Influence of three dimensionality on propulsive flapping

Abstract

Propulsive flapping foils are widely studied in the development of swimming and flying animal-like autonomous systems. Numerical studies in this topic are mainly two-dimensional (2D) studies as they are quicker and cheaper, but, this inhibits the three-dimensional (3D) evolution of the shed vortices from leading- and trailing-edges. In this work, we examine the similarities and differences between 2D and 3D simulations through a case study in order to evaluate the efficacy and limitations of using 2D simulations to describe a 3D system. We simulate an infinite-span NACA0016 foil both in 2D and 3D at a Reynolds number of 5300 and an angle-of-attack of 10º. The foil is subject to prescribed heaving and pitching kinematics with varying trailing-edge deflection amplitude A. Our primary finding is that the flow and forces are effectively 2D at intermediate amplitude-based Strouhal numbers (StA = 2Af/U where U is the freestream velocity and f is the flapping frequency); StA ≈ 0.3 for heaving, StA ≈ 0.3–0.6 for pitching and StA ≈ 0.15–0.45 for coupled motion, while 3D effects dominate outside of these ranges. These 2D regions begin when the fluid energy induced by the flapping motion overcomes the 3D vortex shedding found on a stationary foil, and the flow reverts back to 3D when the strength of the shed vortices overwhelms the stabilizing influence of viscous dissipation. These results indicate that 3D-to-2D transitions or vice-versa are a balance between the strength and stability of leading-/trailing-edge vortices and the flapping energy. 2D simulations can still be used for flapping flight/swimming studies provided the flapping amplitude/frequency is within a given range.

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Identifiers

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

ORCID for Bharathram Ganapathisubramani: orcid.org/0000-0001-9817-0486

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

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