BUILDING PASSIVE COOLING THROUGH UNSATURATED CAPACITIVE POROUS MEDIUM ON ROOF

Transcription

1 Proceedings of Building Siulation 11: BUIDING PASSIVE COOING THROUGH UNSATURATED CAPACITIVE POROUS EDIU ON ROOF Gerson H. dos Santos 1 and Nathan endes 1 Universidade Federal do Paraná UFPR Departent of echanical Engineering Curitiba, Brazil ghsantos@ufpr.br Universidade Católica do Paraná - PUCPR Departent of echanical Engineering Curitiba, Brazil nathan.endes@pucpr.br ABSTRACT A atheatical odel to siulate an unsaturated highly capacitive porous ediu on roof (sand) is considered in order to predict its effects on building passive cooling. The present ethodology is based on the theory of Philip and De Vries, using the therophysical properties for different types of porous ediu (building envelope) with different cheical coposition and porous size distribution. The governing equations were discretized using the finite-volue ethod for describing the physical phenoena of heat and ass transfer in unsaturated porous ediu. The robust ultitridiagonal-atrix Algorith (TDA) was used to solve this strongly-coupled proble, allowing the use of large tie steps for long-ter siulations. In order to precisely predict roo air teperature and huidity, a luped transient approach for a building roo is considered. Coparisons of the sand layer effect in ters of heat fluxes through a horizontal roof, indoor conditions and theral cofort (PV Predicted ean Vote) are presented. INTRODUCTION During the last decades several coputational codes for building siulation have been developed for different purposes. ost building siulation odels address a specific application area of the building physics field, as for exaple, prediction of indoor cliate in association with heating and cooling loads, prediction of solar gains through windows and other passive solar coponents, air infiltration phenoena, HVAC syste behavior, air flow patterns and ventilation efficiency, aong others. However, siplifications on the building envelope odel ay provide unrealistic results. Cobined analysis of heat and oisture transport through porous building eleents is barely explored in the literature due to any difficulties such as odeling coplexity, coputer run tie, nuerical convergence and highly oisture-dependent properties. Besides, the oisture in the envelope of buildings iplies an additional echanis of transport absorbing or releasing latent heat of vaporization, affecting the hygrotheral building perforance or causing old growth (Santos and endes, 9a, 9b, 9c). In this context, taking into account the energy savings and the theral cofort benefits, a layer of oist porous ediu, such as huid sand layer on the roof can counterbalance the heating of fervent solar radiation and outdoor air teperature, which can produce passive cooling effect, ainly for lowrise buildings with large roof area (eng and Hu, 5). In the sae context, iu et al. (1995) showed that the free evaporative cooling in or on an unsaturated porous packed bed that works as a part of roofs or walls in buildings is a highly proising project due to its engineering background and theoretical interests. Green roof technology could be used to reduce the urban heat island effect and to reduce the cooling loads (Onura et al., ; Sailor, 8), however, soe disadvantages have been presented. According to Wanphen and Nagano (9), green roof installation cost is expensive and the aintenance of the syste is required regularly at additional cost. Furtherore, in ters of building structure, an enhanced structural support is required, to ensure sufficient capacity to resist weight load under the soil and vegetation. In this way, to analyse ore precisely the porous edia layer effects in the roof, a atheatical description for predicting envelope building hygrotheral dynaics is required and coplex, due to non-linearities and interdependence aong several variables. The paraetric uncertainties in the odeling, siulation tie steps, external cliate, building schedules, hygrotheral properties and oisture storage and transport also contribute to increase this coplexity. In this case, for ensuring nuerical stability in the present odel, the linearized set of equations was obtained by using the finite-volue ethod and the ultitridiagonal- atrix Algorith (endes et al., ) to solve a 1- D odel to describe the physical phenoena of heat and ass transfer in the building envelope, including the sand layer. The code has been conceived to be nuerically robust with a fast-siulating procedure. The heat and oisture transfer in envelope building was based on the theory of Philip and De Vries (1957), which is one of the ost disseinated and

