on the had presented a mathematical model which described heat and moisture transfer in the earth-sheltered with temperature and relative humidity as driving buildings for getting a better underground potential for coupled heat and moisture transfer in environment. porous wall materials. This model could make the For decades, many researchers have devoted to the discontinuity on the moisture content profile work of modelling of heat and moisture transfer in continuous. However, both the models did not take ground building envelope (Straube et al., 2001). As the influence of the waterproof layer into early as 1960s, Luikov (Luikov, 1966) has firstly consideration and the quasilinearized method could proposed a mathematical model for simultaneous not reflect the heat and moisture variations actually. heat and mass (moisture) transfer in building porous Then the purpose of this paper is to clarify the heat materials. The conservation equations include the and moisture behaviour in the earth-sheltered mass, the momentum and the energy conservation building envelope under the natural condition. equations. The constitutive equations are described by Darcy’s law, Fick’s law and Fourier’s law. PHYSICAL AND MATHEMATICAL However, the solutions are either numerical or MODEL complicated involving complex eigenvalues. Cary To analyse the coupled heat and moisture transfer in and Taylor (Cary et al., 1962; Cary et al., 1962) uses the envelope of the typical earth-sheltered building, - 1850 - this paper takes an underground building in Nanjing Zhang’s model (Zhang et al., 2006), the coupled heat (China) as an example, as depicted in Figure 1. The and moisture transfer model in this paper is derived length (L), with (W), height (h) and the arc height (h1) according to the two. Based on the assumption above, is 50m, 6m, 5.3m and 1.5m, separately. The distance the governing equations describing the heat and between the soil surface and the top of the building is moisture transfer in the envelope and the surrounding 1.5m and the thickness of the envelope is 0.5m soils are as follows. (Suppose the thickness in the different area of the T envelope is same). m cm keff T (1) Y D DT T (2) l X 0 Where d+h2 L T Dv pv , sat L T keff km 1 (3) Rv T 2 Rv h1 Ω1 Dv pv , sat Dl l Rv T D (4) Ω2 Rv T H Dv pv , sat L T h W DT Dl l Rv ln 1 (5) Rv T 2 Rv h2 Dl in Equation (4) is determined by Equation (6) (Valen, 1998), Dv v , sat Dl (6) Figure 1 Cross-section of typical shallow buried Rv T l underground engineering The meaning of the symbols and notations used in Before the mathematical modelling, there are some the equations are given in the Nomenclature. assumptions. The upper surface of the physical domain is exposed Homogeneous and isotropic porous media to solar and long-wave radiations, convection heat (envelope and the surrounding soil) with no and moisture transfer. This way, for Y 0 , the distension and contraction is considered. boundary condition becomes Local thermal equilibrium is satisfied keff T Y 0 hhs To T Y 0 I throughout the porous media. (7) T Y 0 Tsky 4 L T hms o Y 0 4 Capillary pressure on the interfaces of the different material layers is equal, i.e. the and the mass balance is written as D DT T hms o Y 0 hydraulic continuous. (8) The moisture absorption and desorption progress is isothermal without considering The heat and moisture balance on 2 is described as the influence of the capillary hysteresis. The length of the building is relative long keff T Y 0 hhi Ti T 2 (9) compared to the with and height, the two dimensional is adopted. L T hmi i 2 The drive potential for the liquid water in the porous material and the water vapor is D DT T hmi i 2 (10) density gradient and capillary pressure The interface 1 represents the waterproof layer, so gradient. the heat is continuous while the moisture could not The waterproof layre can stop the mositure transfer from it. The boundary is transfer completely. The thermal parameters are constants for D D T T soil 1 0 (11) given material. There is no heat or moisture source in the D D T T envelope 1 0 (12) envelope and the surrounding soils. Tsoil 1 Tenvelope (13) As the Philips and De Vries’ model (Philip et al., 1 1957) was adopted worldwide and the merit of - 1851 - Through the model of natural soil temperature field, the depth formula of the constant temperature layer 40 was deduced by Liu et al. (Liu et al., 2007). So in the Outdoor temperature /C depth of H 20 m, it is supposed that the water table 30 is there and the temperature is constant. As a result, the heat and moisture condition in this layer in 20 Nanjing (China) is written as (Liu et al., 2007) T Y 20 17.5 273.15 K (14) 10 Y 20 90% (15) 0 If it is sufficient far away from the envelope, the heat and moisture transfer can no longer influence the soil -10 0 2000 4000 6000 8000 temperature profile, where is defined as the adiabatic and impermeable. When it refers to the determination Time /h of l , it is another problem. It comes true only l Figure 2 Annual variation of the dry bulb in theory. However, it is unrealistic in the numerical temperature Nanjing (China) form CSWD simulation. 