Difference in tower base moment due to different modeling of tower and floating structure

Thanks for all your help.
I am currently analyzing a semi-submersible floating structure with a 15 MW class wind turbine.
I have made 3 different analytical models and compared the tower base moments. The analysis is inputting irregular waves (Hs=about 13m, Tp=about 13s) which is equivalent to DLC6.1. The tower base moment is an important item in the design of the tower and the floating structure, but the modeling methods produced very different results.
Which results should we believe?

In Case 1, the tower is built with ElastDyn and the floating body is built with potential theory using WAMIT, with ElastDyn damping of 0.2%. The moments in this model appear to be linked to the pitch motion of the floating body.
The damping of ElastDyn and SubDyn is 0.2%. The moments in this model are coupled to the Pitch motion of the floating body, and the response of the first order natural period of the tower (about 3 seconds) is strongly manifested.
In Case 3, the tower is made of SubDyn (elastic body) and the floating body is made of HydroDyn (strip theory, Morrison formula) and SubDyn (elastic body). Moments in this model appear to be more amplified than in Case 1, linked to the Pitch motion of the floating body.

The moment magnitudes are Case1<Case2<Case3, with Case3 being more than twice as large as Case1. fatigue design is expected to be severe.
I am not sure which model response is closer to the truth. I am not sure which model to design.

Dear @Yosuke.Matsumoto,

Given that it looks like your floater is quite rigid, I would not expect the modeling of hydro-elasticity to have a large impact on the tower-base loads. So, I would expect all three models to give more similar results. I would think you’d be able to set the model properties from each Case to give more similar results.

Regarding Case 1, how you are accounting for viscous effects that are captured in Case 3?

Regarding Case 2, how are you modeling the hydrodynamic loads? Are these matching Case 1 or 3?

Regarding Case 3, are you setting the added mass and dynamic pressure coefficients of the strip-theory model so that the added mass and fluid-inertia loads are similar between strip-theory and potential flow? Moreover, given that you are running Case 3, does this mean that you got your OpenFAST model working from the related forum post (Anomalous response when modeling a tower in SubDyn - #20 by Jason.Jonkman); or did you have to lock platform DOFs or limit the number of Craig-Bampton modes to get this response?

Do you have a sense (based on experimental measurements or high-fidelity (e.g., CFD) modeling) which Case is providing a more realistic solution?

Best regards,

Thanks for the reply.

Let me explain about Case1, I am using AxCd and MemberCd. These values are the same as in Case2 and Case3. the AxCd is set at the heave plate position of the side column and at the bottom of the center column. the AxCd is 9.6 based on the example setting of 5MW_OC4Semi_WSt_WavesWN in r-test. MemberCd for cylindrical members (center and side columns) uses 1.170 as the general value for cylinders. MemberCd for rectangular members (pontoons) is based on the general Cd for rectangles, modified to a value corresponding to a cylindrical cross section equivalent to the rectangular cross section defined in HydroDyn. Specifically, it is about 2.0 to 2.5.

The hydrodynamic loads in Case 2 are modeled using the Morrison equation; the Cd is the same as in Case 1. MemberCa for cylindrical members (center and side columns) uses 1.000 as the general value for cylinders. MemberCa for rectangular members (pontoons) is based on the general Ca for rectangles, modified to a value corresponding to a cylindrical cross section equivalent to the rectangular cross section defined in HydroDyn. Specifically, it is about 2. AxCa is set to 0 except for the heave plate. The AxCa of the heave plate has been adjusted so that the RAO of the model calculated by potential theory (Case 1) and the RAO of the model in Case 2 are approximately the same. A dynamic pressure coefficient Cp of 1.0 is used.

Cd, Ca, and Cp in Case3 are the same as in Case2. the model in Case3 is not working correctly at this time. For this reason, I have set the DOFs for Surge, Heave, and Pitch to True and all others to False for Case 3. In other words, I am analyzing the 2D model. The Nmodes of SubDyn is set to 21. Note that Case 1 and Case 2 are the result of setting 6 DOFs to True.

I have not been able to ascertain which case is a realistic response. For this reason, I am wondering which case to use. However, I would like to use Case2 or Case3 which works correctly because I want to find the sectional force of the floating body.

Some of the above mentioned information is assumed due to my lack of knowledge. If you know, please let me know.
I do not know how to calculate AxCd. For this reason, I am using 9.6 to mimic the example.
I do not know how to calculate AxCa. I used the value obtained by dividing the volume of the hemisphere corresponding to the diameter of the heave plate by the volume of the heave plate (about 20), but the natural period of the floating body became very long. We therefore decided that this setting method was incorrect and do not use it anymore.
I do not know how to calculate AxCp and MemberCp. I use 1.0, which is the recommended value in the manual.

Dear @Yosuke.Matsumoto,

Given a potential-flow solution, you should be able determine Ca and Cp of the strip-theory solution so that the strip-theory solution provides a reasonable approximation of the wave-excitation and added mass from the potenial-flow solution over a given frequency range.

