Feasibility Study of a Vortex-Driven Hydro-Electric Plant

Expected Energy Extraction

Over a certain range of Reynolds number flow passing over a stationary bluff body will produce vortices that are shed from alternative sides of the body in a consistent fashion. This phenomenon is known as a Kármán vortex street, after Theodore von Kármán, who explained it theoretically in 1912 [1, p.309]. Many studies on Kármán vortex streets have been conducted on circular cylinders, where the Reynolds number range during which vortex shedding occurs was found to be approximately 40 < Re < 105 [2, pp. 277-279].

Dimensional analysis is a technique used to reduce the number of experimental variables in a system, by grouping them into dimensionless parameters. Additionally, dimensional analysis techniques can be used to scale model results to expected full sized values if certain similarity criteria are met [1, pp. 315-320].

Geometric similarity can be attained by directly scaling the model up to the prototype dimensions. Kinematic similarity ensures that respective points on the model and prototype have homologous positions at corresponding times. Dynamic similarity exists if the model and prototype force and pressure coefficients are identical. In the case of incompressible flow without free surfaces 1, this can be achieved by matching the model and prototype Reynolds numbers. Since we are dealing with an oscillating flow, the Strouhal number also needs to be considered. For the given oscillating bluff body system, dynamic similarity has to be achieved in order to scale up results from the model. Dynamic similarity precludes the requirements of geometric and kinematic similarity.

All tests were performed in a RHRC 2436 water channel. The channel has a 1.82 m (6 ft) long 0.61 m x 0.91 m (2 ft x 3 ft) test section and is capable of providing flow speeds from 0.0025 m/s to 0.30 m/s (0.1 in/s to 12 in/s).

Since all dimensionless parameters have been shown to remain constant for this test series a trend between power coefficient and Reynolds number can be determined and expected to hold true for other bodies meeting the same similarity criteria. It is furthermore expected that a well defined trend between the power coefficient and the Reynolds number can be extrapolated over a greater Reynolds number range to predict the power output of a scaled device as a function of Reynolds number. Density and viscosity values were assumed to be standard values for water at 10 °C.

Note that while the density of water is a relatively constant parameter, the viscosity of water changes considerably as a function of temperature.

When reviewing the following tables an important consideration to keep in mind is the difference between nameplate capacity and production output. The values below represent production output, that is the amount of electricity delivered to the grid. Most kinetic solutions being promoted use nameplate capacity numbers to give the impression that the generation unit is larger than what the actual production numbers represent. As an example a recent three month placement of a 150 kW wave generator only averaged 44 kW's of production at 2 meter high waves. This is a major design consideration difference between the two methodologies. Where wave and tidal devices have to contend with varying power outputs caused by, in one case unpredictable wave generation and in the other from tidal currents that range from zero up to 7 m/s and above, the Vortex Power Drive always delivers the same amount of energy to the system based on predictable, constant ocean currents.

The following table briefly outlines the predicted energy output from a single Vortex Power Drive. The typical installation would stack multiple Drives within the available water column.

Estimated Power Output for a Single Drive

Width (m) Height (m) Flow (m/s) Power Output (W)
3 5 0.5 35
3 5 1.0 210
3 5 1.5 590
3 5 2.0 1200
3 5 2.5 1900
3 5 3 2900

The following table briefly outlines the predicted energy output from an Array of Vortex Power Drives. This installation would connect to a single generation hub located above the water consisting of conventional power generation and switching equipment.

Estimated Power Output - 100 Drive Array - 20 m Water Column*

Width (m) Height (m) Flow (m/s) Power Output (W) Power Output (MW)
3 5 0.5 14000 0.014
3 5 1.0 84000 0.084
3 5 1.5 236000 0.236
3 5 2.0 480000 0.48
3 5 2.5 760000 0.76
3 5 3 1160000 1.16

Estimated Power Output - 100 Drive Array - 30 m Water Column**

Width (m) Height (m) Flow (m/s) Power Output (W) Power Output (MW)
3 5 0.5 21000 0.021
3 5 1.0 126000 0.126
3 5 1.5 354000 0.354
3 5 2.0 720000 0.72
3 5 2.5 1140000 1.14
3 5 3 1740000 1.74

* In a 20 meter water column 4 Drives would stack, one on top of another, on a single drive shaft. A series of 100 drive shafts would contain 400 Vortex Power Drive units. In this configuration the Array acts similar to a solar array where each individual Drive acts to contribute to the whole Array.

** In a 30 meter water column 6 Drives would stack, one on top of another, on a single drive shaft. A series of 100 drive shafts would contain 600 Vortex Power Drive units. Offshore wind turbine installation can occur with conventional installation techniques in ocean depths up to 30 meters. Vortex Power Drive installation is not limited in depth but for comparison purposes we have limited examples to 30 meters.

1) F. M. White, Fluid Mechanics, 6th ed., New York, NY: McGraw Hill, 2008.

2) J. D. Anderson, Fundamentals of Aerodynamics, 5th ed., New York, NY: McGraw Hill, 2010.