Abstract
This article provides plain and handy expressions to decide the most suitable analytical model for the thermal analysis of the ground source in vertical ground-coupled heat pump applications. We perform a comprehensive dimensionless analysis of the reciprocal deviation among the classical infinite, finite, linear and cylindrical heat source models in purely conductive media. Besides, we complete the framework of possible boreholes model with the “hollow” finite cylindrical heat source solution, still lacking in the literature. Analytical expressions are effective tools for both design and performance assessment: they are able to provide practical and general indications on the thermal behavior of the ground with an advantageous tradeoff between calculation efforts and solution accuracy. This notwithstanding, their applicability to any specific case is always subjected to the coherence of the model assumptions, also in terms of length and time scales, with the specific case of interest. We propose several dimensionless criteria to evaluate when one model is practically equivalent to another one and handy maps that can be used for both design and performance analysis. Finally, we found that the finite line source represents the most suitable model for borehole heat exchangers (BHEs), as it is applicable to a wide range of space and time scales, practically providing the same results of more complex models.
Highlights
Ground-source heat pump systems (GSHPs) are one of the most promising high-efficiency technologies in the heating and cooling sector [1,2]
We note that for R ≤ 100, the actual deviation between the FCS and FLS models is practically negligible. This value corresponds to 0.5–1 m for typical boreholes; we can conclude that FLS model is sufficiently accurate at long time scales or to evaluating the thermal interference within a borehole heat exchangers (BHEs) field
We dealt with several analytical models for the ground source in the GSHP context
Summary
Ground-source heat pump systems (GSHPs) are one of the most promising high-efficiency technologies in the heating and cooling sector [1,2]. We will present an expression that relates the dimensionless radial position r/rb to the minimum Fourier number Fob = α g t/rb after which the deviation between ICS and ILS models is negligible; in other words, we provide a dimensionless criterion to evaluate the time and the space scales in which the actual radial dimension of the BHE, rb , does not affect the thermal evolution of the ground. We will present a summary list of the ranges in which each model is practically equivalent to another one, helping the reader to decide which model is more appropriate for his/her purposes
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