Effect of Angle of Attack Kinematics on Passive Flapping Foil Power Generation

EFFECT OF ANGLE OF ATTACK KINEMATICS ON PASSIVE FLAPPING FOIL POWER GENERATION John Young and Joseph C.S. Lai School of Engineering and Information Technology University of New South Wales, Canberra, ACT, 2600, Australia Keywords: flapping foil, power generation Abstract expected to diminish the impact on wildlife. This is due to the entire foil moving at the same A fully passive flapping foil turbine was speed, thereby increasing the proportion of the simulated using a 2D Navier Stokes solver with turbine area working at maximum power two-way fluid structure interaction at a extraction. In the tidal flow and river Reynolds number of 1100. The angle of attack applications, operation is also possible in profile was specified, and variations in the shallower water than for horizontal axis rotary phase and shape of this profile on the power turbines, when the foil is oriented horizontally generation efficiency investigated. Performance and plunges vertically. Here the turbine size was found to be most sensitive to the phase, with may be increased by extending the foil span, relatively lesser effects from variations in the without affecting the plunge motion amplitude. angle of attack during the periods outside stroke A number of different factors affecting reversal. This behaviour was determined chiefly performance have been investigated in recent by the timing of the interaction of a large times, including foil shape (e.g. [6]), laminar leading edge vortex with the trailing edge of the versus turbulent flow conditions (e.g. [2,3]), foil. operation in a shear flow [4], and activation strategy. The latter describes the manner in 1 Introduction which the foil is driven, and may be broadly Flapping foils are under active classified as fully prescribed, partially passive consideration as an alternative to traditional or fully passive. rotary turbines, for power generation in wind, In fully prescribed studies both the tidal and oceanic currents, and rivers (e.g. [1- plunging and pitching motions are given as 4]), following an approach pioneered by functions of time. In partially passive strategies McKinney and DeLaurier [5]. In this concept an only the pitching motion is typically prescribed oscillating pitch motion creates a fluid dynamic (e.g. [7,8]), where some of the power extracted force on the foil, which then translates in an from the plunge motion is diverted to drive a oscillatory manner in response. Power is pitch motor, and thus the pitch motion is typically extracted from this translational indirectly flow-driven. Fully passive strategies (plunge) motion, and performance is measured rely on fluid-structure interaction to determine as for rotary turbines, that is as the percentage both the plunging and pitching motions (e.g. of energy extracted from the fluid stream [2,9,10]). Such systems may alternatively be passing through the frontal area of the turbine classified in terms of the degrees of freedom (in this case the swept area of the foil). and the constraints on the motion, e.g. 2-dof, Such power generation mechanisms strongly constrained pitch motion, loosely promise a number of potential advantages in constrained plunge motion [8]; 1-dof, fully comparison to rotary turbines, including a constrained plunge and pitch motions [11]; or 1- relatively low foil maximum speed which is dof, loosely constrained pitch and plunge motions [2,10]. 1 J. YOUNG, J.C.S. LAI In all these studies flapping kinematics is a foil are driven directly by fluid-structure primary determinant of performance (that is, interaction). Maintaining a given angle of attack greatest extraction of power from the available time history was shown to provide a significant fluid stream) [1]. Most studies have considered benefit in efficiency compared to controlling the sinusoidal profiles in both pitch and plunge, pitch angle without consideration of the angle of although some have studied the effect of non- attack (41% versus 30% for the conditions sinusoidal profiles. considered). This work investigates the effect of Ashraf et al. [12] and Platzer et al. [13] variations in the angle of attack time history. considered prescribed motion for single foils The aim is not finding the optimum angle of and two foils in a tandem arrangement, for attack profile per se (which will be dependent sinusoidal and non-sinusoidal oscillations, a on a wide range of factors including Reynolds range of different phases between pitch and number, foil geometry and plunge amplitudes), plunge, different phases between front and rear rather it is about investigating the effect of foils, and different spacing between the foils. changes in the profile on the flow physics, to For non-sinusoidal motion, the pitch rotation of understand the