Limit-cycle oscillations in unsteady flows dominated by intermittent leading-edge vortex shedding

Abstract

High-frequency limit-cycle oscillations of an airfoil at low Reynolds number are studied numerically. This regime is characterized by large apparentmass effects and intermittent shedding of leading-edge vortices. Under these conditions, leading-edge vortex shedding has been shown to result in favorable consequences such as high lift and efficiencies in propulsion/power extraction, thus motivating this study. The aerodynamic model used in the aeroelastic framework is a potential-flow-based discrete-vortex method, augmented with intermittent leading-edge vortex shedding based on a leadingedge suction parameter reaching a critical value. This model has been validated extensively in the regime under consideration and is computationally cheap in comparison with Navier-Stokes solvers. The structural model used has degrees of freedom in pitch and plunge, and allows for large amplitudes and cubic stiffening. The aeroelastic framework developed in this paper is employed to undertake parametric studies which evaluate the impact of different types of nonlinearity. Structural configurations with pitch-to-plunge frequency ratios close to unity are considered, where the flutter speeds are lowest (ideal for power generation) and reduced frequencies are highest. The range of reduced frequencies studied is two to three times higher than most airfoil studies, a virtually unexplored regime. Aerodynamic nonlinearity re- * Corresponding authorEmail addresses: kiran.ramesh@glasgow.ac.uk (Kiran Ramesh), j.murua@surrey.ac.uk (Joseba Murua), agopalar@ncsu.edu (Ashok Gopalarathnam) Fluids and Structures February 10, 2015 sulting from intermittent leading-edge vortex shedding always causes a supercritical Hopf bifurcation, where limit-cycle oscillations occur at freestream velocities greater than the linear flutter speed. The variations in amplitude and frequency of limit-cycle oscillations as functions of aerodynamic and structural parameters are presented through the parametric studies. The excellent accuracy/cost balance offered by the methodology presented in this paper suggests that it could be successfully employed to investigate optimum setups for power harvesting in the low-Reynolds-number regime. Preprint submitted to Journal of

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

“…where (•) indicates differentiation with respect to time, m is the total mass of the airfoil, and S α and I α are its static and inertia moments about the pivot; c h and c α are structural damping coefficients for plunge and pitch coordinates; F h = F h (h) and F α = F α (α) are the restoring forces in plunge and pitch, respectively, and can include any spring nonlinearity such as cubic hardening/softening, bilinearity or hysteresis [17]. The interested reader may refer to Ramesh et al [37] for more details and the complete derivation. In the present research, only cubic stiffening nonlinearity is considered, for which…”

“…However, when the pitch and plunge oscillations are sufficiently large, flow separation and vortex shedding occur. These aerodynamic nonlinearities prevent the response from increasing indefinitely, resulting in limit-cycle oscillations [37]. The LCOs of the baseline system at a freestream velocity just above the flutter velocity, U * = 1.03U * F are presented in fig.…”

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Leading-edge flow criticality as a governing factor in leading-edge vortex initiation in unsteady airfoil flows

“…This flow feature signals the formation of the shear layer in which there is an eruption of surface flow into the mainstream. As in previous work [58,60], the instant when the spike in the negative C f region first reaches the zero value is taken as the time corresponding to initiation of LEV formation. In Fig.…”

Toward efficient aeroelastic energy harvesting through limit cycle shaping

“…These are the same nonlinear equations of motion that one would arrive at using energy based methods 11 . These are the same nonlinear equations of motion that one would arrive at using energy based methods 11 .…”