On the nonlinear dynamics of self-sustained limit-cycle oscillations in a flapping-foil energy harvester

Abstract

The nonlinear dynamics of an airfoil at Reynolds number Re = 10, 000 constrained by two springs and subject to a uniform oncoming flow is studied numerically. The studies are carried out using open source computational fluid dynamics toolbox OpenFOAM. Under certain conditions related to aerodynamic flutter, this two-degree-of-freedom system undergoes self-sustained limit-cycle oscillations (LCOs) with potential application as an energy harvester. When the system is given a small initial perturbation, it is seen that the response of the system decays to zero at flow velocities below the flutter velocity, or oscillates in a limit cycle at velocities greater than the flutter velocity. The flutter velocity at Re = 10, 000 is shown to deviate significantly from the theoretical prediction (which is derived with an assumption of infinite Reynolds number) owing to the effect of viscosity. The LCOs at freestream velocities higher than the flutter velocity result in unsteady flows that are heavily influenced by leading-edge vortex shedding as well as trailing-edge flow separation. The influence of different system parameters

Constructive interference in a network of elastically-bounded flapping plates

“…These findings were confirmed and enriched by further computational studies in closely comparable conditions [9,10] as well as rather different systems, e.g. with different cross sectional shapes and/or operating at higher-Reynolds regimes [11][12][13][14].…”

“…Wind-tunnel investigations were reported by Pigolotti et al [16][17][18] considering a flat plate in a classical pitch-andplunge arrangement and exploring systematically the effect of several physical parameters on the flutter onset and the nonlinear oscillations in the postcritical regime. A nearly identical system was considered in the work by Wang et al [14] where two-dimensional computations were performed in order to characterize the dependence of limit-cycle oscillations with respect to the governing parameters, initial conditions, spring nonlinearity and extraction (modelled by viscous damping).…”

The effect of cubic stiffness nonlinearity on the vortex-induced vibration of a circular cylinder at low Reynolds numbers

“…It should be noted that the FSI systems in all the aforementioned studies involved a circular cylinder elastically supported by a linear spring and the structural force was provided by a simple spring-damper system, i.e., F struct = −bẏ − ky, where b is the structural damping coefficient, y is the cylinder displacement in the cross-flow direction and a dot denotes differentiation with respect to time. However, recent studies on mechanical and fluid-structure systems with nonlinearities in the restoring forces have re-vealed that the nonlinear restoring forces can either increase the vibration amplitudes and enhance the ranges of stable oscillations with potential applications in vibration energy harnessing (Barton et al, 2010;Gammaitoni et al, 2009;Ramesh et al, 2015;Wang et al, 2018) or decrease the vibration amplitudes viable for vibration suppression (Bert et al, 1990;Lee et al, 2008;Gendelman et al, 2010). Research into the VIV of a circular cylinder supported by nonlinear springs is still quite limited.…”

On the leading-edge suction and stagnation-point location in unsteady flows past thin aerofoils

“…The pressure implicit with splitting of operators (PISO) algorithm is employed to achieve pressure-velocity coupling. This set-up has been previously used to implement the incompressible Navier-Stokes equations and study limit-cycle oscillation of a two-degree-of-freedom aerofoil (Wang et al 2018), and leading-edge vortex shedding on finite wings of different aspect ratios (Bird & Ramesh 2018;Bird et al 2019). In this research, the incompressible Euler equations are implemented in order to best match the conditions under which the theory (potential flow) is derived.…”