Hello, everyone,

I encountered a problem, could you please help me check it?

For a three-bladed wind turbine (FAST 1.5MW, Test13) when I increase the density of blade 1 a little bit, the three blades are imbalanced. When I use a constant pitch angle for the three blades, I thought the blade root bending moments for blade 2 and 3 would be the same only with a time delay. But the simulation results showed that the amplitude of blade 3 is a little higher than that of blade 2. I don’t why. Is there anything wrong?

BTW, the generator torque and power are also constant.

Looking forward to your reply. Thanks a lot.

Best regards,

Yunqian Zhang

Sorry, the wind speed is constant (18m/s).

Dear Yunqian,

I agree that if the rotor is balanced (including mass, twist, pitch, stiffness, etc.) then the amplitudes of the loads should be the same if the rotor is operating in constant uniform wind. Can you explain a bit more what you are simulating and how much imbalance you are seeing? Does the imbalance continue after all start-up transients have died out (after the solution becomes periodic due to gravity, shaft tilt, shear, yaw error, etc.)?

Best regards,

Dear Jason,

Sorry for the late feedback. The inputs of the FAST block are all constant, e.g. genetator torque 8.7127e3, power 1.5e6, yaw position and rate 0, blade pitch angel 0.3344.

The waveform is as follows:

Maybe the difference can be negligible.

What I want to do is that under imbalanced condition, using individual pitch control to control the three blade root bending moments constant and equal to each other, so that the tilt and yaw moments can be reduced. The simulation results show that the three blade root bending moments are the same but not constant, they still fluctuate with frequency Ip.

So I used the constant inputs applied to FAST and found this problem.

Thanks again.

Best regards,

Yunqian Zhang

Dear Yunqian,

If I understand what you are asking is why do the blade-root bending moments of blades 2 and 3 differ in Test13 when you make blade 1 heavier, disable control, and simulate in uniform wind. Is that correct?

My guess is that the rotor imbalance you’ve created is leading to a 1P response throughout the system (including the tower) and this response couples with blade 2 sligthly differently than blade 3 based on their azimuth angle. I suspect that if you disable all structural DOFs except for the blade-bending DOFs, that you would see identical response between blades 2 and 3 (time-shifted by 120 degrees).

I hope that helps.

Best regards,

Dear Jason,

Thanks for your reply. I disabled the DOFs, as you said, the bending moments of blade 2 and 3 are identical.

Thanks again!

Best regards,

Yunqian Zhang

Hi Jason, I am applying mass(by plugging the blade file in ElastoDyn) and pitch imbalance(by plugging the blade file in AeroDyn) in the 5MW test. I have the following questions:

- I want to see the impact of Imbalances on various output channels. Can I get the equations to see the impact e.g how can I solve for TipALxb1 if blade 1 is subjected to mass imbalance? Can the code ElastoDyn.f90 help me in finding a specific relation for that?

m%AllOuts( TipALxb(K) ) = DOT_PRODUCT( LinAccES(:,p%TipNode,K), m%CoordSys%n1(K,p%BldNodes, )

(line 755)
- What if I apply both imbalances i.e aerodynamic and mass imbalances, that means both AeroDyn and ElastoDyn would involve in the calculating output. How do we model both imbalances?

warm regards

Dear @Ahmed.Hassan,

I’m not exactly sure I understand your question, but the equations of motion of ElastoDyn do support mass imbalances and the theoretical basis of AeroDyn does support pitch imbalances.

The ElastoDyn equations of motion are documented here: 4.2.7. ElastoDyn Users Guide and Theory Manual — OpenFAST v3.2.0 documentation, but I can’t point to a specific equation that summarizes the effect of mass imbalance. Naturally, imbalances in the rotor would result in once-per rev (1P) oscillations (and sometimes higher harmonics, 2P, etc.) in the fixed frame of reference.

The equation you reference from *ElastoDyn.f90* simply expresses the absolute acceleration (`LinAccES`

) in a local coordinate system (`n1`

).

Best regards,

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Dear Jason,

Thank you for answering my question. Since I am not a structural engineer, so there are limitations in my understanding. I will try to rephrase my question for a better understanding.

- I have gone through the ElastoDyn documentation(a word file for Loads and motions). To calculate TipALxb1, there is a multitude of equations that need to be solved/calculated in different frames of reference. This is regardless of whether the imbalance is applied or not. I have attached the slide in which those equations are compiled.

Is my understanding correct?

basically, I want a relation as to how TipALxb1 (or other variables) is calculated in FAST so I can model and simulate variables of our interest?

warm regards,

Ahmed

Dear @Ahmed.Hassan,

I agree with chain of equations you compiled. These show the progression of translation and rotational velocities from the platform to the hub. But the acceleration of the blade tips will depend on many more equations than these, i.e., the full equations of motion of the wind turbine.

Best regards,

1 Like