Session A17: Biofluids: Flapping and Flying I

Flying in Two Dimensions

It has long been proposed that insect flight might have evolved on a fluid interface. Surface of a pond provides an ecological niche which is exploited by a large number of species capable of locomotion on a fluid interface. Here we describe the discovery of constrained flight in two dimensions as a novel mode of locomotion used by water lily beetles (genus Galerucella). Because water lily beetles are also capable of three-dimensional free flight, this novel two-dimensional locomotion provides us with a unique model system to explore both the transition between two and three dimensional flight and the associated energetics. Here we present a comparative analysis of this transition in terms of wing stroke angles associated with two and three dimensional flight, as well as modeling surface tension forces on both the horizontal and vertical axes. Special attention is paid to the dynamics and energetics of flight in two-dimensions, focusing on the interaction of the wing strokes with the fluid interface and the capillary-gravity wave drag associated with two-dimensional propulsion.   

Axial flow effects on robustness of vortical structures about actively deflected wings in flapping flight

Flapping wing flight has garnered much attention in the past decade driven by our desire to understand capabilities observed in nature and to develop agile small-scale aerial vehicles. Nature has demonstrated the breadth of maneuverability achievable by flapping wing flight. However, despite recent advances the role of wing flexibility remains poorly understood. In an effort to develop a deeper understanding of wing deflection effects and to explore novel approaches to increasing leading-edge vortex robustness, this three-dimensional computational study explores the aerodynamics of low aspect ratio plates, in hovering kinematics, with isolated flexion lines undergoing prescribed deflection. Major flexion lines, recognized as the primary avenue for deflection in biological fliers, are isolated here in two distinct configurations, resulting in deflection about the wing root and the wing tip, respectively. Of interest is the interaction between axial flow along the span and the vortical structures about the wing. It is proposed that the modes of deflection explored may provide a means of axial flow control for favorably promoting LEV robustness over a broad range of flapping conditions, and provide insight into the nature of flexibility in flapping wing flight.   

Quasi-Steady Limit of Flow Structure on Flapping Wing in Mean Flow

A limiting case of flapping motion of a wing (low aspect ratio plate) in presence of incident steady flow is compared to a rotating wing in quiescent fluid, in order to clarify the effect of advance ratio $J$ (ratio of free-stream velocity to tangential velocity of wing) on the structure of the leading-edge vortex. Stereoscopic particle image velocimetry leads to patterns of vorticity, velocity contours, and streamlines. For each value of $J$, the effective angle of attack is held constant at 45\r{ }, while the wing rotates from rest through 270\r{ }. While at rest, the wing at high angle of attack in the presence of a steady free-stream gives rise to fully stalled flow. After the onset of rotation, the fully stalled region very quickly transforms to a stable leading edge vortex. Despite the change in advance ratio, the development of the flow structure around the wing throughout the rotation maneuver is similar, especially in the leading edge vortex region, as evidenced by patterns of streamline topology. To further demonstrate the effect of $J$, three-dimensional representations of of spanwise-oriented vorticity, spanwise velocity, and $Q$ were constructed for hovering flight and forward flight.   

Inline Motion in Flapping Foils for Improved Force Vectoring Performance

Flapping foils are a promising alternative actuation technique for aerial and underwater vehicles because they can drastically improve maneuverability by vectoring the actuator force. However, the standard implementation of a flapping foil motion, where the foil is oscillated exactly perpendicular to the free stream flow, does not fully develop this force vectoring capability. Many biological examples of flapping foil actuators include an additional degree of freedom, where the foil is allowed to translate parallel to the flow. This degree of freedom can either powerfully augment the mean lift, or mitigate oscillating lift forces for improved thrust efficiency. We develop a parameterization of this inline motion and outline various motion schemes to improve the force vectoring performance of a flapping foil actuator. We then investigate these motion schemes with both CFD solutions and towing tank experiments, thereby expanding the force vectoring options available for the flapping foil actuator.   

Three-dimensional flow measurements of a differentially driven flapping wing mechanism

We present the results of a 3D visualization of the flow field around a differentially driven model of a ladybug wing using Synthetic Aperture PIV (SAPIV) at positions above, below, and 1 chord length behind the wing. Developments in the micro air vehicle field (chord length $<$ 15 cm) have shown advantages in stability and lift generation for flapping wings over fixed wings. These advantages are believed to come from the increased lift caused by various flow structures such as Leading Edge Vortices (LEVs) created by flapping wings, and a ``draining'' process through the core. Visualizations and analysis of the wake structures of flapping wings have been made using Particle Image Velocimetry (PIV) techniques, allowing 2-dimensional slices of the flow to be analyzed. However, the wake structures of flapping wings are 3-dimensional, making traditional PIV techniques inadequate for full visualization of the wake structure. SAPIV provides a method for gathering 3-dimensional flow measurements of the flow around the model of the ladybug wing. Focus is placed on the development of the LEV and the draining process through the core.   

Flight simulations of a two-dimensional flapping wing by the IB-LBM

Two-dimensional symmetric flapping flight is investigated by the immersed boundary-lattice Boltzmann method. First, we investigate the effect of the Reynolds number on flows around symmetric flapping wings under no-gravity field and find that for high Reynolds numbers ($Re \geq55$) asymmetric vortices with respect to the horizontal line appear and the time-averaged lift force is induced on the wings. Secondly, we study the motion of the model with an initial rotational disturbance and find that the motion is rotationally unstable. That is, once the model starts rotating, the rotational motion rapidly increases due to a complicated vorticity field around the wings. Finally, we propose a simple way to control the rotational and horizontal motion by bending and flapping the tip of the wing. With the control we can achieve an upward stable motion in spite of the complicated vorticity field around the wings.   

Numerical modeling of flexible insect wings using volume penalization

We consider the effects of chordwise flexibility on the aerodynamic performance of insect flapping wings. We developed a numerical method for modeling viscous fluid flows past moving deformable foils. It extends on the previously reported model for flows past moving rigid wings (J Comput Phys 228, 2009). The two-dimensional Navier-Stokes equations are solved using a Fourier pseudo-spectral method with the no-slip boundary conditions imposed by the volume penalization method. The deformable wing section is modeled using a non-linear beam equation. We performed numerical simulations of heaving flexible plates. The results showed that the optimal stroke frequency, which maximizes the mean thrust, is lower than the resonant frequency, in agreement with the experiments by Ramananarivo et el. (PNAS 108(15), 2011). The oscillatory part of the force only increases in amplitude when the frequency increases, and at the optimal frequency it is about 3 times larger than the mean force. We also study aerodynamic interactions between two heaving flexible foils. This flow configuration corresponds to the wings of dragonflies. We explore the effects of the phase difference and spacing between the fore- and hind-wing.   

A flight control through unstable flapping flight

We have studied a flight control in a two-dimensional flapping flight model for insects. In this model, the model of center-of-mass can move in both horizontal and vertical directions according to the hydrodynamic force generated by flapping. Under steady flapping, the model converges to steady flight states depending on initial conditions. We demonstrate that simple changes in flapping motion, a finite-time stop of flapping, results in changes in the vortex structures, and the separation of two steady flight state by a quasi-steady flight. The model's flight finally converges to one of the final states by way of the quasi-steady state, which is not observed as a (stable) steady flight. The flight dynamic has been also analyzed.