Three-dimensional thermomechanical modeling of geothermal energy piles with U-tube heat exchangers of different cross-sectional shapes

Abstract

This study explores the thermomechanical performance of a three-dimensional (3D) geothermal energy pile (GEP) system, emphasizing the optimization of heat exchanger (HE) geometry to improve both thermal efficiency and structural integrity. As GEPs offer a promising avenue for integrating renewable geothermal energy into building foundations, their design must balance energy performance with mechanical stability. A finite volume-based numerical model is developed, employing second-order spatial and temporal discretization and the Pressure-Implicit with Splitting of Operators (PISO) algorithm for pressure–velocity coupling. A segregated solution strategy with under-relaxation is used to ensure numerical stability and convergence. The model simulates a concrete-encased U-shaped HE embedded in clayey soil, with three cross-sectional geometries: circular, square, and triangular. Simulation outcomes are validated against analytical predictions and benchmarked with experimental and numerical data from the literature. Among the tested geometries, the triangular HE demonstrates superior thermal and structural performance under both mechanical and thermomechanical loading conditions. Compared to the circular configuration, the triangular U-pipe enhances cooling efficiency by reducing outlet temperature by 1.2 % and increasing heat extraction by 8.6 %. In heating mode, it raises the outlet temperature by 0.6 % but lowers the heat transfer rate by 4.8 %, underscoring the need for season-specific or hybrid designs. Thermomechanically, the triangular configuration exhibits the highest axial compressive stress in summer, increasing by 6.36 %, while in winter, it shows a 4.75 % reduction relative to the purely mechanical load case. Displacement variations at the pile base remain minimal across all geometries, with the triangular HE showing a 1.13 % reduction in summer and a 1.70 % increase in winter. These findings establish the triangular cross-section as the most effective configuration for enhancing both thermal output and structural resilience in GEP systems, providing a valuable design reference for the development of energy-efficient, geothermal-integrated foundations.