Double U-tube Borehole Heat Exchanger Research Articles

Analysis of the Combined Effect of Major Influencing Parameters for Designing High-Performance Single (sBHE) and Double (dBHE) U-Tube Borehole Heat Exchangers

In this paper, a comprehensive analysis of the combined effect of major influencing parameters on heat transfer in a single U-tube BHE (sBHE) and a double U-tube BHE (dBHE) with two independent circuits was performed by using a validated numerical heat transfer model. Geometrical parameters, such as shank spacing (with maximum, average, and minimum values), borehole diameter (large, medium, and small borehole sizes), and borehole depth (shallow, average, and deep borehole depths) as well as the thermal conductivity of soil and grout, which ranges from minimum to high values, were considered. The combined impact of these parameters was included under the following four major cases: (1) the combined effect of borehole depth, borehole size, and shank spacing; (2) the combined effect of borehole depth and soil and grout thermal conductivity; (3) the combined effect of soil and grout thermal conductivity and borehole size; and (4) the combined effect of soil thermal conductivity, borehole size, and shank spacing. Each of these major cases has nine different design options for both sBHEs and dBHEs. A series of results of heat transfer per unit borehole depth were generated for all the considered various cases. With the given parameters, the BHE case that provides the highest heat transfer among the various cases of sBHEs and dBHEs were obtained.

Investigation by monitoring and numerical simulation of the performance of a ground-source heat pump system with and without regeneration in different configurations and operating modes

This paper is focused on restoring the thermal imbalance of the ground caused by conventional GCHP systems through seasonal and continuous regeneration using a geothermal-solar facility with a vertical GCHP combined with photovoltaic (PV) and PV-thermal (PV/T) panels in a heating-dominated climate, located in Timisoara, Romania. Therefore, the performance of a GCHP system integrated into the heat supply system of an experimental office, operating in single and double U-tube borehole heat exchanger (BHE) configuration, with regeneration in the summer months by injecting heat into the ground, is experimentally evaluated. Exploratory research has indicated an increase in the average temperature of the working fluid by 2.4% and an improvement in system performance when using heat injection (seasonal performance factor (SPF) by 3.5% and 6.6% higher and CO2 emission by 1.2% and 3.8% lower in the single and double U-tube BHE configurations, respectively). Additionally, numerical simulations with Polysun software are also used to test the performances of the hybrid GCHP-PV/T system with continuous regeneration throughout the year by PV/T panels and of a conventional GCHP integrated into the heating and DHW production systems for a single-family building. The simulations were experimentally validated through measurements on the geothermal-solar facility for heating and DHW production in the experimental office. The simulation results show that the SPFHP-PV/T values of the hybrid GCHP-PV/T system in the single and double U-tube BHE configurations, equal to 6.00 and 5.79, respectively, are 32% and 34% higher than the SPFHP corresponding to the conventional GCHP system, equal to 4.56 and 4.32, respectively. In addition, the SPFHP-PV/T in the single U-tube BHE configuration is 3.6% higher than in the double U-tube BHE configuration for the GCHP combined with the PV/T array (31.8 m2).

Global sensitivity analysis and uncertainty quantification for design parameters of shallow geothermal systems

To improve the design process of geothermal systems, it is important to know which design parameters particularly affect the performance of the system. This article presents investigations on design parameters for borehole heat exchangers in the shallow subsurface. The study is based on numerical simulations with one double U-tube borehole heat exchanger and approximated models obtained using machine learning. As a result of the global sensitivity analysis, relevant parameters are identified and their respective influence on the performance of a borehole heat exchanger is compared. For example, according to this analysis, the three parameters with the highest sensitivity are the initial temperature, the heat demand and the share of the borehole heat exchanger that is surrounded by groundwater flow. Finally, the effects of uncertainties in the parameters identified as relevant for the design of a borehole heat exchanger are considered in an uncertainty quantification for a fictitious site. Uncertainties for regulatory compliance with respect to temperature limits as well as a large probability of oversizing the system were identified for the considered example. The results of the exemplary uncertainty quantification indicate that it has the potential to be a useful tool for planning practice.

