Drag reduction of flexible plates by reconfiguration

Abstract

Through an extensive and systematic experimental investigation of two geometries of flexible plates in air, it is shown that a properly defined scaled Cauchy number allows collapsing all drag measurements of the reconfiguration number. In the asymptotic regime of large deformation, it is shown that the Vogel exponents that scale the drag with the flow velocity for different geometries of plates can be predicted with a simple dimensional analysis reasoning. These predicted Vogel exponents are in agreement with previously published models of reconfiguration. The mechanisms responsible for reconfiguration, namely area reduction and streamlining, are studied with the help of a simple model for flexible plates based on an empirical drag formulation. The model predicts well the reconfiguration observed in the experiments and shows that for a rectangular plate, the effect of streamlining is prominent at the onset of reconfiguration, but area reduction dominates in the regime of large deformation. Additionally, the model demonstrates for both geometries of plates that the reconfiguration cannot be described by a single value of the Vogel exponent. The Vogel exponent asymptotically approaches constant values for small and for very large scaled Cauchy numbers, but in between both extremes it varies significantly over a large range of scaled Cauchy number.