Hello everyone,

In OpenFast documentation, there is damping force.

I know that radiation force contains two contributions: from added mass and the other from radiation damping. I know also there is structural damping.

So where the damping force in the doc did come from ???

Also, until i don’t know why in articles that contains analytical MDOF models, we omit the memory effect ???

Finally, in linear wave theory, Morison equation is used when the body is small compared to wavelength. The Morison formula contains added mass. So in the equation of motion we have two times added mass matrix ???

Thank you for your help !!!

Dear @Riad.Elhamoud,

I’m not really understanding your questions; please clarify.

Regarding your damping question, can you be more specific which section you are referring to?

Best regards,

Dear @Jason.Jonkman ,

I’m sorry. My questions are not very clear. I have several questions to ask:

1- I was reading in Openfast documentation the theory behind the code. (i didn’t bookmark the page and i can’t find it ). What i read, was the cummins equation which represents the motion of a floating body.

I notice that the equation contains damping matrix which is different from damping coming from radiation. My question is where did this damping come from ???

2- n the litterature, where there is MDOF models based on few DoFs e.g 13 DoF, the authors neglect the memory effect. Why ?

Finally, in linear wave theory, Morison equation is used when the body is small compared to wave length. This formula contains added mass. My question is when we assemble the equation of motion we will {[M] + 2*[A]}*q_double_dot where [M] is the mass matrix and [A] is the added mass matrix at infinite frequency. I multiply [A] by 2 because in the general equation we have added mass and the other comes from Morison equation right ?

Thanks for your help !!!

Dear @Riad.Elhamoud,

Regarding (1), the Cummins equation provides a way for frequency-dependent added mass and damping from wave-radiation to be applied in the time domain, where the damping is expressed as the convolution of the radiation-retardation kernel and the time history of floater velocity. The radiation-retardation kernel is derived from the frequency-dependent radiation-damping matrix via a cosine transform, which is implemented within HydroDyn. See my PhD thesis-turned NREL report for more information: http://www.nrel.gov/docs/fy08osti/41958.pdf.

Regarding (2), I can’t speak specifically about the literature you are referring to, but neglection of the memory effect (or potential flow in general) is often done for small volume structures. I would not expect a factor of 2 to show up when added mass is summed with body mass. When Morison’s equations is combined with potential-flow theory, only the viscous drag contribution should be taken from Morison’s equation if both methods are applied to the same body so as to not double count added mass and wave-excitation loads.

Best regards,

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Dear @Jason.Jonkman

I read chapter 2 in your thesis and the situation now is very clear.

Thank you very much !