Energy harvesting by a purely passive flapping foil from shear flows

A nonlinear energy harvesting system consisting of a flapping foil and an electro-magnetic generator excited by incompressible quasi-steady air flows is investigated. Due to stiffness nonlinearities in pitch and/or heave degrees of freedom, the system behaves a stable limit cycle oscillation when flow velocity exceeds the critical flutter speed, so that the mechanical energy imported from air flow is converted into electricity by the coupled electro-magnetic generator. The power flow equations and variables, including the input, dissipated, transmitted and harnessed powers, of the system are formulated. A fourth-order Runge-Kutta method is used to obtain the system’s dynamical response as well as power flow variables. It shows that increasing the nonlinear stiffness in heave motion or decreasing in pitch motion benefits power generation. The research demonstrates the capability of this nonlinear system to harvest natural energy without extra operation cost. Discussions and planed further research works are given for engineering applications.

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Optimal frequency for flow energy harvesting of a flapping foil

Journal of Fluid Mechanics ◽

10.1017/s0022112011000334 ◽

2011 ◽

Vol 675 ◽

pp. 495-517 ◽

Cited By ~ 110

Author(s):

QIANG ZHU

Keyword(s):

Energy Harvesting ◽

Vortex Shedding ◽

Leading Edge ◽

Energy Extraction ◽

Flapping Foil ◽

Flow Energy ◽

Performance Point ◽

High Efficient ◽

Harvesting Efficiency ◽

Energy Harvesting Efficiency

Inspired by the correlation between the propulsion efficiency of a flapping foil propeller and stability of the wake behind it (which leads to the optimal Strouhal number for propulsion), we numerically simulated a heaving/pitching foil in energy harvesting regime, and investigated the relation between wake stability and the energy harvesting efficiency. The base flow is computed using a Navier–Stokes algorithm and the stability analysis is performed via the Orr–Sommerfeld equation. The wake is found to be convectively unstable and the frequency of the most unstable mode fw is determined. The case when fw ~ f coincides with maximum energy harvesting efficiency of the system (f is the frequency of foil oscillation), suggesting that flow energy extraction is closely related to efficient evolution of the wake. This occurs at a frequency of f ~ 0.15 (f is normalized by the chord length and the flow speed), under the constraint that there is significant vortex shedding from the leading edge at sufficiently large effective angles of attack. Indeed, this ‘foil–wake resonance’ is usually associated with multi-vortex shedding from the leading edge. Furthermore, detailed examination of energy extractions from the heaving and the pitching motions indicates that near the optimal performance point the average energy extraction from the pitching motion is close to zero. This suggests the feasibility of achieving high-efficient energy harvesting through a simple fully passive system we proposed earlier in which no activation is needed.

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Flutter stability analysis of an elastically supported flexible foil. Application to the energy harvesting of a fully-passive flexible flapping-foil of small amplitude

Journal of Fluids and Structures ◽

10.1016/j.jfluidstructs.2021.103454 ◽

2022 ◽

Vol 109 ◽

pp. 103454

Author(s):

R. Fernandez-Feria

Keyword(s):

Stability Analysis ◽

Energy Harvesting ◽

Small Amplitude ◽

Flapping Foil ◽

Elastically Supported

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Optimal Leading Edge Vortex Formation of a Flapping Foil in Energy Harvesting Regime

Volume 1C, Symposia: Gas-Liquid Two-Phase Flows; Gas and Liquid-Solid Two-Phase Flows; Numerical Methods for Multiphase Flow; Turbulent Flows: Issues and Perspectives; Flow Applications in Aerospace; Fluid Power; Bio-Inspired Fluid Mechanics; Flow Manipulation and Active Control; Fundamental Issues and Perspectives in Fluid Mechanics; Transport Phenomena in Energy Conversion From Clean and Sustainable Resources; Transport Phenomena in Materials Processing and Manufacturing Processes ◽

10.1115/fedsm2017-69343 ◽

2017 ◽

Author(s):

Firas F. Siala ◽

Alexander D. Totpal ◽

James A. Liburdy

Keyword(s):

Energy Harvesting ◽

Vortex Formation ◽

Leading Edge ◽

Flux Analysis ◽

Leading Edge Vortex ◽

Flapping Foil ◽

Flow Energy ◽

Edge Vortex ◽

Formation Number ◽

Harvesting Regime

An experimental investigation is conducted to study the leading edge vortex (LEV) evolution of a simultaneously heaving and pitching foil operating in the energy harvesting regime. Two dimensional particle image velocimetry measurements are collected in a wind tunnel at reduced frequencies of k = fc/U = 0.05–0.20. Vorticity flux analysis is performed to calculate the constant C in the vortex formation number equation proposed by J. O. Dabiri [1], and it is shown that for a flapping foil operating in the energy harvesting regime, this constant is approximately equal to 1.33. We demonstrate that the optimal LEV formation number (T̂max ≈ 4) is achieved at k = 0.11, which is well within the range of optimal reduced frequency for energy harvesting applications (k = 0.1–0.15). This suggests that the flow energy extraction is closely related to the efficient evolution process of the LEV.

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Numerical investigation of the power extraction mechanism of flapping foil tidal energy harvesting devices

Energy & Environment ◽

10.1177/0958305x18787320 ◽

2018 ◽

Vol 30 (2) ◽

pp. 193-211 ◽

Cited By ~ 3

Author(s):

Maryam Pourmahdavi ◽

Mohammad Naghi Safari ◽

Shahram Derakhshan

Keyword(s):

Energy Harvesting ◽

Stokes Equations ◽

Critical Role ◽

Pressure Coefficient ◽

Leading Edge ◽

Energy Extraction ◽

Leading Edge Vortex ◽

Power Extraction ◽

Flapping Foil ◽

Edge Vortex

The flapping foil hydrokinetics turbine is a new method to generate energy from incoming flow field. The numerical simulations have been performed computationally by using two-dimensional unsteady Reynolds-averaged Navier–Stokes equations. It was found that the maximum energy efficiency reached about 35.2% when the reduced frequency was 0.11; at this time, the foil experienced a light dynamic stall and two opposite-sign vorticities were shed from the foil per half of the cycle. This report also studied the energy extraction performance of flapping foil device and the correlation between the foil kinematic parameters and the flow fields around it at actual operating Reynolds number comprehensively. In addition, the vortex variation and the pressure coefficient distribution along the foil’s surface were used to demonstrate the mechanism of flapping foil energy generation turbine. The creation and shedding of the leading edge vortex played the critical role in energy transformation between the flow fluid and energy harvesting systems. Therefore, if the timing of the leading edge vortex generation and shedding is controlled, the energy extraction efficiency can be increased considerably.

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