Lumped parameter models of vortex induced vibration with application to the design of aquatic energy harvester

摘要

In the present study, a lumped parameter model for vortex-induced vibrations is analysed. In this work, the vortex-induced vibrations of an elastically mounted rigid cylinder are able to move in-line and transverse to the flow with equal mass ratio and natural frequencies. A simplified lumped mass model is proposed to study the two degree of freedom (dof) structural oscillator. A classical van der Pol equation along with acceleration coupling, models the near wake dynamics describing the fluctuating nature of vortex shedding. The model dynamics is investigated analytically and the results are compared for moderate mass ratios. The results predicted using this model show a good agreement with the experimental data. The dependence of stream-wise displacement on mass and damping is explored. The cause of cross-flow displacement magnification due to freedom to move in stream-wise direction is also explored using the proposed model. Apart from these two degrees of freedom, the cylinder can also undergo rotation about its centre of mass. The effect of freedom to move in this rotational degree of freedom is exploited to our advantage by applying it to the VIVACE (Vortex induced vibration aquatic clean energy) design which was originally proposed by Bernitsas et al. (2008). The original design was not reported to be the optimal one and the set-up was shown to work only for a given flow velocity. But, the flow environment keeps changing and hence there is a need to bring in robustness and optimize the proposed design. The values of optimized spring stiffness have been found using the lumped mass model. The design is made robust by exploiting the rotational mode. This mode is triggered by varying the overhang lengths in accordance with the varying flow velocity in order to strike resonance for a certain flow regime.