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Energy 105 – Wind Turbines II

Mon, 06/21/2010 - 5:08am
Ken Johnson
Ken-JohnsonA couple of statements made about vortices in previous episodes have prompted several comments and queries. Then just recently there was a news story about an airliner incident where it hit an “air pocket” or CAT (Clear Air Turbulence) as it is called. Several passengers were very seriously injured and they were perhaps very lucky the wings stayed on. The NTSB report on it is not out yet, but it is possible they could conclude that it encountered the ‘turbulence wake’ of another aircraft . . . possibly a ‘jumbo jet’. More precisely, it may have been one or both of that other plane’s “trailing vortices”. This isn’t to say that such incidents always involve vortices generated by aircraft, because most turbulences are natural vortices and usually generated along the interface of layers of the atmosphere . . . often at the interface of the ‘jet stream’ (a very high velocity mass of air moving from west to east over the US), and the top of the troposphere where masses of air may be moving slower or even in the opposite direction to the jet stream.

Let’s start with Coriolis vortices, which come about in fluids as a result of moving vertically in a gravitational field on a rotating Earth, such as water going down a drain, or an air mass sweeping up or down the sides of mountains. Fluid Mechanics teaches us that this is indeed true and ‘the interested student’ may find it on several very good sites by Searching: “Vortex theory”. There is a good one at:

http://mysite.du.edu/~jcalvert/tech/fluids/vortex.htm

If you don’t understand vector mechanics (curl, divergence, etc.), you might limit your reading to only the first few and the last few paragraphs at that site.

There was a bit of ridicule from a few of the naysayers who apparently can’t comprehend the possibility that Atlantic hurricanes may get their start from Coriolis vortices generated by westerly moving winds over the mountains of West Africa . . . and tornadoes in the Midwest possibly get their start by winds moving eastward over the south end of the Rocky Mountain chain. It is suggested you to do a Web Search of “vortices, hurricanes” and you may be surprised at the number of hits. For my own acceptance of the concept, all I have to do is keep an eye out when working outside this time of year (prevailing westerly winds). I live in the Southwest, about 6 miles to the east of the base of a tall mountain. Almost on a daily basis, I observe ‘miniature tornadoes’ passing across my property. They travel on roughly a 045 deg. heading and just recently I drew a southwest to northeast ordinate line, on a map, from my property and it passed through Kansas City, along the strip known as ‘Tornado Alley’. The local ones that are carrying dust, straw, leaves, plastic bags, etc., I generally observe as rotating CCW (viewed from above). Size wise, they range from large enough to tear the roof off my storage shed (which one did), down to an observed size of about 1” in diameter . . . which I saw in my driveway last year. I was walking down to get my mail and I heard a very audible high frequency whizzing/whistling sound on the ground nearby, but zeroing in on the sound, revealed nothing visible. Thinking perhaps I had reached the senile state and was hearing things, I then spotted it as it moved into a little patch of sand. It appeared as about a 1” diameter extremely high rotational velocity CCW vortex. As I watched, it moved into the grass and the sound slowly subsided and it disappeared. Because the terrain between my house and the mountain, as well as the area to the east of me, is pretty well covered with trees, grass, and weeds, there is little loose dirt and sand for the vortices to pick up, so in our locale, we don’t see ‘dust devils’, as they are called where the terrain on the leeward side of a mountain is desert-like and the vortices are quite visible because of all the sand and dust available . . . and often growing to great size from the thermal energy picked up from the hot desert floor.

There is a theory in Aerodynamics about the generation of wing lift being the result of a vortex (rotating air mass) formed around the wing, which in combination with the forward motion of the wing, lowers the static pressure on the top of the wing but not on the bottom, so there is an upward force which lifts the plane. The theory further states this vortex is started with the forward motion of the plane and the original starting vortex is left behind but since one is continuously being formed by the wing, it slides off the wing tips, so it is linked by a continuous circular air flow off each tip all the way along the flight path, to the landing and is then shed off the wing when the plane stops. Pictures of airplanes taking off or landing on a dusty, smoky, or foggy runway quite often show those wingtip vortices peeling off the tips quite nicely. Visualize it as like a Slinky (that big coil spring-like child’s toy) with its two ends tied together so it is continuous. Then put your two hands in the center, holding one hand still and moving the other one away, stretching the Slinky out. The width of your hand represents the span of the wing, the stationary part of the Slinky represents the starting vortex, the moving hand represents the airplane, the part of the Slinky coils that are moving with that hand is the vortex being generated on the wing and the rest of the Slinky coils represent the trailing vortices (one from each wing tip) all the way back to takeoff, the energy of which depends mostly on the wing lift (aircraft weight) generated. Due to the fluid friction, the entire vortex will gradually decay . . . unless it encounters some energy source, like another vortex spinning in the same direction or some thermal gradient that might replenish its kinetic energy. An example of a closed circuit fluid vortex can also be seen in a perfectly blown smoke ring by an expert smoker.

