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Experimental and numerical studies on the thermal performance of ground heat exchangers in a layered subsurface with groundwater
Renewable Energy 147 (2020) 620e629
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Experimental and numerical studies on the thermal performance of ground heat exchangers in a layered subsurface with groundwater Wenxin Li a, b, c, Xiangdong Li c, Yuanling Peng a, b, Yong Wang a, b, *, Jiyuan Tu c a
National Centre for International Research of Low-carbon and Green Buildings, Ministry of Science & Technology, Chongqing University, Chongqing, 400045, China b 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
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 May 2019 Received in revised form 17 August 2019 Accepted 3 September 2019 Available online 5 September 2019
Thermal performance of the ground source heat pump (GSHP) system can be significantly affected by the complex geological substructures (such as ground stratification and groundwater advection). This study installed a seepage box inside the two-layered laboratory device to investigate the heat transfer processes of the unsaturated, saturated and infiltrated ground. Various operational and geological conditions were designed to study the temperature distributions at various locations and time experimentally and numerically. The groundwater effect on ground heat exchanger (GHE) thermal performance depends on the thermal properties, flow advection and the relationship between temperatures of the groundwater and ground. If the ground was partially saturated during the heat injection period, the cooling seepage will efficiently remove the heat of GHEs in upper-stream rather than those located in the bottom-stream. Meanwhile, the heat transfer can be enhanced if two legs of the U-tube vertical to the direction of groundwater seepage. The groundwater flow can redistribute the heat within the ground and showed a better recovery performance which advance an even temperature distribution by 3 h. The temperature and carried heat load of the cooler groundwater will increase during the heat injection experiment, and further contributed to various temperature distributions of ground at different locations and time. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Ground heat exchanger Experimental investigation Computational fluid dynamics Ground stratification Groundwater advection
1. Introduction Ground source heat pump (GSHP) systems, which utilize shallow geothermal energy to heat or cool buildings, have been widely applied around the world in recent years due to their high energy-efficiency and environmental friendliness. The heat exchange between buildings and the ground was achieved by the ground heat exchanger (GHE) system. The heat transfer performance of GHEs is strongly affected by the thermo-physical properties of the soil and subsurface [1], which could change with geographic structure [2] and moisture content [3]. Various geological materials showed different temperature distributions, and therefore, different heat transfer efficiencies of GHEs [4,5]. Since the groundwater table depth globally varied from land
* Corresponding author. 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.renene.2019.09.008 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
surface to more than 200 m and highly occurs at the range of 2e30 m [6], it would be common for vertical GHE systems (depths ranging from 15 to 180 m [7]) to be affected by groundwater advection. Many researchers have investigated the effects of groundwater, and due to the water advection, it is proved to have a positive effect on heat transfer enhancement with lower temperature rises and a more steady condition [8]. Luo et al. [9] built a 3D model in a commercial finite elemental software FEFLOW, where the flow in GHE was simplified as 1D discrete element. The simulation results indicate that heat transfer efficiency of GHEs can be increased by 55% within the aquifer. The comprehensive thermal performance could be increased significantly with the increase of the groundwater flow velocity, the decrease of average inlet and outlet water temperatures [10]. Moreover, the increasing water saturation in the adjacent soil can substantially increase the amount of heat recovery [11], and the effects of groundwater flow could be more significant for the long-term performance [12]. With a better heat transfer efficiency on recovery, the groundwater can promote the quick
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Nomenclature Cp G K S T T T0 Tg U
a q
Specific heat capacity at constant pressure (J/kg∙ C) Gravitational acceleration (9.8 m/s2) Intrinsic permeability (m2) Momentum source term (N/m3) Time (s) Temperature ( C) Initial ground temperature ( C) Ground temperature ( C) Velocity (m/s) Permeability (m2) Temperature increase ( C)
thermal rebalancing in the borehole field, even for circumstances where the heat rejection and extraction are unbalance [13]. The heat transfer performance of GHEs largely determined by the thermal and hydraulic properties of the surrounding soil. The ground thermal conductivities are measured to be different in dry and saturated conditions [14], since the thermal conductivity is primarily dependent upon the degree of water saturation and secondary on the flow path [11]. The neglect of variations in moisture content in unsaturated soil would underestimate the heat transfer capacity of the soil, and the ignore of groundwater table fluctuations can result in a 3e4% error in the outlet fluid temperature [15]. During the intermittent period, the performance in unsaturated soil conditions decreased by up to 40% and showed a larger temperature variation compared to that in fully saturated soil conditions [16]. Furthermore, the effects of groundwater could be different in various materials. By simulating with an analytical line source model, Diao et al. [8] conducted that the effects of groundwater flow may usually be neglected except in formations with considerable flow rate such as gravel and coarse sand. For ground with fractures, even at relatively low specific flow rates, the groundwater flow may cause significantly enhanced heat transfer [17]. Based on a finite-element numerical model considering groundwater flow, Chiasson et al. [18] found that the groundwater advection could significantly enhance the heat transfer in geologic materials with high hydraulic conductivity, such as sands, gravels, and rocks exhibiting fractures and solution channels. The effect of thermal dispersion on the temperature plume around GHEs was found to be minor for homogeneous aquifer, and the thermal dispersion can be neglected only for conditions typical for fine sands, clays, and silts with Darcy velocities q < 108 m/s, while showed larger effect for aquifers where medium sands and gravels (q > 108 m/s) dominate [19]. [1]. Although the thermal performance of GHEs with groundwater has been investigated numerically and analytically, most studies assumed the GHEs fully immersed in the groundwater [12,20,21], few has considered both ground stratification and the groundwater advection, which is common in the practical engineering. Many analytical [8,21] and numerical [12,22] models were twodimensional, which cannot take the vertical ground structure into consideration. Furthermore, most studies validated with in-situ experiments which lacked sufficient data of ground temperature distributions, where the ambiguous properties cannot sufficiently support the accuracy of the validations. Therefore, this study introduces a well-controlled laboratory apparatus with sand and clay, where part of them were saturated and considered the groundwater seepage. Properties of the materials were measured and calculated for the further experimental and numerical analysis. Predictions from 3D numerical model were validated against the
l m r r 4
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Thermal conductivity (W/m∙ C) Dynamic viscosity (Pa$s) Density (kg/m3) Cp Specific volumetric heat capacity at constant pressure (J/m3∙ C) Porosity
Subscripts/superscripts Eff Effective F Fluid Mc Clay Ms Sand S Solid
data from a 24 h heat injection experiment, which were further used to investigate the effects of ground stratification and groundwater advection on the thermal performance experimentally and numerically. 2. Methods 2.1. Experiment description Based on the experimental apparatus in our previous studies [4,23], some accessories were added to mimic the groundwater seepage (Fig. 1a). The 6.25 m 1.5 m 1 m laboratory apparatus was installed laterally and filled with sand and clay. Located in the middle of the device is a 2 m-length steel box which consists of a pluviation system to “raining” the groundwater seepage evenly inside the sand and clay. The perforated plate with small holes was installed at the top of the box, and the bottom located the cobblestone layer to contain the sand and clay. The stainless-steel box connected to the high and low cisterns, where the groundwater flows from the high cistern, penetrates through the sand and clay, and later returns to the low cistern. Based on the Darcy's law, the flow rate of the groundwater can be controlled by adjusting the heights of the high and low cisterns. Constant heat inputted by the electric heater was used to heat the water in the tank, and then the heat-carrier water flowed through two GHEs and later returned to the tank. The flow rate of circulating water was controlled by the flow adjust valve and was measured through a turbine flow meter. The accuracy grade of the flow meter was 1%, and the relative uncertainty was calculated to be 8.7%, which was acceptable with a value less than 10%. Detailed T-type thermocouples were installed inside the laboratory device, and two more thermocouples and flow meters were installed to monitor the temperatures and flow rate of the groundwater. The accuracy of T-type thermocouple is 1 C, and the maximum relative error of temperature measurement was 3%. A data logger system was connected to a computer to display and record the temperature data with a time interval of 15 min. Detailed information on the experimental device was listed in Table 1, and also in our previous studies [4,23]. The installed copper-constantan thermocouples were selected to give a detailed distribution in this study. As shown in Fig. 1b, thermocouples were installed at six cross-sections at different depths (z ¼ 1 m, 2.1 m, 2.9 m, 3.1 m, 3.9 m and 5.75 m). Each representative cross-section located 5 points with a spacing of 0.25 m, which denoted as 0e6 from the top (y ¼ 1.5 m) to the bottom (y ¼ 0 m). For example, Z ¼ 2.9 m-3 is the point located at z ¼ 2.9 m, x ¼ 0.5 m and y ¼ 0.75 m. For comparison convenience, L1, L2, L4 and L5 denote the lines compose of all the points ended with 1,
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Table 1 Detailed parameters of the experimental device [4]. Objects
Parameter
Value (m)
Sandbox
Depth Length Width Length Wall thickness Inner diameter Distance between pipe centers
6.25 1.50 1.00 6.25 0.0005 0.005 0.015
U-tube
2, 4 and 5 at every representative cross-section, respectively. These lines located from the top to the bottom within the experimental box.
