WISDEM: rotor blade strains and fatigue calculations

Wind & Water Computer-Aided Engineering Software Tools
1

Hello,
I’d like to have two points clarified about the code in rotor_structure.py (WISDEM version 3.2.0): the first point concerns the computation of blade strains, and the second the computation of blade fatigue damage.

  1. below are excerpts of the ExplicitComponent ComputeStrains relevant to my question:
def setup(self):

       self.add_input("EA", val=np.zeros(n_span), units="N", desc="axial stiffness")

        self.add_input(
            "EI11",
            val=np.zeros(n_span),
            units="N*m**2",
            desc="stiffness w.r.t principal axis 1",
        )
...
       self.add_input(
            "M1",
            val=np.zeros(n_span),
            units="N*m/m",
            desc="distribution along blade span of bending moment w.r.t principal axis 1",
        )
...
       self.add_input(
            "F3",
            val=np.zeros(n_span),
            units="N/m",
            desc="edgewise bending moment along blade span",
        )
        self.add_input(
            "xu_strain_spar",
            val=np.zeros(n_span),
            desc="x-position of midpoint of spar cap on upper surface for strain calculation",
        )
        self.add_input(
            "xl_strain_spar",
            val=np.zeros(n_span),
            desc="x-position of midpoint of spar cap on lower surface for strain calculation",
        )
        self.add_input(
            "yu_strain_spar",
            val=np.zeros(n_span),
            desc="y-position of midpoint of spar cap on upper surface for strain calculation",
        )
        self.add_input(
            "yl_strain_spar",
            val=np.zeros(n_span),
            desc="y-position of midpoint of spar cap on lower surface for strain calculation",
        )
...

        def strain(xu, yu, xl, yl):
            # use profile c.s. to use Hansen's notation
            xuu, yuu = yu, xu
            xll, yll = yl, xl
...
            # compute strain
            x, y = rotate(xuu, yuu)
            strainU = M1 / EI11 * y - M2 / EI22 * x - F3 / EA

            x, y = rotate(xll, yll)
            strainL = M1 / EI11 * y - M2 / EI22 * x - F3 / EA
            return strainU, strainL

        # ----- strains along the mid-line of the spar caps and at the center of the two trailing edge reinforcement thickness (not the trailing edge) -----
        strainU_spar, strainL_spar = strain(xu_strain_spar, yu_strain_spar, xl_strain_spar, yl_strain_spar)
        strainU_te, strainL_te = strain(xu_strain_te, yu_strain_te, xl_strain_te, yl_strain_te)

        outputs["strainU_spar"] = strainU_spar
        outputs["strainL_spar"] = strainL_spar
        outputs["strainU_te"] = strainU_te
        outputs["strainL_te"] = strainL_te

The three terms in the RHS of the equations for strainL and strainU are not dimensionless, but seem to have dimensions of m^-1 (assuming that x and y have dimension of length), so strainU and strainL are strains per unit lenght. Then, have I to multiply strainU_spar, strainL_spar, strainU_te, strainL_te by the blade span to get the final strain values?

  1. I have read a paper presented in 2020 whose authors mention WISDEM evaluation of blade fatigue failure, and use it as a constraint parameter for their optimizations. In rotor_structure.py of WISDEM 3.2.0 there is indeed an ExplicitComponent class named BladeFatigue, but is entirely commented out, so unavailable. Is there a different way to do blade fatigue analysis in WISDEM 3.2.0, or this feature has been removed?

Thank you for your time and help.

2

Hi Henny,

Can you explain a little more about your calculations and concern over the units? To me, I see standard beam bending stress-strain formulas (M*y/(E * I) and F / (E *A)).

Regarding fatigue, at one point WISDEM included a capability to provide DELs computed externally (from OpenFAST or another aero-elastic tool) and WISDEM would compute a damage constraint. This was difficult to get right and very easy to get wrong, so we have mostly removed it. Instead, that coupling can now happen in the WEIS tool ([url]https://github.com/WISDEM/WEIS/tree/develop[/url]) that connects WISDEM & OpenFAST properly.

Best,
Garrett

3

Hi Garret,

According to the units reported in the inputs lines in the setup part of the class, M is a moment per unit lenght and has dimension of [N], F is a force per unit lenght and has dimension of [N/m], EA has dimension of [N], and EI has dimension of [Nm^2]. This makes the dimension of the terms F / (E *A) and [i]My/(E * I)[/i] equal to [1/m] (for the Moment term I am assuming the dimension of y to be [m], since it is a distance).
Now, the definition of strain is dl/l, that is, a length change divided by a lenght, so it’s dimensionless not [1/m]. Then I wondered whether the strains computed by ComputeStrains formulas are actually strains per unit lenght and must be multiplied by a length to have the actual dl/l value.
Since the quantities defined per unit lenght that I found so far are usually defined along the blade span, I thought that this lenght may be the blade span.

Thank you for the explanation about the fatigue analysis and the suggestion of WEIS.

Best,
Henny

4

Any update on this topic?
And best wishes of a happy 2022 to all!