Short time step analysis of vertical ground-coupled heat exchangers: The approach of CaRM

In this paper an improvement of the model CaRM (CApacity Resistance Model) is presented to consider the borehole thermal capacitance, both of the filling material of the borehole and of the heat carrier fluid inside the ground heat exchanger. Several models, numerical and analytical, are available in literature for short time step analyses of ground-coupled heat pump systems. According to the modelling for the surrounding ground, the new approach for the inside of the borehole is based on electrical analogy. In this study the double U-tube ground heat exchanger is analyzed. The new model has been validated by means of a commercial software based on the finite elements method as well as measurements of ground response test, using a suitable plant system. In this last comparison, the contribution of the thermal capacitance of the circulating fluid is investigated, since it is frequently neglected in short time step simulations. In both cases, there is agreement between the CaRM results and data from numerical simulations and measurements as well.     

A review of methods to evaluate borehole thermal resistances in geothermal heat-pump systems

In the design of a ground-source heat pump (GSHP) system, the heat transfer from the fluid to the ground is influenced by the thermal borehole resistance between the fluid and the borehole surface and also by the interference resistance between the two (or four) pipes inside the borehole. Several authors have proposed empirical and theoretical relations to evaluate these resistances as well as methods to evaluate them experimentally. The paper compares the different approaches and proposes good practice to evaluate the resistances. The impact of the different approaches on the design of heat exchanger is also examined. Two-dimensional and fully three-dimensional numerical simulations are used to evaluate the different methods. A new method is also proposed to evaluate the borehole resistances from in situ tests.     

New solutions for the short-time analysis of geothermal vertical boreholes

Many models, either numerical or analytical, have been proposed to analyse the thermal response of vertical heat exchangers that are used in ground coupled heat pump systems (GCHP). In both approaches, most of the models are valid after few hours of operation since they neglect the heat capacity of the borehole. This is valid for design purposes, where the time of interest is in the order of months and years. Recently, the short time response of vertical boreholes became a subject of interest. In this paper, we present a new analytical approach to treat this problem. It solves the exact solution for concentric cylinders and is a good approximation for the familiar U-tube configuration.     

An in situ thermal response test for borehole heat exchangers of the ground-coupled heat pump system

Thermal response tests (TRTs) are crucial for the estimation of the ground thermal properties and thermal performance of the borehole heat exchanger (BHE) of the ground-coupled heat pump (GCHP) system. In this article, a TRT apparatus was designed and built to measure the temperature response of inlet and outlet sections of BHE in the test borehole, the apparatus can effectively operate under both constant heating flux modes and heat injection and extraction modes with a constant inlet temperature. A TRT for a project of GCHP located in the Jiangsu province of China was carried out by the experimental apparatus. Based on the experimental data, the heat transfer performances of BHE under heating and cooling modes were evaluated, and the ground thermal properties, which include the ground thermal conductivity, ground volumetric specific heat, borehole thermal resistance and effective soil thermal resistance, were determined by the line source model. The results indicate that the experimental device and analysis model proposed in this article can be effectively applied to estimate the ground thermal properties and thermal performance of BHE. During the process of thermal response of ground, the fluid temperatures vary acutely at the start-stage of 8 h, and then tend to be a steady state after 40 h. The test data during the start-stage should be discarded for improving the estimation accuracy of ground thermal properties. At the same time, the effective soil thermal resistance increases continuously with time and a steady-state value would be reached after the start-time, and this steady-state thermal resistance can be used to evaluate the required length of BHE. In addition, the heat transfer rate of the BHE under different operating conditions can be used for the further evaluation on long-term operation performance of GCHPs.     

Borehole temperature evolution during thermal response tests

The measurement of temperature inside a borehole at specified depths during a thermal response test, used to infer the subsurface and the borehole thermal properties for the design of a ground-coupled heat pump system, allows the correlation of the subsurface thermal conductivity with stratigraphy. The temperature signal measured in the borehole during heat injection in a ground heat exchanger made with a single U-pipe, however, depends on the location of the temperature sensor in the borehole, which is difficult to determine in practice. Two-dimensional numerical simulations of the borehole temperature evolution during thermal response tests show that the temperature inside the borehole homogenizes rapidly after heat injection is stopped. Monitoring temperature recovery consequently helps to analyze measurements conducted at depth inside the borehole, since recovery measurements are not significantly influenced by the position of the sensor in the borehole. Numerical simulations also indicate that the borehole thermal resistance is best determined using a combination of recovery and heat injection data.     