2.2. Material property measurement To investigate the groundwater effect in this study, heat transfer inside the saturated materials will be compared to the one without groundwater seepage (unsaturated materials), therefore,
Fig. 1. (a) Experimental set-up and (b) Locations of the thermocouples used in this study.
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properties of both saturated and unsaturated materials were provided for further calculation and analysis. Properties of the experimental used materials including density, porosity, water content, particle size distribution, specific heat capacity, thermal conductivity and thermal diffusivity were measured and calculated in detail. Since the air and ground contain moisture, it is impossible and no need to obtain the absolutely dry materials for the experiment. Thus, water contents of the experimental used materials were measured by comparing the weights before and after the drying. For the experiment without groundwater seepage, the water contents of experimental sand and clay were measured to be 10.1% and 28.8%, respectively. The flow of water through soil is controlled by the size and shape of pores, which is in turn controlled by the size and packing of soil particles. Most soils are a mixture of grain sizes, and the grain size distribution is often portrayed as a cumulative-frequency plot of grain diameter (logarithmic scale) versus the weight fraction of grains with smaller diameter. The steeper the slopes of such plots, the more uniform the soil grain-size distribution [24]. The grain size distribution of sand was obtained by sieve analysis, and the grain size distribution (3-cycle semi-log graph paper) of the laboratory used sand is shown in Fig. 2. The range of sand grain diameter was measured to be 0.075e0.25 mm, and it can be considered as very fine sand (USDA, 0.05e0.10 mm) and fine sand (USDA, 0.10e0.25 mm) according to U.S. Department of Agriculture (USDA) classification system [25]. Since the screening test of the clay was affected by its own agglomeration phenomenon, it is hard to decide the size of the clay particle. The porosity (4) of the sand and clay are measured to be 0.46 and 0.50, respectively, which are among the typical value range of 0.26e0.53 for fine sand and 0.34e0.60 for clay [18]. Thermal conductivities of the sand and clay were measured in the laboratory using needle source probe except the unsaturated sand due to the measure interference, and that of the unsaturated sand was estimated based on the thermal conductivities of the dry sand, water content and the relationship between them provided by a reference [26]. The following experiments only consider the groundwater seepage in the sand, and the permeability coefficient of sand was calculated to be 1.46 105 m/s by using data from the seepage test based on Darcy's law, which was considered to be weak permeable. Detailed parameters can be found in Table 2. It should be noticed
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that, when the pores of the ground were filled with water, thermal conductivities and capacities of the materials both increase. Therefore, the addition of water in sand decreases the thermal diffusivity, while it increases the thermal diffusivity in the clay. 2.3. Numerical model Based on the previously introduced laboratory apparatus, a complete 3D CFD model was built to model the heat transfer process for GHEs in a layered subsurface with partial groundwater advection (Fig. 3). The thermal resistance of the tube material was calculated using the so-called thin-wall thermal resistance of FLUENT [27]. The incompressible Navier-Stokes equations together with standard k-ε model [27] were solved for the convective heat transfer of water in the pipes. As the GHEs are partially immersed with the saturated groundwater in a two-layer ground, the computation region of the experimental box can be divided into four regions: sand, sand with groundwater flow, saturated clay and clay. Each material was considered as homogeneous media with certain porosities. For the sand and clay without the groundwater advection, only the conduction is considered, thus the heat transfer through the sand and clay is calculated by
vTk lk ¼ vt rk Cp;k
v2 Tk v2 Tk v2 Tk þ 2 þ 2 vx2 vy vz
! (1)
where lk, rk and Cp,k represents the thermal conductivity, density and specific heat capacity of the sand (k ¼ ms) and the clay (k ¼ mc), respectively. For materials with saturated groundwater, the heat transport was assumed as a porous medium with a constant homogeneous groundwater flow. The heat transfer process consists of conduction by solid matrix and liquid in its pores and convection of the moving groundwater. Porous media are modelled by the addition of a momentum source term to the standard fluid flow equations. If the source terms of convection acceleration and diffusion are ignored, it can be simplified bases on Darcy's law:
m a
Si ¼ ui ði ¼ x; y; zÞ
Fig. 2. (a) Sieve analysis and (b) Grain size distributions of the experimental sand and clay.
(2)
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Table 2 Properties of the materials used in experiments. Properties
Unsaturated sand
Saturated sand
Unsaturated clay
Saturated clay
Groundwater advection (water at 24 C)
Water inside tubes (water at 20 C)
Copper tube
Density (kg/m3) Specific heat capacity J/ (Kg$ C) Thermal conductivity (W/ m$ C) Thermal diffusivity 107 (m2/s) Porosity
1593.39 1348
1814.68 2592
1616.91 2273
1838.35 2479
997.20 4179
998.20 4182
8978 381
1.13
2.03
0.85
2.35
0.61
0.60
387.60
5.27
4.32
2.30
5.16
1.46
1.44
1130
46%
46%
50%
50%
\
\
\
The governing equations of the 3D GHE models were solved using the commercial CFD code ANSYS Fluent-16 (ANSYS, NH, USA). All side walls of the soil domain were considered to be insulated. Boundary conditions of ‘velocity inlet’ and ‘pressure outlet’ were allocated to the inlet and outlet of the tubes, where the varied experimental water inlet temperature was inputted through the FLUENT user defined functions (UDFs) through the Dirichlet boundary condition of the inlet face. All the initial data setup was based on the actual experiments. Prior to performing CFD simulations, grid and time-step independent study was conducted. Mesh refinement was placed in the near wall regions of the HTF tube and the borehole (Fig. 3). Considering the computational efficiency and accuracy, the mesh with elements numbers of 623,610 and timestep of 300 s was used for further simulation in this study.
