Modeling the temperature field in the ground with an installed slinky-coil heat exchanger

Abstract

In order to find the temperature field in the ground with a heat exchanger, it is necessary to determine temperature responses of the ground caused by heat sources and the influence of the environment. To determine the latter, a new model of heat transfer in the ground under natural conditions was developed. The heat flux of the evaporation of moisture from the ground was described by the relationship taking into account the annual amount of rainfall. The analytical solution for the equations of this model is presented. Under the conditions for which the calculations were performed, the following data were obtained: the average ground surface temperature Tsm = 10.67◦C, the ground surface temperature amplitude As = 13.88 K, and the phase angle Ps = 0.202 rad. This method makes it possible to easily determine the undisturbed ground temperature at any depth and at any time. This solution was used to find the temperature field in the ground with an installed slinky-coil heat exchanger that consisted of 63 coils. The results of calculations according to the presented model were compared with the results of measurements from the literature. The 3D model for the ground with an installed heat exchanger enables the analysis of the influence of miscellaneous parameters of the process of extracting or supplying heat from/to the ground on its temperature field.