Blade Stiffness Matrix

Hello everyone,

I built my own rotor/blade model and tried to compare my model with FAST. I used finite element method (15 elements) to built the model and considered both blade flapwise deflection and edgewise deflection. My model is like Mqddot+Cqdot+K*q+f(qdot,q,t)=F, where F is aerodynamic force and f() are some nonlinear forces.
From the compare results, the deflections from my model are close to FAST when pitch angle is greater than 20 degree but differ when pitch angle is less than 15 degree. I have compared my aerodynamic model with FAST and the aerodynamic forces in my model are very close to that in FAST. Now I suspect the difference might be caused by blade stiffness matrix. How does FAST calculate blade stiffness matrix ?

By the way, the wind turbine I choose to compare is 1.5MW wind turbine.

Regards
Dayuan Ju

Dear Dayuan,

FAST v7 or the ElastoDyn module of FAST v8 does not calculate a total blade stiffness matrix per se because the equations of motion consider nonlinearities. For blades, stiffness arises both from elasticity and geometric nonlinearities (centrifugal stiffness). The elastic component is linear, based on the specified distributed bending stiffness and curvature of the specified mode shapes. The geometric stiffness is never formulated as a stiffness matrix directly in FAST. However, the effective stiffness brought about by centrifugal effects is explained in Section 3.2 of my old Master’s thesis, although not all of the information is up-to-date (it is about 13 years old), it doesn’t cover everything, and there a few errors: nrel.gov/docs/fy04osti/34755.pdf (see Eq. (3.77)).

More information on the FAST theory basis is provided in the following forum topic: http://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/1.

Best regards,

Dear Jason Jonkman,

I wonder what method is used to model wind turbine blade in FAST, assumed mode method or finite element method? Looks like FAST uses 20 elements to describe blade properties while uses assumed mode method to choose blade degree of freedom (flapwise and edgewise). Thanks.

Regards
Dayuan Ju

Dear Dayuan,

The blade structural model in FAST v7 and the ElastoDyn module of FAST v8 is essentially a nonlinear beam model where the mode shapes specified are used as shape functions. Because only two shape functions are used for flapwise bending and one shape function is used for edgewise bending, it is important to specify shape functions that correspond to realistic deflections, i.e. the natural mode shapes.

FAST does use not 20 elements. There are two inputs pertaining to the blade discretization and either are arbitrary: (1) NBlInpSt is the number of blade input stations for specifying the distributed mass and stiffness sectional data and (2) BldNodes is the number of blade analysis nodes used to integrate the blade generalized mass and stiffness matrices. Essentially, FAST takes the distributed mass and stiffness section data from the former and interpolates the data to the later. We typically recommend that BldNodes equal 20, but this can be more or less depending on the blade properties, accuracy required, and computational efficiency needed (the higher BldNodes is, the more accurate the solution will be, but slower FAST will run; 20 is often a sufficient comprise between accuracy/speed).

The forum topic linked above provides additional clarification.

Best regards,

Dear Jason,
I have questions regarding centrifugal stiffness implementation in FAST, it was mentioned that centrifugal forces (Your thesis, Page 48) acting on the blade doesn’t change as the blade deflects. My understanding is that centrifugal stiffness is calculated only once assuming the blade deflections are small, so the centrifugal forces don’t change much and their contribution is small. I couldn’t find whether this implementation is changed over time to centrifugal forces as a function of deflections, which would allow for modeling highly flexible blades i.e., high centrifugal stiffening. I’m aware that we can model highly flexible blades in BeamDyn, but I’m not sure about the implementation in BeamDyn.

Regards
Subramani

Dear Anbazhagan,

The statement from the paper you refer does not apply to the structural model of FAST v7 or to the ElastoDyn module of FAST v8, which do consider the change in centrifugal stiffness with blade deflection.

Best regards,