The Energy Harvesting Eel

Two types of vibration

•  Free Vibrations: Internal restoring forces set up free vibrations. Requires low levels of damping compared to spring force of material. Known as movement induced excitation. When the period of the internal restoring force matches that of the external forcing force, resonance occurs.

•  Forced vibrations: Caused by an external force or forcing field. Known as Extraneously Induced Excitation. This is the force of interest for this study. Ender this condition, the damping forces are very high or the material being vibrated has a very low internal spring force.
(Allen and Smits 2001)

Some basic requirements

• Need significant oscilating flow normal to the downstream direction.
• The length of oscilations must of the order of the length of the eel.
• Eel must be thick enough to strain Piezoelectric material. (see Mechanics section)
• Eel must be flexible enough to deform with oscilating flow rather than block oscillations and stream.

Flow mechanism

The general mechanism that meets the above requirements, as shown in the reviewed literature, is the Von Karmen Vortex Street.

Animation of phenomenon. Courtesy, Cesareo de La Rosa Siqueira.

This is a phenomenon responsible for many of the vibrations we see every day. Buzzing of telephone wires in the wind, oscillation of a car antenna at certain speeds, etc. It is the result of low pressure regions alternating from one side of a bluff body to another. This flow form provides the oscilating velocity normal to the main flow direction needed to significantly oscilate an eel placed in the flow.

Streamline or Splitter Plate

Ideally, the eel should act as a streamline fully coupling with the vortical flow. This condition is characterized by the eel's frequency and amplitude of oscillation matching that of the natural undisturbed Von Karmen vortexes. If an eel is too stiff, it will act as a splitter plate, stopping the formation of the vortexes all together. It is worth noting that this splitter plate method is used to control oscillation of smoke stacks and other objects susceptible to oscilation induced by vortex shedding. If the eel is to be a streamline, it must be sufficiently thin and flexible to couple with the flow without stopping the vortex formation.

Laboratory Investigation

Flume tests were conducted to show the range of flows that would produce the desired oscillations with two materials. One was a very thin, overhead projector sheet, plastic eel. 11 inches long with a thickness on the order of hundredths of an inch.. The other was plastic ruler, 18 inches long with a thickness on the order of tenths of an inch. Both were 2.5 inches tall.

Tests were run over a Reynolds number range of 1.4e4 to 2.6e4

Image courtesy of Wikipedia.org

Where Vs was the upstream velocity calculated using flowrate divided by flow depth.
L is the width of the bluff body. All tests took place in water.

Results

The results of the flume tests were very similar to those presented by Allen and Smits. Results will brievly be presented by Reynolds number.

Re~1.5e4 Thin eel oscilates with a regular frequency and low amplitude. Thick eel very nearly undisturbed. Acts as a splitter plate under the low Re number.

Re~1.75e4 Both eels oscillate with the same regular frequency indicating external excitation and resonable coupling of the large eel. Oscillation amplitude is on the order of 4 times larger in the small eel.

Re~2e4 Same trend as 1.75e4 larger amplitude and slightly higher frequency. Both eels well coupled. Moving thick eel back away from bluff body causes higher amplitude. This may be because it is acting a splitter plate diminishing the development of vortexes. Moving it slightly downstream likely allows stronger vortex formation, thus larger oscillations.

Re~2.6e4 Small eel no longer oscillates with a normal frequency. Large eel oscillates sporadically. Overall this seems to be the limit for the short eels tested. Longer eels may be able to capture vortices at this flow, but the 11 and 18 inch eels tended to stream and were buffeted by the general turbulence of the flow.

Video recapping lab findings - 5.5 megs

This link has excellent video showing eels in action.

Discussion

The above results show the range of flows that the eel will be effective is very small. It is evident that there are some changes that would help to improve the eel's response, but the balance of flow force to eel stiffness will always limit the versatility of an eel installation. This balance is of critical importance as energy generation potential is driven by strain. Thicker eels, as shown in the mechanics sections, have a higher potential to produce mechanical strain. As the eel becomes thicker, it requires a larger external force to produce oscillation and, at low flows, can completely cancel vortex formation. Eels are most well suited to flows with small variation. Given a set of conditions, an eel installation should be able to be scaled apropriatly to couple with the flow. Eels could be capable of powering sensors and other equipment in any location with a constant predictable flow; however, given variations in flow, they become much less effective. Constant flows such as open ocean currents and large river channels offer good opportunities for constant energy generation. Tidal flows are predictable enough but would offer a limited durration of energy harvesting.

 

Taylor et al, Ocean Power Technologies Inc. (2001) The energy Harvesting Eel: A small subsurface ocean/river power generator. IEEE journal of oceanic engineering, 26(4), 539-547

Allen J. J., & Smits A. J., (2001) Energy Harvesting Eel. Journal of Fluids and Structures, 15, 629-640

http://www.princeton.edu/~gasdyn/Eelmovies/movlist.html
This link has excelent video showing eels in action.