The Wave Eductor

Wave Eductor and Its Potential Use in Ocean Thermal Energy Conversion
Larry Yin, Alan F. Blumberg, Thomas H. Wakeman III, Jon K. Miller, Raju V. Datla
Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030
[email protected]
1-201-294-2205
The Vision
A good way to harvest wave energy is to use an energy concentration system with a large number of cheap energy collection devices
spreading out at sea converting the wave forcing into a certain form and passing it to a single, well-protected point where the joined
energy is converted all together. The energy collection devices should be simple and lasting - like the floating glass bottles - to survive
the ocean. The idea of concentration takes advantage of the space of an open sea to win in economy by scale.
Frequency
(rad/s)
Wave Height
(cm)
Flowrate
(gpm)
Effectiveness
Coefficient
2.856
5.42
2.3 x 10-2
0.96 x 10-4
3.491
7.02
4.4 x 10-2
0.93 x 10-4
4.189
6.67
5.5 x 10-2
1.89 x 10-4
4.654
5.14
5.1 x 10-2
1.67 x 10-4
5.236
4.68
2.1 x 10-2
1.47 x 10-4
The realization of this vision lies in the invention of the wave eductor and its application in an adapted Ocean Thermal Energy
Conversion (OTEC) system. The wave eductor, based on the working principle of an eductor, pumps water running on wave energy at
no cost. The whole device is in one piece without any moving parts. Groups of wave eductors, replacing the mechanical pumps, feed an
OTEC power plant with cold and warm water from different depths, as the collection of the kinetic and potential energy spread out in the
waves to build up water thermal energy in the OTEC heat exchangers for a centralized conversion into electricity. From another
perspective, the replacement with wave eductors in the OTEC would turn the power consumption in water pumping, about 40% of the
gross output, into additional sales.
The Wave Eductor
The concept of wave eductor is using waves to drive a submerged funnel (or a combination of funnels), to make it oscillate in the alongaxis direction, repeatedly creating low pressure at the narrower sections due to the periodically accelerated internal flow, thereby
sucking in water through the opening on the wall at the narrowest part from a joined suction tube. The pump needs no pistons, no
valves, no sealing, and no lubrication - a structure of simplicity.
Test Results
Model Scale Performance
Prototype Scale Performance
The Adapted OTEC Power Plant
The seawater systems of such a plant are modified to accommodate the use of wave eductors. The altered plant is close-cycle (CC),
deploying two wave eductor groups at locations where the wave conditions are statistically good, one group supplying cold water from a
deep depth to its condensing units and the other supplying warm water from the surface to its evaporating units. The suction tubes (A)
are in parallel, connected to a large-diameter outlet pipe (B) through an interface. The outlet pipe (B) connects to the outlet side of the
heat exchanging units (HX) within the plant housing, while a similar inlet pipe (C) connects to the inlet side of the heat exchanging units
(HX). The other end of the inlet pipe (C) runs out to the point of suction, either at 1000 m deep off the shelf or just below the surface in
the vicinity. The heat exchanging units are located below the water level to avoid elevation head – in the holds of a plant ship below the
draft line for the offshore scenario and in an underground structure by the coast below the lowest tidal level for the onshore scenario.
The piping is all underwater as well, through ship hulls or through drilled tunnels under sands or rocks. The other CC-OTEC
components – turbines, working fluid circuit and so on – remain the same, except that the heat exchangers should be customized to
minimize pressure drop, which is not hard in a shell and tube heat exchanger design. At last, the wave eductors should be placed to a
depth of at least 60 m to prevent negative environmental impact for discharging water[2].
Wave Eductor Model
Model Setup
For proof of concept, a 3-D printed, small-scale wave eductor model of a symmetric double-funnel design and with arbitrary dimensions
was tested in April 2013 in the wave tank at Stevens Institute of Technology. The model was set up in a heaving operation mode with a
cylinder buoy on top and was moored by a tension spring and an anchoring weight. Each test was under monochromatic waves of a
particular frequency generated by a wave maker by the end of the tank. The model was allowed all six degrees of freedom but only
heaving displacement was recorded. Instantaneous wave amplitude was measured by a wire on the side. Red dye was put into the
clear suction tube for observation of the flow. In all the tests, the colored water moved up the tube in a pulsed manner, rushing forward
twice over one wave period (due to the double-funnel design), before it entered the wave eductor and was discharged out of the funnel
mouths. The whole tube of colored water, including the dye that attached to the inner tube wall, was emptied within minutes.
Calculations are made to estimate the required number of wave eductors and the required suction pressure for a traditional 10-MW CCOTEC plant. To simplify the calculation, the flow in all the piping or tubing is considered steady and turbulent as with an averaged flow
rate and the flow in the suction tubes is regarded identical. All the design parameters are based on the best available benchmark values
mostly from literature[3-8].
