Application of Fast Fourier Transform-based Method for the Thermal System of Buried Pipe Heat Exchanger

Abstract

The Fourier transform method for discrete sequences is introduced in this study and applied to decompose the heat flux per unit borehole depth in buried pipe heat exchangers (BPHE) into a summation of Fourier series. The linear relationship between the heat flux per unit borehole depth in BPHE and the cooling and heating load of Ground-Coupled Heat Pumps (GCHP) is delineated. It is demonstrated that, similar to the cooling and heating load of GCHP, the heat flux per unit borehole depth in BPHE exhibits a general trend with periodic variability on an annual scale (8760 hours). The Fourier transform of discrete sequences enables the representation of the heat flux per unit borehole depth in BPHE as a summation of Fourier series, comprising a Step Heat Flux (direct current components) and heat flux in trigonometric forms. Further investigation reveals that the heat flux in trigonometric form does not influence the long-term average temperature of the surrounding soil and rock, whereas the Step Heat Flux significantly affects it. Therefore, the long-term performance of BPHE is predominantly governed by the Step Heat Flux.