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A simple vortex-loop-based model for unsteady rotating wings

Published online by Cambridge University Press:  18 October 2019

Juhi Chowdhury  and
Matthew J. Ringuette Open the ORCID record for Matthew J. Ringuette [Opens in a new window]
Juhi Chowdhury
Affiliation:
Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, NY 14260, USA
Matthew J. Ringuette*
Affiliation:
Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, NY 14260, USA
*
†Email address for correspondence: ringum@buffalo.edu
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Abstract

An analytical model is developed for the lift force produced by unsteady rotating wings; this configuration is a simple representation of a flapping wing. Modelling this is important for the aerodynamic and control-system design for bio-inspired drones. Such efforts have often been limited to being two-dimensional, semi-empirical, sometimes computationally expensive, or quasi-steady. The current model is unsteady and three-dimensional, yet simple to implement, requiring knowledge of only the wing kinematics and geometry. Rotating wings produce a vortex loop consisting of the root vortex, leading-edge vortex, tip vortex and trailing-edge vortex, which grows with time. This is modelled as a tilted planar loop, geometrically specified by the wing size, orientation and motion. By equating the angular impulse of the vortex loop to that of the fluid volume driven by the wing, the circulatory lift force is derived. Potential flow theory gives the fluid-inertial lift. Adding these two contributions yields the total lift formula. The model shows good agreement with a range of experimental and computational cases. Also, a steady-state lift model is developed that compares well with previous work for various angles of attack.

JFM classification

Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex dynamics Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 880 , 10 December 2019 , pp. 1020 - 1035
Copyright
© 2019 Cambridge University Press 

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