3. Results
Fig. 3. Mesh and boundary conditions of the numerical model.
where m is the dynamic viscosity, u is the velocity and a is the permeability of the groundwater. The intrinsic permeability K can be calculated by Ref. [28]:
K¼
rg a m
(3)
Both experiments and numerical studies were conducted to investigate the heat transfer performance of GHEs in ground with groundwater advection. Water temperature, vertical and horizontal ground temperature distributions were investigated for thermal performances in different geological and operating conditions experimentally and numerically.
3.1. Experimental study
where 4 is the porosity of the saturated porous medium, the subscripts s and f represent the solid and fluid, respectively. The effective thermal conductivity (leff) is calculated from the volume average of the fluid and solid conductivities [27]:
Before adding the water into the experimental device, an experiment of dry sand and clay was performed to work as a reference test to evaluate the effects brought by the groundwater advection. Compared to the experiment with dry materials, the other one saturated part of the sand and clay, where the groundwater flowed from the top to the bottom in the saturated sand. Both continuous and intermittent experiments were conducted for the saturated and unsaturated conditions. It should be noticed that the temperature of groundwater was lower than that of ground in Test 2 while higher than the ground temperature in Test 4. These relationships between groundwater and ground temperatures both exist in the practical measurements [29]. Details of these experiments can be found in Table 3. To diminish the influence of the non-uniform initial temperature, the temperature increase (q) is defined as the difference between the testing soil temperature and its corresponding initial temperature [4], which is a positive value for the heat release process. It can reflect the soil temperature rise during heat release period and can be calculated as:
leff ¼ ð1 4Þls þ 4lf
q ¼ Tg ðtÞ T0
where r is the density, and g is the gravitational acceleration (9.8 m/ s2). Based on the intrinsic permeability measured by the test, a1 of the seepage was calculated to be 7.25 1011 m2. With isotropic assumption, same values were set for each directions of the drag coefficients. It is assumed that the velocity u of groundwater transfusion is uniform in the whole domain and the solid skeleton and fluid always have the same temperature, the equilibrium thermal model in the saturated material zone can be calculated by:
h i vT ! vT þ 4 rCp f u ð1 4Þ rCp s þ 4 rCp f ¼ leff V2 T vt vxi
(4)
(5)
where ls and lf are the thermal conductivities of the solid and fluid in the saturated material, respectively.
(6)
where Tg(t) and T0 are the soil temperatures at time t and t ¼ 0, respectively.
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Table 3 Experimental information. Test Test Conditions
Heat injection
Operation modes
Operation time
Fluid circulation velocity
Initial ground temperature
Groundwater velocity
Inlet temperature
1 2
Input heat load of 300 W
continuous 24 h
0.64 m/s 0.64 m/s
15.4 C 24.0 C
\ \ 1.29 105 m/ 23.4 C s
3 4
Inlet water temperature of 32 C
intermittent 34 h (4 h on-2 h off-4 h on-24 h off)
0.63 m/s 0.64 m/s
20.4 C 24.2 C
\ \ 1.09 105 m/ 25.1 s
3.1.1. Effect of groundwater advection on thermal performance distribution Fig. 4 compares the temperatures of the total fluid circulated within the two GHEs in these two tests. Test 1 in dry condition shows higher temperatures for both inlet and outlet, while the test with the flowing groundwater can transfer the heat more efficiently and gave lower fluid temperatures. With the addition of groundwater, the fluid temperatures were decrease by 3 C and the temperature difference between inlet and outlet of GHEs was enlarged by 0.74 C. The heat transfer enhancement is the coupling effects of thermal properties, flow advection and the relationship between ground and groundwater temperatures. Even if the saturated sand has a lower thermal diffusivity, the materials showed a significant enhancement on thermal diffusivity due to the saturated clay. Fig. 5 compared the temperature increases of the ground located at L2 and L4 at t ¼ 12 h and t ¼ 24 h. They shared the same distance to tubes while different depths in ground, where L2 (y ¼ 1 m) located higher than L4 (y ¼ 0.5 m). At the upper part of the ground (as shown in Fig. 5a), compared to Test 1 without groundwater, the thermal distribution can be dramatically affected by the groundwater flow. Even if the addition of water decreases the thermal diffusivity of sand from 5.27 107 m2/s to 4.32 107 m2/s, the
Fig. 4. Fluid temperatures of inlet and outlet, and their temperature differences (Dt) in tests with continuous operational modes.
thermal convection brought by the flow significantly decreased the temperatures of the saturated sand with advection (Test 1). The temperature of groundwater was slightly lower than that of the ground, the flowing seepage took heat away and reduced the ground temperature. However, less significant groundwater effect can be found in the bottom ground (L4), and Test 2 witnessed a similar temperature distribution as Test 1. For the sand located at depths between 2 m and 3 m, the groundwater flow brought the heat from the top tube to the bottom one, and the slightly temperature decrease becomes more obvious with the increase of time. A slightly temperature increase can be found in the temperature variations from the sand to clay, which indicated that the sand with groundwater has a higher heat transfer efficiency than the saturated clay. If the clay was saturated with water, its thermal diffusivity would increase drastically from 2.30 107 m2/s to 5.16 107 m2/ s, and the more efficient heat transfer led to a higher temperature for the ground located at 0.25 m to the tube. The thermal enhancement was even apparent for the upper tube, which could be affected by the neighbouring sand with groundwater advection. For the unsaturated test (Test 1), different temperature distributions for L2 and L4 may attribute to the uneven thermal property of the ground. Fig. 6 compares the temperature distributions at x ¼ 0.5 m and different depths. Compared to Test 1, temperatures of the saturated sand with groundwater advection varied in the flow direction (Fig. 6a). Since the groundwater flowed from the top to the bottom, the upper ground (ending with 1) showed a much lower temperature, while the seepage was heated by the tubes and further increased the temperatures of bottom ground (ending with 3 and 5). Such effect was weakened in the ground at z ¼ 2.9 m (Fig. 6b), because it can be affected by the neighbouring clay. Without the advection, the saturated clay saw a similar condition as the unsaturated clay (Fig. 6c). Since the saturated clay has a higher thermal diffusivity, it transferred the heat more efficiently and showed higher temperatures than the unsaturated one. 3.1.2. Effect of groundwater advection on thermal recovery The groundwater advection not only influences the continuous operation of the thermal performance of ground, but also affects its performance during the recovery periods. Therefore, Test 3 and Test 4 were compared. The temperature difference between inlet and outlet fluid in
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Fig. 5. Ground temperature increases at L2 and L4.
Fig. 6. Ground temperature increases at different depths.
these two tubes were similar in Test 3, where Tube 2 was even more efficient (Fig. 7). For Test 4 where the groundwater flowed through Tube 1 first and then Tube 2, the flow of the seepage enhanced the heat transfer of Tube 1 while diminished that of Tube 2. It should be
Fig. 7. Temperature difference between inlet and outlet fluid in Test 3 and Test 4 during the first 10 h.
noticed that the temperature of groundwater was slightly higher than that of the ground, which indicated the coupling effects of thermal properties and advection plays a more important role in the heat transfer process than the relative temperatures of groundwater and the ground.
Fig. 8. Temperature variations of points Z ¼ 2.1m-3 and Z ¼ 2.1m-5 in Test 3 and Test 4.