OFFSHORE
Deep Water Pipe
A
Condenser Evaporator Condenser Evaporator
A
B
C
Total Heat Transfer Duty (kW)
665,271
635,964
665,271
635,964
Flow Rate (m3/s)
Flow Rate (gpm)
27.7
439,100
52.8
837,600
27.7
439,100
52.8
837,600
A
0.243
0.243
0.243
0.243
B
5.5
5.5
1.6
1.6
C
3.9
4.6
1.6
1.6
A
100
100
100
100
B
100
100
500
500
C
1000
20
3123
500
B
1
1
7
18
C
1
2
7
18
Num of HX Groups in Parallel
4
4
4
4
A
1.49
2.28
2.39
3.25
B
1.17
2.22
1.97
1.46
C
2.32
1.59
1.97
1.46
1.50
1.50
1.50
1.50
A
0.79
1.61
1.90
3.16
B
0.14
0.21
1.88
1.08
C
1.57
0.01
11.00
0.97
Head Loss due to Density (m)
2.00
0.00
2.00
0.00
Head Loss in HX (m)
2.75
1.75
2.75
1.75
Req. Num of Wave Eductors
400
500
250
350
7.48 x 104
3.92 x 104
2.00 x 105
7.58 x 104
B
Pipe Diameter (m)
By analysis[1], the suction pressure of the wave eductor is
1
2𝐷1 + 𝐷2 𝐷1 − 𝐷2
𝑃=𝑐
𝜋𝜌 tan 𝛽
6
𝐷22
2 𝑑2𝑍
𝑑𝑡 2
−𝜌
𝐷1
𝐷2
4
𝐷1
−
𝐷2
2
𝑑𝑍
𝑑𝑡
C
HX
2
Pipe Length (m)
where 𝐷1 is the diameter at the funnel mouth, 𝐷2 the diameter at the funnel sprout and 𝛽 the funnel inclining angle. 𝜌 is the density of
the surrounding water. 𝑍 is the heaving displacement. 𝑐 is an effectiveness coefficient accounting for the energy loss in the internal flow
and the consequence of neglecting the motions other than heaving. It is found that the velocity squared term, the second in the bracket,
dominates the overall suction pressure, whereas the acceleration term plays a minor role but causes the difference between the two
consecutive pulses of suction flow, one stronger and one weaker as observed. The flow in the suction tube is studied by standard pipe
flow analysis and is fitted with observation to obtain the effectiveness coefficients for this particular model. The model is scaled up for a
typical wave condition with scaling ratio 19.14, a response amplitude operator (RAO) 1.136 (from the test) and effectiveness coefficient
10-4. The prototype scale suction tube is 243 mm in diameter and 700 m in length with smooth inner surfaces. The mean suction
pressure is projected to be 714 Pa and the mean flow rate is 0.0312 m3/s, or 495 gpm.
HX
Num of Pipes in Parallel
HX
HX
B
C
A
B
A
C
Mean Velocity (m/s)
Mean Velocity in HX (m/s)
Head Loss in
piping/tubing (m)
B
C
ONSHORE
B
C
HX
HX
Req. Suction Pressure (Pa)
Adapted Seawater Systems
Estimates by Scenarios
Off course, the nature of the ocean waves makes it hard to provide the sought-after base-load electricity. Yet, this can be remedied by
installing a stand-by mechanical pump in a separate outlet pipe, which is short, to guarantee operation when the waves are too weak.
On the other hand, ocean wave energy, in general, is more reliable than solar or wind.
Model Test
Proof of Concept
The performance of wave eductor can be significantly improved. The funnel ratio - the cross-section area ratio between funnel mouth
and sprout - can be easily raised to attain a larger suction pressure. The altered geometry brings about changes mostly in system
added mass and damping coefficient, which can be compensated by reducing weight or modifying the water plane area of the buoy to
ensure that the system natural frequency is tuned to the dominant wave frequency. The tension spring and the anchoring weight used in
the model set-up could be entirely removed in exchange for a shared mooring system for group deployment, provided that the buoyancy
is balanced by additional weight and the rope is replaced by a rigid connection. Furthermore, great interest would be to study the wave
eductor optimal geometry, since the low value of the effectiveness coefficient resulted from an arbitrary design suggests a large margin
for growth.
To summarize, the wave eductor, with a simple and integral structure, is proved to be a working device, able to pump water with wave
forcing by creating pulsed suction flow. The analysis offers strategies for optimization, which, together with further research, could
greatly elevate the pumping performance.
In conclusion, a CC-OTEC power plant adapted to the use of wave eductors is projected to require less than 1000 wave eductors based
on the demands of a traditional 10-MW OTEC plant - an acceptable number given the low cost of the novel pump. The projection sets a
design goal for the wave eductor to achieve a suction pressure on the order of 105 Pa, which is reachable considering its high
customizability and the potential increase in effectiveness with further research. Finally, bear in mind that the adapted power plant that
meets the requirements would have a net output of about 16 MW.
References
Yin, L. (2013). Physical analysis of a wave eductor. Stevens Institute of Technology, Hoboken, NJ, Master’s thesis.
Nihous, G. C., & Vega L. A. (1991). A review of some semi-empirical OTEC effluent discharge models. OCEANS 1991, Honolulu.
Vega, L. A. (2012). Ocean Thermal Energy Conversion. Encyclopedia of Sustainability Science and Technology, Springer, 7296-7328.
Taniguchi, T., Krock, H., & OCEES International. (2006). Preliminary analysis of polymer heat exchangers for ocean thermal energy conversion application.
War, J. C. (2011). Seawater Air Conditioning (SWAC) a renewable energy alternative. OCEANS 2011, 1, 9, 19-22.
Vadus, J. R., & Taylor, B. (1985). OTEC cold-water pipe research. Oceanic Engineering, IEEE, 10, 2, 114-122.
Eldred, M. P., Van Ryzin, J. C., Rizea, S., Chen, I. C., Loudon, R., Nagurny, N. J., Maurer, S., Jansen, E., Plumb, A., Eller, M. R., & Brown, V. R. R. (2011). Heat
exchanger development for Ocean Thermal Energy Conversion. OCEANS 2011, 1, 9, 19-22
8. Thulukkanam, K. (2013). Heat exchanger design handbook. Hoboken: CRC Press.
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