Boundary layer flow dynamics of propulsive flapping foils with increasing Reynolds numbers

Abstract

We study flapping foils at optimally propulsive Strouhal number $St=0.3$ with increasing chord-based Reynolds number at $Re = 10^4$, $10^5$, and $10^6$ to examine changes in their unsteady boundary layers. Despite being prescribed the same freestream, the inner boundary layer characteristics exhibit different trends due to the generation of leading-edge vortices (LEVs) and their advection into the downstream flow. Propulsive flapping foils show an extended laminar region known as the relaminarization, during which the velocity profiles deviate from the standard log law. This relaminarization is accompanied by a significant decrease in the cyclic fluctuation of the wall friction coefficient and an increase in the shape factor while the freestream velocity increases under favourable pressure gradient conditions. This phenomenon intensifies with increasing $Re$. We found that higher $Re$ produces smaller LEVs in greater quantities, with a more rapid but stable breakdown, without resulting in a more chaotic turbulent downstream. This study strongly indicates that the relaminarization could extend beyond $Re=10^6$ as predicted by Fukagata[Annual Review of Fluid Mechanics, 2023]. The results support the potential for further exploration of flapping foils at high $Re$ for noise and drag reduction.