This principle was used many years ago to build sail-less sailing ships. Their ‘sails’ consisted of tall vertical cylinders, rotated by steam engines. Due to the air’s viscosity and ‘skin friction’ of the cylinders, rotating them developed a vortex of air around the cylinder. If an air mass (wind) is then moved across the cylinders, a force is developed on the cylinders. This force is at about 90 deg. to the wind and pushes the ship along. The same principle was used by an experimenter to make a wingless airplane, replacing the wing with an engine rotated cylinder . . . and it worked, but requires a very reliable ‘lift engine’ spinning the cylinder. I once had a kite based on the principle, which always received much interest from the other kite flyers.

Imagine an airplane flying along at altitude and another plane at the same altitude crosses a short distance behind the first at a right angle to its path. The second plane is going to experience two jolts, one from the vortex on each side of the strung out vortex off each wing tip of the first airplane. Depending on the direction it approaches the vortex, it may get a large sudden surge in lift if its lift vortex is in the same rotation direction as the first airplane, followed by a sudden loss of lift as it crosses into the wake from the other wing tip vortex of the first plane because the rotation of that vortex is opposite to the first and cancels the lift on the crossing plane. The FAA attempts to control those possibilities by scheduling two flights at different altitudes if their flight plans bring them in close proximity to each other. It is also why two flights taking off (or landing) have an intentional time delay between them, particularly if the first aircraft is a jumbo jet.

So, what does this have to do with wind turbine fields? Their blades, like all propellers, are essentially rotating wings, with similar cross sectional airfoil shapes. Their maximum ‘lift’ is generated at right angles to their axis of rotation, applying a torque on the output shaft. The lift vortices being shed from the blade tips form large spirals about the axis of rotation and are moving in roughly the same direction and speed as the air exiting the blade ‘disk’, which is much slower than that at which it entered, having converted much of its kinetic energy into ‘mechanical’ energy through the blades to the turbine output shaft.

Imagine a field of twenty-five 3.6 MW turbines running at maximum output (roughly equivalent to one typical fossil fuel power plant built at about half the cost of the turbine field). This particular turbine (Siemens SWT-3.6) has three blades, each of which averages about 8 feet wide and 166 feet long, for a total ‘lifting’ area of approximately 4000 sq. ft., which is about equal to the wing area of the DC-10 . . . so it generates some powerful vortices. Also remember there are 25 of them, perhaps in a several square mile area. Now imagine a private pilot out for a low altitude sightseeing jaunt in his antique Piper Cub. He is not aware of the turbine field because it does not appear on his map as a navigation hazard and crosses a mile or two downwind of the turbine field. He undoubtedly can see the turbines (they are about 400 feet tall) but they are miles away and it does not occur to him he is about to enter a morass of 75 turbine blade tip vortices (3 per turbine), any one of which could suddenly and completely neutralize all his plane’s lift.

I am not trying to play the role of a modern day Don Quixote, fighting windmills, but wind turbines are becoming like the DDT ban many years ago, i.e. a wonderful way to “Save the Planet” . . . but with no consideration of true costs or deleterious side effects. I am sure you are aware that the DDT ban maybe saved a million birds (we don’t really know), but killed over 10 million human beings who died of malaria (we do know that for sure) because of maybe a billion anopheles mosquitoes whose lives were also saved by the environmentalists. Oh, I know they always have the best intentions, but that and $5 will get them a cup of coffee at Starbucks and a pat on the back from their fellow AWG extremist cohorts. Prof. Ken Johnson, Ret.
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