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Experimental investigations of the heat load effect on heat transfer of ground heat exchangers in a layered subsurface
Geothermics 77 (2019) 75–82
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Experimental investigations of the heat load effect on heat transfer of ground heat exchangers in a layered subsurface
T
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Wenxin Lia,b,c, Xiangdong Lic, Ruiqing Dua,b, Yong Wanga,b, , Jiyuan Tuc a
National Centre for International Research of Low-Carbon and Green Buildings, Ministry of Science & Technology, Chongqing University, Chongqing 400045, China Joint International Research Laboratory of Green Buildings and Built Environments, Ministry of Education, Chongqing University, Chongqing 400045, China c School of Engineering, RMIT University, Bundoora, VIC 3083, Australia b
A R T I C LE I N FO
A B S T R A C T
Keywords: Ground source heat pump system Ground heat exchanger Laboratory investigation Ground stratification Heat load
To experimentally investigate the effect of heat loads on the thermal performance of vertical ground heat exchangers (GHEs) in a layered subsurface, a series of experiments were conducted using a testing box filled with sand and clay. Temperature distributions during the operation and recovery periods were different in the layered subsurface, where materials with high thermal diffusivities (e.g. sand) excel in both heat transfer and recovery. With more heat transferred from tubes, the sand and clay located close to the tubes showed drastic temperature variations along the length of tubes, especially around the interface between layers. The thermal interference could enhance the layered thermal distribution in the stratified underground, especially in materials with low thermal diffusivities. Moreover, if the applied power increased by four times, the proportion of the temperature difference between sand and clay to the sand temperature increased from 12.9% to 32.7%, which indicated a more severe thermal stratification. Therefore, it is recommended to consider the effect of ground stratification for multi-GHEs with considerable thermal injection and severe thermal interference, especially in materials with low thermal diffusivities.
1. Introduction Since the buildings consume approximately 40% of the total world energy annually, the application of renewable energy in buildings is highly recommended due to its energy efficiency and environmental friendliness (Omer, 2008a). Geothermal energy is one of the leading sustainable energies utilised by over 80 countries worldwide, while more than half (55.2% in the year 2014) of its direct application is for the ground source heat pump (GSHP) systems (Lund and Boyd, 2016). As one of the most energy-efficient approaches used in buildings (Omer, 2008b), GSHP systems remove the waste heat away from the buildings to the ground through the ground heat exchangers (GHEs). The GHE system plays an important role in achieving an efficient performance of GSHP system, and its efficiency can be greatly influenced by the operational and geological factors (Han and Yu, 2016). The thermal performance of GHE system is largely affected by the heat injection or extraction of the ground, which were determined by the heating and cooling demands, system operating modes and borehole layouts (Qian and Wang, 2014). For a cooling-dominated building, the accumulative ground injection brought by the thermal imbalance of building demands could increase the fluid temperature, and further
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deteriorate the system cooling efficiency and shorten the system lifespan (Li et al., 2018a). Since the ground temperature drift depends primarily on the annual heat imbalance between heating and cooling loads, it is efficient to limit the thermal drift effect by rebalancing the heat loads rather than installing more boreholes (Capozza et al., 2015). Moreover, the discontinuous operation mode can alleviate the system thermal performance deterioration effectively (Cui et al., 2008). The increase of the recovery time can decrease temperatures and thermal radius, and increase the heat transfer rate of GHEs (Cao et al., 2015), which becomes more significant in material with low soil thermal conductivity (Baek et al., 2017). Besides the load demands and patterns, the thermal interaction among boreholes also showed non-negligible impacts on the ground temperature variation, especially for long-term operations (Bernier et al., 2008). Yuan et al. (2016) observed that the heat transfer performance of each GHE in a bore-field remain almost the same, however, the central boreholes were less effective due to the severe thermal interference influence once the thermal interference emerged. Lazzari et al. (2010) studied the long-term performance of GHE system with different layouts, the simulation results showed that the performance deterioration was nearly negligible for a single GHE while became significant for the infinite square GHE field.
Corresponding author at: School of Urban Construction and Environment Engineering, Chongqing University, Chongqing 400045, China. E-mail address: [email protected] (Y. Wang).
https://doi.org/10.1016/j.geothermics.2018.08.011 Received 21 May 2018; Received in revised form 9 August 2018; Accepted 30 August 2018 0375-6505/ © 2018 Elsevier Ltd. All rights reserved.
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Nomenclature A Cp, f ks kc mf P q q* q*radial q*axial
Qg Rk t ΔT T0 Tg Tin Tout Δxs Δxc θ
Heat transfer area (m2) Specific pressure heat capacity of the fluid (J/kg °C) Thermal conductivity of sand (W/m °C) Thermal conductivity of clay (W/m °C) Mass flow rate of the fluid (kg/s) Electric power (W) Heat transfer rate (W) Heat transfer rate per unit area (W/m2) Radial heat transfer rate per unit area (W/m2) Axial heat transfer rate per unit area (W/m2)
Ground heat injection or extraction (W) Thermal resistance (°C/W) Time (s) Temperature difference (°C) Initial ground temperature (°C) Ground temperature (°C) Temperature of water flowing into the tubes (°C) Temperature of water flowing out of the tubes (°C) Distance between two points in sand (m) Distance between two points in clay (m) Temperature increase (°C)
thermal exchange and ground temperature distributions along the depths of tubes. The varied thermal exchange rates along the length of GHEs were also observed in a practical five-layer subsurface (Luo et al., 2014) and even within the individual strata (Olfman et al., 2014). If the homogeneous subsurface assumption was adopted in models with strong heterogeneity, the ground temperatures would be overestimated or underestimated by up to 25% due to the excessive simplification (Abdelaziz et al., 2014; Perego et al., 2016). The inaccuracy brought by the homogeneous model became more pronounced at the soil interface, and it increased with the increasing Fourier number and decreasing
On the other hand, the thermal performance of the GHE system is strongly dependent on the soil type (texture, mineralogical composition) (Leong et al., 1998). Since the typical depth of vertical GHEs ranges widely from 15 to 180 m (ASHRAE, 2011), the ground stratification effect has aroused extensive interests. Lee (2011) conducted numerical simulations with different ground compositions, and the ground layers had negligible effects on the long-term fluid temperature predictions. However, based on a small-scale laboratory apparatus, Li et al. (2018b) found the numerical models with layered and equivalent thermal properties gave similar water temperatures while different
Fig. 1. (a) Schematic diagram and (b) Photos of the experimental rig used in this study. 76
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radius (Zhou et al., 2016). The shortcut of vertical heat flow could redistribute the heat between ground material layers, and further yield significant influence on the long-term predictions of the GHE systems (Olfman et al., 2014). Additionally, the underground thermal energy was found to easily disperse in upper layers, and different outlet tube temperatures were predicted if the sequence of layers inversed (Florides et al., 2013). Moreover, characteristics of the temperature variations in the layered subsurface surrounding GHEs have been investigated theoretically for different distance and time (Abdelaziz et al., 2014), where the ground temperature close to the borehole wall varied more significantly than those far away from the borehole wall during the continuous operation (Hu, 2017). Although the thermal performance of GHEs in the layered subsurface has been investigated numerically and analytically, most studies focused on the simulation models (Abdelaziz et al., 2014; Hu, 2017; Lee, 2011) and effects of the material thermal properties (Florides et al., 2013; Li et al., 2018b; Olfman et al., 2014), few of the existing literature has taken the effect of the heat loads into consideration. Meanwhile, various thermal behaviours of GHEs were found to be affected by the ground thermal properties during both the heat injection (Yang et al., 2013) and the recovery period (Baek et al., 2017; Shang et al., 2011). Since ground injection/extraction and the geological structure are two main impact factors on the thermal performance of the GHE system, the effect of heat loads on the thermal performance of GHEs in layered subsurface need further analysis. Therefore, this study provides an experimental investigation based on a laboratory apparatus from our previous study (Li et al., 2018b). A series of experiments was conducted to study the thermal behaviours of tubes during the operation period and its recovery period, for one or double tubes or with different ground loads. Detailed thermal analyses including the temperatures and heat load distributions were elaborated in the experimental study.
