On the association of secondary hairpin growth and surface pressure gradient for oscillating foils

TL;DR

This study numerically investigates the relationship between secondary hairpin-like vortex structures and surface pressure gradients in the wake of an oscillating foil, revealing a fundamental link that aids understanding of wake dynamics.

Contribution

It introduces a novel method to quantify secondary vortex growth through surface pressure gradients, enhancing understanding of wake structure formation in oscillating foils.

Findings

Secondary hairpin structures are linked to pressure gradients.

Weak secondary LEV undergoes core deformation, generating streamwise vorticity.

Pressure gradients can quantitatively characterize vortex growth.

Abstract

The correspondence of secondary spanwise structures and pressure gradient is numerically evaluated for a foil, performing heaving and pitching motion, at a range of phase offsets (90$^\circ$ $\le \phi \le$ 270$^\circ$) and reduced frequency (0.32 $\le St_c \le$ 0.56). The Reynolds number is $Re =$ 8000. The wake is shown to be dominated by secondary hairpin-like structures that are formed due to an elliptic instability prompted by the paired primary and secondary leading edge vortex ($LEV$). The weaker secondary $LEV$ undergoes a core deformation, resulting in streamwise vorticity outflux across the span of the foil, and hence, the growth of hairpin-like structures. Evaluating pressure gradients on the surface of the foil reveals a unique fundamental measure to quantitatively characterize the growth of these coherent structures. Their dominant presence can be directly linked to the growth of the secondary $LEV$ formed due to the large-scale interactions under localized adverse pressure gradients. These promote a streamwise flow compression in neighboring regions of the primary $LEV$. This association also presents a vivid consistency across a range of kinematics. Therefore, this correspondence provides a novel procedure to investigate the mechanisms involved in the formation of secondary structures in the wake of an oscillating foil.