Fluid Physics and Surrogate Modeling of Low Re Flapping Rigid Flat Plate

Abstract

Two-and three-dimensional, low aspect ratio (AR=4), hovering airfoil/wing aerodynamics at 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 to 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 with implications on the applicability of quasi-steady models.

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

“…This is an interesting consequence that warrants further study. From the instantaneous force histories (see Appendix A in [48]), the agreement in drag coefficients is very close, except at a combination of low plunging amplitudes with low angular amplitudes and low phase lags. Figure 13 measures the sensitivity of the power required to the kinematic variables.…”

“…During normal hovering, 90 , the airfoil/wing is perpendicular to the direction of motion at the ends of translation but has little translational velocity. As the phase lag is perturbed in either direction, the airfoil can have an appreciable velocity while perpendicular to the direction of motion, and whether the body is accelerating when perpendicular, as in delayed rotation cases, or decelerating, as in advanced rotation cases, has a sizable impact on the instantaneous drag that is felt (see Appendix B in [48]) and, consequently, the power required for the maneuver. Quality measures of the surrogate models are tabulated in [33].…”

“…The downward freestream (20% strength) tends to suppress the vortex dynamics and, as such, the 2-D and 3-D force histories remain quite similar. The horizontal freestream, most notably during the headwind, and the upward freestream, on the other hand, show differences due to the 3-D nature of the flow; the reader is referred to [48], which includes further flowfield examinations not described here for the sake of conciseness. In the absence of a prominent freestream, we saw that the 3-D effects could accentuate the 2-D lift by creating a low pressure zone at the tip and by anchoring an LEV that would otherwise detach earlier from the wing.…”

Approximate Aerodynamic and Aeroelastic Modeling of Flapping Wings in Hover and Forward Flight

“…The CFD based results are taken from Ref. [32]. The approximate results were obtained for the following parameters: N θ = 200, r c = 0.1 c, n wksubit = 4, and circulation limit 21 was fixed at 2.0.…”