On Jun 16, 2009, at 1:35 PM, Jed Rothwell wrote:
Latest info. See:
http://www.wired.com/wiredscience/2009/06/highaltitudewindpower/
- Jed
The helicopter variety was discussed here in 2006 and 2007, in part
based on Jed's reference to this article at the time:
http://tinyurl.com/2lqyyr
An edited combined version of various related posts of mine follows.
It probably isn't necessary to locate in North Dakota. Also the
article implies an altitude of 15,000 ft is necessary: "But how do we
get a working turbine up to the necessary height -- at least 15,000
ft (4600 meters) above the earth's surface? That's where helicopter
technology comes in." It doesn't seem likely that altitude is
necessary either. There is a diminishing return for higher altitudes.
http://en.wikipedia.org/wiki/Wind_power
at one time stated: “The wind blows faster at higher altitudes
because of the reduced influence of drag of the surface (sea or land)
and the reduced viscosity of the air. The variation in velocity with
altitude, called wind shear, is most dramatic near the surface.
Typically, the variation follows the 1/7th power law, which predicts
that wind speed rises proportionally to the seventh root of altitude.
Doubling the altitude of a turbine, then, increases the expected wind
speeds by 10% and the expected power by 34%.”
This is now more thoroughly discussed at:
http://en.wikipedia.org/wiki/Wind_profile_power_law
The power from wind is proportional to the cube of the velocity, so
the power increases with the 3/7 power of altitude. At 15,000 ft the
power is only 60 percent more than at 5000 ft. The majority of that
altitude benefit can be obtained by building wind walls on high
rugged mountain tops, which concentrate wind over their ridges. The
power cable, a major weight problem, is more than 3 times heavier at
15,000 ft than 5,000 ft. A major weight problem is associated with
protecting the power cable from lightning strikes, which would be
extremely frequent to say the least.
A non-economic wind power class 2 location at an altitude of 50 m has
average wind speed of 5.6 m/s and power density of 200 W/m^2.
Applying the 1/7th power law, a 1 km tower in that location would
experience an average wind speed of (1000m/50m)^(1/7) *(5.6 m/s) =
1.53*(5.6 m/s) = 8.54m/s. This turns a useless wind class 2
location, like the coast of Georgia, into a wind class 6 location,
with 600 W/m^2 wind power density.
One problem is the fundamental fact that a drag proportional to the
square of the wind velocity is necessary to achieve the power
proportional to the cube of velocity. In any event, for a given
aerodynamic configuration, drag is roughly proportional to the square
of the velocity. At high altitudes fast feathering and getting out
of the sky fast to avoid tether breaking in high wind becomes an
issue. Staying in the sky is also a problem, as well as dealing with
lightning and storms.
One possible solution is to utilize/hybridize solar towers instead of
kites/helicopters.
The tops of solar towers, also known as solar chimneys, should be
ringed with vertical layers of inverted airfoils. In windy
conditions, nearly always present at high altitudes in many
locations, these inverted airfoils about the periphery, with trailing
edges to the inside, have the effect of reducing air pressure at the
top of the chimney. They direct horizontal airflow upwards, thus
reducing air pressure in the chimney. This enhances the Bernoulli
effect already present for such chimneys. This pressure drop
increases airflow and thus turbine output at the base of the
chimney. Use of variable pitch airfoils permits controlled
feathering and continual operation in high winds. The airfoils
increase load on the structure and cost of the structure, but airfoil
pitch control may be of use in preventing resonant vibration buildup
in high wind conditions. The use of such airfoils increases the
optimal chimney aspect ratio to less than that which is optimal
without the airfoils. A typical (height to diameter) aspect ratio
for solar towers is currently 6.
Suppose the effective area of the tower with respect to wind power
extraction is roughly the diameter of the tower squared. A 1 km high
solar tower would thus have a useful wind cross section of (1000 m)
^2. However, due to pressure drop losses in the flue, and other
inefficiencies, only about 10 percent of that power can be
extracted. The wind power available is then (1000 m)^2 * (600 W/m^2)
* 0.10 = 60 MW, but this is 24 hours a day, not just through
daylight, providing a 120 MW solar equivalent enhancement to a 200
MW solar tower.
Use of wind power to enhance solar tower performance has the
advantage that wind power tends to be available when solar is not.
Coastal wind power is larger at dusk and dawn, while solar power
peaks around noon. Wind power also tends to be larger during
overcast or stormy conditions. Solar towers, being ducted with the
power concentrated, can be throttled so as to continue running in
high wind conditions.
Obtaining the wind power requires use of aerodynamic structures at
the tower top to reduce pressure in the chimney there. These can be
static structures - horizontal airfoils, or vortex creating vertical
slits.
One problem with this idea is that solar tower performance data must
necessarily *already* include any Bernoulli effect pressure drop
enhancement due to wind. The incremental performance gain due to
auxiliary airfoil engineering may not be as much as expected. This
also implies that solar towers, already proven economically feasible
through prototypes, may not be economically feasible if built
sufficiently far away from the coast - as proposed in at least one
large project in Australia.
I have often thought it may be economic to build "wind walls", huge
3D geometric structures, possibly mixed geodesic, capable of running
very large windmills mounted to the steel beam structure. Such a
structure should be more economical to build than a single high tower
for each turbine, and could channel wind efficiently.
Alaska often has sustained high winds, hurricane force, at high
elevations. Windmills built along mountain ridges could produce vast
amounts of energy. One problem is avoiding shutdown during peak
energy production periods. This can be accomplished by providing an
additional set of small diameter high wind speed turbines that do not
have to be feathered.
The issue of wildlife safety points out one of the benefits of solar
towers: they are no threat to birds. Wind walls comprised of
strings of merged adjacent towers similar to solar towers would not
be cheap like low aspect ratio turbines, but they can run in any
amount of wind, they operate in the high altitude high wind regime
and, provided nesting niches are included on the walls, they can even
provide bird habitat. They are ideally situated along high mountain
ridges where little wildlife exists. The turbines, located in the
base, can be screened off, and are easier to maintain than stuff
mounted high on a pedestal.
When solar towers were first discussed here I noted the advantage of
building the duct structure along the side of a mountain, especially
a south facing mountain. This provides mostly free structural
support, permits locating the turbines conveniently, permits use of a
transparent side to the tower to gain solar heat, and provides
massive amounts of thermal storage.
Best regards,
Horace Heffner
http://www.mtaonline.net/~hheffner/
