Soil Inertia and Shallow Basement Envelope Impact on Cellar Internal Temperature

Transcription

1 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN Soil Inertia and Shallow Baeent Envelope Ipact on Cellar Internal Teperature Naia Sakai 1, Lahcen Boukhatte 1, Haan Hadi 2 1 EnR2E, CNEREE, Cady Ayyad Univerity, Marrakech, Morocco 2 LMFE URAC27-CNRST, FS, Cady Ayyad Univerity, Marrakech, Morocco akai.na3@gail.co Abtract - Thi tudy deal with a three dienional nuerical tudy of heat tranfer by conduction between the oil and the hallow baeent in the city of Marrakech (Morocco). The heat tranfer equation i olved by the finite difference ethod uing the iplicit alternative direction (ADI). The ernal teperature of the cellar i coputed by uing energy balance equation in the cellar. The objective of the tudy i to evaluate the effect of the nature of the oil, the nature of the wall, the thickne of the wall of the cellar, the ditance L far fro the cellar on the ernal teperature, and the heat exchanged between the oil and the hallow baeent. Keyword - ADI Schee; Internal teperature; Nature of oil; Baeent; Heat flow. Noenclature - L Ditance deliiting the dirupted area along x axi, D Ditance deliiting the dirupted area along y axi, H Depth of the water table, E Thickne, T teperature, C Cp Specific heat, J kg -1 K -1 ρ Denity, kg/ 3 Theral conductivity, W/K ds Internal eleentary urface of the wall, 2 t Tie, h c The overall exchange coefficient, W -2 K -1 V Volue of hallow baeent, 3 α Theral diffuivity, 2 / q Ma flow rate of freh air, kg/ λ SUBSCRIPTS a ab p Air Abient Wall Floor w wall Soil Water table Wall urface Inide hallow baeent I. INTRODUCTION The eret of the tudy of the heat tranfer in the baeent i to how the iportance of the oil inertia in the hot region uch a Marrakech. Owing to the very high theral capacity of the oil, the teperature of the ground i lower than that of the outdoor air in the uer and higher in the wer. Conequently, the heating and cooling energy of a building coniderably unk o ground i lower than that one above the ground. Thu, accurate etiation of load and energy conuption due to theral eraction between a building and the ground i needed. Thi i a difficult tak ince thi analyi need to include the ultidienional nature of ot earth-coupled heat tranfer procee, large phae lag caued by oil theral a, liited practical ability to odel oil theral proprietie and the variability of oil teperature with ground urface condition [1]. It i difficult to derive analytical olution for 3D tranient ground-coupled heat tranfer even for the iple rectangular lab-on-ground proble. The only available 3D analytical expreion i the teady-tate olution derived by Delante et al. [2] for a rectangular lab-on-ground with the auption of a linear teperature ditribution along the bae (wall/ground erface) of the external wall. A eianalytical ethod er-zone teperature profile etiation (ITPE) ha been developed by Krarti et al. [3]. It cobine analytical olution for regularhaped coponent and nuerical technique to connect thee coponent to contruct the ground odel. The ITPE ethod i ued to calculate the approxiate analytical olution for the three- 3

