An optimally-controlled RANS Actuator force model for efficient computations of tidal turbine arrays

A steady-state Actuator force model using the RANS equations is developed to calculate the power production and the flow through arrays of tidal or river Darrieus turbines. It uses detailed three dimensional force distributions depending on the position on the turbine, obtained beforehand by a set of blade-resolved URANS simulations of the turbine. New power coefficient and force coefficient laws depending on the local velocity instead of the upstream velocity are established and appear to be independent from the local turbine blockage in an array. Those laws are used to construct a model that adapt the Actuator force distributions to the local velocity of the flow reaching each turbine, in order to simulate each turbine functioning close to its maximum efficiency point. The model is validated against experimental measurements on a reduced-scale Darrieus turbine. A fence farm configuration and a two row farm configuration are investigated and compared to results of the same model adapted in two dimensions. The local blockage effect is more favorable for fences than for staggered turbine configurations, increasing the local velocity and the power production for each turbine.