Abstract
Ground-coupled heat pump (GCHP) systems usually utilize buried vertical heat exchangers, named borehole heat exchangers (BHEs). The accurate design or simulation of a GCHP system requires the calculation of the time-dependent outlet temperature from the BHEs, Tout. However, the most widely employed BHE simulation models yield the time evolution either of the mean temperature of the BHE-ground surface, Tsm, or of that of the fluid, Tfm. In transient regime, it is not easy to relate Tout to either Tsm or Tfm. In this paper we determine, through 3D finite element simulations, simple expressions of a dimensionless coefficient φ allowing the calculation of Tout by means of a simulation model that yields Tfm. These expressions hold for single U-tube BHEs, both in quasi-steady and in unsteady working conditions. We validate our 3D simulation code by comparison with an analytical BHE model. Then, we present applications of our expressions of φ to calculate the time-dependent values of Tout through a BHE model that yields those of Tfm. Finally, we show that the values of φ in quasi-steady working conditions can be used for a simple calculation of the effective borehole thermal resistance.
Highlights
The diffusion of ground-source heat pumps, and in particular, of ground-coupled heat pumps (GCHPs), is rapidly increasing
We determine Tfm by the analytical borehole heat exchangers (BHEs) model by Man et al [35] and Tout by the correlations for φ, and we point out the errors that occur in the short time if one employs simpler methods, such as the finite line-source (FLS) model combined with either Rb or Rbeff, or the model by
The obtained expressions of φ hold for single U-tube BHEs with any diameter between 130 and 170 mm, any shank spacing compatible with the diameter, and any BHE length between 50 m and 200 m, both in quasi-stationary and in transient regime
Summary
The diffusion of ground-source heat pumps, and in particular, of ground-coupled heat pumps (GCHPs), is rapidly increasing. New correlations to determine φ are provided, for single U tube BHEs, through the best fit of the results of 3D numerical simulations These correlations can be employed to obtain an accurate evaluation of the time evolution of Tout by means of a BHE simulation code that yields the time evolution of Tfm. These correlations can be employed to obtain an accurate evaluation of the time evolution of Tout by means of a BHE simulation code that yields the time evolution of Tfm An example of this use is reported, in the case of constant flow rate and constant power supplied to the ground, by evaluating the time evolution of Tfm through the simple analytical BHE model proposed by Man et al [35], and that of Tout through Equation (6). It is shown that the correlation for φ valid for the quasi-stationary regime can be employed for an immediate calculation of the effective BHE thermal resistance
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