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Numerical study of earth-to-air heat exchanger: The effect of thermal insulation
Energy and Buildings 85 (2014) 356–361
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Short Communication
Numerical study of earth-to-air heat exchanger: The effect of thermal insulation J. Xamán a,∗ , I. Hernández-Pérez a , J. Arce a , G. Álvarez a , L. Ramírez-Dávila b,1 , F. Noh-Pat c,2 a
Centro Nacional de Investigación y Desarrollo Tecnológico, CENIDET-TNM-SEP, Prol. Av. Palmira S/N, Col. Palmira, Cuernavaca, Morelos CP 62490, México Building energy efficiency, Bee, EUA, 13640 Briarwick Drive, Suite 180, Austin, TX CP 78729, USA Universidad Autónoma de Baja California, UABC, Centro de Ingeniería y Tecnología (Unidad Valle de las Palmas), CITEC, Blvd., Universitario # 1000, Tijuana, Baja California, CP 21500, México b c
a r t i c l e
i n f o
Article history: Received 10 March 2014 Received in revised form 13 August 2014 Accepted 15 September 2014 Available online 8 October 2014 Keywords: Earth-to-air heat exchanger Thermal insulation
a b s t r a c t A numerical study was conducted for prediction of the thermal performance of an Earth-to-Air Heat Exchanger (EAHE) for three cities in México. The climatic conditions correspond to a temperate climate (México City), a humid-hot climate (Mérida, Yucatán) and an extreme weather (Cd. Juárez, Chihuahua). The effect of thermal insulation at the outlet section of the EAHE is investigated. In México City, the insulation with a thickness of 0.05 m (2 ) is recommended because it improved the performance of the EAHE. In winter, the insulation increased the heating effect up to 2 ◦ C with respect to the EAHE without insulation. In summer, thermal insulation provided an improvement on the cooling effect up to 1.3 ◦ C. In Mérida the results indicate that thermal insulation with a thickness of 0.05 m is also the best option. In winter, this measure improved the heating effect up to 2.6 ◦ C with respect to the EAHE without insulation. Particularly, for Cd. Juárez during the summer, the thermal behavior of the EAHE was not improved due to the thermal insulation. Therefore for México and Mérida the suggested value of insulation made the EAHE to function properly during all months in summer, since it avoided the undesirable heat gain from the soil at the outlet. In other words, the insulation improved the cooling effect up to 5 ◦ C with respect to the EAHE without insulation. © 2014 Elsevier B.V. All rights reserved.
1. Introduction During the last decade, there has been a rising interest in implementing heating and cooling systems for buildings based on renewable energy sources. Because of its high thermal inertia, the soil attenuates the temperature fluctuations that occur at the ground surface. Further, it causes a time lag between the temperature at the surface and the temperature in the soil. Therefore, at a sufficient depth, the ground temperature is lower than the temperature of the outdoor air during the summer and it is higher than the temperature of the air during the winter. When the air from the ambient is drawn through an Earth-to-Air Heat
∗ Corresponding author. Tel.: +52 777 3 62 77 70; fax: +52 777 3 62 77 95. E-mail addresses: [email protected], [email protected] (J. Xamán), [email protected] (I. Hernández-Pérez), [email protected] (J. Arce), [email protected] (G. Álvarez), [email protected] (L. Ramírez-Dávila), [email protected] (F. Noh-Pat). 1 Tel.: +1 (512) 3 64 06 88; fax: +1 (512) 3 64 06 86. 2 Tel.: +52 664 6 76 82 22. http://dx.doi.org/10.1016/j.enbuild.2014.09.064 0378-7788/© 2014 Elsevier B.V. All rights reserved.
Exchanger (EAHE), which consists in pipes buried in the soil, the air can be cooled during the summer and it can be heated during the winter. As a result, an EAHE may improve the thermal comfort inside buildings or even reduce the energy destined for heating or cooling [1–5]. Recent studies aimed to evaluate the temperature profiles in soil are still implementing 1-D analytic formulation proposed over 50 years ago by Carslaw and Jaeger [6], that are still distant from representing reality since they do not consider soil’s thermophysical variation [7–14]. A study of this kind was carried out by Salah ElDin [15], who predicted the variation of the soil temperature with depth in a 1-D model based on an energy balance at the ground surface. They considered the variation of the solar radiation, air temperature and latent heat flux due to evaporation; however, it was considered that soil has uniform thermophysical properties. In regard with the studies focused in EAHEs, those that are based in thermodynamics energy balance do not represent the phenomena in an appropriate way since the air flow through the pipe is not considered by disregarding its velocity [12,16–18]. One of these studies was conducted by Cucumo et al. [17], who considered a one-dimensional transient study where thermal
J. Xamán et al. / Energy and Buildings 85 (2014) 356–361
Nomenclature a cp Hx Hy Q Re T inlet Tave out Tave x,y
thickness of insulation, m specific heat. J kg−1 K−1 depth of the soil, m width of the soil, m heat flux, W m−2 Reynolds number temperature, ◦ C average temperature of the air at inlet, ◦ C average temperature of the air at outlet, ◦ C dimensional coordinates, m
Greek symbols thermal conductivity, W m−1 K−1 density, kg m−3 Subscripts ave average conduction heat transfer cond conv convection heat transfer rad radiation heat transfer
perturbation in soil and water condensation inside of the heat exchanger tubes were taken in to account. However, the variation of soil’s thermophysical properties have been disregarded. Costa [19] is the exception in these kind of studies, who conducted a thermodynamical study where the air mass flow rate through the pipe is actually considered, but the study of the soil temperature profile is one-dimensional. Also, it is considered that the convective coefficient is a known value, but in reality it is not. On the other hand, by using computational fluid dynamics, most of the numerical studies consider the existence of an air flow through the pipe in laminar or turbulent flow regime [7,9,20–27]. However, these studies assume that the convective coefficient is a known parameter, when in a real phenomenon; it is not. From the authors’ knowledge, the only work that does not consider the convective coefficient as a known value was published by Sehli et al. [28]. However, the thermal influence that other dimensions could have in their results is disregarded, because the study was in 1-D. Another interesting numerical approach was carried out by Yoon et al. [27] who modeled the circular pipes as rectangular ducts applying the same peripheral length as the circular pipe in order to