A transient multipole method for short-term simulations of ground heat exchangers (GHEs) is presented. The two-dimensional unsteady heat equation over a GHE cross-section is separated into two problems: (i) a transient heat equation with homogeneous boundary conditions, and (ii) a steady-state heat equation with nonhomogeneous boundary conditions. An eigenfunction expansion is proposed for the solution of the transient heat equation, where the treatment of boundary conditions is considered by a multipole expansion of the eigenfunctions. A singular value decomposition is applied to extract the eigenvalues of the problem. The solution of the steady-state heat equation is obtained from a multipole expansion. The proposed method is validated against reference results for the evaluation of the eigenvalues and for the steady-state temperature field. The complete transient solution is validated against finite element analysis simulations. The proposed method is meshless, and its accuracy is only dependent on the evaluation of eigenvalues and on the number of terms in each of the multipole expansions.
A new method is presented to evaluate thermal interactions between vertical geothermal boreholes. The finite line source (FLS) solution is extended to consider thermal interactions between groups of boreholes. Groups of boreholes that share similar temperatures and heat extraction rates are identified using hierarchical agglomerative clustering, and each group is represented in the model as a single equivalent borehole. Each equivalent borehole is split into segments, and temporal and spatial superposition of the FLS solution are employed to calculate the total temperature change along the length of the equivalent boreholes. The new method is shown to provide an accurate calculation of the g-function, with a mean absolute percentage error below 0.612 % on the g-functions of regular borefields of up to 144 boreholes using only 3 to 5 equivalent boreholes. Calculation times are significantly reduced : the g-function of a borefield of 1024 randomly positioned boreholes is calculated in 3.65 seconds.
KEYWORDSground-coupled heat pumps; geothermal boreholes; g-functions; finite line source; thermal interactions; hierarchical agglomerative clustering CONTACT Carlos Prieto.
The study of heat transfer in ground heat exchangers (GHEs) considering the fluid advection inside the pipes; the heat transfer between the fluid and the ground through the grout material; and the thermal interaction between GHEs is a challenging task. The present paper presents a new semi-analytical method that takes into account the aforementioned effects to consider both the short- to long-term effects of GHEs. The heat transfer between the fluid and grout was studied by a transient multipole expansion considering time-dependent fluid temperatures and an advection model for the pipes obtained from an energy balance on the heat carrier fluid. Thermal interactions were analyzed using an equivalent borehole method while penalizing the transient multipole expansion to include thermal interaction effects. Validation of the short-term predictions was performed by comparing the proposed model to experimental data found in the literature and to an FEA model. The proposed model was then compared with a FEA model in long-term simulations of a geothermal field comprised of 24 GHEs for multi-annual simulation. The method resulted in substantial reduction in computational time while preserving good accuracy when compared with the FEA model.
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