Low-Reynolds-Number Aerodynamics of a Flapping Rigid Flat Plate

Abstract

Two-and three-dimensional low-aspect-ratio (AR 4) hovering airfoil/wing aerodynamics at a low Reynolds number (Re 100) are numerically investigated. Regarding fluid physics, in addition to the well-known leading-edge vortex and wake-capture mechanisms, a persistent jet, induced by the shed vortices in the wake during previous strokes, and tip vortices can significantly influence the lift and power performance. While in classical stationary wing theory the tip vortices are seen as wasted energy, here, they can interact with the leading-edge vortex to contribute to the lift generated without increasing the power requirements. Using surrogate modeling techniques, the two-and three-dimensional time-averaged aerodynamic forces were predicted well over a large range of kinematic motions when compared with the Navier-Stokes solutions. The combined effects of tip vortices, leading-edge vortex, and jet can be manipulated by the choice of kinematics to make a three-dimensional wing aerodynamically better or worse than an infinitely long wing. The environmental sensitivity during hovering for select kinematics is also examined. Different freestream strengths and orientations are imposed, with the impact on vortex generation and wake interaction investigated.

Scaling law and enhancement of lift generation of an insect-size hovering flexible wing

“…Here, we consider a non-dimensional flow field with unit density initiated by a hovering two-dimensional flat plate with unit chord, thickness ratio of 0.02 and flat edges [19]. The flow field is governed by the unsteady Navier-Stokes equations with constant density and viscosity as…”

“…The superscript asterisk (*) indicates non-dimensional variables. In absence of a freestream in hovering wings, we take the maximum translation velocity U of the flat plate at the LE as the reference velocity, such that U ¼ 2pfh a ¼ 1 [19,22]. Note that reduced frequency in hover becomes a geometric quantity: k ¼ c/(2h a ) [19].…”

“…The interplay of the fluid flow with the shape compliance and transient response is nonlinear and intriguing even at Re ¼ 100, which is addressed in this study. In this Reynolds number regime, the fluid flow can be considered as laminar and the computational accuracy of the Navier-Stokes equation solver employed in this study is satisfactory [19]. The instantaneous flow field is synchronized with the dynamic displacement field of the wing structure in a carefully validated fully coupled aeroelastic framework [23].…”

“…Furthermore, the relationship between structural flexibility and flapping kinematics has not been fully explored. The rigid wing studies [3,19] indicate that the timing between translation and rotation of the wing can be critical to lift generation. Specifically, when the wing is in advanced rotational mode, i.e.…”

“…Specifically, when the wing is in advanced rotational mode, i.e. the wing rotates before it reaches the end-of-the-stroke, the highest lift coefficients are obtained [3,19]. Moreover, tethered flying Drosophila actively control left/right wing rotation timing to initiate yaw turns [20].…”