2 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN dienion heat tranfer between lab-on-grade floor and rectangular baeent under teady-periodic condition. W.R. Bahnfleth developed a detailed three-dienional finite difference odel for heat conduction fro lab-on-grade floor and baeent, including a detailed ground urface energy balance. [4]. M. P. Deru [5] ued the two dienional finite eleent to tudy the effect of oiture on the heat tranfer fro two baic type of building foundation, a lab-on-grade and a baeent. A two-dienional finite eleent heat and oiture tranfer progra i ued to how the effect of precipitation, oil type, foundation inulation, water table depth, and freezing on the heat tranfer fro the building foundation. Recently M. Staniec and H. Nowak [6] deterined the earth heltered building heating and air-conditioning energy deand depending on the type of oil in which it i founded. For coparion, the correponding reult for the above ground building are preented. In Marrakech, everal tudie have been ade to analyze the heat exchange between the ground and a building. A. Abdelbaki generated a two-dienional tranfer function coefficient (TFC) for a lab-ongrade floor [7]. Later, TFC have been derived uccefully for hallow baeent [8, 9] and earthheltered building [1]. It ha been hown [7, 9] that the reult obtained uing the tranfer function ethod fully agree with thoe obtained uing the ITPE technique and the ADI technique. Recently L. Boukhatte [11, 12] ued the ADI ethod to tudy the effect of the paraeter of ortar on the heat exchange between the oil and the two building: buried building and ei-buried building. In thi work, the reearcher have developed a coputer code that allow the to tudy the effect of the nature of the oil, the nature of the wall of the underground building, the thickne of the wall, the ditance L of the dirupted area on the ernal teperature, and the heat exchanged between the oil and the hallow baeent. II. MATHEMATICAL FORMULATIONS AND BOUNDARY CONDITIONS A. Configuration of the tudied Shallow baeent The configuration treated in thi work i illutrated in Figure 1. The baeent ha a rectangular hape with a width of 2b, a length of 2a and a depth of c. The wall and the floor are aued to have identical theral conductivity and theral diffuivity. The reult preented in thi ection are obtained for: a=2 ; b=2 ; c=2 and e =.26 The overall heat tranfer coefficient [3, 8, 11] i: hc=8.3 W -2 K -1. Shallow baeent Fig.1. Building with a hallow baeent Becaue of the yetry of the tudied configuration, the tudy i reduced to a quarter of the hallow baeent (Figure 2) Fig.2. Shallow baeent configuration B. Matheatical odel The unteady three-dienional heat tranfer equation can be written a follow: T T T T C P i t x y z Thi equation wa olved by an iproved alternatingdirection-iplicit (ADI) finite-difference nuerical ethod. A FORTRAN progra wa built for thi analyi. Soil (1) 31

3 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN Miniu cell dienion were etablihed in accordance with the accuracy and tability criteria et forth by the nuerical ethod eployed in the tudy. Grid pacing in the preent odel in the vicinity of the building foundation ranged fro.2 to.3, while pacing at far-field and deep-ground boundarie wa a large a 1.3. d y and For T ( x, y,z,t ) y yd For L x and h z h z (5) C. Real cliate of Marrakech The iulation by the ADI ethod i ade by conidering the real abient teperature of Marrakech. Thi teperature wa eaured by the weather tation of AGDAL Marrakech. Figure 3 how the variation of ediu abient teperature during one year (28). The water table at a depth of 13 below the oil urface i aained contant at 2 C Fig.3. External air teperature The Boundary condition of the tudied proble are: T x In the two plane of yetry: ( x,y,z,t) x For d y and h z T x ( x,y,z,t) y For L x and h z T x Far fro building: ( x, y,z,t ) xl J F M A M J J A S O N D (2) (3) (4) Interface ernal air-ide of the building : T λ ( x, y,z,t) hc ( T (-a, y,z,t) T ) x For b y xa and c z T λ ( x, y, z,t) hc ( T (x,-b, z,t) T ) y For a x yb and c z T λ ( x, y,z,t) hc ( T (x, y,-c,t) T ) (8) z zc b y For a x and Interface oil-external wall of building : T T λ ( x, y,z, t) λ ( x, y,z, t) x x( ae ) x x( ae) b e y and For T T λ ( x, y, z, t) λ ( x, y, z, t) x y(b e ) x y(b e) a e x and c e z For T T λ ( x, y,z, t) λ ( x, y,z, t) x z(c e ) x z(c e) For a e x and c e z b e y Air teperature and water table teperature: (6) (7) (9) (1) (11) T( x, y,) Tab and T( x, y, h) Tw (12) For L x and d y The heat flow i calculated by the following equation: 32

