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Energy from a two-pipe, earth-to-air heat exchanger
Energy 24 (1999) 519–523 www.elsevier.com/locate/energy
Energy from a two-pipe, earth-to-air heat exchanger M. Bojic´a,*, G. Papadakisb, S. Kyritsisb a Mas˘inski fakultet u Kragujevcu, Kragujevac University, Sestre Janjic 6, 34000 Kragujevac, Yugoslavia Agricultural University of Athens, Agricultural Engineering Department, 75 Iera Odos st, GR 11855 Athens, Greece
b
Received 28 August 1997
Abstract Solar energy accumulated in the soil may be utilized with an air-to-earth heat exchanger (ATEHE) which has two pipes buried in the soil, one made of PVC and one of steel. During the winter, air is heated; during the summer, it is cooled and then used in an air-conditioning device. To obtain the mathematical model of the ATEHE, we divided the soil and pipes into elementary volumes, used steady-state energy equations, and applied a time-marching method. We determined how the season, soil thermal conductivity and pipe spacing influence energy transfer from the soil to the ATEHE and also the steel-pipe contribution to this energy transfer. 1999 Elsevier Science Ltd. All rights reserved.
Nomenclature a c f H k L m P p q R
Absorptivity for solar radiation Soil volume heat capacity, J/m3-K Internal heat-transfer surface of the pipe, m2 Solar radiation intensity, J/m2 Thermal conductivity, W/m-K Parallelepiped-element dimension in the heat-flux direction, m Number of pipe elements Heat transferred to the PVC pipe, J Number of time intervals Heat flux, W Parallelepiped-element dimension perpendicular to the heat-flux direction, m
* Corresponding author. Tel.: ⫹ 381-34-330-196; fax: ⫹ 381-34-330-196; e-mail: [email protected] 0360-5442/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 5 4 4 2 ( 9 9 ) 0 0 0 1 2 - 2
520
S t v W u
M. Bojic et al. / Energy 24 (1999) 519–523
Heat transferred to the steel pipe, J Temperature, °C Element volume, m3 Parallelepiped-element dimension perpendicular to the heat-flux direction, m Heat-transfer coefficient between soil and pipe air, W/m2-K
Greek letters
␣
Heat-transfer coefficient, W/m2-K Time, s
Other symbols a Air e Soil f Direction opposite to the Z axis j Running index k Running index o Environment p PVC r Direction opposite to the Y axis s Steel u Direction opposite to the X axis x Direction of the X axis y Direction of the Y axis z Direction of the Z axis 1 Beginning of calculation 2 End of calculation Abbreviations ATEHE C H N F
Air-to-earth heat exchanger Winter Summer Pipe spacing of 0.4 m Pipe spacing of 3 m
1. Introduction Energy savings are of major concern everywhere. To save energy by preheating air for heating and by precooling air for cooling of buildings, we propose using the ATEHE (Fig. 1(a)) consisting of two pipes buried in the soil [1,2]. Existing literature [3–13] does not show how the season, soil thermal conductivity, ATEHE-pipe material and ATEHE-pipe spacing influence the heat
M. Bojic et al. / Energy 24 (1999) 519–523
521
Fig. 1. Air-to-earth heat exchanger: (a) model configuration, (b) schematic of a longitudinal cut of the calculation region showing the soil and pipe elements.
exchanged between the soil and the air in the ATEHE pipes. To fill this gap, we employ finite volumes and time marching to develop a mathematical model of the ATEHE. The model does not allow for water in the soil.
2. Mathematical model The calculation region consists of the soil and two pipes (Fig. 1(b)). This region has boundary surfaces that are assumed to be adiabatic, except for the soil-environment interface. The region is divided into volume elements. Heat fluxes through these elements are obtained by using 8 steady-state equations with 6 equations describing the heat fluxes qj (j ⫽ x,u,y,r,z,f) perpendicular to the faces of the soil elements in 6 directions, one equation describes the heat flux qo perpendicular to the soil-environment interface, and one equation describes the heat flux qa between the soil element and pipe air [14,15], viz., qj ⫽ [2kkj (tj ⫺ t1)/(kLj ⫹ kj L)]RW, j ⫽ 1 to 6, qo ⫽ ␣o(to ⫹ aH/␣o ⫺ te,1), qa ⫽ uf(ta,1 ⫺ te,1).
