Olivier Doaré

Energy harvesting efficiency of piezoelectric flags in axial flows

Self-sustained oscillations resulting from fluid–solid instabilities, such as the flutter of a flexible flag in axial flow, can be used to harvest energy if one is able to convert the solid energy into electricity. Here, this is achieved using piezoelectric patches attached to the surface of the flag, which convert the solid deformation into an electric current powering purely resistive output circuits. Nonlinear numerical simulations in the slender-body limit, based on an explicit description of the coupling between the fluid–solid and electric systems, are used to determine the harvesting efficiency of the system, namely the fraction of the flow kinetic energy flux effectively used to power the output circuit, and its evolution with the system’s parameters. The role of the tuning between the characteristic frequencies of the fluid–solid and electric systems is emphasized, as well as the critical impact of the piezoelectric coupling intensity. High fluid loading, classically associated with destabilization by damping, leads to greater energy harvesting, but with a weaker robustness to flow velocity fluctuations due to the sensitivity of the flapping mode selection. This suggests that a control of this mode selection by a careful design of the output circuit could provide some opportunities to improve the efficiency and robustness of the energy harvesting process.

Flutter of long flexible cylinders in axial flow

We consider the stability of a thin flexible cylinder considered as a beam, when subjected to axial flow and fixed at the upstream end only. A linear stability analysis of transverse motion aims at determining the risk of flutter as a function of the governing control parameters such as the flow velocity or the length of the cylinder. Stability is analysed applying a finite-difference scheme in space to the equation of motion expressed in the frequency domain. It is found that, contrary to previous predictions based on simplified theories, flutter may exist for very long cylinders, provided that the free downstream end of the cylinder is well-streamlined. More generally, a limit regime is found where the length of the cylinder does not affect the characteristics of the instability, and the deformation is confined to a finite region close to the downstream end. These results are found complementary to solutions derived for shorter cylinders and are confirmed by linear and nonlinear computations using a Galerkin method. A link is established to similar results on long hanging cantilevered systems with internal or external flow. The limit case of vanishing bending stiffness, where the cylinder is modelled as a string, is analysed and related to previous results. Comparison is also made to existing experimental data, and a simple model for the behaviour of long cylinders is proposed.

Experimental and numerical study of the shear layer instability between two counter-rotating disks

The shear layer instability in the flow between two counter-rotating disks enclosed by a cylinder is investigated experimentally and numerically, for radius-to-height ratio Γ=R/h between 2 and 21. For sufficiently large rotation ratio, the internal shear layer that separates two regions of opposite azimuthal velocities is prone to an azimuthal symmetry breaking, which is investigated experimentally by means of visualization and particle image velocimetry. The associated pattern is a combination of a sharp-cornered polygonal pattern, as observed by Lopez et al. (2002) for low aspect ratio, surrounded by a set of spiral arms, first described by Gauthier et al. (2002) for high aspect ratio. The spiral arms result from the interaction of the shear layer instability with the Ekman boundary layer over the faster rotating disk. Stability curves and critical modes are experimentally measured for the whole range of aspect ratios, and are found to compare well with numerical simulations of the three-dimensional time-dependent Navier–Stokes equations over an extensive range of parameters. Measurements of a local Reynolds number based on the shear layer thickness confirm that a shear layer instability, with only weak curvature effect, is responsible for the observed patterns. This scenario is supported by the observed onset modes, which scale as the shear layer radius, and by the measured phase velocities.

Effect of Plant Interaction on Wind-Induced Crop Motion

Plant motion due to wind affects plant growth, a phenomenon called thigmomorphogenesis. Despite intensive studies of the turbulence over plant canopies, the study of plant motion induced by wind has often been limited to individual trees or cereal plants. Few models of global canopy motions are available. Moreover the numerical analysis of models that are based on individual stems becomes time consuming when dealing with crops. A model of motion within the canopies is proposed here using a wave propagation equation within a homogenized continuous medium, and a forcing function representing turbulent gusts advected over the canopy. This model is derived from a discrete model of a set of plant shoots represented as individual oscillators, including elastic contacts between shoots. Such contacts induce nonlinearities into the wave equation. A new experimental method to measure stem dynamical properties and elastic collision properties is presented with an illustration on alfalfa stems. Results obtained modeling plant motions in an alfalfa crop are presented.

