Dynamic Formulation of the Double Multiple Stream Tube Model of Offshore Vertical Axis Wind Turbines

Abstract The paper proposes a novel algorithm to simulate Vertical Axis Wind Turbines in floating motion based on a low-fidelity approach. The conventional Double Multiple Stream Tube Model is formulated as a steady state model to deal with the inherent unsteady aerodynamics of VAWTs. The Double Multiple Stream Tube Model makes use of an average contribution of the blade passages over a revolution to solve the Blade Element Momentum equation. The model reduces the dependence of the solution (the induction field) to a space variable. Floating Vertical Axis Wind Turbines undergoes a variation of aerodynamic quantities according to wave periods, also different from the rotor period. This paper provides a new formulation of the Double Multiple Stream Tube Model to solve the turbine rotation in time and space, introducing the variation of the platform velocity and a revised approach to the downstream actuator disc. The most impactful parameter is found to be the wave frequency: wave periods at full-scale are lower than the ones of the turbine rotor, featuring optimal operating points at low tip speed ratios. The increase of the wave frequency highlights the differences of the average torque prediction for a single blade up to 10% between the unsteady and the standard formulation. In this context, the development of fast low-fidelity computational tools play a key role in the assessment of the preliminary designs of Floating Offshore Vertical Axis Wind Turbines and it will be used to optimise the aerodynamic design of the laboratory scaled model under surge motion.