simplify the study without affecting accuracy in the results. This approximation has been adopted in the present work. A study to consider 3-D earth modeling was published by Florides et al. [22]. They conducted a sensitive study of an EAHE with a ‘U’ pipe configuration using a 3-D mathematical model for heat conduction in earth, and a 1-D approach for mass air flow and convective heat transfer in the pipe. It was observed that the larger the diameter of the pipe, the more heat flux will be transferred to the soil. Same effect is also obtained by increasing soil’s thermal conductivity. Bojic et al. [21] proposed a model for multi-pipes. However, the heat transfer between the side pipes is not considered since a one-dimensional model was used to predict temperature in the ground. In regard to the experimental studies, they provide reliable results describing EAHE thermal behavior under specific conditions [29,30] and its importance lies in the fact that they establish the basis for validation of theoretical studies. However, the financial investment and time required to set them up are high, which represents a restriction for this kind of studies. Amara et al. [31] determined the viability of using an EAHE for air-conditioning in a building in Adrar, Algeria. The pipe was buried in a depth where climatic changes in the surface cannot influence soil’s temperature,
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which is close to the average annual temperature. Therefore, the air at the outlet of the pipe has the tendency to reach this temperature the whole year, lowering the thermal impact from the outdoor temperature. Ozgener et al. [32] conducted an exergoeconomic test to determine the optimal design of an EAHE for a greenhouse in Izmir, Turquia. The results show that the main sources of exergy destruction are the pipe and the fan. The fan is a main source of exergy destruction due to losses related with mechanical and electrical efficiencies. They concluded that the implementation of methodologies aimed in thermo-economical optimization can contribute in finding the optimal design for an EAHE. In a previous work developed by the authors [33], a numerical study on the thermal performance of an EAHE was conducted for three different climates of México (Cd. Juárez, Chihuahua; México city and Mérida, Yucatán). It was shown that in locations with extreme and moderate climate (Cd. Juárez and México City), the EAHE worked well during cold and warm seasons. However, it was observed that the EAHE did not work properly for cooling purposes in the location with humid-hot climate (Mérida). The high relative humidity values affected the soil temperature increasing the air temperature at the outlet of the EAHE. Based on this, it was concluded that to avoid the undesirable gains of heat, it is recommended to insulate the vertical section at the outlet of the EAHE. Therefore, in this work, we analyze the effect of thermal insulation at the outlet section of the previously studied EAHE model [33]. The EAHE is analyzed for three cities for one year (México city, Mérida and Cd. Juárez) in order to investigate whether insulation improves the outlet air temperature for cooling and heating purposes. 2. Case of study The geometry of the EAHE is shown in Fig. 1. This figure presents both configurations, the EAHE without insulation and the EAHE with thermal insulation (polystyrene) at the outlet vertical section. The dimensions of the EAHE are presented in Table 1. The soil is considered a solid medium where heat is transferred by conduction. On the other hand, there is convective heat transfer through the pipe, and a heat exchange between the walls of the pipe and the soil. These phenomena were modeled by mass, momentum and energy equations. The mathematical model with their respective boundary conditions is [33]:
∂(u) ∂(v) + =0 ∂x ∂y
(1)
∂(uu) ∂(vu) ∂P ∂ ∂u ∂ ∂u + + =− + ∂x ∂y ∂x ∂x ∂x ∂y ∂y
∂(uv) ∂(vv) ∂P ∂ ∂v ∂ ∂v + + =− + ∂x ∂y ∂y ∂x ∂x ∂y ∂y ∂(uT ) ∂(vT ) ∂ + = ∂x ∂y ∂x
∂T CP ∂x
∂ + ∂y
∂T CP ∂y
(2)
(3)
(4)
Table 1 Geometric dimensions for the EAHE. Section
Dimension
Soil’s depth Pipe depth Pipe diameter Pipe length Length of soil at left and right sides Thickness of the insulation material
Hy = 12 m Hy3 = 10 m Hx2 = Hx4 = Hy2 = 0.15 m Hx3 = 5 m Hx1 = Hx5 = 0.5 m a = 0.025, 0.05, 0.075 m
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In y = Hy, ground temperature remains constant beyond this boundary (10 m depth), which approaches the annual average air temperature [26]. Therefore, it can be considered: ∂T = 0. For x = 0 ∂y
and In x = Hx, adiabatic conditions are used for this boundary since any thermal influence coming from these boundaries is disregarded: ∂T = 0. ∂x On the other hand, pipe’s boundary conditions are: (a) for inlet air, it is at the outdoors’s temperature and constant velocity and (b) outlet air, developed flow conditions are used for temperature and velocity. The system is treated as if it all were a fluid. Therefore, thermophysical properties assigned are variable according to the location in the system, where its values are recalculated at the control-volume faces by interpolations. Subsequently, a blockingoff method is used, which consists of setting up the velocity components equal to zero in the solid region, this way, the hydrodynamic effect in soil gets restricted and heat transfer is then governed only by conduction. The coupled elliptic partial differential equations of the convective model were solved using a finite volume method [34]. A summary for the numerical solution is as follows: (1) an initial value for every different variable is guessed (u, v,...T), (2) non-uniform grid generation, (3) assignment of thermophysical properties which value depends on the position, (4) the pressure–velocity (u, v, P) fields are calculated with the SIMPLEC algorithm, (5) with the new calculated values of velocity, the temperature (T) field in the EAHE is obtained and (6) the convergence criterion is applied on all variables for each control volume, if the convergence criterion is not fulfilled return to step (4) until this criterion is achieved. The grid independence study and the verification of the numerical code was presented by the authors in [33].
3. Results (effect of thermal insulation)
Fig. 1. EAHE physical model (a) without and (b) with thermal insulation.
The boundary conditions for the above equations are: In y = 0, the next energy balance [12] is used for the ground surface: −
∂T |y=0 = CE − LR + SR − LE ∂y
(5)
Where, CE is the convective energy exchanged between the air and soil surface, LR is the long-wave radiation for horizontal surfaces, SR is the solar radiation absorbed from the ground surface and LE is the latent heat flux from the ground surface due to evaporation.