(1)
Here, t1 stands for the initial temperature of some volume element. Next, we calculate temperatures of the soil elements, heat S exchanged between the soil and air in the steel pipe and finally the heat P exchanged between the soil and the PVC-pipe air by using the following equations: te,2 ⫽ te,1 ⫹ [(qx ⫹ qu ⫹ qy ⫹ qr ⫹ qz ⫹ qf ⫹ qo ⫹ qa)/(cv)]d, S
冘冘 p
⫽
m
冘冘 p
qa,s,kd, P ⫽
j⫽1 k⫽1
m
qa,p,kd.
j⫽1 k⫽1
(2)
522
M. Bojic et al. / Energy 24 (1999) 519–523
3. Results and analysis The ATEHE was located at 44° N. It had parallel steel and PVC pipes. The pipes were 150 mm in O.D., 140 mm in I.D., 50 m in length and buried 1.5 m deep in the soil. The soil had a volume heat capacity of c ⫽ 630 000 J/m3-K and soil absorptivity for solar radiation of a ⫽ 0.91. The ATEHE performance was calculated for different seasons, soil thermal conductivities and pipe spacings. The calculation was performed for January 1 from midnight to 2 p.m, and also for July 1 from 1 a.m. to 2 p.m. The outside temperatures and solar radiation intensities on the soil surface for these two days are given in Ref. [3]. The temperature of the 2.4-m deep soil was 8°C in the winter and 16°C in the summer. The soil temperature was initially undisturbed. The thermal conductivity of the soil k was in the range 0.123 to 8.7 W/m-K during calculation, and the pipe spacing Ls was either 0.4 or 3 m. The performance of the ATEHE was evaluated by calculating |P ⫹ S| and |S/(P ⫹ S)|. The results are shown in Figs. 2 and 3. Here, |P ⫹ S| stands for the heat exchanged between the soil and the two pipes, and |S/(P ⫹ S)| stands for the steel-pipe contribution to this exchanged heat. Fig. 2 shows the effects of the season, k and pipe spacing on the exchanged heat |P ⫹ S|. For the summer day, |P ⫹ S| is on average about 1.3 times higher than the value for the winter day. For both days and soil with k ⫽ 8.7 W/m-K, |P ⫹ S| is on average 4 times greater than for soil with k ⫽ 0.123 W/m-K. When the pipe spacing is 3 m, then |P ⫹ S| is about 1.045 times greater than for a spacing of 0.4 m. Fig. 3 shows the effects of the season, k and pipe spacing on the steel-pipe contribution |S/(P ⫹ S)| to the energy exchange. For the summer day, |S/(P ⫹ S)| is on average 1.1 times greater than for the winter day. For both days and soil with k ⫽ 8.7 W/m-K, |S/(P ⫹ S)| averages about 1.03 times the value for soil with k ⫽ 0.123 W/m-K. For a pipe spacing of 3 m, |S/(P ⫹ S)| is almost the same as for a pipe spacing of 0.4 m.
Fig. 2. The exchanged heat |P ⫹ S| between two pipes vs the soil conductivity k. The distances between pipes are 0.4 m (case N) and 3 m (case F). The seasons are winter (case C) and summer (case H).
M. Bojic et al. / Energy 24 (1999) 519–523
523
Fig. 3. The steel-pipe contribution |S/(P ⫹ S)| to the heat exchanged vs the soil conductivity k. The distances between pipes are 0.4 m (case N) and 3 m (case F). The seasons are winter (case C) and summer (case H).
Acknowledgement The authors thank P. Mourdoukoutas (US) for many thoughtful comments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Givoni B. Energy and Buildings 1991;17:177. Steemers T. Solar Energy 1991;10:5. Bojic M, Trifunovic N, Papadakis G, Kyritsis S. Energy—The International Journal 1997;22:1151. Diener R, Avery J, Mosely J, McNeer M. J Agric Engng Res 1986;34:187. Boluard T, Razafinjohany E, Baille A. Agricultural and Forest Meteorology 1989;45:185. Puri V. Transactions of the ASAE 1987;30:514. Tiwari G, Lugani N, Singh A. Energy and Buildings 1993;19:249. Baxter D. Transaction of ASAE 1992;35:1. Boluard T, Razafinjohany E, Baille A. Agricultural and Forest Meteorology 1989;45:175. Mavroyanopoulos G, Kyritsis S. Agricultural and Forest Meteorology 1986;36:263. Santamouris M, Argiriou A, Vallindras M. Solar Energy 1994;52:371. Tombazis A, Argiriou A, Santamouris M. Int J Solar Energy 1990;9:1. Trombe A, Pettit M, Bourret B. Renewable Energy 1991;1:699. Papadakis G, Frangoudakis A, Kyritsis S. A numerical simulation method of two dimensional transient heat conduction in greenhouse soil, Energia and Agricoltura, 2a Conferenza Internazionale, Sirmione/ Brescia, Italia, 1986. [15] Papadakis G, Frangoudakis A, Kyritsis S. J Agric Engng Res 1989;43:231.