0.5l 15 20 m in many simulations (Adjali et al., 1998; dos Santos et al., 2003) is 1.0 adopted here. Symmetry reduces the modelling domain to half of the model. It gets a symmetry boundary on X 0 . Relative humidity /% 0.8 SIMULATION 0.6 The governing equations were solved using COMSOL Multiphysics (COMSOL AB, 2008). COMSOL Multiphysics is a powerful interactive 0.4 environment for modelling and solving all kinds of scientific and engineering problems based on partial 0.2 differential equations (PDEs). With this software you can easily extend conventional models for one type 0 2000 4000 6000 8000 of physics into multiphysics models that solve coupled physics phenomena—and do so Time /h simultaneously. The software runs the finite element Figure 3 Annual variation of relative humidity analysis together with adaptive meshing and error Nanjing (China) form CSWD control using a variety of numerical solvers. 1000 horizontal global irradiation /(W m ) Suppose the material of the envelope consists of 2 concrete, and the soils surrounding the underground building is made of lime rock. The thermophysical 800 parameters of them are listed in Table 1. Table 1 600 Thermophysical parameters of the building materials and the soils (Ma et al., 1986) 400 MATERIAL LIME ROCK CONCRETE [kg/m3] 1700 2200 200 c [J/(kg K)] 930 840 K [W/(m K)] 0.93 1.28 0 Dv [m2/s] 6.9 106 1.4 105 0 2000 4000 6000 8000 The CSWD, Chinese Standard Weather Data, (China Time /h Meteorological Bureau Climate Information Center Figure 4 Annual variation of horizontal global Climate Data Office et al., 2005) for the city of irradiance Nanjing (China) form CSWD Nanjing was used, with a constant convection heat transfer coefficient of 15 and 8.14 W/(m2 K) for hhs The approximate expression of mass convection and hhi (Yuan, 2005), an absorptivity of 0.5 (dos coefficient is determined by (Galbraith, 1992) Santos et al., 2003) and emissivity of 0.9 (Liu et al., hm 9.28 104 hh (16) 1983). Figure 2-Figure 5 present the annual variation of temperature, relative humidity, horizontal global irradiation and equivalent sky temperature in Nanjing. - 1852 - The moisture absorption and desorption process lines Figure 6 Temperature profile of the earth-sheltered for concrete and lime rock are provided with the building envelope and the surrounding soils at the following equations (Ma et al., 1986; Pei et al., 1999), time of 2 years 0.000392 w (17) 1 1.8504 0.9874 2 w 0.014 4 0.021 3 0.014 2 (18) 0.0014 0.00042 320 300 Sky temperature /K 280 260 Figure 7 Relative humidity profile of the earth- 240 sheltered building envelope and the surrounding soils at the time of 2 years 0 2000 4000 6000 8000 Figure 6 and Figure 7 present the temperature and Time /h relative humidity spatial distributions at 14:00 on Figure 5 Annual variation of the equivalence sky July 20th. It is possible to notice in Figure 6 that the temperature Nanjing (China) form CSWD existance of the earth-sheltered building had influenced the soil’s temperature distribution a lot. RESULTS AND DISCUSSIONS For the indoor air have a constant temperature of In this numerical simulation, the finite element 26°C, the heat is tranfered from the envelope to the method is triangle and 945 mesh points, 1760 soil in summer. While the waterproof layer had not elements were used. Take 15:00 on July 20th, which affect the heat transfer progess on the interface of the is the time of outdoor maximal temperature (37.2°C), envelope and the rock, it did effect the moisture as the initial time for the simulation. For initial transfer (see in Figure 7). Note that in Figure 7, the condition for the soil, a temperature of 17.5°C and a left colorbar is for the rock and the right one for the relative humidity of 50% were utilized. While for the envelope. After a whole year, the moisture had envelope, temperature of 17.5°C and a relative absorped by the upper lay of soil in this simulation. humidity of 90%. Suppose the underground space is Due to the waterproof layer, the moisture in the soils air-conditioned by the HVAC system, and the didn’t transfer to the envelope, and the moisture in temperature and relative humity maintains 26°C and the envelope had been transferred into the indoor 60%, separately. The simulation period is 2 year environment afer construction. (17520 hours) and time step is 1 hour (Wang, 2007). 