17th Australasian Fluid Mechanics Conference Auckland, New Zealand 5-9 December 2010 Analysis of Ornithopter-Wing Aerodynamics A. Valiyff, J. R. Harvey, M. B. Jones, S. M. Henbest, and J. L. Palmer Air Vehicles Division, Defence Science and Technology Organisation, Fishermans Bend, VIC, 3207 Australia Abstract The aim of the work presented in this paper is to characterise the flapping-flight aerodynamics of ornithopter wings through experimentation and analysis. Time-resolved and mean mea- surements have been made of the thrust produced by two com- mercially available ornithopters in a low-speed wind tunnel at varying air speeds and flapping frequencies. In order to gain a better understanding of flapping flight and for comparison with the experimental results, an aerodynamic model relying on blade-element theory has been utilised. Introduction Accurate aerodynamic modelling of the flapping flight of in- sects, birds, and bats and their mechanical counterparts (insect- and bird-like devices, known as entomopters and ornithopters, respectively) is difficult, due to the relatively low Reynolds numbers at which most operate and the typically low aspect ra- tios of their wings, which promote strong tip vortices and rolling instabilities. Furthermore, accounting for wing structural flexi- bility is a complex task and therefore is generally neglected. Several attempts have been made previously to characterise the aerodynamics of flapping-wing micro air vehicles (MAVs) by use of experimental and analytical methods. Hu et al. [5] and Motamed and Yan [8] performed force measurements with bench-top flapping mechanisms. Although not appropriate for implementation in a functional MAV (given the significant size and weight of the driving mechanisms), their approaches per- mitted accurate force measurements to be conducted with com- plex wing kinematics. Other researchers have made force mea- surements directly on operational MAVs. For example, Mueller et al. [9] recently developed a test stand for measuring the time- resolved thrust and lift generated by a 15-g flapping-wing MAV. The focus of this study was to characterise the aerodynamics of two commercially available ornithopters using experimental and analytical methods. Tests were performed in a low-speed wind tunnel, where the thrust generated by each ornithopter was measured using a load sensor at various air speeds and flap- ping frequencies. The time-resolved and mean thrust measure- ments were compared with analytical predictions obtained from a blade-element model. Blade-Element Aerodynamic Model Aerodynamic models of flapping-wing flight fall into two dis- tinct categories, those that account for unsteady effects through extensive modelling of the wake and those relying on an as- sumption that the flow is quasi-steady. In quasi-steady models, the details of the wake are rendered less important by the as- sumption that the flapping frequency is low enough that shed- wake effects are insignificant. In this paper, the blade-element approach by DeLaurier [2] has been selected as the basis of a quasi-steady aerodynamic model. The following is a brief outline; for a comprehensive review, re- fer to [2]. The wing is flapped by a periodic variation of its root-dihedral angle, and the prescribed deflections of the struc- ture generate a spanwise twist distribution. The model accounts U θ a ˙ h Flapping axis y z dN x θ U dF x γ Figure 1: Root-flapping wing (adapted from [2]). for partial leading-edge suction and post-stall behaviour, as well as vortex-wake effects [2, 3]. The wing leading edge is taken to be a rigid axis about which wing twist occurs, and the magnitude of the wing twist is a pre- scribed function of spanwise coordinate (y) and time (t ). The wing is divided into a finite number of segments, each of which is analysed independently. As indicated in figure 1, the x and y axes lie along the chord and span of a given wing section, re- spectively. The motion of each section consists of a plunging velocity at the leading edge ( ˙ h) and a local pitch angle (θ). The plunging displacement (h) is described by h(y , t )= Γy cos(ωt ), (1) where Γ is the maximum flapping angle and ω is the flapping rate (ω = 2π f , where f is in Hz and ω is in rad/s). The pitch an- gle (θ) is the sum of: the angle of the flapping axis with respect to the freestream (θ a ); the mean pitch of the chord with respect to the flapping axis (θ w ); and the dynamically varying pitch an- gle (δθ), which is due to the prescribed wing twist. Thus, θ(y , t )= θ a + θ w (y)+ δθ(y , t ), (2) where δθ(y , t )= −β 0 y sin(ωt ) (3) and β 0 is a constant representing the twist angle per unit dis- tance along the span. Figure 2 shows the orientations and positions of the forces act- ing on a wing section, where the elemental forces have been resolved in the chordwise (x) and normal (z) directions. Each wing segment operates in one of two distinct flight regimes, at- tached or separated flow, determined by the relative angle of attack at the leading edge. The normal force (dN) acting on each section is dN =  dN c − dN a for attached flow (dN c ) sep − (dN a ) sep for separated flow, (4) where dN c is the normal force due to circulation, dN a is the nor- mal force due to apparent mass, and the subscript “sep” denotes these forces for the case of separated flow. For attached flows, the circulatory force is given by dN c = ρUV 2 C n (y)cdy , (5)