sensitivity of the power output to the foil was compressed so that it occurred at these changes as a first step towards developing the top of the upstroke and bottom of the a robust control system. downstroke with periods of constant pitch angle in between. This increased the power output by up to 17% over sinusoidal motions, by presenting the foil to the flow with the highest angle for a greater proportion of the flapping stroke than for sinusoidal motion. Similarly Xiao et al. [14] simulated = 1.0 × 10 flow over a NACA0012 foil. They explored4 the effect of different periods푅푒 of constant pitch angle, and predicted similar performance increases as seen by [12,13]. Hover et al. [15] noted that a quasi-steady consideration of the kinematics leads to the conclusion that the angle of attack should be held at the largest possible value for the longest Fig. 1. Regimes of operation of a flapping foil, and the possible time throughout the flapping cycle, to associated angle of attack and force directions throughout the flapping cycle. Top: propulsion mode. Bottom: power create the largest time-averaged aerodynamic generation mode. Adapted from [16,17]. forces. While this was in the context of flapping foil propulsion, it is also applicable to power generation. This may be seen in Fig. 1, where 2 Flapping Foil Kinematics the phase of the angle of attack relative to the plunge motion is the determinant of whether the 2.1 Foil Motion foil produces thrust or power. It is therefore The flapping wing turbine is modeled as a natural to explore the effect of the angle of two-dimensional foil undergoing both pitching attack trajectory (i.e. time history) for the power and plunging motions. The motion is defined by generation problem, particularly noting that this plunge position and pitch angle , as shown in application has been shown to be highly Fig. 2. The angle of attack of the foil is given unsteady and dependent on the formation, by: 푦 휃 evolution and interaction of LEVs [1,2], which are in turn sensitive to angle of attack. = tan (1) This work extends a previous study by −1 Young et al. [2] on a fully passive turbine 푦̇ 훼 휃 − ∞ design (that is, both plunging and pitching of the 푈 2 EFFECT OF ANGLE OF ATTACK KINEMATICS ON PASSIVE FLAPPING FOIL POWER GENERATION The plunge and pitch motion are linked to fluid dynamic torque transmitted to the flywheel the rotation of a flywheel as in Young et al. [2], by the mechanism linking the pitch and plunge so that the system is reduced from 2-dof (pitch motions to the flywheel rotation. and plunge) to 1-dof (flywheel angle). Power The power output of the turbine is extraction from the system is modeled as a measured as the time-average of the rate of viscous damper attached to the flywheel. The energy dissipation in the flywheel damper: equation of motion of the combined foil- 1 flywheel system is determined via the = 푡+푇 (5) conservation of energy as: 2 푃 � 푐푓푙푦 훽̇ 푑푡 + + The efficien푇 cy푡 is determined in the usual = + (2) manner via comparison with the available 푓표푖푙 푓표푖푙 ̇ ̈ 푓푙푦 ̇ ̈ power in the flow passing휂 through the frontal 푚 푦̇푦̈ 퐼 휃휃 퐼 훽2훽 퐿푦̇ 푀휃̇ − 푐푓푙푦훽̇ area swept by the foil (the 'Betz power'), where where is the flywheel angle, is the foil unit span is assumed, and is the total inertia measured about the pivot푓표푖푙 point, is excursion of the trailing or leading edges of the the flywheel훽 inertia measured about퐼 its centre, 푓푙푦 foil, whichever푠 is greater: 푑 and is the viscous damper strength. 퐼 1 = (6) 푓푙푦 2 푐 3 푃푎 휌푈∞ 푠푑 = (7) 푃 휂 푃푎 2.2 Angle of Attack Profile The angle of attack profile is created as a Fig. 2. Plunging motion and pitching motion of the piecewise continuous polynomial in foil, and the associated angle of attack. Lift , drag and parameterised in such a way as to generate a moment about the pivot푦 point also shown. 휃 퐿 퐷 wide range of possible profiles, from a sinusoid훽 In 푀what follows, the plunge motion and to a square wave. The profile consists of two angle of attack are specified as functions of second-order (i.e. parabolic) polynomial the flywheel angle rather than as functions푦 of sections, with position, slope and curvature time, and the pitch훼 angle is determined from specified as parameters. The parabolic sections Eq. (1), which may 훽be recast as: are linked by sixth-order polynomials matched 휃 to the parabolic section endpoints position, ( ) = ( ) + tan (3) slope and curvature, and thus are fully constrained once the parabolic parameters have −1 푦훽훽̇ been specified. This is shown in Fig. 3. Here where 휃 훽= 훼 훽 . The equation∞ of motion is 푈 values of 0th, 1st and 2nd derivative at points C solved in terms of : 푦훽 휕푦⁄휕훽 and B', and 0th derivative at point D, give seven 1 conditions requiring a sixth order polynomial = 훽 + + passing through C-D-B'.

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