Wind turbines: any equation defining the relationship between pitch angle and angle of attack?

[Victarion]

Greetings. I am trying to calculate the performance characteristics (thrust, torque, power) of a wind turbine rotor using the blade element momentum method (Chapter 6, sub chapter 6.1 and 6.8 in the book "Gasch, R., & Twele, J. (2012). Wind Power Plants Fundamentals, Design, Construction and Operation".

The problem is with determining the angle of attack for each segment of the blade. Every segment has a different twist angle, relative wind velocity, and the pitch of the blade during pitch control. These three parameters will determine the angle of attack for a specific segment, and the angle of attack will determine the corresponding Cl (lift coefficient) and (drag coefficient). Cl and Cd will be used to calculate the thrust, lift, torque, and ultimately power of the rotor.

The method written in the book does not consider the effect of pitch, which I think is the reason that my calculation results differ from my QBlade simulations.

Does anyone might know any equation relating pitch angle and angle of attack? Or even better, maybe between pitch angle, angle of attack, twist angle, and relative velocity angle?

 

[RRiver]

Interesting question so I looked it up myself. Seems pitch is controlled by electric motors or hydraulics and the angle is determined by electronic control settings for the desired efficiency output. The electronics monitor things like wind speed and power demand. Nothing on blade design. It might fall under the "trade secrets" concept.

 

[rb1957]

They are all inter-related … like folks incestuously breeding for generations.

You start with the twist profile of the blade, which defines (naturally enough) the local blade section with respect to some datum, lets call this "angle_t" = f(x) as x goes from the root to the tip.

Incidentally you are probably also changing the blade section along the blade (from fat at the root to thin at the tip) and probably changing the location of maximum thickness.

Now the nominal angle of attack of your blade is from the datum (basis of twist) to the wind direction. Note the local wind direction is the velocity of the global wind direction and the local rotational velocity component (so that the angle of attack (to the datum surface) changes along the blade, call it "angle _r".

Then you presumably also control the position of the blade datum surface with "pitch" control.

So the local angle of attack depends on the global wind direction, the pitch control angle, the radial position, and the twist distribution. There's no "equation", "just" summing these components.

another day in paradise, or is paradise one day closer ?

 

[3DDave]

I would expect a significant portion is an optimization problem for the most likely wind speed range and the operating RPM desired where the section and nominal twist is determined for every foot or so along the span; then all off-optimum speeds are met with gross blade pitch changes. No doubt some equation with a few hundred million terms could be used, but I expect that would be cumbersome. Balance that against stiffness and strength requirements so the blades are stable while operating and durable enough for the desired life. This will limit the lift distribution and the amount of pitch moment applied to the hub.

I'm starting to think this is more than the effort that an afternoon might handle.

 

[Victarion]

@RRiver
Thanks for the reply. Indeed, and it is an interesting topic as well!

@rb1957
Thanks for the reply. I see. I looked up the stuff earlier and the closest things to an equation are diagrams showing the angle components in a turbine blade. It is as you explained. Thanks!

@3DDave
Thanks for the reply. Fortunately, in my case not every parameter is taken into the optimization problem. The blade chord length is optimized using simple equations by Betz and while the Betz has a method for optimizing the twist, I used the built-in twist optimization algorithm in QBlade (also using Betz's method. There are also other optimization methods)

 

[rb1957]

I think we overuse the term "optimised", or possibly use it too generally … we say "optimised" and not "optimised for X against Y and Z". Nothing is truly optimised.

I think maybe your problem is you've got a blank sheet of paper and don't know where to start.

So start with something (presumably like something already out there). then play with it … change cross-sections, twist profile (I start with a twist that generated the same AoA along the span, ie countering the radial velocity component). With some clever designing you may be able to get the tips to off-load and so control the blade loads in extreme wind events. If you are "optimising" state "optimising X with respect to Y and Z".

Turbine blades are interesting in that they are designed to produce torque (not thrust like a conventional propeller).

another day in paradise, or is paradise one day closer ?

 

[RRiver]

The history of airplane prop design was all trial and error in a wind tunnel. Of course they didn't have computers and MATLAB. But even with computers and MATLAB, garbage in, garbage out.

 

[rb1957]

yes, but the garbage out is so seductively pretty ...

another day in paradise, or is paradise one day closer ?

 

[rb1957]

can you ask your design program to plot aoa spanwise ?

You'll have one design point where the conditions along the blade are what you really want, some global wind condition (speed and direction) such that the blade produces max torque (ideally every section working as it should). I understand that turbine want to turn at a specific rate (30 rpm ?) … which may help limit your design conditions. It'd be nice if you designed the blade (using composite cloth to tune the stiffness, as they did with the X29? fwd swept wing) so that it deflected under load so that it unloaded itself (under load the tip deflects to reduce the local AoA and reduce it's load).

another day in paradise, or is paradise one day closer ?

 

[GregLocock]

Hmmm. I like optimisation problems. Shouldn't you be optimising on a monte carlo of windspeeds, for a maximum energy output, rather than that one optimum? That is, an optimum adjusted to the likely windspeeds rather than just one, or in SE speak, a robust solution.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[Victarion]

Thanks again for the replies, everyone.

@rb1957
The design points are chosen, and it is indeed at a specific rate (190 rpm because it is a small wind turbine). Designing the blade with the unloading function as you mentioned might be too complex for my application and capability, but I will look into that for curiosity purposes.

Regarding plotting aoa spanwise, QBlade has no such capability for a "multi parameter BEM simulation" application (as far as I know). That's why it's quite confusing initially, but I believe your explanation yesterday sorted everything out.

Another problem that I now encounter (unrelated to the current topic, so I might make a new thread) is that the "XFOIL Direct Analysis" function in QBlade is uncapable of getting Cl and Cd values for AoA too high or too low. I have increased the iteration limit to 1000, and it only succeeds in simulating AoA as high as 17.8 degrees.

I am now trying to use XFOIL to do this, however so far it is not working either. I am now increasing the panel (elements?) number to the maximum of ~500 and iteration to 1000. In case this does not work, does anyone know what might be the cause of this and maybe other software that could work properly in giving me airfoil analysis results for very low or high angle of attacks? Thank you

 

[RRiver]

"""The design points are chosen, and it is indeed at a specific rate (190 rpm because it is a small wind turbine). Designing the blade with the unloading function as you mentioned might be too complex for my application and capability, but I will look into that for curiosity purposes."""

If you step back from the blade geometry and engineering for a bit and research the economics of what you're asking about there's interesting information available. Mainly if you're not planning on going in to production with your design it is much less expensive to buy your blades than it is to make them. Bear in mind in the US, Canada, India, etc. and many other countries, before you can put a wind turbine up that's more than a maximum specified height and size the blades, turbine and tower have to be certified and that doesn't seem to be cheap. If you don't have the necessary credentials you have to pay someone who does.

 

[rb1957]

it would appear that Xfoil does not like it when the airfoil stalls (at extreme AoA) ? This is a complete step-change in the aerodynamics.

if Qblade can't consider multiple AoA, then 1) get other software or 2) If you're stuck with this limited software (I suspect you are) then run multiple cases (at different spanwise locations … the tip will be very different compared to the root).

another day in paradise, or is paradise one day closer ?