2 Proceedings of Building Siulation 11: accepted atheatical forulation for studying heat and oisture transfer through porous edia, considering both vapor diffusion and capillary igration. In this paper, the weather data of Brasilia-Brazil were utilized for coputing external boundary conditions and coparisons in ters of heat fluxes through a horizontal roof, indoor conditions and theral cofort (PV Predicted ean Vote) are presented. ATHEATICA ODE The physical proble is divided into two doains: building envelope (walls and roof) and roo air. At the external surfaces, the heat transfer due to shortwave radiation and heat and ass convection were considered as boundary conditions and the long-wave radiation losses were taken into account only at the roof. At the internal surfaces, besides the convection heat and ass transfer, long-wave radiation heat exchange between the surfaces was also considered. Building Envelope Doain The governing equations, based on the theory of Philip and De Vries (1957), to odel heat and ass transfer through porous edia, are given by Eqs. (1) and (). The energy conservation equation is written in the for ρ c θ ) =. ( λ θ ) T ) ( T )(. jv ) (1) t and the ass conservation equation as j =. t, () ρ l where ρ is the solid atrix density (kg/³), c, the ean specific heat (J/kg K), T, teperature ( C), λ, theral conductivity (W/ K),, latent heat of vaporization (J/kg), θ, voluetric oisture content (³/³), j v,vapor flow (kg/² s), j, total flow (kg/² s) and ρ l the water density (kg/³). The total 1-D oisture flow (j) - given by suing the vapor flow (j v ) and the liquid flow (j l ) - can be described as j = ρ l with Tl D T θ ) + D ( T θ ) D + θ,, (3) T = DTl DTv and Dθ Dθ l + Dθv =, where D is the liquid phase transport coefficient associated to a teperature gradient (²/s K), D Tv, vapor phase transport coefficient associated to a teperature gradient (²/s K), D θ l, liquid phase transport coefficient associated to a oisture content gradient (²/s), D θ v, vapor phase transport coefficient associated to a oisture content gradient (²/s), D, ass transport coefficient associated to a T teperature gradient (²/s K) and D θ, ass transport coefficient associated to a oisture content gradient (²/s). The internal boundary conditions () for teperature can be atheatically expressed as: λ i= 1 θ ) + ( ( T ) j ) = h( T T ) fεσ ( T 4 sur T 4 v ) + T and the external surface (), as: λ + αq int ( ) h ( ρ ρ ) v,int + v, θ ) + ( ( T ) j ) = h( T T ) r + T v ( ) h ( ρv, ext ρv, ) εrlw where ( T ) h int, ext T x =, ext (4) (5) represents the heat exchanged by convection with the internal and external air, α q (W/²) is the absorbed short-wave r T h ρ v, int, ext ρv,, radiation and ( ) ( ), the phasechange energy ter. The long-wave radiation loss (horizontal surface) is defined as R lw (W/²) and ε is the surface eissivity. The solar absorptivity is represented by α and the ass convection coefficient by h, which is related to h by the ewis relation. Siilarly, the ass balance at the internal surface is written as D h ρ l θ θ ) + D θ ) ( ρ ρ ) v,int T and for the external surface, as D h ρ l θ θ ) + D θ ) ( ρ ρ ) v, ext T = =, (6), (7) For the floor, at x =, an ipereable and adiabatic condition was adopted. Equations (6) and (7) show a vapor concentration difference, ρ v, on their right-hand side. This difference is between the porous surface and air and is norally deterined by using the values of

