Find in Library

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, <i>T_out</i>. However, the most widely employed BHE simulation models yield the time evolution either of the mean temperature of the BHE-ground surface, <i>T_sm</i>, or of that of the fluid, <i>T_fm</i>. In transient regime, it is not easy to relate <i>T_out</i> to either <i>T_sm</i> or <i>T_fm</i>. In this paper we determine, through 3D finite element simulations, simple expressions of a dimensionless coefficient <i>&#966;</i> allowing the calculation of <i>T_out</i> by means of a simulation model that yields <i>T_fm</i>. 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 <i>&#966;</i> to calculate the time-dependent values of <i>T_out</i> through a BHE model that yields those of <i>T_fm</i>. Finally, we show that the values of <i>&#966;</i> in quasi-steady working conditions can be used for a simple calculation of the effective borehole thermal resistance.