Development of a Three-Dimensional Numerical Model of the Vertical Ground-Coupled Heat Exchanger Considering the Effects of the Thermal Capacity

내부 열용량을 고려한 수직 지중열교환기의 3차원 수치 모델 개발

  • Received : 2016.04.06
  • Accepted : 2016.07.03
  • Published : 2016.07.10


A three-dimensional (3D) numerical model of the vertical ground-coupled heat exchanger is useful for analyzing the modern ground source heat pump system. Furthermore, a detailed description of the inner side of the exchanger allows to account for the effects of the thermal capacity. Thus, both methods are included in the proposed numerical model. For the ground portion, a FDM (Finite Difference Method) scheme has been applied using the Cartesian coordinate system. Cylindrical grids are applied for the borehole portion, and the U-tube configuration is adjusted at the grid, keeping the area and distance unchanged. Two sub-models are numerically coupled at each time-step using an iterative method for convergence. The model is validated by a reference 3D model under a continuous heat injection case. The results from a periodic heat injection input show that the proposed thermal capacity model reacts more slowly to the changes, resulting in lower borehole wall temperatures, when compared with a thermal resistance model. This implies that thermal capacity effects may be important factors for system controls.


Vertical ground heat exchangers;Ground-coupled heat pump;Thermal capacity;Three-dimensional numerical model


  1. Yang, H., Cui, P., and Fang, Z., 2010, Vertical-borehole ground-coupled heat pumps : a review of models and systems, Applied Energy, Vol. 87, No. 1, pp. 16-27.
  2. Cimmino, M. and Bernier, M., 2014, A semi-analytical method to generate g-functions for geothermal bore fields, International Journal of Heat and Mass Transfer, Vol. 70, pp. 641-650.
  3. Claesson, J. and Javed, S., 2011, An analytical method to calculate borehole fluid temperatures for time-scales from minutes to decades, ASHRAE Transaction, Vol. 117, No. 2, pp. 279-288.
  4. He, M., Rees, S., and Shao, L., 2009, Simulation of a domestic ground source heat pump system using a transient numerical borehole heat exchanger model, Proceedings, Building Simulation, Glasgow, Scotland, pp. 607-614.
  5. Lamarche, L. and Beauchamp, B., 2007, New solutions for the short-time analysis of geothermal vertical boreholes, International Journal of Heat and Mass Transfer, Vol. 50, No. 7-8, pp. 1408-1419.
  6. Lee, C. K. and Lam, H. N., 2008, Computer simulation of borehole ground heat exchangers for geothermal heat pump systems, Renewable Energy, Vol. 33, No. 6, pp. 1286-1296.
  7. Hellstrom, G., 1991, Ground heat storage, Thermal analysis of duct storage systems : Part I. Thoery, Doctoral Thesis, Department of Mathematical Physics, University of Lund, Sweden.
  8. Lee, C. K. and Lam, H. N., 2012, A modified multiground- layer model for borehole ground exchangers with an inhomogeneous groundwater flow, Energy, Vol. 47, No. 1, pp. 378-387.


Supported by : 한국에너지기술연구원