Effect of combined heaving and pitching on propulsion of single and tandem flapping foils

Abstract

Flow dynamics across flapping foils in tandem arrangement at Reynolds number of Re = 1100 has been numerically investigated in the present study. The kinematic motion of the foils consists of sinusoidal heaving and pitching motion. The two-dimensional computation has been carried out through the arbitrary Lagrangian-Eulerian (ALE) moving mesh based algorithm with the variational modeling of the incompressible flow equations. The effects of the heave amplitude, pitch amplitude and the flapping frequency on the propulsive performance have been comprehensively studied for a single as well as tandem system of foils at two gaps of 4 and 7 times the downstream foil's chord length. It is found that the effective angle of attack, effective projected area, type of vortex interaction and the timing of the interaction during the downstroke of the flapping motion influence the propulsive performance. Increasing the heave amplitude of the upstream foil leads to an increase in the average thrust generated by the downstream foil for the gap of 7, while the opposite effect is observed for gap of 4. The propulsion of the downstream foil increases monotonically with the heave amplitude of the downstream foil. Upstream foil's pitch amplitude is noticed to have a minor effect on the performance of the downstream foil, while an increase in the pitch amplitude of the downstream foil increases the thrust for larger gap between the foils. The study of the propulsive performance in the frequency-pitch amplitude parametric space for the tandem foils has been performed for the first time, where a more complex behavior is observed. The trends in the thrust coefficient and the propulsive efficiency are corroborated by the study of various vortex interaction mechanisms leading to favorable or unfavorable thrust generating conditions. Finally, the three-dimensional flapping dynamics of the tandem configuration is demonstrated, where no spanwise wake structures are noted, indicating the wake interaction to be inherently two-dimensional.