different distances to tubes were selected. Specifically, L1 denotes the one located far away from tubes and between double GHEs at x = 0.5 m, y = 0.75 m, where placed 6 thermocouples named 3# to 8#; L2 denotes one located close to the return tube of the upper GHE (x = 0.4 m, y = 1 m), with 6 points named 9# to 14#. Since the impact of surrounding environment can be reflected by the variations of farfield wall temperatures, two locations denoted as 15# (0.5, 0, 1) and 16# (0, 1, 5.75) were selected. The temperatures were monitored by the data logger system with a time interval of 15 min. All the thermocouples were fixed with accurate positioning of ± 1 mm. The accuracy of the T-type thermocouple is 1 °C, and its maximum absolute error is ± 0.23 °C after calibration. The accuracy of the data logger is ± 0.5 °C. The accuracy grade of the flow meter is 1%, and the relative uncertainty of the measured flow rate was 8.7%. Accuracy grade of the electric heater is 1%, and its relative uncertainty was 8.9% in the experiments. The accuracy of the measurements in all experiments was acceptable with a less than 10% maximum relative uncertainties. To diminish the effect of initial conditions, a long enough recovery period follows every heat injection experiment. Good reproducibility and reliability of the laboratory box were validated in our previous study (Li et al., 2018b), where a ± 2% relative deviation was achieved in the fluid temperatures from three repetitive experiments. 2.2. Heat transfer analysis The temperature distributions along the length of tubes were illustrated by six representative points where thermocouples placed: S1 to S3 (in sand) and C4 to C6 (in clay), and two typical temperature distributions (denoted as Ta and Tb) along the length of tubes were showed in Fig. 2. To quantify the variations of heat conduction rates along the depth direction, the heat transfer rates per unit area (q*) of the representative points were calculated and analysed. Each point was affected by the heat transfers from tubes in the radial direction (q*radial), and along the tubes in the axial direction (q*axial). With the same heat transfer area (A) assumed, q* can be calculated based on the Fourier’s law:
2. Methods 2.1. The experimental rig The experimental apparatus from our previous study (Li et al., 2018b) was used in this study. As shown in Fig. 1, the system consists of two U-tubes installed in a box filled with sand and clay, a water tank with electric heater, the auxiliary equipment including pipes, pumps and flow rate adjust valve, and measurement devices including flow meter, thermocouples and data logger system. Constant heat from the electric heater was used to warm the water in the tank, and then the heated water flowed through two GHEs and released heat to the surrounding ground before returning to the tank. The experimental box was enveloped with 240 mm-thick brick walls and a 30 mm-thick thermal insulation mortar added to the interior, and the water pipes outside the box were also well insulated to reduce the ambient temperature influence (Fig. 1b). The 6.25 m × 1.5 m × 1 m testing box was designed based on the similarity theory of heat transfer (Yang and Tao, 2006). Besides the geometrical similarity, Reynolds number (Re) for water in tubes from the model testing box and the corresponding prototype GHE system should be the same, therefore a same Nusselt number for cases with the same Prandtl number and fluid conditions. The testing box was installed laterally with two copper U-tubes, which were installed in parallel with a 90° cross-section rotation. Since the laboratory device was built in Chongqing, China, sand and clay, two typical soil materials in Chongqing, were selected and filled uniformly in the box to investigate the ground stratification effect. Their thermal properties were shown in Table 1. Ground temperature distributions were provided by 16 out of 76 copper-constantan thermocouples installed within the experimental box. The overall heat load variation could be reflected by the temperatures of water flowing into or out of the tubes monitored by 1# and 2# thermocouples. To investigate the temperature difference between materials, thermocouples located along the length of tubes and at
q* =
q ΔT =− A Rk
(1)
where q is the heat transfer rate, ΔT is the temperature difference between the monitored points, Rk is the thermal resistance of the heat transfer material. Δx
s ⎧ ks , in sand ⎪ Δx R k = k c , in clay ⎨ c ⎪ Δxs + Δx c , at the interface of sand and clay kc ⎩ ks
(2)
where Δxs and Δxc are the distance between two points in sand and clay, respectively; ks and kc are the thermal conductivities of sand and clay, respectively. Since this study focused on the heat transfer along the length of tubes, q*axial is calculated and compared. A positive value of q*axial indicates the heat flux is transferred along the length of the tubes (from left to right), while a negative value means a reversed heat transfer direction. It should be noticed that, if homogeneous material assumed, ΔT * q axial = − Δx ·ks is proportional to the vertical temperature variation s
Table 1 Thermal properties of materials used in the experiments.
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Materials
Thermal conductivity W/m °C
Specific heat capacity J/kg °C
Density kg/m3
Thermal diffusivity m2/s
Sand Clay
1.5 0.862
1798 1439
1285 1430
6.49 × 10−7 4.19 × 10−7
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3.1. Thermal behaviours during operation and recovery periods (Test 1) Thermal performance of tubes in a layered subsurface during the operation and recovery periods were investigated by adopting the data from Test 1. Both the water temperatures and ground heat injection increased during the operation period. Since the water temperatures were monitored by thermocouples (1# and 2#) installed in the sand, the heat accumulated surrounding the tubes were removed quickly to the far-field sand. Therefore, the water temperature decreased drastically in the first two-hour during the recovery period, and the ground heat injection dropped to 80 W remaining in the fluid (Fig. 3). Although constant heat load input was provided by the electric heater, part of the inputted heat was firstly used to warm the existing water in the water tank at the early stage of the heat injection period. Thus, the practical ground heat injection was less than the inputted electrical power, and it became steady after the first ten hours. Fig. 4 illustrates the ground temperature distributions of L1 (x = 0.5 m, y = 0.75 m) and L2 (x = 0.4 m, y = 1 m) during operation and recovery periods. Due to a higher thermal diffusivity, the sand achieved a higher temperature rising speed than the clay. Along the length of L1 (from left to right), a sharp temperature decrease appeared at the interface of two materials (from 5# to 6#) because of the thermal property difference. The slope of the temperature decline at the interface varied with the ground heat injection, in which the decline was only 0.16 °C at t = 12 h, while the maximum temperature drop (0.44 °C) occurred at t = 36 h (Fig. 4a). The higher thermal diffusivity of sand also yielded a more drastic temperature decline in the homogeneous sand (from 3# to 5#) than clay (from 6# to 8#). It should be noticed that at t = 48 h, the temperature rise rate of sand decreased while the clay one kept constant, therefore the increasing clay temperature led to a slight temperature decline (from 5# to 6#) at the interface between layers. The reducing temperature rise of sand may attribute to the heat accumulation and the relative higher temperature of surrounding sand. However, once the system shut down, the ground temperatures of L1 decreased greatly during the following 24 h recovery period (Fig. 4b). Due to a higher thermal conductivity, the sand recovers faster and eventually varied 2.22 °C (point 3#) at t = 72 h, while the clay one such as point 8# recovered around 0.81 °C. Then the lower sand temperature led to a slight temperature increase from sand to clay at the interface. Similar temperature drops achieved at each point due to the similar heat release rates during the recovery period. Temperatures of the sand and clay at L2 showed similar increase rates, which reduced with time during the 48 h operation period (Fig. 4c). Located closer to the tubes, with more q*radial transferred from the tubes, the temperatures of L2 were higher and varied more drastically than L1. Significantly affected by the heat released from the tubes, more drastic temperature variations even could be found in the homogeneous sand and clay. The increasing clay temperature generated a higher temperature of upper clay (12#), which transferred heat to the adjacent bottom sand (11#) with a relatively lower temperature, therefore a temperature rise occurred at the interface. The temperature distributions of the surrounding material could also affect that of the fluid in turn. When the high-temperature fluid transferred from sand to clay around the interface, the heat transfer efficiency in sand could be higher than that in the clay, and the ground stratification could narrow
Fig. 2. Typical temperature distributions along the length of tubes in a layered subsurface.