A computational capacity resistance model (CaRM) for vertical ground-coupled heat exchangers

Several models are available in literature to simulate ground heat exchangers. In this paper an approach based on electrical analogy is presented, for this reason named CaRM (CApacity Resistance Model). In some cases several information are needed during design: both the borehole and the surrounding ground are affected by thermal exchange. The model here presented allows to consider the fluid flow pattern along the classical vertical ground heat exchangers as a single U-tube, a double U-tube or coaxial pipes. Besides, ground temperature at different distances from borehole are calculated, taking into account also the thermal interference between more boreholes. Starting from the supply temperature to the heat exchanger, the outlet fluid temperature is calculated and the ground temperature in each node, step by step. The model has been validated by means of a commercial software based on the finite differences method. Further comparisons have been carried out against data from a ground thermal response test and from the survey of an office building equipped with a ground coupled heat pump and vertical double U-tube heat exchangers. The agreement of results validates the model here presented.     

Unit-response function for ground heat exchanger with parallel,series or mixed borehole arrangement

A novel approach is presented that allows to predict fluid temperatures entering a Ground Heat Exchanger (GHE) for parallel, series and mixed arrangements of boreholes. The method determines at each time step the heat transfer rates occurring at each borehole so as to reproduce the fluid temperature at the GHE inlet for a specific borehole arrangement. The analytical finite line source model is used to compute the borehole wall temperatures, whereas the fluid temperatures are assumed to vary linearly along the pipes. The method requires to solve a linear system of equations at a small number of time steps. The different systems of equations for each arrangement are determined. A comprehensive 3D finite element numerical model shows good agreement with the computed fluid temperatures. The proposed approach is computationally very efficient. The fluid temperature unit response function can be convolved with any desired heat load to estimate fluid temperatures at the GHE inlet for a wide variety of scenarios.     

A two-region simulation model of vertical U-tube ground heat exchanger and its experimental verification

Heat transfer around vertical ground heat exchanger (GHE) is a common problem for the design and simulation of ground coupled heat pump (GCHP). In this paper, an updated two-region vertical U-tube GHE analytical model, which is fit for system dynamic simulation of GCHP, is proposed and developed. It divides the heat transfer region of GHE into two parts at the boundary of borehole wall, and the two regions are coupled by the temperature of borehole wall. Both steady and transient heat transfer method are used to analyze the heat transfer process inside and outside borehole, respectively. The transient borehole wall temperature is calculated for the soil region outside borehole by use of a variable heat flux cylindrical source model. As for the region inside borehole, considering the variation of fluid temperature along the borehole length and the heat interference between two adjacent legs of U-tube, a quasi-three dimensional steady-state heat transfer analytical model for the borehole is developed based on the element energy conservation. The implement process of the model used in the dynamic simulation of GCHPs is illuminated in detail and the application calculation example for it is also presented. The experimental validation on the model is performed in a solar-geothermal multifunctional heat pump experiment system with two vertical boreholes and each with a 30 m vertical 1 1/4 in nominal diameter HDPE single U-tube GHE, the results indicate that the calculated fluid outlet temperatures of GHE by the model are agreed well with the corresponding test data and the guess relative error is less than 6%.     

Computer simulation of borehole ground heat exchangers for geothermal heat pump systems

Computer simulation of borehole ground heat exchangers used in geothermal heat pump systems was conducted using three-dimensional implicit finite difference method with rectangular coordinate system. Each borehole was approximated by a square column circumscribed by the borehole radius. Borehole loading profile calculated numerically based on the prescribed borehole temperature profile under quasi-steady state conditions was used to determine the ground temperature and the borehole temperature profile. The two coupled solutions were solved iteratively at each time step. The simulated ground temperature was calibrated using a cylindrical source model by adjusting the grid spacing and adopting a load factor of 1.047 in the difference equation. With constant load applied to a single borehole, neither the borehole temperature nor the borehole loading was constant along the borehole. The ground temperature profiles were not similar at different distances from the borehole. This meant that a single finite difference scheme was not sufficient to estimate the performance of a borefield by superposition. The entire borefield should be discretized simultaneously. Comparison was made between the present method and the finite line source model with superposition. The discrepancies between the results from the two methods increased with the scale of borefield. The introduction of time schedule revealed a discrepancy between the load applied to the ground heat exchanger and that transferred from the borehole to the ground, which was usually assumed to be the same when using analytical models. Hence, in designing a large borefield, the present method should give more precise results in dynamic simulation.     