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Take two points (Z ¼ 2.1m-3, Z ¼ 2.1m-5) in the sand with groundwater advection for instance (Fig. 8). For Test 3 without groundwater, Z ¼ 2.1m-3 shows a higher temperature than Z ¼ 2.1m-5 due to the heat transferred from double tubes. However, for Test 4 with groundwater advection, these two points have similar temperatures around 24.5 C. With a steeper temperature increase, the short recovery period (from 4 h to 6 h) is found to efficiently recover and lead to an even temperature distribution, which will further benefit the following operation period. Since the heat transferred outward during the recovery period, the temperatures of both points increased and then decreased due to a further heat transfer. It should be noticed that the peak temperature occurred around 12 h in Test 4 while that delayed to 15 h in Test 3, which indicated that the groundwater advection can enhance the heat recovery and decrease the time to recover. Moreover, these two points showed similar temperatures for Test 4 while a large discrepancy for Test 3, the better uniformity also represented a better recovery. Compared to the single tube affected point Z ¼ 2.1m-5 in the unsaturated condition of Test 3, it was heated by the seepage flowing through these two tubes in Test 4, to some extent, it was affected by two tubes, therefore, similar temperature variations can be found in points Z ¼ 2.1m-3 and Z ¼ 2.1m-5. Compared to the heat load, the groundwater advection shows a more significant impact on the heat transfer performance. 3.2. Numerical study Experiments of Test 2 was further used to validate the numerical data to give a more detailed investigation on the thermal performance predictions.
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temperature and heat load of groundwater seems constant and started to increase. At t ¼ 4 h, more heat ground absorption increased the temperature and the heat brought by the groundwater, which could enhance the groundwater effects. It reminds us that the impacts of the groundwater on the thermal performance predictions varied with the operation time and locations. 3.2.2. Ground temperature The temperature distributions of ground at various locations were different due to different heat transfer (Fig. 10). Good agreements were achieved between predictions and measurements with an averaged uncertainty of 3%. The unexpected discrepancy occurring at z ¼ 3.9 m at L1 may be caused by the accidental measurement uncertainty. The sand with groundwater advection at L1 (Fig. 10a), L2 (Fig. 10b) and L4 (Fig. 10d) has a lower temperature than the others, it is clear that the groundwater advection delayed the temperature increase. While L5 (Fig. 10c) showed an opposite trend, the temperature of saturated sand had a much higher temperature than the surrounding ground, and their discrepancy can be up to 3.5 C. It is because the seepage brought the heat extracted from two tubes to L5. Because the saturated clay has a similar thermal diffusivity to the unsaturated sand, the clay located between 3 and 4 m showed a similar temperature as the sand between 1 and 2 m. A detailed ground temperature distribution can be found in Fig. 11. At the end of the 24 h - operation period, seepage flowing through the sand made the temperature distribution an oval shape. The influential area was larger in the bottom sand (z ¼ 2.5 m), and a higher temperature was expected when compared to other locations. 4. Conclusions
3.2.1. Water temperature As shown in Fig. 9a, the water temperature differences of these two tubes were over predicted, and a larger discrepancy was found in Tube 2. The simulation gave similar temperature predictions for the water inside these two tubes, while the measurements showed a significant effect of the groundwater advection. Part of the reason is caused by the groundwater advection, and some is because of the ununiform thermal properties of the ground. With more heat absorbed, the outlet temperature of the groundwater increased during the operation time (Fig. 9b). At the beginning stage, less heat was transferred to the ground, and the
Based on a double-layered small-scale laboratory apparatus in our previous studies, partial sand and clay was saturated with groundwater to presents the unsaturated, saturated sand and clay with or without groundwater seepage. Moreover, a 3D numerical model considering both ground stratification and groundwater advection was built and validated against the experimental data. Effects of ground stratification and groundwater advection were investigated experimentally and numerically via the temperature and heat load distributions of water, sand and clay. The conclusions arising from this study are summarized as follows:
Fig. 9. Temperatures and heat loads variations of (a) Circulation water and (b) Groundwater.
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Fig. 10. Comparisons of experimental and predicted ground temperatures and temperature increases at (a) L1 (x ¼ 0.5 m, y ¼ 1.25 m), (b) L2 (x ¼ 0.25 m, y ¼ 1 m), (c) L5 (x ¼ 0.5 m, y ¼ 0.25 m) and L4 (x ¼ 0.25 m, y ¼ 0.5 m) at t ¼ 24 h.
Fig. 11. Ground temperature distributions at different locations at t ¼ 24 h.
(1) Compared to the experiment without groundwater, the overall fluid temperatures were decreased by 3 C with a
larger temperature difference between inlet and outlet of GHEs. The effect of groundwater on heat transfer
W. Li et al. / Renewable Energy 147 (2020) 620e629
performance of GHEs depends on the thermal properties, flow advection and the relationship between temperatures of the groundwater and ground. (2) The groundwater has positive effects on the pipes in upper stream rather than those in lower stream. Significant effect of groundwater advection can be found in pipes both legs opposite to the flow rather than those parallel to the flow. (3) The groundwater flow would redistribute the heat load within the ground. A better recovery was found in the ground with groundwater flow, and a 2-h break would advance an even temperature distribution by 3 h. (4) The temperature and carried heat load of the cooler groundwater will increase during the heat injection experiment, and further contributed to various temperature distributions of ground at different locations and time. Acknowledgements The financial supports provided by the Nature Science Foundation of China (Grant No. 51576023 and No. 91643102), the Fundamental Research Funds for the Central Universities (Project ID: 106112016CDJCR211221) and the 111 Project (Project ID: B13041) are gratefully acknowledged. References [1] A. Casasso, R. Sethi, Efficiency of closed loop geothermal heat pumps: a sensitivity analysis, Renew. Energy 62 (2014) 737e746. [2] H.J.L. Witte, G.J. Van Gelder, J.D. Spitler, In situ measurement of ground thermal conductivity: a Dutch perspective, ASHRAE Transact. 108 (2002) 263e272. [3] W.H. Leong, V.R. Tarnawski, A. Aittom€ aki, Effect of soil type and moisture content on ground heat pump performance, Int. J. Refrig. 21 (8) (1998) 595e606. [4] W. Li, X. Li, Y. Peng, Y. Wang, J. Tu, Experimental and numerical investigations on heat transfer in stratified subsurface materials, Appl. Therm. Eng. 135 (2018) 228e237. [5] W. Li, X. Li, Y. Wang, R. Du, J. Tu, Effect of the heat load distribution on thermal performance predictions of ground heat exchangers in a stratified subsurface, Renew. Energy 141 (2019) 340e348. [6] Y. Fan, H. Li, G. Miguez-Macho, Global patterns of groundwater table depth, Science 339 (6122) (2013) 940e943. [7] ASHRAE, ASHRAE Handbook - Heating, Ventilating, and Air-Conditioning Applications (SI), American Society of Heating, Refrigerating and AirConditioning Engineers, Inc., Atlanta, 2011. [8] N.R. Diao, Q.Y. Li, Z.H. Fang, Heat transfer in ground heat exchangers with groundwater advection, Int. J. Therm. Sci. 43 (12) (2004) 1203e1211. [9] J. Luo, J. Rohn, W. Xiang, M. Bayer, A. Priess, L. Wilkmann, H. Steger, R. Zorn, Experimental investigation of a borehole field by enhanced geothermal response test and numerical analysis of performance of the borehole heat
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Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Experimental and numerical studies on the thermal performance of ground heat exchangers in a layered subsurface with groundwater Wenxin Li a, b, c, Xiangdong Li c, Yuanling Peng a, b, Yong Wang a, b, *, Jiyuan Tu c a
National Centre for International Research of Low-carbon and Green Buildings, Ministry of Science & Technology, Chongqing University, Chongqing, 400045, China b 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
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 May 2019 Received in revised form 17 August 2019 Accepted 3 September 2019 Available online 5 September 2019