gradient, which is the slope of the temperature variation profile (Fig. 2). For a typical temperature variation of Ta, where the temperature of sand is much higher than that of the clay due to more q*radial received by the upper sand. Since homogenous material was filled, linear temperature variations along the axial direction were captured by these representative points, and a sharp temperature decline appears at the interface between different layers. However, the temperature of clay would increase with more transferred and accumulated heat as shown in Tb, once the clay (C4) close to the interface has a higher temperature than the adjacent sand (S3), a temperature increase would be found at the interface and the heat transferred from clay to sand, which could also affect the temperatures of surrounding sand and clay. 2.3. Evaluation parameters During the heat injection period, the heat load releasing from the fluid determines the surrounding ground temperature distributions and affects the fluid temperature in return. To reflect the total heat exchange within the box, a global parameter, the ground heat injection (Qg), is used to calculate the heat absorbed by the ground. Qg can be calculated by the temperatures of fluid flowing into (Tin) or out (Tout) of the tubes:
Qg = CP, f ·mf ·(Tin−Tout )
(3)
where Cp, f and mf are the specific pressure heat capacity and mass flow rate of the fluid, respectively. Since it is impossible to have a uniform initial temperature distribution throughout the large testing box, a local parameter, the temperature increase (θ), is used in the specific thermocouple locations. During the heat injection, a positive θ can be obtained by the testing and the corresponding initial ground temperatures (Yang et al., 2016):
θ = Tg (t )−T0
(4)
where Tg(t) and T0 are the ground temperature at time t and at time t = 0, respectively. 3. Results and discussions
Table 2 Experimental information.
Based on the previous laboratory apparatus, a series of experiments were conducted to investigate the operation and recovery thermal behaviours (Test 1), the effects of multi-tube interference (Test 1 and 2) and different ground heat injections (Test 1, 3, 4) on the thermal performance of tubes in the stratified subsurface. Water temperature, ground temperatures and heat load distributions along the length of tubes were investigated. Detailed information of these tests was shown in Table 2. 78
Tests
Electrical power
Single/ double tubes
Operation time
Recovery Time
Flow rate
Initial ground temperature
1 2 3 4
300 W 150 W 600 W 150 W
Double Single Double Double
48 h 20 min 48 h 48 h 48 h
24 h / / /
0.64 m/s 0.64 m/s 0.74 m/s 0.64 m/s
13.85 °C 12.23 °C 10.17 °C 17.17 °C
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Fig. 5. Variations of q*axial along L1 (x = 0.5 m, y = 0.75 m) and L2 (x = 0.4 m, y = 1 m) at the operation (t = 36 h) and recovery (t = 72 h) time.
Fig. 3. Variations of water temperatures and ground heat injection during the operation and recovery periods.
were compared in Fig. 5. Compared to the slight variations in the homogeneous materials, significant variations occurred around the interface with vertical short-cut between different layers at t = 36 h. The q*axial transferred at the interface accounted for 52.8% of the total q*axial along the length of tubes. Located closer to tubes, more radial heat transfer from tubes drove more vertical heat transferred along the length of L2, especially at the interface. Opposite to the temperature variation at the interface of L1, that of L2 showed a negative q*axial indicating the heat was transferred from clay to sand due to a higher clay temperature. Once the system shut down (t = 72 h), both L1 and L2 shared similar heat transfer rates along the tubes, and the q*axial transferred at the interface accounted for 42.6% and 49.6% of the total q*axial for L1 and L2, respectively. Since the sand recovered faster and achieved a lower temperature, the heat transfer from clay to sand resulted in a negative q*axial at the interface. It can be concluded that the
their discrepancy. Once the system shut down and no additional heat was inputted through the tubes, the accumulated heat surrounding the tubes (L2) was removed to the far-field sand (L1) immediately. With a much higher temperature, L2 showed a better temperature recovery and the temperature at L2 (Fig. 4d) dropped more significantly than that at L1 (Fig. 4b) in the first few hours. As more heat was removed from the center to the far-field ground, L2 later achieved similar temperatures as L1 (e.g. t = 60 h, 66 h and 72 h). It seems that the radial heat transfer from the tubes could affect the vertical heat transfer along the length of tubes, thus, the significant effect of ground stratification on the temperature distributions could be found in materials located close to the tubes, which was largely affected by the radial heat transfer. Variations of heat transfer rates per unit area (q*axial) along L1 and L2 at representative operating (t = 36 h) and recovery (t = 72 h) time
Fig. 4. Temperature distribution variations of L1 (x = 0.5 m, y = 0.75 m) and L2 (x = 0.4 m, y = 1 m) during operation and recovery periods. 79
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constant temperatures kept in the side-wall points (15# and 16#) in the experiment with P = 300 W, drastic temperature increases could be found in the experiment with 600 W electrical power (Fig. 10). More heat input accelerated the heat transferred from the fluid to the surrounding materials, and it reached the far-field wall around 24 h. Due to a higher thermal diffusivity, the temperature of the side-wall sand increased faster and reached a higher value than the one in clay. Since the side-wall was well-insulated, the transferred heat was accumulated within the box and warmed the materials and fluid in turn, and the heat transfer efficiency decreased especially at the end of the experiment. For a 48 h experiment in this testing box with limited size, the electric power of P = 300 W was optimal to give evident temperature variations without the effect of far-field walls. More drastic temperature variations could be found in both homogeneous materials and the interface between them in the experiment with P = 600 W among these experiments (Fig. 11a). Compared to a temperature decline of 0.20 °C monitored at the interface by the experiment with P = 150 W, the P = 300 W experiment provided a value of 0.21 °C, while the experiment with P = 600 W witnessed a more drastic temperature variation of 1.01 °C from the sand to clay. For the experiment with P = 600 W, the relatively high ground temperatures decreased the heat transfer efficiency from fluid to ground in turn. Both temperatures of sand and clay increased faster in the experiment with a higher electrical power (Fig. 11b). The temperature discrepancy between sand (4#) and clay (7#) for experiments with P = 600 W, 300 W and 150 W accounted for 32.7%, 20.2% and 12.9% of the sand temperature at the end of the 48h operation period. The increasing proportion indicated that the effect of ground stratification could be more significant with the increase of the ground heat injections. Fig. 12 compares q*axial along L1 at a typical operational time t = 36 h. More ground heat injection from the tubes generated more q*axial transferred along the length of tubes. Therefore, the thermal short-cut at the interface accounted for 51.1%, 52.8% and 53.4% of the total q*axial transferred along the length for experiments with P = 150 W, 300 W and 600 W, respectively. The large amount of heat transferred at the interface also enhanced the heat transfer in the adjacent sand around the interface.
thermal distribution of q*axial, especially at the interface between different layers, is susceptible to the radial heat transfer from the tubes. 3.2. Effect of multi-tube (Tests 1, 2) To investigate the interference effect of multi-tube, thermal behaviors of the double tubes (Test 1) and the single tube (Test 2) were compared. Electric powers (P) of 150 W and 300 W were used in experiments with single and double tubes to guarantee the similar heat transfer rates per length. Proportional to the electric power of the heater, the ground heat injection became steady around 120 W and 300 W at the late stage for experiments with single and double tubes, respectively (Fig. 6). Fig. 7 compares the variations of temperature and heat flux along the length of the single and double tubes at L1 (x = 0.5 m, y = 0.75 m). Compared to the experiment with double tubes, the ground affected by single tube showed lower temperatures and steadier temperature variations (Fig. 7a). Without the interference from double tubes, slight temperature variations were found along the length, especially in the homogeneous materials. Same temperatures achieved by the upper sand 3# and 4# in the single-tube experiment indicated that the sand at 3# transferred heat efficiently to the surrounding ground without the thermal interference effect. With a small temperature discrepancy of sand and clay, the temperature variation at the interface was small in the single-tube experiment, which was around one-third of that in the double-tube experiment. After the 48 h operation period, the temperatures of sand (4#) and clay (7#) monitored by the one-tube experiment accounted for 53.5% and 44.5% of those from the experiment with double tubes, respectively (Fig. 7b). The larger discrepancy in clay between these two experiments indicated that the interference effect could be more severe in materials with low thermal diffusivities such as clay. Vertical heat flux (q*axial) transferred along L1 from these experiments at the representative time t = 36 h were compared in Fig. 8. The vertical heat transferred through the interface between layers accounted for 52.8% of the total q*axial in the experiment with double tubes, while the proportion of q*axial at the interface for the single-tube experiment was 45.3%, which indicated that the effect of ground stratification could be enlarged by the thermal interference effect.
