Additional velocity due to platform translation

Dear Jonkman,

I am trying to figure out your way which was applied to calculate additional velocity on wind turbine rotor blade due to 6DOFs platform motion. I am referring the following paper title:
J.M. Jonkman, “Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine”, Technical Report NREL/TP-500-41958 November 2007.

In section “2.3 Support Platform Kinematics and Kinetics Modeling”, you described transformation matrix to calculate additional wind on rotor blade due to 3DOFs rotation modes of platform motion? Am I right? It was based upon small rotation assumption.

My question is how to calculate additional wind on rotor blade due to 3DOFs translation modes of platform motion? Can I write out this data to external file for each time step? Where is it in FAST code?

Second question is the effect of distance from mass center location (full system) to rotor blade. As I understand, this value may play key role for design of platform type. This value is larger and larger, additional wind due to rotation modes tend to increase higher and higher.

I am looking forward your help.

Cheers,
ToanThanh.Tran
Graduate Student, South Korea

ToanThanh Tran,

The transformation simply relates a vector expressed in global coordinates to a vector expressed in local coordinates due to rotation of the local coordinate system relative to the global coordinate system.

The additional velocity for any point in the rotor due to platform motion can be expressed using typical expressions for the kinematics of a point in a moving reference frame:

v_Total = v_Trans + omega x position,

where,
v_Total = total velocity
v_Trans = translational velocity of the platform reference point (origin of the moving reference frame)
omega = rotational velocity of the platform (moving reference frame)
position = position vector of the point relative to the platform reference point (origin of the moving reference frame)

Such kinematics expressions are included in the source code of FAST. You can output the translational and rotational velocities of many points in the system directly through the FAST outputs. The position vectors are defined by the input geometry.

I’m not sure I understand your second question.

Best regards,

Dear Jonkman,

Thank you for your quickly response.

According to your expression of kinematic equation (v_Total = v_Trans + omega x position), the term of “position” depend on center gravity location of full floating offshore wind turbine system. That’s what I would like to ask you in second question. This location (CG) may be significant effect to additional velocity on any point rotor blade.

Other question I am little bit confuse is to involve to second-order hydrodynamic of FAST program. According to your discussion (http://forums.nrel.gov/t/questions-about-the-hydrodyn-module/596/1), if pre-processing program (WAMIT, SWIM, AQWA, etc) can prepare second order hydrodynamic (second-order exciting force,…), is it directly use by FAST code? As I understand the following paper, WAMIT was used to create second-order hydrodynamic data for FAST code.
Line Roald, Jason Jonkman, Amy Robertson, Ndaona Chokani, “The Effect of Second-order Hydrodynamics on Floating Offshore Wind Turbines”, Energy Procedia Vol. 35, 2013, Pages 253–264…

I am looking forward your help.

Cheers,
ToanThanh.Tran
Graduate Student, South Korea

Dear ToanThanh Tran,

The term “position” is not necessary tied to the center of gravity. The center of rotation of a floating wind system depends on its center of gravity, center of buoyancy, and mooring system. While “position” may be large for some floating wind turbines, “omega” may in fact be quite small.

The HydroDyn module of FAST currently only makes use of first-order hydrodynamic coefficients. We are working on an extension of HydroDyn that will allow it to make use of the second-order hydrodynamic coefficients (e.g., the complete hydrodynamic quadratic transfer function (QTF) computed from WAMIT second-order), but this feature will not be available until sometime in 2014.

Best regards,

Dear Jonkman,

Thank you for your reply. Your information is very helpful.

However, I still confuse about term of “position” which you mentioned that it is not necessary tied to the center of gravity. I agree that the center of rotation of a floating wind system depends on its center of gravity, center of buoyancy, and mooring system. In case you do not tie to the center of gravity, which point (or coordinate system) did you refer?

As I understand, the hydrodynamic force and moment will exert to CG point (CG of full FOWT system). Then, CG point (as local axis system) will move with respect to fixed reference axes (FRA) due to hydrodynamic force, external force, etc. Due to CG motion, any point on FOWT will rotate with respect to local axis system. Any point on FOWT can be seen as movement with respect to fixed coordinate axis. Thus, additional velocity should be calculated with respect to CG point due to rotation modes.

Cheers,
Coordinate.jpg

Dear ToanThanh Tran,

In FAST, “position” is defined relative to the platform reference point, which for an undisplaced floater is the intersection of the tower centerline with the still water level. While the system CG may be important for the system dynamics, the equation I stated for v_Total applies even when the platform reference point is not tied to the system CG. In fact, the CG of a floating offshore wind turbine in FAST is not a fixed point, but moves with the system deflections (geometric nonlinearities).

Best regards,

Dear Jonkman,

Thank you for your kindly response. I realized a lot of information from you.
In fact, the FOWT simulation is very interesting for me.

I would like to ask you about mass & inertia of the rigid body of full FOWT system. In fact, I just want to know your confirmation for it. According to your post ([url]Inertial Moments of OC3-Hywind Components]), I can obtain desire parameter for my analysis. But, I calculated this parameter based on moments of inertia theory, again. The only Izz component has good correlation each other. The comparison data will be given as attached file.

I am looking forward your help

Best regards
Mass_Inertia Data.xlsx (88.3 KB)

Dear ToanThanh Tran,

I didn’t check everything in your spreadsheet, but I do see a few problems:

*The tower mass in cell D10 does not match the tower mass in D13.
*The RNA inertias you entered in row 9 should be the inertias about the RNA CG, but you are using the inertias about the tower-top.
*The inertias given in your second sheet are the inertias about the platform reference point whereas the inertias you are calculating on the 3rd sheet are about the full system CG. So, you wouldn’t expect these to match.

Best regards,

Dear Jonkman,

I am sorry for my mistake in spreadsheet, particularly tower mass which does not match between cell D10 and D13.

As I mentioned in the top of third sheet, all inertias was calculated at their CG location. The CG point of RNA was referred to platform reference point to calculate new CG point of full FOWT system.

As you mentioned, the inertias in my second sheet was calculated at the platform reference point whereas the inertias in my third sheet is calculating about the full system CG. However, Ixx and Iyy inertia components between ADAM calculation and my hand calculation still does not match when I translated inertias from platform reference point to full system CG point.

I am looking forward your help.

Best regards
Mass_Inertia Data_ver01.01.xlsx (179 KB)

Dear ToanThanh Tran,

Your transformation from the reference point to the system CG on the 2nd-sheet is not correct. The inertia about the CG should be less than the inertia about the reference point. You have a plus sign where you should have a minus sign. When you change this sign, the inertias match those form the 3rd sheet.

By the way, the RNA inertias you entered in row 9 of the 3rd sheet are still incorrect (as I identified above), but this error doesn’t appear to make a big difference.

Best regards,

Dear Jonkman,

Thank you for your responses. I got my problem according to your detail explanation.

Best regards,