Hybrid model for generating short-time g-functions

Abstract

A hybrid numerical/analytical approach is proposed to predict short-time g-functions. Transient heat transfer in the borehole is solved numerically while ground heat transfer is evaluated analytically using the infinite cylindrical heat source solution. Grid independence checks indicate that 40 radial nodes and a time step of 3 minutes represent a good compromise between computational time and accuracy. The proposed model is successfully validated against test cases, which include transient heat transfer in a plane wall and experimental data from a sand box.

In the application section of the paper, the classic ASHRAE sizing equation is modified to account for borehole thermal capacity using short-time g-functions. It is shown that the inclusion of borehole thermal capacity has a direct effect on the daily and monthly effective ground thermal resistances which reduces the required borehole length by a few percent. It is concluded that borehole thermal capacity should be included when sizing a bore field.