SL-08-042 -- A New Approach to Modeling Ground Heat Exchangers in the Initial Phase of Heat-Flux Build Up PDF

For the design or simulation of ground-source heat pump systems, knowledge of the thermal response characteristics of the borehole heat exchanger in the early stage of a step heat input is essential. In a real system, the heat flux across the borehole boundary builds up gradually as the rise of the fluid temperature is dampened by the thermal mass of the aggregate fluid. Presently the analytical models used are based on a steady flux assumption, while the thermal capacity of the fluid is ignored. Consequently, they have limited usefulness for predicting early stage behavior. In this paper, a classical analytical solution has been used to model the temperature response of the fluid directly. This also uses the thermal capacity of the fluid as a key variable. The results are validated through Finite Element Modeling (FEM). The effect of changing the tube spacing ratio of the U-tube geometry in different media is studied. With the appropriate values of a dimensionless variable Biot number (Bi), the analytical solution agrees closely with the results of the FE models of the complete U-tube geometry within certain limits of the spacing ratios and Bi values. For the grouted boreholes, the model predicts with reasonable accuracy both the “early” and “late” stage responses as well as a distinct transition time. Further research is required to model the width of the transition zone and the corresponding response curve.

Units: Dual