Thermal performance of the ground source heat pump (GSHP) system can be significantly affected by the complex geological substructures (such as ground stratification and groundwater advection). This study installed a seepage box inside the two-layered laboratory device to investigate the heat transfer processes of the unsaturated, saturated and infiltrated ground. Various operational and geological conditions were designed to study the temperature distributions at various locations and time experimentally and numerically. The groundwater effect on ground heat exchanger (GHE) thermal performance depends on the thermal properties, flow advection and the relationship between temperatures of the groundwater and ground. If the ground was partially saturated during the heat injection period, the cooling seepage will efficiently remove the heat of GHEs in upper-stream rather than those located in the bottom-stream. Meanwhile, the heat transfer can be enhanced if two legs of the U-tube vertical to the direction of groundwater seepage. The groundwater flow can redistribute the heat within the ground and showed a better recovery performance which advance an even temperature distribution by 3 h. The temperature and carried heat load of the cooler groundwater will increase during the heat injection experiment, and further contributed to various temperature distributions of ground at different locations and time. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Ground heat exchanger Experimental investigation Computational fluid dynamics Ground stratification Groundwater advection
1. Introduction Ground source heat pump (GSHP) systems, which utilize shallow geothermal energy to heat or cool buildings, have been widely applied around the world in recent years due to their high energy-efficiency and environmental friendliness. The heat exchange between buildings and the ground was achieved by the ground heat exchanger (GHE) system. The heat transfer performance of GHEs is strongly affected by the thermo-physical properties of the soil and subsurface [1], which could change with geographic structure [2] and moisture content [3]. Various geological materials showed different temperature distributions, and therefore, different heat transfer efficiencies of GHEs [4,5]. Since the groundwater table depth globally varied from land
* Corresponding author. 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.renene.2019.09.008 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
surface to more than 200 m and highly occurs at the range of 2e30 m [6], it would be common for vertical GHE systems (depths ranging from 15 to 180 m [7]) to be affected by groundwater advection. Many researchers have investigated the effects of groundwater, and due to the water advection, it is proved to have a positive effect on heat transfer enhancement with lower temperature rises and a more steady condition [8]. Luo et al. [9] built a 3D model in a commercial finite elemental software FEFLOW, where the flow in GHE was simplified as 1D discrete element. The simulation results indicate that heat transfer efficiency of GHEs can be increased by 55% within the aquifer. The comprehensive thermal performance could be increased significantly with the increase of the groundwater flow velocity, the decrease of average inlet and outlet water temperatures [10]. Moreover, the increasing water saturation in the adjacent soil can substantially increase the amount of heat recovery [11], and the effects of groundwater flow could be more significant for the long-term performance [12]. With a better heat transfer efficiency on recovery, the groundwater can promote the quick
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Nomenclature Cp G K S T T T0 Tg U
a q
Specific heat capacity at constant pressure (J/kg∙ C) Gravitational acceleration (9.8 m/s2) Intrinsic permeability (m2) Momentum source term (N/m3) Time (s) Temperature ( C) Initial ground temperature ( C) Ground temperature ( C) Velocity (m/s) Permeability (m2) Temperature increase ( C)
thermal rebalancing in the borehole field, even for circumstances where the heat rejection and extraction are unbalance [13]. The heat transfer performance of GHEs largely determined by the thermal and hydraulic properties of the surrounding soil. The ground thermal conductivities are measured to be different in dry and saturated conditions [14], since the thermal conductivity is primarily dependent upon the degree of water saturation and secondary on the flow path [11]. The neglect of variations in moisture content in unsaturated soil would underestimate the heat transfer capacity of the soil, and the ignore of groundwater table fluctuations can result in a 3e4% error in the outlet fluid temperature [15]. During the intermittent period, the performance in unsaturated soil conditions decreased by up to 40% and showed a larger temperature variation compared to that in fully saturated soil conditions [16]. Furthermore, the effects of groundwater could be different in various materials. By simulating with an analytical line source model, Diao et al. [8] conducted that the effects of groundwater flow may usually be neglected except in formations with considerable flow rate such as gravel and coarse sand. For ground with fractures, even at relatively low specific flow rates, the groundwater flow may cause significantly enhanced heat transfer [17]. Based on a finite-element numerical model considering groundwater flow, Chiasson et al. [18] found that the groundwater advection could significantly enhance the heat transfer in geologic materials with high hydraulic conductivity, such as sands, gravels, and rocks exhibiting fractures and solution channels. The effect of thermal dispersion on the temperature plume around GHEs was found to be minor for homogeneous aquifer, and the thermal dispersion can be neglected only for conditions typical for fine sands, clays, and silts with Darcy velocities q < 108 m/s, while showed larger effect for aquifers where medium sands and gravels (q > 108 m/s) dominate [19]. [1]. Although the thermal performance of GHEs with groundwater has been investigated numerically and analytically, most studies assumed the GHEs fully immersed in the groundwater [12,20,21], few has considered both ground stratification and the groundwater advection, which is common in the practical engineering. Many analytical [8,21] and numerical [12,22] models were twodimensional, which cannot take the vertical ground structure into consideration. Furthermore, most studies validated with in-situ experiments which lacked sufficient data of ground temperature distributions, where the ambiguous properties cannot sufficiently support the accuracy of the validations. Therefore, this study introduces a well-controlled laboratory apparatus with sand and clay, where part of them were saturated and considered the groundwater seepage. Properties of the materials were measured and calculated for the further experimental and numerical analysis. Predictions from 3D numerical model were validated against the
l m r r 4
621
Thermal conductivity (W/m∙ C) Dynamic viscosity (Pa$s) Density (kg/m3) Cp Specific volumetric heat capacity at constant pressure (J/m3∙ C) Porosity
Subscripts/superscripts Eff Effective F Fluid Mc Clay Ms Sand S Solid
data from a 24 h heat injection experiment, which were further used to investigate the effects of ground stratification and groundwater advection on the thermal performance experimentally and numerically. 2. Methods 2.1. Experiment description Based on the experimental apparatus in our previous studies [4,23], some accessories were added to mimic the groundwater seepage (Fig. 1a). The 6.25 m 1.5 m 1 m laboratory apparatus was installed laterally and filled with sand and clay. Located in the middle of the device is a 2 m-length steel box which consists of a pluviation system to “raining” the groundwater seepage evenly inside the sand and clay. The perforated plate with small holes was installed at the top of the box, and the bottom located the cobblestone layer to contain the sand and clay. The stainless-steel box connected to the high and low cisterns, where the groundwater flows from the high cistern, penetrates through the sand and clay, and later returns to the low cistern. Based on the Darcy's law, the flow rate of the groundwater can be controlled by adjusting the heights of the high and low cisterns. Constant heat inputted by the electric heater was used to heat the water in the tank, and then the heat-carrier water flowed through two GHEs and later returned to the tank. The flow rate of circulating water was controlled by the flow adjust valve and was measured through a turbine flow meter. The accuracy grade of the flow meter was 1%, and the relative uncertainty was calculated to be 8.7%, which was acceptable with a value less than 10%. Detailed T-type thermocouples were installed inside the laboratory device, and two more thermocouples and flow meters were installed to monitor the temperatures and flow rate of the groundwater. The accuracy of T-type thermocouple is 1 C, and the maximum relative error of temperature measurement was 3%. A data logger system was connected to a computer to display and record the temperature data with a time interval of 15 min. Detailed information on the experimental device was listed in Table 1, and also in our previous studies [4,23]. The installed copper-constantan thermocouples were selected to give a detailed distribution in this study. As shown in Fig. 1b, thermocouples were installed at six cross-sections at different depths (z ¼ 1 m, 2.1 m, 2.9 m, 3.1 m, 3.9 m and 5.75 m). Each representative cross-section located 5 points with a spacing of 0.25 m, which denoted as 0e6 from the top (y ¼ 1.5 m) to the bottom (y ¼ 0 m). For example, Z ¼ 2.9 m-3 is the point located at z ¼ 2.9 m, x ¼ 0.5 m and y ¼ 0.75 m. For comparison convenience, L1, L2, L4 and L5 denote the lines compose of all the points ended with 1,
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Table 1 Detailed parameters of the experimental device [4]. Objects
Parameter
Value (m)
Sandbox
Depth Length Width Length Wall thickness Inner diameter Distance between pipe centers
6.25 1.50 1.00 6.25 0.0005 0.005 0.015
U-tube
2, 4 and 5 at every representative cross-section, respectively. These lines located from the top to the bottom within the experimental box.