The numerical results for the EAHE were obtained with a Reynolds number of 1500 and the climatic conditions in México City, Mérida and Cd. Juárez for 12 months over silt, clay and sand soil, respectively. The meteorological conditions of the three cities were presented in [33]. The thicknesses of polystyrene (cp = 1800 J kg−1 K−1 , = 0.033 W m−1 K−1 , = 28 kg m−3 [35]) considered in the simulations are: 0.025, 0.05 and 0.075 m (1 , 2 and 3 ). For Mexico City, the temperature difference between the outlet out − T inlet ) of the EAHE is presented in Table 2. and inlet (T = Tave ave As mentioned in [33], the EAHE without insulation behaved as expected during all months in this city; the temperature of the air at the outlet increased during the cold months (Jan–Mar, Oct–Dec) and it decreased during the hot months (Apr–Sep). However, in order to investigate whether thermal insulation at the outlet section improves the thermal performance of the EAHE for cooling and heating, this modification was analyzed. During the cold season, the EAHE with an insulation of a = 0.025 m improved slightly the air temperature at the outlet, just 0.5 ◦ C above the EAHE without insulation (a = 0 m). In contrast, the EAHE with an insulation of a = 0.05 m improved the heating effect, in January, it was able to increase the outlet air temperature up to 5.7 ◦ C above the inlet temperature (2.0 ◦ C higher than the outlet temperature of the EAHE without insulation). The EAHE with an insulation of a = 0.075 m had almost the same behavior than the EAHE with the insulation of a = 0.05 m; the maximum temperature difference at the outlet between these two cases is just 0.3 ◦ C. On the other hand, during the hot season the EAHE with a = 0.025 m had not significant contribution to the cooling effect with respect to the EAHE without insulation. On the contrary, the EAHE with an insulation of 0.05 m improved the outlet air temperature, in August and September the cooling effect of the EAHE increased by 1.3 ◦ C with respect to the
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Table 2 Average temperature difference (◦ C) between the outlet and inlet temperature in function of “a” for a year (México City). Season
Month
inlet Inlet temperature Tave
out inlet T = Tave − Tave
Without insulating material
With insulating material
a=0m
a = 0.025 m
a = 0.05 m
a = 0.075 m
Cold
Jan Feb Mar
1.8 4.1 6.8
3.7 2.1 1.5
4.2 2.6 2.0
5.7 4.3 3.3
5.9 4.6 3.5
Hot
Apr May Jun Jul Aug Sep
27.2 28.0 27.9 25.1 25.0 25.2
−5.4 −3.5 −3.9 −2.3 −2.0 −1.9
−5.4 −3.8 −4.1 −2.5 −2.3 −2.3
−5.4 −4.6 −4.8 −3.3 −3.3 −3.2
−5.4 −4.8 −4.9 −3.4 −3.3 −3.3
Cold
Oct Nov Dec
7.0 3.1 3.2
1.9 3.5 3.5
2.3 3.9 3.9
3.5 5.2 5.2
3.6 5.5 5.4
Fig. 2. Inlet and outlet average temperatures (◦ C) of the EAHE in function of the thickness (a) of insulating material for a year (México City).
case without insulation. As happened in cold season, the EAHE with an insulation of a = 0.075 m had almost the same performance than the EAHE with a = 0.05 m, then higher insulation thicknesses are not needed. This behavior can be observed in Fig. 2. The Table 3 presents the air temperature difference between the inlet and outlet of the EAHE in Mérida for the cases of study. In addition, it also presents the results for the case without insulation [33]. Regarding the months in the cold season (Jan–Mar, Oct–Dec), the effect of insulation with a = 0.025 m on the EAHE is negligible. With respect to the case without insulation, this thickness
provided a maximum increment of 0.6 ◦ C (Jan). The insulation with a = 0.05 m avoided an important loss of heat at the outlet section of the EAHE. In January, the outlet temperature of the air reached up to 5.8 ◦ C above the inlet temperature (2.6 ◦ C above of the case without insulation). For heating purposes, the EAHE with an insulation of a = 0.075 m had almost the same behavior than a = 0.05 m. On the other hand, as previously mentioned, in Mérida the EAHE without insulation did not work well for cooling purposes. Due to the high values of humidity in this city, the section at the outlet was hot enough to increase the outlet air temperature above the inlet temperature during May, June and July [33]. Because the insulation may avoid heat gains from the soil, this improvement was recommended in the previous work of the authors. Using an insulation of a = 0.025 m at the outlet section improved slightly the behavior of the EAHE. For instance, with respect to the cases without insulation, in May and July the temperature at the outlet was reduced 1.1 ◦ C and 0.9 ◦ C, respectively (Table 3). However, with this thickness of insulation the EAHE is still not working in June. In contrast, the thermal insulation with a = 0.05 m caused the EAHE to function properly during all months in the hot season (Fig. 3). This measure avoided important heat gains from the soil, therefore, the EAHE with an insulation of a = 0.05 m had an important contribution to the cooling effect during hot months. In June the temperature at the outlet reached 1.5 ◦ C below the inlet temperature (5 ◦ C below the outlet temperature of the case without insulation) and in April the temperature at the outlet reached 4.3 ◦ C below the inlet temperature (2.6 ◦ C below the outlet temperature of the case without insulation). For cooling purposes, the EAHE with an insulation of a = 0.075 m had almost the same behavior than
Table 3 Average temperature difference (◦ C) between the outlet and inlet temperature in function of “a” for a year (Mérida, Yucatán). Season
Month
inlet Inlet temperature Tave
out inlet T = Tave − Tave
Without insulating material
With insulating material
a=0m
a = 0.025 m
a = 0.05 m
a = 0.075 m
Cold
Jan Feb Mar
10.1 12.0 14.3
3.2 3.9 3.2
3.8 4.3 3.5
5.8 5.6 4.6
6.1 5.8 4.8
Hot
Apr May Jun Jul Aug Sep
39.6 41.2 38.2 38.4 37.0 36.3
−1.7 0.9 3.5 0.5 −0.4 −1.1
−2.3 −0.2 2.2 −0.4 −1.0 −1.8
−4.3 −3.4 −1.5 −2.9 −3.0 −3.4
−4.7 −4.0 −2.1 −3.3 −3.3 −3,1
Cold
Oct Nov Dec
16.8 14.2 12.3
4.8 3.0 4.5
4.8 3.4 4.9
4.8 4.6 5.8
4.8 4.8 6.0
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Table 4 Average temperature difference (◦ C) between the outlet and inlet temperature in function of “a” for a year (Cd. Juárez, Chihuahua). Season
Month
inlet Inlet temperature Tave
out inlet T = Tave − Tave
Without insulating material
With insulating material
a=0m
a = 0.025 m
Cold
Jan Feb Mar
−0.6 3.2 7.5
3 2.1 −0.8
3.7 2.7 −0.1
6.3 4.9 2.4
6.8 5.4 2.9
Hot
Apr May Jun Jul Aug Sep
25.3 31.1 33.3 33.6 31.3 29.1
−5.2 −4 −9.5 −8 −6.9 −6.2
−5.0 −4.2 −9.2 −8.0 −6.8 −6.1
−4.3 −5.1 −8.4 −7.7 −6.6 −5.7
−4.1 −5.2 −8.2 −7.7 −6.5 −5.6
Cold
Oct Nov Dec
