Is Over 100% Solidity Normal for Wind Turbine Blades Near the Hub?

[fugg]

Hello. I'm calculating the different parameters of a turbine design but I have some trouble with the solidity. The solidity near the hub exceeds 100%, but is an average of ~27% for a 6 bladed turbine. I'm just wondering if anyone has had experience in turbine design and if +100% solidity is normal (i.e. normal for blades to overlap each other near hub) or not. Any help would be much appreciated.

 

[Topher925]

I have a little experience in wind turbine design, and no a solidity of greater than 100% is not normal. A wind turbine with 6 blades isn't normal either. Solidity over 10% of the entire turbine is relatively uncommon for most modern HAWTs.

 

[fugg]

As the blade count increases, the solidity naturally does too. Sorry it wasn't 27% I was thinking of a different figure, but ~12%, which given that a 3 blade turbine would be ~9% seems reasonable. A 6 bladed turbine is indeed not conventional, but noise and tip speed ratio are my priorities hence the blade count.
I'm attaching an Excel sheet detailing the calculations. Am I missing something very obvious? The following equations were used:

Tip Speed Ratio: λ= ΩR/U, at distance r: λ_r=λ r/R
Angle of relative wind: φ= 2/3 〖tan〗^(-1) 1/λ_r
Local cord length: cl= (8πr/(BC_l ))(1-cosφ)
Optimum solidity for B blade number: σ≅ B/Nπ (N∑(i=1)(cl/R))

N=number of blade sections, 10 in this case.
Doesn't copy very well but you get the idea. I assumed the Coefficient of lift (Cl) to be 1 across the span to make it simple though I don't think it's too much of a stretch?

 

[fugg]

Aww, no one has worked in wind turbine design?

 

[kitesurfercha]

The equations you have listed are correct. It is easy to check your work, just do a few hand calculations to confirm the equations have been properly entered.

As for the results you should get solidity between ~7% (although single blade designs are even less) and ~30%. To check a specific turbine make sure that in the case of a high solidity the tip speed ratio is low and for low solidity the tip speed ratio is high. There are equations for finding the most efficient ratio, but not all turbines are efficient so use this as a guideline and not a rule. To make this simple I have attached a graph of solidity vs tip speed ratio.



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