Chang-kwon Kang

Effects of Flexibility on the Aerodynamic Performance of Flapping Wings

Effects of chordwise, spanwise, and isotropic flexibility on the force generation and propulsive efficiency of flapping wings are elucidated. For a moving body immersed in viscous fluid, different types of forces, as a function of the Reynolds number, reduced frequency (k), and Strouhal number (St), acting on the moving body are identified based on a scaling argument. In particular, at the Reynolds number regime of O(10 10) and the reduced frequency of O(1), the added mass force, related to the acceleration of the wing, is important. Based on the order of magnitude and energy balance arguments, a relationship between the propulsive force and the maximum relative wing tip deformation parameter (γ) is established. The parameter depends on the density ratio, St, k, natural and flapping frequency ratio, and flapping amplitude. The lift generation, and the propulsive efficiency can be deduced by the same scaling procedures. It seems that the maximum propulsive force is obtained when flapping near the resonance, whereas the optimal propulsive efficiency is reached when flapping at about half of the natural frequency; both are supported by the reported studies. The established scaling relationships can offer direct guidance for MAV design and performance analysis.

Can Tip Vortices Enhance Lift of a Flapping Wing

AEROSPACE LETTERS are brief communications (approximately 2000 words) that describe new and potentially important ideas or results, including critical analytical or experimental observations that justify rapid publication. They are stringently prescreened, and only a few are selected for rapid review by an Editor. They are published as soon as possible electronically and then appear in the print version of the journal.

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

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

We report a comprehensive scaling law and novel lift generation mechanisms relevant to the aerodynamic functions of structural flexibility in insect flight. Using a Navier–Stokes equation solver, fully coupled to a structural dynamics solver, we consider the hovering motion of a wing of insect size, in which the dynamics of fluid–structure interaction leads to passive wing rotation. Lift generated on the flexible wing scales with the relative shape deformation parameter, whereas the optimal lift is obtained when the wing deformation synchronizes with the imposed translation, consistent with previously reported observations for fruit flies and honeybees. Systematic comparisons with rigid wings illustrate that the nonlinear response in wing motion results in a greater peak angle compared with a simple harmonic motion, yielding higher lift. Moreover, the compliant wing streamlines its shape via camber deformation to mitigate the nonlinear lift-degrading wing–wake interaction to further enhance lift. These bioinspired aeroelastic mechanisms can be used in the development of flapping wing micro-robots.

Aerodynamics, sensing and control of insect-scale flapping-wing flight

There are nearly a million known species of flying insects and 13 000 species of flying warm-blooded vertebrates, including mammals, birds and bats. While in flight, their wings not only move forward relative to the air, they also flap up and down, plunge and sweep, so that both lift and thrust can be generated and balanced, accommodate uncertain surrounding environment, with superior flight stability and dynamics with highly varied speeds and missions. As the size of a flyer is reduced, the wing-to-body mass ratio tends to decrease as well. Furthermore, these flyers use integrated system consisting of wings to generate aerodynamic forces, muscles to move the wings, and sensing and control systems to guide and manoeuvre. In this article, recent advances in insect-scale flapping-wing aerodynamics, flexible wing structures, unsteady flight environment, sensing, stability and control are reviewed with perspective offered. In particular, the special features of the low Reynolds number flyers associated with small sizes, thin and light structures, slow flight with comparable wind gust speeds, bioinspired fabrication of wing structures, neuron-based sensing and adaptive control are highlighted.

Fluid Dynamics of Pitching and Plunging Flat Plate at Intermediate Reynolds Numbers

A combined numerical and experimental study of two- and three-dimensional pitching and plunging flat plates at Reynolds numbers of O(104) is presented. The focus of this paper is the interplay between the geometry, kinematics, Reynolds numbers, and three-dimensional effects with the resulting aerodynamic forces and flow structures. A shallow-stall and a deep-stall motion with higher maximum effective angles of attacks are considered. Under both kinematic motions, massive leading-edge separation is observed at the sharp leading edge of the flat plate. This geometric effect is seen to dominate over other viscosity effects, and the Reynolds number dependence is limited. Compared with the blunter SD7003 airfoil, where the flow is mostly attached for the shallow-stall motion at Re=6×104, the sharper leading edge of the flat plate leads to earlier and stronger leading-edge vortex formation and greater lift and drag. Finally, the presence of a tip vortex significantly reduces lift generation during the downstrok...