4. Conclusions
3.3. Effect of ground heat injection (Test 1, 3, 4)
By using a small-scale laboratory device containing double layers and two tubes, the effects of heat load on the heat transfer of GHEs in a layered subsurface were analysed experimentally. A series of experiments were conducted to investigate the effects of the recovery period, multi-tube and different ground heat injections on the thermal
Experimental data from three tests with electrical powers (P) of 600 W, 300 W and 150 W were compared to investigate the effect of different ground heat injections. The more heat input, the higher water temperatures and the ground heat injection (Fig. 9). With a doubled load input, the experiment with P = 300 W showed more drastic water temperature rises when compared to the one with P = 150 W, and they both operated within a reliable and acceptable temperature range (Fig. 9a). However, the experiment with P = 600 W saw the largest temperature rise among these experiments, and the fluid temperatures were heated to over 40 °C, which is unacceptable for the practical situation. Meanwhile, the heat released to the surrounding ground peaked around 417.8 W, 326.4 W and 164.7 W for experiments with P = 600 W, 300 W and 150 W, respectively (Fig. 9b). The increase of electric powers from 300 W to 150 W doubled the corresponding ground heat injections, while the same increase rate of the heat release could not be guaranteed in the experiment with P = 600 W. Since the inputted heat cannot be removed to the surrounding materials efficiently, more heat was accumulated around the tubes, which contributed to a higher temperature of fluid. It seems that the heat transfer ability was limited by the ground, thus, excessive heat input led to a decreasing heat transfer efficiency. Due to the continuous heat input to the high-temperature fluid and the surrounding material, the ground heat injection decreased especially during the last 12 h. Moreover, the far-field walls also had a non-negligible effect on the drastic decrease of the heat transfer efficiency. Unlike the relatively
Fig. 6. Variations of the fluid temperatures and ground heat injections of experiments with single and double tubes. 80
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Fig. 7. Comparisons of ground temperatures variations for experiments with single and double tubes.
Fig. 8. Variations of q*axial along L1 (x = 0.5 m, y = 0.75 m) for experiments with single and double tubes.
Fig. 10. Far-field ground temperature variations in experiments with electrical power (P) of 600 W and 300W.
performance of a stratified subsurface. The conclusions arising from this study are summarized as follows:
at the interface between layers, which showed a more significant influence of the ground stratification. (3) Compared to the experiment with a single tube, more heat transferred at the interface in the double-tube experiment indicated that the effect of temperature stratification could be enlarged by the thermal interference. Since temperatures of sand and clay from the one-tube experiment accounted for 53.5% and 44.5% of those from the experiment with double tubes, the thermal interference effect could be more significant in materials with low thermal diffusivities such as clay. (4) After a 48 h heat injection, the temperature discrepancies between
(1) Since the materials with high thermal diffusivities (e.g. sand) transferred and recovered faster than other materials, the temperature increases or decrease at a significantly different speed in different subsurface materials during the operation and recovery periods. (2) Affected by more heat transferred from tubes, the sand and clay located closer to the tubes had higher temperatures and more drastic temperature variations along the length of tubes, especially
Fig. 9. Variations of (a) water temperatures and (b) ground heat injections for experiments with different electrical powers (P). 81
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Fig. 11. Comparisons of ground temperatures variations from experiments with different electric powers (P). vertical ground heat exchanger with various intermittent ratios. Geothermics 54, 115–121. Capozza, A., Zarrella, A., De Carli, M., 2015. Long-term analysis of two GSHP systems using validated numerical models and proposals to optimize the operating parameters. Energy Build. 93, 50–64. Cui, P., Yang, H., Fang, Z., 2008. Numerical analysis and experimental validation of heat transfer in ground heat exchangers in alternative operation modes. Energy Build. 40 (6), 1060–1066. Florides, G.A., Christodoulides, P., Pouloupatis, P., 2013. Single and double U-tube ground heat exchangers in multiple-layer substrates. Appl. Energy 102, 364–373. Han, C., Yu, X., 2016. Sensitivity analysis of a vertical geothermal heat pump system. Appl. Energy 170, 148–160. Hu, J., 2017. An improved analytical model for vertical borehole ground heat exchanger with multiple-layer substrates and groundwater flow. Appl. Energy 202, 537–549. Lazzari, S., Priarone, A., Zanchini, E., 2010. Long-term performance of BHE (borehole heat exchanger) fields with negligible groundwater movement. Energy 35 (12), 4966–4974. Lee, C.K., 2011. Effects of multiple ground layers on thermal response test analysis and ground-source heat pump simulation. Appl. Energy 88 (12), 4405–4410. Leong, W.H., Tarnawski, V.R., Aittomäki, A., 1998. Effect of soil type and moisture content on ground heat pump performance. Int. J. Refrig. 21 (8), 595–606. Li, W., Li, X., Wang, Y., Tu, J., 2018a. An integrated predictive model of the long-term performance of ground source heat pump (GSHP) systems. Energy Build. 159, 309–318. Li, W., Li, X., Peng, Y., Wang, Y., Tu, J., 2018b. Experimental and numerical investigations on heat transfer in stratified subsurface materials. Appl. Therm. Eng. 135, 228–237. Lund, J.W., Boyd, T.L., 2016. Direct utilization of geothermal energy 2015 worldwide review. Geothermics 60, 66–93. Luo, J., Rohn, J., Bayer, M., Priess, A., Xiang, W., 2014. Analysis on performance of borehole heat exchanger in a layered subsurface. Appl. Energy 123, 55–65. Olfman, M.Z., Woodbury, A.D., Bartley, J., 2014. Effects of depth and material property variations on the ground temperature response to heating by a deep vertical ground heat exchanger in purely conductive media. Geothermics 51, 9–30. Omer, A.M., 2008a. Energy, environment and sustainable development. Renew. Sustain. Energy Rev. 12 (9), 2265–2300. Omer, A.M., 2008b. Ground-source heat pumps systems and applications. Renew. Sustain. Energy Rev. 12 (2), 344–371. Perego, R., Guandalini, R., Fumagalli, L., Aghib, F.S., De Biase, L., Bonomi, T., 2016. Sustainability evaluation of a medium scale GSHP system in a layered alluvial setting using 3D modeling suite. Geothermics 59, 14–26. Qian, H., Wang, Y., 2014. Modeling the interactions between the performance of ground source heat pumps and soil temperature variations. Energy Sustain. Dev. 23, 115–121. Shang, Y., Li, S., Li, H., 2011. Analysis of geo-temperature recovery under intermittent operation of ground-source heat pump. Energy Build. 43 (4), 935–943. Yang, S., Tao, W., 2006. Heat Transfer, 4 ed. Higher Education Press, Beijing. Yang, W., Chen, Y., Shi, M., Spitler, J.D., 2013. Numerical investigation on the underground thermal imbalance of ground-coupled heat pump operated in cooling-dominated district. Appl. Therm. Eng. 58 (1–2), 626–637. Yang, W., Lu, P., Chen, Y., 2016. Laboratory investigations of the thermal performance of an energy pile with spiral coil ground heat exchanger. Energy Build. 128, 491–502. Yuan, Y., Cao, X., Wang, J., Sun, L., 2016. Thermal interaction of multiple ground heat exchangers under different intermittent ratio and separation distance. Appl. Therm. Eng. 108, 277–286. Zhou, G., Zhou, Y., Zhang, D., 2016. Analytical solutions for two pile foundation heat exchanger models in a double-layered ground. Energy 112, 655–668.