3 Proceedings of Building Siulation 11: ious iterations for teperature and oisture content, generating additional nuerical instability. Due to the instability created by this source ter, the solution of the linear set of discretized equations norally requires the use of very sall tie steps, which can be exceedingly tie consuing especially in long-ter soil siulations; in soe research cases, a tie period of several decades has to be siulated, taking into account the three-diensional heat and oisture transfer through a very refined grid. In order to increase the siulation tie step, endes et al. () presented a procedure to calculate the vapor flow, independently of ious values of teperature and oisture content. In this way, the ter ( ρv ) was linearized as a linear cobination of teperature and oisture content, viz., ( ρ ρ ( s) ) v, ( θ v = ( T 1 θ ( s)) + where 1 = A φ ; R 3 Ps ( s) = T s R ( ) 3 T ( s)) +, (8) φ s ( ) P s ( s) + R( θ ( s)) = T ( s). R φ ( R( T ) R( T ( s))) In the equations above, the index (s) represents the surface on contact with air and ( ) the air far fro P that surface, R is a residual function of s, P s, T saturated pressure (Pa), R, universal gas constant (J/kol K),, olecular ass (kg/kol), φ, relative huidity,, ious iteration and A is the straight-line coefficient fro the approxiation P s = AT B T +. Internal Air Doain The present work uses a dynaic odel for analysis of hygrotheral behavior of a roo without HVAC syste or infiltration/exfiltration. Thus, a luped forulation for both teperature and water vapor is adopted. Equation (9) describes the energy conservation equation applied to a control volue that involves the roo air, which is subitted to loads of conduction, convection, short- wave solar radiation, inter-surface long-wave radiation and infiltration: ; dt E int t = ρ int cintvint dt, (9) where: E & t is the energy flow that crosses the roo (W), ρ int, the roo air density (kg/ 3 ), c int, the roo air specific heat (J/kg-K), the V int roo volue ( 3 ) and T int, the roo air teperature ( o C). The sensible heat flow rate released by the building envelope is calculated as [ ( t) T ( t) ] Q ( t) = hint A T = int (1) S x and the latent heat flow rate is calculated as [ ρ ( t) ( t) ] Q ( t) = ( T ( t)) h A v, ρv, int. (11) In Eq. (1) A represents the area of the internal surface (²), h int the internal convection heat transfer coefficients (W/² K), T x = ( ) the teperature at the internal surface of the building ( C) and T int ( t) the roo air teperature ( C). In Eq. (11),, the vaporization latent heat (J/kg), h, the internal ass convection coefficient (/s), ρ, the roo air t v, int vapor concentration (kg/³) and ρ v, the vapor concentration of the internal surface (kg/³). The teperature and vapor density are calculated by the cobined heat and oisture transfer odel by using the values of teperature, oisture content and sorption isother. In ters of water vapor ass balance, the luped forulation becoes: h D [ W ] A W dwint = int = intvint, (1) dt v, x ρ where h D is the ass transfer coefficient (kg/² s), W, the huidity ratio of the internal surface (kg v, water/kg dry air), W int, the roo air huidity ratio (kg water/kg dry air), ρ int, the roo air density (kg dry air/ 3 ) and Vint the roo volue ( 3 ). SIUATION PROCEDURE For the siulations, a 5- single-zone building as shown in Fig. 1 has been used. Openings were not considered to increase the iportance of the roof load on the building theral perforance. For the conduction loads, 1-c brick were considered

4 Proceedings of Building Siulation 11: Figures 3 and 4 show the values of teperature, relative huidity and total solar radiation in January (1 st 7 th ) fro TRY (Test Reference Year) weather data for the city of Brasília-Brazil Figure 1: Diensions (in eter) of the single-zone building studied. The roof has been represented by 3 layers: sand (1 c), sealing layer and brick (1 c), as shown in Fig.. Teperature ( C) Teperature Relative Huidity Figure 3: Values of teperature and relative huidity for Brasilia Brazil, on January (1 st 7 th ) Relative Huidity (%) 1 1 Figure : Physical doain of the roof. The differential equations of energy and ass conservation for each node of the roof were discretized by using the finite-volue ethod (Patankar, 198), with a central difference schee, a unifor grid and a fully-iplicit approach. The solution of the set of algebraic equations was obtained by using the TDA (ulti-tridiagonal- atrix Algorith - endes et al., ). In the roof odel, a regular esh of was utilized for each control volue. In this work, highly teperature and oisture dependent properties