2.2. Material property measurement To investigate the groundwater effect in this study, heat transfer inside the saturated materials will be compared to the one without groundwater seepage (unsaturated materials), therefore,
Fig. 1. (a) Experimental set-up and (b) Locations of the thermocouples used in this study.
W. Li et al. / Renewable Energy 147 (2020) 620e629
properties of both saturated and unsaturated materials were provided for further calculation and analysis. Properties of the experimental used materials including density, porosity, water content, particle size distribution, specific heat capacity, thermal conductivity and thermal diffusivity were measured and calculated in detail. Since the air and ground contain moisture, it is impossible and no need to obtain the absolutely dry materials for the experiment. Thus, water contents of the experimental used materials were measured by comparing the weights before and after the drying. For the experiment without groundwater seepage, the water contents of experimental sand and clay were measured to be 10.1% and 28.8%, respectively. The flow of water through soil is controlled by the size and shape of pores, which is in turn controlled by the size and packing of soil particles. Most soils are a mixture of grain sizes, and the grain size distribution is often portrayed as a cumulative-frequency plot of grain diameter (logarithmic scale) versus the weight fraction of grains with smaller diameter. The steeper the slopes of such plots, the more uniform the soil grain-size distribution [24]. The grain size distribution of sand was obtained by sieve analysis, and the grain size distribution (3-cycle semi-log graph paper) of the laboratory used sand is shown in Fig. 2. The range of sand grain diameter was measured to be 0.075e0.25 mm, and it can be considered as very fine sand (USDA, 0.05e0.10 mm) and fine sand (USDA, 0.10e0.25 mm) according to U.S. Department of Agriculture (USDA) classification system [25]. Since the screening test of the clay was affected by its own agglomeration phenomenon, it is hard to decide the size of the clay particle. The porosity (4) of the sand and clay are measured to be 0.46 and 0.50, respectively, which are among the typical value range of 0.26e0.53 for fine sand and 0.34e0.60 for clay [18]. Thermal conductivities of the sand and clay were measured in the laboratory using needle source probe except the unsaturated sand due to the measure interference, and that of the unsaturated sand was estimated based on the thermal conductivities of the dry sand, water content and the relationship between them provided by a reference [26]. The following experiments only consider the groundwater seepage in the sand, and the permeability coefficient of sand was calculated to be 1.46 105 m/s by using data from the seepage test based on Darcy's law, which was considered to be weak permeable. Detailed parameters can be found in Table 2. It should be noticed
623
that, when the pores of the ground were filled with water, thermal conductivities and capacities of the materials both increase. Therefore, the addition of water in sand decreases the thermal diffusivity, while it increases the thermal diffusivity in the clay. 2.3. Numerical model Based on the previously introduced laboratory apparatus, a complete 3D CFD model was built to model the heat transfer process for GHEs in a layered subsurface with partial groundwater advection (Fig. 3). The thermal resistance of the tube material was calculated using the so-called thin-wall thermal resistance of FLUENT [27]. The incompressible Navier-Stokes equations together with standard k-ε model [27] were solved for the convective heat transfer of water in the pipes. As the GHEs are partially immersed with the saturated groundwater in a two-layer ground, the computation region of the experimental box can be divided into four regions: sand, sand with groundwater flow, saturated clay and clay. Each material was considered as homogeneous media with certain porosities. For the sand and clay without the groundwater advection, only the conduction is considered, thus the heat transfer through the sand and clay is calculated by
vTk lk ¼ vt rk Cp;k
v2 Tk v2 Tk v2 Tk þ 2 þ 2 vx2 vy vz
! (1)
where lk, rk and Cp,k represents the thermal conductivity, density and specific heat capacity of the sand (k ¼ ms) and the clay (k ¼ mc), respectively. For materials with saturated groundwater, the heat transport was assumed as a porous medium with a constant homogeneous groundwater flow. The heat transfer process consists of conduction by solid matrix and liquid in its pores and convection of the moving groundwater. Porous media are modelled by the addition of a momentum source term to the standard fluid flow equations. If the source terms of convection acceleration and diffusion are ignored, it can be simplified bases on Darcy's law:
m a
Si ¼ ui ði ¼ x; y; zÞ
Fig. 2. (a) Sieve analysis and (b) Grain size distributions of the experimental sand and clay.
(2)
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Table 2 Properties of the materials used in experiments. Properties
Unsaturated sand
Saturated sand
Unsaturated clay
Saturated clay
Groundwater advection (water at 24 C)
Water inside tubes (water at 20 C)
Copper tube
Density (kg/m3) Specific heat capacity J/ (Kg$ C) Thermal conductivity (W/ m$ C) Thermal diffusivity 107 (m2/s) Porosity
1593.39 1348
1814.68 2592
1616.91 2273
1838.35 2479
997.20 4179
998.20 4182
8978 381
1.13
2.03
0.85
2.35
0.61
0.60
387.60
5.27
4.32
2.30
5.16
1.46
1.44
1130
46%
46%
50%
50%
\
\
\
The governing equations of the 3D GHE models were solved using the commercial CFD code ANSYS Fluent-16 (ANSYS, NH, USA). All side walls of the soil domain were considered to be insulated. Boundary conditions of ‘velocity inlet’ and ‘pressure outlet’ were allocated to the inlet and outlet of the tubes, where the varied experimental water inlet temperature was inputted through the FLUENT user defined functions (UDFs) through the Dirichlet boundary condition of the inlet face. All the initial data setup was based on the actual experiments. Prior to performing CFD simulations, grid and time-step independent study was conducted. Mesh refinement was placed in the near wall regions of the HTF tube and the borehole (Fig. 3). Considering the computational efficiency and accuracy, the mesh with elements numbers of 623,610 and timestep of 300 s was used for further simulation in this study.