Fig. 12. Variations of q*axial along L1 for experiments with different electrical powers (P).
sand and clay accounted for 32.7%, 20.2% and 12.9% of the sand temperatures for experiments with electrical powers of 600 W, 300 W and 150 W, respectively. The effect of ground stratification became more significant with the increase of the ground heat injections. Acknowledgements The financial supports provided by the National Nature Science Foundation of China (Grant Nos. 51576023 and 91643102), the Fundamental Research Funds for the Central Universities (Project ID: 106112016CDJCR211221), the 111 Project (Project ID: B13041) and the China Scholarship Council for the scholarship (CSC Student ID: 201506050034) are gratefully acknowledged. References Abdelaziz, S.L., Ozudogru, T.Y., Olgun, C.G., Martin, J.R., 2014. Multilayer finite line source model for vertical heat exchangers. Geothermics 51, 406–416. ASHRAE, 2011. ASHRAE Handbook – Heating, Ventilating, and Air-conditioning Applications (SI). American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta. Baek, S.H., Yeo, M.S., Kim, K.W., 2017. Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger. Energy Build. 136, 63–72. Bernier, M.A., Chahla, A., Pinel, P., 2008. Long-term ground-temperature changes in geoexchange systems. ASHRAE Trans. 114, 342–350. Cao, X., Yuan, Y., Sun, L., Lei, B., Yu, N., Yang, X., 2015. Restoration performance of
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Geothermics journal homepage: www.elsevier.com/locate/geothermics
Experimental investigations of the heat load effect on heat transfer of ground heat exchangers in a layered subsurface
T
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Wenxin Lia,b,c, Xiangdong Lic, Ruiqing Dua,b, Yong Wanga,b, , Jiyuan Tuc a
National Centre for International Research of Low-Carbon and Green Buildings, Ministry of Science & Technology, Chongqing University, Chongqing 400045, China Joint International Research Laboratory of Green Buildings and Built Environments, Ministry of Education, Chongqing University, Chongqing 400045, China c School of Engineering, RMIT University, Bundoora, VIC 3083, Australia b
A R T I C LE I N FO
A B S T R A C T
Keywords: Ground source heat pump system Ground heat exchanger Laboratory investigation Ground stratification Heat load
To experimentally investigate the effect of heat loads on the thermal performance of vertical ground heat exchangers (GHEs) in a layered subsurface, a series of experiments were conducted using a testing box filled with sand and clay. Temperature distributions during the operation and recovery periods were different in the layered subsurface, where materials with high thermal diffusivities (e.g. sand) excel in both heat transfer and recovery. With more heat transferred from tubes, the sand and clay located close to the tubes showed drastic temperature variations along the length of tubes, especially around the interface between layers. The thermal interference could enhance the layered thermal distribution in the stratified underground, especially in materials with low thermal diffusivities. Moreover, if the applied power increased by four times, the proportion of the temperature difference between sand and clay to the sand temperature increased from 12.9% to 32.7%, which indicated a more severe thermal stratification. Therefore, it is recommended to consider the effect of ground stratification for multi-GHEs with considerable thermal injection and severe thermal interference, especially in materials with low thermal diffusivities.
1. Introduction Since the buildings consume approximately 40% of the total world energy annually, the application of renewable energy in buildings is highly recommended due to its energy efficiency and environmental friendliness (Omer, 2008a). Geothermal energy is one of the leading sustainable energies utilised by over 80 countries worldwide, while more than half (55.2% in the year 2014) of its direct application is for the ground source heat pump (GSHP) systems (Lund and Boyd, 2016). As one of the most energy-efficient approaches used in buildings (Omer, 2008b), GSHP systems remove the waste heat away from the buildings to the ground through the ground heat exchangers (GHEs). The GHE system plays an important role in achieving an efficient performance of GSHP system, and its efficiency can be greatly influenced by the operational and geological factors (Han and Yu, 2016). The thermal performance of GHE system is largely affected by the heat injection or extraction of the ground, which were determined by the heating and cooling demands, system operating modes and borehole layouts (Qian and Wang, 2014). For a cooling-dominated building, the accumulative ground injection brought by the thermal imbalance of building demands could increase the fluid temperature, and further
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deteriorate the system cooling efficiency and shorten the system lifespan (Li et al., 2018a). Since the ground temperature drift depends primarily on the annual heat imbalance between heating and cooling loads, it is efficient to limit the thermal drift effect by rebalancing the heat loads rather than installing more boreholes (Capozza et al., 2015). Moreover, the discontinuous operation mode can alleviate the system thermal performance deterioration effectively (Cui et al., 2008). The increase of the recovery time can decrease temperatures and thermal radius, and increase the heat transfer rate of GHEs (Cao et al., 2015), which becomes more significant in material with low soil thermal conductivity (Baek et al., 2017). Besides the load demands and patterns, the thermal interaction among boreholes also showed non-negligible impacts on the ground temperature variation, especially for long-term operations (Bernier et al., 2008). Yuan et al. (2016) observed that the heat transfer performance of each GHE in a bore-field remain almost the same, however, the central boreholes were less effective due to the severe thermal interference influence once the thermal interference emerged. Lazzari et al. (2010) studied the long-term performance of GHE system with different layouts, the simulation results showed that the performance deterioration was nearly negligible for a single GHE while became significant for the infinite square GHE field.
Corresponding author at: School of Urban Construction and Environment Engineering, Chongqing University, Chongqing 400045, China. E-mail address: [email protected] (Y. Wang).
https://doi.org/10.1016/j.geothermics.2018.08.011 Received 21 May 2018; Received in revised form 9 August 2018; Accepted 30 August 2018 0375-6505/ © 2018 Elsevier Ltd. All rights reserved.