were gathered fro Oliveira et al. (1993). The brick properties were obtained fro Perrin (1985). The basic dry-basis aterial properties are shown in Tab. 1. Table 1: Dry-basis properties of the sand and brick. aterial ρ (kg/³) c (J/kg K) porosity Sand Brick In the internal region, a constant convection heat transfer coefficient of 3 W/²K was considered. The external region were subitted to the TRY (Test Reference Year) weather data for the city of Brasilia- Brazil (South latitude of ), with a constant convective heat transfer coefficient of 1 W/²K and a solar absorptivity of.5 for both sand and brick layers. Total Solar Heat (W/²) RESUTS Figure 4: Values of total solar radiation for Brasilia Brazil, on January (1 st 7 th ). In order to predict the sand layer effect on building passive cooling, the Brasilia TRY weather data file has been chosen and siulations have been carried out fro Jan. 1 st to Jan. 7 th, using a 3-sec siulation tie step. The results presented in this section Figs. 5-9 are related to January 7 th, in order to reduce the initial conditions effects. Siulations in the roof were perfored with or without a sand layer. It can be noticed, in Fig. 5, teperature differences close to 4 C for peak values at the internal surface of the roof. The cooling effect was observed during daylight period, between 1 a and 6 p, with different behaviour in the night period. As observed in Fig. 6, the sall difference on the external surface teperature (with or without sand layer) shows that the internal surface

5 Proceedings of Building Siulation 11: teperature is doinantly affected by the sand layer inertia rather than evaporative cooling. Teperature ( C) without sand with sand Figure 5: Teperature at the internal surface of the roof on January 7 th. Teperature ( C) Teperature - without sand Teperature - with sand Relative Huidity - without sand Relative Huidity - with sand Figure 6: Teperature and relative huidity at the external surface of the roof on January 7 th Relative Huidity (%) are sall, they cause a higher effect on the PV index. Figure 9 shows an iproveent on the theral cofort index (clo =.66, et =.79, air velocity =.1 /s) during all day long. It should be entioned that no internal gain has been considered in the siulation, in order to avoid isinterpretations fro the effect of the coupled heat and oisture transfer through the roof. Heat Flux (W/²) Teperature ( C) Teperature - without sand Teperature - with sand Relative Huidity - without sand Relative huidity - with sand Figure 7: Roo air teperature and relative huidity on January 7 th. Sensible Heat - without sand Sensible Heat - with sand atent Heat - without sand atent Heat - with sand Relative Huidity (%) Figure 6 also shows that evaporation at the external surface during the daylight period is counterbalanced by solar radiation. An interesting physical aspect noticed in Fig. 6 is the relative huidity at the sand surface. As the external surface teperature decreases below the dew point due to the negative net radiation balance at the surface, the sand becoes saturated at the surface for a 9-h period and then dries out rapidly thanks to the high short-wave radiation on the horizontal surface during day tie. As the uikov nuber is low (Dantas et al., ) and the sand is very theral capacitive, this effect does not have uch influence on the teperature. Figure 7 shows the roo air teperature and relative huidity teporal evolution, where a variation of 1 C on the teperature and 4% on the relative huidity in the peak values is noticed. This effect is attributed to the reduction of sensible heat flux at the ceiling internal surface when the sand layer is considered, as illustrated in Fig. 8. Although the roo air teperature and relative huidity variations PV Figure 8: Sensible and latent heat flux at the internal surface of the roof on January 7 th PV - without sand PV - with sand Figure 9: Predicted ean vote (PV) on January 7 th

