Topology optimization of geothermal bore fields using the method of moving asymptotes

A new method is proposed to optimize the configurations of vertical ground heat exchangers using topology optimization and the method of moving asymptotes. The problem formulation minimizes the required number of boreholes of a given length with simultaneous constraints on the entering fluid temperature in cooling and heating mode. The method relies on the adaptation of the alternative ASHRAE design method and a new analytical formulation for the calculation of $g$-functions based on a boundary condition of equal average fluid temperature. The method is applied to large bore fields consisting of more than a hundred boreholes. The paper also studies the effect of different types of domains and ground load profiles on the optimized configurations. It is shown that the shape of the domain has minimal impact on the optimized configurations. A higher density of boreholes on the perimeter of the domain compared to the center is recommended in the case where one operation mode is dominant. A uniform configuration is better suited when the load profile is balanced.