1、4726 Multidimensional Effects of Ground Heat Transfer on the Dynamics of Building Thermal Performance Gerson H. dos Santos Nathan Mendes ABSTRACT This paper describes a model for investigating pure conduction heat transfer through the ground and its influence on room air temperature, The diflerentia
2、l equation of enerD conservation for each node of the building envelope was discretized by using the jnite-diference method, a uniform grid, and afully implicit scheme. In order to investigate the use of simpler models for reducing computer run time of yearly building simulation programs, we conside
3、red three approaches, First, a one-dimensional model for the ground is adopted and then compared with two-dimensional and three- dimensional models. Also considered is lumped approach for a building, which is externally subjected to convection, solar radiation, long-wave radiation, and injltration.
4、Internally, interchange long-wave radiation and convec- tion are considered. People, equipment, and lighting are also considered in formulation as internal energy gain. In conclusion, we show that it may be important to take into account the use of three-dimensional ground heat transfer modeling in
5、building simulation programs for thermal load calculation and thermal comfort evaluations of low-rise build- ings. INTRODUCTION Data of the Energy Secretariat of the So Paulo State, Brazil, show that the electric energy consumption in Brazilian buildings represents more than 30% of the total consume
6、d in the country. However, the use of new technologies and mate- rial and the rational adequacy of criteria and architecture projects can reduce up to 60% of the energy consumption in buildings (www. energia. sp . gov.br) . Since the 1970s, many simulation programs, such as TRNSYS (1975), and, morer
7、ecently, ENERGY PLUS (1999) and DOMUS (2001), have been developed to simulate build- ing energy performance so that rational policies of energy conservation could be applied. However, these codes present some simplification of their calculation routines for heat trans- fer through the ground, which
8、may be important to take into account for thermal load calculation and thermal comfort eval- uations of low-rise buildings. The first experimental studies concluded that the heat lost through the ground is proportional to its perimeter. However, Bahnfleth (1 989) observed that the area and shape mus
9、t be also taken into account. ASHRAE (1 997) provides a mathematical formulation where the amount of heat transferred through the floor is proportional to the perimeter of the construction, the differ- ence between the external and internal temperatures, and to a factor that depends on the climate,
10、on the region, and on the type of the building. In this context, simulations involving computational methods as finite volumes are being used more and more. Davies et al. (1995), using the finite-volume approach, compared multidimensional models and observed that the use of three-dimensional soil si
11、mulation provides better predic- tion of building temperature and heating loads than two- dimensional simulation when these results are compared with experimental data. In other works, cited by Davies et al. (1995), Speltz (1980), and Walton (1987), using finite-differ- ence models found discrepanci
12、es of up to 50% for the thermal load, comparing two- and three-dimensional ground heat transfer models. BLAST (1977), DOE-1 (1978),NBSLD (1974), ESP (1974), Gerson H. dos Santos is with the Automation and Systems Laboratory and Nathan Mendes is with the Thermal Systems Laboratory at the Pontifical C
13、atholic University of Paran, Curitiba, Brazil. 02004 ASHRAE. 345 Adjali et al. (1999), with a three-dimensional model and using the finite-volume technique, camed out a sensitivity analysis on the discrepancy between experimental results and simulated ones for ground thermal conductivity. The influe
14、nce of snow and rain on the distortions of these temperatures was also analyzed. It was verified mainly that a purely conductive model can predict results close to experimental data. Currently, new techniques of simulation can be found. Zoras et al. (2001) used a combination that incorporates struc-
15、 tural response factors into a three-dimensional numerical solu- tion of the conductive heat transfer equation. Besides the ground, other parameters are inconsistent with the reality for application to building simulation programs, especially in the heat and mass transfer area. The mathematical desc
16、ription for predicting building hygrother- mal dynamics is also very complex due to the nonlinearities and interdependence among several variables. The parametric uncertainties in the modeling, simulation time steps, external climate, building schedules, and moisture content also contribute to incre
17、ase this complexity. Hence, in this work, we present a mathematical model in order to test the thermal performance of buildings. Heat diffu- sion through building envelopes is calculated by Fouriers law by considering only the pure conduction of heat, which is treated by the finite-difference method
