Phase angle of wave excitation loads for offset body, and added mass and radiation damping matrix for multibodies in AQWA

[hachikoi1]

Dear izabala123

I found some issues about the phase angle of wave excitation loads for offset body, and added mass and radiation damping matrix for multibodies. The issues were originally posed in A designed two-body hinged raft wave energy converter: From experimental study to annual power prediction for the EMEC site using WEC-Sim by Siya.

Let me briefly describe the problem. For an offset body with its COG away from the origin of global coordinate system in the XY plane (this configuration is usually found in multibody cases), the phase angle output by AQWA is defined as the local parameter phase angle. But the phase angle output by WAMIT is defined as the global phase angle, which is equal to the local parameter phase angle + global wave phase angle (global wave phase angle is defined as the phase angle of the local coordinate origin with relative to the global coordinate origin, and is related to the spatial location of the body)

AQWA

WAMIT

For a body with its COG located at the origin of global coordinate system in the XY plane

PhaseAngleWAMIT = -PhaseAngleAQWA

But the definition is not perfect, because it is given based on the premise that the wave phase angle is zero (COGx = COGy = 0). For an offset body, the correct phase angle should be

PhaseAngleWAMIT = -PhaseAngleAQWA - k * [x * cos(beta) + y * sin(beta)]
where PhaseAngleAQWA is the phase angle ouput by AQWA, k is the wave number, x and y are locations of the body, and beta is the wave heading.

The real parts of wave excitation loads in 0 degrees wave heading obtained based on -PhaseAngleAQWA are (0.5 and 0.75 are the damping coefficients of external lid, which have no effects on the results)

The corrected results in 0 degrees wave heading are

The corrected results in 10 degrees wave heading are

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Another issue arises in the added mass and radiation damping matrices

I convert the AQWA results into WAMIT format using BEMRosetta, the dimensioned added mass (1,2,wave frequency = 0.0329999 rad/s) * 1025 is -1.7339E+06, and added mass (2,1,wave frequency = 0.0329999 rad/s) * 1025 is -1.8397E+06.

However, for the converted WAMIT results, the added mass (1,7,wave period = 1.903996E+02 s) is -1.794829E+03 (the dimensioned added mass is -1.8397e+06), and the added mass (7,1,wave period = 1.903996E+02 s) is -1.691610E+03 (the dimensioned added mass is -1.7339e+06)

It appears that additional converisons need to be applied to the added mass and radiation damping matrices for multibody cases.

WEC-Sim BEMIO seems to have the same issues regarding the wave phase angle and radiation coefficients.

Some related results can be found here

I hope these efforts meet with your approval

Best regards,
Tianyuan

[izabala123]

Hi Tianyuan

You are absolutely right, and you have explained it very well. We have been aware of this problem for a long time, but in order to make conclusive tests we needed Wamit.
We have just started a collaboration with a team that does have Wamit, and we hope to find an answer to this problem soon.
We will keep you informed.

Best regards
Iñaki

[hachikoi1]

Hi Iñaki
Perhaps I made a mistake in the treatment of added mass and radiation damping. In WEC-Sim, the cross coupling of boty-to-body case always place the accelerations of BODY 1 at A (1:6), and place the accelerations of BODY 2 at A (7:12), etc.

[hachikoi1]

Hi Iñaki
Perhaps I made a mistake in the treatment of added mass and radiation damping. In WEC-Sim, the cross coupling of boty-to-body case always place the accelerations of BODY 1 at A (1:6), and place the accelerations of BODY 2 at A (7:12), and so on.

Therefore, the added mass (1,2,wave frequency) in AQWA .AH1 file should be placed to (7:12,1:6) of added mass matrix during the time-domain caculations, and added mass matrix (7:12,1:6) would multiply with A (1:6). The results of added mass matrix (7:12,1:6) * A (1:6) represent the effects of the radiation wave caused by the motions of the first body on the second body.
From this point, the conversion of radiation coefficient in BEMRosetta has no problem
Please let me know your thoughts

Best regards,
Tianyuan

[izabala123]

Hi Tianyuan

Yes, as far as I know there is no possible misunderstandings with the hydrodynamic coefficients in multibody cases, but about the phase of the forces. We will soon carry out the analysis and propose a possible common approach. We will comment on this.

Best regards
Iñaki

[hachikoi1]

Hello Iñaki izabala123
Any progress on this issue? I am more than happy to contribute if there are any challenges.

Best regards,
Tianyuan

[izabala123]

Hi Tianyuan

Thank you for your follow-up. For external reasons the issue has been delayed, but we are now giving it a boost. If you have a special urgency for higher order reasons, please contact me directly and we will make a special effort.

Iñaki