11.3 3.3 0.8
2.5 2.1 3.7
2.6 2.7 4.2
3.1 4.9 6.3
3.2 5.3 6.7
a = 0.05 m since the maximum difference between the temperature at the outlet of these two cases is just 0.6 ◦ C. Therefore, it is not necessary to use higher thickness than 0.05 m (Fig. 3). Similarly to Mexico city and Mérida, the Table 4 presents the air temperature difference between the inlet and outlet of the EAHE in Cd. Juárez. In general, when considering the influence of the insulation from a thermal point of view, the EAHE works as expected during the cold and hot months in Cd. Juárez. During the first period of cold months (Jan–Mar), the value of T obtained when a = 0.025 m is not significant respect to the results from the case without insulation. When a = 0.05 m, the maximum temperature increment of the air at the outlet is 3.3 ◦ C (January) and the minimum increment is 2.8 (February) with respect to the corresponding values when a = 0 m. When the thickness of the insulation increases from 0.05 m to 0.075 m, the air temperature just increases 0.5 ◦ C. Similar results are obtained for the second period of cold months (Oct–Dec), where improvements are given by the insulation with a = 0.05 m, up to 2.8 ◦ C in November with respect to the case without insulation. The behavior of the EAHE is presented in Fig. 4. During most of the period of summer (Apr–Sep), the thermal insulation does not provides a reduction of the air temperature at the outlet of the EAHE with respect to the case without insulation; May is the exception, where the air temperature decreases 1.1 ◦ C. Therefore, for the summer, the thermal behavior of the EAHE does not improves when installing thermal insulation at the outlet of the EAHE mainly due to the low humidity in the ambient
a = 0.05 m
a = 0.075 m
Fig. 4. Inlet and outlet average temperatures (◦ C) of the EAHE in function of the thickness (a) of insulating material for a year (Cd. Juárez).
out depends of the combination of the In general, the value of Tave different parameters involved in the EAHE system (climatic conditions, considerations in the physical and mathematical model, etc.). Particularly, for the climatic conditions of Mérida, we observed that a relative humidity higher than 60% causes an increase of the soil temperature. By increasing the soil temperature, the fluid toward the outlet of the EAHE significantly increases its temperature. Hence, to avoid the undesirable gains of heat in Mérida, it is recommended to insulate the vertical section at the outlet of the EAHE.
4. Conclusions
Fig. 3. Inlet and outlet average temperatures (◦ C) of the EAHE in function of the thickness (a) of insulating material for a year (Mérida).
In this work was studied the effect of thermal insulation at the outlet section of an EAHE. It was developed for three cities in México and the following is concluded: In Mexico City, the insulation with a thickness of 0.05 m (2 ) at the outlet section is recommended because it improved the performance of the EAHE, a higher insulation thickness did not increase the cooling or heating effect from that provided by 0.05 m of insulation. In winter, the EAHE had an outlet temperature up to 2.0 ◦ C higher than the temperature of the EAHE without insulation. On the other hand, the cooling effect of the EAHE increased up to 1.3 ◦ C with respect to the case without insulation. In Mérida the results indicate that thermal insulation with a thickness of 0.05 m (2 ) at the outlet section of the EAHE is also the best option. The EAHE with this insulation complied its purpose for a humid-hot climate, it heated the air during winter and it cooled
J. Xamán et al. / Energy and Buildings 85 (2014) 356–361
the air during summer. In winter, this measure avoided the losses of heat from the air to the soil at the outlet of the EAHE, the air temperature reached 2.6 ◦ C above the outlet temperature of the case without insulation. In summer, the thermal insulation avoided important heat gains from the soil to the air, the air temperature at the outlet reached up to 5 ◦ C below the outlet temperature of the EAHE without insulation. In Cd. Juárez, when using thermal insulation at the outlet of the EAHE only improves the air temperature during the winter months, whereas during the summer months the insulation does not have a significant influence due to the low values of humidity in the ambient. Acknowledgments The authors are grateful to the Consejo Nacional de Ciencia y Tecnología (CONACYT), whose financial support made this work possible. References [1] R.L. Sawhney, D. Buddhi, N.M. Thanu, An experimental study of summer performance of a recirculation type underground airpipe air conditioning system, Building and Environment 34 (1998) 189–196. [2] A. Trombe, L. Serres, Air-earth exchanger study in real site experimentation and simulation, Energy and Buildings 21 (1994) 155–162. [3] V. Badescu, D. Isvoranu, Pneumatic and thermal design procedure and analysis of earth-to-air heat exchangers of registry type, Applied Energy 88 (2011) 1266–1280. [4] A. Chel, Performance evaluation and life cycle cost analysis of earth to air heat exchanger integrated with adobe building for New Delhi composite climate, Energy and Buildings 41 (2009) 56–66. [5] Jens Pfafferott, Evaluation of earth-to-air heat exchangers with a standardised method to calculate energy efficiency, Energy and Buildings 35 (2003) 971–983. [6] H. Carslaw, J. Jaeger, Conduction of Heat in Solids, Oxford at the Claredon Press, New York, 1959. [7] R. Cichota, E.A. Elias, Quirijn de Jong van Lier, Testing a finite-difference model for soil heat transfer by comparing numerical and analytical solutions, Environmental Modeling 19 (2004) 495–506. [8] M. De Paepe, A. Janssens, Thermo-hydraulic design of earth-air heat exchangers, Energy and Buildings 35 (2003) 389–397. [9] C. Gauthier, M. Lacroix, H. Bernier, Numerical simulation of soil heat exchangerstorage system for greenhouses, Solar Energy 60 (1997) 333–346. [10] G. Mihalakakou, M. Santamouris, D. Asimakopoulos, Modelling the thermal performance of earth-to-air heat exchangers, Solar Energy 53 (1994) 301–305. [11] G. Mihalakakou, M. Santamouris, D. Asimakopoulos, N. Papanikolau, Impact of ground cover on the efficiencies of earth-to-air heat exchangers, Applied Energy 48 (1994) 19–32. [12] G. Mihalakakou, M. Santamouris, D. Asimakopoulos, On the application of the energy balance equation to predict ground temperature, Solar Energy 60 (1997) 181–190. [13] P. Tittelein, G. Achard, E. Wurtz, Modeling earth-to-air heat exchanger behavior with the convolutive response factors method, Applied Energy 86 (2009) 1683–1691.
