At this point in the project, it is only possible to present a preliminary estimate of
the size and number of turbines involved. This will provide some idea of the magnitude
of the undertaking. We start with a review of the purpose of the turbines.
The Gulf Stream transports warm water from the Caribbean Sea up to the vicinity of
Cape Hatteras. From this point, the winds push the water in a northeasterly
direction across the North Atlantic, and some of this warm water crosses the
Greenland - Shetland Island ridge to supply the heat load to the Arctic cooling
system. A reduction in the amount of warm water supplied by the Gulf Stream should
decrease the temperature of the water crossing the ridge without decreasing the
flow rate. This speculation is based on the observation that the Gulf Stream seems
to dissipate its momentum in the meanders and eddies that form while crossing the
Atlantic Ocean. This leads to the conclusion that the wind delivers the water to
the Arctic cooling system, and the cooling capacity determines how fast the water
can be made to sink and return to the Atlantic as cold bottom water.
Adjusting the flow rate of the Gulf Stream determines the quantity of warm
Caribbean water that goes into the mix that crosses the Atlantic. This flow rate
reduction might be achieved by simply dissipating the mechanical energy of the
stream with a network of submerged cables. This would certainly be a minimum cost
option whose sole benefit would be the reduction of the heat load on the Arctic
cooling system. But the calculations are greatly simplified and the stability of
the Stream is more certain if useful power is extracted. This minimizes the
production of eddies and turbulence, whose effects are difficult to predict. Also,
the extraction of useful power may be more cost effective than merely dissipating
power.
There is some history of power generation in the Gulf Stream. Blue Energy Canada,
Inc. [http://www.bluenergy.com] is the successor to Tracor Marine and Nova Energy.
These companies built a 4 kW Davis Hydro Turbine which used a squirrel cage
configuration of four straight blades parallel to the axis of rotation. The rotor
turned inside a shroud that collected water from an area somewhat larger than the
length times diameter of the rotor. The rotor diameter was 1.2 m and the length
also was 1.2 m. In the Spring of 1985 it was moored in mid-stream at a 200 ft depth.
The stream depth was 1000 ft. It produced 4 kW, and these companies claim that this
was the first time that electric power was derived from the Gulf Stream. This and
other proposed projects were not carried further because there was no demonstrable
cost advantage over conventional generation.
For help in understanding the following
calculations, refer to "Some Simple Calculations" in the section on the
Arctic Cooling System.
The Davis Hydro Turbine turns in the same direction when the direction of flow reverses, as in the case of tidal flows. A submerged axial flow turbine using a multi-blade marine screw propeller should be more suitable for the Gulf Stream, which flows in the same direction all the time. Because of the greater public familiarity with wind powered turbines we will borrow from that terminology and refer to the screw propeller as a rotor. We will also exploit the similarity between the hydrodynamics of marine rotors and the aerodynamics of wind turbine rotors. To simplify the discussion we will employ the present tense, as if the equipment were already in existence.
The rotor shaft extends from the downstream end of a watertight streamlined nacelle
which encloses the alternator, gear box (if used), bearings, and seals. The
trailing rotor simplifies the mooring and float design because it aligns naturally
with the flow direction. For the initial design, we will assume a rotor diameter of
10 m, giving a swept area of 78.5 m2.
The power passing through the swept area of the rotor is equal to
(swept area) (.5) (water density) (stream velocity)3
The superscript 3 is an exponent that tells us to write the stream
velocity factor three times in the formula. We then multiply all the
factors in the formula together.
(78.5 m2) (.5) (1023 kg/m3)
(1.79 m/s)3 = 230,000 (kg m2/s2)/s =
230,000 J/s = 230 kW
This is the power that passes through the swept area of the rotor when
the rotor is absent and does not interfere with the flow of water.
With the rotor in place and turning, the turbine cannot extract all of this 230 kW
because the water must retain enough kinetic energy to flow out of the way after it
has interacted with the rotor. The water gives up energy to the rotor, so it moves
away from the rotor at a lower velocity than the velocity it had before it
encountered the rotor. The streamlines must spread out in order to move the same
amount of water at the reduced velocity. Reference 7, page 289 has an excellent
discussion of this in connection with wind turbines.
At this time, we do not have an accurate estimate of how much power our turbine can extract from the stream. However, the opacity (fraction of swept area blocked by blades) of our rotor is probably about the same as the opacity of the multi-blade rotor seen on farm windmills all over America. The American farm windmill (Windmills pump water. Wind turbines generate electricity.) extracts about 30% of the power passing through its swept area when it is rotating at its optimum rate. Using this same 30% factor, we estimate that our water turbine extracts 69 kW.
In the section on the Arctic Cooling System we estimated that the Florida Current power was 41,700 Megawatts. We guessed that extracting 10% of this, or about 4000 Megawatts should make an observable change in the Arctic heat load. It would take 58,000 turbines to accomplish this. They could not all be located in the Florida Straits. They would have to be distributed along the entire path of the Florida Current and the Gulf Stream almost up to Cape Hatteras, where the stream leaves the coast and starts across the Atlantic Ocean. The electric power delivered to the grid would be less than 4000 MW because of the inefficiency of the alternators, power conditioning equipment, and transmission lines. Also, when the hydrodynamic drag of the rotors, housings, moorings and power cables is included, we would not need to extract 4000 MW to reduce the kinetic energy transport by 4000 MW. Therefore, fewer turbines would be required, say 50,000.
If the 50,000 turbines were distributed along the approximately 1080 km of stream path from the Straits of Florida to the boundary between South and North Carolina, they would be spaced 21.6 m apart. The turbine design would have to be modified to optimize it for the different velocities encountered along this path. They could be offset different distances from the path centerline so that no turbine would have to work in the disturbed wakes of the upstream turbines.
Using an estimate for installed cost of $1 / Watt, 4000 MW of generation would require an investment of $ 4 billion. These rough estimates of the project's size and cost emphasize the need to maximize efficiency and seaworthiness, and minimize cost. In this example, the configuration and size were picked arbitrarily. Instead of a single free stream rotor, the optimum configuration may be a ducted multi-rotor design with floats and mooring struts integrated into the package. For any chosen configuration, the optimum size must be determined.
As a check on our turbine calculation, we can scale up the results for the
Davis Hydro Turbine reported by Blue Energy Canada Inc. [Ref.18]. Their
ducted squirrel cage rotor interaction cross section was 1.44 m2, and their
sketches seem to show that the stream area intercepted was about twice as
great, or 2.9 m2. Our free stream turbine intercept area is
78.5 m2.
Multiplying their 4 kW measured output by the ratio of intercept areas
indicates that we might expect 108 kW output. This is 1.57 times the 69 kW
that we calculated using the assumed 30% extraction factor. This indicates
that we should try to extract more than 30%. The theoretical limit for a wind
turbine, referred to as the Betz limit, is 59.3% [Ref. 7, p.289]. To achieve
this, narrow rotor blades and high rotation speeds are required.
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