All wind turibne use low lift coefficent airfoils from 1.0 to 1.5.
Why not use high CL airfoils to get maximum torque?
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$\begingroup$ What do the manufacturers use? which manufacturers have you checked? What about lambda? $\endgroup$– Solar MikeJan 6, 2022 at 9:42
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$\begingroup$ @SolarMike all manufactures use low Cl airfoils, you can see it just looking at blade ,very little camber, almost symetrical airfoils $\endgroup$– user207141Jan 6, 2022 at 9:45
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$\begingroup$ Did you follow up on the answers you were given here: engineering.stackexchange.com/q/48998/10902 ? $\endgroup$– Solar MikeJan 6, 2022 at 10:14
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$\begingroup$ could the situation driving this design decision be the high-wind scenario? $\endgroup$– Pete WJan 6, 2022 at 19:01
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$\begingroup$ In light air, the best coefficient of performance might come with Cl of 0.5. When there is decent wind, you might be running down around 0.1 to 0.2. So you don't need it. For torque-governed systems like pumping water for livestock, you don't care about efficiency, just that you are pumping something, and very high torque, low efficiency designs using a lot of blades are common - like the Star Wheel type. $\endgroup$– Phil SweetJan 6, 2022 at 21:11
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3 Answers
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I've finally got a few minutes to try to answer this.
Torque is bad. It's necessary, but it is bad. Ideally, you want the turbine to spin infinitely fast at almost zero torque, not slowly at high torque.
To understand why, lets look at how energy is extracted from the air and transferred to the rotor. If we take an earth reference frame aligned to the free stream air, and have a rotor plane that is perpendicular to that freestream, then the freestream has a velocity components of u=wind speed, v=0, w=0. Downstream of the rotor, we have u=ud, v=vd, w=wd. sqrt(vd^2 +wd^2) is the wake swirl velocity in the rotor plane. Wind speed - ud is the change in axial velocity of the flow.
The transition between the freestream conditions and the wake conditions happens gradually. The swirl acceleration and axial flow deceleration begin well upstream of the rotor and continue well downstream of the rotor. It turns out to be rigorously true that the conditions at the rotor are halfway between the freestream and the fully developed wake. We adjust the freestream flow to the conditions at the rotor with an axial induction factor and a swirl induction factor. Both vary across the radius of the rotor. Then we account for the blade motion to compute the actual angle of incidence of the wind to the spinning blade in the rotor plane.
So now we have a new reference frame in which the blade element is fixed, and the speed and angle of the incident air is correctly accounted for. Since the blade element is fixed in this reference frame, the air does no work, and energy and momentum are conserved as the flow develops from freestream to fully developed wake. This is only true in this blade element frame of reference.
To get maximum power out, we need to maximize the product of mass flow through the rotor times the energy change per unit mass of air. As the axial velocity slows down, the air stream has to get fatter to preserve mass continuity, so air goes around the rotor instead of through it and mass flow is reduced. If you don't slow the air down, all the air goes through the rotor, but you don't get any energy out of it, so power is zero. If you slow the air way down, the energy extraction per unit mass is high, but the mass flow is very small, so power is very low. You need to create a modest axial velocity change which permits a high mass flow rate to get best performance.
So what has this to do with torque? Driving torque creates an equal and opposite reaction in the wake - wake swirl. All the swirl energy in the wake is energy that is being robbed from the rotor. The only way the wake can gain swirl velocity is at the expense of axial velocity (conservation of energy). So swirl causes a lower downstream axial velocity, and that lowers the mass flow rate through the rotor. This is the hard part, that the force from the fixed rotor causes a swirl momentum, but when you apply conservation of energy, the axial velocity has to slow down to keep the system energy balanced. This is not at all intuitive, because there doesn't appear to be any force slowing the air axially. But there is a force, and it is called induced drag.
So at this point, there is an ideal wake shape that can be computed. It has some swirl and some radial expansion at the rotor plane, and the axial flow is somewhat slower than free stream. But the shape, ie the relative size of the induction factors, is the same for all HAWTs under ideal conditions. And when you design a blade set to produce this ideal wake (called inverse design) and account for friction and structural mechanics, you don't want a high Cl blade. You want high rpm (high tip speed ratio), low blade count, low solidity, and low torque.
This entire argument is usually handled a bit differently from a mathematical standpoint because the relationship between axial velocity and swirl velocity can be gotten at in different ways. But wake swirl lowers the mass flow through the rotor and lowers the available energy per unit mass as well. So you want to make it small. And wake swirl is torque.
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One reason I can think of is Because increasing the $c_L $ increases also significantly the coefficient of drag.
The increase of drag is a result of increasing flow detachment from the airfoil.
Supplement
After reading PeteW comment
could the situation driving this design decision be the high-wind scenario?
I realised that I was only thinking about fixed blade wind turbines, which are usually small wind turbines (just a few kW at best).
Most commercial windturbines (around or above 1MW) adjust many times per second the pitch of the blades. And the pitch of the blade controls the angle of attack. And the angle of attack controls the $C_L$ and the $C_D$.
Figure: Gliding ratio (Cl/Cd) distribution of the airfoil at the root, middle, and tip parts of the blades (source Youjin Kim)
What the above image shows is that $C_L$ is proportional to $C_D$ and the ratio is near unity for a very small region (beyond that the drag overwhelms the lift).
FIGURE: optimal values for $C_L$ and $C_D$ (source wikipedia)
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$\begingroup$ Also, the moment could become a structural problem. $\endgroup$– DKNguyenJan 6, 2022 at 19:56
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The wind turbines are designed to work under a wide range of wind velocities.
They adjust their angle of attack and $ C_l$ to the optimal for the existing condition.
They use high $C_l$ for when the wind starts to pick up speed and the blades need to use a high torque to accelerate and position themselves at a rotation speed that provides the design angle of attack with relative wind angle which is not at all the wind angle with respect to the horizon. (more on this later)
They reduce the angle of attack and $C_l$ later to keep the best position to extract the kinetic energy of the wind.
They bring the lift to zero in very high wind to protect the turbine from destruction.
Relative angle of attack:
Relative wind angle is the resultant vector sum of wind velocity and the speed of the airfoil perpendicular to the wind, for example, if the wind velocity is horizontal 20ms and the airfoil at point $X$ is rotating, ascending, with a velocity pointing up with 3.5ms, the relative wind angle is 10 degrees. And if the airfoil has a chord angle of 8 degrees the angle of attack of the airfoil will be $8+10=18, \ $ and the turbine will stall. It is, for this reason, the wind turbine blades are twisted because the angle of attack changes relative to the position of $X$.
I will add a sketch later.