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Short Communication
Numerical study of earth-to-air heat exchanger: The effect of thermal insulation J. Xamán a,∗ , I. Hernández-Pérez a , J. Arce a , G. Álvarez a , L. Ramírez-Dávila b,1 , F. Noh-Pat c,2 a
Centro Nacional de Investigación y Desarrollo Tecnológico, CENIDET-TNM-SEP, Prol. Av. Palmira S/N, Col. Palmira, Cuernavaca, Morelos CP 62490, México Building energy efficiency, Bee, EUA, 13640 Briarwick Drive, Suite 180, Austin, TX CP 78729, USA Universidad Autónoma de Baja California, UABC, Centro de Ingeniería y Tecnología (Unidad Valle de las Palmas), CITEC, Blvd., Universitario # 1000, Tijuana, Baja California, CP 21500, México b c
a r t i c l e
i n f o
Article history: Received 10 March 2014 Received in revised form 13 August 2014 Accepted 15 September 2014 Available online 8 October 2014 Keywords: Earth-to-air heat exchanger Thermal insulation
a b s t r a c t A numerical study was conducted for prediction of the thermal performance of an Earth-to-Air Heat Exchanger (EAHE) for three cities in México. The climatic conditions correspond to a temperate climate (México City), a humid-hot climate (Mérida, Yucatán) and an extreme weather (Cd. Juárez, Chihuahua). The effect of thermal insulation at the outlet section of the EAHE is investigated. In México City, the insulation with a thickness of 0.05 m (2 ) is recommended because it improved the performance of the EAHE. In winter, the insulation increased the heating effect up to 2 ◦ C with respect to the EAHE without insulation. In summer, thermal insulation provided an improvement on the cooling effect up to 1.3 ◦ C. In Mérida the results indicate that thermal insulation with a thickness of 0.05 m is also the best option. In winter, this measure improved the heating effect up to 2.6 ◦ C with respect to the EAHE without insulation. Particularly, for Cd. Juárez during the summer, the thermal behavior of the EAHE was not improved due to the thermal insulation. Therefore for México and Mérida the suggested value of insulation made the EAHE to function properly during all months in summer, since it avoided the undesirable heat gain from the soil at the outlet. In other words, the insulation improved the cooling effect up to 5 ◦ C with respect to the EAHE without insulation. © 2014 Elsevier B.V. All rights reserved.
1. Introduction During the last decade, there has been a rising interest in implementing heating and cooling systems for buildings based on renewable energy sources. Because of its high thermal inertia, the soil attenuates the temperature fluctuations that occur at the ground surface. Further, it causes a time lag between the temperature at the surface and the temperature in the soil. Therefore, at a sufficient depth, the ground temperature is lower than the temperature of the outdoor air during the summer and it is higher than the temperature of the air during the winter. When the air from the ambient is drawn through an Earth-to-Air Heat
∗ Corresponding author. Tel.: +52 777 3 62 77 70; fax: +52 777 3 62 77 95. E-mail addresses: [email protected], [email protected] (J. Xamán), [email protected] (I. Hernández-Pérez), [email protected] (J. Arce), [email protected] (G. Álvarez), [email protected] (L. Ramírez-Dávila), [email protected] (F. Noh-Pat). 1 Tel.: +1 (512) 3 64 06 88; fax: +1 (512) 3 64 06 86. 2 Tel.: +52 664 6 76 82 22. http://dx.doi.org/10.1016/j.enbuild.2014.09.064 0378-7788/© 2014 Elsevier B.V. All rights reserved.
Exchanger (EAHE), which consists in pipes buried in the soil, the air can be cooled during the summer and it can be heated during the winter. As a result, an EAHE may improve the thermal comfort inside buildings or even reduce the energy destined for heating or cooling [1–5]. Recent studies aimed to evaluate the temperature profiles in soil are still implementing 1-D analytic formulation proposed over 50 years ago by Carslaw and Jaeger [6], that are still distant from representing reality since they do not consider soil’s thermophysical variation [7–14]. A study of this kind was carried out by Salah ElDin [15], who predicted the variation of the soil temperature with depth in a 1-D model based on an energy balance at the ground surface. They considered the variation of the solar radiation, air temperature and latent heat flux due to evaporation; however, it was considered that soil has uniform thermophysical properties. In regard with the studies focused in EAHEs, those that are based in thermodynamics energy balance do not represent the phenomena in an appropriate way since the air flow through the pipe is not considered by disregarding its velocity [12,16–18]. One of these studies was conducted by Cucumo et al. [17], who considered a one-dimensional transient study where thermal
J. Xamán et al. / Energy and Buildings 85 (2014) 356–361
Nomenclature a cp Hx Hy Q Re T inlet Tave out Tave x,y
thickness of insulation, m specific heat. J kg−1 K−1 depth of the soil, m width of the soil, m heat flux, W m−2 Reynolds number temperature, ◦ C average temperature of the air at inlet, ◦ C average temperature of the air at outlet, ◦ C dimensional coordinates, m
Greek symbols thermal conductivity, W m−1 K−1 density, kg m−3 Subscripts ave average conduction heat transfer cond conv convection heat transfer rad radiation heat transfer
perturbation in soil and water condensation inside of the heat exchanger tubes were taken in to account. However, the variation of soil’s thermophysical properties have been disregarded. Costa [19] is the exception in these kind of studies, who conducted a thermodynamical study where the air mass flow rate through the pipe is actually considered, but the study of the soil temperature profile is one-dimensional. Also, it is considered that the convective coefficient is a known value, but in reality it is not. On the other hand, by using computational fluid dynamics, most of the numerical studies consider the existence of an air flow through the pipe in laminar or turbulent flow regime [7,9,20–27]. However, these studies assume that the convective coefficient is a known parameter, when in a real phenomenon; it is not. From the authors’ knowledge, the only work that does not consider the convective coefficient as a known value was published by Sehli et al. [28]. However, the thermal influence that other dimensions could have in their results is disregarded, because the study was in 1-D. Another interesting numerical approach was carried out by Yoon et al. [27] who modeled the circular pipes as rectangular ducts applying the same peripheral length as the circular pipe in order to simplify the study without affecting accuracy in the results. This approximation has been