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

Abstract

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 ∘ C and 0.26 ∘ C , respectively). At last, the high efficiency of the new frequency-domain expression is demonstrated, with the computing times ( 0.04 s and 0.01 s ) being 100 and 8 times faster than the original formulation in both scenarios.