| This dissertation studies harnessing of the hydrokinetic energy of water-currents by utilizing single degree-of-freedom Vortex-Induced Vibrations (VIV) of a circular cylinder. A mathematical model is developed based on a novel approach of energy phenomenology supported by experimental measurements of harnessed energy. VIV is a complex fluid-structure interaction. Computational fluid dynamics has limited success due to the necessity to resolve the smallest scales. Phenomenological models are based on linear, mass-spring-dashpot equations or van der Pol oscillators with experimentally defined sinusoidal forcing missing the underlying physics of VIV. Van der Pol oscillators do not model VIV, just classical flutter. In all models, the vortex-shedding mode is limited to 2-Single vortices per cylinder cycle, while experiments show broad variety of vortex structures. In this dissertation, a new math model is developed through rigorous derivation of the energy of a cylinder, boundary layer, shear layer, and attached vortices, allowing for small-scale variations to be smoothed out, leaving the large-scale variations as the drivers for VIV. Due to the rigorous derivation, all parameters are physically meaningful and experimentally measurable. No curve-fitting is used to develop the model and there was no intended final form of the equation. Hamilton's principle is used to develop the force equation. The developed model has high level of qualitative and quantitative success capturing: (a) The phase-shift between the lift force and the cylinder displacement at synchronization lock-in. (b) The cylinder frequency lock-in response around the natural frequency. (c) The higher cylinder frequency response for very low mass ratio. (d) Lock-out at desynchronization. (e) The vortex-shedding frequency not locking in at synchronization. This allows for the model to respond to various vortex shedding modes, with both the traditional 2-Single and 2-Pair modes documented, along with even higher modes observed in the output. (f) The amplitude response, qualitatively, in the representation of initial, upper, and lower branches within the range of synchronization, followed by desynchronization.;The model yet fails to capture the actual amplitudes, but small changes in energy have nonlinearly large effects on the amplitude. In future research, the model will be updated to capture all of the energy affecting the system. |
