EXPERIMENTAL INVESTIGATION OF A FLAPPING WING MODEL: SOME CHALLENGES FROM UNSTEADY AERODYNAMICS

A flapping-wing model has been experimentally investigated in the large (2.2m x 2.9m), low-speed wind tunnel of the Technische Universtität Darmstadt. All tests were conducted at Reynolds numbers between 26,500 and 135,000 and throughout a range of reduced frequencies between 0.029 and 0.29, where the reduced frequency is defined as k=(πfc)/U∞ (f is the wingbeat frequency, U∞ the free-stream velocity, and c the average wing chord.) The relationships between flight parameters and the change in circulation during the course of a wing-beat cycle have been investigated. Particle Image Velocimetry (PIV), synchronized with the wing-beat cycle, has been used for flow field measurements and visualization. This yields the phase-averaged reconstruction of the flow field in measurement planes behind the wing parallel and perpendicular to the flow direction. This visualizes the shedding vortices from the wing trailing edge and the tip vortices in the far-field wake, respectively. The results of the flow visualization study are then used to calculate the phase resolved forces acting on the model. INTRODUCTION Accompanying the recent development of Micro Air Vehicles (MAVs), a keen interest in the fundamental aerodynamics of flapping flight has arisen. Simultaneously, the aerodynamics of bird and insect flight are currently being studied in great detail by biologists in an effort to understand better the interaction of mechanics, morphology and the energy budget of these species (Ellington 1999, Dickinson et al. 1999, Sane 2003, Rayner and Gordon 1998, Spedding et al. 2003). In comparison with conventional propulsion systems, flapping flight allows for a very high manoeuvrability, an important advantage when flying in confined spaces. However, to date many aerodynamic questions must still be resolved in order for flapping flight to be used in technical applications. Animal flight can contribute to our understanding of the mechanisms of flapping flight especially at low Reynolds numbers. One challenge facing such studies is the direct force measurement on swimming and flying animals, which generally will not fly or swim in an undisturbed manner when tethered. A handful of successful direct-force measurements have been made with insects such as locusts (Zarnack 1969, Cloupeau et al. 1979, Wilkin 1990), moths (Wilkin 1991, Wilkin and Williams 1993) and fruit flies (Dickinson and Gotz 1996) but there always remains some doubt correlating the experimental results with real-life flying or swimming behaviour. Pressure measurements on animals are similarly very complicated (Usherwood et al. 2003, 2005) and time consuming. Therefore the visualization of the wake structure generated by the moving animal is now being more frequently used to indirectly analyze the generated aerodynamic or hydrodynamic forces. Recent advances in optical measurement techniques such as particle image velocimetry (PIV) allow not only a qualitative analysis (Spedding et al. 1986, 1987a, 1987b, Willmott et al. 1997) but also a quantitative investigation of the wake in terms of the instantaneous velocity and vorticity fields (Drucker and Lauder 1999, Spedding et al. 2003, Warrick et al. 2005). Using the control-volume approach and applying the momentum equation, it is possible to obtain the aerodynamic forces acting on the body by taking into account the total surface forces over the entire control volume. However, even in steady locomotion conditions such as in cruising flight there exists a periodic acceleration and deceleration over most, if not all of the animal’s body. Because of the unsteady flow moving around the body an exact determination of aerodynamic or hydrodynamic forces requires in theory the net flow of momentum out of the control volume surface as well as the time rate of change due to the unsteady fluctuations inside the control volume itself (Dabiri 2005). In practice it is nearly impossible to measure all this information simultaneously. However, one can measure the velocity field on a two-dimensional plane out of the control volume. From this velocity field one can infer the vorticity field in the measurement plane. In the context of bird flight, and applying Helmholtz’s vortex laws, one assumes that the circulation in a closedvortex ring is equal throughout. Therefore one can surmise that the tip-vortex circulation of a single wing should equal that of the bound vortex circulation, and thus the lift produced through the Kutta-Joukowsky theorem (Panda and Zaman 1994). Therefore depending on what measurement plane is used, one can either capture the changes in the bird’s lift (observed in the circulation change in the wake on a plane parallel to the flow direction) or the total lift (measured by the circulation of the wing-tip vortex on a plane normal to the flow direction). This hypothesis is tested in the present investigation for a flapping bird model. EXPERIMENTAL FACILITY AND METHODS The life-sized flapping-wing model is based on the aerodynamic characteristics of a goose, with a span of 1.13m and a wing-beat frequency up to 2.2Hz. The Reynolds number was varied between 26,500 and 135,000, while the wing-motion amplitude and the angle of attack were adjusted at the shoulder joint. A realistic bird-like wing profile was not used since there exists a large