Experimentally investigating and numerically simulating the performances of various low-temperature hydronic heating/cooling systems connected to a vertical closed-loop ground-coupled heat pump

The method used in this study consists of evaluating different terminal heating/cooling systems in an experimental office at the Polytechnic University of Timișoara, Romania, through experimentation and numerical simulation. This paper is focused on the energy efficiency exploratory research of various low- and very low-temperature hydronic radiant heating/cooling systems (floor, wall, ceiling, combined floor-ceiling) and of the medium-temperature radiator heating system, connected to a vertical ground-coupled heat pump (GCHP) in double U-tube borehole heat exchanger (BHE) configuration. The main performance parameters are obtained for five weeks of operation in heating mode and three weeks in cooling mode, and a comparative analysis of these parameters together with indoor thermal comfort is carried out. The four simple heating systems (radiator, floor, wall, ceiling) have relatively small differences (maximum 7.4 %) in their coefficient of performance (COP) values, but the number of starts/stops in the case of radiator heating is twice that of floor heating, which leads to greater wear and tear on the heat pump equipment. Under the same operating conditions, the CO2 emission of the radiator heating system are 0.7–16 % higher than those of the heating system with radiant panels (floor, wall, and ceiling). The floor-ceiling combined radiant heating system has the highest COPsyst of 5.45 as well as the lowest CO2 emission value of 2.15 kg. The predicted mean vote (PMV) index (pair 1.1 met-0.29 clo) has values approximately equal to 0 only in the case of the floor-ceiling heating, when the percent of likely dissatisfied with the thermal comfort is 5 %. The three cooling radiant systems show differences in their energy performance, namely the radiant ceiling cooling system has the best COPsyst, 39.8 % higher than that of the radiant floor and only 5.9 % higher than that of the radiant wall. The values of the PMV index (pair 1 met-0.9 clo) for the radiant wall cooling system are 31–41 % lower than those of the radiant floor and 10.4–14.2 % lower than those of the radiant ceiling. Finally, numerical simulations of the useful thermal energy and the system COP in heating and cooling modes are performed with TRNSYS software for a duration of 8760 h and then analysed and compared with the experimental tests to validate the simulation models.

Experimental investigation of effectiveness variation of borehole heat exchangers for cooling mode operation

• Parallel configuration shows higher effectiveness of 0.88 than series configuration with 0.81. • Borehole limiting ratio for parallel configuration is higher than that of series one. • Experimental study of space cooling operation using ground dource heat pump system. • Maximum rise in the tube-interface temperature is observed at 73 m depth of borehole. In the present research work, a novel technique is proposed to estimate real time variation of borehole temperature based on measured interface temperature along the depth of a double U-tube borehole heat exchanger (BHE). Experimentally determined transient variation of effectiveness of BHE is discussed in detail for experimental simulation of line source model and actual operation of a GSHP system for cooling mode operation. The real time borehole temperature computed using the present technique during actual operation of a GSHP system makes it possible to compute the actual variation of effectiveness of BHE. The above set of experiments were performed for both single and double U-tube BHEs considering series and parallel mode operations during peak summer conditions at a location situated closer to the Himalayan region in northern part of India. Effectiveness of BHEs was computed using varying borehole temperature obtained from line source model and the real time varying borehole temperature proposed in the present work. For the actual cooling mode GSHP experiments, the average value of thermal effectiveness of double U-tube BHE computed with constant borehole temperature is observed to be 0.72 for both series and parallel mode operations. However, with the use of real time varying borehole temperature, the effectiveness is observed to increase by 12% and 22% for series and parallel flow operations respectively.

Experimental Study of Heat Extraction and Soil Recovery During Space Heating Application Using Ground Source Heat Pump System

Abstract The present research paper reports experimental results on the coupled phenomena of heat extraction and heat recovery by a double U-tube borehole heat exchanger (BHE) and its thermal performance for space heating application using a ground source heat pump (GSHP) system. Experiments were performed on a 5-ton cooling capacity GSHP system installed at Roorkee located in the northern part of India, during peak and moderate winter seasons. The heat interaction by the GSHP system with the ground is achieved by five double U-tube BHEs and one single U-tube BHE of 120 m depth each. Experimental trials were conducted for parallel and series flow of heat transfer fluid (water) in the BHE. Temperature of water and power consumption by the GSHP was monitored continuously during heat extraction for 12 h and heat recovery of soil as well. For the peak winter season, during heat extraction, a 5 °C temperature rise was observed in BHE water for series connection, which is about 10% higher than that of the parallel case. Maximum heat extraction of 14.8 kW was obtained for the series connection, which is 20% higher than the parallel one, thus resulting in a 20% higher value of the overall coefficient of performance (COP) of the system for series mode compared to the parallel mode operation during the peak winter season. However, the ground near the BHE has taken lesser time for heat recovery in parallel mode compared to the series mode.