The flow-induced instability of long hanging pipes

The effect of increasing length on the stability of a hanging fluid-conveying pipe is investigated. Experiments show that there exists a critical length above which the flow velocity necessary to cause flutter becomes independent of the pipe length. The fluid-structure interaction is thus modelled by following the work of Bourrieres and of Paidoussis. Computations using a standard Galerkin method confirm this evolution. A short pipe model is then considered, where gravity plays a negligible role. Transition between this short length model and the asymptotic situation is found to occur where a local stability criterion is satisfied at the upstream end of the pipe. For longer pipes, a model is proposed where the zone of stable waves is totally disregarded. Comparison of these models with experiments and computations show a good agreement over all ranges of mass ratios between the flowing fluid and the pipe.

Non-linear dynamic thermomechanical behaviour of shape memory alloys

The non-linear dynamic thermomechanical behaviour of superelastic shape memory alloys is investigated. To this end, the Zaki–Moumni model, initially developed for quasi-static loading cases, is extended to simulate the uniaxial forced oscillations of a shape memory alloy device. First, the influence of loading rate is accounted for by considering the thermomechanical coupling in the behaviour of NiTi shape memory alloy. Comparisons between simulations and experimental results show good agreement. Then, the forced response of a shape memory alloy device is investigated at resonance. Both isothermal and non-isothermal conditions are studied, as well as non-symmetric tensile-compressive restoring force. In the case of large values of forcing amplitudes, simulation results show that the dynamic response is prone to jumps, bifurcations and chaotic solutions.

Influence and optimization of the electrodes position in a piezoelectric energy harvesting flag

Abstract Fluttering piezoelectric plates may harvest energy from a fluid flow by converting the plate׳s mechanical deformation into electric energy in an output circuit. This work focuses on the influence of the arrangement of the piezoelectric electrodes along the plate׳s surface on the energy harvesting efficiency of the system, using a combination of experiments and numerical simulations. A weakly nonlinear model of a plate in axial flow, equipped with a discrete number of piezoelectric patches is derived and confronted to experimental results. Numerical simulations are then used to optimize the position and dimensions of the piezoelectric electrodes. These optimal configurations can be understood physically in the limit of small and large electromechanical coupling.

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 systems harvesting efficiency. These results suggest promising efficiency enhancements of such flow energy harvesters through the output circuit optimization.

Synchronized flutter of two slender flags

The interactions and synchronization of two parallel and slender flags in a uniform axial flow are studied in the present paper by generalizing Lighthills Elongated Body Theory (EBT) and Lighthills Large Amplitude Elongated Body Theory (LAEBT) to account for the hydrodynamic coupling between flags. The proposed method consists in two successive steps, namely the reconstruction of the flow created by a flapping flag within the LAEBT framework and the computation of the fluid force generated by this nonuniform flow on the second flag. In the limit of slender flags in close proximity, we show that the effect of the wakes have little influence on the long time coupled-dynamics and can be neglected in the modeling. This provides a simplified framework extending LAEBT to the coupled dynamics of two flags. Using this simplified model, both linear and large amplitude results are reported to explore the selection of the flapping regime as well as the dynamical properties of two side-by-side slender flags. Hydrodynamic coupling of the two flags is observed to destabilize the flags for most parameters, and to induce a long-term synchronization of the flags, either in-phase or out-of-phase.

Flow energy harvesting with piezoelectric flags

In this article, energy harvesting with a fluttering can-tilevered plate covered by piezoelectric patches in an axial flow is adressed. A theoretical model is presented which is then discretized and numerically integrated to perform a parametric study of the energy harvesting efficiency of the system. When one, two or three piezoelectric patches cover the plate, the optimal distributions of the patches that maximize the efficiency are obtained. Experimental results are presented, which are in good agreement with the model. When a significantly high number of patches of small size are considered, a continuous model is used to study the influence of a resonant harvesting circuit. A lock-in phenomenon is evidenced, which is able to significantly increase the efficiency.