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.

Automated summary

This paper introduces a new approach to calculate the transfer functions for large diameter, shallow bore helical Ground Heat Exchangers using mean fluid temperature. The proposed method shows promising results in estimating the performance of Helical GHEs by analyzing the mean fluid temperature for different mass flowrates. The study provides mathematical formulations and a simplified resistance-based model for calculating the g-functions, demonstrating the effectiveness of the approach in predicting the thermal performance of the systems.