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Open AccessArticle

Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics

Department of Mechanical and Aerospace Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA
Department of Civil and Mechanical Engineering, United States Military Academy at West Point, West Point, NY 10996, USA
Author to whom correspondence should be addressed.
Fluids 2018, 3(4), 81;
Received: 20 September 2018 / Revised: 16 October 2018 / Accepted: 21 October 2018 / Published: 24 October 2018
(This article belongs to the Special Issue Bio-inspired Flow)
Various tools have been developed to model the aerodynamics of flapping wings. In particular, quasi-steady models, which are considerably faster and easier to solve than the Navier–Stokes equations, are often utilized in the study of flight dynamics of flapping wing flyers. However, the accuracy of the quasi-steady models has not been properly documented. The objective of this study is to assess the accuracy of a quasi-steady model by comparing the resulting aerodynamic forces against three-dimensional (3D) Navier–Stokes solutions. The same wing motion is prescribed at a fruit fly scale. The pitching amplitude, axis, and duration are varied. Comparison of the aerodynamic force coefficients suggests that the quasi-steady model shows significant discrepancies under extreme pitching motions, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge. The differences are as large as 1.7 in the cycle-averaged lift coefficient. The quasi-steady model performs well when the kinematics are mild, i.e., the pitching motion is small, long, and occurs near the mid-chord with a small difference in the lift coefficient of 0.01. Our analysis suggests that the main source for the error is the inaccuracy of the rotational lift term and the inability to model the wing-wake interaction in the quasi-steady model. View Full-Text
Keywords: insect flight; flapping wing; unsteady aerodynamics; quasi-steady models; Navier–Stokes equations insect flight; flapping wing; unsteady aerodynamics; quasi-steady models; Navier–Stokes equations
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Pohly, J.A.; Salmon, J.L.; Bluman, J.E.; Nedunchezian, K.; Kang, C.-K. Quasi-Steady versus Navier–Stokes Solutions of Flapping Wing Aerodynamics. Fluids 2018, 3, 81.

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