Non-dimensional scaling of passive adaptive blades for a marine current turbine
Authors: Van Ness Katherine , Aliseda Alberto , Polagye Brian 
Published: September 2023

For tidal energy to support access to off-shore electricity, further development is needed to decrease costs and increase reliability of current turbines at relevant scales. Blade pitch control strategies can significantly reduce structural loads in above-rated flow conditions by shedding power through decreased angles of attack. This can be accomplished through an active strategy using motorized blades or a passive adaptive strategy using flexible, self-twisting blades. We focus this study on the passive adaptive approach in which the composite fibers of the blade are oriented off-axis to produce a coupling between bend and twist deformations.
Extending laboratory results to larger, open-water designs requires an understanding of hydrodynamic and hydroelastic scaling. While dimensionless scaling relations have been extensively studied for current turbines with rigid blades, relatively few studies discuss appropriate hydroelastic scaling for passive adaptive blades. In this study, we experimentally apply non-dimensional scaling laws to laboratory-scale passive adaptive turbine blades and demonstrate similarity in blade deformation and non-dimensional loads across scales.
When Cauchy similarity is achieved between model and full-scale, the same steady-state blade loading and blade deformation are expected. We define Cauchy number as Ca = ρUo2/E, where ρ is the water density, Uo is the freestream velocity upstream of the turbine, and E is the transverse flexural modulus of the blade (i.e., elasticity corresponding to bending in the flapwise direction). We tested the effectiveness of Cauchy-scaling by designing an experiment in which blade bending stiffness and flow speed varied, but Cauchy number remained constant. The first blade used a 7-ply carbon fiber spar while the second blade used a 5-ply carbon fiber spar, both fabricated with unidirectional fibers oriented 10° off-axis and cast in a semi-rigid polyurethane using the same mold. All other non-dimensional parameters relevant to hydrodynamic scaling were held constant, where possible.
As hypothesized, we observed agreement in thrust coefficient, deflection, and twist when Cauchy similarity was achieved, particularly when flow remained attached over the entire blade span. Small differences of 0-7% were observed in normalized thrust, deflection, and twist compared to 50-65% when Cauchy number was allowed to vary by 50%. We did not observe this similarity for normalized mechanical power between the 5-ply and 7-ply blades, but hypothesize that the source of the disagreement was a small surface defect in the urethane on the 5-ply blade. The experiment will be repeated to confirm this hypothesis and included in future presentations of this work.
Our experimental result partially demonstrates the effectiveness of using Cauchy number to scale passive adaptive marine current turbine blades and model their steady-state hydrodynamic and hydroelastic behaviors in a consistent, non-dimensional manner. Accurate experimental models are critical to support the development of passive adaptive blades, which may obviate the need for an active pitch mechanism, thereby increasing reliability and decreasing maintenance costs. Finally, we present initial results from a field-scale turbine equipped with rigid and passive adaptive blades, demonstrating a path towards validating our conclusions from lab-scale testing.