Single U-tube Ground Heat Exchangers Research Articles

Performance analysis of a solar-assisted ground source heat pump with a single vertical U-tube ground heat exchanger

Owing to higher heat loads than cooling loads in cold climates, the performance of ground source heat pumps (GSHPs) can significantly degrade over time, leading to eventual system failure for systems not properly sized or when there is insufficient regeneration. Solar-assisted ground source heat pump (SAGSHP) systems are receiving increasing interest as a means of enhancing heating performance and maintaining ground thermal balance in cold regions. However, a critical gap remains in the literature: no study has comprehensively analyzed configurations of SAGSHP systems to enhance their overall performance considering long-term performance and realistic operating conditions. For this purpose, a comprehensive investigation of the long-term performance of single U-tube and double U-tube ground heat exchangers (GHEs) for solar-assisted ground source heat pump systems (SAGSHPs) was carried out and compared with the conventional GSHP. The effect of collector tilt angles (0–90°) on the performance of the single U-tube SAGSHP was also examined. A finite volume computational fluid dynamic model was developed and coupled with an actual building energy load profile and a solar irradiation profile based on Calgary’s weather conditions using a novel custom-coded thermodynamic model. Results show that the yearly average heating coefficient of performance (COP) increases by a factor of 1.21 and 1.18 for the single U-tube SAGSHP and double U-tube SAGSHP, respectively, when compared with the conventional GSHP. However, the average annual cooling COP reduces by 0.65 for the single U-tube and 0.72 for the double U-tube SAGSHPs. Moreover, considering the effect of tilt angle on the single U-tube SAGSHP, it is possible to improve the cooling COP when the collector tilt angle is 90°, at the expense of lower heating COP. However, the highest heating COP and annual energy savings are achieved with a tilt angle of 45°. This study provides practical insight into SAGSHP performance enhancements in cold climates.

A Simplified Numerical Model as a Design Tool for Vertical Single U-Tube Ground Heat Exchangers

A Simplified Numerical Model as a Design Tool for Vertical Single U-Tube Ground Heat Exchangers

Novel Methodology for Sizing a Single U-Tube Ground Heat Exchanger Useful at the Early Design Stage

Renewable energy system (RES) is an environmentally friendly source of energy. A suitable design of RES is crucial to implement an energy-efficient building such as a zero energy building (ZEB). The significance of appropriate decision-making for the successful implementation of energy-efficient buildings has been increasing. In addition, the identification of the sizing of RES is equally important for architects or HVAC engineers. In this study, a novel sizing method for a single U-tube ground heat exchanger (GHE) is proposed. A transient thermal analysis for a single GHE is performed by considering ground temperature recovery effect as well as other major design parameters. The results are used to design the proposed sizing method and were verified by transient simulations for different design cases. Additionally, it was observed that the coefficient of variation of root mean square error (CV(RMSE)) for all ten design cases was lower than 15% during the heating and cooling seasons. Thus, the proposed design method can be used for sizing a GHE in the early design stage.

Thermal performance of a single U-tube ground heat exchanger: A parametric study

Thermal performance of a single U-tube ground heat exchanger: A parametric study

Parametric analysis, response surface, sensitivity analysis, and optimization of a novel spiral-double ground heat exchanger

This paper proposes a novel spiral-double ground heat exchanger (GHX) that decreases conventional construction costs, facilitates installation, promotes heat transfer, and reduces thermal resistance. In this study, a new and effective installation procedure was proposed. Three-dimensional, transient, and conjugated finite volume simulations were conducted to compare the thermo-hydraulic performance of the traditional single U-tube and spiral GHXs with the proposed spiral-double GHX under two different flow rates. Moreover, a parametric analysis was conducted to study the impact of the design, operating, and geological parameters on the thermal performance of the new spiral-double GHX. Finally, surface response and sensitivity analyses, as well as optimization, were carried out using the ANSYS workbench. The comparison revealed that the spiral-double GHX yields higher thermal effectiveness (E) and heat transfer rate (Q) than single-U tubes GHX by 40.8% and 44.1%, respectively. In addition, it has a lower thermal resistance of 75.3% than the single-U tube GHX under turbulent flow conditions. Furthermore, the parametric study and sensitivity analysis concluded that the spiral radius has the most significant impact, followed by flow velocity, tube diameter, and pitch distance. Moreover, the recommended fluid velocity does not exceed 0.21 m/s, pitch distance of 0.0625 m, a spiral radius of 0.2 m, and grout conductivity of 2.1 W/m.K.

