Scaling of thrust and drag of a rigid low-aspect-ratio pitching plate*

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 (span to length) ranging from 0.1 to 0.5 are considered, for a Reynolds number based on the plate's length and the incoming flow velocity of 2000. The validity of a scaling law for viscous drag, previously established for uniform plate's normal velocity, is assessed for the pitching motion. The pressure force along the moving plate is shown to decompose into a thrust part, interpreted in tems of elongated body theory, and a pressure force deficit, often analyzed as vortex drag induced by the vortices at the plate's lateral edges. Here, this time-averaged pressure drag is interpreted as a Bernoulli-type effect associated with the high transverse velocity, allowing for a scaling law using a potential model. The pressure force prediction using this composite scaling fits remarkably well with the numerical simulation results, the pressure thrust being reduced, compared to what would be predicted by the elongated body theory, by more than 30 % for the aspect ratios considered.