Optimal configuration of a tidal current turbine farm in a shallow channel

This study investigates the macroscopic features of tidal farm layouts optimized to maximize power production in an idealized shallow channel with steady unidirectional flow. By varying the number of turbines and optimization constraints, numerical experiments were conducted using OpenTidalFarm, an open-source solver for tidal farm optimization using PDE-constraint gradient-based optimization. To alleviate the computational complexity for identifying a global optimum, a concept of quasi-global optimum was introduced, a local optimum that serves as a global optimum in a crude sense. From extensive numerical results, notable patterns in the shape of the quasi-global optimal layout were observed and explained by a nondimensional parameter, E, the ratio of the shortest hypothetical linear fence to the length of the lateral farm site constraint. The quasi-global optimal layout had a linear fence shape when E <= 1. The layout evolved into a downstream-concave parabola and subsequently into a V-shape as E increased beyond 1. Moreover, as more turbines were added to an array, the quasi-global optimal layout was no longer a single fence, and some turbines were separated from the main body. From the quantitative perspective, it is shown that the power production could be increased by up to 50% by tuning the optimization constraints.