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

Jeremy Pohly,James Bluman,Kabilan Nedunchezian,Chang-Kwon Kang,James Salmon

doi:10.3390/fluids3040081

Jeremy Pohly, James Bluman + Show 3 more

Open Access

https://doi.org/10.3390/fluids3040081

Copy DOI

Abstract

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.

Highlights

A preliminary version of this paper was presented at the AIAA SciTech Conference, Grapevine, Texas, in 2017 [1].Micro air vehicles (MAVs), typically 15 cm or less in size, will likely be used in a host of applications in the coming years, from military use cases to agricultural and industrial functions, and even recreational pursuits
In addition to the challenges associated with manufacture of MAVs, the design of MAVs is hampered by the complex aerodynamics of flapping wing flight, which are quite different from the aerodynamics that govern larger manned vehicles
When the pitching motion is extreme, i.e., the pitching motion is large, quick, and occurs about the leading or trailing edge, large force and moment magnitudes are seen at the beginning and end of the strokes

Summary

Introduction

A preliminary version of this paper was presented at the AIAA SciTech Conference, Grapevine, Texas, in 2017 [1].Micro air vehicles (MAVs), typically 15 cm or less in size, will likely be used in a host of applications in the coming years, from military use cases to agricultural and industrial functions, and even recreational pursuits. MAVs come with their own set of technical challenges, which is why they are currently still an area of active research It was only recently through the miniaturization of electronics as well as the ability to fabricate micro-scale parts from a variety of materials that MAVs can start to be realized [2]. In addition to the challenges associated with manufacture of MAVs, the design of MAVs is hampered by the complex aerodynamics of flapping wing flight, which are quite different from the aerodynamics that govern larger manned vehicles. They operate under a Reynolds number that is orders of magnitude smaller, i.e., O(102 )–O(104 ), as opposed to O(106 ) or higher for more conventional aircraft

Objectives

Methods

Discussion

Conclusion