4 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN c wall (13) Heat flow h ds T T D. The local heat balance The energy conervation law for the ernal ediu of the hallow baeent, which i conidered a an open yte i: de Q W dt t t (14) E i the total ernal energy of the ediu; Q i the heat croing the yte boundary; W i the total work that i a u of the work done by the preure force on the control urface and the flow work. Thu, the volue V of the control volue reain contant, and a a reult, the boundary work i zero. The kinetic and potential energie of air in the cellar are neglected. The air i conidered a an ideal ga and the teperature of thi one i unifor in the tudied cellar, Fro the above auption, the equation 14 reduce to: T 3 acp V qc a p T a ab T hcd T Twall t i1 III. A. Code validation ( ) ( ) RESULTS AND INTERPRETATION (15) The reearcher have elaborated a code that calculate the exchanged heat flow between a oil and hallow baeent in 2D and 3D configuration. For coputer code validation, they copared the reult obtained by the preent code and thoe of M. Krarti [1] carried out for the ae geoetric which i characterized by depth b=3, width a=2, total width L=9 and for thick wall e=.4 in 3D configuration. A non-unifor eh in both direction, contructed uing a geoetric progreion, wa adopted with grid dienion. Figure 4 how good agreeent between the reult obtained by the propoed code and thoe of S. Ajad. The heat flow i calculated by the following equation: Heat flow h ds T T Heat flow(w) c wall Fig.4. Variation of the onthly heat flux. B. Effect of the ditance L At a large ditance fro the foundation, the effect of the hallow baeent on the ground becoe negligible. To deterine thi ditance, the reearcher recognized everal iulation by varying the ditance L each tie. Table 1 how the onthly heat flow for each ditance. Thi reult indicated that little or no change in predicted heat flow occur when the far-field boundary i at 8 or ore away fro the building. Table 1. Heat flow for different ditance L. heat flow heat flow heat flow heat flow Month L=2 L=4 L=6 L=8 J F M A M J -1.E+2-1.6E+2-1.7E+2-1.7E+2 JU A S O N D preent work S.Ajad Month 33

5 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN C. Effect of oil type To evaluate the oil type effect on the cellar ernal teperature enitivity to change in the external environent, the reearcher have perfored iulation for three different oil type whoe characteritic are preented in Table II. Table 2. Characteritic of the tudied oil. Type of oil Type 1 Type 2 Type Theral conductivity W/K Theral diffuivity (1-7 ) 2 / Figure 5 how the change in the ernal teperature of the cellar for three type of tudied oil. The theral conductivity and theral diffuivity of wall and floor are λ=1.73 W/K, and = /, repectively. In general, it i oberved that there i tability in the ernal teperature of the cellar throughout the year that can be explained by the coniderable effect of inertia of the oil. Thi tability i even ore iportant for oil 3 which i characterized by low conductivity and low theral diffuivity Soil 1 Soil 3 Soil 2 Tab 3 Month J F M A M J J A S O N D Fig.6. Hourly variation of indoor and outdoor teperature for one week of the uer period for three oil type. During the wer period, the reearcher found out that the cellar teperature doe not decent below C for the three oil type, while the outer teperature recorded negative value in the range of -1 C. They alo found out that the ernal teperature provide tability throughout the day with a all aplitude of 2 C for oil type 1(clay) and 3 C for oil type 3 (and) for a weather teperature that have an aplitude of 12 C (Figure 7) Soil 3 Soil 1 Soil 2 Tab Soil 1 Soil 3 oil 2 Tab Fig.5. Daily variation of the external teperature and the ernal teperature for three type of oil during a year. Fig.7. Hourly variation of indoor and outdoor teperature for one week of the wer period for three oil type. In uer tie, the outide teperature increae to 45 C while that of the erior doe not exceed 25 C for and and 23 C for clay with.27% oiture content. One can ee a difference in indoor teperature between oil 2 and oil 3. Thi i due to the oiture content that influence the ernal teperature of the hallow baeent (Figure 6). Therefore, when analyzing the type of oil urrounding the building one hould ue accurate eaureent of oil theral proprietie (conductivity and diffuivity). D. Effect of the aterial type of the wall The deterination of effect of contruction aterial on the ernal teperature iulation wa ade for oil type 2 and for two building aterial: reinforced 34

