Blade Displacement Response and Aerodynamic Damping

[peterfakhry]

Hello there, so i have been stuck for months trying to figure out why there is a bias between my produced numerical model and FAST regarding blade response (i get perfect agreement between the curves when i manually add a 0.35m in the in plan and 0.5m in the out of plan responses for all the three blades). As you can see that the FAST response never goes to the negative side (does that mean wind loading is much higher than gravity effect?). Also i have noticed an important thing, the response frequency content is sensitive to aerodynamic damping in my model. How is aerodynamic damping is implemented in FAST?.

[jjonkman]

Dear @peterfakhry,

Presumably the "Numerical" result is from your own custom solver; can you clarify?

From the plots you show, I would guess that the aerodynamic loads are higher in FAST than in your solver. I would suggest =first comparing the models in the absence of blade flexibility. How do the models compare for rigid blades?

Aerodynamic damping is not written as a distinct term in FAST / OpenFAST. Instead, the aerodynamic loads are computed based on the relative velocity between the wind and the blade aerodynamic nodes, including elastic velocity. So, aerodynamic damping is intrinsic to the aero-elastic coupling.

Best regards,

[peterfakhry]

I turned off all the degrees of freedom regarding the FAST and multiplied my stiffness in my numerical model by 1000. As expected Professor, all results are zeros however i got again negative values in my model.

[jjonkman]

Now that the deflections are zero (or near zero in your case), how do the applied aerodynamic loads compare?

[peterfakhry]

Thanks a lot for your efforts Professor and sorry for late reply. I get my aerodynamic loads from BEM equations in terms of normal (out of plan) and tangential (in plan) using the following formulas (Hansen 2015):

Finally i multiply the PN by the flapmode shape (expressed in terms of x along the blade length) and the PT by the edgewise modeshape and integrate along from 0 to Lb to get a modal load as (where phi as the respective modeshape):

As for the tower, i get the resultant of the three blades (tangential) in the edgewise direction and multiply by the respective cosine azimuth angle as

For the fore-aft direction , i get the resultant of the three blades (normal) as

Is that compare to "RootFxb1" and RootFyb1" in FAST and how to run AeroDyn to compute the aerodynamic loads.

[jjonkman]

Your equations sound reasonable for a case without precone, tilt, deflection, etc, but there are many details in any BEM formulation.

ElastoDyn outputs RootFxb1 and RootFyb1 are reaction loads that include not only the applied aerodynamic loads, but also the weight/inertia of the blade. I would suggest comparing your pure aerodynamic loads, e.g. p_N(x) and p_T(x) in your nomenclature, against the equivalent loads computed and output by AeroDyn (e.g., BαNβFx and BαNβFy for output node Nβ of blade Bα).

Best regards,

[peterfakhry]

Thanks a lot Professor for your reply i really appreciate your help.
I have followed the steps in AeroDyn manual to run it in a standalone mode. Also have adjusted the .dvr and .dat files to match my case and got the following results

I can see that they are not changing over time since the wind speed was set to 12m/sec with shear exp 0 and have adjusted the turbine dimensions to match my case. According to my knowledge the all the Fx corresponds to the out of plan forces and the Fy correspond to the in plan froces. Now i have assumed that the 9 nodes are equally spaced along a 61.5m blade (which is not the case as seen in Figure 3. in the AeroDyn manual) and have generated a polynomial to the 4th degree between the distance along the blade and the aerodynamic load. For each time step multiply the later value by the corresponding modeshape and integrate from 0 to Lb as in

Below are the load values of my numerical model and the AeroDyn. There is some sort of matching in the in plan loads however out of plan loads are far away.

• Why there are just 9 nodes although there are 17 specified in the ElastoDyn of FAST?
• What is the appropriate spacing between these nodes as this will help much in generating the polynomial expression?

[ebranlard]

Hi @peterfakhry

Are you comparing the integrated loads at the blade root in the figure you enclosed?

As Jason recommended, I agree that you might have to match the aerodynamic loads first, and it will help to plot Fx and Fy as function of the blade radius r for OpenFAST and your code.

Regarding your questions about radial locations:

• AeroDyn and ElastoDyn use different number of nodes and node locations for the user convenience, and there is no limit on the number of nodes you can use. OpenFAST takes care of "mapping" the loads and motions between the mesh of AeroDyn and ElastoDyn.
• ElastoDyn will always have equidistant node locations, based on the parameter (BldNodes). You can find the formula for the nodes here. ElastoDyn uses a mid-point rule when performing integrals, so you'll find differences with your method if you use trapezoidal integration and different node locations. You might need at least 100 nodes before the differences between the two approaches (mid-point or trapezoidal) is negligible. Most users use few radial stations for ElastoDyn, but I would personally recommend 40 or more to ensure "convergence" of the integrals. This will increase the computational time though.
• AeroDyn nodes do not need to be equidistant. Some people choose a cosine distribution to have more "resolution" towards the tip and root, where the load gradients are usually largest. I would nevertheless recommend to use an equidistant spacing with about 40-50 nodes. For your debugging, you can use fewer stations of course.
• The "old nodal outputs" of AeroDyn and ElastoDyn are limited to 9 radial locations which are selected amongst the set of radial locations of each module. We have now introduced "new nodal outputs" at the end of the input files to output quantities at all the radial locations of the module. See here for AeroDyn. You can use these outputs to compare the radial loads obtained between your BEM code and AeroDyn.

Here's some additional recommendations for the aerodynamics:

• Simplify your blade: no prebend, presweep, precone (this will simplify the aerodynamics, and the structure. With prebend/cone etc, OpenFAST might use a different coordinate system than you do for your aerodynamic calculation)
• Compare without inductions first (WakeMod=0, a=0, a'=0). The angle of attack is then the geometrical angle of attack and it should match exactly. Then if the angle of attack match, the Cl, Cd, Cm should also match exactly.
• Introduce inductions (WakeMod=1), and compare a and a', then Fx and Fy.

Looking at the elasticity, some other sources of differences might arise, here are some additional considerations:

• As I mentioned above, the nodal locations, and the integration method will affect your integrals.
• ElastoDyn uses "twisted" shape functions, where the structural twist is used to combine the flap and edge shape functions. You might need to remove the structural twist in the ElastoDyn file at first when comparing with your method. This can be a large source of differences.
• Also remove precone, prebend, presweep from the blade file at first, as this might be handled differently in your code and ElastoDyn.
• ElastoDyn includes non-linear geometrical stiffening corrections that are likely not included in your model.
• You can try to match your structural model with ElastoDyn by running OpenFAST simulations without AeroDyn, using some initial values of the in-plane and out-of-plane deflections, with or without rotation.

I hope that helps,

Emmanuel

[peterfakhry]

Thanks a lot for your help. I really appreciate your and Professor Jonkman efforts