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Just as the double-pipe heat exchanger is being utilized in an increasing number of applications, its research content is also deepening. For this paper, based on the air-conditioning cold and heat source project of a building in Handan, Hebei Province, a 300-meter medium-shallow well double-pipe heat exchanger was used for heating and cooling, and a corresponding heat transfer model was established. The changes of parameters such as the inlet and outlet temperature, heat exchange (with and without a temperature gradient), and borehole wall temperature distribution between a single borehole, double boreholes, and four boreholes over one year in medium-shallow wells were simulated and analyzed. By comparing the obtained experimental data and the simulation data, the accuracy of the heat transfer model was verified. This provides a theoretical basis for the further advancement of the project and lays the foundation for an in-depth study of multi-borehole double-pipe heat exchangers. [ABSTRACT FROM AUTHOR]

• A numerical heat transfer model of UGHE was developed. • A novel EBBC considering spectrally selective properties of ground was proposed. • The influence of precipitation on atmospheric transmittance was considered. • The thermal responses of UGHE with different GSBCs were compared. • The suggestions for employing appropriate GSBCs in different climate zones were given. To better understand the influence of ground surface boundary conditions (GSBC) on the thermal performances of U-shaped ground heat exchangers (UGHE), this study proposes a numerical model with one energy balance boundary condition (EBBC) considering the spectrally selective properties of ground. This study comprehensively discusses the effects of operation and design parameters on the thermal responses of various GSBCs and UGHE. Additionally, the geographical performances of the EBBC are compared. The main results indicate that implementing EBBC in UGHE reduces prediction errors for water and borehole wall temperatures, with a maximum decrease of 1.70 °C and 1.78 °C, respectively. Regarding the average water temperature, the variation induced by different GSBCs can be reduced by 51.0% as the borehole depth increases from 50 to 125 m. Similarly, the difference induced by different GSBCs can be reduced by 22.7%, with ground thermal conductivity decreasing from 3.0 to 1.5 W/(m · K). Based on the geographical analysis, the convective GSBC can be imposed on UGHE for engineering approximation in only temperate and tropical regions. For other climate regions, the use of EBBC is recommended. Finally, the sensitivity analysis results indicate that borehole depth is the most important dependent variable, followed by ground conductivity and volumetric heat capacity. [ABSTRACT FROM AUTHOR]

An energy pile with U-tubes is a special type of ground heat exchanger (GHE) formed by setting U-tubes into a concrete pile during the construction of building foundations. The parallel U-tubes increase heat transfer area, thereby improving energy pile performance. The analytical and numerical heat transfer models of U-tube energy piles are established in this study, considering homogenous and heterogeneous thermal properties of the pile and surrounding soil. Analytical solutions are obtained using the Laplace method and superimposition principle. The solutions of the analytical heat transfer model are verified using the numerical model with finite element method. The results provide a method for designing pile heat exchangers with U-tubes in parallel. • Develop numerical and analytical heat transfer models for energy pile with U-tube. • Obtain analytical solutions of the temperatures of the pile and soil. • The influence of different properties between pile and soil to thermal performance is analyzed. • The thermal effectiveness is defined and investigated by analytical model. [ABSTRACT FROM AUTHOR]

The development of ground source heat pump system (GSHP) is hindered by some factors such as high initial investment, difficult construction process of ground heat exchangers (GHEs) and imbalanced underground heat transfer. The heat transfer model of the GHEs is very complicated, and so many influential parameters are involved. The length of the buried pipe cannot be calculated by manual calculation. Accordingly, this paper mainly introduces the optimization design method of the hybrid GHSP system with the auxiliary gas source boiler, and the special software including software interface, internal algorithms and result analysis is developed. Both the practicality of hybrid ground source heat pump system with gas boiler and the reliability of the design simulation software are verified by the actual project. The results demonstrate that the gas boilers can effectively reduce the peak-load of the GHE, and therefore reduce the designed length of the buried pipe, solve the problem of underground thermal imbalance and improve the efficiency of the unit. Meanwhile, the software can simulate the operating conditions of the composite system for a long time, which can provide both theoretical support and technical guidance for both research and engineering application of the hybrid GSHP system in the future. [ABSTRACT FROM AUTHOR]

