Asymmetric wake, origin, generation, and suppression behind asymmetrically pitching hydrofoil

Abstract

The wakes behind a symmetrically and a quasi-symmetrically pitching hydrofoil are numerically studied. To understand the generation mechanism of the asymmetric wake behind a symmetrically pitching hydrofoil, we shed light on the timing of vortex shedding and convection velocity of vortices in the wake. The centers of the vortices in the wake are tracked using a method based on the critical point theory. The tracks of the vortex centers reveal crucial insights into the dependence of the vortex convection velocity on pitching frequency and pitching amplitude. The vortex strength and the spatial separation between the vortices embody the wake deflection. We find the inherent inability of the shear-layer rolling up at par with the pitching motion results in an uneven temporal separation (Δtʹ) between two consecutive vortices, which dictates the spatial separation between the vortices. The uneven temporal separation facilitates formation of vortex dipoles, which gives rise to the asymmetric wake formation. To substantiate the hypothesis of the uneven temporal generation of vortices, we used quasi-symmetric pitching of the hydrofoil, which can even the timing of vortex shedding and can metamorphose the asymmetric wake into a symmetric wake. On the contrary, relaxing the shear-layer roll-up can transmute a symmetric wake to an asymmetric wake. The detailed analysis of symmetrically pitching hydrofoil, quasi-symmetrically pitching hydrofoil, flexible hydrofoil, and asymmetrically pitching hydrofoil reveals that Δtʹ = 0.5, Δtʹ < 0.5 and Δtʹ > 0.5 correspond to a symmetric wake, an upward deflected wake and a downward deflected wake, respectively.