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Hydrokinetic Oscillators for Undersea Energy Sources
Kinetic Energy Harvesters Driven by Flow-Induced Vibration Generate Potential Renewable Energy Underwater

By Wayne Liu
Mechanical Engineer, Maritime Systems
Space and Naval Warfare Systems Center Pacific
San Diego, California

While surface oceanographic monitoring stations can benefit from advancing technologies powered by solar, wind and wave energy, submerged and seafloor remote sensing applications must look to other renewable energy sources, ideally with a simple and compact energy harvesting method.

To provide such an undersea energy source, the Space and Naval Warfare Systems Center Pacific (SSC Pacific) is researching the use of hydrokinetic oscillators that would twitch constantly in low-speed flows using flow-induced vibration (FIV) mechanisms to generate 10-hertz tip deflections. These cantilevered cylinder oscillators would then drive tip-mounted kinetic energy harvester (KEH) devices that transduce vibrations into useable power.

Flow-induced vibration demonstrated on an accelerometer-tipped cylinder with kinetic energy harvester (KEH) pod mock-up. The KEH pod can carry SSC Pacific KEH devices that will convert vibrations into power.

FIV (e.g., vortex-induced vibrations, wake galloping) is often responsible for perturbations, flow noise and occasional structural failures in offshore structures, cables, chimneys and heat-exchanger tubes. These ubiquitous flow excitations can be exploited to drive an oscillator (e.g., cylinder, cable) and provide highly predictable and stable vibration inputs for an attached KEH device.

FIV-based hydrokinetic power has been demonstrated by Vortex Hydro Energy's (Ann Arbor, Michigan) Vortex-Induced Vibration Aquatic Clean Energy (VIVACE) platform, which was installed in the St. Clair River in Port Huron, Michigan. The demonstration sought to prove the viability of applying FIV for commercial power by using river flow to drive an array of large-diameter (more than 6 inches), vertically oscillating cylinders. While such a large-scale installation would be suitable for industrial applications, it may be inappropriate for powering small remote sensors with watt-level power needs.

For energy-harvesting applications, KEH devices have been demonstrated by SSC Pacific scientist Dr. Richard Waters to convert ambient ground and machinery vibrations into power for wireless sensors. For root mean square vibration inputs of 9.8 to 19.6 meters per second squared, or 1 to 2 g, expected power from a KEH can range from 200 to 800 milliwatts.

Designing for FIV with Given Cylinder and Flow
To drive a KEH-tipped cylinder with FIV, one would design the cylinder to resonate at the KEH operational frequency by using FIV available at the expected flow speeds. The operational frequency for SSC Pacific's KEH was 10 to 13 hertz and the expected nominal flow speed was 1 meter per second.

FIV excitation from the vortex shedding (Fs), measured in hertz) of a fixed, non-oscillating cylinder (with diameter D), can be related to the cross-flow velocity (U) through the Strouhal number (St) definition of: St = 0.20 = Fs∗D/U.

The St of 0.20 is valid for a range of flow speeds and cylinder diameters in Reynolds number flows of 1,000 to 100,000. (The Reynolds number is the ratio of inertial forces to viscous forces for given flow conditions.)

For each unique cylinder diameter, this equation shows a linear relationship between excitation frequency (Fs) and flow speed (U). For example, a 12.7-millimeter cylinder is shown to undergo a 13-hertz excitation in 0.8-meter-per-second (approximately 1.6-knots) flow.

If cylinder mass and cantilevered end mount are then tuned to present a structural natural frequency (Fn) that matches the 13-hertz Fs, significant FIV displacements can be expected at a critical velocity (Uc) of 0.8 meter per second to drive an attached KEH device.

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Wayne Liu is developing ocean energy methods at SSC Pacific as a mechanical engineer. Prior to SSC Pacific, he conducted submarine hydrodynamic trials at the Naval Surface Warfare Center Carderock. He holds bachelor's and master's degrees in mechanical engineering from Virginia Tech and University of California, Los Angeles, respectively.

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