A simplified analytical model to predict heating performance of single U-tube ground heat exchangers

In underground U-tube heat exchangers (boreholes) it is important to predict its heating performance to design and select the proper parameters such as length, diameter, material etc. to have an optimized borehole from the point of view of heat capacity and economical aspects. For this reason, having trusty equations is vital to foresee borehole heating performance and applying it in design issues. In this study a single vertical U-tube borehole with constant wall temperature is considered and analytical equations for temperature distribution in the surrounding ground around the borehole is evaluated based on one and two dimensional heat conduction respectively. The analytical equation is compared to experimental data for a borehole with 50 m depth in which warm water of 40 C is pumped into it a time period of 120 hours and the heat transfer rate per unit length is recorded. The comparison between analytical expression and experimental data shows a good agreement between them. Also the borehole entropy generation number is studied and the optimized parameters are evaluated to minimize it. It is concluded that for the considered borehole, entropy generation number is decreased by increasing its length and by decreasing the borehole radius and pipe outer radius.

Parameters optimization of borehole and internal thermal resistance for single U-tube ground heat exchangers using Taguchi method

The borehole thermal resistance and internal thermal resistance are both the significant design factors for the ground heat exchanger (GHE). Careful design procedures are required for these two values to decrease GHE’s length and initial cost. In this study, the effects of eight parameters (flow rate, pipe size, borehole diameter, pipe-pipe distance, layered soil, grout thermal conductivity, pipe thermal conductivity, and borehole depth) on the value of borehole thermal resistance and internal thermal resistance are investigated. In order to implement the analysis, L32 orthogonal array has been established. An improved 3D numerical model with the four-resistance model is applied to calculate corresponding thermal resistances in all cases. Furthermore, the Taguchi method is carried out to obtain the optimal scenarios of parameters combination. Results using the optimal parameters set reveal 67.64% increase in the borehole thermal resistance and 148.29% decrease in the internal thermal resistance. The heat transfer performance can be enhanced by 9.63% at least, up to a maximum of 77.07%. The analysis of variance (ANOVA) technique is carried out lastly to figure out the relative importance of tested parameters. The results indicate that the pipe-pipe distance has the most significant impact on the borehole thermal resistance, whereas the flow rate and layered soil almost play no role in it. The pipe size and flow rate are important driving parameters in determining the internal thermal resistance while the layered soil and borehole diameter’s impact can be nearly neglected.

Experimental validation of a hybrid model for vertical ground heat exchangers under on-off operation conditions

This work presents an experimental validation of a two-dimensional hybrid model for vertical single U-tube ground heat exchanger. It is based on the use of the electrical analogy to model heat transfer within the borehole and thermal response factors (short and long time-step g-functions) to estimate heat flow to the surrounding ground. The substitution of ground nodes with short and long-term g-functions allows the simulation with short time steps keeping the possibility of simulating periods of several years. The model was experimentally validated by using reference data sets drawn from different tests at GeoCool plant, located at the Polytechnic University of Valencia (Spain). Validation process took into account the stop-start intervals of the geothermal heat pump operation. In a test of one week with 5-min time steps, model results agree very well with experimental data achieving RMSE values smaller than 1 °C for output fluid temperatures. The capability of the model to reproduce vertical distribution of borehole temperature was also studied. Furthermore, a comparison with the simulated results from a refined CFD model was made.

