Recent progress in flapping wing aerodynamics and aeroelasticity

Classifications, applications, and design challenges of drones: A review

It is the objective of this paper to review recent developments in the understanding and prediction of flapping-wing aerodynamics. To this end, several flapping-wing configurations are considered. First, the problem of single flapping wings is treated with special emphasis on the dependence of thrust, lift, and propulsive efficiency on flapping mode, amplitude, frequency, and wing shape. Second, the problem of hovering flight is studied for single flapping wings. Third, the aerodynamic phenomena and benefits produced by the flapping-wing interactions on tandem wings or biplane configurations are discussed. Such interactions occur on dragonflies or on a recently developed micro air vehicle. The currently available two- and three-dimensional inviscid and viscous flapping-wing flow solutions are presented. It is shown that the results are strongly dependent on flapping frequency, amplitude, and Reynolds number. These findings are substantiated by comparison with the available experimental data.

Flapping Wing Aerodynamics: Progress and Challenges

Low Speed Aerodynamics

This paper studies the trajectory tracking problem of flapping-wing micro aerial vehicles &#x0028 FWMAVs &#x0029 in the longitudinal plane. First of all, the kinematics and dynamics of the FWMAV are established, wherein the aerodynamic force and torque generated by flapping wings and the tail wing are explicitly formulated with respect to the flapping frequency of the wings and the degree of tail wing inclination. To achieve autonomous tracking, an adaptive control scheme is proposed under the hierarchical framework. Specifically, a bounded position controller with hyperbolic tangent functions is designed to produce the desired aerodynamic force, and a pitch command is extracted from the designed position controller. Next, an adaptive attitude controller is designed to track the extracted pitch command, where a radial basis function neural network is introduced to approximate the unknown aerodynamic perturbation torque. Finally, the flapping frequency of the wings and the degree of tail wing inclination are calculated from the designed position and attitude controllers, respectively. In terms of Lyapunov&#x02BC s direct method, it is shown that the tracking errors are bounded and ultimately converge to a small neighborhood around the origin. Simulations are carried out to verify the effectiveness of the proposed control scheme.

Modeling and trajectory tracking control for flapping-wing micro aerial vehicles

Unsteady aerofoil flows are often characterized by leading-edge vortex (LEV) shedding. While experiments and high-order computations have contributed to our understanding of these flows, fast low-order methods are needed for engineering tasks. Classical unsteady aerofoil theories are limited to small amplitudes and attached leading-edge flows. Discrete-vortex methods that model vortex shedding from leading edges assume continuous shedding, valid only for sharp leading edges, or shedding governed by ad-hoc criteria such as a critical angle of attack, valid only for a restricted set of kinematics. We present a criterion for intermittent vortex shedding from rounded leading edges that is governed by a maximum allowable leading-edge suction. We show that, when using unsteady thin aerofoil theory, this leading-edge suction parameter (LESP) is related to the term in the Fourier series representing the chordwise variation of bound vorticity. Furthermore, for any aerofoil and Reynolds number, there is a critical value of the LESP, which is independent of the motion kinematics. When the instantaneous LESP value exceeds the critical value, vortex shedding occurs at the leading edge. We have augmented a discrete-time, arbitrary-motion, unsteady thin aerofoil theory with discrete-vortex shedding from the leading edge governed by the instantaneous LESP. Thus, the use of a single empirical parameter, the critical-LESP value, allows us to determine the onset, growth, and termination of LEVs. We show, by comparison with experimental and computational results for several aerofoils, motions and Reynolds numbers, that this computationally inexpensive method is successful in predicting the complex flows and forces resulting from intermittent LEV shedding, thus validating the LESP concept.

Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding

Airfoil aerodynamic loads are expected to have quasi-steady, linear dependence on the history of input disturbances, provided that small-amplitude bounds are observed. We explore this assertion for the problem of periodic sinusoidal streamwise gusts, by comparing experiments on nominally 2D airfoils in temporally sinusoidal modulation of freestream speed in a wind tunnel vs. sinusoidal displacement of the airfoil in constant freestream in a water tunnel. In the wind tunnel, there is a streamwise unsteady pressure gradient causing a buoyancy force, while in the water tunnel one must subtract the inertial load of the test article. Both experiments have an added-mass contribution to aerodynamic force. Within measurement resolution, lift and drag, fluctuating and mean, were in good agreement between the two facilities. For incidence angle below static stall, small-disturbance theory was found to be in good agreement with measured lift history, regardless of oscillation frequency. The circulatory component of fluctuating drag was found to be independent of oscillation frequency. For larger incidence angles, there is marked departure between the measured lift history and that predicted from Greenberg's formula. Flow visualization shows coupling between bluff-body shedding and motion-induced shedding, identifiable with lift cancellation or augmentation, depending on the reduced frequency. Isolating the buoyancy effect in the wind tunnel and dynamic tares in the water tunnel, and theoretical calculation of apparent-mass in both cases, we arrive at good agreement in measured circulatory contribution between the two experiments whether the flow is attached or separated substantiating the linear superposition of the various constituents to total lift and drag, and supporting the idea that aerodynamic gust response can legitimately be studied in a steady freestream by oscillating the test article.

Airfoil longitudinal gust response in separated vs. attached flows

The AIAA Fluid Dynamics Technical Committee’s Low Reynolds Number Discussion Group has introduced several “canonical” pitch motions, with objectives of (1) experimental-numerical comparison, (2) assessment of closed-form models for aerodynamic force coefficient time history, and (3) exploration of the vast and rather amorphous parameter space of the possible kinematics. The baseline geometry is a flat plate of nominally 2.5% thickness and round edges, wall-to-wall in ground test facilities and spanwise-periodic or 2D in computations. Motions are various smoothings of a linear pitch ramp, hold and return, of 40 and 45 amplitude. In an attempt to discern acceleration effects, sinusoidal and linear-ramp motions are compared, where the latter have short runs of high acceleration and thus high noncirculatory lift and pitch. Parameter variations include comparison of the flat plate with an airfoil and ellipse, variation of reduced frequency, pitch pivot point location and comparison of pitch to quasi-steady equivalent plunge. All motions involve strong leading edge vortices, whose growth history depends on pitch pivot point location and reduced frequency, and which can persist over the model suction-side for well after motion completion. Noncirculatory loads were indeed found to be localized to phases of motion where acceleration was large. To the extent discernable so far, closed-form models of lift coefficient on the pitch upstroke are relatively straightforward, but not so on the downstroke, where motion history effects complicate the return from stall. Broad Reynolds number independency, in flowfield evolution and lift coefficient, was found in the 10 to 10 range.

http://www.seas.ucla.edu/sofia/AIAA20101085.pdf

Résumé of the AIAA FDTC Low Reynolds Number Discussion Group's Canonical Cases

Vortical Structures in High Frequency Pitch and Plunge at Low Reynolds Number

Rectilinearly surging wings are investigated under several different velocity profiles and incidence angles. The primary wing studied here was an aspect ratio 4 rectangular flat plate. Studies on acceleration distance, ranging from 0.125c to 6c, and incidence angles 5°–45° were performed to obtain a better understanding of the force and moment histories during an extended surge motion over several chord-lengths of travel. Flow visualization and particle image velocimetry were performed to show the flow structures responsible for variations in force and moment coefficients. It was determined that the formation and subsequent shedding of a leading edge vortex correspond to oscillations in force coefficients for wings at high angle of attack. Comparing unsteady lift results to static force measurements, it was determined that for cases with large flow separation, even after 14 chords traveled at a constant velocity, the unsteady forces do not converge to the fully developed values. Forces were then broken up...

Michael V. Ol

Papers

Discrete-vortex method with novel shedding criterion for unsteady aerofoil flows with intermittent leading-edge vortex shedding

Airfoil longitudinal gust response in separated vs. attached flows

Résumé of the AIAA FDTC Low Reynolds Number Discussion Group's Canonical Cases

Vortical Structures in High Frequency Pitch and Plunge at Low Reynolds Number

Unsteady aerodynamic characteristics of a translating rigid wing at low Reynolds number