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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. 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 tra- ditional 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 desynchroniza- tion. 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.
VIVACE is the first known device that could harness energy from most of the water currents around the globe because it works in flows moving slower than 2 knots (about 2 miles per hour.) Most of the Earth's currents are slower than 3 knots. Turbines and water mills need an average of 5 or 6 knots to operate efficiently.
Michael Bernitsas, professor in the Department of Naval Architecture and Marine Engineering, stands before a prototype of his VIVACE hydrokinetic energy device. (Photo: Scott Galvin)
VIVACE stands for Vortex Induced Vibrations for Aquatic Clean Energy. It doesn't depend on waves, tides, turbines or dams. It's a unique hydrokinetic energy system that relies on "vortex induced vibrations."