Development of g-functions for large diameter shallow bore helical ground heat exchangers

In this paper, a new approach to calculate the transfer functions (g-functions) for simulating the thermal performance of large diameter, shallow bore helical Ground Heat Exchangers (He-GHE) is proposed using mean fluid temperature rather than borewall temperature. The g-functions are generated using a validated numerical Capacitance Resistance Model-Helical GHE (CaRM-He) for different bore diameters, bore depth and helical pipe pitch. Mathematical formulation is presented which allows calculation of the combined g-function for multiple bores using the g-functions for individual cases. A simplified resistance-based model which enables the calculation of traditional borewall temperature-based g-functions using the mean fluid g-functions for different mass flowrates is also presented. Finally, mean fluid temperature is calculated for an array of eight He-GHEs for Sacramento climate zone using (a) CaRM-He model, (b) mean fluid temperature-based g-function and (c) borewall temperature-based g-functions for maximum (0.128 kg s−1), reference (0.063 kg s−1) and minimum (0.057 kg s−1) mass flowrates. For the reference mass flowrate case, the predicted mean fluid temperature Root Mean Square Deviation (RMSD) between the CaRM-He simulation and the g-function approaches is less than 5% and 6% of the yearly average temperature difference between the inlet and outlet for the mean fluid and borewall based g-functions respectively. For the other mass flowrates, the RMSD in mean fluid temperature varies between 9% and 17% of the yearly average temperature difference between the inlet and outlet temperature. Overall, the proposed g-function approach can be used effectively to estimate the performance of large diameter helical GHEs.