Performance analysis of helical ground heat exchangers with different configurations

Recently, various configurations especially single U-tube ground heat exchangers have been studied to improve the thermal performance of ground heat exchangers. Although helical ground heat exchangers generally have better thermal performance than the others, only two simple types of them, a helix with an internal outlet pipe and helix with an external outlet pipe have been studied in past years. So, the novelty of this paper is comparing eight new types of helical ground heat exchangers to a single U-tube heat exchanger in terms of heat exchange rate, pressure drop, thermal resistance, effectiveness, and thermal performance capability, in order to find the best one. The considered models have the same heat transfer area, and all numerical simulations are performed by commercial CFD software. The validation of the numerical simulations is done based on experimental results. The results indicated that the triple helix heat exchanger has considerably the best thermal performance compared with other ground heat exchangers. It followed by double helix and helix (W-tube) ground heat exchangers those which approximately have the same thermal performance. In general, it can be concluded that a single U-tube heat exchanger has the worst thermal performance and the minimum pressure drop in comparison with all helical ground heat exchangers.

An improved infinite composite-medium cylindrical source model for single U-tube ground heat exchanger

In this paper, a new heat transfer model for single U-tube ground heat exchanger is proposed. By considering the influence of U-tube heat capacity, an improved infinite composite-medium cylindrical source model is established to calculate the average fluid temperature, and then combined with a quasi-3D heat transfer model in borehole, the inlet and outlet fluid temperatures are derived as functions of average fluid temperature and the heat flow, therefore the inlet and outlet fluid temperatures of U-tube can be calculated. To verify the feasibility of the proposed model, it is applied to a sandbox experiment and compared to other models. The result shows that the inlet and outlet fluid temperatures calculated by the proposed model are accurate in the whole time period. Compared to other models, the inlet and outlet fluid temperatures calculated by the proposed model are in better agreement with the experimental data especially during short time, and the mean absolute percentage error, maximum absolute error, mean absolute error and root mean squared error are basically smaller. The mean absolute errors of the inlet and outlet fluid temperatures predicted are 0.11 °C and 0.09 °C, respectively, and the maximum absolute errors are less than 0.4 °C.

An Improved Thermal-Resistance-Capacitance Model for Vertical Single U-Tube Ground Heat Exchanger

Abstract Based on four-thermal-resistance-capacitance network within a borehole, an improved thermal-resistance-capacitance model (TRCM), which takes into account the effect of nonuniform temperature distribution along the borehole perimeter, is proposed for vertical single U-tube ground heat exchanger. For a given geometric and physical parameters of ground heat exchanger, the numerical simulations of the conventional TRCM based on three-thermal-resistance-capacitance network within borehole, the improved TRCM based on four-thermal-resistance-capacitance network within borehole and three-dimensional (3D) finite volume computational fluid dynamics (CFD) model by using fluent software were conducted, respectively. Through the comprehensive comparisons of simulation results between these above-mentioned three models for vertical single U-tube ground heat exchanger, it could be concluded that the proposed improved TRCM could not only provide relatively high accurate results, but also remarkably decrease the solving time as compared to the benchmark 3D finite volume CFD model. Since the proposed TRCM has better performance than the one based on three-thermal-resistance-capacitance network within borehole and 3D finite volume CFD model, a new reliable and feasible TRCM for vertical single U-tube ground heat exchanger could be available for the design and optimization of ground heat exchanger, the data interpretation of thermal response test (TRT) and other applications of ground heat exchanger in real industrial engineering.

Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers

Borehole thermal resistance is both an important design parameter and a key performance characteristic of a ground heat exchanger. Another quantity that is particularly important for ground heat exchangers is the internal thermal resistance between the heat exchanger pipes. Both these resistances can be calculated to a high degree of accuracy by means of the well-known multipole method. However, the multipole method has a fairly intricate mathematical algorithm and is thus not trivial to implement. Consequently, there is considerable interest in developing explicit formulas for calculating borehole resistances. This paper presents derivation and solutions of newly derived second-order and higher-order multipole formulas for calculating borehole thermal resistance and total internal thermal resistance of single U-tube ground heat exchangers. A new and simple form of the first-order multipole formula is also presented. The accuracy of the presented formulas is established by comparing them to the original multipole method. The superiority of the new higher-order multipole formulas over the existing formulas is also demonstrated.

Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers

The borehole thermal resistance – that is, the thermal resistance between the fluid in the U-tube and the borehole wall – is both a key performance characteristic of a closed-loop borehole ground heat exchanger and an important design parameter. Lower borehole thermal resistance leads to better system performance and/or lower total borehole length and possibly lower installation costs. Borehole thermal resistance may be determined using in situ thermal response testing, but for design purposes, it is important to be able to predict the borehole thermal resistance prior to installation. Due to the complexity of calculating it, numerous simplified methods have been proposed. This paper reviews published methods for calculating borehole thermal resistance for grouted boreholes with single U-tubes and compares their results against a rigorous analytical method.Another quantity that is particularly important for deep boreholes is the internal thermal resistance – that is, the thermal resistance between the upward-flowing and downward-flowing fluid paths in the borehole. Short-circuiting between the two legs has the effect of reducing the total heat transfer and can be quantified as an adjustment to the borehole thermal resistance, resulting in an effective borehole thermal resistance. A few simplified methods for calculating internal thermal resistance are compared against a rigorous analytical method.The simplified methods for calculating both borehole thermal resistance and internal thermal resistance are compared in parametric studies spanning the range of borehole diameters, pipe spacing, ground thermal conductivities and grout thermal conductivities found in practice. Many of the simplified methods work well with some combinations of parameters and poorly with others. The first-order multipole expressions are closed-form algebraic expressions that give results within 2% (for borehole thermal resistance) and 6% (for internal thermal resistance) over the entire range of parameters. This represents significantly better accuracy than any of the other simplified methods and, therefore, the first-order multipole algorithm is recommended for single U-tube applications when the tubes are symmetrically placed.

Numerical and experimental validation of a new hybrid model for vertical ground heat exchangers

A numerical and experimental validation of a new simplified model to simulate single U-tube ground heat exchangers is presented in this paper. The model is based on the use of the electrical analogy to model heat transfer within the borehole and thermal response factors (short and long time-step g-functions) to estimate heat flow to the surrounding ground. The substitution of ground nodes with short and long-term g-functions allows the simulation with short time steps, keeping the possibility of simulating periods of several years. The model has been validated experimentally by using the reference data sets drawn from two tests (constant heat input rate and interrupted tests) made under controlled laboratory conditions. The results have also been compared with the simulated data from a detailed Computational Fluid Dynamics model of the experimental system. A very good agreement has been observed for the modeled outlet fluid and borehole temperatures, with root mean square and relative error values smaller than 0.2°C and 0.3%, respectively.

A new RC and g-function hybrid model to simulate vertical ground heat exchangers

This paper presents a new hybrid two-dimensional model to simulate single U-tube ground heat exchangers based on the use of the electrical analogy to model heat transfer within the borehole and thermal response factors (short and long time-step g-functions) to estimate heat flow to the surrounding ground. Unlike other similar models, heat transfer equations are discretized only within the borehole domain, with two nodes for the fluid and two additional nodes for the grouting material, reducing the number of equations as ground temperature nodes are not considered. The substitution of ground nodes with short and long-term g-functions allows the simulation with short time steps keeping the possibility of simulating periods of several years. A complete analysis of the influence of characteristic parameters of the model in terms of the heat conduction path, vertical discretization level and equivalent heat capacity, has been carried out. The model shows a good performance for short simulation time-steps of five minutes for the prediction of both the short-term and long-term response. It has been successfully validated through comparison with a numerical computational fluid dynamic (CFD) reference model, achieving good RMSE values, which were smaller than 0.15 °C for water outlet temperature and borehole surface mean temperature.

