# Blade-Element/Momentum Theory and Implementation

Hello all,

Did anyone try to consider blade velocity in BEMT implementation by using equation (2) in “AeroDyn Theory Manual”? I always get convergence problem if I use equation (2) for BEMT implementation. If I use equation (1) in “AeroDyn Theory Manual”, it works well. I think blade velocity is important for wind turbine aeroelastic analysis and it should be included in inflow angle calculation. If anyone have met this problem, can you explain to me how you solved it? Thanks.

Best regards
Dayuan Ju

Dear Dayuan,

AeroDyn v12-v14 does use Eq. (2) without problems. In AeroDyn v15, the induction is also applied to the structural motion v_e-op and v_e-ip, also without problems.

Best regards,

First of all I would like to thank you for being part of this community. Congratulations to the Team for the work, helping students and professionals in the field.

I am a master’s student and I am studying the control of structural vibrations in wind turbines. I’m building a wind turbine model and I use Fast to validate it. But despite all my effort in developing the model it still responds very differently from Fast and to solve this error I need the help of experts in implementing the BEM method.

The same conditions were used to simulate the displacement of the structure in my model and Fast. I used NREL’s 5MW reference turbine. The wind was simulated in steady conditions varying exponentially with height with a wind speed of 12m/s in hub height. The BEM method with steady airfoil aerodynamics model was used in the simulation. The structural movement was added the equations of the BEM method, to include aerodynamic damping.

I checked the inflow angle and other parameters of the BEM method, I noticed a significant difference in the values ​​between the model and the Fast, but I can not identify what caused this difference in the displacement in the plane of rotation. The amplitude of the gravitational force is greater than the amplitude of the aerodynamic force, making the total force contrary to the rotation. How do I correct this?

I am attaching pictures to illustrate the difference between the answers.

I am very grateful for your help in this implementation.

Best Regards
Guilherme Terceiro

Dear Guilherme,

I’m sorry, but I’m not sure I understand what your question is enough to answer it. Also, the images you uploaded are a bit too coarse to interpret e.g. I’m not sure which curve is FAST and which is your model. Please clarify your question.

Best regards,

Dear Jason,

I’m sorry for the confusing question. First of all by clarifying the image, the FAST response is in blue, while the response taken from the model is black. Second, in the image it can be seen that the out-of-plane displacement are very close in both simulations (Fast and Model), but the in-plane displacement is very different.
For example, the tip blade in-plane displacement on FAST oscillates around -0.5 whereas in the model the mean is zero. And in the tower, the model’s displacement is very small compared to the FAST’s displacement.
My question is wider and I’m sorry for that, but I checked the model and I did not find something that would make that difference. I would like to know, with your experience, what could cause this difference only in displacement in the plane?

Thank you for your patience and cooperation.

Best Regards
Guilherme Terceiro

Dear Guilherme,

Does your model account for structural pretwist, as FAST does? As discussed in the following forum topic: http://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/1, because the blade flapwise stiffness is typically quite a bit less than the edgwise stiffness, the influence of the edgwise bending on the flapwise tip deflection (due to pretwist) will be much less than the influence of flapwise bending on the edgewise tip deflection. Perhaps this is why the results between FAST and your model match for out-of-plane deflection, but not for in-plane deflection.

Best regards,

Dear Jason,

Yes, my model account for structural pretwist. But after reading the topic you recommended, I do not know if I’m doing it right.
In the model I used the second area product of inertia obtained through the principal second area moments to take into account the coupling. I used the mode shape of the first edgewise mode as in-plane mode shape and the first flapwise mode as out-of-plane mode shape.
Can this big difference in results be due to these considerations? The equations that I used are attached.

Again, thank you very much for the help.

Best Regards
Guilherme Terceiro

Dear Guilherme,

Your approach for accounting for the structural pretwist is definitely different than the approach used within FAST. Without going into the details, your approach seems to be missing the influence of the twist on the beam curvatures. Many years ago back in graduate school, I wrote a paper about finite elements of pretwisted beams; please find this paper attached and compare equation (21) to your formulation of the strain energy of the beam. Hopefully a review of this paper will help you resolve the problem.

Best regards,
PretwistedBeamReport.pdf (391 KB)

Dear Jason,

Thank you very much for the answer and for the article. Your article explained me a lot about pretwist beam and made me find the axis orientation error in my model.
I checked the equation (21) of your article and noticed that it is in the local coordinate. When I transformed the whole equation to the global coordinate, it equals the equation I used (in my last post). The term that adds the influence of the twist on the beam is the second area product of inertia, it was exactly in that term where the error was. So you hit it right when you said that my model was not represented the coupling correctly. Many thanks for your guidance.