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Nomenclature A Cp, f ks kc mf P q q* q*radial q*axial
Qg Rk t ΔT T0 Tg Tin Tout Δxs Δxc θ
Heat transfer area (m2) Specific pressure heat capacity of the fluid (J/kg °C) Thermal conductivity of sand (W/m °C) Thermal conductivity of clay (W/m °C) Mass flow rate of the fluid (kg/s) Electric power (W) Heat transfer rate (W) Heat transfer rate per unit area (W/m2) Radial heat transfer rate per unit area (W/m2) Axial heat transfer rate per unit area (W/m2)
Ground heat injection or extraction (W) Thermal resistance (°C/W) Time (s) Temperature difference (°C) Initial ground temperature (°C) Ground temperature (°C) Temperature of water flowing into the tubes (°C) Temperature of water flowing out of the tubes (°C) Distance between two points in sand (m) Distance between two points in clay (m) Temperature increase (°C)
thermal exchange and ground temperature distributions along the depths of tubes. The varied thermal exchange rates along the length of GHEs were also observed in a practical five-layer subsurface (Luo et al., 2014) and even within the individual strata (Olfman et al., 2014). If the homogeneous subsurface assumption was adopted in models with strong heterogeneity, the ground temperatures would be overestimated or underestimated by up to 25% due to the excessive simplification (Abdelaziz et al., 2014; Perego et al., 2016). The inaccuracy brought by the homogeneous model became more pronounced at the soil interface, and it increased with the increasing Fourier number and decreasing
On the other hand, the thermal performance of the GHE system is strongly dependent on the soil type (texture, mineralogical composition) (Leong et al., 1998). Since the typical depth of vertical GHEs ranges widely from 15 to 180 m (ASHRAE, 2011), the ground stratification effect has aroused extensive interests. Lee (2011) conducted numerical simulations with different ground compositions, and the ground layers had negligible effects on the long-term fluid temperature predictions. However, based on a small-scale laboratory apparatus, Li et al. (2018b) found the numerical models with layered and equivalent thermal properties gave similar water temperatures while different
Fig. 1. (a) Schematic diagram and (b) Photos of the experimental rig used in this study. 76
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radius (Zhou et al., 2016). The shortcut of vertical heat flow could redistribute the heat between ground material layers, and further yield significant influence on the long-term predictions of the GHE systems (Olfman et al., 2014). Additionally, the underground thermal energy was found to easily disperse in upper layers, and different outlet tube temperatures were predicted if the sequence of layers inversed (Florides et al., 2013). Moreover, characteristics of the temperature variations in the layered subsurface surrounding GHEs have been investigated theoretically for different distance and time (Abdelaziz et al., 2014), where the ground temperature close to the borehole wall varied more significantly than those far away from the borehole wall during the continuous operation (Hu, 2017). Although the thermal performance of GHEs in the layered subsurface has been investigated numerically and analytically, most studies focused on the simulation models (Abdelaziz et al., 2014; Hu, 2017; Lee, 2011) and effects of the material thermal properties (Florides et al., 2013; Li et al., 2018b; Olfman et al., 2014), few of the existing literature has taken the effect of the heat loads into consideration. Meanwhile, various thermal behaviours of GHEs were found to be affected by the ground thermal properties during both the heat injection (Yang et al., 2013) and the recovery period (Baek et al., 2017; Shang et al., 2011). Since ground injection/extraction and the geological structure are two main impact factors on the thermal performance of the GHE system, the effect of heat loads on the thermal performance of GHEs in layered subsurface need further analysis. Therefore, this study provides an experimental investigation based on a laboratory apparatus from our previous study (Li et al., 2018b). A series of experiments was conducted to study the thermal behaviours of tubes during the operation period and its recovery period, for one or double tubes or with different ground loads. Detailed thermal analyses including the temperatures and heat load distributions were elaborated in the experimental study.
different distances to tubes were selected. Specifically, L1 denotes the one located far away from tubes and between double GHEs at x = 0.5 m, y = 0.75 m, where placed 6 thermocouples named 3# to 8#; L2 denotes one located close to the return tube of the upper GHE (x = 0.4 m, y = 1 m), with 6 points named 9# to 14#. Since the impact of surrounding environment can be reflected by the variations of farfield wall temperatures, two locations denoted as 15# (0.5, 0, 1) and 16# (0, 1, 5.75) were selected. The temperatures were monitored by the data logger system with a time interval of 15 min. All the thermocouples were fixed with accurate positioning of ± 1 mm. The accuracy of the T-type thermocouple is 1 °C, and its maximum absolute error is ± 0.23 °C after calibration. The accuracy of the data logger is ± 0.5 °C. The accuracy grade of the flow meter is 1%, and the relative uncertainty of the measured flow rate was 8.7%. Accuracy grade of the electric heater is 1%, and its relative uncertainty was 8.9% in the experiments. The accuracy of the measurements in all experiments was acceptable with a less than 10% maximum relative uncertainties. To diminish the effect of initial conditions, a long enough recovery period follows every heat injection experiment. Good reproducibility and reliability of the laboratory box were validated in our previous study (Li et al., 2018b), where a ± 2% relative deviation was achieved in the fluid temperatures from three repetitive experiments. 2.2. Heat transfer analysis The temperature distributions along the length of tubes were illustrated by six representative points where thermocouples placed: S1 to S3 (in sand) and C4 to C6 (in clay), and two typical temperature distributions (denoted as Ta and Tb) along the length of tubes were showed in Fig. 2. To quantify the variations of heat conduction rates along the depth direction, the heat transfer rates per unit area (q*) of the representative points were calculated and analysed. Each point was affected by the heat transfers from tubes in the radial direction (q*radial), and along the tubes in the axial direction (q*axial). With the same heat transfer area (A) assumed, q* can be calculated based on the Fourier’s law:
2. Methods 2.1. The experimental rig The experimental apparatus from our previous study (Li et al., 2018b) was used in this study. As shown in Fig. 1, the system consists of two U-tubes installed in a box filled with sand and clay, a water tank with electric heater, the auxiliary equipment including pipes, pumps and flow rate adjust valve, and measurement devices including flow meter, thermocouples and data logger system. Constant heat from the electric heater was used to warm the water in the tank, and then the heated water flowed through two GHEs and released heat to the surrounding ground before returning to the tank. The experimental box was enveloped with 240 mm-thick brick walls and a 30 mm-thick thermal insulation mortar added to the interior, and the water pipes outside the box were also well insulated to reduce the ambient temperature influence (Fig. 1b). The 6.25 m × 1.5 m × 1 m testing box was designed based on the similarity theory of heat transfer (Yang and Tao, 2006). Besides the geometrical similarity, Reynolds number (Re) for water in tubes from the model testing box and the corresponding prototype GHE system should be the same, therefore a same Nusselt number for cases with the same Prandtl number and fluid conditions. The testing box was installed laterally with two copper U-tubes, which were installed in parallel with a 90° cross-section rotation. Since the laboratory device was built in Chongqing, China, sand and clay, two typical soil materials in Chongqing, were selected and filled uniformly in the box to investigate the ground stratification effect. Their thermal properties were shown in Table 1. Ground temperature distributions were provided by 16 out of 76 copper-constantan thermocouples installed within the experimental box. The overall heat load variation could be reflected by the temperatures of water flowing into or out of the tubes monitored by 1# and 2# thermocouples. To investigate the temperature difference between materials, thermocouples located along the length of tubes and at
q* =
q ΔT =− A Rk
(1)
where q is the heat transfer rate, ΔT is the temperature difference between the monitored points, Rk is the thermal resistance of the heat transfer material. Δx
s ⎧ ks , in sand ⎪ Δx R k = k c , in clay ⎨ c ⎪ Δxs + Δx c , at the interface of sand and clay kc ⎩ ks
(2)
where Δxs and Δxc are the distance between two points in sand and clay, respectively; ks and kc are the thermal conductivities of sand and clay, respectively. Since this study focused on the heat transfer along the length of tubes, q*axial is calculated and compared. A positive value of q*axial indicates the heat flux is transferred along the length of the tubes (from left to right), while a negative value means a reversed heat transfer direction. It should be noticed that, if homogeneous material assumed, ΔT * q axial = − Δx ·ks is proportional to the vertical temperature variation s
Table 1 Thermal properties of materials used in the experiments.
