Superposition of the single point source solution to generate temperature response factors for geothermal piles

Geothermal piles are a very promising technique to exploit the low enthalpy resource for ground coupled heat pumps. In fact, they are heat exchangers integrated in the foundation structures of the buildings, with reduced need in term of ground surface availability and diminished drilling costs. Unfortunately, to evaluate the ground thermal response to their presence it is not possible to use classical analytical solutions due to their low aspect ratio and to the relevant effect of the heat capacity of the inner cylindrical volume. In addition, different shapes of the pipe arrangement are possible: helix around the foundation pile or a series of vertical pipes connected through U bends at top and bottom of the cylindrical volume. This study proposes a semi-analytical method to model ground heat exchangers with a great flexibility concerning their shape. The method, called Multiple Point Sources (MPS), applies the spatial superposition of the analytical solution for the Single Point Source. It has been validated by means of the comparison with literature analytical methods and FEM results for helix heat exchangers. Finally, it has been applied to find the temperature response factor for different shapes of heat exchanger in geothermal piles.