Downscaling NREL 5MW structural properties (blade and tower)

Wind & Water Structural Analysis
1

Dear all,

I am currently modelling in OpenFAST a turbine where I have the blade geometry and aerofoil characteristics (polars and shapes).
However, I do not have the structural properties available. In order to perform aeroelastic simulations I plan on using the NREL 5MW structural properties from [1] for the tower and blade. The doubt I have is on the scaling method to use. The blade I have is 45m long and the rated power is 2MW.

Knowing that:
FlpStff = double integral of E(x,y) * x^2 dxdy
EdgStff = double integral of E(x,y) * y^2 dxdy

The stiffness seems to vary with the square of the surface. To define the scaled down stiffness coefficient I then used the ratio of the sectionnal areas, at the same r/R position, squared times the stiffness coefficient:

FlpStff_new_i = (Area_i_new_turbine / Area_i_NREL)^2 * FlpStff_NREL_i

Where:
FlpStff_new_i: is the scaled down flapwise stiffness coefficient for “my” turbine
i: is the same radial position (between 0 and 1) e.g. 50% span
Area_i_new_turbine: is the aerofoil cross sectional area in m^2 of “my” turbine
Area_i_NREL: is the aerofoil cross sectional area in m^2 of the NREL 5MW turbine
FlpStff_NREL_i: is the flapwise stiff corresponding to the spanwise position, e.g. 5% span.

The approach is then repeated for the edge stiffness and for the tower (since the tower diameter and height changes).

Using this approach I am able to ignore the issue of similarity in strains or stress, since I do not possess the targeted values. The aim was to use purely a geometrical approach.

Is this approach correct ? If so, is the ratio as defined above correct or should it be modified ?

Thanks for any help provided!

Best regards,

Thomas

[1] J. Jonkman, S. Butterfield, W. Musial, and G. Scott, ‘Definition of a 5-MW Reference Wind Turbine for Offshore System Development’, NREL/TP-500-38060, 947422, Feb. 2009. doi: 10.2172/947422.

2

Dear Thomas,

I agree with your equations for the flapwise and edgewise stiffness. But assuming that the material is the same at both scales, the equation is:

FlpStff = EI_yy
EdgStff = EI_xx

where the sectional inertias, I_xx and I_yy, have the units of length^4. So, I would think you’d need to take the ratio of the sectional inertias, rather than the ratio of sectional areas, to maintain geometrical scaling (or simply scale each sectional stiffness by length^4).

Best regards,

3

Dear Jason,

Thanks for your quick reply. I intended to use the same material therefore your proposal is better suited for my end goal.

Thanks again,

Best regards,

Thomas