# BEM convergence problem

Hello everyone,

I have built my own rotor/blade model and I am trying to see how the transient response of rotor speed will be when rotor speed starts from 0. My rotor/blade model contains both dynamic and aerodynamic model. I use BEMT to build my aerodynamic model. If I set rotor speed to 0 as initial condition (tip speed ratio 0), then as the BEM iteration procedure goes, the inflow angle switches between pi/2 and –pi/2 and never converges to a reasonable value. It looks that tip speed ratio has to be a reasonable value in steady BEM theory. Low tip speed ratio or high tip speed ratio all cause problems. How can we deal with the situation when tip speed ratio is too high or too low? How does FAST deal with the situation when rotor speed is 0? I have done the simulation when rotor speed is 0 in FAST and FAST works well. Also, FAST can deal with the situation when tip speed ratio is large.

Kindly regards
Dayuan Ju

Dear Dayuan Ju,

The BEM algorithm in FAST’s existing AeroDyn aerodynamics module is quite robust, but still has its limitations. We’ve been working on an overhaul of AeroDyn, including the BEM algorithm and associated BEM corrections. The new algorithm is very robust. You can read about it in our recently published AIAA SciTech paper: nrel.gov/docs/fy15osti/63217.pdf.

Best regards,

Dear Dr.Jason Jonkman,

Thanks for your reply. I write the code and solve the problem. I am wondering if the new robust BEM method make any physical sense. Seems to me that there’s only numerical difference in these two methods.

Regards
Dayuan Ju

Dear Dayuan,

I agree. The new robust BEM algorithm involves the same physics as the more conventional implementation, but uses a reformulation that improves the numerics.

Best regards,

Dear Dr.Jason Jonkman,

Am I correct saying that robust BEM is just trying to find solutions under extreme tip speed ratio conditions (too low or too high) and these solutions don’t make physical sense?

Regards
Dayuan Ju

Dear Dayuan Ju,

I wouldn’t characterize it that way. The Robust BEM algorithm has a guaranteed solution (where a solution physically exists) unlike conventional implementations, which rely on solving for two unknowns (a and a’), with no guarantee for convergence.

Best regards,