  Bioinspired flexible blades have been recently shown to significantly improve
the versatility of horizontal-axis wind turbines, by widening their working
range and increasing their efficiency. The aerodynamic and centrifugal forces
bend the blade along its chord, varying the pitch angle by means of
non-consuming mechanisms. Here we introduce a general method based on a
universal scaling, which finds the optimal soft materials for the blades to
maximize the overall turbine efficiency or rotational power, for any required
geometry of classical horizontal-axis turbines. The optimization problem, which
depends on various parameters, such as the wind velocity, the rotation rate,
the density, the rigidity and the geometry of the blade, is reduced to only two
dimensionless parameters: the Cauchy number and the centrifugal number. The
blade-element momentum theory is coupled to a torsion spring-based model for
the blade deformation. Taking into account realistic incoming wind-velocity
distributions in the North Sea and a large wind-turbine geometry, we found a
significant increase of the total harvested power, up to +35%. In addition, the
optimal soft material corresponding to the maximal efficiency over the entire
working range for a given wind turbine geometry is, within the limits of small
blade deformations, scale-independent. Thus experiments on small wind turbines
are a possible way to determine the optimal soft materials for larger ones.
These flexible blades are found to be between 5% and 20% lighter than the
current rigid blades.
