Session R26: Aerodynamics V

Low Reynolds Number Wing Transients in Rotation and Translation

The unsteady aerodynamic forces and flow fields generated by a wing undergoing transient motions in both rotation and translation were investigated. An aspect ratio~2 flat plate wing at a 45\,deg angle of attack was driven over 84\,deg of rotation (3~chord-lengths of travel at 3/4~span) and 3~and 10~chord-lengths of translation in quiescent water at Reynolds numbers between 2,500 and 15,000. Flow visualization on the rotating wing revealed a leading edge vortex that lifted off of the wing surface, but remained in the vicinity of the wing for the duration of the wing stroke. A second spanwise vortex with strong axial flow was also observed. As the tip vortex grew, the leading edge vortex joined the tip vortex in a loop-like structure over the aft half of the wing. Near the leading edge, spanwise flow in the second vortex became entrained in the tip vortex near the corner of the wing. Unsteady force measurements revealed that lift coefficient increased through the constant-velocity portion of the wing stroke. Forces were compared for variations in wing acceleration and Reynolds number for both rotational and translational motions. The effect of tank blockage was investigated by repeating the experiments on multiple wings, varying the distance between the wing tip and tank wall.   

Unsteady Lift Response and Energy Extraction in Gusting Flows

The unsteady aerodynamic forces associated with streamwise (surging) and transverse (plunging) oscillating motions are studied to understand the dynamic response to gusts and the potential for energy extraction. We focus on 2D thin airfoils at low sub- and super-critical Reynolds number so that the role of wake instability can be isolated. Simulations are performed in a large parameter space of angle of attack, reduced frequency, and oscillation amplitude. At low angle of attack, the magnitude and phase of the fluctuating lift are in reasonable agreement with classical theory at all reduced frequencies. In this case, the quasi-steady force is modified by contributions from shed vorticity at the trailing edge and added-mass at high reduced frequency. At high angle of attack, the fluctuating forces are found to be enhanced or attenuated by a leading-edge vortex, depending on the reduced frequency. Resonance with the wake instability is also investigated.   

Transient Vortex Structures in the Near Wake of a Wing during Pitch Up/Down Maneuvers

The vorticity distribution in the wake of a thin airfoil reflects the lift and bound circulation history of the wing. During a pitch-up maneuver from 0 degrees to some higher angle of attack (assuming attached flow), a ``starting vortex'' is formed in the wake whose circulation is opposite in strength to the bound circulation in the wing. However, a finite time is required for the starting vortex to fully develop, and if the wing pitches down to a smaller angle of attack before the first starting vortex has reached full strength then an imbalance in the wake circulation occurs. The delay time between the up/down pitch motions and the maximum angle of attack determine which additional vortices must be formed to satisfy Kelvin's theorem. In addition to the irrotational flow vortices that form, vorticity associated with the viscous boundary layers also accumulates into discrete vortices that accompany each ``starting vortex.'' The complicated distributions of vortices and their evolution in the wake are examined with detailed PIV, smoke-visualization, and numerical simulations at Re = 240 to 70,000.   

Effects of wing flexibility on aerodynamic performance in hovering flight

In this study, we use a strong-coupling approach to simulate three dimensional flexible flapping wings in hovering flight. The approach is based on a uniform description of both fluid and solid in global Eulerian framework. There has been extensive validation of the current approach with other numerical simulation and experiments. Then we apply our approach to simulate flapping wings with different flexibility and other control parameters. The simulation results allow us to study directly the effects of wing flexibility on the aerodynamic performance of hovering flight.   

Optimization of the airfoil stroke in a high Reynolds number flow for energy harvesting

We investigate the heaving and pitching stroke of an airfoil for maximum energy extraction from the flow of the ambient fluid. This analysis is targeted towards optimization of oscillating airfoil or hydrofoils for wind and hydrokinetic energy conversion respectively. The goal is to study the influence of unsteady aerodynamic effects like leading edge vortex, unsteady boundary layer separation, vortex recapture, etc. We are inspired by the mechanics of insect and bird flight, which are believed to use unsteady aerodynamics for enhanced performance. Our airfoil has two degrees of freedom, heaving and pitching, and these degrees of freedom are actuated independently. We employ a variational framework for optimizing the transient stroke of the airfoil with the objective function being the time-averaged harvested power.   

Experimental and Numerical investigations of flapping flight

Insects have been observed to produce higher lift than predicted by conventional steady-aerodynamics using a combination of unsteady aerodynamic mechanisms. The wing kinematics and the flow fields produced during flapping flight is essentially 3D. ~Recently, in our group ~it has been shown, using flow visualization and 2D simulations, that the asymmetric flapping where, down-stroke is faster than the upstroke, can produce sustained lift. Also by introducing controlled wing flexibility, one can increase the magnitude of the lift. In order to verify these predictions quantitatively we are measuring forces produced ~by a mechanical flapper using a force-balance. Results of this study will be presented that includes the forces measured in symmetric and asymmetric flapping at different flapping frequencies. Similar understanding of various wing-kinematics during a forward flight can be achieved by doing transient, 3D simulations. A fast, accurate and simple 3D scheme which is capable of dealing with moving boundaries using Lattice Boltzmann has been developed for this purpose. Benchmarking of this scheme has been done for a forward flapping of the wing with elliptical cross-section. The results on the benchmarking and other preliminary results will be presented in the conference.   

