Analysis of short-to-long term heat flow in GSHP systems based on heat pump power. (5th June 2020) - BniLam, Noori; Al-Khoury, Rafid
Highlights: A semi-analytical model based on the spectral element method is introduced. The model conducts short-to-long term analysis in a single run. Hourly, daily and seasonally switching ON and OFF for many years can be considered. Heat flow can be calculated based on both Dirichlet and Neumann boundary conditions. The Neumann heat flux is derived directly from the heat pump power. Abstract: This paper presents a semi-analytical model based on the spectral element method for three-dimensional, short-to-long term heat flow in multiple borehole, multilayer ground source heat pump systems. The model is distinguished by its computational technique for expressing the input signal at the boundary of the borehole heat exchanger, giving rise to two important engineering features. First, the calculation can be conducted from seconds to years in a single run. This is achieved by discretizing the input signal at the inlet boundary of the borehole heat exchanger using a tailored fast Fourier transform with multiple time-stepping algorithm. Second, the calculation can be conducted using a Neumann boundary condition, instead of the commonly utilized Dirichlet boundary condition. This is achieved by mathematically relating the heat pump power to the heat flux at the inlet of the borehole heat exchanger, allowing direct use of the heat pump power signal as input instead of the inlet temperature. These features make the model computationally efficient that can readily be utilized for system design and included in inverse calculations. The two features are discussed in detail, verified against experimental measurements, and their functionality is highlighted by numerical examples.