Double U-tube Borehole Heat Exchanger Research Articles

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.

Effects of the temperature distribution on the thermal resistance of double u-tube borehole heat exchangers

The effects of the surface temperature distribution on the thermal resistance of a double U-tube Borehole Heat Exchanger (BHE) are studied by finite element simulations. It is shown that the thermal resistance of a BHE cross section is not influenced by the bulk-temperature difference between pairs of tubes, but is influenced by the thermal conductivity of the ground when the shank spacing is high. Then it is shown that, if the real mean values of the fluid bulk temperature and of the BHE external surface are considered, the 3D thermal resistance of the BHE coincides with the thermal resistance of a BHE cross section, provided that the latter is invariant along the BHE. Finally the difference between the BHE thermal resistance and the effective BHE thermal resistance, defined by replacing the real mean temperature of the fluid with the average of inlet and outlet temperature, is evaluated in some relevant cases.

Finite-element analysis of the fluid temperature distribution in double U-tube Borehole Heat Exchangers

In the evaluation of Thermal Response Tests (TRTs) and in the design of Borehole Heat Exchanger (BHE) fields, the mean temperature of the fluid Tm is usually approximated by the arithmetic mean Tave of inlet and outlet temperatures. This approximation can yield errors in the estimation of the thermal conductivity of the ground, of the BHE thermal resistance, and of the heat pump performance. An expression for the evaluation of Tm has been proposed by Marcotte and Pasquier (Marcotte D, Pasquier P 2008, Renewable Energy, 33 2407) for single U-tube BHEs. In this paper, the difference between Tm and Tave is determined by 3D finite- element simulations for a typical double U-tube BHE in 6 unsteady working conditions. The results are validated qualitatively through an approximate analytical method, and show that the expression proposed by Marcotte and Pasquier underestimates the difference between Tm and Tave when applied to a typical double U-tube BHE. Therefore, new relations to evaluate this difference for double U-tube BHEs would be useful.

A spectral model for transient heat flow in a double U-tube geothermal heat pump system

This paper introduces a semi-analytical model based on the spectral analysis method for the simulation of transient conductive-convective heat flow in an axisymmetric shallow geothermal system consisting of a double U-tube borehole heat exchanger embedded in a soil mass. The proposed model combines the exactness of the analytical methods with an important extent of generality in describing the geometry and boundary conditions of the numerical methods. It calculates the temperature distribution in all involved borehole heat exchanger components and the surrounding soil mass using the fast Fourier transform, for the time domain; and the complex Fourier and Fourier-Bessel series, for the spatial domain. Numerical examples illustrating the model capability to reconstruct thermal response test data together with parametric analysis are given. The CPU time for calculating temperature distributions in all involved components, pipe-in, pipe-out, grout, and soil, using 16,384 FFT samples, for the time domain, and 100 Fourier-Bessel series samples, for the spatial domain, was in the order of 3 s in a normal PC. The model can be utilized for forward calculations of heat flow in a double U-tube geothermal heat pump system, and can be included in inverse calculations for parameter identification of shallow geothermal systems.

New g-functions for the hourly simulation of double U-tube borehole heat exchanger fields

A new method for the hourly simulation of fields of long BHEs (borehole heat exchangers) is presented, in dimensionless form. The method considers also the internal structure of the BHE, with reference to double U-tube BHEs. The analytical expressions of new g-functions (time evolutions of the dimensionless temperature, averaged along the BHE length, due to a uniform and constant heat load) are presented, which complement those reported in Zanchini E., Lazzari S., Energy 2013; 59: 570–80. The new g-functions yield the dimensionless temperature at the interface tubes-grout, and allow a more precise determination of the time evolution of the temperature of the operating fluid during hourly peak loads. Moreover, g-functions at the interface tubes-grout and at several radial distances are reported also for BHEs with a ratio 500 between length and diameter, a value not considered in the previous paper. Due to its higher accuracy, the new method is recommended for the hourly simulation and the optimization of ground-coupled heap pump systems with double U-tube BHEs.

Thermal performance and economic evaluation of double U-tube borehole heat exchanger with three different borehole diameters

This paper presents the results from experimental study of borehole heat exchangers (BHE) installed in a ground source heat pump (GSHP) system in Nuremberg, Germany. The BHE was constructed with 18 boreholes that can be grouped into three blocks: block I of 121mm, block II of 165mm and block III of 180mm. The operation of the GSHP system had been monitored between March 2009 and October 2012 for analysis. Over years of the system operation, the thermal performance of BHEs is observed to be slightly improved for larger borehole diameters (block II and III). For the comparison among the three blocks, thermal loads of block II is 1.64% and block III is 3.45% larger than that of block I, respectively. Furthermore, saving-to-investment ratio (SIR) is evaluated for two parts: the basic part (SIRI) for block I; the extra parts (SIRII-I, SIRIII-I) for block II and block III. Over a thirty-year period the SIR is estimated to be 4.80, 2.14 and 3.18 for SIRI, SIRII-I and SIRIII-I, respectively. These findings suggest that block I has the highest economic profitability. Based on these evaluations, the acceptable drilling costs for block II and block III are also analyzed and discussed.

