Free Surface Double Actuator Disc Theory and Double Multiple Streamtube Model for In-Stream Darrieus Hydrokinetic Turbines

According to the literature, the last improvement to the Actuator Disc Theory for hydrokinetic turbines in channel flows included blockage ratio and Froude number as independent variables in a single-disc formulation. The authors attempted to solve these equations in a Blade Element Momentum model for axial-flow turbines, ensuring satisfactory results. To our best knowledge, no Blade Element Momentum code was developed for Darrieus rotors including an extended double-disc theory so far. In this perspective, a Free Surface double-disc LMADT is implemented to solve the governing equations in a Double Multiple Streamtube model, facilitating the assessment of In-Stream Darrieus hydrokinetic turbines. Rigid Lid equations, derived for higher-depth applications, are included for completeness. A further numerical procedure allows to set up the channel flow from downstream and update the inflow data due to the resistance induced by the turbine operation in a subcritical flow. In addition to corrections for flow curvature, shading of the downstream flow due to the shaft, and losses due to the mechanical struts, this work encloses an effective sub-model accounting for the turbine installation depth. The Double Multiple Streamtube model is finally validated with previous experimental data of a Darrieus turbine deployed in a narrow channel.