Heat transfer analysis of single and double U-tube borehole heat exchanger with two independent circuits

Borehole heat exchanger (BHE) is a very suitable and cost-effective technology for heat storage and extraction of heat from the ground. In this paper, comprehensive analysis of major influencing parameters on thermal performance of single U-tube BHE (sBHE) and double U-tube BHE (dBHE) was performed by using validated numerical heat transfer model. Combined effect of increasing borehole size and soil or grout thermal conductivity (for different cases of shank spacing) on performance of sBHE and dBHE was studied. Detailed comparative analysis of thermal performance was made among sBHE and dBHE with small and large borehole sizes. The impact of borehole depth and diameter, fluid inlet temperature, mass flow rate, U-tube pipe material type and diameter on total heat transfer per unit borehole depth, borehole thermal resistance and thermal effectiveness was also investigated. The simulation result revealed that when the shank spacing is kept at high or low value in sBHE and dBHE (both with small and large borehole size), dBHE with larger borehole size has the highest thermal performance while sBHE with smaller borehole size has the lowest performance; and the highest and the lowest thermal resistance is obtained for sBHE with smaller borehole size and dBHE with larger borehole size, respectively. Grout with high thermal conductivity is preferred in terms of improving thermal effectiveness and reducing thermal resistance of the BHE when the soil thermal conductivity is sufficiently high; while low grout thermal conductivity is preferred with large borehole size and high shank spacing. For high soil thermal conductivity (4W/m.K), the heat transfer rate per unit borehole depth increases with grout thermal conductivity to a maximum value; and then further increasing of the grout conductivity results in smooth declining of the heat transfer in the BHE. Thus, ground and grout thermal conductivity have an optimal range to achieve a lower value of the BHE thermal resistance, and consequently for better BHE sizing. With increasing fluid inlet temperature (15oC to 42oC), the total heat transfer is improved by 51.5 W/m and 36.2 W/m for dBHE and sBHE respectively; and more heat is injected into the borehole when dBHE is used than sBHE, particularly at higher inlet temperature showing that dBHE is preferable than sBHE for system that works with higher fluid inlet temperature. The result obtained can be used as a quick reference for the design, operation optimization and performance study of ground coupled heat pump system where BHE is used as aborehole thermal energy storage.

Comprehensive simulation based thermal performance comparison between single and double U-tube borehole heat exchanger and sensitivity analysis

In the ground coupled heat pump system that delivers space heating and cooling to the buildings, often questions are raised as to which borehole heat exchanger configuration (single or double U-tube) provides higher thermal performance. To answer this question, in this paper, detailed comparative transient heat transfer analysis between single and double U-tube borehole heat exchanger (BHE) with two independent circuits (that can operate with the same or different mass flowrate and inlet fluid temperature) is conducted. Validated numerical heat transfer model was applied to perform the dynamic simulation and analysis. The two borehole heat exchangers are compared from the perspectives of their thermal performance in the heating and cooling mode of operation. Detailed sensitivity analysis of the BHE has also been performed by investigating the impact of the important borehole parameters, thermal properties and working fluids on the thermal performance of the double U-tube BHE. The simulation result revealed that the heat injected and extracted by the double U-tube BHE at steady state is 21.8 (77%) and 10.2 W/m (71.8%) more than that of the single U-tube BHE respectively. The simulation results also indicate that the thermal effectiveness of the single and double U-tube BHE at steady state are 0.24 and 0.31 respectively. The single U-tube BHE showed higher borehole thermal resistance than that of the double U-tube BHE with values of 0.47 and 0.31 m.K/W, respectively. The results of the study also revealed that among the studied working fluids, CaCl2 (25%) solution showed better thermal performance than other anti-freeze solutions with thermal effectiveness of 35.6%. The simulation result of this work is crucial as an input for the optimization studies made to obtain a single set of optimal borehole paramaters and thermal properties that results in the best performance of BHE coupled to ground source heat pump system designed to provide space heating and cooling of buildings.

Analysis of double U-tube ground heat exchanger for renewable energy applications with two-region simulation model by combining analytical and numerical techniques

This research is concerned on heat transfer analysis and modelling in a double U-tube borehole heat exchanger (BHE), via dividing the borehole into two separate regions. The inner part region of the borehole was analyzed analytically, while the outer region of the borehole was studied numerically. The two analyses were joined with the borehole wall temperature. The transient heat transfer of the borehole outer region was analyzed with thermal resistance model using the implicit numerical technique. In the contrary the thermal capacitance of the inner region of the borehole was ignored in this analysis as the inner portion of the borehole is insignificant compared to the outer borehole region and its modelling was only treated with analytical method. Variation of borehole temperature with time, the variation of rate of heat transfer between the borehole inner region to the outer region, radial temperature profile of the ground, and variation in mean temperature of ground with respect to time were investigated for three borehole operation scenarios (i.e. double charging, double discharging, simulations charging and discharging).

