Moment of inertia, data interpolation in OpenFast, linear added mass matrix, linear hydrostatic matrix

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Dear @Jason.Jonkman ,

1- I read your replies concerning the linear added mass matrix. You said that the matrix was calculated at the reference (0,0,0) i.e SWL. My question is why at SWL ? For example it could be calculated at the center of mass of the Spar. How would this affect the solution ?

2- The data in OpenFast was interpolated using linear polynomials ? Or there is other functions (exponential, gaussians, …)

3- I want to be sure that the mass moment of inertia of the tower present in the "Definition of the floating system for phase IV of OC3 " is calculated at the bottom of the tower ?

4- For the linear hydrostatic matrix, I notice that it depends on “zG” which is the coordinate of the center of gravity. This coordinate is calculated in which frame ? And in OpenFast, you calculated the linear hydrostatic matrix at the reference like the linear added mass matrix or the hydrostatic matrix does not depend on the reference point ?

Best regards,

Riad

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Dear @Riad.Elhamoud,

Here are my responses to your questions:

  1. You must ensure that the hydrodynamic data in the potential-flow solution is provided at the reference point used by HydroDyn. As of OpenFAST v2.6 and newer, you can now specify the reference point for the hydrodynamic data in the potential-flow solution via HydroDyn inputs PtfmRefxt, PtfmRefyt, and PtfmRefzt (previously, these were assumed to be zero).
  2. I’m not sure what “data” you are referring to; please clarify.
  3. From which table in the report you reference are you referring to?
  4. As with (1), you must ensure that the hydrodynamic data in the potential-flow solution is provided at the reference point used by HydroDyn. This also applies to the hydrostatic matrix. But the hydrostatic data in the potential-flow solution should not depend on the vertical center of gravity of the structure because HydroDyn does not consider the body mass, which is accounted for elsewhere within OpenFAST.

Best regards,

3

Dear @Jason.Jonkman ,

1- Ok but i was wondering about the reference. For example, in OpenFast v2.7, if the reference was at the center of gravity of the floater and i run decay test and obtain the natural frequencies. And for the same wind turbine, i use OpenFast v2.5 to run decay test to obtain the natural frequencies. I should obtain the same natural frequencies no ?
In other words, the choice of the reference for these two matrices depend on the reference chosen for kinematics of the tower ?

2- Here i was refering to data like tower mass density (kg/m), or blade stiffness in flapwise, …

3- I’m sorry, i was working on several topics and i don’t remember where i found the value :frowning:

4- In OpenFast documentation section 4.2.8.4.8.3 you give the linear hydrostatic matrix. I think it’s given at the reference (0,0,0) i.e SWL, is it right ? I said this because i saw that the integrals should be done at the undisplaced waterplane area of the platform.

5- When we said “platform”, that means we are talking about the whole wind turbine not only the floater right ?

6- The parameters in the linear hydrostatic matrix corresponds to the floater only or the whole platform ? For example if we take C44, it contains zG. Here zG is the center of gravity of the whole turbine ?

7- Can you suggest a book or a method to be able to calculate the position of the center of buoyancy of a floater knowing the position of the center of buoyancy for the same floater but containing ballast ?

8- In the technical report “Definition of the floating system for phase IV of OC3” page 7, you give the linear hydrostatic matrix. For the C33, the formula : rho * 9.81 * pi * 6.5^2 * 0.25 works well. But, for the coefficients C44 and C55 the formula: rho * 9.81 * (volume_undisplaced * distance(COB,COG)+pi * D^4/64) doesn’t work and also you obtained negative numbers. Could you please explain why ?

9- I realized also that you add a damping matrix to account for radiation damping page 14 in the technical report “Definition of the floating system for phase IV of OC3”. I thought that the viscous drag term in Morison’s formula takes into account the radiation damping but my question is why did you have zero for roll and pitch and non zero diagonal terms for the other motion ?

Sorry for bothering you :frowning:

Thank you in advance for your explanations and for your help,

Riad

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Dear @Riad.Elhamoud,

Here are my responses:

  1. I’m not really sure I understand your question; please clarify.
  2. Yes, the distributed blade and tower mass and stiffness data are interpolated linearly within ElastoDyn from the input stations to the analysis nodes.
  4. Yes, the matrix shown in that section of the documentation is relative to a reference point located at (0,0,0) m.
  5. The term “platform” in ElastoDyn refers to the structure below the tower not modeled in SubDyn or a mooring module.
  6. Again, the structural modules of OpenFAST already account for gravitational restoring of the structural masses considered within those modules. So, when defining a hydrostatic stiffness matrix in HydroDyn, the contribution to these structural masses does not need to be considered. Please note that as of OpenFAST v2.6 and newer, the strip-theory solution now directly considers the effect of displacement on the hydrostatic loads of the strip-theory members, so, AddCLin is no longer needed in general.
  7. The center of buoyancy is the center of the displaced volume and is independent of ballast (unless the ballast is changing the center of the displaced volume).
  8. Again, the COG effect is not included in the hydrostatic matrix because it is accounted for elsewhere in OpenFAST.
  9. I believe you are referring to the additional linear damping matrix. This matrix expresses additional damping not directly captured through radiation damping (memory effect) or viscous drag. This matrix was derived through calibration against model-test data. No additional damping was needed in the roll and pitch directions.

Best regards,

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