adopted in the present work. A study to consider 3-D earth modeling was published by Florides et al. [22]. They conducted a sensitive study of an EAHE with a ‘U’ pipe configuration using a 3-D mathematical model for heat conduction in earth, and a 1-D approach for mass air flow and convective heat transfer in the pipe. It was observed that the larger the diameter of the pipe, the more heat flux will be transferred to the soil. Same effect is also obtained by increasing soil’s thermal conductivity. Bojic et al. [21] proposed a model for multi-pipes. However, the heat transfer between the side pipes is not considered since a one-dimensional model was used to predict temperature in the ground. In regard to the experimental studies, they provide reliable results describing EAHE thermal behavior under specific conditions [29,30] and its importance lies in the fact that they establish the basis for validation of theoretical studies. However, the financial investment and time required to set them up are high, which represents a restriction for this kind of studies. Amara et al. [31] determined the viability of using an EAHE for air-conditioning in a building in Adrar, Algeria. The pipe was buried in a depth where climatic changes in the surface cannot influence soil’s temperature,
357
which is close to the average annual temperature. Therefore, the air at the outlet of the pipe has the tendency to reach this temperature the whole year, lowering the thermal impact from the outdoor temperature. Ozgener et al. [32] conducted an exergoeconomic test to determine the optimal design of an EAHE for a greenhouse in Izmir, Turquia. The results show that the main sources of exergy destruction are the pipe and the fan. The fan is a main source of exergy destruction due to losses related with mechanical and electrical efficiencies. They concluded that the implementation of methodologies aimed in thermo-economical optimization can contribute in finding the optimal design for an EAHE. In a previous work developed by the authors [33], a numerical study on the thermal performance of an EAHE was conducted for three different climates of México (Cd. Juárez, Chihuahua; México city and Mérida, Yucatán). It was shown that in locations with extreme and moderate climate (Cd. Juárez and México City), the EAHE worked well during cold and warm seasons. However, it was observed that the EAHE did not work properly for cooling purposes in the location with humid-hot climate (Mérida). The high relative humidity values affected the soil temperature increasing the air temperature at the outlet of the EAHE. Based on this, it was concluded that to avoid the undesirable gains of heat, it is recommended to insulate the vertical section at the outlet of the EAHE. Therefore, in this work, we analyze the effect of thermal insulation at the outlet section of the previously studied EAHE model [33]. The EAHE is analyzed for three cities for one year (México city, Mérida and Cd. Juárez) in order to investigate whether insulation improves the outlet air temperature for cooling and heating purposes. 2. Case of study The geometry of the EAHE is shown in Fig. 1. This figure presents both configurations, the EAHE without insulation and the EAHE with thermal insulation (polystyrene) at the outlet vertical section. The dimensions of the EAHE are presented in Table 1. The soil is considered a solid medium where heat is transferred by conduction. On the other hand, there is convective heat transfer through the pipe, and a heat exchange between the walls of the pipe and the soil. These phenomena were modeled by mass, momentum and energy equations. The mathematical model with their respective boundary conditions is [33]:
∂(u) ∂(v) + =0 ∂x ∂y
(1)
∂(uu) ∂(vu) ∂P ∂ ∂u ∂ ∂u + + =− + ∂x ∂y ∂x ∂x ∂x ∂y ∂y
∂(uv) ∂(vv) ∂P ∂ ∂v ∂ ∂v + + =− + ∂x ∂y ∂y ∂x ∂x ∂y ∂y ∂(uT ) ∂(vT ) ∂ + = ∂x ∂y ∂x
∂T CP ∂x
∂ + ∂y
∂T CP ∂y
(2)
(3)
(4)
Table 1 Geometric dimensions for the EAHE. Section
Dimension
Soil’s depth Pipe depth Pipe diameter Pipe length Length of soil at left and right sides Thickness of the insulation material
Hy = 12 m Hy3 = 10 m Hx2 = Hx4 = Hy2 = 0.15 m Hx3 = 5 m Hx1 = Hx5 = 0.5 m a = 0.025, 0.05, 0.075 m
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J. Xamán et al. / Energy and Buildings 85 (2014) 356–361
In y = Hy, ground temperature remains constant beyond this boundary (10 m depth), which approaches the annual average air temperature [26]. Therefore, it can be considered: ∂T = 0. For x = 0 ∂y
and In x = Hx, adiabatic conditions are used for this boundary since any thermal influence coming from these boundaries is disregarded: ∂T = 0. ∂x On the other hand, pipe’s boundary conditions are: (a) for inlet air, it is at the outdoors’s temperature and constant velocity and (b) outlet air, developed flow conditions are used for temperature and velocity. The system is treated as if it all were a fluid. Therefore, thermophysical properties assigned are variable according to the location in the system, where its values are recalculated at the control-volume faces by interpolations. Subsequently, a blockingoff method is used, which consists of setting up the velocity components equal to zero in the solid region, this way, the hydrodynamic effect in soil gets restricted and heat transfer is then governed only by conduction. The coupled elliptic partial differential equations of the convective model were solved using a finite volume method [34]. A summary for the numerical solution is as follows: (1) an initial value for every different variable is guessed (u, v,...T), (2) non-uniform grid generation, (3) assignment of thermophysical properties which value depends on the position, (4) the pressure–velocity (u, v, P) fields are calculated with the SIMPLEC algorithm, (5) with the new calculated values of velocity, the temperature (T) field in the EAHE is obtained and (6) the convergence criterion is applied on all variables for each control volume, if the convergence criterion is not fulfilled return to step (4) until this criterion is achieved. The grid independence study and the verification of the numerical code was presented by the authors in [33].
3. Results (effect of thermal insulation)
Fig. 1. EAHE physical model (a) without and (b) with thermal insulation.
The boundary conditions for the above equations are: In y = 0, the next energy balance [12] is used for the ground surface: −
∂T |y=0 = CE − LR + SR − LE ∂y
(5)
Where, CE is the convective energy exchanged between the air and soil surface, LR is the long-wave radiation for horizontal surfaces, SR is the solar radiation absorbed from the ground surface and LE is the latent heat flux from the ground surface due to evaporation.
