Electro-hydrodynamic synchronization of piezoelectric flags

Hydrodynamic coupling of flexible flags in axial flows may profoundly influence their flapping dynamics, in particular driving their synchronization. This work investigates the effect of such coupling on the harvesting efficiency of coupled piezoelectric flags, that convert their periodic deformation into an electrical current. Considering two flags connected to a single output circuit, we investigate using numerical simulations the relative importance of hydrodynamic coupling to electrodynamic coupling of the flags through the output circuit due to the inverse piezoelectric effect. It is shown that electrodynamic coupling is dominant beyond a critical distance, and induces a synchronization of the flags' motion resulting in enhanced energy harvesting performance. We further show that this electrodynamic coupling can be strengthened using resonant harvesting circuits.Comment: 14 pages, 10 figures, to appear in J. Fluids Struc

Lattices of hydrodynamically interacting flapping swimmers

Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one- and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row "phalanx" formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory

Effect of Boundary Constraints on the Nonlinear Flapping of Filaments Animated by Follower Forces

Elastically driven filaments subjected to animating compressive follower forces provide a synthetic way to mimic the oscillatory beating of active biological filaments such as eukaryotic cilia. The dynamics of such active filaments can, under favorable conditions, exhibit stable time-periodic responses that result due to the interplay of elastic buckling instabilities, geometric constraints, boundary conditions, and dissipation due to fluid drag. In this paper, we use a continuum elastic rod model to estimate the critical follower force required for the onset of the stable time-periodic flapping oscillations in pre-stressed rods subjected to fluid drag. The pre-stress is generated by imposing either clamped-clamped or clamped-pinned boundary constraints and the results are compared with those of clamped-free case, which is without pre-stress. We find that the critical value increases with the initial slack--that quantifies the pre-stress, and strongly depends on the type of the constraints at the boundaries. The frequency of oscillations far from the onset, however, depends primarily on the magnitude of the follower force, not on the boundary constraints. Interestingly, oscillations for the clamped-pinned case are observed only when the follower forces are directed towards the clamped end. This finding can be exploited to design a mechanical switch to initiate or quench the oscillations by reversing the direction of the follower force or altering the boundary conditions

Fluid-solid-electric lock-in of energy-harvesting piezoelectric flags

The spontaneous flapping of a flag in a steady flow can be used to power an output circuit using piezoelectric elements positioned at its surface. Here, we study numerically the effect of inductive circuits on the dynamics of this fluid-solid-electric system and on its energy harvesting efficiency. In particular, a destabilization of the system is identified leading to energy harvesting at lower flow velocities. Also, a frequency lock-in between the flag and the circuit is shown to significantly enhance the system's harvesting efficiency. These results suggest promising efficiency enhancements of such flow energy harvesters through the output circuit optimization.Comment: 8 pages, 8 figures, to appear in Physical Review Applie

Universal scaling law in drag-to-thrust wake transition of flapping foils

Reversed von K\'arm\'an streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude $A$ and frequency $f$ because the transition also depends sensitively on other details of the kinematics. In this work we replace $A$ with the cycle-averaged swept trajectory $\mathcal{T}$ of the foil chord-line. Two dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless $\mathcal{T}-f$ we show that the drag-to-thrust wake transition of all tested modes occurs for a modified Strouhal $St_{\mathcal{T}}\sim 1$. Physically the product $\mathcal{T}\cdot f$ expresses the induced velocity of the foil and indicates that propulsive jets occur when this velocity exceeds $U_{\infty}$. The new metric offers a unique insight into the thrust producing strategies of biological swimmers and flyers alike as it directly connects the wake development to the chosen kinematics enabling a self similar characterisation of flapping foil propulsion.Comment: Rev

The effect of non-uniform damping on flutter in axial flow and energy harvesting strategies

The problem of energy harvesting from flutter instabilities in flexible slender structures in axial flows is considered. In a recent study, we used a reduced order theoretical model of such a system to demonstrate the feasibility for harvesting energy from these structures. Following this preliminary study, we now consider a continuous fluid-structure system. Energy harvesting is modelled as strain-based damping and the slender structure under investigation lies in a moderate fluid loading range, for which {the flexible structure} may be destabilised by damping. The key goal of this work is to {analyse the effect of damping distribution and intensity on the amount of energy harvested by the system}. The numerical results {indeed} suggest that non-uniform damping distributions may significantly improve the power harvesting capacity of the system. For low damping levels, clustered dampers at the position of peak curvature are shown to be optimal. Conversely for higher damping, harvesters distributed over the whole structure are more effective.Comment: 12 pages, 10 figures, to appear in Proc. R. Soc.