6 Proceedings of Building Siulation 11: Although this section shows that the sand layer produces a better indoor theral cofort, this effect could be increased with a layer of a aterial coposed of larger porous, i.e., volcanic ash and siliceous shale. Waphen and Nagano (9) investigated the hygrotheral perforance of several non-porous and porous potential roofing aterials and it was observed that under the conditions of no solar radiation, unchanging teperature and relative huidity, a high aount of latent heat could be released fro finer aterials such as silica sand and porous particles with saller sizes due to capillary action. On the other hand, when a cliatic situation was analysed, particles at the surface layer of large sized saples tended to dry faster due the ventilation and solar radiation penetration in large gaps, enhancing the evaporation. Soe paraeters such as the eissivity did not deonstrate a significant ipact on the results (not shown). However, there is a significant uncertainty degree on the hygrotheral properties that needs to be carefully exained, which is part of an international study in the frae of the International Energy Agency Annex 55. CONCUSION A atheatical odel to siulate an unsaturated highly capacitive porous ediu on roof (sand) was proposed to predict its effects on building passive cooling. Coparisons of the sand layer effect in ters of heat fluxes through a horizontal roof, indoor conditions and PV index were presented. It has been shown that the sand layer inertia effect is doinant when copared to the one fro evaporative cooling. Although the roo air teperature and relative huidity variation has been sall with a sand layer, it caused a better PV index during all day long. This effect is attributed by sensible heat flux decreasing at the internal surface and it could be increased in low-rise buildings with large roof area. For further work, sensitivity and uncertainty analyses should be carried out on the hygrotheral properties, besides a profound investigation on the validity and liitations of conventional heat and oisture transfer odels to be used to siulate a coplex phenoenon in non-consolidated porous edia such as sand. ACKNOWEDGEENT The authors thank the Brazilian Research Council (CNPq) of the Secretary for Science and Technology of Brazil and EETROBRAS (Centrais Eletricas Brasileiras) for support of this work. REFERENCES Dantas,. B., Orlande, H. R. B., Cotta, R..,, Estiation of Diensionless Paraeters of uikov s Syste for Heat and ass Transfer in Capillary Porous edia, Int. J. Ther. Sci., V. 41, pp iu, W., Peng, S. W., izuk, K., 1997, oisture Evaporation and igration in Thin Porous Packed Bed Influenced by Abient and Operating Conditions, International Journal of Energy Research, V. 1, pp endes, N., Philippi, P. C., aberts, R.,, A New atheatical ethod to Solve Highly Coupled Equations of Heat and ass Transfer in Porous edia International Journal of Heat and ass Transfer, V. 45, pp eng, Q, Hu, W., 5, Roof Cooling Effect with Huid Porous édiu. Energy and Buildings, V. 37, pp Oliveira, A. A. J; Freitas, D. S., 1993, Influência do eio nas Difusividades do odelo de Phillip e Vries., Relatório de Pesquisa, UFSC, Onura S, atsuoto, Hokoi S.,, Study on Evaporative Cooling Effect of Roof awn Gardens, Energy and Buildings, V. 33, pp Patankar, S.V., 198, Nuerical Heat Transfer and Fluid Flow, Heisphere Publishing Corporation. Perrin, B., 1985, Etude des Transferts Couplés de Chaleur et de asse dans des atériaux Poreux Consolidés non Saturés Utilisés en Génie Civil", Thèse Docteur d'etat, Université Paul Sabatier de Toulouse, Toulouse, France. Philip, J. R., de Vries, D. A., 1957, oisture oveent in Porous edia under Teperature Gradients Trans. A. Geophysical Union, V. 38, pp. -3. Sailor, D. J., 8, A Green Roof odel for Building Energy Siulation Progras, Energy and Buildings, V. 4, pp Santos, G. H., endes, N., 9, Cobined Heat, Air and oisture (HA) Transfer odel for Porous Building aterials, Journal of Building Physics, V. 3, pp. 3-. Santos, G. H., endes, N., 9, Heat, Air and oisture Transfer Through Hollow Porous Blocks, International Journal of Heat and ass Transfer, V. 5, pp Santos, G. H., endes, N., Philippi, P. C., 9, A Building Corner odel for Hygrotheral Perforance and ould Growth Risk Analyses, International Journal of Heat and ass Transfer, V. 5, pp Wanphen, S., Nagano, K., 9, Experiental Study of the Perforance of Porous aterials to oderate the Roof Surface Teperature by its Evaporative Cooling Effect, Building and Environent, V. 44, pp