Performance assessment of a simplified hybrid model for a vertical ground heat exchanger

A simplified model to simulate single U-tube ground heat exchangers is presented in this paper. The model is based on the electrical analogy to simulate heat transfer within the borehole and the use of thermal response factors (g-functions) to estimate injection–extraction heat flow to surrounding ground. The inclusion of two capacities for the heat carrier fluid and the grout material makes the model suitable for short time step simulations. The thermal resistance of the borehole has been changed considering different heat conduction paths. Several variants of the model have been validated through comparison with a refined computational fluid dynamic (CFD) reference model. Good results have been obtained for the different variables analysed (outlet temperature and surface borehole temperature). RMSE (Root Mean Squared Error) values were smaller than 1°C while relative errors were under 5%.

Study on Engineering Construction with Three-Dimensional Heat Transfer Modeling for Double U-Tube Heat Exchangers in Ground-Source Heat Pump Systems

There are many ground source heat pumps in engineering construction application. However, Research on heat exchanger models of single-hole buried vertical ground source heat pump mostly focuses on single U-tube ground heat exchangers other than double U-tube ones in China currently. Compared with single U-tubes, double U-tubes have the heat transfer particularity of asymmetry. Therefore, the use of the traditional single tube models would have large error in the simulation of the actual double U-tube heat exchangers. This paper frames a three-dimensional heat transfer model for the vertical single-hole buried double u-tube heat exchanger in a ground source heat pump system. The model considers the performance of U-bube material and uses a dual coordinate system and makes the control elemental volumes superimposed.

Single and double U-tube ground heat exchangers in multiple-layer substrates

The efficiency of ground-source heat pumps depends on the correct sizing of the associated ground heat exchangers (GHEs). Multiple ground layers with regard to GHE and the presence of more than one loops in each borehole (multiple U-tubes) are sparsely raised in the literature. Therefore the accurate prediction of the performance of the GHE under these conditions is of fundamental importance. A newly developed and validated model is applied to a multiple layer ground regime with different properties and the effect of the layer sequence on the outlet temperature is examined. The model is also modified to allow the study of a double U-tube GHE in a single borehole and the assessment of its efficiency with regard to its building cost. Various configurations are then compared to show that an in-series double GHE is the most efficient. The numerical model developed for energy flows and temperature changes in and around a borehole, when a fluid circulates through single and double U-tubes, is validated upon comparing its results with established experimental results for a single GHE. This model is an improvement of a previous one, based on the time-dependent convection–diffusion equation.

Effective Borehole Thermal Resistance of A Single U-Tube Ground Heat Exchanger

The effective borehole thermal resistance of a vertical, single U-tube ground heat exchanger is numerically studied. The nonuniform temperature distributions along the perimeter of both borehole and outside diameter of two pipes are taken into account to evaluate effective borehole thermal resistance. A best-fit correlation for effective borehole thermal resistance is proposed, and the dimensionless borehole thermal resistances are compared between the present correlation and other available equations in the literature. It is found that the present correlation of effective borehole thermal resistance is more accurate than those of available formulas.

New Correlations for Thermal Resistances of Vertical Single U-Tube Ground Heat Exchanger

A new 2D numerical model of a single U-tube ground heat exchanger is proposed and a four-thermal-resistance model is adopted to evaluate the effective pipe-to-borehole, pipe-to-pipe, and borehole-to-borehole thermal resistances. The influence of temperature distributions on both borehole surface and outer diameter of two pipes to these thermal resistances has been thoroughly studied. The best-fit correlations of effective pipe-to-borehole, pipe-to-pipe, and borehole-to-borehole thermal resistances are proposed and compared with the available equations in the literature. It is found that the present correlations of thermal resistances for ground heat exchanger are more accurate than those of available formulas. Furthermore, based on these obtained thermal resistance correlations, an analytical model is proposed to evaluate the heat transfer performance of the ground heat changer.