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Title: Developing analytical heat transfer models for ground heat exchangers under actual ground conditions
Authors: Pan, Aiqiang
Degree: Ph.D.
Issue Date: 2019
Abstract: Ground coupled heat pumps (GCHP), utilizing the ground as the heat source or sink, have much higher coefficient of performance (COP) than traditional air source heat pumps (ASHP), as the temperature of ground soil is much more stable than the ambient air. The ground is also used as thermal energy storage medium through GCHP, utilizing the property of large thermal capacity of the ground. The COP of a typical GCHP can be twice the value of a typical ASHP. The ground heat exchanger (GHE) is the key component in GCHP systems, and its heat transfer analysis is extremely important for the optimal design and control of GCHP systems. Analytical heat transfer models that are fast in calculation are effective tools for practical engineering. Heat transfer modeling of vertical GHE is commonly based on the two-region approach. One region is inside the borehole wall, the other is outside borehole wall. The models for heat transfer outside borehole wall provide the temperature on the borehole wall, while the models for heat transfer inside borehole wall give the circulating fluid temperature at GHE outlet with the borehole wall temperature and inlet fluid temperature. The outside heat transfer models that currently adopted in practical engineering might still be the finite line or cylindrical heat source models. However, the outside models have some certain assumptions, failing to consider the effects of some actual ground conditions. For example, the ground surface conditions would affect the thermal performance of vertical GHE, and the ground soil stratification would result in different temperature responses in different ground layers due to their different thermal properties. Also, most of current inside heat transfer models for shallow borehole GHE assume a uniform borehole wall temperature, which is obviously not acceptable for deep borehole heat exchangers (DBHE), since the borehole wall temperature would increase with depth because of the geothermal gradient in deep ground. In view of these, the thesis successfully developed three analytical models accordingly so that the thermal performance of vertical GHE can be calculated under the three real ground conditions: various ground surface conditions; layered ground; geothermal gradients in deep ground. A brief introduction of the development of the three models are given below. Ground surface conditions are important for the modeling of both horizontal and vertical GHE. For vertical GHE, the Dirichlet boundary condition, which cannot accurately represent the real ground surface condition, has been commonly defined on ground surface. A new analytical model for vertical GHE with Robin boundary condition is successfully developed by employing the integral transform method. This method is new for developing analytical models of GHE. The new model is flexible in defining ground surface conditions and gives straightforward expressions of vertical heat flux around vertical GHE. Using the newly developed and validated model, the effects of employing different types of ground surface boundary conditions (Dirichlet, Neumann, and Robin boundary conditions) on modeling vertical GHE are studied theoretically. It is found that the effects would be limited in the dimensionless depth of about 200, so it would be more important to employ the Robin boundary condition on ground surface for vertical GHE with shorter depth. Moreover, by defining a Robin boundary condition, the thermal impact (the additional temperature and vertical flux through ground surface caused by the operation of vertical GHE) can be, and for the first time, calculated. Generally, the smaller the convective heat transfer coefficient on ground surface defined in the Robin boundary condition, the smaller the vertical heat flux through ground surface, but the larger the additional temperature on ground surface.
To calculate the temperature response of vertical GHE in layered subsurface, a new multilayer cylindrical heat source model was successfully developed. The cylindrical heat source is firstly divided according to ground layer interfaces. Then, the temperature response in each soil layer of each divided cylindrical heat source is determined. Finally, the temperature response of the whole cylindrical heat source in each soil layer is obtained by adding the temperature response of each divided cylindrical heat source. The new multilayer cylindrical heat source model was validated by numerical simulation and a laboratory-scale experiment of cylindrical heat source buried in a double-layer soil. Using the new multilayer cylindrical heat source model, temperature responses of vertical GHE in layered ground are compared with those in homogeneous soil. It is observed that the temperature on the GHE wall is significantly different due to different soil thermal properties of layered ground. Therefore, using homogeneous models yield error and the error gets larger with time. In layered ground, the thermal interaction between layers would be stronger when the differences in thermal conductivity are larger, affecting temperature response in respective ground layers. The error of using multilayer line heat source model to predicting temperature response of vertical GHE is also studied by comparing its results with that of multilayer cylindrical heat source model. In conclusion, using homogeneous heat source model to predict temperature response of vertical GHE in layered ground fails to give the right temperature profile along depth, and the error would be larger in the long term. Also, compared with multilayer line heat source model, the multilayer cylindrical heat source model is more accurate to predict temperature response of vertical GHE with larger GHE radius, and thermal load. For GCHP with DBHE, the geothermal gradient in the deep ground also makes the previous inside heat transfer models for shallow borehole GHE that assume a uniform borehole wall temperature inapplicable. Current models, which are mostly numerical rather than analytical, are inconvenient for system optimal design and control. Since coaxial tubes are commonly adopted in DBHE in practical engineering, a new analytical inside heat transfer model was successfully derived for DBHE with coaxial tube. The increasing borehole wall temperature with depth was considered in the new model. The new analytical model is validated by an existing numerical model. The temperature distributions of circulating fluid along the depth of DBHE calculated by the analytical model show very good agreement with the results by the numerical model. Using the new analytical model, the effects of various parameters on the thermal performance of DBHE (i.e. circulating fluid temperature at the outlet of DBHE) were investigated. The parameters include flow direction, thermal conductivity of borehole grout and pipes, radius of pipes, and mass flow rate. The rapid calculation ("click and done") feature of the new analytical model makes it an effective tool for the optimal design and control of DBHE. In addition, the model can be used as a benchmark for validating and checking the accuracy of numerical models. In summary, this thesis successfully developed three analytical heat transfer models for vertical GHE. The first model was developed to consider more real ground surface boundary condition. The second model was developed to calculate the temperature response of vertical GHE installed in layered ground. The third model was developed for GCHP with DBHE, where the borehole wall temperature generally increases with depth due to the geothermal gradient in the deep ground. All the three new analytical models can be effective tool for the optimal design and control of vertical GHE under the actual ground conditions.
Subjects: Hong Kong Polytechnic University -- Dissertations
Heat pumps
Ground source heat pump systems
Heat exchangers
Heat -- Transmission
Pages: xxvii, 201 pages : color illustrations
Appears in Collections:Thesis

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