Thrust and drag scaling of a rigid low-aspect-ratio pitching plate

Abstract

The flow around a rigid rectangular pitching plate immersed in a free stream is numerically investigated, addressing the force and drag generated by the oscillatory motion. Several aspect ratios (plate’s span to plate’s length) lower than 0.5 are considered, for a Reynolds number based on the plate’s length and the incoming flow velocity of 2000. The validity of the scaling law for viscous drag production, previously established for finite-span plates in uniform flapping motion, is investigated for the pitching motion, which is more representative in the context of propulsion modeling. The time averaged pressure force is shown to decompose into a propulsive part, scaling linearly with the aspect ratio and induced by the plate’s movement, and an opposite pressure force deficit, often interpreted as vortex induced drag and generally associated with the pair of longitudinal vortices at the plate’s lateral edges. A scaling for the time averaged pressure deficit is proposed, by analyzing the pressure drop along the span in terms of a Bernoulli-type effect induced by the transverse flow velocity. It is shown, that the pressure thrust is reduced, compared to what would be predicted by the elongated body theory, by more than 30% for the aspect ratios considered.