Liquid desiccant air conditioning (LDAC) system has been more and more widely used in some commercial and industrial buildings which require a relative lower humidity ratio of supply air. This paper mainly focuses on the investigation of the dehumidification performance of a cross-flow dehumidifier for an industrial plant. The theoretical model of the cross-flow dehumidifier is established based on the energy and mass conservation. The numerical solutions are obtained according to the finite difference method within the MATLAB environment. The influences of the different operation parameters and the dehumidifier geometric size on the dehumidification performance are analyzed and discussed for various operation conditions. The results show that the solution mass concentration has the most critical effect on the dehumidification performance, follows by the solution mass flow rate and air mass flow rate. The air temperature has little influence on the performance. [ABSTRACT FROM AUTHOR]

Energy pile is a novel ground heat exchanger (GHE) of ground source heat pump (GSHP) system, and the spiral coils are set into pile to form this type of GHE. However, the on-site heat transfer experiments combined with engineering projects are not much, and the corresponding validation of model is a little. This paper describes both heat transfer experiments and models of energy pile. During the experiments, some parameters of circulating fluid of spiral coils are recorded, and meanwhile the thermal resistors are installed at the pile’s surface to observe the temperature response induced by spiral coils. The heat transfer models of energy pile are explained and the corresponding characteristics are investigated. Afterwards, the comparisons between experimental data and model’s results are made to explore the differences, the difference is small and therefore the heat transfer models can be validated. Thus, the validation is a significant contribution and the model can provide guideline for project design; the research of the paper is helpful to promote further development of GSHP system. [ABSTRACT FROM AUTHOR]

This paper presents the analytical heat transfer models for the vertical ground heat exchangers (GHEs) and the attendant program named “GEOSTAR” developed for use in design and simulation of vertical GHEs. The program used spatial superposition for multiple boreholes and sequential temporal superposition principles to account for time-varying loads. Coupled with the models of the heat pump and building loads, the GEOSTAR can predict time-varying heat pump energy consumption, heat transfer rates of GHEs, and other variables of interest. Finally, the program is applied to design an existing GCHP project and to simulate the system performance. The results demonstrate the usefulness of the simulation model and attendant program as a tool for designing GCHP systems. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the transient heat conduction around the buried spiral coils which could be applied in the ground-coupled heat pump systems with the pile foundation as a geothermal heat exchanger. A transient ring-coil heat source model is developed, and the explicit analytical solutions for the temperature response are derived by means of the Green’s function theory and the image method. The influences of the coil pitch and locations are evaluated and discussed according to the solutions. In addition, comparisons between the ring-coil and cylindrical source models give that the improved finite ring-coil source model can accurately describe the heat transfer process of the pile geothermal heat exchanger (PGHE). The analytical solutions may provide a desirable and better tool for the PGHE simulation/design. [Copyright &y& Elsevier]

• An analytical model for heat transfer inside deep borehole heat exchangers (DBHE). • Convolution theorem to address vertically increasing borehole wall temperature. • Relationships between DBHE thermal performance and various parameters. • An effective tool fast and easy enough for the design and optimization of DBHE. Deep borehole heat exchangers (DBHE) provide an effective solution for ground coupled heat pump (GCHP) systems in cold climate region where heating is dominant. Concerning the analytical heat transfer models, the simplification that borehole wall temperature is constant along the depth of ground heat exchangers (GHE) which the existing quasi-three-dimensional models have assumed in the application of shallow borehole GHE, can no longer be accepted in the application of DBHE due to the geothermal gradient in deep ground. Making this simplification cannot give the real temperature distribution of circulating fluid along the depth of DBHE. Therefore, this paper developed a new analytical model for DBHE with coaxial pipes by successfully addressing the increasing borehole wall temperature using the convolution theorem, so that the widely employed quasi-three-dimensional models for shallow borehole GHE is extended for DBHE with coaxial pipes for the first time. The new analytical model is validated by comparing with an existing numerical model. Using the newly developed analytical model, the trends revealing the relationships between thermal performance of DBHE and various parameters are firstly plotted. Because of the high accuracy and quick calculation, this new analytical model can be used as a benchmark for numerical models. More importantly, the proposed analytical model can be an effective tool for the design and optimization of DBHE, since current numerical models are always calculation-demanding, time-consuming and difficult for engineers and designers to use. Also, the method this paper proposed to address the varying borehole wall temperature can certainly be employed to improve the existing quasi-three-dimensional models for shallow borehole GHE so that they can be applicable in some other cases, for example, GHE installed in layered soils, or affected by underground seepage flow in partial depth. [ABSTRACT FROM AUTHOR]

