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

Abstract

AbstractFlowrate 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.Keywords: Ground-source heat pump systemtime-variant flowratessimulation of ground heat exchangernon-stationary convolutionDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also.