Aerodynamic effects of flexibility in flapping wings

Liang Zhao Qingfeng Huang Xinyan Deng ( Sanjay P. Sane ) 0 National Centre for Biological Sciences, Tata Institute of Fundamental Research , GKVK Campus, Bellary Road, Bangalore 560 065, India 1 Department of Mechanical Engineering, University of Delaware, 126 Spencer Laboratory , Newark, DE 19716, USA Articles on similar topics can be found in the following collections Receive free email alerts when new articles cite this article - sign up in the box at the top right-hand corner of the article or click here References Subject collections Email alerting service To subscribe to J. R. Soc. Interface go to: http://rsif.royalsocietypublishing.org/subscriptions Aerodynamic effects of flexibility in flapping wings Recent work on the aerodynamics of flapping flight reveals fundamental differences in the mechanisms of aerodynamic force generation between fixed and flapping wings. When fixed wings translate at high angles of attack, they periodically generate and shed leading and trailing edge vortices as reflected in their fluctuating aerodynamic force traces and associated flow visualization. In contrast, wings flapping at high angles of attack generate stable leading edge vorticity, which persists throughout the duration of the stroke and enhances mean aerodynamic forces. Here, we show that aerodynamic forces can be controlled by altering the trailing edge flexibility of a flapping wing. We used a dynamically scaled mechanical model of flapping flight (Re 2000) to measure the aerodynamic forces on flapping wings of variable flexural stiffness (EI). For low to medium angles of attack, as flexibility of the wing increases, its ability to generate aerodynamic forces decreases monotonically but its lift-todrag ratios remain approximately constant. The instantaneous force traces reveal no major differences in the underlying modes of force generation for flexible and rigid wings, but the magnitude of force, the angle of net force vector and centre of pressure all vary systematically with wing flexibility. Even a rudimentary framework of wing veins is sufficient to restore the ability of flexible wings to generate forces at near-rigid values. Thus, the magnitude of force generation can be controlled by modulating the trailing edge flexibility and thereby controlling the magnitude of the leading edge vorticity. To characterize this, we have generated a detailed database of aerodynamic forces as a function of several variables including material properties, kinematics, aerodynamic forces and centre of pressure, which can also be used to help validate computational models of aeroelastic flapping wings. These experiments will also be useful for wing design for small robotic insects and, to a limited extent, in understanding the aerodynamics of flapping insect wings. 1. INTRODUCTION The aerodynamic forces generated by flapping wings depend on several physical factors. These include the kinematics and geometry of the wings, their material architecture and the fluid environment around the wing. Besides these, the solid fluid interactions between the wing surface and its surrounding air medium also play a key role in aerodynamic force generation. Until recently, it was difficult to numerically model these aeroelastic interactions, because they involve the mechanics and mutual interactions of both the solid and fluid continua. At every iterative step, it is therefore necessary to ensure that the numerical models provide convergent solutions for both the solid and fluid case, which is computationally very Electronic supplementary material is available at http://dx.doi.org/ 10.1098/rsif.2009.0200 or via http://rsif.royalsocietypublishing.org. intensive (Kamakoti & Shyy 2004). Because of these complications, most numerical studies (Liu 2002; Ramamurti & Sandberg 2002, 2007; Sun & Tang 2002; Wang 2004; Wang et al. 2004) have focused their attention on rigid wings for which the aeroelastic coupling of solid and fluids can be ignored. Similarly, most experimental studies (Dickinson et al. 1999; Sane & Dickinson 2001; Usherwood & Ellington 2002a,b; Prempraneerach et al. 2003) have also focused on rigid rather than flexible wings. Recently, with the availability of better computational power, there have been some attempts to numerically model aeroelastic interactions to determine the role of wing flexibility in aerodynamic force production (Ho et al. 2003; Shyy et al. 2008). However, these efforts were stymied by the lack of availability of appropriate empirical data required for validation. The aerodynamics of flapping wings has been most extensively investigated in recent years in the context of insect flight (for reviews see Lehmann 2008; Sane 2003; Wang 2005). However, even here, the role of the Aerodynamics of flapping, flexible wings L. Zhao et al. solid mechanics of the flapping wings has received surprisingly little attention although wing flexibility has long been recognized as an important factor for insect flight aerodynamics (Wootton 1992, 1993; Wootton et al. 2003; Walker et al. 2009). Combes & Daniel (2003a,b) showed that wing flexural stiffness varies by as many as four orders of magnitude across insect taxa, and wing flexibility is strongly correlated with wing size. Indeed, the absolute wing-span and chord length account for more than 95 per cent of the observed variation in flexural stiffness values for insect wings. The flexible wing surface adapts its shape in response to external fluid forces and thus influences aerodynamic force production during flapping flight (Wootton 1993). Because the patterns of wing flexion are governed primarily by the inertial properties of the wing rather than pressure gradients arising from wing air aeroelastic interactions, these studies concluded that the aeroelastic feedback was negligible and the wings may be treated as purely inertial, flexible structures in the case of flapping insect wings (Combes & Daniel 2002). Thus, computational simulations of insect wings need only prescribe a pattern of bending that matches the flexibility pattern of actual insect wings. Another important factor to consider when investigating the role of wing flexibility in insects is the presence of wing veins. Like flexibility or wing shape, wing venation patterns are also remarkably diverse across insect taxa, ranging from the extensive venation in the twisting and bending wings of dragonflies (Wootton 1998) to the sparse venation in butterfly forewings. Wing venation may also play a key role in determining the asymmetric dorso-ventral resistance of insect wings in response to aerodynamic forces and therefore also its efficiency in force production (Wootton et al. 2000). In this paper, we study how wing flexibility influences aerodynamic force generation in flapping flight. Rather than replicate the intricate, anisotropic material and mechanical architecture of insect wings, we approached this problem from purely physical considerations using wings made (...truncated)