3. Results
Fig. 3. Mesh and boundary conditions of the numerical model.
where m is the dynamic viscosity, u is the velocity and a is the permeability of the groundwater. The intrinsic permeability K can be calculated by Ref. [28]:
K¼
rg a m
(3)
Both experiments and numerical studies were conducted to investigate the heat transfer performance of GHEs in ground with groundwater advection. Water temperature, vertical and horizontal ground temperature distributions were investigated for thermal performances in different geological and operating conditions experimentally and numerically.
3.1. Experimental study
where 4 is the porosity of the saturated porous medium, the subscripts s and f represent the solid and fluid, respectively. The effective thermal conductivity (leff) is calculated from the volume average of the fluid and solid conductivities [27]:
Before adding the water into the experimental device, an experiment of dry sand and clay was performed to work as a reference test to evaluate the effects brought by the groundwater advection. Compared to the experiment with dry materials, the other one saturated part of the sand and clay, where the groundwater flowed from the top to the bottom in the saturated sand. Both continuous and intermittent experiments were conducted for the saturated and unsaturated conditions. It should be noticed that the temperature of groundwater was lower than that of ground in Test 2 while higher than the ground temperature in Test 4. These relationships between groundwater and ground temperatures both exist in the practical measurements [29]. Details of these experiments can be found in Table 3. To diminish the influence of the non-uniform initial temperature, the temperature increase (q) is defined as the difference between the testing soil temperature and its corresponding initial temperature [4], which is a positive value for the heat release process. It can reflect the soil temperature rise during heat release period and can be calculated as:
leff ¼ ð1 4Þls þ 4lf
q ¼ Tg ðtÞ T0
where r is the density, and g is the gravitational acceleration (9.8 m/ s2). Based on the intrinsic permeability measured by the test, a1 of the seepage was calculated to be 7.25 1011 m2. With isotropic assumption, same values were set for each directions of the drag coefficients. It is assumed that the velocity u of groundwater transfusion is uniform in the whole domain and the solid skeleton and fluid always have the same temperature, the equilibrium thermal model in the saturated material zone can be calculated by:
h i vT ! vT þ 4 rCp f u ð1 4Þ rCp s þ 4 rCp f ¼ leff V2 T vt vxi
(4)
(5)
where ls and lf are the thermal conductivities of the solid and fluid in the saturated material, respectively.
(6)
where Tg(t) and T0 are the soil temperatures at time t and t ¼ 0, respectively.
W. Li et al. / Renewable Energy 147 (2020) 620e629
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Table 3 Experimental information. Test Test Conditions
Heat injection
Operation modes
Operation time
Fluid circulation velocity
Initial ground temperature
Groundwater velocity
Inlet temperature
1 2
Input heat load of 300 W
continuous 24 h
0.64 m/s 0.64 m/s
15.4 C 24.0 C
\ \ 1.29 105 m/ 23.4 C s
3 4
Inlet water temperature of 32 C
intermittent 34 h (4 h on-2 h off-4 h on-24 h off)
0.63 m/s 0.64 m/s
20.4 C 24.2 C
\ \ 1.09 105 m/ 25.1 s
3.1.1. Effect of groundwater advection on thermal performance distribution Fig. 4 compares the temperatures of the total fluid circulated within the two GHEs in these two tests. Test 1 in dry condition shows higher temperatures for both inlet and outlet, while the test with the flowing groundwater can transfer the heat more efficiently and gave lower fluid temperatures. With the addition of groundwater, the fluid temperatures were decrease by 3 C and the temperature difference between inlet and outlet of GHEs was enlarged by 0.74 C. The heat transfer enhancement is the coupling effects of thermal properties, flow advection and the relationship between ground and groundwater temperatures. Even if the saturated sand has a lower thermal diffusivity, the materials showed a significant enhancement on thermal diffusivity due to the saturated clay. Fig. 5 compared the temperature increases of the ground located at L2 and L4 at t ¼ 12 h and t ¼ 24 h. They shared the same distance to tubes while different depths in ground, where L2 (y ¼ 1 m) located higher than L4 (y ¼ 0.5 m). At the upper part of the ground (as shown in Fig. 5a), compared to Test 1 without groundwater, the thermal distribution can be dramatically affected by the groundwater flow. Even if the addition of water decreases the thermal diffusivity of sand from 5.27 107 m2/s to 4.32 107 m2/s, the
Fig. 4. Fluid temperatures of inlet and outlet, and their temperature differences (Dt) in tests with continuous operational modes.
thermal convection brought by the flow significantly decreased the temperatures of the saturated sand with advection (Test 1). The temperature of groundwater was slightly lower than that of the ground, the flowing seepage took heat away and reduced the ground temperature. However, less significant groundwater effect can be found in the bottom ground (L4), and Test 2 witnessed a similar temperature distribution as Test 1. For the sand located at depths between 2 m and 3 m, the groundwater flow brought the heat from the top tube to the bottom one, and the slightly temperature decrease becomes more obvious with the increase of time. A slightly temperature increase can be found in the temperature variations from the sand to clay, which indicated that the sand with groundwater has a higher heat transfer efficiency than the saturated clay. If the clay was saturated with water, its thermal diffusivity would increase drastically from 2.30 107 m2/s to 5.16 107 m2/ s, and the more efficient heat transfer led to a higher temperature for the ground located at 0.25 m to the tube. The thermal enhancement was even apparent for the upper tube, which could be affected by the neighbouring sand with groundwater advection. For the unsaturated test (Test 1), different temperature distributions for L2 and L4 may attribute to the uneven thermal property of the ground. Fig. 6 compares the temperature distributions at x ¼ 0.5 m and different depths. Compared to Test 1, temperatures of the saturated sand with groundwater advection varied in the flow direction (Fig. 6a). Since the groundwater flowed from the top to the bottom, the upper ground (ending with 1) showed a much lower temperature, while the seepage was heated by the tubes and further increased the temperatures of bottom ground (ending with 3 and 5). Such effect was weakened in the ground at z ¼ 2.9 m (Fig. 6b), because it can be affected by the neighbouring clay. Without the advection, the saturated clay saw a similar condition as the unsaturated clay (Fig. 6c). Since the saturated clay has a higher thermal diffusivity, it transferred the heat more efficiently and showed higher temperatures than the unsaturated one. 3.1.2. Effect of groundwater advection on thermal recovery The groundwater advection not only influences the continuous operation of the thermal performance of ground, but also affects its performance during the recovery periods. Therefore, Test 3 and Test 4 were compared. The temperature difference between inlet and outlet fluid in
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Fig. 5. Ground temperature increases at L2 and L4.
Fig. 6. Ground temperature increases at different depths.
these two tubes were similar in Test 3, where Tube 2 was even more efficient (Fig. 7). For Test 4 where the groundwater flowed through Tube 1 first and then Tube 2, the flow of the seepage enhanced the heat transfer of Tube 1 while diminished that of Tube 2. It should be
Fig. 7. Temperature difference between inlet and outlet fluid in Test 3 and Test 4 during the first 10 h.
noticed that the temperature of groundwater was slightly higher than that of the ground, which indicated the coupling effects of thermal properties and advection plays a more important role in the heat transfer process than the relative temperatures of groundwater and the ground.
Fig. 8. Temperature variations of points Z ¼ 2.1m-3 and Z ¼ 2.1m-5 in Test 3 and Test 4.