77
Materials
Thermal conductivity W/m °C
Specific heat capacity J/kg °C
Density kg/m3
Thermal diffusivity m2/s
Sand Clay
1.5 0.862
1798 1439
1285 1430
6.49 × 10−7 4.19 × 10−7
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3.1. Thermal behaviours during operation and recovery periods (Test 1) Thermal performance of tubes in a layered subsurface during the operation and recovery periods were investigated by adopting the data from Test 1. Both the water temperatures and ground heat injection increased during the operation period. Since the water temperatures were monitored by thermocouples (1# and 2#) installed in the sand, the heat accumulated surrounding the tubes were removed quickly to the far-field sand. Therefore, the water temperature decreased drastically in the first two-hour during the recovery period, and the ground heat injection dropped to 80 W remaining in the fluid (Fig. 3). Although constant heat load input was provided by the electric heater, part of the inputted heat was firstly used to warm the existing water in the water tank at the early stage of the heat injection period. Thus, the practical ground heat injection was less than the inputted electrical power, and it became steady after the first ten hours. Fig. 4 illustrates the ground temperature distributions of L1 (x = 0.5 m, y = 0.75 m) and L2 (x = 0.4 m, y = 1 m) during operation and recovery periods. Due to a higher thermal diffusivity, the sand achieved a higher temperature rising speed than the clay. Along the length of L1 (from left to right), a sharp temperature decrease appeared at the interface of two materials (from 5# to 6#) because of the thermal property difference. The slope of the temperature decline at the interface varied with the ground heat injection, in which the decline was only 0.16 °C at t = 12 h, while the maximum temperature drop (0.44 °C) occurred at t = 36 h (Fig. 4a). The higher thermal diffusivity of sand also yielded a more drastic temperature decline in the homogeneous sand (from 3# to 5#) than clay (from 6# to 8#). It should be noticed that at t = 48 h, the temperature rise rate of sand decreased while the clay one kept constant, therefore the increasing clay temperature led to a slight temperature decline (from 5# to 6#) at the interface between layers. The reducing temperature rise of sand may attribute to the heat accumulation and the relative higher temperature of surrounding sand. However, once the system shut down, the ground temperatures of L1 decreased greatly during the following 24 h recovery period (Fig. 4b). Due to a higher thermal conductivity, the sand recovers faster and eventually varied 2.22 °C (point 3#) at t = 72 h, while the clay one such as point 8# recovered around 0.81 °C. Then the lower sand temperature led to a slight temperature increase from sand to clay at the interface. Similar temperature drops achieved at each point due to the similar heat release rates during the recovery period. Temperatures of the sand and clay at L2 showed similar increase rates, which reduced with time during the 48 h operation period (Fig. 4c). Located closer to the tubes, with more q*radial transferred from the tubes, the temperatures of L2 were higher and varied more drastically than L1. Significantly affected by the heat released from the tubes, more drastic temperature variations even could be found in the homogeneous sand and clay. The increasing clay temperature generated a higher temperature of upper clay (12#), which transferred heat to the adjacent bottom sand (11#) with a relatively lower temperature, therefore a temperature rise occurred at the interface. The temperature distributions of the surrounding material could also affect that of the fluid in turn. When the high-temperature fluid transferred from sand to clay around the interface, the heat transfer efficiency in sand could be higher than that in the clay, and the ground stratification could narrow
Fig. 2. Typical temperature distributions along the length of tubes in a layered subsurface.
gradient, which is the slope of the temperature variation profile (Fig. 2). For a typical temperature variation of Ta, where the temperature of sand is much higher than that of the clay due to more q*radial received by the upper sand. Since homogenous material was filled, linear temperature variations along the axial direction were captured by these representative points, and a sharp temperature decline appears at the interface between different layers. However, the temperature of clay would increase with more transferred and accumulated heat as shown in Tb, once the clay (C4) close to the interface has a higher temperature than the adjacent sand (S3), a temperature increase would be found at the interface and the heat transferred from clay to sand, which could also affect the temperatures of surrounding sand and clay. 2.3. Evaluation parameters During the heat injection period, the heat load releasing from the fluid determines the surrounding ground temperature distributions and affects the fluid temperature in return. To reflect the total heat exchange within the box, a global parameter, the ground heat injection (Qg), is used to calculate the heat absorbed by the ground. Qg can be calculated by the temperatures of fluid flowing into (Tin) or out (Tout) of the tubes:
Qg = CP, f ·mf ·(Tin−Tout )
(3)
where Cp, f and mf are the specific pressure heat capacity and mass flow rate of the fluid, respectively. Since it is impossible to have a uniform initial temperature distribution throughout the large testing box, a local parameter, the temperature increase (θ), is used in the specific thermocouple locations. During the heat injection, a positive θ can be obtained by the testing and the corresponding initial ground temperatures (Yang et al., 2016):
θ = Tg (t )−T0
(4)
where Tg(t) and T0 are the ground temperature at time t and at time t = 0, respectively. 3. Results and discussions
Table 2 Experimental information.
Based on the previous laboratory apparatus, a series of experiments were conducted to investigate the operation and recovery thermal behaviours (Test 1), the effects of multi-tube interference (Test 1 and 2) and different ground heat injections (Test 1, 3, 4) on the thermal performance of tubes in the stratified subsurface. Water temperature, ground temperatures and heat load distributions along the length of tubes were investigated. Detailed information of these tests was shown in Table 2. 78
Tests
Electrical power
Single/ double tubes
Operation time
Recovery Time
Flow rate
Initial ground temperature
1 2 3 4
300 W 150 W 600 W 150 W
Double Single Double Double
48 h 20 min 48 h 48 h 48 h
24 h / / /
0.64 m/s 0.64 m/s 0.74 m/s 0.64 m/s
13.85 °C 12.23 °C 10.17 °C 17.17 °C
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Fig. 5. Variations of q*axial along L1 (x = 0.5 m, y = 0.75 m) and L2 (x = 0.4 m, y = 1 m) at the operation (t = 36 h) and recovery (t = 72 h) time.
Fig. 3. Variations of water temperatures and ground heat injection during the operation and recovery periods.
were compared in Fig. 5. Compared to the slight variations in the homogeneous materials, significant variations occurred around the interface with vertical short-cut between different layers at t = 36 h. The q*axial transferred at the interface accounted for 52.8% of the total q*axial along the length of tubes. Located closer to tubes, more radial heat transfer from tubes drove more vertical heat transferred along the length of L2, especially at the interface. Opposite to the temperature variation at the interface of L1, that of L2 showed a negative q*axial indicating the heat was transferred from clay to sand due to a higher clay temperature. Once the system shut down (t = 72 h), both L1 and L2 shared similar heat transfer rates along the tubes, and the q*axial transferred at the interface accounted for 42.6% and 49.6% of the total q*axial for L1 and L2, respectively. Since the sand recovered faster and achieved a lower temperature, the heat transfer from clay to sand resulted in a negative q*axial at the interface. It can be concluded that the
their discrepancy. Once the system shut down and no additional heat was inputted through the tubes, the accumulated heat surrounding the tubes (L2) was removed to the far-field sand (L1) immediately. With a much higher temperature, L2 showed a better temperature recovery and the temperature at L2 (Fig. 4d) dropped more significantly than that at L1 (Fig. 4b) in the first few hours. As more heat was removed from the center to the far-field ground, L2 later achieved similar temperatures as L1 (e.g. t = 60 h, 66 h and 72 h). It seems that the radial heat transfer from the tubes could affect the vertical heat transfer along the length of tubes, thus, the significant effect of ground stratification on the temperature distributions could be found in materials located close to the tubes, which was largely affected by the radial heat transfer. Variations of heat transfer rates per unit area (q*axial) along L1 and L2 at representative operating (t = 36 h) and recovery (t = 72 h) time
Fig. 4. Temperature distribution variations of L1 (x = 0.5 m, y = 0.75 m) and L2 (x = 0.4 m, y = 1 m) during operation and recovery periods. 79
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constant temperatures kept in the side-wall points (15# and 16#) in the experiment with P = 300 W, drastic temperature increases could be found in the experiment with 600 W electrical power (Fig. 10). More heat input accelerated the heat transferred from the fluid to the surrounding materials, and it reached the far-field wall around 24 h. Due to a higher thermal diffusivity, the temperature of the side-wall sand increased faster and reached a higher value than the one in clay. Since the side-wall was well-insulated, the transferred heat was accumulated within the box and warmed the materials and fluid in turn, and the heat transfer efficiency decreased especially at the end of the experiment. For a 48 h experiment in this testing box with limited size, the electric power of P = 300 W was optimal to give evident temperature variations without the effect of far-field walls. More drastic temperature variations could be found in both homogeneous materials and the interface between them in the experiment with P = 600 W among these experiments (Fig. 11a). Compared to a temperature decline of 0.20 °C monitored at the interface by the experiment with P = 150 W, the P = 300 W experiment provided a value of 0.21 °C, while the experiment with P = 600 W witnessed a more drastic temperature variation of 1.01 °C from the sand to clay. For the experiment with P = 600 W, the relatively high ground temperatures decreased the heat transfer efficiency from fluid to ground in turn. Both temperatures of sand and clay increased faster in the experiment with a higher electrical power (Fig. 11b). The temperature discrepancy between sand (4#) and clay (7#) for experiments with P = 600 W, 300 W and 150 W accounted for 32.7%, 20.2% and 12.9% of the sand temperature at the end of the 48h operation period. The increasing proportion indicated that the effect of ground stratification could be more significant with the increase of the ground heat injections. Fig. 12 compares q*axial along L1 at a typical operational time t = 36 h. More ground heat injection from the tubes generated more q*axial transferred along the length of tubes. Therefore, the thermal short-cut at the interface accounted for 51.1%, 52.8% and 53.4% of the total q*axial transferred along the length for experiments with P = 150 W, 300 W and 600 W, respectively. The large amount of heat transferred at the interface also enhanced the heat transfer in the adjacent sand around the interface.
