Different StrcTwst and AeroTwst

[Tim.Gerloff]

Dear FAST-Community,

does anyone has experience how different StrcTwst and AeroTwst angle effect the results for flapwise bending moment along the blade ? I do have a bld-file with an StrcTwst angle for the principal elastic axes from 45 to 0 degrees and my AeroTwst angle only differs between 15 to 0 degrees. The difference → deltaAngle = StrTwst-AeroTwst turns out to be almost 30 degrees close to the root of the blade. This is causing a lot of spikes and unsteady behaviour for the flapwise bending moment along the blade close to the root. As in my mechanical understanding the increase in flapwise bending moment should be smooth, steady and linear, but unfortunately this is not the case. Therefore I was wondering if a maximum difference between those angles exists before the results for bending moment become unreal.

Thanks,
Tim

[Jason.Jonkman]

Dear Tim,

I’m not aware of any limitation to the structural or aerodynamic twist angles in FAST/AeroDyn. FAST and AeroDyn use sines and cosines of these angles (as opposed to small-angle approximations) in their calculations. When FAST was developed, we also performed some benchmark tests with a beam twisted up to 90 degrees to ensure that the implementation was accurate. Please explain more what problems you are running into.

Best regards,

[Tim.Gerloff]

Dear Jason,

reading through the FAST User’s Guide I gained an understanding of the structural twist, as the angle for which the flap wise and edge wise stiffness reach their maximum and the couple term for the edge and flap wise stiffness turns to zero.
The structural twist indicates the orientation for the principal elastic axes and should be zero for e.g. if the direction for the edgewise stiffness is parallel to the plane of rotation.

Having the orientation of the principal elastic axes in mind, structural twist and aerodynamic twist can differ from each other. Is that thought correct?

I ran two simulations to find out, if my assumption about the structural twist is correct.
For the first simulation the flap and edgewise stiffness were rotated so that aero twist and structural twist are the same. Neglecting the error made by not regarding the cross term and assuming a plane bending in edge and flap wise direction.

For the second simulation the structural twist was adapted, so that no cross term exists.

In the following attachment you can see how structural and aero twist differ.

By running both simulations I expected similar results for bending moments MLx and MLy.
Unfortunately the curve for MLx and MLy differ totally and I do not know the reason why.
I attached 3 figures for MLx, MLy and the out-of-plane deflection for the same loadcase (wind speed of 12ms with a shear of 0.2) at the same time with the same starting values, the same blade. All values for MLx and MLy are along the blade length. For all results with a naming of “XXX-AeroTwist” aero twist and structural twist are identical. All results with a naming of “XXX-StructuralTwist” aero twist and structural twist are different as shown.

The curves for the moments along the blade do not make any sense in my opinion, if the structural twist differs from the aero twist. What is wrong in my thinking and does FAST any recalculating of the stiffness? Does neglecting any cross terms for the stiffness leads to a deviation in the modelling of the blades?

A short answer to get my thinking clear would really be helpful.

Best Regards
Tim

[Jason.Jonkman]

Dear Tim,

Your understanding of the structural twist is correct. And “yes,” the structural twist can certainly be independent of the aerodynamic twist in FAST (and in real life).

I’m assuming that the “MLx” and “MLy” you are plotting are taken directly from FAST’s bending moment outputs at the strain gages – that is, outputs Spn<J=1,2,…,9>MLxb<K=1,2,3> and Spn<J=1,2,…,9>MLyb<K=1,2,3> for the J’th strain gage and K’th blade. You should be aware that these bending moments are output in the local coordinate system determined by the structural twist that is oriented with the principal elastic axes and moves with the deflected blade. When the blade is undeflected, the principal elastic axes and the blade (pitch) coordinate system are related by:

xb = COS(StrcTwst)*Lxb + SIN(StrcTwst)*Lyb
yb = -SIN(StrcTwst)*Lxb + COS(StrcTwst)*Lyb
zb = Lzb

where (xb,yb,zb) is the blade (pitch) coordinate system, (Lxb,Lyb,Lzb) is the local coordinate system that is oriented with the principal elastic axes, and StrcTwst is the local structural twist angle. The bending moments can be transformed using the same transformation.

When the blade deflects, however, the blade (pitch) coordinate system is still relative to the undeflected blade, but the local coordinate system that is oriented with the principal elastic axes moves with the deflected blade, The transformation in this case is complicated by the slopes of the out-of-plane and in-plane blade deflections (which, in turn, are related to the contributions of each mode shape).

With this interpretation of MLx and MLy, I believe your results make sense. A large change in the structural twist will lead to a large change in MLx and MLy when the orientation of the applied loads is unchanged.

I hope that helps.

Best regards,

[Tim.Gerloff]

Dear Jason,

Thanks a lot for your explanation. I also took a look at the “unofficial” theory manual for FAST you send me and I got my thinking clear. So all loads are given in the structural coordinate system and NOT in the aerodynamic/ chord coordinate system.
I was able to transform all loads from the structural system into the chord coordinate system.
Unfortunately the “FAST User Guide” only mentions blade loads are given in the x_bi, y_bi, z_bi coordinate system and those axes are named as “local principal axes”. As a non English native speaker I got confused and thought about the chord coordinate system. Maybe something like “principal elastic axes” would make it more self-explanatory.
Sorry for any inconvenience.

Best regards,

Tim

[Jason.Jonkman]

Dear Tim,

OK, I’m glad I could help out.

Thanks for the suggestion. We’ll try to clarify the descriptions in a future release of the FAST manual.

Best regards,

[Masoud.Abbaszadeh]

When the blade deflects, however, the blade (pitch) coordinate system is still relative to the undeflected blade, but the local coordinate system that is oriented with the principal elastic axes moves with the deflected blade, The transformation in this case is complicated by the slopes of the out-of-plane and in-plane blade deflections (which, in turn, are related to the contributions of each mode shape).

1- I get the local blade accelerations in Lxb, Lyb and Lzb, at axial distance r from the root and I need to transform the output to xb, yb, zb.

I found the the following linear from:

eye(3)+skew(sigma(phi_dot(r)*q)),

where skew is the skew symmetric tensor, q is the generalized coordinate (blade state expressed in the blade root coordinated), phi_dot is the derivative of the corresponding displacement mode shape, evaluated at axial distance r from the root. The linear approximation seem to create dc offsets.

Can someone please describe the rotation matrix from deflected to undeflected blade in terms of the blade states and mode shapes, or point me to a reference that given the actual rotation matrix?

2- In what coordinate system the mode shapes are calculated in FAST. xb, yb, zb or Lxb, Lyb, Lzb?

[Jason.Jonkman]

Dear Masoud,

FAST uses a nonlinear form of the rotation matrix you’ve stated. The rotation matrix depends on the flapwise and edgewise mode shapes, the displacements of the blade DOFs, and the structural twist angle. The exact matrix is described in the “Unofficial FAST Theory Manual” mentioned in the following forum topic: Coupled blade modes in FAST. I believe I’ve already sent this to you by e-mail.

The mode shapes are specified in FAST in the blade coordinate system (xb/yb/zb).

Best regards,