Validity ranges of three analytical solutions to heat transfer in the vicinity of single boreholes

In ground-coupled heat pump systems, accurate prediction of transient ground heat transfer is important to establish the required borehole length and to determine precisely the resulting fluid temperature. Three analytical solutions to transient heat transfer in the vicinity of geothermal boreholes are presented. These solutions are referred to as the infinite line source (ILS), the infinite cylindrical source (ICS) and the finite line source (FLS) models, which vary in complexity and are based on simplifications of the borehole geometry. The results of these models are compared and their validity domains are determined.     

Heat extraction thermal response test in groundwater-filled borehole heat exchanger – Investigation of the borehole thermal resistance

In groundwater-filled borehole heat exchangers (BHEs) convective flow influences the heat transfer in the borehole. During heat extraction thermal response tests (TRTs) the effect of the changing convective flow is more dominant than during heat injection tests. Water is heaviest around 4 °C and when exceeding this temperature during the test, the convective flow is stopped and restarted in the opposite direction resulting in a higher borehole thermal resistance during that time. Just before 0 °C the convective flow is the largest resulting in a much lower borehole thermal resistance. Finally, during the freezing period phase change energy is released and material parameters change as water is transformed into ice, resulting in a slightly higher borehole resistance than at a borehole water temperature of 0 °C. The changes in borehole thermal resistance are too large for ordinary analysis methods of thermal response tests to work. Instead another method is introduced where the borehole thermal resistance is allowed to change between different time intervals. A simple 1D model of the borehole is used, which is matched to give a similar mean fluid temperature curve as the measured one while keeping the bedrock thermal conductivity constant during the whole test. This method is more time-consuming than ordinary TRT analyses but gives a good result in showing how the borehole thermal resistance changes. Also, a CFD-model with a section of a simplified borehole was used to further study the effect of convection and phase change while the temperature was decreased below freezing point. The test and the model show similar results with large variations in the borehole thermal resistance. If the knowledge of changing borehole thermal resistance was used together with a design program including the heat pump and its efficiency, a better BHE system design would be possible.     

热响应测试在土壤热交换器设计中的应用

分析了土壤热交换器系统的影响因素以及设计与施工中存在的问题,介绍了自主研制的移动式地源热响应测试装置原理与构成。针对天津市某地源热泵项目,阐述了热响应测试的方法与步骤,得到了项目所在地的无干扰地温以及地埋管系统的供回水温度响应曲线。利用线源理论,得到了地埋管换热器钻孔的导热系数及热阻,分析了测试装置与环境的热损失和热增益、测试时间、供电稳定性、无干扰地温、不同深度土壤热导率的变化以及地下水流动对热响应测试造成的影响。测试结论对于指导土壤热交换器设计与施工具有一定的参考价值。     

Reference data sets for vertical borehole ground heat exchanger models and thermal response test analysis

Ground source heat pump systems often use vertical boreholes to exchange heat with the ground. Two areas of active research are the development of models to predict the thermal performance of vertical boreholes and improved procedures for analysis of in situ thermal conductivity tests, commonly known as thermal response tests (TRT). Both the models and analysis procedures ultimately need to be validated by comparing them to actual borehole data sets. This paper describes reference data sets for researchers to test their borehole models. The data sets are from a large laboratory “sandbox” containing a borehole with a U-tube. The tests are made under more controlled conditions than can be obtained in field tests. Thermal response tests on the borehole include temperature measurements on the borehole wall and within the surrounding soil, which are not usually available in field tests. The test data provide independent values of soil thermal conductivity and borehole thermal resistance for verifying borehole models and TRT analysis procedures. As an illustration, several borehole models are compared with one of the thermal response tests.     

A matrix approach for steady-state simulation of heat exchanger networks

A steady-state simulation scheme for heat exchanger networks is presented. This proposal is based on a matrix approach composed by linear equations where network connectivity is addressed in the model explicitly using graph theory. The structure of the algorithm is flexible allowing the inclusion of the evaluation of heat transfer coefficients, physical properties variation in relation to temperature and pseudo-stationary simulations. The application of the proposed scheme is illustrated by the simulation of a heat exchanger network during a certain period considering the fouling rate.     