Now the only difference between my response and the FAST response is in the tower displacement in the plane of rotation. I am attaching an image with the answers. In the following forum topic (Why do tower top side-to-side deflections have non-zero average? - #4 by Jason.Jonkman) you comment on the application of torque at the top of the tower. I think that this error in the response occurs by the lack of the addition of this torque on the top of the tower. I did not add the rotor torque on my model, I just considered the forces. Am I right in suspecting the lack of torque at the top of the tower? How does FAST add that torque to the tower, considering only the following DOFs (FlapDOF1; EdgeDOF1; TwFADOF1; TwSSDOF1)?

Again, thank you for the great collaboration.

Best Regards
Guilherme Terceiro

Dear Guilherme,

Yes, I would assume that the absence of torque in your model is the cause of this difference.

The tower DOFs are related to bending, so, a bending moment (induced by rotor torque) is natural to induce bending of the tower. Regardless, FAST considers all loads (both forces and moments) in its equations of motion.

Best regards,

Dear Jason,

Forgive me for the stupid mistakes. I added the momentum induced by the rotor at the top of the tower. As we suspected, the model response approached the FAST response, but has a slightly higher frequency. What would cause this behavior (attached image)? I have already added aerodynamic and structural damping and the influence of gravity on the stiffness.

Thank you for your help.

Best Regards
Guilherme Terceiro

Dear Guilherme,

The higher frequency in your model would imply a higher stiffness or lower mass in your model.

Best regards,

Dear Guilherme,

Could you explain a bit more what was the error in the product moment of inertia? Are the equations in the above post (Fri Nov 18, 2016 6:00 pm) correct to obtain the product inertia (in/out of plane)?

Best regards,
Koen

Dear all,

Regarding to know Cp, Ct, power and thrust load in each element of the airfoil, thought I set “Print” (PrnElm) in AeroDyn input file, the fast does not make element.plt file, I was wondering to know what would be the probable solution or is there any other way to know lift, drag, extracted power for each blade element in FAST.

Thank you for your time.

regards;
Saeedeh

Dear Saeedeh,

Which version of FAST and AeroDyn are you using?

Best regards,

Dear Jason

As I’m working on small wind turbine I need tailfin motion, I am using FAST version 7 (v7.02.00) and I think my AeroDyn version is 12.50.

Best Regards;
Saeedeh

Dear Saeedeh,

In FAST v7.02, if you used enabled “PRINT” for one or more aerodynamic elements in AeroDyn, then you should get an output file with a *.elm extension that contains the AeroDyn output. Do you get that file?

Best regards,

Dear Jason

Thank you for your prompt help, according to ‘FAST User’s Guide’ I was looking for element.plt but now I find " *-elm" as an output file.

Best regards;
Saeedeh

Dear All,

I’m Gabriel a PhD student from Edinburgh and I’m investigating the effects of unsteady hydrodynamics on tidal turbine blades.

I have implemented the BEMT model used in Aerodyn v15, exactly as described by Ning et al. 2015, AIAA, (nrel.gov/docs/fy15osti/63217.pdf). I have attempted to validate my implementation with CP and CT values generated using AeroDyn v15. It is a simple steady-state case, the blade comprises of constant thickness NREL S814 profiles, zero yaw, zero pitch, default AeroDyn settings.

For CP agreement is good for tip-speed ratios (TSR) up to about 5. However, above this, my implementation is underpredicting as shown in the attached figure. For CT agreement is worse, I am overpredicting from 3.5 - 9, then underpredicting. I encounter negative CL and CD values above TSR = 8 due to high flow angles. I wonder if anyone has any insight into where I am going wrong? I have read the AeroDyn change log and believe my implementation in terms of theory and convergence method is the same. I suspect it is a case of numerical implementation.

Dear Gabriel,

Ning et al’s AIAA SciTech 2015 paper formed a solid basis for the implementation of BEMT within AeroDyn v15; however, there were several modifications (especially in newer versions of AeroDyn v15) that were made to ensure the robustness of the implementation within the aero-elastic solution of FAST. Unfortunately, we have not had the time/funding to publish an update to the BEMT algorithm. It is difficult for me to guess what specifically would lead to differences between your and AeroDyn’s solutions.

I would suggest simplifying the model as mush as possible (e.g. fewer analysis nodes, no skewed flow, steady inflow) and looking at the details of the solution (e.g. calculated values of the inflow angle, inductions, and lift and drag coefficients) to identify the sources of the differences. You could also look at the AeroDyn source code to see how the BEMT has actually been implemented within AeroDyn v15.

Best regards,