Question about axial drag in Morison.f90

Hello everybody,

I am sorry to bother, but I was taking a look at the source code of OpenFAST and I could not understand a section of Morison.f90, so I was hoping that someone would be kind enough to explain it to me. It concerns the calculation of axial drag and is located around line 4610 of the file, as reproduced below:

vmag =  nodeInWater * ( vrel(1)*p%L_An(1,J) + vrel(2)*p%L_An(2,J) + vrel(3)*p%L_An(3,J) )
AnProd = p%L_An(1,J)**2 + p%L_An(2,J)**2 + p%L_An(3,J)**2
IF (EqualRealNos(AnProd, 0.0_ReKi)) THEN
	dragFactor = 0.0
        dragFactor = p%Nodes(nodeIndx)%JAxCd*p%WtrDens*abs(vmag)*vmag / ( 4.0_ReKi * AnProd )

Quoting the comment right above this block of code, vmag is “the dot product of the relative velocity vector with the directional Area of the Joint”, and I guess this is why AnProd is dividing the product abs(vmag)*vmag in the expression of dragFactor. However, I did not understand why the expression is divided by 4 and not by 2, as I would expect. Looking at the OC4 test case that is shipped with Fast v8, I noticed that the specified value of AxCd is 9.6, i.e. twice the one documented in “Definition of the semisubmersible floating system for Phase II of OC4”, and I was wondering if this is related to this division by 4. If so, since only the bottom joint has a non-zero AxCd, this would lead to a “total” AxCd of 4.8, wouldn’t it? Please tell me whether this is the case or whether I completely misunderstood this part of the code.

Best regards

Hi Lucas,

The factor of 4 instead of 2 is intentional and related to the use of AxCd = 9.6 instead of 4.8 in the OC4-DeepCwind semisubmersible model.

The HydroDyn module applies loads to the ends of strip-theory members on both sides of the member. A flat disk can be modeled as a member with very short length. Normally, for a flat disk, the drag is the result of increased pressure on the front side and decreased pressure on the back side. So, we developed HydroDyn to capture this effect. E.g., if you want a flat disk to have an axial drag coefficient of 2.0, you can set AxCd = 2.0 on the each end of the member, and rather than getting twice the drag, you’ll get the drag force you’d expect because a factor of 1/4 will be applied to both ends (instead of a factor of 1/2).

For the OC4-DeepWind semi, we knew wanted a drag coefficient of 4.8 based on the full cross-sectional area of the offset lower column. Because the top end of the offset lower column is not fully wetted (due to the offset upper column), we decided it would be easier to specify twice the drag coefficient, but only applied to the lower end of the offset bottom column.

For more information on the strip-theory solution of HydroDyn, see slides 11-14 of the following presentation given at a past FAST modeling workshop: … onkman.pdf.

Best regards,

Thank you very much for your prompt reply, Dr. Jonkman! Both your answer and the presentation were very helpful.

Best regards,