**6. Conclusions**

The modified BEMT code for a tensioned mooring turbine itself is a very efficient tool and provides a fast simulation process. A 3 min simulation of a 0.1 [s] time step for 20 elements per blade and 0.5 [m] mooring line element lengths on a personal computer with 4 i7 cores takes approximately 1 h. The output contains various data, for example, inflow conditions on blade elements and forces on each element. The status of the turbine can be checked at every time step, and a simple animation can be generated for motions of the turbine. This is an efficient methodology for a highly dynamic system, such as a tensioned mooring supported turbine and other taut mooring systems, for checking its performance under various environmental conditions.

The dynamic marine climate causes significant load fluctuations on TSTs. This study found that the tensioned mooring supported system has a positive effect on thrust load reduction in most sea states. The system performance is satisfactory in swell waves, which have a long wavelength. Both thrust and torque fluctuations decrease significantly. The tensioned mooring-supported TSTs are useful for the swell environment or Stokes waves with long wavelengths. Therefore, installing this system can improve fatigue performance when compared with rigid supported TSTs.

In extreme conditions, such as harsh winter storms, the tensioned mooring supported TSTs significantly reduce the thrust loading; however, the turbine should be shut down and protected from potential damage to the blade due to negative torque. Furthermore, this stall phenomenon can be investigated by improving the blade design and adding a high angle of attack pitch angle to the blade so that the turbine can work under extreme conditions with a favourable load reduction.

The loading on the turbine is always calculated by a quasi-static method in most floating tidal turbine simulations, but the station keeping system uses a quasi-dynamic analysis. This study tried to combine the turbine loading calculation and dynamics of the mooring system by a modified BEMT code. However, this model can be enhanced with the addition of the torque calculation due to the added mass effect on blade sections caused by the quasi-static method, which results in the torque fluctuations. Further investigation should be done into the mass effects added to the mooring supported turbine blade.

In Stokes waves with short wavelengths, such as sea state 3 in the previous sections, the tensioned mooring supported TST can operate at the position where the wave particle paths can reach the whole turbine. For this, the diameter of the turbine must not to be too large and the buoy must supply a larger buoyancy when compared with the thrust loading

on the turbine. The turbine can operate at an appropriate location in a water column. However, the load reduction in this condition is still not as satisfactory as under the other sea states; the performance is approaching that of the rigid supported turbine. Therefore, to obtain a satisfactory load reduction in thrust, the tensioned mooring supported system must be designed for application in environments where the water is not excessively deep.

The vertical velocity component of the wave motion had a large influence on the rotor out-of-plane bending moment of a turbine. Furthermore, the tension mooring supported turbine itself has a vertical velocity because it can move in a vertical direction, thus the out-of-plane bending moment may be greater than a rigid supported turbine. Furthermore, the torque on the rotor is also affected by the vertical velocity of the turbine itself due to the Morison effect. It is obvious that the vertical motion of the turbine has a significant impact on the design of the TST's drive train or internal components; therefore, investigations of the influence of the turbine's vertical velocity on the rotor out-of-plane bending moment should be further investigated in the future. On the other hand, future modifications to the original Morison effects may not be applicable to the blade elements on a turbine that can move in a vertical direction; therefore, modifications of Morison effects should be improved in the future. In extreme sea states, such as harsh winter storms, greater blade profiles and pitch angles should be investigated in order to avoid the negative torque. Adjustable rotor speed will be an another research target in the future and should be applied to the model in order to produce a reliable torque result.

**Author Contributions:** Conceptualization, S.F. and C.J.; methodology, S.F.; software, S.F.; validation, S.F. and C.J.; formal analysis, S.F.; investigation, S.F.; resources, S.F.; data curation, S.F.; writing original draft preparation, S.F.; writing—review and editing, S.F. and C.J.; supervision, C.J.; project administration, C.J.; funding acquisition, C.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by EPSRC, UKRI grant No. EP/K013319/1.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable No new data were created or analyzed in this study. Data sharing is not applicable to this article.

**Acknowledgments:** The authors would like to thank EPSRC, UK RI for their support of this research via the award of Grant No. EP/K013319/1 Reducing the Costs of Marine Renewables via Advanced Structural Materials (ReC-ASM).

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

#### **References**