Horizontal geothermal heat exchangers (HGHEs) with vertical spiral coils have been increasingly used in ground source heat pump (GSHP) systems. Research studies have been conducted using field tests and simulations trying to reveal the heat transfer mechanism of HGHEs with vertical spiral coils and to provide a good heat transfer performance. However, there is no analytical solution has been established for HGHEs with vertical spiral coils. Of particular interest is the temperature variation at the soil surface. The study presented in this paper proposes the development of a mathematical vertical ring-coil model used to describe the heat transfer process of HGHEs with vertical spiral coils. In this new model, the spiral heat exchanger is simplified as a series of ring coils that inject/extract heat in/from a semi-infinite medium. A single ring model in an infinite medium is first introduced. Using images and superposition, a multiple ring-coils analytical solution is then given. The significant influence on the heat transfer performance of HGHEs temperature variation of the ground surface is then considered. A periodically changed boundary condition is being taken into consideration in the modeling process. The validity of the model was examined by a field test and a 3-D simulation model. The analytical solutions may provide a desirable and better tool for the simulation/design HGHEs with vertical spiral coils. [ABSTRACT FROM AUTHOR]

This paper presents a new transient analytical model for describing the heat transfer process of pile geothermal heat exchangers with spiral coils (PGHE-SC). A numerical model has been established based on the finite element method to validate this new analytical model, which shows a good agreement between the two models. The temperature responses for different heat transfer conditions were calculated and are discussed. When the thermal conductivities of pile is twice as the one of soil, the dimensionless temperature at middle of the pile is 0.3832 which almost twice as the temperature response of homogeneous case. The results indicate that the thermal difference between pile and soil is an important factor influencing PGHE-SC simulation/design. As this new model not only successfully takes the limited length of an energy pile into consideration but also distinguishes thermal properties in its modeling process, it may provide a desirable and better design tool for the PGHE-CS. [ABSTRACT FROM AUTHOR]

This paper presents a new spiral source heat transfer model for simulating the heat transfer performance of pile foundation ground heat exchangers (GHEs) with existence of groundwater transfusion. The model takes heat conduction and convection of groundwater into account and is more accurate than those previously proposed such as solid cylindrical model and ring-coil model to describe the heat transfer behavior. Besides, some shortages and deficiencies are improved and overcome, especially in terms of the configuration of spiral heat transfer tubes. The analytical solutions of the model are obtained to exhibit the temperature response at any point in the underground medium around the pile foundation GHEs. The parameters that exert impacts on the heat transfer process has been investigated and discussed in the paper. The pure conduction case and combined heat transfer case are compared, and the heat exchange efficiency between the pile foundation GHEs and surrounding medium can be improved as a result of the influence of groundwater transfusion. The meliorative effect is becoming increasingly evident with time or velocity of groundwater. The research contributes to more understanding of the potential for pile foundation GHEs and the degrees which the heat transfer efficiency affected by groundwater flow. [ABSTRACT FROM AUTHOR]

Aimed at applications in ground-coupled heat pump and thermal energy storage systems, this paper presents a heat transfer model of a deep borehole cluster, taking into account the geothermal gradient in the subsurface and the real connection conditions of the two regions inside and outside the borehole. The superposition principle is proven valid in a mathematical sense for such models in certain conditions, and the three-dimensional heat conduction problem for a multi-borehole heat exchanger may be decomposed into a number of two-dimensional single-borehole problems. Then, a new dimension reduction algorithm is proposed for simulation of heat transfer in the deep borehole cluster. Using this algorithm, comparisons with other commercial model and simulations on example cases show that computational efficiency can be improved by orders of magnitude compared with traditional three-dimensional software. • A new heat transfer model of a deep borehole cluster was developed. • The geothermal gradient and connection conditions on boreholes were considered. • The superposition principle was proven valid on the boundary of the borehole walls. • A dimension reduction algorithm was proposed for a deep borehole cluster. • The proposed model has a high computational efficiency. [ABSTRACT FROM AUTHOR]

An increasing number of high-rise buildings are being designed, enabling the use of pile foundation to also act as ground heat exchangers (GHEs) of ground source heat pumps (GSHPs). These so-called energy piles include heat exchange pipes already cast into the pile foundation to produce a new type of GHE. Groundwater seepage, by means of advection, plays an important role in improving the heat transfer performance of energy pile. Existing research has studied heat transfer mechanism of energy pile when groundwater is considered to flow in one direction only, and in two directions also. No studies, however, have been introduced explaining the effects of three-dimensional (3-D) groundwater seepage (i.e. in three directions) on the heat transfer between pile and underground medium. This paper presents a new mathematical model about the heat transfer of energy pile with 3-D groundwater seepage, whereby the analytical temperature responses solutions induced by both infinite and finite models are obtained. Comparisons between pure conduction and combined heat transfer were made, and the temperature distributions in a 3-D seepage environment are explained. In addition, the characteristics involved in the new model were explored and then the factors exerting influence on heat transfer are described. The 3-D groundwater seepage is more advanced and realistic, and the research described in this paper is usefully relevant to promoting the development of energy piles of GSHP. [ABSTRACT FROM AUTHOR]

