Rémi Bourguet

On the efficiency of energy harvesting using vortex-induced vibrations of cables

Many technologies based on fluid–structure interaction mechanisms are being developed to harvest energy from geophysical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using vortex-induced vibrations (VIV) of cables is addressed in this paper, through two reference configurations: (i) a long tensioned cable with periodically-distributed harvesters and (ii) a hanging cable with a single harvester at its upper extremity. After validation against either direct numerical simulations or experiments, an appropriate reduced-order wake-oscillator model is used to perform parametric studies of the impact of the harvesting parameters on the efficiency. For both configurations, an optimal set of parameters is identified and it is shown that the maximum efficiency is close to the value reached with an elastically mounted rigid cylinder. The variability of the efficiency is studied in light of the fundamental properties of each configuration, i.e. body flexibility and gravity-induced spatial variation of the tension. In the periodically-distributed harvester configuration, it is found that the standing-wave nature of the vibration and structural mode selection plays a central role in energy extraction. In contrast, the efficiency of the hanging cable is essentially driven by the occurrence of traveling wave vibrations.

Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier-Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations.

Capturing transition features around a wing by reduced-order modeling based on compressible Navier-Stokes equations

The three-dimensional transition in the flow around a NACA0012 wing of constant spanwise section at Mach number 0.3, Reynolds number 800, and incidence 20° is investigated by direct numerical simulation and reduced-order modeling. The interaction between the von Karman and the secondary instabilities is analyzed. Irregular events in the flow transition modulating the spanwise undulation are highlighted and quantified. These transition features, including “local intermittencies” in the secondary instability pattern, are efficiently captured by a reduced-order model derived by means of the Galerkin projection of the compressible flow Navier–Stokes equations onto a truncated proper orthogonal decomposition basis.

Anisotropic eddy-viscosity concept for strongly detached unsteady flows

The accurate prediction of the flow physics around bodies at high Reynolds number is a challenge in aerodynamics nowadays. In the context of turbulent flow modeling, recent advances like large eddy simulation (LES) and hybrid methods [detached eddy simulation (DES)] have considerably improved the physical relevance of the numerical simulation. However, the LES approach is still limited to the low-Reynolds-number range concerning wall flows. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach remains a widespread and robust methodology for complex flow computation, especially in the near-wall region. Complex statistical models like second-order closure schemes [differential Reynolds stress modeling (DRSM)] improve the prediction of these properties and can provide an efficient simulationofturbulent stresses. Fromacomputational pointofview, the main drawbacks of such approaches are a higher cost, especially in unsteady 3-D flows and above all, numerical instabilities.

Vortex-induced vibrations of a flexible cylinder at large inclination angle

The free vibrations of a flexible circular cylinder inclined at 80° within a uniform current are investigated by means of direct numerical simulation, at Reynolds number 500 based on the body diameter and inflow velocity. In spite of the large inclination angle, the cylinder exhibits regular in-line and cross-flow vibrations excited by the flow through the lock-in mechanism, i.e. synchronization of body motion and vortex formation. A profound reconfiguration of the wake is observed compared with the stationary body case. The vortex-induced vibrations are found to occur under parallel, but also oblique vortex shedding where the spanwise wavenumbers of the wake and structural response coincide. The shedding angle and frequency increase with the spanwise wavenumber. The cylinder vibrations and fluid forces present a persistent spanwise asymmetry which relates to the asymmetry of the local current relative to the body axis, owing to its in-line bending. In particular, the asymmetrical trend of flow–body energy transfer results in a monotonic orientation of the structural waves. Clockwise and counter-clockwise figure eight orbits of the body alternate along the span, but the latter are found to be more favourable to structure excitation. Additional simulations at normal incidence highlight a dramatic deviation from the independence principle, which states that the system behaviour is essentially driven by the normal component of the inflow velocity.

Vortex-Induced Vibrations

Starting at a low Reynolds number of about 50, and reaching the highest Reynolds numbers recorded, bluff bodies placed within an external flow form an unstable wake that results in the formation of a regular pattern of vortices, the Karman street. If the structure is flexible or flexibly mounted, these vortices may cause vibrations, leading to stresses and fatigue damage. This motion of the body influences, in turn, the vortex formation process, establishing a feedback mechanism that may lead to stable or unstable dynamic equilibria. As a result, vortex-induced vibrations are controlled by complex physical mechanisms characterized by rich dynamic properties. When elongated, flexible structures are placed in a sheared cross-flow, the fluid–structure interaction process is distributed along their length, resulting in added complexity, as parts of the structure act to transfer energy from the flow to the structure, while other parts damp the response.

