Oscillating foils of high propulsive efficiency

Abstract

Thrust-producing harmonically oscillating foils are studied through force and power measurements, as well as visualization data, to classify the principal characteristics of the flow around and in the wake of the foil. Visualization data are obtained using digital particle image velocimetry at Reynolds number 1100, and force and power data are measured at Reynolds number 40 000. The experimental results are compared with theoretical predictions of linear and nonlinear inviscid theory and it is found that agreement between theory and experiment is good over a certain parametric range, when the wake consists of an array of alternating vortices and either very weak or no leading-edge vortices form. High propulsive efficiency, as high as 87%, is measured experimentally under conditions of optimal wake formation. Visualization results elucidate the basic mechanisms involved and show that conditions of high efficiency are associated with the formation on alternating sides of the foil of a moderately strong leading-edge vortex per half-cycle, which is convected downstream and interacts with trailing-edge vorticity, resulting eventually in the formation of a reverse Kármán street. The phase angle between transverse oscillation and angular motion is the critical parameter affecting the interaction of leading-edge and trailingedge vorticity, as well as the efficiency of propulsion. IntroductionFish and cetaceans employ their oscillating tails to produce propulsive and maneuvering forces. The tails of some of the fastest swimming animals closely resemble high-aspect-ratio foils. Because of the presumed optimal propulsive performance of fish, oscillating foils have been studied extensively using theoretical and numerical techniques (Lighthill 1975;Wu 1961Wu , 1971Longvinovich 1971;Cheng & Murillo 1984;Karpouzian, Spedding & Cheng 1990;McCune & Tavares 1993), and experimentally (Scherer 1968;DeLaurier & Harris 1982;Lai, Bose & McGregor 1993).A foil in steady forward motion and a combination of steady-state harmonic heaving and pitching motion produces thrust through the formation of a flow downstream from the trailing edge, which when averaged over one period of oscillation has the form of a jet. This average jet flow is unstable, acting as a narrow-band amplifier of perturbations. The harmonic motion of the foil causes unsteady shedding of vorticity from the trailing edge, while there are conditions when leading-edge vortices form as well. The interaction between the unsteady vorticity shed by the foil and the inherent dynamics of the unstable wake result in the formation of patterns of

Performance augmentation mechanism of in-line tandem flapping foils

“…Red is high thrust and blue is low thrust, white represents the value of a single foil. known to consist of two primary vortices of alternating sign shed by the foil per cycle (Gopalkrishnan et al 1994;Anderson et al 1998;Read et al 2003). This wake structure is similar to a drag-producing von Kármán street of a bluff body, although the signs of the vortices on each side of the 'street' is reversed in the flapping foil case because it produces thrust instead of drag.…”

The wake structure and thrust performance of a rigid low-aspect-ratio pitching panel

“…The generation of dynamic stall vortices that combine with vorticity shed from the trailing edge has been associated with enhanced thrust production in two-dimensional unsteady propulsors (Anderson et al 1998). Visualizations of the wakes of airfoils and finite wings actuated in pitching and heaving motions have shown dynamic stall vortices to be a robust feature of unsteady propulsion (Freymuth 1988;Anderson et al 1998;von Ellenrieder et al 2003;Guglielmini 2004;Dong et al 2005).…”

“…They supported their conclusion with experimental data and observations of the swimming gaits of a variety of aquatic animals. Anderson et al (1998) conducted a detailed parametric study of the thrust performance and wake structure of a pitching and heaving NACA 0012 airfoil and compared their measurements with the predictions of linear and nonlinear analytical models. Although, for a given set of kinematic parameters, the models predicted a single peak in efficiency within the range 0.1 < St < 0.2, in several cases, the experimental data revealed a second peak within the range 0.3 < St < 0.4, which was attributed to the wake dynamics described above.…”

“…Efficient propulsion is frequently commensurate with the generation of leading-edge vortices which are shed at an appropriate phase to coalesce with vortices shed by the trailing edge, forming a reverse Kármán street (Oshima & Natsume 1980;Oshima & Oshima 1980;Freymuth 1988;Ohmi et al 1990Ohmi et al , 1991Anderson et al 1998). Under suboptimal conditions, the leadingand trailing-edge vortices fail to combine, forming four vortices per oscillation.…”

Examination of the three‐dimensional geometry of cetacean flukes using computed tomography scans: Hydrodynamic implications

“…At typical swimming speeds (2.5 m/sec and above) of dolphins, such as Tursiops truncatus (Williams et al, 1999;Fish and Rohr, 1999;Rohr et al, 2002), the maximum angle of attack is close to or below the 17 degrees stall angle for the NACA 63-021 foil (Fish, 1993). Indeed, angles of attack up to 30 degrees may be sustained by oscillating hydrofoils similar to dolphin flukes without stalling (Triantafyllou and Triantafyllou, 1995;Anderson et al, 1998). An oscillating foil can function at high angles of attack because of unsteady effects that enhance the pressure difference between the two sides of the foil and result in greater lift production.…”