Structural response and energy extraction of a fully passive flapping foil

Abstract The structural response and energy extraction of a foil undergoing two-degree-of-freedom fully passive flapping motions in a two-dimensional flow are numerically investigated at R e = 400 . The simulations of the fluid–structure interaction were conducted using the Immersed Boundary Method (IB Method). In the parametric space of flow reduced velocity and pivot location investigated, five response regimes are identified. This paper focuses on the stable synchronisation regime, which is characterised by harmonic wake-body synchronisation with stable large-amplitude oscillations. Correspondingly, a novel wake pattern composed of a triplet of vortices and a pair of vortices shed per cycle, referred to as T+P pattern, is encountered. An analysis of the dynamic nonlinearity showed that the inertia forces can induce perturbations in the form of harmonics to the dynamics of the system. Furthermore, the highest cycle-averaged power output coefficient and efficiency were found to be C P = 0 . 95 and η = 0 . 32 , respectively. The present results suggest that high-efficiency case in fully passive flapping motions is associated with a large pitch–plunge phase and a 2S wake pattern composed of two strong single LEVs shed per cycle.

[1]  Hisanori Abiru,et al.  Study on a Flapping Wing Hydroelectric Power Generation System , 2009 .

[2]  R. Bourguet,et al.  In-line flow-induced vibrations of a rotating cylinder , 2015, Journal of Fluid Mechanics.

[3]  Suhas V. Patankar,et al.  A Calculation Procedure for Two-Dimensional Elliptic Situations , 1981 .

[4]  C. Williamson,et al.  The effect of two degrees of freedom on vortex-induced vibration at low mass and damping , 2004, Journal of Fluid Mechanics.

[5]  Rémi Bourguet,et al.  Flow-induced vibrations of a rotating cylinder , 2013, Journal of Fluid Mechanics.

[6]  X. Jing,et al.  Modes of vortex formation and transition to three-dimensionality in the wake of a freely vibrating cylinder , 2014 .

[7]  Qiang Zhu,et al.  Optimal frequency for flow energy harvesting of a flapping foil , 2011, Journal of Fluid Mechanics.

[8]  Qiang Zhu,et al.  Energy harvesting by a purely passive flapping foil from shear flows , 2012 .

[9]  C. Williamson,et al.  Modes of vortex formation and frequency response of a freely vibrating cylinder , 2000, Journal of Fluid Mechanics.

[10]  Qiang Zhu,et al.  A review on flow energy harvesters based on flapping foils , 2014 .

[11]  M. Dickinson,et al.  Force production and flow structure of the leading edge vortex on flapping wings at high and low Reynolds numbers , 2004, Journal of Experimental Biology.

[12]  Max F. Platzer,et al.  Numerical Analysis of an Oscillating-Wing Wind and Hydropower Generator , 2011 .

[13]  J. Sheridan,et al.  Fluid–structure interaction of a square cylinder at different angles of attack , 2014, Journal of Fluid Mechanics.

[14]  Guy Dumas,et al.  Numerical optimization of a fully-passive flapping-airfoil turbine , 2017 .

[15]  Charles H. K. Williamson,et al.  Prediction of vortex-induced vibration response by employing controlled motion , 2009, Journal of Fluid Mechanics.

[16]  C. Williamson,et al.  Fluid Forces and Dynamics of a Hydroelastic Structure with Very Low Mass and Damping , 1997 .

[17]  V. Yang,et al.  Generation of Vortex Lift Through Reduction of Rotor/Stator Gap in Turbomachinery , 2016 .

[18]  Bradley James Simpson,et al.  Experimental studies of flapping foils for energy extraction , 2009 .

[19]  V. Yang,et al.  Vortex-Lift Mechanism in Axial Turbomachinery with Periodically Pitched Stators , 2016 .

[20]  Scott T. Davids A Computational and Experimental Investigation of a Flutter Generator. , 1999 .

[21]  John Sheridan,et al.  Controlled oscillations of a cylinder: forces and wake modes , 2005, Journal of Fluid Mechanics.

[22]  Franz S. Hover,et al.  Effect of angle of attack profiles in flapping foil propulsion , 2004 .

[23]  Max F. Platzer,et al.  A review of progress and challenges in flapping foil power generation , 2014 .

[24]  C. Peskin The immersed boundary method , 2002, Acta Numerica.

[25]  Xueming Shao,et al.  Inertial effects of the semi-passive flapping foil on its energy extraction efficiency , 2015 .

[26]  James DeLaurier,et al.  Wingmill: An Oscillating-Wing Windmill , 1981 .

[27]  T. Kinsey,et al.  Parametric Study of an Oscillating Airfoil in a Power-Extraction Regime , 2008 .

[28]  D. Spalding,et al.  A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows , 1972 .

[29]  Qiang Zhu,et al.  Energy harvesting through flow-induced oscillations of a foil , 2009 .

[30]  L. He,et al.  Method of Simulating Unsteady Turbomachinery Flows with Multiple Perturbations , 1992 .

[31]  A. Roshko,et al.  Vortex formation in the wake of an oscillating cylinder , 1988 .

[32]  Adrian L. R. Thomas,et al.  Leading-edge vortices in insect flight , 1996, Nature.

[33]  Qiang Zhu,et al.  Mode coupling and flow energy harvesting by a flapping foil , 2009 .

[34]  Max F. Platzer,et al.  Numerical Simulation of Fully Passive Flapping Foil Power Generation , 2013 .

[35]  John Sheridan,et al.  Chaotic vortex induced vibrations , 2014 .

[36]  R. B. Srygley,et al.  Unconventional lift-generating mechanisms in free-flying butterflies , 2002, Nature.

[37]  N. Zhao,et al.  Role of induced vortex interaction in a semi-active flapping foil based energy harvester , 2015 .