I'm writing a Wind Generators FE model in Matlab. I'm implementing the BEM model you suggest in the AaeroDyn Theory Manual. I use the Tip-Loss Model, the Hub-Loss Model and the Buhl Correction for evaluate the axial induction factor (a) when CT (thrust coefficient) >0.96*F. I don't consider the Dynamic Stall Model and the Skewed Wake Correction (I assume the wind flow always perpendicular to the rotor plane).
In the iterative process to evaluate the axial induction factor (a) and the tangential induction factor (a'), i encounter these problems:
1) Often when the local angle of attack (α) is negative, CT results negative and for the relation  page 10 of the AeroDyn theory Manual, the axial induction factor (a) results >1 and the local flow angle (ϕ) results negative. So the Tip-Loss Factor and the Hub-Loss Factor results complex number! I have to evaluate the Tip-Loss Factor and the Hub-Loss Factor assuming the absolute value of the local flow angle, i.e. |ϕ| ?
Furthermore, the pressure normal to the rotor plane acting on this blade portion results of opposite direction respect to the wind flow, is physically correct ?
2) Sometimes, the iterative process doesn't converge to calculate the axial induction factor (a) ? So i force the convergence. Have you ever encounter this event ? How can i do ? Which could be the reason ?
3) If the wind flow i considered stochastic, do you assume U∞ (= mean wind speed) + the fluctuating contribution of the wind speed for the calculation of the axial induction factor ? In your relations doesn't appear the fluctuating part of the wind speed, why ?
I really thank you for your support, best regards
I moved your topic to the Rotor Aerodynamics section because it really has nothing to do with testing. One of our interns (Dave Maniaci of Penn State) wrote a paper on convergence issues for WT_Perf. You should read it:
Dear Marshall Buhl,
I have read the paper you suggest to me; and I have insert in my Matlab program the sine curve singularity transition model but still it doesn’t converge? The problem is with low wind speed. If i have correctly understood with that modification now the your program converge always ?
Is it necessary to write your new iterative process with a two-dimensional Newton-Raphson iteration routine, iterating on both a and a‟ rather than separating them into two separate iteration loops ?
Does AeroDyn use the BEM model routine that is implemented in WT_Perf ?
In Full-Field wind condition, when you calculate the axial induction factor (a) and the tangential induction factor (a’) do you use the local wind velocity in the current element (U_local = U_mean + U_fluctuating in the current blade element) ?
In reference to the AeroDyn Theory Manual formules (from page 4 to page 10), I don’t understand exactly if in the term U∞ (= mean wind speed) AeroDyn considers also the fluctating component of the wind ?
Doesn’t AeroDyn calculate a and a’ factors also in function of the local fluctuating speed acting on the current blade element (U_fluctuating) ? Is the induced speed function only of the U_mean of the wind ?
And, in upwind rotor condition, do you add to Ulocal the term - Utower_shadow_effect ((Ulocal = Umean + Ufluctuating - Utower_shadow_effect in the current blade element) ?
a and a’ in AeroDyn are function of the wind speed U∞ = Umean + Ufluctuating - Utower_shadow_effect in the current blade element ?
I really thank you for your fundamental help, best regards
First, there is not always a solution to the full BEM equations. If you can’t get it to converge, eliminate the tangential induction.
You can iterate a and a’ separately, but it will probably take longer to converge.
The AeroDyn implementation of BEM is slightly different and it incorrectly applies the tip loss factor to the tangential induction.
I don’t know the answers to the rest of the questions, and, sadly, do not have time to investigate. Sorry. If I did, I would review the AeroDyn theory manual and also read the code, which is included in the archive.