6 0.5 5 0.4 Moisture flux Heat flux m2) 4 0.3 Heat flux q/(W 3 /(g m2 h ) 0.2 2 Moisture flux 1 1 0.1 0 00 00 00 00 0 0 0 0 00 00 00 00 20 40 60 80 10 12 14 16 Time /h Figure 8 Variation of the heat and moisture flux on the wall of the earth-sheltered building - 1853 - Figure 8 shows the variation of the heat and moisture coupled heat and moisture flow in soils (Shen, 1986), flux on the wall of the earth-sheltered building. The results from the coupled model were compared to moisture flux varies similarly with the heat flux. The results obtained when the governing equations were maximum moisture flux in this simulation is decoupled. For the sand simulation, a 9% greater 3.03g/(m2 h) and it fluctuates between 0.1-0.3 g/(m2 wall heat loss during the winter and almost a 50% h), Which meets the experimental results of 1.7g/(m2 increase in summer heat gain occurred due to h) and 0.12 g/(m2 h) in China (Editorial Group, 1983). coupling. Due to the lack of thermophysical So the models in this paper is validated based on the parameters of the building materials, only the lime assumption that the waterproof layre can stop the rock and concrete were studied in this paper. mositure transfer completely. However, both the results indicates that the couple heat and moisture transfer model should be 3.0 0.7 considered in some cases. 2.8 2.5 0.6 CONCLUSION /(g m2 h ) 1 2.3 0.5 Based on the theory of Philips and De Vries’ and 2.0 0.4 Zhang’s model, this paper built a mathematical 1.8 0.3 model to analyze the coupled heat and moisture 1.5 Ceiling transfer in the envelope of earth-sheltered building Moisture flux 0.2 1.3 Wall and the surrounding soils. The COMSOL 1.0 Floor 0.1 Mutiphysics was utilized to solve the governing 0.8 0.0 equations in the porous materials. The software could 0.5 couple the temperature field with the moisture field 0.3 and solve the nonlinear problem effectively. It may 0.0 be conclude from the results that, 0 00 00 00 00 0 0 0 0 00 00 00 00 1. The waterproof layer could prevent the moisture 20 40 60 80 10 12 14 16 tranfering between the envelope and the Time /h surrounding soils, while the temperature field is Figure 9 Variation of the moisture flux in the ceiling, still coutinuous. The mathematical model could floor and wall of the earth-sheltered building describe the coupled heat and moisture transfer in the different porous material simultaneously 40 and independently. 2. The moisture flux in the wall, ceiling and floor of q/(W m2) the earth-sheltered building is different. Of the 30 three, moisture flux in the ceiling is the biggest. Coupled heat and moisture Heat only Becasuse the heat transfer in the ceiling is 20 affected by the ourdoor meteorologic paratmeters Heat flux more. Accordingly, the moisture transfer is infuenced by the temprature. 10 3. The couple heat and moisture transfer model should be considered in some cases when do 0 investigation of heat transfer in the porous materials. 0 00 00 00 00 0 0 0 0 00 00 00 00 20 40 60 80 10 12 14 16 The research may reflect the heat and moisture Time /h transfer in the underground engineering envelope and Figure 10 Comparison of the heat flux by the model the surrounding soils objectively and the results in this paper and the heat transfer only model could afford the basis of heat and moisture load calculation for underground engineering. As the The difference of moisture flux in the ceiling, floor results were obtained by the numerical simulation, it and wall of the earth-sheltered building is depicted in is necessary to do verification and analysis by both Figure 9. The moisture flux on the ceiling fluctuated the experiments in the lab and field test further. more than the one on the floor or wall. It may due to the influence of the vaiation of outdoor meteorologic ACKNOWLEDGEMENT paratmeters. Figure 10 compares the heat flux on the The ﬁnancial support from China National Civil Air surface of the underground engineering envelope Defense Ofﬁce (Project NO. ZC1302K30) is based on the coupled heat and moisture transfer gratefully acknowledged. model and heat transfer model, separately. The mean relative error during the simulation is 11.4%. Shen REFERENCES did an an investigation of transient, two-dimensional Adjali, M. H., M. Davies and J. Littler.1998. Three- dimensional earth-contact heat flows: A - 1854 - comparison of simulated and measured data for a heat loss via the ground. Building and buried structure. Renewable Energy, 15 (1-4): Environment, 39 (7): 825-836. 356-359. Liu, S. and Y. Huang. 1983. Discussion on effective Carmody, J. and D. Derr.1982. The use of sky temperature. ACTA ENERGIAE SOLARIS underground space in the People's Republic of SINIC, 4 (1): 63-68. 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