This study investigates the effect of heat storage in the non-heating season on the heat extraction capacity and the economy of heat storage in a coaxial borehole mid-deep borehole heat exchanger (MBHE). A heat transfer model of the MBHE containing heat extraction and storage modes is presented and validated using experimental data reported in the literature; the results show that the established model has high accuracy. The effects of the operation time, annual heat storage time, inlet temperature of heat storage fluid, and heat storage fluid flow rate on the heat extraction capacity of the MBHE and the ground temperature are studied, and the economy of heat storage is analyzed. The results show that long-term heat storage can significantly improve the heat extraction capacity of the MBHE. Furthermore, heat storage can improve the heat extraction capacity of the MBHE only when the inlet temperature of heat storage fluid is greater than the critical heat storage temperature. The increase in the annual heat storage time, inlet temperature of the heat storage fluid, and heat storage fluid flow rate can improve the heat extraction capacity of the MBHE. The heat extraction capacity of the MBHE increases approximately linearly with the increase of the inlet temperature of the heat storage fluid; moreover, the MBHE heat extraction capacity increases with the increase in the annual heat storage time and the heat storage fluid flow rate, but the heat extraction capacity increase rate gradually decreases. The higher the inlet temperature of the heat storage fluid, the better the heat extraction capacity of the MBHE. The recommended annual heat storage time range and fluid flow rate ranges are 3–4 months and 4–6 kg/s, respectively. [ABSTRACT FROM AUTHOR]

A model is proposed to analyze the heat transfer of deep borehole heat exchanger (DBHE)arrays. Based on this, a dimension reduction algorithm is proposed for the numerical simulation of heat transfer of DBHE arrays, which can improve calculation speed by several orders of magnitude compared with that by the CFD software. An index of heat extraction capacity (HECI) is adopted to evaluate the heat extraction capacity of DBHE arrays. The influence of borehole spacing, operation time, annual heating duration, terrestrial heat flow rate, borehole depth, soil thermal parameters, pipe diameter and circulating fluid flow rate on DBHE array heat extraction capacity and its attenuation are analyzed. The results show that the borehole spacing, operation time, and annual heating duration all have apparent influence on DBHE array heat extraction capacity and its attenuation rate, while the others only have apparent influence on the heat extraction capacity. According to the calculation results, when the DBHE arrays have a service lifetime of 20–50 years, the recommended borehole spacing range is 40–70 m. • The heat transfer model of deep borehole heat exchanger (DBHE) arrays in cylindrical coordinate system is established. • The calculation speed of the model is several orders of magnitude faster than Ansys Fluent. • An index (HECI) is prosed to evaluate the heat extraction capacity of DBHE. • Borehole spacing, annual heating duration and total operation time significantly affect HECI and its attenuation. • When the DBHE arrays have a service lifetime of 20–50 years, the recommended borehole spacing range is 40–70 m. [ABSTRACT FROM AUTHOR]

The effect of groundwater flow on the heat transfer performance of pile geothermal heat exchanger (PGHE) with spiral coils was simulated by a 3-D simulation model using finite element method. Different groundwater flow conditions were taken into consideration by applying different hydraulic gradients. Based on the moving ring-coils model and simulation results, an improved analytical model is developed by introducing a key parameter of effective dimensionless velocity. The calculation results shows that the improved model can better describe the heat transfer performance of PGHE with spiral coils. Both numerical and analytical results indicated that the groundwater flow has an enhancing effect on the heat transfer performance of the PGHE with spiral coils and can accelerate the heat transfer process into stability. When the groundwater flow mean velocity equal to 6.98E−06 m/s, the amount of heat exchange is higher than 26.72% than it of non-advection situation. The improved ring-coils analytical model can be used as a reliable tool for the design of pile geothermal heat exchanger with spiral coils under groundwater flow. [ABSTRACT FROM AUTHOR]

Highlights: [•] Investigate the temperature response when groundwater seepage exists. [•] Discuss the influence which every parameter exerts on the whole process. [•] Make comparisons between pure conduction and combined heat exchange. [•] Illustrate the significance of groundwater seepage. [ABSTRACT FROM AUTHOR]

