Blade Element Method

Hi Sir
i am working with my BEM matlab Code , and i have to be sure about three points before going further:

  1. I noticed that always the relative velocity over the radius of the blade is linear. is it always the case?
  2. for blade optimization the optimun value of axial induction factor is 1/3 , is there any optimal value for tangiential induction factor?
  3. i am looking for big data base for all airfoils aoa vs cl,cd , if you can recommand me the best .

thank you

Dear Nacer,

Here are my answers to your questions:

  1. The relative velocity may be dominated by the rotor rotation, omega x r, which is linear with radius (r), but there are other factors that can impact the relative velocity, including shear, yaw, turbulence, turbine vibrations, etc.

  2. An axial induction of 1/3 is Betz optimal for ideal conditions. The tangential induction is associated with wake rotation, and the ideal (from Betz theory) would be 0. For a high TSR rotor, I would expect small values of the tangential induction (close to zero).

  3. The following forum post from many years ago has links to several publicly available airfoil data tables, but some of the links are broken nowadays: I’m not aware that NREL currently supports a database of publicly available wind turbine airfoils.

Best regards,

hi jason

using a BEM code , after converging for 7 m/s as wind velocity .
i got this vector of angals of attack along spanwise (–> r ) for 24 elements of wind blade :

alpha=[ 62.1688 57.4165 52.0483 41.5811 42.7538 44.8896 45.7601 46.2280 45.4738 45.1333 44.1188 42.4482 40.6009 40.5213 38.7097 36.8680 35.5087 35.1695 33.6172 32.7870 32.5561 31.6383 30.5935 29.8976]

my question what is the meaning to have such grate numbers of AOA after convergence !!?? physically is that make sens ?? it seems to me over estimate. but after many example , code runing, AOA is always that big !! ,
any explanation !!

thank you

Dear Nacer,

I agree those AoA are large (indicating the entire rotor is in deeps stall), but I don’t know what much about your simulation set up to know if that makes sense for your simulated condition.

Best regards,

hi jason ,
i will inssist with coupl questions on this point of AOA, i am working on optimization project. i have to be sure to understand it cristal clear.
here it is some of my execution simulations :

input for simulation using BEM :
wind turbine : NREL
pitch=3 degrees

for: V0=7 m/s wind velocity;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

angal of attack along spanwise:

alpha=[28.7057 22.3392 16.7248 8.1866 8.4064 9.0716 9.3231 9.5227 9.4090 9.3486 9.1601 8.8310
8.4447 8.4269 8.0335 7.6273 7.3521 7.2830 6.9765 7.2629 7.3298 7.2354 7.2555 7.3101]

for: V0=10 m/s %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

alpha=[40.3829 34.2967 27.0039 16.6524 16.8969 17.6630 17.9323 17.9719 17.4628 17.2635 16.7259 15.8957
15.0368 15.0002 14.1945 13.3653 12.7773 12.6328 11.9890 12.2129 12.2179 11.9326 11.7173 11.6071]

for: V0=13 m/s %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

alpha=[47.9035 42.2982 35.9462 23.4737 23.8624 24.9518 25.4825 25.5597 24.7654 24.4840 23.7507 22.6929
21.4812 21.4240 20.1383 18.8219 18.0157 17.8146 16.8857 16.9243 16.8659 16.3863 15.9208 15.6480]

also i have some questions :

1* on each station ( for given "r " position spanwise) , the AOA represent AOA of a ring from the disc ??!! because its abvious if we imagine the blade rotating we will wander at which position we took the AOA , is it somkinde of the avrege of the ring ??

2* if the values of AOA after BEM code convergence are above 18 degrees , can we be sure its a stall , or there is other numerical meaning ??

3* i read on some plications that the optimum air velocity of wind blade design and optimization is 7 m/s !!?? any idea about it.!!

thank you jason

Dear Nacer,

By the “NREL” wind turbine, do you mean the UAE Phase VI rotor? It has been many years since I looked at this data, so, I don’t have a gut feel what the AoA should be at each wind speed, although I do recall the airfoils being mostly stalled at 10 m/s and higher wind speed. You could always compare your MATLAB-based BEM solution to NREL’s AeroDyn solution or the like if you are concerned what your BEM solver is giving you.

Regarding your questions:

  1. In uniform, unwskewed flow, this question is moot. For sheared, skewed, and/or turbulent flow, in AeroDyn, the local wind conditions at a given aerodynamic analysis node are used to calculate the angle of attack, which may differ between all nodes of all blades.

  2. Stall is defined at the airfoil level and you can review the airfoil polar data you are using to confirm if 18 degrees AoA is past stall (most likely it is).

  3. For a rigid rotor, optimal power refers to the maximum of the power coefficient surface as a function of tip-speed ratio and pitch. So, the optimal power is found at an optimal tip-speed ratio and pitch. For a flexible rotor, the wind speed also plays a role, but this is turbine dependent.

Best regards,