Effect of Backfill on the Performance of a Vertical U-Tube Ground Coupled Heat Pump

Abstract

The present work is concerned with developing a discretized analytical model to investigate the effect of a backfill on the performance of a vertical U-tube ground-coupled heat pump. This work involves the development of an analytical solution and an expression for the equivalent diameter, and the experimental verification of their applications in the system model. The approximate analytical solution was developed to the transient heat­ conduction problem in an infinite composite medium composed of a backfill and the soil with an internal cylindrical heat source. This was intended to improve the prediction of the performance of a U-tube ground heat exchanger. The generalized orthogonal expansion technique was utilized in deriving this solution. Solutions are presented in a wide range of the Fourier number for the non-dimensional temperature as a function of the ratios of thermal conductivities and diffusivities of the backfill and soil Sensitivities of the results to assumptions about the sizes of the backfilling region and the far-field boundary were also examined. To verify the correctness of the solution, comparisons were made between this solution, and the classical homogeneous cylindrical solution and a finite difference solution.. To improve the equivalent diameter approach to the thermal interference problem between the legs of the U-tube, a general expression for the equivalent diameter was derived under steady state. The transient analytical solution, developed earlier combined with the superposition method and the conformal mapping technique were used to justify this expression. A small-scale U-tube test facility was constructed for the experimental validation of the system model of the U-tube heat exchanger using the analytical solution and the equivalent diameter expression. Two types of backfill materials: bentonite/masonry sand and bentonite/copper powder were chosen for the tests. Finally, the parametric studies were conducted to characterize the effects of the thermal properties of the backfill, the leg spacing as well as the size of the backfill region. A backfill effectiveness was proposed and discussed. These studies provide a number of insights into the heat transfer behavior of the U-tube heat exchanger buried in a non­ homogeneous medium.