The drag coefficients (Cd) of the strip-theory solution can only really be tuned against results from measurements and/or high-fidelity modeling for complex floater geometry such as semisubmersibles. One work package of the upcoming OC7 project being proposed soon within IEA Wind will focus on developing recommend practices for determining Cd.

Best regards,

Can you please elaborate on the first sentence?
Do you mean to use the WAMIT output file (extension 1) to find Ca and Cp?

Dear @Yosuke.Matsumoto,

Yes, the WAMIT *.1 file contains the frequency-dependent added mass matrix, with which you can use to calibrate Ca, and the WAMIT *.3 file contains the frequency- and direction-dependent wave-excitation load vector, with which you can use to calibrate Ca+Cp.

Best regards,

Please let me know how to proofread, or what literature you have written on how to do so.

I have tried to calculate Ca using the WAMIT *.1 file, but I am not sure if this is the right approach.

  1. Multiply the dimensionless quantity in the WAMIT *.1 file by the density of seawater 1025 kg/m3 to get the unit of kg.
  2. In the case of A(3,3), dividing by (drainage volume x 1000), I obtained a value that seems to be the added mass coefficient. In the case of A(5,5), dividing by the moment of inertia of the entire system yielded a value that appeared to be the added mass coefficient.

Also, I am not sure how to use this going forward. Should this Ca be set uniformly for the elements defined in the strip theory? How should I distinguish between element lateral and axial directions?

As for the WAMIT *.3 file, it is more complicated and I could not imagine how it could be used to calibrate Ca+Cp.

Question in response to your initial response.

  1. How should I set up the hydrodynamic forces on the floating body in order to get approximately the same result for the moments at the base of the tower for the three models?

  2. I am having trouble deciding which of the responses from Case 1 to Case 3 is more certain. Which one do you think is more plausible? Just knowing whether the moment at the base of the tower of a floating offshore wind turbine is dominated by the natural periodic oscillation of the floating body’s pitch as in Case 1 or by the natural periodic oscillation of the tower as in Case 2 would be helpful to me.

In case you are interested, you can obtain the hydrostatic stiffness matrix and the added mass matrix from the strip-theory model by linearizing HydroDyn. To do that, you have to use the HydroDyn standalone version. I believe this is not included in the official OpenFAST release yet, but you can use the executable and input files from here: HydroDyn_linearization - Google Drive

To run this, you only need to call the executable and provide the driver (*.dvr) as input file. Check line 12 of the driver to understand at what location in the space the matrices are expressed. These matrices will be written down in a YAML file.

We performed some code-to-code verifications between HydroDyn and RAFT during the OC6 Phase IV project (TetraSpar design). See below for reference:

I hope that helps.

1 Like

Thank you very much. I will try it.

Hi Yosuke,

I am not aware of any reference that explains this procedure of tuning Ca based on results from a radiation/diffraction code such as WAMIT. However, the strip theory method implemented in HydroDyn is detailed in the user’s guide (https://www.nrel.gov/wind/nwtc/assets/downloads/HydroDyn/HydroDyn_Manual.pdf). From that, the idea would be to use those equations to approximate the hydrodynamic coefficients obtained with WAMIT. These coefficients are the added mass matrices, given in WAMIT .1 file, and the wave exciting forces, given in WAMIT .2 or .3 file (depending on how you set WAMIT to solve the problem).

I would say that you are in the right direction in this post of yours, but the problem is that different parts of the structure do not contribute equally to the added mass (or wave loads) in each of the six degrees of freedom. For instance, this example where you divided A(3,3) by the total mass of the cylinder would work for a horizontal cylinder, as its whole length would be perpendicular to the direction of motion. But it would not work for a vertical cylinder, in which case the volume used to dimensionalize the added mass coefficient is different than the volume of the cylinder. Mind you, even the added mass coefficient would be a different one in the HydroDyn input file, as in the axial direction the software uses axCa instead of the one relative to the transverse direction, Ca. This is explained in details in the user’s guide linked above.

Also, as you noticed, you would need a frequency dependent added mass coefficient to match the results from WAMIT. This is due to wave radiation, an effect that is not captured by strip theory. What I usually do is to try to match the added mass at the expected natural frequencies of motion, while also trying to match the excitation wave forces. It is usually (if ever, for a real structure) not possible to match both the added mass and the excitation wave forces with a given set of added mass coefficients, so you have to find a middle ground that is good enough for you. I dare to say that this is some kind of art :wink:

I tried to organize a Jupyter notebook based on some scripts that I use, which you can find here. I included an example that corresponds to a slightly modified version of the UMaine VolturnUS semisubmersible, so that you can run the notebook. There are some comments in the scripts that I hope can be useful to understand/use this method of tuning the strip theory solution based on WAMIT outputs.

1 Like

Thank you for your valuable information. I will check it out.