Three-dimensional aspects of flapping foils

Abstract

Propulsive flapping foils are widely studied in the development of animal-like autonomous systems, energy harvester and other engineering applications. The numerical studies of this topic are mainly two-dimensional (2D) using strip theory for quick and inexpensive results but excluding the three-dimensional (3D) evolution of both onboard and shed vortices. In this work, we are trying to clearly separate the applicability of 2D to 3D studies because of 3D effects. We simulate a NACA0016 foil both in 2D and 3D simulations at a Reynolds number of 5300 with prescribed kinematics based on heave and pitch in 2D motion frame. A general parameter used for flapping foil is the amplitude-based Strouhal number StA representing the flow dynamics produced by the kinematics. StA is constructed from two main components i.e. peak-to-peak amplitude 2A and frequency f normalised by the inflow U∞. Firstly, we study the infinite foil in comparison with 2D (strip) simulation and discovered an intermediate range of StA where both 2D and 3D simulations are equal and the flow structures are uniform —allowing the strip theory application. The range is StA ≈ 0.3 for heaving but wider for pitching and coupled motion, whereas the 3D effects dominate outside of these ranges. The 2D range starts when the flapping motions overpower the 3D vortex shedding of a stationary foil with 10◦ angle of attack, and it ends with vortex spanwise perturbation because the strength of the shed vortices overwhelms the stabilizing influence of viscous dissipation. Secondly, we study the finite flapping foil where 3D effects dominate the flow but the average peak forces show the possibility to scale from 2D simulation (strip theory). A finite foil experiences 3D kinematics of roll and twist, a linearly increased 2D kinematics of heave and pitch towards the tip, in various A. The lowest A is more affected by the pitch/heave derivative, whereas the highest A is less affected thus exhibits similarity to infinite foil. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in finite flapping-foil design. Lastly, we study the importance of the leading-edge sweep angle used by unsteady swimming and flying animals where mixed conclusions are shown in the results of biologists and fluid experimentalists. We provide extensive studies with careful control on variables using 3D simulations of a finite foil undergoing tail-like (pitch-heave) and flipper-like (twist-roll) iv kinematics for a range of sweep angles. No significant change is observed in mean force, power, moment and efficiency for tail-like and flipper-like motions as the sweep angle increase. This leads to a conclusion that fish tails, flukes and flippers can have a large range of potential sweep angles without a negative impact on hydrodynamic performance, and a slight adjustment in kinematics to maintain high thrust and efficiency at the same time.

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Identifiers

ORCID for Andhini Nasution: orcid.org/0000-0003-1924-3507

ORCID for Gabriel Weymouth: orcid.org/0000-0001-5080-5016

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