Wake-Structure Formation of a Heaving Two-Dimensional Elliptic Airfoil K. B. Lua, * T. T. Lim, † and K. S. Yeo † National University of Singapore, Singapore 119260, Republic of Singapore and G. Y. Oo ‡ DSO National Laboratories, Singapore 118230, Republic of Singapore DOI: 10.2514/1.25310 This paper is prompted by a recent numerical study (Lewin, G. C., and Haj-Hariri, H., “Modelling Thrust Generation of a Two-Dimensional Heaving Airfoil in Viscous Flow,” Journal of Fluid Mechanics, Vol. 492, Oct. 2003, pp. 339–362) that shows that for a two-dimensional (2-D) elliptic airfoil undergoing prescribed heaving motion in a viscous fluid, both leading-edge vortices and trailing-edge vortices contributed to the formation of the wake structures. However, an earlier dye-visualization study (Lai, J. C. S., and Platzer, M. F., “Jet Characteristics of a Plunging Airfoil,” AIAA Journal, Vol. 37, No. 12, 1999, pp. 1529–1537) on a heaving NACA 0012 airfoil appears to show that the wake structures were derived from trailing-edge vortices only. The dissimilarity in the two studies remains unclear because there is no corresponding experimental data on a 2-D heaving elliptic airfoil. In this study, digital particle image velocimetry technique was used to investigate the wake-structure formation of a 2-D elliptic airfoil undergoing simple harmonic heaving motion. For the range of flow conditions investigated here, our results show that the type of wake structures produced is controlled by when and how the leading-edge vortices interact with the trailing-edge vortices. Nomenclature A = heaving amplitude c = chord length, 20 mm (reference length) f = heaving frequency h = A=c k = 2fc=U 1 kh = 2fA=U 1 L = length of airfoil, 200 mm Re = U 1 c= Sta = advance ratio, fA=U 1 Stc = reduced frequency, fc=U 1 T = heaving period t = time U 1 = freestream velocity (reference speed) Y = heaving motion  = kinematic viscosity I. Introduction B IOLOGICAL fliers and swimmers, such as insects and fishes, use flapping foils to generate high lift and thrust in fluids. The earliest studies on flapping foils were carried out independently by Knoller [1] and Betz [2], who recognized that a flapping foil generates an effective angle of attack, with the resulting normal force producing both lift and thrust components. This finding was verified by Katzmayr [3], who measured the thrust of a stationary airfoil subjected to a sinusoidally oscillating freestream. A subsequent analysis by Glauert [4] using classical linear theory of an oscillating wing in an inviscid incompressible fluid found that for a fixed advance ratio, there is no preferred frequency, and the thrust coefficient and efficiency increased monotonically with decreasing frequency. A later analysis by Garrick [5] on plunging and pitching plates, based on the assumption of small-amplitude oscillations in an inviscid incompressible fluid, found a rapid reduction in the propulsive efficiencies of flapping foils, from a value of 1.0 at a low flapping frequency to about 0.5 as the frequency is increased. This finding was later confirmed in an experiment by Silverstein and Joyner [6] in 1939. However, von Kármán and Burgers [7] were the first to provide theoretical explanation of drag and thrust production based on the orientation of the wake vortices; the well-known drag- producing Kármán vortex street and thrust-producing reverse Kármán vortex street were identified by them and were later verified experimentally by Bratt [8]. Further theoretical works by Wu [9] and Lighthill [10] showed that flapping foils can generate different kinds of spatially periodic patterns of vortices that were used as a form of propulsion by aquatic animals (see also [11–15]). In the following decades, numerous theoretical and experimental studies [16–28] were conducted to better understand flapping-foil aerodynamics and propulsion, and the recent interest in using flapping wings [29–40] to generate lift and propulsion in applications such as micro air vehicles has given research in this area a further impetus. Although the bulk of the investigations on flapping foils were concentrated on pure pitching or combined heaving and pitching motions, some studies have also been conducted on pure heaving motion. It is well established that the motion of a heaving airfoil is described by three nondimensional parameters: namely, Sta, Stc, and Re, although in some cases, A=c is used in place of Sta. Depending on the heaving frequency and amplitude, studies by Freymuth [16], Jones et al. [23], Lai and Platzer [24], Lewin and Haj-Hariri [25], and Young and Lai [26] showed that the wake structures of a heaving airfoil can be characterized by a drag- producing Kármán vortex street, thrust-producing reverse Kármán vortex street, or neutral wake (in which two vortices of the same sign are produced in every half-cycle). In a numerical study by Lewin and Haj-Hariri [25] (henceforth referred to as LH) on a heaving two-dimensional (2-D) elliptic airfoil in a viscous fluid, the Received 19 May 2006; revision received 23 February 2007; accepted for publication 17 March 2007. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/07 $10.00 in correspondence with the CCC. * Research Fellow, Department of Mechanical Engineering, 10 Kent Ridge Crescent. † Associate Professor, Department of Mechanical Engineering, 10 Kent Ridge Crescent. ‡ Member of the Technical Staff, 20 Science Park Drive. AIAA JOURNAL Vol. 45, No. 7, July 2007 1571