Numerical Simulation of the Flow in the Wake of Ahmed Body Using Detached Eddy Simulation and URANS Modeling

The flow around Ahmed car body is studied for a 35° slant angle case and 25° slant angle case. For the steady 35° case, RANS modelling have shown good results but is not efficient in the 25° configuration, beeing unable to capture the detachment of the flow over the slant of the body. Then, DES and DDES modelling are performed on the 25° configuration showing better results.

Distributed Wake-Body Resonance of a Long Flexible Cylinder in Shear Flow

The fluid-structure interaction mechanisms involved in the development of narrowband and broadband vortex-induced vibrations of long flexible structures placed in non-uniform currents are investigated by means of direct numerical simulation. We consider a tensioned beam of aspect ratio 200, free to move in both the in-line and cross-flow directions, and immersed in a sheared flow at Reynolds number 330. Both narrowband and broadband multi-frequency vibrations may develop, depending on the velocity profile of the sheared oncoming current.Narrowband vibrations occur when lock-in, i.e. the synchronization between vortex shedding and structure oscillations, is limited to a single location along the span, within the high current velocity region; thus, well-defined lock-in versus non-lock-in regions are noted along the span. In contrast, we show that broadband responses, where both high and low structural wavelengths are excited, are characterized by several isolated regions of lock-in, distributed along the length. The phenomenon of distributed lock-in impacts the synchronization of the in-line and cross-flow vibrations, and the properties of the fluid-structure energy transfer, as function of time and space.Copyright

Low-Order Modeling for Unsteady Separated Compressible Flows by POD-Galerkin Approach

A low-dimensional model is developed on the basis of the unsteady compressible Navier-Stokes equations by means of POD-Galerkin methodology in the perspective of physical analysis and computational savings. This approach consists in projecting the complex physical model onto a subspace determined to reach an optimal statistical content conservation. This leads to a drastic reduction of the number of degrees of freedom while preserving the main flow dynamics. The high-order system formulation is modified and an inner product which couples the contributions of both kinematic and thermodynamic state variables is selected. The associated reduced order model is a quadratic polynomial ordinary differential equation system which presents an inherent sensitivity to POD basis truncation for long-term prediction. A calibration process based on the minimisation of the prediction error with respect to reference dynamics is implemented. The predictive capacities of the low-order approach are evaluated by comparison with results issued from the 2D Navier-Stokes simulation of a transonic flow around a NACA0012 airfoil, at zero angle of incidence. This configuration is characterised by a complex unsteadiness caused by a von Karman instability mode induced by shock/vortex interaction, and a low frequency buffeting mode.

Effect of Mass Ratio on the Vortex-Induced Vibrations of a Long Tensioned Beam in Shear Flow

The flow past a cylindrical tensioned beam of aspect ratio 200 is predicted by direct numerical simulation of the three-dimensional Navier-Stokes equations. The beam is free to oscillate in inline and crossflow directions and submitted to a linearly sheared oncoming flow. The ratio between high and low inflow velocities is 3.67 , with a maximum Reynolds number of 330 . Two structure/fluid mass ratios are considered, 6 and 3 . Structure vortex-induced vibrations are characterized by mixed standing-traveling wave patterns. A reduction of mass ratio from 6 to 3 leads to purer, more pronounced traveling wave responses and larger amplitude vibrations in both directions. While multifrequency structure vibrations are observed at m = 6 , case m = 3 exhibits monofrequency responses. A large zone of synchronization between vortex shedding and structure vibration (lock-in) is identified in the high velocity region. The topology of fluid-structure energy exchanges shows that the flow can excite the structure at lock-in and damps its vibrations in non-lock-in region. Inline/crossflow motion synchronization is monitored. Similar zigzagging patterns of inline/crossflow motion phase difference are put forward for both mass ratios, highlighting a predominant character of counterclockwise orbits in the excitation region.© 2010 ASME