Analysis of short helical and double U-tube borehole heat exchangers: A simulation-based comparison

This paper makes a comparative analysis between a helical-shaped pipe and a double U-tube ground heat exchanger. The two configurations were installed at a shallow depth and studied, since a depth limit is mandatory in some areas. When installed this way, the interaction between the ground surface and the ambient environment needs to be taken into account when the thermal behaviour of the ground heat exchangers is investigated.A detailed numerical simulation tool was used to carry out this research. The problem of heat transfer was solved with an equivalent electrical circuit of thermal resistances and capacitances. This simulation tool was also used on a double U-tube heat exchanger in order to include axial heat conduction in the ground and the borehole.The two borehole heat exchangers were analyzed over both long- and short-term periods; the thermal properties of the ground, energy loads and the axial effects of weather conditions were also taken into account. Finally, a reduction in the borehole length for the helical-shaped pipe was also assessed and compared with the performance of the double U-tube.

Long-term performance of large borehole heat exchanger fields with unbalanced seasonal loads and groundwater flow

The effects of groundwater flow on the long-term performance of large Borehole Heat Exchanger (BHE) fields with unbalanced winter and summer loads are studied, in a dimensionless form, by finite-element simulations implemented through COMSOL Multiphysics (©COMSOL AB). Peclet numbers in the range [0,0.8] are considered. First, two regular time periodic heat loads, with a period of one year, are considered, with either a partial compensation of winter heating and summer cooling or no compensation. In this part of the study, each BHE is sketched as a cylindrical heat source, and the following BHE field configurations, with a distance of 40 diameters between adjacent BHEs, are analyzed: a single line of infinite BHEs; two staggered lines of infinite BHEs; four staggered lines of infinite BHEs. Then, the effects of hourly peak loads are determined, for double U-tube BHEs, with reference to typical dimensionless daily heat loads, for winter heating and summer cooling. The ground is modelled as a Darcy porous medium. The results show that, in the range of Peclet numbers considered, the groundwater flow does not reduce the effects of hourly peak loads but yields an important improvement of the long-term performance.

Short time-step performances of coaxial and double U-tube borehole heat exchangers: Modeling and measurements

Several authors have investigated the long time-step performance of borehole heat exchangers. In that time scale, the borehole thermal capacitance is generally neglected, since the time span of interest is on the order of months or years. The borehole thermal capacitance consists both of grouting material and heat carrier fluid, and it mostly affects the short time-step behavior, when hourly or shorter time intervals are considered. Some models are available in the literature for short time-step simulations of borehole heat exchangers. In this article, short time-step analyses of coaxial and double U-tube heat exchangers are performed by means of numerical capacity resistance model. The capacity resistance model is compared with field measurements, analytical solutions available in the literature, and commercial software based on the finite-element method. Further comparisons between coaxial and common double U-tube heat exchangers are carried out by means of measurements performed in a suitable plant system. Furthermore, the series and parallel arrangements for double U-tube heat exchangers are investigated considering the borehole thermal capacitance.

Long-term performance of BHE (borehole heat exchanger) fields with negligible groundwater movement

Abstract The long-term performance of double U-tube BHE (borehole heat exchanger) fields is investigated by finite element simulations, performed through the software package COMSOL Multiphysics ( © COMSOL, Inc.), for grounds in which the effects of groundwater movement are negligible. Six time periodic heat loads with period of 1 year are examined, with either full compensation, or partial compensation or no compensation of winter heating with summer cooling. A single BHE surrounded by infinite ground and the following BHE field configurations are analyzed: a single line of infinite BHEs, two staggered lines of infinite BHEs, a square field of infinite BHEs. For each BHE field configuration, four different distances between adjacent BHEs and two values of the ground thermal conductivity are considered. The undisturbed ground temperature is assumed equal to 14 °C, and −5 °C is prescribed as the lowest allowed temperature for the working fluid. For each BHE field geometry, heat load and ground thermal conductivity, plots of the minimum annual value of the fluid temperature for a period of 50 years are reported, and the pairs “distance – heat load” which keep the fluid temperature above the prescribed limit are evidenced.

Efficient numerical modeling of borehole heat exchangers

This paper presents a finite element modeling technique for double U-tube borehole heat exchangers (BHE) and the surrounding soil mass. Focus is placed on presenting numerical analyses describing the capability of a BHE model, previously reported, to simulate three-dimensional heat transfer processes in multiple borehole heat exchangers embedded in a multi-layer soil mass, in a computationally efficient manner. Geothermal problems which require very fine meshes, of the order of millions of finite elements, can be simulated using coarse meshes, of the order of a few hundred to a few thousand elements. Accordingly, significant reduction of CPU time is gained, rendering the model suitable for utilization in engineering practice. A validation example comparing computed results with measured results is presented. Parametric analyses are also presented describing the possible utilization of the model for research works and design optimization.