Aerodynamic force in lateral direction

[Fede-274]

I would like to extract the lateral aerodynamic force at the tower-top for the IEA 15 MW monopile. So I need the output of AeroDyn ‘RtAeroFyi’ which is expressed with respect to the inertial axis Yi.

Specifically, I would like to convert this force to the Yp axis where the SS displacement of the tower top ‘YawBrTDyp’ is oriented, what rotations do I need to do in post-processing?

I ask this information for 2 different situations of degrees of freedom granted in ElastoDyn:

1. all degrees of freedom granted, except ‘TeetDOF’, ‘DrTrDOF’ and ‘YawDOF’
2. all degrees of freedom granted, except ‘TeetDOF’ and ‘DrTrDOF’ (i.e. having granted ‘YawDOF’)

[jjonkman]

Dear @Fede-274,

The tower-top/base-plate ("p") coordinate system in ElastoDyn will depend on the platform rotation and tower-bending deflection, but it won't depend on the motion above the tower-top (including yaw, drivetrain, teeter, blade-bending, etc.).

The rotational transformation matrices used by ElastoDyn are documented in its theory basis: https://openfast.readthedocs.io/en/main/_downloads/c9ae932057ea1e64c79154b36d3ab30a/FASTCoordinateSystems.doc. In this document, the internal "b" system (page 3) is related to the external ("p") system as follows:
xp = b1
yp =-b3
zp = b2

I hope that helps.

Best regards,

[Fede-274]

Dear @jjonkman ,
thank you for your gentle reply.
I understand that the tower-top/base-plate (‘p’) reference system is not related to the g.d.l. that I have inhibited (yaw, drivetrain, teeter).

I have read the attached file, but I cannot understand the post-processing I have to perform. I would like to express the lateral aerodynamic force at the tower-top ‘RtAeroFyi’ (expressed with respect to the inertial axis Yi) along the axis Yp (where the SS displacement of the tower top ‘YawBrTDyp’ is oriented).

Is it possible to do this by post-processing the output vector ‘RtAeroFyi’? if so, how? or are the parameters ‘RtAeroFyi’ and ‘YawBrTDyp’ already oriented in the same direction?

Thank you in advance

[jjonkman]

Dear @Fede-274,

Do you have platform and tower degrees of freedom enabled in ElastoDyn? If not, yi and yp are oriented in the same direction.

Note that the internal inertial frame system "z" is related to the external system "i" as follows:
xi = z1
yi =-z3
zi = z2

If you have the platform degrees of freedom enabled in ElastoDyn, you can use the following equivalencies:
PtfmRoll * D2R = qR
PtfmPitch * D2R = qP
PtfmYaw * D2R = qY

where D2R = pi/180 to convert from degrees to radians. With this information, you can convert RtAeroFxi, RtAeroFyi, and RtAeroFzi from the external "i" system to the internal tower-base / platform "a" system.

If you have the tower-bending degrees of freedom enabled in ElastoDyn, you can use the following equivalencies:
TTDspRDxt * D2R = thetaSS(TwrFlexL)
TTDspRDyt * D2R = -thetaFA(TwrFlexL)

With this information, you can convert from the "a" system to the "b" system, and use equivalency in my prior post to get to "p" system.

Best regards,

[Fede-274]

Dear @jjonkman,
yes I have both tower and platform d.o.f. activated. This is my section of ElastoDyn concerning the d.o.f.:

I cannot understand what are the parameters (qR,qP,qY) and (thetaSS(TwrFlexL),thetaFA(TwrFlexL)) and how they can convert "RtAeroFyi" from the Yi axis to the Yp axis.
Also, in the Excel file of possible outputs, I cannot find the parameters "TTDspRDxt" and "TTDspRDyt", what do they refer to?

Considering the above d.o.f. of my simulations and the fact that my only interest is the aerodynamic force in the lateral direction, could you write me the analytical expressions that convert just "RtAeroFyi" from the Yi axis to the Yp axis?
Also, can you confirm me that this system conversion does not change if the YawDOF is deactivated or activated?

Thank you in advance

[jjonkman]

Dear @Fede-274,

I wrote the equivalencies of qR,qP,qY from the ElastoDyn theory documentation in terms of ElastoDyn outputs PtfrmRoll,PtfmPitch,PtfmYaw in my previous reply above.

I incorrectly reported the ElastoDyn tower-top / yaw bearing rotational deflections as TTDspRDxt,TTDspRDyt; these should have been YawBrRDxt,YawBrRDyt, or equivalently, TTDspRoll, TTDspPtch. I've corrected these equivalencies below:
YawBrRDxt * D2R = TTDspRoll * D2R = thetaSS(TwrFlexL)
YawBrRDyt * D2R = TTDspPitch * D2R = -thetaFA(TwrFlexL)

Combining the information from my responses above, the final equations converting the aerodynamic applied loads from the external "i" system (RtAeroFxi,RtAeroFyi,RtAeroFzi) to the "p" system (which I'll call RtAeroFxp,RtAeroFyp,RtAeroFzp) are as follows:

{ RtAeroFxp, RtAeroFzp, -RtAeroFyp }^T = [ TransMat( theta1 = YawBrRDxt * D2R, theta2 = 0, theta3 = -YawBrRDyt * D2R ) ] * [ TransMat( theta1 = PtfmRoll * D2R, theta2 = PtfmYaw * D2R, theta3 = -PtfmPitch * D2R ) ] * { RtAeroFxi, RtAeroFzi, -RtAeroFyi }^T

where TransMat is shown in the ElastoDyn theory documentation.

Because the "p" system is independent of the nacelle-yaw angle, its orientation won't be affected by YawDOF.

Best regards,