Periodic heat flux composite model for borehole heat exchanger and its application

• We present a model of a periodic cylinder heat source in composite media and give its solution in frequency domain.
• A frequency decomposition hybrid algorithm is specially designed for the periodic composite model.
• The equivalent relationship between constant heat flux model and periodic heat flux model is illustrated.
• The periodic model is applied on the data analysis of oscillatory thermal response test.

Most existing borehole heat exchanger models are based on constant heat flux solutions. This paper first proposes a periodic heat flux composite model for a borehole heat exchanger to reproduce the periodic nature of real loads. An explicit analytical solution of a periodic cylinder-source in composite media is derived using a harmonic method. The periodic thermal response factor is defined to characterize the thermal behaviour of a borehole subjected to a periodic heat flux. The periodic thermal responses factors for high- and low-frequency periodic heat flux are dominantly determined by the thermal properties of the content inside the borehole and the ground outside the borehole, respectively. A frequency decomposition hybrid algorithm is specially designed according to the frequency response characteristic of borehole. The proposed periodic heat flux model is verified through an inter-model comparison with existing constant heat flux models and the comparison indicates an equivalent relationship between the two types of models. An annual simulation is performed using the hybrid algorithm and the accuracy of the algorithm is verified. The paper also presents a new method to analyse the data of an oscillatory thermal response test by using the periodic composite model. The effective heat capacities of the ground and grout are estimated. The simulation results of the periodic composite model are in good agreement with the experimental data.