18、. For the ground, a one- dimensional model was adopted first, imposing a null heat flux as the boundary condition at a depth of 4 m. For comparison purposes, two-dimensional and three-dimensional models were developed, where the solar radiation is imposed as a boundary condition for the external upp
19、er ground surface. The room can be subjected to loads of solar radiation, inter-surface long-wave radiation, convection, infiltration, and internal gains fiom light, equipment, and people. To calculate the room air temperature and relative humidity, we have used a lumped formulation for energy and w
20、ater vapor balances, as presented by Mendes and Santos (2001). This lumped approach was compared with a differential control volume produced by a program (CFX 2002) for simulating heat trans- fer and fluid dynamics problems in engineering. MATHEMATICAL MODEL The physical problem is divided into thre
21、e domains: soil, building walls, and internal air. The solar radiation and convection were considered boundary conditions at extemal surfaces. In the internal surfaces of a building, beyond the convection, long-wave radiation was considered. The thermo- physical properties (p, c, A) were assumed to
22、be constant and moisture effects were neglected on the calculation of conduc- tion loads. SOIL DOMAIN Considering Fouriers law, q = h,VT, (2) and constant thermophysical properties, the following equa- tion is obtained: PSCSZ dT - h,V2T (3) or, for the three-dimensional case, the following energy co
23、nservation equation: (4) Figure 1 shows the physical domain that represents the problem where Equation 4 is applied. According to Figure I, the boundary conditions for the most generic case (three- dimensional) can be mathematically expressed as follows: Surface1 (in contact with internal air): Surf
24、ace 2 (in contact with external air): The second right-hand term in Equation 5 corresponds to the long-wave radiant heat exchanged with the internal surfaces of a single-zone building, which floor is coincident with surface 1 (see Figure 1). In this way, the first right-hand term in Equation 5 is th
25、e heat exchange by convection between surface 1 and indoor air. Surface 2 is the interface between the ground and the outdoor air. Therefore, the first right-hand term in Equation 6 represents the convective heat exchanged at surface 2. In this equation, the second and third right-hand terms model t
26、he I The governing partial differential equation of conductive heat transfer applied to an elemental control volume of soil can be expressed as Egure 1 Physical domain for ground andflool: L I 346 ASHRAE Transactions: Research short-wave and long-wave radiation contributions to the energy balance at
27、 surface 2. The other surfaces shown in Figure 1 are considered adia- batic so that Directions on the y- and x-axes were kept for the two- dimensional analysis and only on the y-axis for the one- dimensional case. BUILDING ENVELOPE DOMAIN For the building envelope, including walls and roof, a one-di
28、mensional heat transfer model was considered (Figure 2). In this way, the internal surface temperature is calculated by an energy balance equation in an elemental control volume, using Fouriers law as presented in Equation 2 for the soil domain. On the external side of the room, the walls, roof, doo
29、rs, and windows are exposed to solar radiation and to convective heat transfer. In this way, the external boundary condition (x=O) can be mathematically expressed as On the internal side (x = L), we have included the inter- surface long-wave radiation as I- 1 On the other hand, for the roof, long-wa
30、ve radiation losses were considered (R,) so that Equation 8 has assumed the following form: where the term Eroof represents the roof emissivity at the surface. It has been assumed that surrounding surfaces that face the building envelope and the building envelope surfaces are nearly at the same temp
31、erature. In this way, the long-wave radiation term is only considered in Equation 1 O. The solar radiation (direct, reflected, and diffuse) came from models presented by Szokolay (1993) and ASHRAE (1997) and are conveniently projected to each surface consid- ered in both envelope and soil domains. I
32、n this way, the numer- ical value of qr shown in Equations 1 through 10, is modified according to the projection of the solar beam at each simula- tion time step. ASHRAE Transactions: Research J N Figure 2 Dimensions of the single-zone building studied (units are in meters). INTERNAL AIR DOMAIN The
33、present work uses a dynamic model for analysis of hygrothermal behavior of a room without an HVAC system. Thus, a lumped formulation for both temperature and water vapor is adopted. Equation 1 1 describes the energy conserva- tion equation applied to a control volume involving the room air, which is
