A Numerical Study on the Flapping Dynamics of a Heaving Flexible Foil in a Uniform Flow

Abstract

The problem of heaving the leading edge of a flexible foil whose trailing edge is free to undergo flapping motion in a uniform axial flow is widely studied because of its practical applications and also due to the rich physics involved in it. In this work, we perform systematic parametric direct numerical simulations to understand the effect of heaving motion, that is, the influence of the leading edge heaving amplitude and frequency on the flapping response, frequency, and vortex dynamics. Amplitude-frequency combinations arising from non-dimensional frequency values of f = 0.25 and 0.5, and non-dimensional amplitude values of A = 0.05, 0.1, and 0.15 are presented. In addition to the heaving amplitude and frequency at the leading edge, the passive interactions between the flexible foil and the incompressible flow field also depend on three non-dimensional parameters, namely: (a) unit mass of the structure interacting with a surrounding flow field (m*), (b) non-dimensional flexural rigidity of the foil (K_B) and (c) Reynolds number (Re). The parametric simulations have been carried out for m* = 0.1, K_B = 0.0004, and Re = 1000 (for all amplitude-frequency combinations) with the aid of a finite element based quasi-monolithic fluid–structure solver, which is numerically stable even for small m*. Fluid–solid dynamics emerging from the combinations of above mentioned non-dimensional parameters are elaborated by comparing it with the flapping dynamics of a flexible foil with a fixed leading-edge, that is, A = 0.