A numerical model for transient simulation of borehole heat exchangers


Proposed numerical model is able to simulate thermal behavior of borehole heat exchangers.

Both short and long-time responses can be predicted using this model.

Model is validated by numerical, analytical and experimental data.

Effect of time step size on the accuracy of the results is investigated.


A numerical model is developed to simulate the borehole heat exchanger both in the short and long time. In this regard, the computational domain is divided into the inside and outside borehole regions. A two-dimensional finite volume method is implemented in a cylindrical coordinate system for modeling of the outside borehole. Also, a thermal resistance-capacity model is presented for the borehole cross section. This model is extended to take into account the fluid transport through the U-tube and the temperature variation of the borehole components with depth. The governing equations of the two regions are solved iteratively in each time step. The proposed model is verified with the previously reported numerical, experimental and analytical results. Furthermore, the ability of the model in predicting the short-time response is evaluated in comparison with a three-dimensional computational fluid dynamics (CFD) model with a fine grid. The results show that the proposed model has a good performance in the prediction of the thermal response of the borehole in a wide time interval from 1 min to over 10 years. Moreover, the effects of time step size and number of capacity nodes on the results are investigated.


  • Borehole;
  • Short-time response;
  • Long-time response;
  • Ground-source heat pump;
  • Ground heat exchanger

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