An analytical model for the short-term response of energy piles considering temperature variation effect at the pile-soil interface

Energy piles are an innovative type of ground-source heat pump system that provide heating or cooling for buildings by exchanging heat between the pile foundation and surrounding soil. Heat transfer at the energy pile- soil interface plays a crucial role in determining the temperature distribution in the surrounding soil and the heat exchange efficiency of energy piles. Current models typically rely on simplifying assumptions such as a constant power heat source, continuous interface temperatures, and constant temperature boundaries, which can lead to inaccuracies in predicting the soil temperature response. To address this issue, a novel layered heat transfer model for energy piles was proposed in this study, which incorporates the actual effects of soil interfacial thermal resistance, pile-soil heat transfer, and convective heat exchange between the ground surface and air. This model offers a more accurate representation of the thermal response of the energy pile system. Semi-analytical solutions for the short-term response of energy pile were derived using the finite Hankel and Laplace transforms, and the Crump method was employed to numerically invert the Laplace-domain solutions to obtain the corresponding time-domain solutions. The model's accuracy and validity were verified by comparisons with the existing analytical solutions, numerical simulations, and experimental data. The findings of this study indicate that, compared to the traditional constant power source model, the pile-soil heat transfer model used in this work more effectively simulates the actual soil temperature distribution, particularly improving the prediction accuracy by approximately 45 % to 95 % in the short-term response phase. The results of parametric study indicate that for every increase of 1 W/(K & sdot;m2) in the pile-soil heat transfer coefficient, the soil temperature increased by approximately 0.1 to 0.5 degrees C, corresponding temperature growth rate decreases from 92.7 % to 1.8 %. For each 200 W increase in heat pump power, the soil temperature rose by about 0.5 degrees C, with a percentage increase of 2 % to 4 %. Moreover, an increase in the air convective heat transfer coefficient led to higher shallow soil temperatures. Specifically, for every 2 W/(K & sdot;m2) increase in the convective heat transfer coefficient, the soil temperature increased by approximately 0.08 to 2.48 degrees C, with a percentage rise of 2.3 % to 22.9 %.