Dear all,
Is there any way for extracting the damping matrix of OC4 semisubmersible?
Best regards
Kajal Thakur
Dear @Kajal.Thakur,
You haven’t said what type of damping matrix you are seeking (linearized viscous?, radiation?, aerodynamics during operation?, combined?, for a rigid or flexible body?), but the linearization functionality of OpenFAST can be used to linearize a nonlinear model about a given operating point and export its linear state-space equivalent model.
Best regards,
1 Like
Dear @Jason.Jonkman ,
Actually I’m trying to match the decay response obtained from OpenFAST with MATLAB model based on following equation:
m x_ddot + c x_dot +k x = 0
The initial conditions for this are listed as below:
For MATLAB model the mass (m) matrix I have taken is composed of full system and infinite frequency added mass matrix which are shown as below:
The stiffness (k) matrix I have taken is of mooring system which is obtained from MAP ++ file and is as shown below:
[7.08E+04, 0, 0, 0, -1.08E+05, 0;
0, 7.08E+04, 0, 1.08E+05, 0, 0;
0, 0, 1.91E+04, 0, 0, 0;
0, 1.07E+05, 0, 8.73E+07, 0, 0;
-1.07E+05, 0, 0, 0, 8.73E+07, 0;
0, 0, 0, 0, 0, 1.17E+08]
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In order to match the two responses i.e. MATLAB and OpenFAST what should be the damping (c) matrix I should use ?
-
The mass and stiffness matrix I have taken are okay or I have to make some more additions to them for response matching ?
Best regards,
Kajal Thakur
Dear @Kajal.Thakur,
I gather from your response that you are modeling a rigid system without aerodynamics and waves.
Your 6x6 rigid-body mass, added mass, and mooring stiffness matrices match what I would expect to see for the rigid NREL 5-MW baseline wind turbine atop the OC4-DeepCwind semisubmersible. But you’d also need a hydrostatic restoring matrix with nonzero terms in heave, roll, and pitch, which you haven’t stated.
The OpenFAST model of this system supports a hybrid combination of linear radiation damping (with memory effect) and quadratic viscous drag. So, if you perform free-decay simulations with the OpenFAST model, you will see both linear and quadratic damping, which will not be possible to fully capture with a linearized damping matrix. I would suggest running free-decay simulations in both models and calibrating the linear damping matrix of your linearized MATLAB model to “best match” the free decay response of the OpenFAST model. This should be fairly straightforward in heave and yaw, which are likely quite independent (and thus, have damping terms solely on the diagonal). This will be a bit trickier in surge/pitch and sway/roll, which will have coupled responses (and thus, have both on- and off-diagonal terms in the damping matrix).
Best regards,
Dear @Jason.Jonkman ,
Thank you for your fast and quick response.
Could you please tell me what damping matrix should I use in MATLAB model in order to simulate free decay ?
Best regards
Kajal Thakur
Dear @Kajal.Thakur,
I’m suggesting that you calibrate the linear damping matrix of your linear MATLAB model to match the free-decay response of OpenFAST. That is, start with c = 0. Calibrate a nonzero c(3,3) term against heave free-decay. Calibrate a nonzero c(6,6) term against yaw free-decay. Calibrate nonzero c(1,1), c(5,5), c(1,5)=c(5,1) terms against surge and pitch free-decay. And calibrate nonzero c(2,2), c(4,4), c(2,4)=c(4,2) terms against sway and roll free-decay.
Best regards,
Dear @Jason.Jonkman ,
I have some doubts which I want to clarify.
- The hydrostatic restoring matrix you are talking about is the one which is attached below ?
This matrix I have taken from " Definition of the Semisubmersible Floating System for Phase II of OC4 ".
- The hydrostatic coefficients given in .hst file is different from above coefficients which is attached below:
So should I use this one or previously defined (mentioned in documentation) hydrostatic restoring matrix?
Best regards,
Kajal Thakur
Dear @Kajal.Thakur,
The value of the hydrostatic restoring matrix from the OC4-DeepCwind semisumbersible specifications report is correct. The value from the WAMIT .hst file is also correct, but it is expressed in nondimensional form and includes some numerical round-off errors due to the way the panels where defined in WAMIT; to redimensionalize this matrix, you’ll need to multiply by rho * g, where rho is the water density and g is gravitational acceleration, which should then match the reported values well (other than a small amount of numerical round-off).
This matrix is one component of the hydrostatic restoring that you’ll have to include in your linear MATLAB model; the other term is the restoring effect of body weight (gravitational restoring) in pitch and roll, which should be calculated as m * g * z_CG, where m is the full-system mass and z_CG is the full-system center of gravity in the vertical direction.
Best regards,
Dear @Jason.Jonkman ,
Thank you for your fast reply sir, I have few more doubts about this.
-
Are you trying to say that the hydrostatic restoring matrix is composed of 2 parts, i.e.
k_hydrostatic = k_documentation + k_gravitational ? -
Could you please give me some more hint about gravitational restoring? The formula you have discussed is only for pitch or roll or for both?
Best regards,
Kajal Thakur
Dear @Kajal.Thakur,
Regarding (1), yes. The documentation mentions that the gravitational term is not included in the stated hydrostatic matrix because it often intrinsically accounted for in structural solvers (as it is in OpenFAST).
Regarding (2), the equation I state applies to both the roll (4,4) and pitch (5,5) terms. The full-system mass and vertical center of mass of the NREL 5-MW baseline wind turbine atop the OC4-DeepCwind semisubmersible is available in my post dated Feb 13, 2020 in the following forum topic: OC4-DeepCwind semisubmersible - WAMIT Files.
Best regards,
Dear @Jason.Jonkman ,
Thank you for your reply this helped me alot.
By considering the MATLAB model M x_ddot + C x_dot +K x = 0, the decay responses I got are somewhat matching as attached in below image. In this image I had also mentioned the ‘MCK’ matrices that I have used. The C matrix I had taken is random as per your suggestion by calibration.
- From this attached image it is clearly visible that the MATLAB responses are somewhat amplified then the OpenFAST decay response.
What could be possible reason for this ?
- Secondly I had tried to match the two responses i.e. MATLAB and OpenFAST for a cosine wave.
In this case I simulated the responses in OpenFAST by setting wavemod = 1P0 in Hydrodyn input file with no initial conditions.
The MATLAB model that I had considered for this case is M x_ddot + C x_dot +K x = F_ext, where F_ext I have inputed from the output file which is obtained by running the above mentioned OpenFAST model simulation, which typically includes 6 forces i.e. HydroFxi, HydroFyi, HydroFzi, HydroMxi, HydroMyi, HydroMzi. Here MCK matrices considered are same as decay response case.
Is I’m doing the second case right or I’ve making some mistake in it because I’m getting totally bad responses?
Best regards,
Kajal Thakur
Dear @Kajal.Thakur,
Regarding (1), I haven’t checked all of your matrices again, but it looks like your damping is good in yaw, but your damping in heave, surge-pitch, and roll-sway could be calibrated better.
Regarding (2), it sounds like you are double-counting terms, because HydroDyn outputs HydroFxi, etc. include the total contribution from all hydrodynamic loads, some of which you are accounting for on the left-hand side (added mass, linear damping, hydrostatic stiffness).
Best regards,