34、 subjected to loads of conduction, convection, short-wave solar radiation, inter-surface long-wave radiation, and infiltration. The term E, on the energy conservation equation includes heat gains from building envelope (convection), fenestration (conduction and solar radiation), and openings (ventil
35、ation and infiltration). The conductive heat rate-o( t) -that crosses the room control surface is calculated by the Newtons law for cooling, where A is the area of the six considered surfaces and T, = L( t) is the internal temperature of the considered building envelope surface. The infiltration loa
36、ds formulation was taken from ASHRAE (1997). In terms ofwater-vapor balance, gains from ventilation, infiltration, and internal generation from equip- ment and human breath were considered so that the lumped formulation becomes (rizjnf+ rizvent)( we, - WjJ + hb + ger = P air V air dWint. - dt (13) E
37、quations 1 1 and 13 were solved in an analytical and iter- ative way between themselves, as shown in Equations 14 and 15: 347 Figure 3 Dimensions of the ground andpoor domain used in the simulation. -B - -epcrPf(A - BT,) +A B T. = rnt and where T, and WprW are the temperature and the humidity ratio
38、calculated at the previous iteration, respectively. To solve Equations 14 and 15, the mass and energy conservation applied to the room control volume are: Tint A-BTi, = cV- dt C+DWint = pV- Wint dt where n A = C hAiTj + Egs + Egr( W,) i= 1 n B= ChAi i= 1 D = -m. 2 nf The water-vapor mass flow from p
39、eoples breath is calcu- lated as described in ASHRAE (1997), which takes into account the room air temperature, humidity ratio, and physical activity as well. Table 1. Thermophysical Properties (Incropera 1998) SIMULATION PROCEDURE A C code was elaborated for the prediction of the building thermal p
40、erformance dynamics. For the simulation, a 25-m2 single-zone building with two windows (single-glass layer) and one door, distributed as shown in Figure 2, was consid- ered. For the conductive load calculation, O. 19-m-thick walls composed of three layers were used: mortar (2 cm), brick (1 5 cm), an
41、d another layer of mortar (2 cm). In those typical Brazilian walls, the contact resistance between two different layers was not considered. The differential equations of energy conservation for each node of the building envelope (Figure 2) and for the ground (Figure 1) were discretized by using the
42、finite-difference method (Patankar 1980) with a central difference scheme, a uniform grid, and a fully implicit scheme. The solution of the set of algebraic equations was obtained by using the TDMA (TriDiagonal-Matrix Algorithm). For the presented single-zone building, a 0.35-m concrete floor was co
43、nsidered within the soil domain, as can be seen in Figure 3. For the building envelope, a one-dimensional model was considered since the temperature gradients are certainly much higher in the normal direction. The thermophysical properties of soil and building envelope materials were gath- ered from
44、 Incropera (1 998) and considered constant, as shown in Table 1. The sun effect (short-wave radiation) on the ground was considered on the east side until noon and on the west side from noon until 6 p.m. On the north side, solar radiation was considered all day and at no moment on the south side as
45、the analyzed building is located in the city of Curitiba (south of Brazil at a latitude of -25.4). In one-dimensional, two-dimensional (x-y plane), and three-dimensional models, an amount of 2 1,44 1 (2 1 x 2 1) and 9,261 (21 x 21 x 21) nodes were used, respectively. The external climate was represe
46、nted by Equations 18, 19, and 20 for temperature, relative humidity, and solar radi- ation, respectively. The sinusoidal variation of temperature during the day between 15C and 25OC and of external relative humidity between 50% and 70% were considered. The value for total solar radiation (direct + d
47、ifise) is valid between 6 a.m. and 6 p.m., with a peak value at noon, and, elsewhere, it is equal to zero. 348 ASHRAE Transactions: Research Tex, = 20 + Ssin K + - ( 43x2100) = 0.60- -0.10sin(x + $0) q, = 400sin(;n + 4320 zJ RESULTS In this section, results are presented in terms of compar- isons be
48、tween one-dimensional, two-dimensional, and three- dimensional approaches for the soil domain. However, before presenting the comparative results, the lumped approach for the internal air domain and the three-dimensional differential approach for soil model are checked by using the commercial packag
49、e (CFX 2002). Validation of the Soil Domain The dimensions of the domain for the soil considered in this work are presented in Figure 4. For the boundary conditions, the lateral and lower surfaces were considered adiabatic. At the surface in contact with external air (upper ground face), a constant convective X -it 10 m * Figure 4 Soil domain dimensions. 33 21 19 : I o o5 1 15 2 25 3 3.5 4 Depth (m) Figure 5 Temperature profiles within the soil domain using a time step ofone hour: heat transfer coefficient of 10 W/m2K and a temperature of 32C were adopted. As