The numerical results for the EAHE were obtained with a Reynolds number of 1500 and the climatic conditions in México City, Mérida and Cd. Juárez for 12 months over silt, clay and sand soil, respectively. The meteorological conditions of the three cities were presented in [33]. The thicknesses of polystyrene (cp = 1800 J kg−1 K−1 , = 0.033 W m−1 K−1 , = 28 kg m−3 [35]) considered in the simulations are: 0.025, 0.05 and 0.075 m (1 , 2 and 3 ). For Mexico City, the temperature difference between the outlet out − T inlet ) of the EAHE is presented in Table 2. and inlet (T = Tave ave As mentioned in [33], the EAHE without insulation behaved as expected during all months in this city; the temperature of the air at the outlet increased during the cold months (Jan–Mar, Oct–Dec) and it decreased during the hot months (Apr–Sep). However, in order to investigate whether thermal insulation at the outlet section improves the thermal performance of the EAHE for cooling and heating, this modification was analyzed. During the cold season, the EAHE with an insulation of a = 0.025 m improved slightly the air temperature at the outlet, just 0.5 ◦ C above the EAHE without insulation (a = 0 m). In contrast, the EAHE with an insulation of a = 0.05 m improved the heating effect, in January, it was able to increase the outlet air temperature up to 5.7 ◦ C above the inlet temperature (2.0 ◦ C higher than the outlet temperature of the EAHE without insulation). The EAHE with an insulation of a = 0.075 m had almost the same behavior than the EAHE with the insulation of a = 0.05 m; the maximum temperature difference at the outlet between these two cases is just 0.3 ◦ C. On the other hand, during the hot season the EAHE with a = 0.025 m had not significant contribution to the cooling effect with respect to the EAHE without insulation. On the contrary, the EAHE with an insulation of 0.05 m improved the outlet air temperature, in August and September the cooling effect of the EAHE increased by 1.3 ◦ C with respect to the
J. Xamán et al. / Energy and Buildings 85 (2014) 356–361
359
Table 2 Average temperature difference (◦ C) between the outlet and inlet temperature in function of “a” for a year (México City). Season
Month
inlet Inlet temperature Tave
out inlet T = Tave − Tave
Without insulating material
With insulating material
a=0m
a = 0.025 m
a = 0.05 m
a = 0.075 m
Cold
Jan Feb Mar
1.8 4.1 6.8
3.7 2.1 1.5
4.2 2.6 2.0
5.7 4.3 3.3
5.9 4.6 3.5
Hot
Apr May Jun Jul Aug Sep
27.2 28.0 27.9 25.1 25.0 25.2
−5.4 −3.5 −3.9 −2.3 −2.0 −1.9
−5.4 −3.8 −4.1 −2.5 −2.3 −2.3
−5.4 −4.6 −4.8 −3.3 −3.3 −3.2
−5.4 −4.8 −4.9 −3.4 −3.3 −3.3
Cold
Oct Nov Dec
7.0 3.1 3.2
1.9 3.5 3.5
2.3 3.9 3.9
3.5 5.2 5.2
3.6 5.5 5.4
Fig. 2. Inlet and outlet average temperatures (◦ C) of the EAHE in function of the thickness (a) of insulating material for a year (México City).
case without insulation. As happened in cold season, the EAHE with an insulation of a = 0.075 m had almost the same performance than the EAHE with a = 0.05 m, then higher insulation thicknesses are not needed. This behavior can be observed in Fig. 2. The Table 3 presents the air temperature difference between the inlet and outlet of the EAHE in Mérida for the cases of study. In addition, it also presents the results for the case without insulation [33]. Regarding the months in the cold season (Jan–Mar, Oct–Dec), the effect of insulation with a = 0.025 m on the EAHE is negligible. With respect to the case without insulation, this thickness
provided a maximum increment of 0.6 ◦ C (Jan). The insulation with a = 0.05 m avoided an important loss of heat at the outlet section of the EAHE. In January, the outlet temperature of the air reached up to 5.8 ◦ C above the inlet temperature (2.6 ◦ C above of the case without insulation). For heating purposes, the EAHE with an insulation of a = 0.075 m had almost the same behavior than a = 0.05 m. On the other hand, as previously mentioned, in Mérida the EAHE without insulation did not work well for cooling purposes. Due to the high values of humidity in this city, the section at the outlet was hot enough to increase the outlet air temperature above the inlet temperature during May, June and July [33]. Because the insulation may avoid heat gains from the soil, this improvement was recommended in the previous work of the authors. Using an insulation of a = 0.025 m at the outlet section improved slightly the behavior of the EAHE. For instance, with respect to the cases without insulation, in May and July the temperature at the outlet was reduced 1.1 ◦ C and 0.9 ◦ C, respectively (Table 3). However, with this thickness of insulation the EAHE is still not working in June. In contrast, the thermal insulation with a = 0.05 m caused the EAHE to function properly during all months in the hot season (Fig. 3). This measure avoided important heat gains from the soil, therefore, the EAHE with an insulation of a = 0.05 m had an important contribution to the cooling effect during hot months. In June the temperature at the outlet reached 1.5 ◦ C below the inlet temperature (5 ◦ C below the outlet temperature of the case without insulation) and in April the temperature at the outlet reached 4.3 ◦ C below the inlet temperature (2.6 ◦ C below the outlet temperature of the case without insulation). For cooling purposes, the EAHE with an insulation of a = 0.075 m had almost the same behavior than
Table 3 Average temperature difference (◦ C) between the outlet and inlet temperature in function of “a” for a year (Mérida, Yucatán). Season
Month
inlet Inlet temperature Tave
out inlet T = Tave − Tave
Without insulating material
With insulating material
a=0m
a = 0.025 m
a = 0.05 m
a = 0.075 m
Cold
Jan Feb Mar
10.1 12.0 14.3
3.2 3.9 3.2
3.8 4.3 3.5
5.8 5.6 4.6
6.1 5.8 4.8
Hot
Apr May Jun Jul Aug Sep
39.6 41.2 38.2 38.4 37.0 36.3
−1.7 0.9 3.5 0.5 −0.4 −1.1
−2.3 −0.2 2.2 −0.4 −1.0 −1.8
−4.3 −3.4 −1.5 −2.9 −3.0 −3.4
−4.7 −4.0 −2.1 −3.3 −3.3 −3,1
Cold
Oct Nov Dec
16.8 14.2 12.3
4.8 3.0 4.5
4.8 3.4 4.9
4.8 4.6 5.8
4.8 4.8 6.0
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Table 4 Average temperature difference (◦ C) between the outlet and inlet temperature in function of “a” for a year (Cd. Juárez, Chihuahua). Season
Month
inlet Inlet temperature Tave
out inlet T = Tave − Tave
Without insulating material
With insulating material
a=0m
a = 0.025 m
Cold
Jan Feb Mar
−0.6 3.2 7.5
3 2.1 −0.8
3.7 2.7 −0.1
6.3 4.9 2.4
6.8 5.4 2.9
Hot
Apr May Jun Jul Aug Sep
25.3 31.1 33.3 33.6 31.3 29.1
−5.2 −4 −9.5 −8 −6.9 −6.2
−5.0 −4.2 −9.2 −8.0 −6.8 −6.1
−4.3 −5.1 −8.4 −7.7 −6.6 −5.7
−4.1 −5.2 −8.2 −7.7 −6.5 −5.6
Cold
Oct Nov Dec
11.3 3.3 0.8
2.5 2.1 3.7