6 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN concrete and hollow brick (Table III). The reearcher oberved that there i no ignificant difference between etiated teperature for both aterial. It can be deduced later that there i no effect on the nature of the wall of the ernal teperature of the cellar for the tudied cae (Figure 8). Table 3. Characteritic of the tudied wall. Material type of the wall Hollow brick Reinforced concrete Theral conductivity W/K Theral diffuivity (1-7 ) 2 / thicknee of the wall for a week during the wer period. e=,26 e=,4 Fig.1. Hourly variation of the ernal teperature for two thicknee of wall for a week during the uer period Hollow brick Reinforced concrete IV. CONCLUSION In thi tudy, the reearcher have developed a detailed FORTRAN code to calculate three dienional heat tranfer for an envelope in contact with the ground. It allowed the to calculate the exchange of heat between the oil and the baeent through the ue of finite difference ethod in three dienion and alo calculate the ernal teperature of the cellar, in the real cliate of Marrakech. Fig.8. Hourly variation of indoor and outdoor teperature for one week of the uer period for two wall type. E. Effect of the thickne of the wall Figure 9 and Figure 1 are obtained for a oil type 2, reinforced concrete wall and for different wall thicknee in the real cliate of Marrakech. Thee reult how that the influence of the wall thickne i not iportant; thi i ainly due to the predoinance of the theral inertia of the oil copared to the wall cavity e=,26 e=, Fig.9. Hourly variation of the ernal teperature for two We deontrated the ignificant effect of the inertia of the oil on the tabilization of the ernal teperature of the cellar. Indeed, the average teperature inide the hallow baeent varie between C and C throughout the year, with a agnitude of 8 C. On the other hand, the abient teperature i between 4 C and 34 C with the aplitude of 3 C. Thi inertia i largely influenced by the theral characteritic of the oil. In fact; the ernal teperature i ore table with the ground having a low theral conductivity and theral diffuivity. During the uer eaon, the ernal teperature doe not exceed C (Soil 1) and 25 C (oil 3) when the abient teperature reache 44 C. During the wer eaon, the abient teperature decend down to -2 C, while the ernal teperature did not decend below 15 C (oil 1) and C (oil 3). The tudy of the effect of the thickne of the wall and the wall-type how that there i a difference of le than 1 C between the different tudied ituation (thickne and type of wall). So we can conclude that 35

7 Journal of Renewable Energy and Sutainable Developent (RESD) Volue 2, Iue 1, June 2 - ISSN the type of wall and it thickne ha little influence on the ernal teperature of the cellar. In concluion, we deduce that the ei-buried building reduce the cooling and the heating load through the tabilization of the ernal teperature. On the other hand, the theral characteritic of the ground are a great influence on the teperature inide the building in coparion to the type and thickne of the wall. V. ACKNOWLEDGEMENTS Thi tudy i a part of the RafriBAT project financially upported by a grant fro the Haan II Royal Acadey of Science and Technique, Morocco. REFERENCES [1] D. Chen, Dynaic three-dienional heat tranfer calculation for uninulated lab-onground contruction, Energy and Building, No 6, pp , 213. [2] A.E. Delante, A.N. Stoke, and P.J. Walh, Application of Fourier tranfor to periodic heat flow o the ground under a building, International Journal of Heat Ma Tranfer, Vol. 26, No.1, pp , [3] S. Choi, M. Krarti, Therally optial inulation ditribution for underground tructure, Energy and building, No.32, pp , 2. [4] W.P. Bahnfleth, A three-dienional nuerical tudy of lab-on-grade heat tranfer, ASHRAE Tranaction, No. 96, pp , 199. [5] M.P. Deru, Ground-coupled heat and oiture tranfer fro building, National Renewable Energy Laboratory. NREL/CP , February 21. [6] M. Staniec and H. Nowak, Analyi of the energy perforance of earth-heltered houe with outhern elevation expoed, Eleventh International IBPSA Conference Glagow, Scotland July 27-3, 29. [7] A. Abdelbaki, Contribution à la odéliation de tranfert therique à traver le plancher d un habitat ur terre-plein, DES thei, Faculty of Science Selalia, Marrakech, Morocco, [8] A. Abdelbaki, S. Ajad, and Z. Zrike, Prediction of heat tranfer fro hallow baeent to the oil by the two-dienional tranfer function ethod, in: Proceeding of the 3rd Renewable Energy Congre, Reading, UK, [9] S. Ajad, Contribution à l étude du coporteent therique de bâtient eienterré, DES thei, Faculty of Science Selalia, Marrakech, Morocco, [1] S. Ajad, A. Abdelbaki, and Z. Zrike, Adaptation de la éthode de fonction de tranfert à une cavité enterrée, in: Proceeding of the 3rd Mechanical Congre, Tétouan, Morocco, pp ,1997. [11] L. Boukhatte, A. Bendou, R. Mir, and M. Kourchi, Siulation et optiiation de tranfert de chaleur entre un bâtient coplèteent enterré et le ol, Revue Internationale d'héliotechnique, Energie Environneent, No 36, pp , 27. [12] L. Boukhatte, A. Bendou, H. Hadi, and D.R. Roue, Siulation bidienionnelle du tranfert d énergie entre un bâtient eienterré et le ol en régie variable, Revue ernationale d'héliotechnique, N.44, pp ,