# Energy and work of wind turbine

1. Sep 12, 2014

### R.G

Hi guys

something basic that I cant understand:

if I have a wind turbine , rotating due to some wind with no load , and no mechanical or drag losses in the blades or in the mechanics (no drag at all, I know its impposible ,but still) , the forces on the blades, create a Moment that accelarate the blades ( J*w_dot = M) , with no load or friction ,as I understand it the blades will accelarate to infinite angular velocity(as there is nothing stopping them) -STATEMENT 1

Here is my understanding problem , The rotor can take only P power from the wind , but P should be equall to w*M (angular velocity of the turbine multiplied by Moment) , but if the turbine have infinite w ,the Torque M=P/w should be very small, close to zero , so the wind turbine cant accelarate .but that is oppoitve from my first statement!

where I gone wrong?

Last edited by a moderator: Sep 12, 2014
2. Sep 12, 2014

### Staff: Mentor

You cannot have lift without drag. Those two things balance out in a free-spinning rotor, to determine the rotational speed of the rotor versus the wind speed.

3. Sep 12, 2014

### duri

I hope you are not looking into the aerodynamics of wind turbine. Though this is not practical, you can at least model this using potential equations. Your statement 1 says blade will accelerate to infinite angular velocity this is wrong. Applied torque will give change in angular velocity based on the moment of inertia of the blade. This doesn't mean that it will accelerate to infinity. Angular velocity will attain new finite value. Also, angle of attack will increase with angular velocity which leads to negative effect. In case if you assume pitch of the blade changes with velocity and no structural effects then ideally rpm can go very high.
In second statement as you said when w is infinity, then T is zero. But infinityXzero has indefinite value. This kind of argument doesn't hold. Power is not the cause, it is the effect and it is normalized for one second. Torque is the cause of rotation and it keep on increase the angular velocity based on moment of inertia. Then if torque is applied for one second continuously and angular velocity goes infinity means either torque is infinite or moment of inertia is zero. This clarifies your second question. In your case moment of inertia is zero.

4. Sep 12, 2014

### AlephZero

The amount of lift (i.e. torque) and drag force on the blade depends on the angle of the airflow between the wind and the blades. If the blades have a fixed pitch, the torque force (i.e. the lift) decreases as the RPM increases, until you get to the speed where the air flows "straight through" the blades and produces very little lift or drag. If the turbine was spinning faster than that, it would not be a turbine but a fan, putting energy into the air not taking it out.

With variable pitch blades you can make the turbine work more efficiently over a range of speeds, but the basic idea still applies.

5. Sep 13, 2014

### R.G

All the answers here, talked about the decreasing efficiency of the blades to get power from the wind due to aerodynamics issues(angle of attack), and that the solution to that problem can be pitch control of the blades.

So if I take a Wind Turbine with no load, and check the applied Forces and Torque in time t1,t2 , t2>t1
In [t1, w1(angular velocity of the blades), aplha1*(angle of attack) ] , The forces acting on the blades are F1, so the torque is Q1(just by blade geometry and forces distribution)

In t2, I change the blades pitch to get the same Forces on the blade as in t1,so the torque is also the same Q2=Q1 ,I thing that the angle of attack is not the same to get equality in Forces as the united velocity(wind+rotor velocity) that the blade sees in not the same

The power I extracted in t1 is: P1=w1*Q1 and in t2 is : P2=w2*Q2 , as w2>w1 and Q2=Q1 -> P2>P1
So with the same wind , I got more power from the wind , just because the blade rotates faster. Angle of attack is not an issue here , as I changed the rotor pitch , but these scenario is impossible as I get more and more power extracted from the wind !
That’s why I said previously that the rotor will rotate faster and faster to infinity, extracting more and more power from the wind.
something basic in my understanding is wrong…

6. Sep 15, 2014

### duri

You are always looking at one side of the equilibrium. Power on the shaft is torque*angular velocity but power from wind is function of change in swirl. When angular velocity increases with same free stream condition difference in swirl will decrease and torque would linear goes to zero. This will in turn reduce angular acceleration and eventually attains equilibrium.

7. Sep 20, 2014

### R.G

duri
Please tell me if I got it right , you say that even if I use pitch control , to get the same angle of attack on the blades(to get the same forces, and the same moment) in diffrent rotation velocity , I will get less torque from the wind due to decreasing change in swirl?