What is a Darrieus Machine?

Wind is blowing up.
Rotation of the machine is clockwize.

To the right is a simulation of the localized flow at specific points along the periphera of the Darrieus machine. It is animated to show how the flow changes with different rotational speed per wind speed, which is the number in the lower right corner.

basically I used a speed triangle to create this analysis. The rotor has a given tangential speed for a certain RPM, and I vary the wind speed. This gives rise to a couple interesting points:

• Maximum speed is obtained at the 3 O'Clock position. Following, minimum speed occurs at the 9 O'Clock position.
• There is a singularity point at 9 O'Clock.
• For a fixed blade angle, Angle of attack is continuously varying between 90 degrees and 0 degrees.

Lets take for example a couple of specific speed ratios. Lets start with rotational speed vs. wind speed of .75.

Looking between 9:00 and 12:00, You can see that if we have a fixed angle of attack of 0 degrees, the angle of attack is almost 90 degrees, so we are making almost no force. The only thing we are creating is a lot of drag, but in this case, drag is helpful.

In the next quadrant (between 12:00 and 3:00), the angle of local flow goes between 45 degrees and 0 degrees. Here we can create some useful lift. With flow averaging about 20 degrees angle of attack, with an elipse as an airfoil we can get some good lift. Now, IANAAE¹, but what happens is that the turbulent airflow on the outside surface creates enough of a boundry layer that we get an effective airfoil shape that has a negative angle of attack (it is pointed inward). so we not only get lift, but the lift is pointed in the propper direction.

In the third quadrant (3:00 to 6:00), we have the same effect. The effective airfoil has a negative angle of attack, which produces a torque about the center axis of the machine.

Fourth Quadrant. Angle of attack goes from 45 degrees to 90 degrees. What really is interesting here is what happens at exactly 90 degrees. If you compair the stream here (directly up) with a flow at a ratio above 1, you will see that the flow instentaneously changes. At a ratio of exactly 1, the relative wind magnitude is exactly zero. Since we are below a ratio of 1, the relative wind is still vaguely in the direction of the real wind, so we would be better off increasing drag (rather than relying on lift) through this quadrant.

So that is it. One cycle in a Darrieus machine.

Now lets take a look at a more advanced flow. With a rotational speed vs wind speed of 1.10, we see a slightly different picture. Quadrants 2 and 3 are very similar. ####, all the quadrants are similar. But look at 9:00. Notice it is pointing down. Notice that the stream line below 9:00 is pointing in the opposite direction of the same stream line for .75. We have a flow reversal somewhere along there.

At this point (9:00) it doesn't make too much sense to become a drag device. if you did, you would actually accelerate the air at 9 O'Clock! So the conclusion is that if you make a drag device you are never going to exceed a ratio of 1.

So Radius is governed by nominal wind speed. Increased windspeed matches increased radius with a constant rotational speed (keeping the ratio to 1). Of course, Power increases linearly with radius (and height too).

Things to do:

• I am not sure what the big boys ratio works out to, but I will find out. generally 5-7
• To do a torque/phase/ratio surface, I need to know stall angles and lift coefficients for an ellipse. (it's the next step up from a torque/phase curve)
  looks like an ellipse stalls at 10 degrees angle of attack and a 1 foot cord, 6 foot long blade will generate about 34 lbs of lift at 42 mph. aim for a thickness about 20% chord width. (a flat plate will do about 29 lbs of lift under the same conditions... is it worth it?

Why did I do this?
I think Darrieus Machines look cool.

-James