The aerodynamic cost of flight in bats---comparing theory with measurement

Aerodynamic theory has long been used to predict the aerodynamic power required for animal flight. However, even though the actuator disk model does not account for the flapping motion of a wing, it is used for lack of any better model. The question remains: how close are these predictions to reality? We designed a study to compare predicted aerodynamic power to measured power from the kinetic energy contained in the wake shed behind a bat flying in a wind tunnel. A high-accuracy displaced light-sheet stereo PIV system was used in the Trefftz plane to capture the wake behind four bats flown over a range of flight speeds (1--6m/s). The total power in the wake was computed from the wake vorticity and these estimates were compared with the power predicted using Pennycuick's model for bird flight as well as estimates derived from measurements of the metabolic cost of flight, previously acquired from the same individuals.   

Flow Structure on a Flapping Wing: Quasi-Steady Limit

The three-dimensional flow structure on a rotating wing is determined using stereoscopic particle image velocimetry. The wing is a rectangular flat plate with an aspect ratio $AR$ = 2; the effective angle of attack is $\alpha_{eff}$ = 45$^\circ$ and the Reynolds number $Re$ = 15,150. Emphasis is on comparison of the early stages of rotation with the late stage corresponding to the steady-state. The flow structure in the early stage involves a stable leading-edge vortex, and root, tip, and shed vortices. Along the span of the wing, the leading-edge vortex has pronounced concentrations of chordwise-oriented vorticity. These concentrations arise from the large-magnitude spanwise flow along the surface of the wing. At large angles of rotation, there is loss of the tip vortex, which is accompanied by loss of the chordwise-oriented vorticity due to eruption of the spanwise flow from the wing surface. In addition, patterns of downwash, spanwise velocity and spanwise vorticity flux are correlated with the local scale and degree of concentration of spanwise vorticity of the leading-edge vortex.   

Thrust Enhancement of Flapping Wings in Tandem and Biplane Configurations by Pure Plunging Motion

The propulsion performance of flapping NACA0012 airfoils undergoing harmonic plunging motion in tandem and biplane wing configurations is investigated numerically. An unstructured finite volume solver based on Arbitrary Lagrangian-Eulerian formulation is utilized in order to solve the incompressible unsteady Navier-Stokes equations. Four different tandem and four different biplane wing combinations are considered. Various instantaneous and time-averaged aerodynamic parameters including lift and drag coefficients, vorticity contours and streamlines are calculated for each case and compared with each other. As a reference the single wing case corresponding to the deflected jet phenomenon in Jones and Platzer (\textit{Exp. Fluids} 46:799-810, 2009) is also studied. In these simulations, the Reynolds number is chosen as 252, the reduced frequency of plunging motion ($k=2\pi f/U_{\infty}$) is 12.3 and the plunge amplitude non-dimensionalized with respect to chord is 0.12. The solutions of the single wing case indicate dependence on the location of start-up vortices. Meanwhile the multiple wing configurations indicate that the highest thrust enhancement is obtained in one of the biplane cases where the two wings closely moving towards each other namely biplane asynchronous-closer case.   

Flight Stabilization with Flapping Wings in Gusty Environments

Achieving stable flight with flapping wings, is one of the major challenges for designing micro- aerial- vehicles (MAVs) but is part of the natural behavior of flying insects. To better understand how flying insects flyers can stabilize themselves during hovering flight, we use a computational model, which couples the Navier-Stokes equations for the aerodynamics with a six-degree of freedom (NS-6-DOF) flight dynamics model to recreate the free hovering flight of a hawkmoth. The NS-6DOF model indicates that a hovering hawkmoth is open-loop unstable. Examination of the aerodynamic forces and flight dynamics coupled with observations of the animal in the laboratory suggest a bioinspired strategy for close-loop stabilization of the hovering hawkmoth and this strategy is explored using the NS-6DOF insect model. Simulations are conducted both for quiescent and highly ``gusty'' ambient conditions and the computed response of the ``stabilized'' animal compared to experimental observations.   

Adjoint-based optimization for flapping wings

Adjoint-based methods show great potential in flow control and optimization of complex problems with high- or infinite-dimensional control space. It is attractive to solve an adjoint problem to understand the complex effects from multiple control parameters to a few performance indicators of the flight of birds or insects. However, the traditional approach to formulate the adjoint problem becomes either impossible or too complex when arbitrary moving boundary (e.g. flapping wings) and its perturbation is considered. Here, we use non-cylindrical calculus to define the perturbation. So that, a simple adjoint system can be derived directly in the inertial coordinate. The approach is first applied to the optimization of cylinder oscillation and later to flapping wings.