2D flapping wing by Michael Alletto

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2D flapping wing

You can download the case file sphereSplashSend.tar.gz !!!!!!!!!!!!!!!! here.

Introduction

In this tutorial an additional application of the overset methodology is illustrated: the flapping motion of a two dimensional wing. A flapping wing motion is used by many insects and also vertebrates to execute hoovering manoeuvres. See [1] for a review. Key feature of the hoovering fly is the larger lift generated because of the unsteady wing motion in comparison to the steady flow around a wing. For a two dimensional wing a leading edge vortex is formed. It is responsible for the greatest amount of lift generated since it remains attached throughout almost the whole stroke. The interested reader is referred the review article of [2]. Furthermore during stroke reversal the rotating wing generates a circulation which also contributes to the generation of additional lift.

Set up

The Simulation setup is inspired by the experiments of [3]. The experiments consisted in a flat plate which rotates about the stroke axis with an angle of 0 <= Φ <= 90° and pitches about the rotational axis with an angle of β = +- 50°. The details of the kinematics are described in [3]. The wing span was R = 107mm and the thickness was s = 3.4mm (see [4] since in [3] the thickness of the plate was not described). The distance from the rotational axis to the wing root was ΔR = 71.5mm (private communications). In order to perform a two--dimensional simulation, the rotatory motion of the point located at mid-span is projected on a horizontal plane. That means that the displacement of the point located at the center of the wing in the experiment is the same as the horizontal displacement of the wing in the simulation. The pitching motion is the same in the experiment and in the simulation.


References

[1] Diana D Chin and David Lentink. Flapping wing aerodynamics: from insects to vertebrates. Journal of Experimental Biology, 219(7):920-932, 2016.

[2] Je D Eldredge and Anya R Jones. Leading-edge vortices: mechanics and modeling. Annual Review of Fluid Mechanics, 51:75-104, 2019.

[3] Swathi Krishna, Melissa A Green, and Karen Mulleners. Flowfield and force evolution for a symmetric hovering at-plate wing. AIAA Journal, 56(4):1360{1371, 2018.

[4] Swathi Krishna, Melissa A Green, and Karen Mulleners. Effect of pitch on the flow behavior around a hovering wing. Experiments in Fluids, 60(5):86, 2019.

[5] YJ Lee, KB Lua, and TT Lim. Aspect ratio effects on revolving wings with rossby number consideration. Bioinspiration & biomimetics, 11(5):056013, 2016.