Salient White Elephant

March 12, 2009

Helically Stacked Darrieus or Savonius Rotor

Darrieus Turbines have a number of well know advantages. The generator and gearbox are located at or near to ground level, the turbine doesn’t require yaw angle regulation, blade loads are largely tensile, and so forth. One well known disadvantage is that the power output fluctuates from about 100% to zero at the rate of twice per revolution of the rotor.

One way around this problem is to twist the two blades into a helical shape. This very cool idea was patented in 2001 by Professor Alexander M. Gorlov of the Northeastern University. (See Gorlov Helical Turbine on Wikipedia.)

Helical Rotor

Unfortunately, this approach is not very effective for utility scale wind turbines. The problem is that although the helical blades smooth the power output, the mechanical loads that the blades and tower components must support are very large.

The Helically Stacked Darrieus Rotor

The power smoothing characteristic of the Helical Rotor may be closely approximated by stacking traditional two bladed Darrieus rotors one on top of another in helical fashion:

Helically Stacked Darrieus Rotor

This combines the power smoothing advantages of the helical rotor with the favorable mechanical properties of the traditional Darrieus machine. (For simplicity, only two guy wires are shown in the above diagram. In reality, at least three guy wires are required.)

Multi-Level Guy Wires

One potential advantage of stacking rotors is that guy wires may attach to the tower between levels:

Helically Stacked Darrieus Rotor with Multi-Level Guy Wires

Another option increases the diameter of the stacked rotors for the lower levels. This is possible because the guy wires on the lower levels are closer to horizontal.

Three Bladed Darrieus

It would seem that adding more and more blades to a Darrieus rotor would make its power output smoother and smoother. This intuitive idea is a little misleading. In some cases, mother nature has endowed the number three with magical properties. For example, while single phase and two phase electrical circuits deliver fluctuating power, the output power of a three phase circuit is constant – it doesn’t fluctuate at all. This same effect renders the output of a three bladed Darrieus rotor nearly constant. Why nearly and not perfectly constant? Actually, I don’t know, but I suspect it is because wind must “fan out” as it flows through a turbine rotor:


Why does the wind fan out like this? Because slower moving wind requires a larger cross-sectional area in order to maintain the same volume rate of flow as the faster moving wind that approaches the rotor. This is closely related to the Betz Limit – the law that says that a turbine rotor cannot extract more than 16/27 = 59.3% of the kinetic energy in the wind. (See Betz’ Law in Wikipedia.)

Once upon a time, a company called Flowind built and tested a three bladed Darrieus turbine. I heard that the torque ripple at the gearbox for this machine was only 15%.

One disadvantage of the helically stacked Darrieus rotor is that various levels of the tower tube are torqued by the blades at different rotational angles. For this reason, it may be desirable to provide each level with three blades rather than two. These three bladed levels may still be rotated with respect to their upstairs and downstairs neighbors in order to further smooth power output in the manner of a helical rotor. We can also make more efficient use of the space between the guy wires by letting the rotors overlap (vertically) somewhat with their upstairs and downstairs neighbors. The following diagram gives a general idea of what I am talking about.

Helically Stacked Three Bladed Darrieus Rotors With Multi-Level Guy Wires

Helically Stacked Savonius Rotor

Just as you can smooth power by stacking Darrieus rotors in a helical fashion, you can also smooth power by stacking Savonius rotors in a helical fashion. Not only does this smooth output power, it also makes the machine much easier to manufacture. Savonius rotors have been built with their “vanes” twisted into a helical shape. I don’t know much about aerodynamics, but I suspect that a helical Savonius might not be such a good idea. My suspicion stems from noting that the helical Savonius shape tends to deflect wind in a partially vertical direction. Any vertical kinetic energy that remains in the wind after it leaves the region occupied by the rotor is kinetic energy that was not converted into electricity, and it would seem that this energy represents an innefficiency of the helical Savonius design. No worries – we can get the same power smoothing effect by stacking traditional Savonius rotors one on top of another in helical fashion. Flat disks are placed between each Savonius rotor and its upstairs and downstairs neighbor rotors. The disks aerodynamically isolate each rotor from its neighbors.

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