Effect of Phase Difference on the Aperiodic Transition in the Flow-Field of a Pitching-Plunging Foil

The present work explores the role of phase-difference on the transitional flow dynamics of a pitching-plunging foil. An extensive parameter space of plunge amplitude ($h$) and phase offset ($\phi$) between pitch-plunge motions is considered keeping the pitch amplitude and non-dimensional flapping frequency constant ($\alpha = 15^o\ \&\ k=4$). Numerical simulations are performed at a low Reynolds number ($Re = 300$) using an Immersed Boundary Method based in-house Navier-Stokes solver. The phase offset is found to be a crucial parameter in determining the onset of the aperiodic transition. In the range of $10\pi/8\le\phi\le14\pi/8$, the flow-field and, therefore, the aerodynamic loads remain periodic even for $h$ values as high as $h=0.475$. Significant enhancement in thrust generation is also observed in this range of $\phi$, at all $h$ values. On the other hand, the flow-field turns aperiodic even at lower $h$ values (quasi-periodic at $h=0.25$ and chaotic at $h=0.375$) approximately in the range of $-\pi/8\le\phi\le9\pi/8$. A novel scaling relation is achieved in terms of the effective angle-of-attack and the Strouhal number (based on the peak-to-peak amplitude of the leading edge), which differentiates the distinct dynamical regimes in the parameter space in a robust manner.