Energy from a two-pipe, earth-to-air heat exchanger M. Bojic´a,*, G. Papadakisb, S. Kyritsisb a Mas˘inski fakultet u Kragujevcu, Kragujevac University, Sestre Janjic 6, 34000 Kragujevac, Yugoslavia Agricultural University of Athens, Agricultural Engineering Department, 75 Iera Odos st, GR 11855 Athens, Greece
b
Received 28 August 1997
Abstract Solar energy accumulated in the soil may be utilized with an air-to-earth heat exchanger (ATEHE) which has two pipes buried in the soil, one made of PVC and one of steel. During the winter, air is heated; during the summer, it is cooled and then used in an air-conditioning device. To obtain the mathematical model of the ATEHE, we divided the soil and pipes into elementary volumes, used steady-state energy equations, and applied a time-marching method. We determined how the season, soil thermal conductivity and pipe spacing influence energy transfer from the soil to the ATEHE and also the steel-pipe contribution to this energy transfer. 1999 Elsevier Science Ltd. All rights reserved.
Nomenclature a c f H k L m P p q R
Absorptivity for solar radiation Soil volume heat capacity, J/m3-K Internal heat-transfer surface of the pipe, m2 Solar radiation intensity, J/m2 Thermal conductivity, W/m-K Parallelepiped-element dimension in the heat-flux direction, m Number of pipe elements Heat transferred to the PVC pipe, J Number of time intervals Heat flux, W Parallelepiped-element dimension perpendicular to the heat-flux direction, m
* Corresponding author. Tel.: ⫹ 381-34-330-196; fax: ⫹ 381-34-330-196; e-mail: [email protected] 0360-5442/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 5 4 4 2 ( 9 9 ) 0 0 0 1 2 - 2
520
S t v W u
M. Bojic et al. / Energy 24 (1999) 519–523
Heat transferred to the steel pipe, J Temperature, °C Element volume, m3 Parallelepiped-element dimension perpendicular to the heat-flux direction, m Heat-transfer coefficient between soil and pipe air, W/m2-K
Greek letters
␣
Heat-transfer coefficient, W/m2-K Time, s
Other symbols a Air e Soil f Direction opposite to the Z axis j Running index k Running index o Environment p PVC r Direction opposite to the Y axis s Steel u Direction opposite to the X axis x Direction of the X axis y Direction of the Y axis z Direction of the Z axis 1 Beginning of calculation 2 End of calculation Abbreviations ATEHE C H N F
Air-to-earth heat exchanger Winter Summer Pipe spacing of 0.4 m Pipe spacing of 3 m
1. Introduction Energy savings are of major concern everywhere. To save energy by preheating air for heating and by precooling air for cooling of buildings, we propose using the ATEHE (Fig. 1(a)) consisting of two pipes buried in the soil [1,2]. Existing literature [3–13] does not show how the season, soil thermal conductivity, ATEHE-pipe material and ATEHE-pipe spacing influence the heat
M. Bojic et al. / Energy 24 (1999) 519–523
521
Fig. 1. Air-to-earth heat exchanger: (a) model configuration, (b) schematic of a longitudinal cut of the calculation region showing the soil and pipe elements.
exchanged between the soil and the air in the ATEHE pipes. To fill this gap, we employ finite volumes and time marching to develop a mathematical model of the ATEHE. The model does not allow for water in the soil.
2. Mathematical model The calculation region consists of the soil and two pipes (Fig. 1(b)). This region has boundary surfaces that are assumed to be adiabatic, except for the soil-environment interface. The region is divided into volume elements. Heat fluxes through these elements are obtained by using 8 steady-state equations with 6 equations describing the heat fluxes qj (j ⫽ x,u,y,r,z,f) perpendicular to the faces of the soil elements in 6 directions, one equation describes the heat flux qo perpendicular to the soil-environment interface, and one equation describes the heat flux qa between the soil element and pipe air [14,15], viz., qj ⫽ [2kkj (tj ⫺ t1)/(kLj ⫹ kj L)]RW, j ⫽ 1 to 6, qo ⫽ ␣o(to ⫹ aH/␣o ⫺ te,1), qa ⫽ uf(ta,1 ⫺ te,1).
