Edgewise Bending Moment, Unidentified Vibration

Dear all,

I have been running some simulations using FAST, I think that I understand most of the results I’m getting expect one details concerning the Edgewise bending moment. Blades have a small structural damping however the Flapwise tip velocity rapidly decreases towards the response to a sinusoidal forcing. I believe this is due to the aerodynamic damping obtained when adding the blades velocity for the calculations of the angle of attack?

On the other hand, the results obtained for edgewise bending moment suggest a strong correlation with the 1st natural edgewise Frequency. I believe there is an aerodynamic damping due to edgewise blade displacement but I’m expecting this to be much smaller. Could it be due to another force resulting from the edgewise displacement?

5MW Offshore wind turbine
Wind files - wind shear only
Blade files - by default (0.47% for structural damping ratio)
All structural DOF Off - except Edgewise and Flapwise ON.

I have read other posts about inertial loadings so I investigated different possibilities but I can’t be sure. The rotor plane is fixed hence there are no gyroscopic load. The only load that seems logical to me would be the centrifugal one, but for slowly rotating large wind turbine I didn’t expect such a large influence. Or could it simply be that in addition to the external forces, the local blade acceleration is used to calculate the local force and then used for bending calculations ?

Thanks for your help,

Dear Terence,

The blade loads output by FAST are not the applied aerodynamic loads, but the reaction loads within the blade (the reaction loads include contributions from aerodynamics, gravity, inertia, etc.). For edgewise bending, the aerodynamic damping is typically quite low; the gravity load also plays an important roll.

I hope that helps.

Best regards,

Dear Jason,

Thanks for your help. I have modified my code to obtain the reaction loads that matches pretty well with fast’s results, however it seems I have some trouble with the centrifugal loading. When I compare my code with fast I find quite a big difference.

For extended test I removed Gravity and Aerodynamic forces moreover Flap-wise and Edge-wise blade motion are the only DOF turned on. By doing so I assumed that the centrifugal force should be the dominant external load on the blade.

the centrifugal force at radial location x is calculated by:
Fcentri(x) = integral of [ omega^2* LinearDensity * x]dx

The Out Of Plane force due to centrifugal loading ( neglecting the blade deflection angle) is calculated by:
Fcentri_OOp(x) =Fcentri(x) * sin (coneangle)

I have read in the Fast theory ( your master thesis) that the blade deflection angle was not included into the calculation of the Oop centrifugal Force. Is it still correct or did you modify this?
By doing so, while pitch=0, I obtain a steady state (not mentioning inertial load) Out Of Plane Deflection of 2 meters at the blade tip, whereas the results given by fast only predict a steady state deflection of 0.3meter.

I even tried to add the blade deflection angle, to reduce the blade displacement, in the calculation of the force:
Fcentri_OOp(x) =Fcentri(x) * sin (coneangle - blade_deflection_angle)

The new results predicted where half of the previous one, so 1 meter deflection at tip, still quite different from fast’s results. Am I making a mistake in my calculations or neglecting something I shouldn’t?

In addition, when exiting the blades by centrifugal forces only I sometimes observed divergence in the blade flapwise vibrations, It however converges if I increase the structural damping.

Thanks for your time.

Dear Terence,

FAST does include the out-of-plane (and edgewise) deflection into account in its calculation of centrifigul forces. The statement from my M.S. thesis is incorrect. (I wrote it too long ago to know why that was written; it is likely the assumption in Modes, but not FAST.)

What is critical in the centrifugal stiffening calculation is that you include the “shorterning” term (that is, the blade tip must get closer to the shaft as the blade deflects out-of-plane). Are you including this “shortening” term in your code? Are you also including the bending moment brought about by crossing the blade deflection with the centrifugal force? FAST includes both of these terms.

Best regards,

Dear Jason,

Thanks for your reply. I managed to take the stiffening into account but I found something else that I cannot explain.

At low mean wind speeds the edgewise vibration of the blade tip displacement is as I expect but there is no (not even one) vibration present in the edgewise root bending moment due to the blade natural frequencies. It’s a perfectly smooth sinusoidal of period equal to the blade rotation. The results I obtain are very similar, that is an edgewise moment driven by gravitational forces at low wind speed but with the addition of natural frequency vibrations.

However if I add an initial edgewise tip displacement, the vibrations appear as expected. Should I concluded that by some ‘kind of process’ the edgewise forces acting on the blade at low wind speed are not exciting the blade natural frequencies? This would be very unlikely no?

Thank you for your time.

Dear Terence,

I would look at the spectrum of the edgewise tip displacement (or edgwise bending moment) to see if the edgewise mode is being excited.

At low wind speeds, the gravity term may very well dominate over any aerodynamically induced edgewise vibrations.

Best regards,

Dear Jason,

Thanks for your reply. I have managed to found the problem. It seems that ‘only’ for the blade that starts at 0 azimuth angle at low wind speed, the external forces don’t excite the blade edgewise natural frequencies. This is quite unexpected to me. My Finite Element Model however doesn’t agree for that particular case.

Thanks again.