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Take two points (Z ¼ 2.1m-3, Z ¼ 2.1m-5) in the sand with groundwater advection for instance (Fig. 8). For Test 3 without groundwater, Z ¼ 2.1m-3 shows a higher temperature than Z ¼ 2.1m-5 due to the heat transferred from double tubes. However, for Test 4 with groundwater advection, these two points have similar temperatures around 24.5 C. With a steeper temperature increase, the short recovery period (from 4 h to 6 h) is found to efficiently recover and lead to an even temperature distribution, which will further benefit the following operation period. Since the heat transferred outward during the recovery period, the temperatures of both points increased and then decreased due to a further heat transfer. It should be noticed that the peak temperature occurred around 12 h in Test 4 while that delayed to 15 h in Test 3, which indicated that the groundwater advection can enhance the heat recovery and decrease the time to recover. Moreover, these two points showed similar temperatures for Test 4 while a large discrepancy for Test 3, the better uniformity also represented a better recovery. Compared to the single tube affected point Z ¼ 2.1m-5 in the unsaturated condition of Test 3, it was heated by the seepage flowing through these two tubes in Test 4, to some extent, it was affected by two tubes, therefore, similar temperature variations can be found in points Z ¼ 2.1m-3 and Z ¼ 2.1m-5. Compared to the heat load, the groundwater advection shows a more significant impact on the heat transfer performance. 3.2. Numerical study Experiments of Test 2 was further used to validate the numerical data to give a more detailed investigation on the thermal performance predictions.
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temperature and heat load of groundwater seems constant and started to increase. At t ¼ 4 h, more heat ground absorption increased the temperature and the heat brought by the groundwater, which could enhance the groundwater effects. It reminds us that the impacts of the groundwater on the thermal performance predictions varied with the operation time and locations. 3.2.2. Ground temperature The temperature distributions of ground at various locations were different due to different heat transfer (Fig. 10). Good agreements were achieved between predictions and measurements with an averaged uncertainty of 3%. The unexpected discrepancy occurring at z ¼ 3.9 m at L1 may be caused by the accidental measurement uncertainty. The sand with groundwater advection at L1 (Fig. 10a), L2 (Fig. 10b) and L4 (Fig. 10d) has a lower temperature than the others, it is clear that the groundwater advection delayed the temperature increase. While L5 (Fig. 10c) showed an opposite trend, the temperature of saturated sand had a much higher temperature than the surrounding ground, and their discrepancy can be up to 3.5 C. It is because the seepage brought the heat extracted from two tubes to L5. Because the saturated clay has a similar thermal diffusivity to the unsaturated sand, the clay located between 3 and 4 m showed a similar temperature as the sand between 1 and 2 m. A detailed ground temperature distribution can be found in Fig. 11. At the end of the 24 h - operation period, seepage flowing through the sand made the temperature distribution an oval shape. The influential area was larger in the bottom sand (z ¼ 2.5 m), and a higher temperature was expected when compared to other locations. 4. Conclusions
3.2.1. Water temperature As shown in Fig. 9a, the water temperature differences of these two tubes were over predicted, and a larger discrepancy was found in Tube 2. The simulation gave similar temperature predictions for the water inside these two tubes, while the measurements showed a significant effect of the groundwater advection. Part of the reason is caused by the groundwater advection, and some is because of the ununiform thermal properties of the ground. With more heat absorbed, the outlet temperature of the groundwater increased during the operation time (Fig. 9b). At the beginning stage, less heat was transferred to the ground, and the
Based on a double-layered small-scale laboratory apparatus in our previous studies, partial sand and clay was saturated with groundwater to presents the unsaturated, saturated sand and clay with or without groundwater seepage. Moreover, a 3D numerical model considering both ground stratification and groundwater advection was built and validated against the experimental data. Effects of ground stratification and groundwater advection were investigated experimentally and numerically via the temperature and heat load distributions of water, sand and clay. The conclusions arising from this study are summarized as follows:
Fig. 9. Temperatures and heat loads variations of (a) Circulation water and (b) Groundwater.
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Fig. 10. Comparisons of experimental and predicted ground temperatures and temperature increases at (a) L1 (x ¼ 0.5 m, y ¼ 1.25 m), (b) L2 (x ¼ 0.25 m, y ¼ 1 m), (c) L5 (x ¼ 0.5 m, y ¼ 0.25 m) and L4 (x ¼ 0.25 m, y ¼ 0.5 m) at t ¼ 24 h.
Fig. 11. Ground temperature distributions at different locations at t ¼ 24 h.
(1) Compared to the experiment without groundwater, the overall fluid temperatures were decreased by 3 C with a
larger temperature difference between inlet and outlet of GHEs. The effect of groundwater on heat transfer
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performance of GHEs depends on the thermal properties, flow advection and the relationship between temperatures of the groundwater and ground. (2) The groundwater has positive effects on the pipes in upper stream rather than those in lower stream. Significant effect of groundwater advection can be found in pipes both legs opposite to the flow rather than those parallel to the flow. (3) The groundwater flow would redistribute the heat load within the ground. A better recovery was found in the ground with groundwater flow, and a 2-h break would advance an even temperature distribution by 3 h. (4) The temperature and carried heat load of the cooler groundwater will increase during the heat injection experiment, and further contributed to various temperature distributions of ground at different locations and time. Acknowledgements The financial supports provided by the Nature Science Foundation of China (Grant No. 51576023 and No. 91643102), the Fundamental Research Funds for the Central Universities (Project ID: 106112016CDJCR211221) and the 111 Project (Project ID: B13041) are gratefully acknowledged. References [1] A. Casasso, R. Sethi, Efficiency of closed loop geothermal heat pumps: a sensitivity analysis, Renew. Energy 62 (2014) 737e746. [2] H.J.L. Witte, G.J. Van Gelder, J.D. Spitler, In situ measurement of ground thermal conductivity: a Dutch perspective, ASHRAE Transact. 108 (2002) 263e272. [3] W.H. Leong, V.R. Tarnawski, A. Aittom€ aki, Effect of soil type and moisture content on ground heat pump performance, Int. J. Refrig. 21 (8) (1998) 595e606. [4] W. Li, X. Li, Y. Peng, Y. Wang, J. Tu, Experimental and numerical investigations on heat transfer in stratified subsurface materials, Appl. Therm. Eng. 135 (2018) 228e237. [5] W. Li, X. Li, Y. Wang, R. Du, J. Tu, Effect of the heat load distribution on thermal performance predictions of ground heat exchangers in a stratified subsurface, Renew. Energy 141 (2019) 340e348. [6] Y. Fan, H. Li, G. Miguez-Macho, Global patterns of groundwater table depth, Science 339 (6122) (2013) 940e943. [7] ASHRAE, ASHRAE Handbook - Heating, Ventilating, and Air-Conditioning Applications (SI), American Society of Heating, Refrigerating and AirConditioning Engineers, Inc., Atlanta, 2011. [8] N.R. Diao, Q.Y. Li, Z.H. Fang, Heat transfer in ground heat exchangers with groundwater advection, Int. J. Therm. Sci. 43 (12) (2004) 1203e1211. [9] J. Luo, J. Rohn, W. Xiang, M. Bayer, A. Priess, L. Wilkmann, H. Steger, R. Zorn, Experimental investigation of a borehole field by enhanced geothermal response test and numerical analysis of performance of the borehole heat
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