2.6 2.7 4.2
3.1 4.9 6.3
3.2 5.3 6.7
a = 0.05 m since the maximum difference between the temperature at the outlet of these two cases is just 0.6 ◦ C. Therefore, it is not necessary to use higher thickness than 0.05 m (Fig. 3). Similarly to Mexico city and Mérida, the Table 4 presents the air temperature difference between the inlet and outlet of the EAHE in Cd. Juárez. In general, when considering the influence of the insulation from a thermal point of view, the EAHE works as expected during the cold and hot months in Cd. Juárez. During the first period of cold months (Jan–Mar), the value of T obtained when a = 0.025 m is not significant respect to the results from the case without insulation. When a = 0.05 m, the maximum temperature increment of the air at the outlet is 3.3 ◦ C (January) and the minimum increment is 2.8 (February) with respect to the corresponding values when a = 0 m. When the thickness of the insulation increases from 0.05 m to 0.075 m, the air temperature just increases 0.5 ◦ C. Similar results are obtained for the second period of cold months (Oct–Dec), where improvements are given by the insulation with a = 0.05 m, up to 2.8 ◦ C in November with respect to the case without insulation. The behavior of the EAHE is presented in Fig. 4. During most of the period of summer (Apr–Sep), the thermal insulation does not provides a reduction of the air temperature at the outlet of the EAHE with respect to the case without insulation; May is the exception, where the air temperature decreases 1.1 ◦ C. Therefore, for the summer, the thermal behavior of the EAHE does not improves when installing thermal insulation at the outlet of the EAHE mainly due to the low humidity in the ambient
a = 0.05 m
a = 0.075 m
Fig. 4. Inlet and outlet average temperatures (◦ C) of the EAHE in function of the thickness (a) of insulating material for a year (Cd. Juárez).
out depends of the combination of the In general, the value of Tave different parameters involved in the EAHE system (climatic conditions, considerations in the physical and mathematical model, etc.). Particularly, for the climatic conditions of Mérida, we observed that a relative humidity higher than 60% causes an increase of the soil temperature. By increasing the soil temperature, the fluid toward the outlet of the EAHE significantly increases its temperature. Hence, to avoid the undesirable gains of heat in Mérida, it is recommended to insulate the vertical section at the outlet of the EAHE.
4. Conclusions
Fig. 3. Inlet and outlet average temperatures (◦ C) of the EAHE in function of the thickness (a) of insulating material for a year (Mérida).
In this work was studied the effect of thermal insulation at the outlet section of an EAHE. It was developed for three cities in México and the following is concluded: In Mexico City, the insulation with a thickness of 0.05 m (2 ) at the outlet section is recommended because it improved the performance of the EAHE, a higher insulation thickness did not increase the cooling or heating effect from that provided by 0.05 m of insulation. In winter, the EAHE had an outlet temperature up to 2.0 ◦ C higher than the temperature of the EAHE without insulation. On the other hand, the cooling effect of the EAHE increased up to 1.3 ◦ C with respect to the case without insulation. In Mérida the results indicate that thermal insulation with a thickness of 0.05 m (2 ) at the outlet section of the EAHE is also the best option. The EAHE with this insulation complied its purpose for a humid-hot climate, it heated the air during winter and it cooled
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the air during summer. In winter, this measure avoided the losses of heat from the air to the soil at the outlet of the EAHE, the air temperature reached 2.6 ◦ C above the outlet temperature of the case without insulation. In summer, the thermal insulation avoided important heat gains from the soil to the air, the air temperature at the outlet reached up to 5 ◦ C below the outlet temperature of the EAHE without insulation. In Cd. Juárez, when using thermal insulation at the outlet of the EAHE only improves the air temperature during the winter months, whereas during the summer months the insulation does not have a significant influence due to the low values of humidity in the ambient. Acknowledgments The authors are grateful to the Consejo Nacional de Ciencia y Tecnología (CONACYT), whose financial support made this work possible. References [1] R.L. Sawhney, D. Buddhi, N.M. Thanu, An experimental study of summer performance of a recirculation type underground airpipe air conditioning system, Building and Environment 34 (1998) 189–196. [2] A. Trombe, L. Serres, Air-earth exchanger study in real site experimentation and simulation, Energy and Buildings 21 (1994) 155–162. [3] V. Badescu, D. Isvoranu, Pneumatic and thermal design procedure and analysis of earth-to-air heat exchangers of registry type, Applied Energy 88 (2011) 1266–1280. [4] A. Chel, Performance evaluation and life cycle cost analysis of earth to air heat exchanger integrated with adobe building for New Delhi composite climate, Energy and Buildings 41 (2009) 56–66. [5] Jens Pfafferott, Evaluation of earth-to-air heat exchangers with a standardised method to calculate energy efficiency, Energy and Buildings 35 (2003) 971–983. [6] H. Carslaw, J. Jaeger, Conduction of Heat in Solids, Oxford at the Claredon Press, New York, 1959. [7] R. Cichota, E.A. Elias, Quirijn de Jong van Lier, Testing a finite-difference model for soil heat transfer by comparing numerical and analytical solutions, Environmental Modeling 19 (2004) 495–506. [8] M. De Paepe, A. Janssens, Thermo-hydraulic design of earth-air heat exchangers, Energy and Buildings 35 (2003) 389–397. [9] C. Gauthier, M. Lacroix, H. Bernier, Numerical simulation of soil heat exchangerstorage system for greenhouses, Solar Energy 60 (1997) 333–346. [10] G. Mihalakakou, M. Santamouris, D. Asimakopoulos, Modelling the thermal performance of earth-to-air heat exchangers, Solar Energy 53 (1994) 301–305. [11] G. Mihalakakou, M. Santamouris, D. Asimakopoulos, N. Papanikolau, Impact of ground cover on the efficiencies of earth-to-air heat exchangers, Applied Energy 48 (1994) 19–32. [12] G. Mihalakakou, M. Santamouris, D. Asimakopoulos, On the application of the energy balance equation to predict ground temperature, Solar Energy 60 (1997) 181–190. [13] P. Tittelein, G. Achard, E. Wurtz, Modeling earth-to-air heat exchanger behavior with the convolutive response factors method, Applied Energy 86 (2009) 1683–1691.
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