thermal distribution of q*axial, especially at the interface between different layers, is susceptible to the radial heat transfer from the tubes. 3.2. Effect of multi-tube (Tests 1, 2) To investigate the interference effect of multi-tube, thermal behaviors of the double tubes (Test 1) and the single tube (Test 2) were compared. Electric powers (P) of 150 W and 300 W were used in experiments with single and double tubes to guarantee the similar heat transfer rates per length. Proportional to the electric power of the heater, the ground heat injection became steady around 120 W and 300 W at the late stage for experiments with single and double tubes, respectively (Fig. 6). Fig. 7 compares the variations of temperature and heat flux along the length of the single and double tubes at L1 (x = 0.5 m, y = 0.75 m). Compared to the experiment with double tubes, the ground affected by single tube showed lower temperatures and steadier temperature variations (Fig. 7a). Without the interference from double tubes, slight temperature variations were found along the length, especially in the homogeneous materials. Same temperatures achieved by the upper sand 3# and 4# in the single-tube experiment indicated that the sand at 3# transferred heat efficiently to the surrounding ground without the thermal interference effect. With a small temperature discrepancy of sand and clay, the temperature variation at the interface was small in the single-tube experiment, which was around one-third of that in the double-tube experiment. After the 48 h operation period, the temperatures of sand (4#) and clay (7#) monitored by the one-tube experiment accounted for 53.5% and 44.5% of those from the experiment with double tubes, respectively (Fig. 7b). The larger discrepancy in clay between these two experiments indicated that the interference effect could be more severe in materials with low thermal diffusivities such as clay. Vertical heat flux (q*axial) transferred along L1 from these experiments at the representative time t = 36 h were compared in Fig. 8. The vertical heat transferred through the interface between layers accounted for 52.8% of the total q*axial in the experiment with double tubes, while the proportion of q*axial at the interface for the single-tube experiment was 45.3%, which indicated that the effect of ground stratification could be enlarged by the thermal interference effect.
4. Conclusions
3.3. Effect of ground heat injection (Test 1, 3, 4)
By using a small-scale laboratory device containing double layers and two tubes, the effects of heat load on the heat transfer of GHEs in a layered subsurface were analysed experimentally. A series of experiments were conducted to investigate the effects of the recovery period, multi-tube and different ground heat injections on the thermal
Experimental data from three tests with electrical powers (P) of 600 W, 300 W and 150 W were compared to investigate the effect of different ground heat injections. The more heat input, the higher water temperatures and the ground heat injection (Fig. 9). With a doubled load input, the experiment with P = 300 W showed more drastic water temperature rises when compared to the one with P = 150 W, and they both operated within a reliable and acceptable temperature range (Fig. 9a). However, the experiment with P = 600 W saw the largest temperature rise among these experiments, and the fluid temperatures were heated to over 40 °C, which is unacceptable for the practical situation. Meanwhile, the heat released to the surrounding ground peaked around 417.8 W, 326.4 W and 164.7 W for experiments with P = 600 W, 300 W and 150 W, respectively (Fig. 9b). The increase of electric powers from 300 W to 150 W doubled the corresponding ground heat injections, while the same increase rate of the heat release could not be guaranteed in the experiment with P = 600 W. Since the inputted heat cannot be removed to the surrounding materials efficiently, more heat was accumulated around the tubes, which contributed to a higher temperature of fluid. It seems that the heat transfer ability was limited by the ground, thus, excessive heat input led to a decreasing heat transfer efficiency. Due to the continuous heat input to the high-temperature fluid and the surrounding material, the ground heat injection decreased especially during the last 12 h. Moreover, the far-field walls also had a non-negligible effect on the drastic decrease of the heat transfer efficiency. Unlike the relatively
Fig. 6. Variations of the fluid temperatures and ground heat injections of experiments with single and double tubes. 80
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Fig. 7. Comparisons of ground temperatures variations for experiments with single and double tubes.
Fig. 8. Variations of q*axial along L1 (x = 0.5 m, y = 0.75 m) for experiments with single and double tubes.
Fig. 10. Far-field ground temperature variations in experiments with electrical power (P) of 600 W and 300W.
performance of a stratified subsurface. The conclusions arising from this study are summarized as follows:
at the interface between layers, which showed a more significant influence of the ground stratification. (3) Compared to the experiment with a single tube, more heat transferred at the interface in the double-tube experiment indicated that the effect of temperature stratification could be enlarged by the thermal interference. Since temperatures of sand and clay from the one-tube experiment accounted for 53.5% and 44.5% of those from the experiment with double tubes, the thermal interference effect could be more significant in materials with low thermal diffusivities such as clay. (4) After a 48 h heat injection, the temperature discrepancies between
(1) Since the materials with high thermal diffusivities (e.g. sand) transferred and recovered faster than other materials, the temperature increases or decrease at a significantly different speed in different subsurface materials during the operation and recovery periods. (2) Affected by more heat transferred from tubes, the sand and clay located closer to the tubes had higher temperatures and more drastic temperature variations along the length of tubes, especially
Fig. 9. Variations of (a) water temperatures and (b) ground heat injections for experiments with different electrical powers (P). 81
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Fig. 12. Variations of q*axial along L1 for experiments with different electrical powers (P).
sand and clay accounted for 32.7%, 20.2% and 12.9% of the sand temperatures for experiments with electrical powers of 600 W, 300 W and 150 W, respectively. The effect of ground stratification became more significant with the increase of the ground heat injections. Acknowledgements The financial supports provided by the National Nature Science Foundation of China (Grant Nos. 51576023 and 91643102), the Fundamental Research Funds for the Central Universities (Project ID: 106112016CDJCR211221), the 111 Project (Project ID: B13041) and the China Scholarship Council for the scholarship (CSC Student ID: 201506050034) are gratefully acknowledged. References Abdelaziz, S.L., Ozudogru, T.Y., Olgun, C.G., Martin, J.R., 2014. Multilayer finite line source model for vertical heat exchangers. Geothermics 51, 406–416. ASHRAE, 2011. ASHRAE Handbook – Heating, Ventilating, and Air-conditioning Applications (SI). American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc., Atlanta. Baek, S.H., Yeo, M.S., Kim, K.W., 2017. Effects of the geothermal load on the ground temperature recovery in a ground heat exchanger. Energy Build. 136, 63–72. Bernier, M.A., Chahla, A., Pinel, P., 2008. Long-term ground-temperature changes in geoexchange systems. ASHRAE Trans. 114, 342–350. Cao, X., Yuan, Y., Sun, L., Lei, B., Yu, N., Yang, X., 2015. Restoration performance of
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