Abstract: The uniform dispersion of carbon nanotubes (CNTs) in poly(ethylene terephthalate) (PET) was achieved by the liquid bisphenol A bis(diphenyl phosphate) (BDP) assisted pre-dispersion melt mixing. Most of the CNTs existed in a filamentous stretched state and a percolation threshold was achieved at 0.28 vol.% CNTs. In addition, the uniformly dispersed CNTs, acting as a framework to support the char produced by the oxidation of the PET and BDP, inhibited the vigorous bubbling process during combustion. The char adhering to the CNTs lowered their heat-transfer efficiency and made the CNT network layer more compact. Thus, the flame-retardant property was significantly improved since the network layer consisted of CNTs and chars, acting as a heat shield, more effectively reduced the exposure of the PET resin to the external air and heat feedback of the heat flux. [Copyright &y& Elsevier]

• Coaxial pipe and U-type deep borehole heat exchangers (BHEs) are analyzed and compared. • The comparison shows that U-type BHEs have a much better performance. • The effects of several parameters on the heat extraction rate are evidenced. • The temperature changes in space and time of circulating fluid and rock soil are studied. This paper discusses the advantages of medium-deep geothermal energy and describes the structural principles of coaxial pipe and U-type deep borehole heat exchangers (BHEs). The heat transfer performances of the two types of deep BHEs are compared. The preconditions and heat transfer mechanism are explained to reveal the substance of heat transmission. Energy equations are established for circulating fluid, grout, steel pipe and underground media, and the implications of related parameters are discussed. The heat transfer performances of deep BHEs are analyzed, the heat extractions and the temperatures of circulating fluid and rock soils are investigated, and related elements influencing these parameters are explored. Therefore, the changes of heat absorption or temperatures with the correlative elements are shown, and comparisons are made to demonstrate the differences of the two types of deep BHEs. The heat transfer performance of a U-type deep BHE is better than that of a coaxial pipe deep BHE. The comparative analysis of coaxial pipe and U-type deep BHEs enables the selection of BHEs according to a project's actual situation. This is beneficial to the rational utilization of medium-deep geothermal energy, and it promotes the development of heating technology used in geothermal energy applications. [ABSTRACT FROM AUTHOR]

The paper describes a U-type deep borehole heat exchanger (DBHE) containing both two vertical boreholes and one horizontal boreholes for the application of medium-deep geothermal energy, the circulating fluid flows through every borehole in turn and therefore more underground heat can be absorbed. The boreholes are called as descending, horizontal and ascending boreholes, and the heat transfer tubes in the corresponding boreholes are called as descending, horizontal and ascending tubes, respectively. The backfill grout is set between borehole wall and the corresponding tube. The characteristics and the working principles of the U-type DBHE are discussed. The governing equations of heat transfer are established, and the numerical finite difference methods are employed to build the node equations for both the fluids in the heat transfer tubes and the underground medium, and the pursuit method is taken into consideration to obtain the temperatures used in the node equations. In addition, An actual project that uses U-type DBHE to heat the buildings was investigated. The research work can promote the further development and application of medium-deep geothermal heating technology. [Display omitted] • Describe the structural composition and working principle of borehole heat exchanger. • Explain the governing equations and the corresponding conditions. • Establish the node equations for fluid of tubes. • Establish the node equations for underground rock soil. • Investigate the change of important parameters of one actual project. This paper describes a U-type deep borehole heat exchanger (DBHE) containing both two vertical boreholes and one horizontal boreholes for the application of medium-deep geothermal energy, and presents the heat exchanger's characteristics and the working principles. Compared with the single DBHE, the ability of the U-type DBHE to extract underground energy is better, and therefore a higher heating load of buildings can be assumed. First, the preconditions are explained, and the governing equations of heat transfer are established. Second, the numerical finite difference methods are employed to build the node equations for both the fluids in the heat transfer tubes and the underground medium. In addition, the pursuit method is taken into consideration to obtain the temperatures used in the node equations. Accordingly, the temperatures of the different locations in both the tubes and the underground medium can be acquired. Finally, one actual project is studied based on the models and the corresponding equations; the nominal heat absorption is analyzed, and the factors that exert an influence on it are discussed; the inlet and outlet temperatures of the circulating fluid in vertical and horizontal boreholes are investigated, and then, the temperatures of the underground medium at typical locations near the DBHEs are explored. The research results for the U-type DBHEs are beneficial to the improvement of heat transfer models of medium-deep geothermal energy, and they promote the development of heating technology used in geothermal energy applications. [ABSTRACT FROM AUTHOR]