Flutter instability theory guides the design and improvement of flexible flapping-foil energy harvesters


Airplane wings are highly susceptible to flutter instabilities. Above a critical speed, the dynamic instability often induces self-sustained oscillations characterized by great violence, which could impair the airplane’s functionality. Since the onset of flight, dynamic instability has been extensively studied. In most cases, the unstable aerodynamic forces on a flexible oscillating foil are widely used in flutter instability-related studies. It has provided a feasible means of mitigating the aerodynamic-related effects in aeronautics.

Recently, research interest in pitch plunge (coupled mode) flutter instability has been renewed owing to its perceived relevance in energy harvesting using hydrokinetic flapping-foil turbines. These turbines are based on the energy transferred by the fluid to a flapping foil submerged in a fluid current. Despite the complex mechanisms of these turbines, most studies have focused on constrained flapping-foil turbines due to their alleged better energy harvesting performance and efficiencies. Nevertheless, recent findings have revealed that simpler and fully-passive systems with elastically supported rigid-foil degrees of freedom could achieve better efficiencies than most semi-passive or constrained systems.

Investigating the energy harvesting performance of fully-passive flapping-foil turbines requires two things. First is the thorough understanding of large-amplitude motions associated with coupled-mode and stall flutter instabilities. Second, determining the onset of the stability from small perturbations is also important as it enables accurate estimation of parametric ranges for improved energy harvesting performance without the need for costly experiments. This requires simple analytical expressions.

Herein, Professor Ramon Fernandez-Feria from Universidad de Málaga investigated the flutter stability of a fully-passive flexible flapping-foil turbine and its potential application in energy harvesting. A combination of the linearized fluid-structure interaction through the first three moments of the Euler-Bernoulli beam equation and the expressions derived from the existing studies on unsteady aerodynamics were employed in this work to derive the pitch-plunge-flexural expressions. The flexible and rigid foils regarding the energy harvesting of the turbines were discussed and validated by comparing with those obtained via recent numerical simulations. The work is published in the journal, Journal of Fluids and Structures.

The author demonstrated that an increase in the foil stiffness would weaken, lead to the disappearance or even enhance the coupled-mode flutter instability depending on the other parameters, especially those determining the location of the center of mass with respect to the pivot. The theoretical formulation was suitable for deriving the near-optimal conditions and first operating estimation of a fully-passive flapping-foil turbine in a simple manner considering the effects of non-dimensional parameters, such as stiffness, location of pivotal axis and center of mass, that could affect energy harvesting performance of the devices.

The presented linear theory was valid for relatively large stiffness ratios and small pitching, heaving and flexural deflection amplitudes. The analysis also analytically characterized the flutter instability onset and the associated leading frequency of the oscillations in terms of flow velocity and other system structural parameters. Thus, it was possible to determine the optimal values of other parameters via numerical or experimental means for optimal energy harvesting configuration.

In summary, Professor Ramon Fernandez-Feria developed a new analytical tool able in determining the flutter instability onset of an elastically supported flexible 2D foil in an incompressible and inviscid flow. This is the first study to consider the effects of the flexural deflection of the foil coupled with the plunge and pitch motions of a foil mounted elastically to torsional and translational dampers and springs at arbitrary pivot axis locations. The presented analysis could guide the search for appropriate parameter ranges for enhancing the energy harvesting performance of a fully-passive flexible flapping-foil hydrokinetic turbine considering the effects of relevant non-dimensional parameters. In a statement to Advances in Engineering, Professor Ramon Fernandez-Feria explained that his study findings would advance our knowledge in the field of energy harvesting.

Flutter instability theory guides the design and improvement of flexible flapping-foil energy harvesters - Advances in Engineering

About the author

Ramon Fernandez-Feria received the Batchelor degree in Industrial Engineering with specialization in Chemical Engineering from the University of Seville, Spain, in 1984, the MSc in 1986 and the Ph.D. in 1987, both in Mechanical Engineering from Yale University, USA. He is full professor in the Industrial Engineering School at the University of Malaga, Spain, and head of Malaga’s Fluid Mechanics research group. Formerly he was director of the Industrial Engineering School of the University of Malaga for two terms (2004-2012).

His current research interests are mainly focused on unsteady aerodynamics, vortical flows and fluid-structure interaction applied to the bioinspired flapping-foil propulsion of micro air vehicles and swimming robots, and to flapping-foil energy harvesters.


Fernandez-Feria, R. (2022). Flutter stability analysis of an elastically supported flexible foil. Application to the energy harvesting of a fully-passive flexible flapping-foil of small amplitudeJournal of Fluids and Structures, 109, 103454.

Go To Journal of Fluids and Structures

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