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.

Oscillations and translation of a free cylinder in a confined flow

An oscillatory instability has been observed experimentally on an horizontal cylinder free to move and rotate between two parallel vertical walls of distance H; its characteristics differ both from vortex shedding driven oscillations and from those of tethered cylinders in the same geometry. The vertical motion of the cylinder, its rotation about its axis and its transverse motion across the gap have been investigated as a function of its diameter D, its density s, of the mean vertical velocity U of the fluid and of its viscosity. For a blockage ratio D/H above 0.5 and a Reynolds number Re larger then 14, oscillations of the rolling angle of the cylinder about its axis and of its transverse coordinate in the gap are observed together with periodic variations of the vertical velocity. Their frequency f is the same for the sedimentation of the cylinder in a static fluid (U = 0) and for a non-zero mean flow (U 6= 0). The Strouhal number St associated to the oscillation varies as 1/Re with : St.Re = 3 $\pm$ 0.15. The corresponding period 1/f is then independent of U and corresponds to a characteristic viscous diffusion time over a distance ~ D, implying a strong influence of the viscosity. These characteristics differ from those of vortex shedding and tethered cylinders for which St is instead roughly constant with Re and higher than here

The effect of spacing on the vortex-induced vibrations of two tandem flexible cylinders

Vortex-induced vibrations (VIV) of two flexible cylinders arranged in tandem are studied using a two-way fluidstructure interaction (FSI) method with different spacing ratios (Sx/D) at Reynolds number Re = 500 using a twoway fluid-structure interaction (FSI) method. The main objective of this study is to investigate the effect of spacing on the hydrodynamic interactions and the VIV responses of these cylinders. The responses of the two flexible cylinders are found to be similar to the classical VIV responses at small Sx/D. Once Sx/D is large enough for the vortices to become detached from the upstream cylinder, the response of the upstream cylinder is similar to the typical VIV response whereas the downstream cylinder undergoes wake-induced vibration (WIV). The characteristics of the response of the downstream cylinder in the present study are similar to those of the first two response regimes classified by previous researchers. The third regime is not observed for the flexible downstream cylinder with both ends fixed. The two changes in the phase relation between the cross-flow displacements of the two tandem flexible cylinders are discovered to be linked with the initial-upper branch transition and the upperlower branch transition, respectively. The correlation lengths of the two flexible cylinders decrease significantly in the transition range between the upper and lower branches. Three modes of vortex shedding (2S, P + S and 2P) have been identified in the present study. The upper-branch 2P mode is found to be associated with largeamplitude vibration of the upstream cylinder and the P + S mode is observed to be related to large-amplitude vibration of the downstream cylinder for Sx/D = 3.5 and 5. On the other hand, the lower-branch 2P mode leads to small-amplitude vibration of the downstream cylinder in the post-lock-in range at Sx/D = 2.5. The relative phase shifts of the sectional lift coefficients on different spanwise cross sections can be attributed to the variation of the vortex shedding flow along the flexible cylinders, and these phase shifts result in poor phasing between the forces and the displacements which is related to the decrease of the correlation lengths

A smart pipe energy harvester excited by fluid flow and base excitation

This paper presents an electromechanical dynamic modelling of the partially smart pipe structure subject to the vibration responses from fluid flow and input base excitation for generating the electrical energy. We believe that this work shows the first attempt to formulate a unified analytical approach of flow-induced vibrational smart pipe energy harvester in application to the smart sensor-based structural health monitoring systems including those to detect flutter instability. The arbitrary topology of the thin electrode segments located at the surface of the circumference region of the smart pipe has been used so that the electric charge cancellation can be avoided. The analytical techniques of the smart pipe conveying fluid with discontinuous piezoelectric segments and proof mass offset, connected with the standard AC–DC circuit interface, have been developed using the extended charge-type Hamiltonian mechanics. The coupled field equations reduced from the Ritz method-based weak form analytical approach have been further developed to formulate the orthonormalised dynamic equations. The reduced equations show combinations of the mechanical system of the elastic pipe and fluid flow, electromechanical system of the piezoelectric component, and electrical system of the circuit interface. The electromechanical multi-mode frequency and time signal waveform response equations have also been formulated to demonstrate the power harvesting behaviours. Initially, the optimal power output due to optimal load resistance without the fluid effect is discussed to compare with previous studies. For potential application, further parametric analytical studies of varying partially piezoelectric pipe segments have been explored to analyse the dynamic stability/instability of the smart pipe energy harvester due to the effect of fluid and input base excitation. Further proof between case studies also includes the effect of variable flow velocity for optimal power output, 3-D frequency response, the dynamic evolution of the smart pipe system based on the absolute velocity-time waveform signals, and DC power output-time waveform signals