深层地埋管换热器换热性能模拟及稳定性研究

以深层地源热泵地埋管换热器为研究对象,对其换热特性进行数值模拟和实验研究。建立考虑轴向地温梯度的深层地埋管换热器传热模型并进行模拟计算,通过示范工程现场测试数据验证该模型的正确性。对深层地埋管换热器换热的性能稳定性进行研究,发现深层地埋管换热器连续长期运行及间歇长期运行下换热性能基本稳定。当按不同运停比运行时,岩土温度恢复效果良好。研究结果表明深层地源热泵有较好的换热性能及运行稳定性,为深层地热能的开发利用提供了新思路。     

Extremum seeking control for efficient operation of hybrid ground source heat pump system

The Hybrid Ground Source Heat Pump (GSHP) systems combine the renewable geothermal energy and cooling tower for rejecting the cooling load, which is often adopted for high cooling demand. Model based control can be limited due to variations in ambient conditions, ground-loop heat exchanger (GHE) and equipment characteristics, cost and reliability of sensors. A self-optimizing control scheme is proposed for efficient operation of the hybrid GSHP based on Extremum Seeking Control (ESC), with feedback of the total power consumption and the control inputs of the relative flow rate of cooling tower and the water pump speed. The cooling capacity of the heat pump regulates the evaporator leaving water at 7 °C. A Modelica based dynamic simulation model is developed for a Hybrid GSHP system, with the vertical GHE model adopted from Modelica Buildings Library. The transient heat transfer is implemented with a finite volume method inside and outside the borehole. The proposed ESC scheme is evaluated under the scenarios of fixed cooling load, ramp change in the evaporator inlet water temperature, diurnal sinusoidal cycle of air wet-bulb temperature, and realistic ambient and cooling load condition. Simulation results show the proposed ESC strategy effectively achieves nearly optimal efficiency without the need for plant model.     

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.     

同轴地埋管换热器岩土热响应试验研究

岩土热物理性质是影响地源热泵系统设计和运营的关键因素,对位于武汉市洪山区的2口不同深度的同轴地埋管换热孔分别进行48 h的热响应试验,并对同轴地埋管换热器内外管之间环形空间中的平均流体温度进行测试.根据同轴地埋管换热器的几何特性,以简便实用的方式测量同轴地埋管换热器环状空间传热流体的平均温度,结合同轴地埋管换热器钻孔热...     

Model reduction by the Modal Identification Method in forced convection: Application to a heated flow over a backward-facing step

This numerical study focuses on the use of the Modal Identification Method to build reduced models for problems of heat convection and diffusion. The principle is to minimize a cost function based on the difference between the outputs (velocity and/or temperature) of a detailed model and the outputs of a reduced one. The reduced model structure is defined from the partial differential equations governing fluid mechanics and heat transfer in the physical system. In this paper, an advection–diffusion problem is studied: forced heat convection is considered with an incompressible, stationary, laminar 2D flow. Physical properties of the fluid are temperature independent, hence velocity is independent of temperature. The system under consideration is a channel flow over a backward-facing step with a time-varying heat flux density applied upstream of the step. Three types of reduced models have been investigated: steady fluid mechanics only, unsteady heat transfer for a given constant Reynolds number, and unsteady heat transfer for any constant Reynolds number within the range [100:800]. In this last case, the thermal reduced model is weakly coupled to the fluid reduced one. Results show that reduced models fit very well with detailed ones, and allow a large decrease of computing time.     

A new model and solutions for a spiral heat exchanger and its experimental validation

A spiral heat exchanger was applied in a ground source heat pump (GSHP) system that is primarily used for residential indoor heating. Studies that have been performed on the heat transfer of spiral heat exchanger have focused on field measurements and numerical analysis; however, theoretical research on the subject is absent in the literature. In this study, a methodology is proposed to analyze the heat performance of a spiral heat exchanger. A ring source model was established and solved analytically to describe the temperature variation of the ground caused by a spiral heat exchanger. The validity of the model was examined by an experiment on the soil temperature variation with a spiral heater. The virtual ring tube surface temperature response of unit ring circle was calculated by a superposition of the contributions of the ring source itself and adjacent ring sources. Furthermore, a fast algorithm was created to compute the average tube surface temperature resulting from the dimensionless temperature rise at a point far from the ring source that is constant when the non-dimensional distance is less than 0.13. The author confirmed that the calculation time of this proposed algorithm decreased by a factor of 100 compared with the traditional integration method. A system designer will find this algorithm helpful when determining the size of a heat exchanger under a required heating load, particularly for different arrangement of spiral heat exchangers.