Aerodynamic effects of corrugation and deformation in flapping wings of hovering hoverflies

We investigated the aerodynamic effects of wing deformation and corrugation of a three-dimensional model hoverfly wing at a hovering condition by solving the Navier-Stokes equations on a dynamically deforming grid. Various corrugated wing models were tested. Insight into whether or not there existed significant aerodynamic coupling between wing deformation (camber and twist) and wing corrugation was obtained by comparing aerodynamic forces of four cases: a smooth-plate wing in flapping motion without deformation (i.e. a rigid flat-plate wing in flapping motion); a smooth-plate wing in flapping motion with deformation; a corrugated wing in flapping motion without deformation (i.e. a rigid corrugated wing in flapping motion); a corrugated wing in flapping motion with deformation. There was little aerodynamic coupling between wing deformation and corrugation: the aerodynamic effect of wing deformation and corrugation acting together was approximately a superposition of those of deformation and corrugation acting separately. When acting alone, the effect of wing deformation was to increase the lift by 9.7% and decrease the torque (or aerodynamic power) by 5.2%, and that of wing corrugation was to decrease the lift by 6.5% and increase the torque by 2.2%. But when acting together, the wing deformation and corrugation only increased the lift by ~3% and decreased the torque by ~3%. That is, the combined aerodynamic effect of deformation and corrugation is rather small. Thus, wing corrugation is mainly for structural, not aerodynamic, purpose, and in computing or measuring the aerodynamic forces, using a rigid flat-plate wing to model the corrugated deforming wing at hovering condition can be a good approximation.