Study on the Coupled Heat Transfer Model Based on Groundwater Advection and Axial Heat Conduction for the Double U-Tube Vertical Borehole Heat Exchanger

In this paper, a dynamic heat transfer model for the vertical double U-tube borehole heat exchanger (BHE) was developed to comprehensively address the coupled heat transfer between the in-tube fluid and the soil with groundwater advection. A new concept of the heat transfer effectiveness was also proposed to evaluate the BHE heat exchange performance together with the index of the heat transfer rate. The moving finite line heat source model was selected for heat transfer outside the borehole and the steady-state model for inside the borehole. The data obtained in an on-site thermal response test were used to validate the physical model of the BHE. Then, the effects of soil type, groundwater advection velocity, inlet water flow rate, and temperature on the outlet water temperature of BHE were explored. Results show that ignoring the effects of groundwater advection in sand gravel may lead to deviation in the heat transfer rate of up to 38.9% of the ground loop design. The groundwater advection fosters the heat transfer of BHE. An increase in advection velocity may also help to shorten the time which takes the surrounding soil to reach a stable temperature. The mass flow rate of the inlet water to the BHE should be more than 0.5 kg·s−1 but should not exceed a certain upper limit under the practical engineering applications with common scale BHE. The efficiency of the heat transfer of the double U-tube BHE was determined jointly by factors such as the soil’s physical properties and the groundwater advection velocity.

Effects of the Circuit Arrangement on the Thermal Performance of Double U-Tube Ground Heat Exchangers

Given that the issue of variations in geometrical parameters of the borehole heat exchanger (BHE) revolves around the phenomenon of thermal resistance, a thorough understanding of these parameters is beneficial in enhancing thermal performance of BHEs. The present study seeks to identify relative changes in the thermal performance of double U-tube BHEs triggered by alterations in circuit arrangements, as well as the shank spacing and the borehole length. The thermal performance of double U-tube BHEs with different configurations is comprehensively analyzed through a 3D transient numerical code developed by means of the finite element method. The sensitivity of each circuit configuration in terms of the thermal performance to variations of the borehole length and shank spacing is investigated. The impact of the thermal interference between flowing legs, namely thermal short-circuiting, on parameters affecting the borehole thermal resistance is addressed. Furthermore, the energy exchange characteristics for different circuit configurations are quantified by introducing the thermal effectiveness coefficient. The results indicate that the borehole length is more influential than shank spacing in increasing the discrepancy between thermal performances of different circuit configurations. It is shown that deviation of the averaged-over-the-depth mean fluid temperature from the arithmetic mean of the inlet and outlet temperatures is more critical for lower shank spacings and higher borehole lengths.

Multi-objective optimisation of a seasonal solar thermal energy storage system for space heating in cold climate

Seasonal solar thermal energy storage (SSTES) system is a promising technology to minimise greenhouse gas emissions (GHGE) by harnessing solar energy for space heating applications. The SSTES system in this study includes double U-tube borehole heat exchanger, ground-coupled heat pump and evacuated tube solar collectors. The aim of this investigation is to optimise the design variables of a SSTES system for space heating in cold climate locations. Six cold climate locations were studied namely: Lukla (Nepal), Dras (India), Sivas (Turkey), Harbin (China), Ulaanbaatar (Mongolia), and Verkhoyansk (Russia). The optimisation variables considered are the total solar collector area and total borehole length. There are three separate optimisation investigations: two single-objective and one multi-objective for the SSTES system. The first investigation is to minimise total life cycle greenhouse gas emissions and the second investigation is to minimise total life cycle cost included cost of GHGE. The third investigation is to minimise both life cycle cost of SSTES system and cost of GHGE (multi objectives). The simulation model was developed using TRNSYS 17 and the Multi-Objective Building Optimisation (MOBO) tool was applied for optimisations. The optimal set of design variables and the corresponding value of the objective function were determined for each single-objective optimisation investigation. Pareto front for each location was also identified for the multi-objective optimisation investigation. The technical and financial performance were also analysed and presented.

