Tidal turbines in the East River facing fundamental limits
After a New York Times article this morning, Ben and I were hashing over the potential for successful tidal turbines (well, he was ranting; I was hashing).
Ben pointed out quite astutely that the requirements for a tidal turbine are actually surprisingly similar to a requirements for a wind turbine. The power density of both situations are similar. Wind velocity at a prime turbine location is in the low 10’s of mph, while tides are in the low single digits of mph. However, the power density scales with the cube of the velocity, to wind gains a factor of 1000 over water. This is roughly canceled by the ~800x difference in density between water and air.
Additionally, the Reynolds numbers for both situations are similar . The Reynolds number is Re = density * velocity * characteristic length / viscosity. Water is about 100 times more viscous than air, but that gets canceled by water’s ~800x higher density and 10x lower velocity.
This means that you want roughly the same blade geometry and tip speed ratio for a wind turbine as for a tidal turbine. The problem is that to get the same tip speed ratio in a medium that’s moving 10x slower, you have to reduce the angular velocity by a factor of 10 as well.
The folks at Verdant, featured in the New York Times article, have figured this out; they say that their turbines peak at 32 rpm. According to an interview with one of Verdant’s engineers, the turbines are about 5 m in diameter.
In the wind turbine world, Paul Gipe cites a 7 m wind turbine as having a peak speed of 310 rpm in his 2003 book Wind Power (p. 102), and Southwest Windpower’s new Skystream turbine, with a diameter of 3.7 m, nominally peaks at 325 rpm. So, Verdant has the right tip speed ratio– what’s the problem?
The problem is that the power density is the same, the size is the same, the angular velocity is 10x lower, and wind turbine blades are already made of composite materials to withstand high torques. Power is torque * angular velocity, so for a constant power, if the angular velocity drops by X, the torque goes up by X. It’s no wonder that Verdant’s turbines are getting ripped apart. Their plan now is to use cast aluminum, which has a yield strength around 150 MPa; composite materials are an order of magnitude higher (and remember, they need to beat wind turbines by 10x, not just match them).
The New York Times quotes the founder of Verdant: “‘The only way for us to learn is to get the turbines into the water and start breaking them,” said Trey Taylor, the habitually optimistic founder of Verdant Power.”
Just to be clear, while I do work in the renewable energy field, I’m not a friend or enemy of Verdant; I had not heard of them before today. I don’t have any investments in Verdant or any of their competitors.
Related links:
Some guy’s comment on Reddit
August 16th, 2007 at 12:23 pm
I won’t pretend to understand much of what you wrote, but another kind of “fundamental limit” on this kind of project are the limits of political acceptance. I’ve recently been reading Cape Wind by Wendy Williams and Robert Whitcomb and I find myself shocked and amazed by the lengths to which a small group of wealthy and politically connected people who should know better (Kennedy, Kerry, David McCullogh, Cronkite, etc.) were able to sow enough FUD to turn public opinion against the project. I think its a must-read for anyone who would like a similar project to succeed where Cape Wind surely has failed.
August 28th, 2007 at 11:47 pm
Brandon,
Such a pity to find that you are still daydreaming about these hare-brained perpetual motion machines of yours. Why are you not discussing methods for capturing the energy emitted by 2008 presidential primary candidates’ zealous exhortations? Already, these methods are revolutionizing the energy industry.
For example, it is well known that a Democratic candidate and a YouTube-connected webcam will react violently when placed inside of an appropriate reaction vessel. This is because the candidate, upon detecting the presence of the camera, will enter an excited state characterized by the emission of sound bites such as “A stitch in time saves nine” or “Make sure to touch my name firmly on election day.” However, as soon as the camera is deactivated, the Democratic candidate will relax back to its ground state, resulting in the emission of a single quantum of energy, in proportion to the product of the candidate’s wavelength and Planck’s constant. This quantum can then be used to do mechanical work, such as turning the starter crank on a Ford Model T or adjusting the Mt. Rushmore Global Thermostat (as George Bush has recently proposed).
Because 2008 presidential candidates are fed a diet of corn-based ethanol, this proposal has been embraced by both agribusiness interests and environmentalists. (The unlikeliest of bedfellows to be sure!) Moreover, webcams can be manufactured inexpensively in China, where tough government regulations have helped to maintain the pristine, water-free state of industrial solvent rivers that might otherwise contain dangerous wildlife and toxic biological matter.
I encourage you to check out my blog at http://pingswept.org/2006/01/16/gplv3/#comments for more information about this and many other subjects.
Sincerely,
L. Martyr
September 2nd, 2007 at 5:57 pm
@ L. Martyr: I thought you were a BSD martyr.
Also, do you think that it’s a sign of neurosis that every time you go on some trip somewhere (like your current trip to Zimbabwe, mentioned in our recent confidential e-correspondence), you start emailing me and comment-blogging on my blog multiple times per day?
September 3rd, 2007 at 7:59 am
I was a BSD Martyr, but then I set fire to myself to protest the lack of a journaling file systsem in FreeBSD. Christ, do people think it’s still 1982 or something? Anyhoo, I captured some Kodak Fun Pix of my self-immolation: http://upload.wikimedia.org/wikipedia/en/f/fd/Thich_Quang_Duc_-_Self_Immolation.jpg
Now, to answer your bloody question, yes, let’s face it, too many years of Ctrl+Alt+Backspacing my troubles away have left me incapacitated and deranged. Why else would I read your blog?!
P.S. If you sift through the 5000 emails I sent to you while I was in Africa, you will find one PDF with the first few panels of a Pysolar comic strip. May I suggest that, if I ever finish the comic, you agree post it on your Sourceforge site? Just think: more HA HAs => more PySolar downloads => more cash in your pocket!
November 19th, 2008 at 6:57 pm
[...] down to the sea floor for operation and release for service. Unlike their competitors in New York, Verdant Power, they have no cantilevered blades. Sauer says they can get 250 kW per bladeset in a 6 knot current; [...]