New formulations and experimental validation of non-stationary convolutions for the fast simulation of time-variant flowrates in ground heat exchangers

Flowrate control can have a significant positive impact on the thermal performance and economic profitability of ground-source heat pump systems. Including dynamic advective processes in the design phase, however, remains a challenging task, as few computationally efficient modeling tools allow for their adequate and accurate representation. The present work addresses this issue by presenting new formulations of non-stationary convolutions, an efficient simulation algorithm that relies on the theory of linear time-variant systems for predicting the thermal response of a ground heat exchanger to both dynamic heat loads and flow rates. First, the new original formulations are presented, which include (1) a simple time-domain expression and (2) a fast frequency-domain expression. Then, the efficiency and validity of the new formulations are verified using experimental multi-flowrate thermal response tests involving dynamic circulation, pumping and bleed flow rates in closed-loop and standing column well ground heat exchangers. Results show that the new formulations can reproduce the outlet fluid temperature of both experimental test cases with good accuracy (MAE=0.06 circle C and 0.26 circle C, respectively). At last, the high efficiency of the new frequency-domain expression is demonstrated, with the computing times (0.04s and 0.01s) being 100 and 8 times faster than the original formulation in both scenarios.

Automated summary

This study presents new formulations of non-stationary convolutions for predicting the thermal response of ground-source heat pump systems. Experimental tests show that the new formulations accurately reproduce the outlet fluid temperature and have significantly faster computing times compared to the original formulation.