Data analysis and discussion of thermal response test under a power outage and variable heating power

In this research, a comprehensive study of power outage and variable heating power were conducted during an in-situ thermal response test (TRT) with a 261-m deep double U-tube borehole heat exchanger. The TRT data obtained during a power outage were measured using the indirect, superposition, equivalent time, and separation methods to obtain the thermal properties of rock-soil. The thermal conductivity of rock-soil, volumetric heat capacity, and thermal resistance were 1.21 W/(m·°C), 2413 kJ/(m3·°C), and 0.41 m2·°C/W, respectively. In the analysis of the test data of the variable heating power conditions, the additional heating as a result of the pump power cannot be ignored, and heat generated by the circulating water pump was stable. The heat transfer rate and average fluid temperature gradually stabilized as the test progressed, and the relationship between them is linear. The trends in the heat exchange rate and average fluid temperature after changing the heating power were expressed using a formula. A thermal response test method with variable heating power was proposed for this test, and the thermal conductivity and initial ground temperature of rock-soil were obtained using this method.

Transient heat transfer simulation, analysis and thermal performance study of double U-tube borehole heat exchanger based on numerical heat transfer model

This paper proposes numerical unsteady heat transfer model that predicts the transient heat transfer in the double U-tube borehole heat exchanger (BHE) where the U-tubes can operate with either different or equal mass flow rate and inlet fluid temperature. The implicit numerical method applied on heat transfer equations, obtained from energy balance on fluid, grout and ground nodes, was utilized to get the solution. The profile of the borehole loading as well as the net heat exchange on each leg of the U-tube along the borehole depth were obtained for simultaneous charging, discharging, and charging-discharging conditions. Axial variation of the mean fluid temperature, grout and borehole wall average temperature for charging and discharging cases were investigated. The model is extended to consider the axial and radial variation of ground temperature outside the borehole. Dynamic simulation was performed for different operating conditions to investigate various temperature response, borehole thermal resistance as well as thermal performance of the BHE. The proposed model was verified with the previously published experimental results. The performed modeling, simulation and analysis are important for the vertical BHE system optimization, efficiency testing as well as for the quick investigation of the impact of the borehole parameters and thermal properties on the overall performance of the BHE. The model is crucial in the design, optimization and performance study of ground source heat pump and borehole thermal energy storage systems.

Optimization of geothermal interaction of a double U-tube borehole heat exchanger for space heating and cooling applications using Taguchi method and utility concept

Optimization results for thermal interaction of a double U-tube borehole heat exchanger (BHE) used along with a 5 ton capacity ground source heat pump system (GSHP), are discussed in this paper. Heat transfer from the BHE is computed using thermal resistance concept for space cooling and heating mode operations. The main objective of optimization is to achieve maximum heat extraction during space heating and maximum heat rejection during space cooling operations. For the purpose of optimization, eight control variables consisting of geometric parameters, thermo-physical parameters and mass flow rate are considered at three levels for a series connected double U-tube BHE of 120 m depth. For Taguchi method L27 orthogonal array has been employed for the computation of heat transfer and S/N ratios for both modes of operations. Results obtained show that optimum values of 9270 W and 7210 W heat can be rejected to and extracted from the ground. Taguchi results are combined to obtain a single set of optimum levels of control variables using the utility concept. Mass flow rate of water in the BHE is found to be the most influential variable. For variation in the duration of cooling and heating mode operations, the optimum heat that could be rejected and absorbed becomes the same and equal to 6180 W for equal duration. It is observed that the heat transfer calculated from the utility concept is 11.11% and 42.86% less than those values calculated by Taguchi method for cooling and heating mode of operations respectively.

Simulation-Based Comparison Between the Thermal Behavior of Coaxial and Double U-Tube Borehole Heat Exchangers

In this study, the thermal behavior of the coaxial and double U borehole heat exchangers was investigated using numerical simulations in both the long- and short-term. As a reference for borehole heat exchanger specifications, the existing coaxial and double U probes of a geothermal heat pump installed within the Horizon 2020 research project named “Cheap GSHPs” were considered. Nine years of simulations revealed that when borehole heat exchangers are subjected to a balanced thermal load, and intermittent operating modes of the ground source heat pump system are set, the coaxial pipes’ configuration provides better thermal performance due to the higher thermal capacitance of the heat-carrier fluid and the lower borehole thermal resistance. The analysis was conducted considering two different types of ground with different thermal conductivity values. As result, the more conductive ground type highlights the higher yield of the coaxial probe.

