New Correlations for Thermal Resistances of Vertical Single U-Tube Ground Heat Exchanger

Abstract

A new 2D numerical model of a single U-tube ground heat exchanger is proposed and a four-thermal-resistance model is adopted to evaluate the effective pipe-to-borehole, pipe-to-pipe, and borehole-to-borehole thermal resistances. The influence of temperature distributions on both borehole surface and outer diameter of two pipes to these thermal resistances has been thoroughly studied. The best-fit correlations of effective pipe-to-borehole, pipe-to-pipe, and borehole-to-borehole thermal resistances are proposed and compared with the available equations in the literature. It is found that the present correlations of thermal resistances for ground heat exchanger are more accurate than those of available formulas. Furthermore, based on these obtained thermal resistance correlations, an analytical model is proposed to evaluate the heat transfer performance of the ground heat changer.

Accuracy of borehole thermal resistance calculation methods for grouted single U-tube ground heat exchangers

“…Several analytical and empirical methods have been proposed in this regard. These include works of Kavanaugh [30], Hellström [11], Paul [31], Gu and O'Neal [32], Shonder and Beck [33], Sharqawy et al [34], Bauer et al [35], Claesson and Hellström [22], Liao et al [36], and Abd Elatty et al [37].…”

Explicit Multipole Formulas for Calculating Thermal Resistance of Single U-Tube Ground Heat Exchangers

“…Figure 1 shows an example of such a network for a single U-tube borehole. Other networks forms can also be formulated, e.g., see [11,24] but any such representation is an approximation to reality under network-specific assumptions and restrictions. The three resistance Δ network of Figure 1 is based on the following relations between heat flows q1 and q2 and fluid temperatures Tf1 and Tf2.…”

“…He [18] studied four cases of different borehole diameters and grout conductivities using a three-dimensional numerical model and the multipole method, and reported a maximum difference of 0.19%. Liao et al [11] compared the first-order multipole method with a two-dimensional numerical method and noted a maximum relative difference of 0.2% for 18 combinations of shank spacing and grout conductivities. Al-Chalabi [19] studied 12 different cases of pipe positioning, and grout and soil conductivities, using the first-order multipole method and a two-dimensional finite element method, and observed a maximum difference of 1.3% between the two methods.…”

“…The theoretical methods to estimate borehole thermal resistance include analytical [5][6][7] or empirical [8][9][10][11] formulas based on one-dimensional or two-dimensional steady-state conductive heat transfer in the borehole. As demonstrated by [12,13], there exists a great disparity between borehole thermal resistance values calculated from different theoretical methods.…”

Second-order Multipole Formulas for Thermal Resistance of Single U-tube Borehole Heat Exchangers

“…Several representations of the thermal resistance network are possible (Hellström, 1991;Liao et al, 2012;Spitler et al, 2016b), but any such representation is an approximation to reality under network-specific assumptions and restrictions. The simplest approach is to consider a Δ thermal network as shown in Figure 1.…”