*5.4. Influence of Mooring Line Length*

In order to study the influence of line length on the responses of the integrated system, two additional mooring line lengths (924 m and 968 m, which are 5% and 10% longer than the original length 880 m, respectively) are chosen, with an assumption of unchanged locations of fairleads and anchors. The cross-sectional area of each line is inversely proportional to its length so that the total mass of each line is unchanged. The time histories of responses for different line lengths under case 3 are illustrated in Figure 19. It is observed that for the cage responses, the increase in mooring line length mainly influences the surge motion, while the heave and pitch motions are slightly affected. The statistics of surge motion are illustrated in Figure 20. Note that the percentages in the figure indicate the reduction of the corresponding index relative to the result with respect to the 880-m-long line. The positive and negative values indicate increase and decrease, respectively. For example, 404.8% indicates that the maximum surge motion with a 924-mlong line is 404.8% larger than that with an 880-m-long line. It is seen that with the increase in line length, the surge motion becomes remarkable.

(**a**)

**Figure 19.** *Cont*.

**Figure 19.** Comparison of time histories of the fishing cage and wind turbine responses for three mooring line lengths under case 3. (**a**) Cage responses. (**b**) Wind turbine responses.

**Figure 20.** Statistics of surge responses for three line lengths.

As for the response of the wind turbine, although the surge movement is markedly affected, the increasing line length has a slight impact on them, which is attributed to the function of the wind turbine controller. However, the response curves have a certain offset backward. This is due to the large surge motion caused by the significant increase in line length, which delays the time for the wind to reach the rotor, thus, delaying the wind turbine responses.

Figure 21 shows the comparison of the upwind mooring line tension at the fairlead for three line lengths. It is found that with the increase in mooring line length, the maximum and mean line tensions reduce. This change in trend is opposite to that of the surge motion. The increase in line length has less effect on the standard deviation of line tension, which is related to the fact that the increasing line length has little influence on cage pitch and heave motions, as shown in Figure 19a. In addition, it is seen that a further increase in line length does not further significantly reduce the line tension. To be specific, when the line length increases by 5%, the maximum line tension decreases by 45.7%, while when the line length increases by 10%, the maximum line tension only decreases by 52.9%. The same change trend occurs in the mean line tension.

**Figure 21.** Comparison of upwind line tension at fairlead for three line lengths. (**a**) Time histories. (**b**) Statistics.

#### **6. Conclusions**

In this paper, a state-of-the-art concept of a floating offshore wind turbine integrated with a steel fishing cage is investigated. First, the structural configuration and dimensions of this integrated system are presented. Second, the dynamics model of the integrated system is established through FAST and AQWA. Specifically, the upper wind turbine system is modeled in FAST, while the lower fishing cage is modeled in AQWA. Information exchanges between the two codes. Third, for the designed integrated system, a blade-pitch generator-torque controller is applied. A coupled aero-hydro-elastic-servo model is then constructed. Finally, a series of simulations under selected load cases are performed to explore the dynamic response behaviors of the integrated system. The influence of mooring line length is additionally studied. Key conclusions of this work are listed as follows.

(1) For the operating conditions, the rated wind speed condition is the most important condition for the integrated system because large pitch motion occurs, which, in turn, influences the generator power production. On the other hand, in the extreme wind conditions, surge motion becomes higher and exhibits significant oscillation.

(2) Overall, the turbulent wind has some influence on the surge and pitch motions, but with no influence on the heave motion. The wave frequency component can be seen in the surge, pitch and heave responses of the fishing cage, especially in the heave response. Additionally, the surge and pitch motions have no influence on the heave motion.

(3) The tower–base fore-aft bending moment is mostly affected by turbulent wind, in addition to the cage pitch motion, irregular waves, and blade rotation effect. For the blade– root out-of-plane bending moment, the turbulent wind and 1P-effect have an important effect on the blade response.

(4) At the above-rated condition, compared with heave and pitch motions, the cage surge motion is more affected by the increase in mooring line length. The wind turbine responses are slightly influenced by the increasing line length, but exhibit delay caused by the large surge motion. In addition, with the increase in mooring line length, the maximum and mean line tensions reduce, but the standard deviation of line tension is less affected. A further increase in line length does not further remarkably reduce the line tension.

It must be pointed out that the focus of this paper is to provide an idea of conceptual design, modeling and simulation analysis for the integrated wind turbine-fishing cage system. More detailed structural design optimizations, strength checks and experimental tests for the integrated system need to be further carried out in future.

**Author Contributions:** C.Z.: Simulation, Data curation, Writing-original draft, Writing-review & editing; J.X.: Investigation, Data curation; J.S.: Information retrieval, Software; A.L.: Simulation; M.C.: Funding acquisition; H.L.: Supervision, Methodology; C.G.: Data curation; S.X.: Supervision, Methodology, Writing-original draft. All authors have read and agreed to the published version of the manuscript.

**Funding:** This paper was funded by Key R & D program of Shandong Province demonstration project of deep sea aquaculture technology (No.: 2021SFGC0701); National Natural Science Foundation of China (No.: 41976194), Project of Science and Technology Research Program of Chongqing Education Commission of China (No.: KJQN202101133), and Scientific Research Foundation of Chongqing University of Technology (No.: 2020ZDZ023).

**Data Availability Statement:** The data is in the article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

