To better understand the reason for the divergence of the previously analyzed results (see quote), I chose to carry out an analysis only on the hydrodynamic part, thus setting CompAero = 0 and defining the initial rotor speed = 0. In this way it is possible to neglect the loads at the base of the turbine throughout the simulation.
Lorenzo.Cottura wrote:Dear Jason,
Thanks for checking.
I have tried to investigate further what can cause the differences between my outputs and those of FAST, and I have noticed that the cause is the resultant moment Mx.
In fact, I compared, for each DOF, that the equation was verified:
M * a = Fhydro + Fturbine + Fmoor - Frestoring - Fnonlinear
thus obtaining from the product M * a the resulting Fx, Fy, Fz, Mx, My, Mz which I had to obtain from the sum of the contributions to have the same accelerations as FAST.
To do this I used:
- M: variable mass matrix with the movement of the platform
- a: acceleration outputs of FAST ('PtfmTAxi', 'PtfmTAyi', 'PtfmTAzi', 'PtfmRAxi', 'PtfmRAyi', 'PtfmRAzi')
- Fhydro: outputs FAST ('HydroFxi', 'HydroFyi' 'HydroFzi', 'HydroMxi', 'HydroMyi', 'HydroMzi')
- Fturbine: forces at the base of the turbine tower, obtained starting from the aerodynamic forces / moments on the rotor ('RtAeroFxh', 'RtAeroFyh', 'RtAeroFzh', 'RtAeroMxh', 'RtAeroMyh', 'RtAeroMzh'), transported in the fixed reference of the nacelle and then transported to the base of the tower.
- Fmoor: starting from the forces in the 3 directions for each line obtained by MAP ++, the moments were obtained
- Frestoring: where the contribution on Mx is given by m * x_g * 'PtfmYaw' - m * z_g * 'PtfmRoll' where m = total mass of the system, (x_g, y_g, z_g) coordinates of the center of mass with respect to the origin of the inertial reference system
- Fnonlinear: as regards the moments, I used the formula omega x I dot omega (with omega = ['PtfmRVxi', 'PtfmRVyi', 'PtfmRVzi'] and I: inertia matrix 3x3, depending on platforms movements)
The equation of dynamics then becomes:
M * a = Fhydro + Fmoor - Frestoring - Fnonlinear
where each component is defined as in the quote, with the exception of the restoring moment where the changes you suggest have been inserted.
As I did earlier, I have compared forces-moments with M * a in all directions:
Comparing the results, I recorded the following errors on the rms values:
Fx: 2,5% Fy: 2,4% Fz: 0,4% Mx: 15,1% My: 6,7% Mz: -99%
As you can see, Mx has a small error especially in the first part of the simulation. The resultant of Mz, on the other hand, is of the order of ten while the corresponding M * a has values of hundreds: I cannot understand the reason given that HydroMz, MoorMz and NonlinMz have values of the order of unity, while the restoring moment is null in rz direction.
Is there any advice you can give me?
Thanks for the attention,