Transient Response of Gradient-Based Optimization for Ground Source Heat Exchangers

Abstract

The efficiency of ground source heating and cooling can be improved during installation by utilizing non-uniform properties of the soil. This paper presents a transient analysis of a computed optimal distribution of heterogeneous soils with varying thermal conductivities. This optimal configuration was computed via a gradient descent approach. The numerically simulated case studies demonstrate an improved performance when utilizing this approach to maximize the overall efficiency. The focus of this study is optimization of the soil heterogeneity surrounding the ground heat exchanger composed of pipes buried 2 meters underground. Finite element mathematics is used for the optimization algorithm. The finite element cells are treated as isotropic material voxels. The variation of material thermal conductivity in individual cells is employed as the optimizing variable. The updated conductivities are verified to ensure they are within the design domain. This method computes the sensitivities for the search direction (i.e. the gradient descent direction) utilizing the equations employed in the finite element mathematics. The optimization solution commences with the finite element model and applied boundary conditions. An initial guess is made of the elements’ conductivity. Based on these conductivities, the initial temperature is computed and later implemented to estimate the gradient. The global geometric conductivity matrix is assembled once in this process from the element geometric conductivity matrices. The objective function presented in this work maximizes the temperature at the critical locations. For this study, the critical locations are the location of the pipes. A three-dimensional, transient thermal simulation is developed based upon the optimized configuration for the soil. The monthly mean diurnal ambient air temperature variations for the months in the Northeast United States representing winter and summer are implemented in this study along with typical solar loading for each season. The results are presented for both a baseline homogeneous soil configuration and the optimized configuration. The results illustrate the benefits of an optimized soil configuration to maximize performance.