Temperature sensor module for groundwater flow detection around borehole heat exchangers

We present a temperature sensor module (TSM) for detecting the groundwater flow velocity and direction in the vicinity of a borehole heat exchanger (BHE). We demonstrate the method for double U-tube BHEs, which can also be applied to coaxial BHEs. TSMs can be installed together with a BHE to monitor the temperature distribution in the horizontal plane of a BHE. They consist of 16 digital temperature sensors equally distributed on two concentric rings and a compass, which provides the TSM orientation. While the eight sensors located on the inner ring mainly map the temperatures of the inlet and outlet tubes, the temperatures measured on the outer ring are influenced by advective heat transport due to groundwater flow. We study the sensitivity of the TSM to groundwater flow by numerical simulations and suggest a method for deriving both the groundwater flow velocity and direction. Moreover, we designed a TSM prototype and tested it in a sandbox experiment. This test confirmed the operational principle of the TSM and the method for determining the groundwater flow velocity and direction. The digital temperature sensors used in the TSM prototype resolve temperature changes down to 0.02 K. Both the numerical simulations and the experimental measurements show that such a temperature resolution enables the detection of groundwater flow velocities above 10−7 m s−1 (> 30 m a−1).

Investigation on the thermal behavior of energy piles and borehole heat exchangers: A case study

Constant-flux and operation thermal behavior of ground heat exchangers are meaningful for system design and control strategy of ground-coupled heat pump systems. Based on a ground-coupled heat pump project, four thermal performance tests and an operation test were conducted to compare the constant-flux and operation thermal behavior of spiral-tube energy piles with that of double U-tube borehole heat exchangers. The thermal performance of energy piles is more efficient than that of borehole heat exchangers. A large radial scale of heat source, a long heat exchange tube per unit depth of holes and a backfilled material with large thermal conductivity is helpful to improve the heat transfer efficiency of ground heat exchangers. The short-term thermal response of energy piles is more rapid than that of borehole heat exchangers. The short-term thermal resistance of energy piles is much less than that of borehole heat exchangers. In operation test heat transfer rate per unit length of pile and per unit length of pipe for energy piles is greater than those for borehole heat exchangers. The regular fluctuations in fluid temperature and heat transfer rate in operation should be determined by heating capacity of heat pumps and thermal loads of buildings.

Transient heat transfer performance of a vertical double U-tube borehole heat exchanger under different operation conditions

Abstract The transient thermal performance of a vertical double U-tube borehole heat exchanger (BHE) was numerically studied by validated heat transfer model. Further, the influence of several operation parameters, including inlet velocity, temperature and operation interval, on radial/axial soil temperature distribution were investigated. The simulation result showed that the increased amplitude of the BHE’s heat transfer rate was similar when charging temperature was increased under the same velocity conditions. Meanwhile, the difference of the heat transfer rate between 0.1 and 0.3 m/s was greater than that of the 0.3 and 0.5 m/s when the inlet temperature kept constant. The charging temperature had a more vital influence than the flow velocity on soil temperature lifting, and the flow velocity around 0.3 m/s was recommended under the conditions in this work. Moreover, the heat charging time had a more obvious effect on the heat transfer sensitive zone in the radial direction than the other two parameters. Finally, the choice of charging temperature, appropriate interval, space and depth of borehole were discussed. This study could contribute to the comprehensive understanding of the dynamic thermal behaviour and operation parameter optimization of BHE and its further application in the field of borehole thermal energy storage.

Correlations to determine the mean fluid temperature of double U-tube borehole heat exchangers with a typical geometry

In the evaluation of thermal response tests and in the dynamic simulation of ground-coupled heat pumps, the mean temperature Tm of the working fluid in a borehole heat exchanger is usually approximated by the arithmetic mean of inlet and outlet temperature. In thermal response tests, this approximation causes an overestimation of the thermal resistance of the heat exchanger. In the dynamic simulation of ground-coupled heat pumps, this approximation introduces an error in the evaluation of the outlet temperature from the ground heat exchangers. In this paper, by means of 3D finite element simulations, we provide tables of a dimensionless coefficient that allows an immediate evaluation of Tm in any working condition, with reference to double U-tube borehole heat exchangers with a typical geometry. These tables allow a more accurate estimation of the borehole thermal resistance by thermal response tests and a more accurate evaluation of the outlet temperature in dynamic simulations of ground-coupled heat pump systems. Criteria for the extension of the results to other geometries are also provided.