(1)
Here, t1 stands for the initial temperature of some volume element. Next, we calculate temperatures of the soil elements, heat S exchanged between the soil and air in the steel pipe and finally the heat P exchanged between the soil and the PVC-pipe air by using the following equations: te,2 ⫽ te,1 ⫹ [(qx ⫹ qu ⫹ qy ⫹ qr ⫹ qz ⫹ qf ⫹ qo ⫹ qa)/(cv)]d, S
冘冘 p
⫽
m
冘冘 p
qa,s,kd, P ⫽
j⫽1 k⫽1
m
qa,p,kd.
j⫽1 k⫽1
(2)
522
M. Bojic et al. / Energy 24 (1999) 519–523
3. Results and analysis The ATEHE was located at 44° N. It had parallel steel and PVC pipes. The pipes were 150 mm in O.D., 140 mm in I.D., 50 m in length and buried 1.5 m deep in the soil. The soil had a volume heat capacity of c ⫽ 630 000 J/m3-K and soil absorptivity for solar radiation of a ⫽ 0.91. The ATEHE performance was calculated for different seasons, soil thermal conductivities and pipe spacings. The calculation was performed for January 1 from midnight to 2 p.m, and also for July 1 from 1 a.m. to 2 p.m. The outside temperatures and solar radiation intensities on the soil surface for these two days are given in Ref. [3]. The temperature of the 2.4-m deep soil was 8°C in the winter and 16°C in the summer. The soil temperature was initially undisturbed. The thermal conductivity of the soil k was in the range 0.123 to 8.7 W/m-K during calculation, and the pipe spacing Ls was either 0.4 or 3 m. The performance of the ATEHE was evaluated by calculating |P ⫹ S| and |S/(P ⫹ S)|. The results are shown in Figs. 2 and 3. Here, |P ⫹ S| stands for the heat exchanged between the soil and the two pipes, and |S/(P ⫹ S)| stands for the steel-pipe contribution to this exchanged heat. Fig. 2 shows the effects of the season, k and pipe spacing on the exchanged heat |P ⫹ S|. For the summer day, |P ⫹ S| is on average about 1.3 times higher than the value for the winter day. For both days and soil with k ⫽ 8.7 W/m-K, |P ⫹ S| is on average 4 times greater than for soil with k ⫽ 0.123 W/m-K. When the pipe spacing is 3 m, then |P ⫹ S| is about 1.045 times greater than for a spacing of 0.4 m. Fig. 3 shows the effects of the season, k and pipe spacing on the steel-pipe contribution |S/(P ⫹ S)| to the energy exchange. For the summer day, |S/(P ⫹ S)| is on average 1.1 times greater than for the winter day. For both days and soil with k ⫽ 8.7 W/m-K, |S/(P ⫹ S)| averages about 1.03 times the value for soil with k ⫽ 0.123 W/m-K. For a pipe spacing of 3 m, |S/(P ⫹ S)| is almost the same as for a pipe spacing of 0.4 m.
Fig. 2. The exchanged heat |P ⫹ S| between two pipes vs the soil conductivity k. The distances between pipes are 0.4 m (case N) and 3 m (case F). The seasons are winter (case C) and summer (case H).
M. Bojic et al. / Energy 24 (1999) 519–523
523
Fig. 3. The steel-pipe contribution |S/(P ⫹ S)| to the heat exchanged vs the soil conductivity k. The distances between pipes are 0.4 m (case N) and 3 m (case F). The seasons are winter (case C) and summer (case H).
Acknowledgement The authors thank P. Mourdoukoutas (US) for many thoughtful comments. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
Givoni B. Energy and Buildings 1991;17:177. Steemers T. Solar Energy 1991;10:5. Bojic M, Trifunovic N, Papadakis G, Kyritsis S. Energy—The International Journal 1997;22:1151. Diener R, Avery J, Mosely J, McNeer M. J Agric Engng Res 1986;34:187. Boluard T, Razafinjohany E, Baille A. Agricultural and Forest Meteorology 1989;45:185. Puri V. Transactions of the ASAE 1987;30:514. Tiwari G, Lugani N, Singh A. Energy and Buildings 1993;19:249. Baxter D. Transaction of ASAE 1992;35:1. Boluard T, Razafinjohany E, Baille A. Agricultural and Forest Meteorology 1989;45:175. Mavroyanopoulos G, Kyritsis S. Agricultural and Forest Meteorology 1986;36:263. Santamouris M, Argiriou A, Vallindras M. Solar Energy 1994;52:371. Tombazis A, Argiriou A, Santamouris M. Int J Solar Energy 1990;9:1. Trombe A, Pettit M, Bourret B. Renewable Energy 1991;1:699. Papadakis G, Frangoudakis A, Kyritsis S. A numerical simulation method of two dimensional transient heat conduction in greenhouse soil, Energia and Agricoltura, 2a Conferenza Internazionale, Sirmione/ Brescia, Italia, 1986. [15] Papadakis G, Frangoudakis A, Kyritsis S. J Agric Engng Res 1989;43:231.