Towards Self Similarity of Wake Transitions in Flapping Foils*

The present study aims to examine the key factors responsible for wake transitions in flapping foils regardless of the imposed kinematics. Here we focus on two types of transition: Von Karman wake reversal and wake deflection, which loosely correspond to the generation of thrust and side force respectively. Using two-dimensional numerical simulations of a Boundary Data Immersion (BDIM) solver, we examine these transitions for sinusoidal heaving, pitching and coupled (pitching and heaving) motions. Other factors under consideration include different effective angles of attack as well as pivot points when present. We explore a wide range of thickness based Strouhal numbers (Sr) and non-dimensional TE amplitudes (A_D) as done in previous studies. In the A_D-Sr phase map, the transitions are found to be clearly dependent on the kinematics. Various possible length and time scales that can universally capture the transitions are explored. The cycle averaged swept area of the foil appears to be a suitable length scale that can capture these transitions independent of the kinematics. We link the flapping kinematics and wake formation by shedding light on the underlined physics.

Key Words: Flapping Foils, BvK Wake, Deflection.