A Surrogate Model Approach in 2-D Versus 3-D Flapping Wing Aerodynamic Analysis

Flapping wing MAV aerodynamics is challenging to understand due to its complexities. Surrogate modeling offers an effective tool to predict information at off-design points, measure the sensitivity of design variables involved, and illustrate general trends in the data. We have investigated 2D and 3D hovering airfoil/wing aerodynamics considering three kinematic parameters, i.e. plunge amplitude, angular amplitude, and phase lag, at Re = 100. While leading edge vortex, a persistent downward jet, and wake capture are three noticeable fluid dynamics features in 2D and 3D, tip vortices in 3D and instantaneous AoA can substantially affect the relative importance of them. Surrogate models of the 2D and 3D wing with aspect ratio of 4 show that for i) power required, the magnitudes and global trends of the predicted response between 2D and 3D are similar, ii) lift, the phase lag changes from a non-linear response in 2D to a monotonic one in 3D. The overall consequence is that in 3D, kinematic combinations of higher lift with lower power requirements can be attained. Global sensitivity analysis shows that the lift is the most sensitive to the phase lag in 3D as opposed to the angular amplitude in 2D. The ensemble surrogate strategies performed employed performed quite well compared to independent test data.

Analytical model for instantaneous lift and shape deformation of an insect-scale flapping wing in hover

In the analysis of flexible flapping wings of insects, the aerodynamic outcome depends on the combined structural dynamics and unsteady fluid physics. Because the wing shape and hence the resulting effective angle of attack are a priori unknown, predicting aerodynamic performance is challenging. Here, we show that a coupled aerodynamics/structural dynamics model can be established for hovering, based on a linear beam equation with the Morison equation to account for both added mass and aerodynamic damping effects. Lift strongly depends on the instantaneous angle of attack, resulting from passive pitch associated with wing deformation. We show that both instantaneous wing deformation and lift can be predicted in a much simplified framework. Moreover, our analysis suggests that resulting wing kinematics can be explained by the interplay between acceleration-related and aerodynamic damping forces. Interestingly, while both forces combine to create a high angle of attack resulting in high lift around the midstroke, they offset each other for phase control at the end of the stroke.

Fluid Dynamics of Pitching and Plunging Airfoils of Reynolds Number between 1×10 4 and 6×10 4

We consider a combined experimental (two-dimensional particle image velocimetry in a water tunnel) and computational (two-dimensional Reynoldsaveraged Navier-Stokes) investigation to examine the effects of chord Reynolds number on the dynamics of rigid SD7003 airfoil undergoing pitching and plunging motion in nominally two-dimensional conditions. Appreciable qualitative distinction in a moderately dynamically-stalled case in going from Re = 1×10 4 to Re = 6×10 4 was observed, suggesting nontrivial impact of viscosity even in conditions of strong forcing by motion kinematics. Additionally, computed lift coefficient time history is compared with Theodorsen’s unsteady linear airfoil theory. The velocity and vorticity fields were in excellent agreement between experiment and computation for those phases of motion where the flow was attached; moderate agreement was achieved when the flow was separated. The small disagreements were consistent with the expected inaccuracies due to the turbulence model used. Similarly, Theodorsen’s theory was able to predict the computed lift coefficient quite well when the flow was attached, and moderately acceptable otherwise.

Unsteady Fluid Physics and Surrogate Modeling of Low Reynolds Number, Flapping Airfoils

To improve our understanding of the fluid physics related to micro air vehicles (MAVs), the current work investigates the low chord Reynolds (Re) number, between 10 and 10, fluid physics of a 2D flapping airfoil via direct numerical simulation and surrogate modeling. Addressed are the impacts of kinematic parameters and Re number under freestream/hovering conditions. The kinematic parameters include plunging amplitude, angular amplitude, and pitching/plunging phase angle. Composite surrogate models are constructed and global sensitivity evaluations of these variables are analyzed. Wake capture, delayed stall, and interaction with a jet-like flow feature all influence the performance of the airfoil. It is found that the plunging amplitude and reduced frequency play a surprisingly small role in determining the airfoil performance in the design space examined. Interestingly, in normal hovering studied here, the kinematic variables are largely uncoupled, and while the aerodynamics are complex, that the cumulative effect can be largely explained with a linear superposition of individual influences. Furthermore, delayed stall and the jet interaction exhibit major influence on the overall lift. As expected, the kinematics requiring the least amount of power occurred at high angular amplitudes, with minimum delayed stall and angle of attack at the maximum translational velocity (Φ=90).