Asymptotic study of the propulsive motion of a flapping cylindrical wing with an elliptical cross-section
https://doi.org/10.26907/2541-7746.2025.4.759-776
Abstract
The propulsive motion of a cylindrical flapping wing with an elliptical cross-section in a viscous incompressible fluid is investigated to develop an analytical model for predicting the cruising speed of such a wing without resorting to computationally expensive numerical methods. The mathematical formulation of the problem is based on the unsteady Navier–Stokes equations. The wing motion is described as a planar translational-rotational oscillation with prescribed velocities. The problem is solved using an asymptotic approach, under the assumption of high-frequency and low-amplitude oscillations. A structural formula is derived that describes the variation of the cruising speed in relation to the angle of translational oscillations, the phase shift between translational and rotational oscillations, the amplitude of rotational oscillations, and the aspect ratio of the elliptical cross-section. The consistency of the results with known analytical solutions for a circular cylinder is demonstrated. The limits of the model’s applicability with respect to the oscillation frequency are considered.
Keywords
flapping wing,
viscous incompressible fluid,
Navier–Stokes equation,
asymptotic model,
cruising speed
Supporting agencies: This study was supported by the Russian Science Foundation (project no. 22-79-10033-P).
About the Authors
A. N. Nuriev
Kazan Federal University
Russian Federation
Russian Federation
Artem N. Nuriev, Dr. Sci. (Physics and Mathematics), Associate Professor, Leading Researcher, Laboratory of Intelligent Biomimetic and Nature-Inspired Systems
A. R. Baimuratova
Kazan Federal University
Russian Federation
Russian Federation
Angelina R. Baimuratova, Junior Researcher, Laboratory of Intelligent Biomimetic and Nature-Inspired Systems
O. N. Zaitseva
Kazan Federal University
Russian Federation
Russian Federation
Olga N. Zaitseva, Cand. Sci. (Pedagogy), Senior Researcher, Laboratory of Intelligent Biomimetic and Nature-Inspired Systems
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For citations:
Nuriev A.N., Baimuratova A.R., Zaitseva O.N. Asymptotic study of the propulsive motion of a flapping cylindrical wing with an elliptical cross-section. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2025;167(4):759-776. (In Russ.) https://doi.org/10.26907/2541-7746.2025.4.759-776
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