# Directionality Effects of Aligned Wind and Wave Loads on a Y-Shape Semi-Submersible Floating Wind Turbine under Rated Operational Conditions

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Specification of the Semi-Submersible Floating Wind Turbine

- (1)
- Prestressed concrete is used to construct the major structure, which is expected to reduce manufacturing cost and a better resistance against corrosion and fatigue compared with steel;
- (2)
- Three rectangle section pontoons are arranged between the outer columns and the center column for connection, providing sufficient strength and stiffness for the platform. No brace arm is designed so as to reduce fatigue occurred at the joints [8];
- (3)
- The base columns and large-section pontoons are helpful to provide space for ballast, lower the center of gravity and alleviate the motion response, especially the heave motion.

^{3}is adopted for the platform construction. By carrying out preliminary structural analysis, the platform wall of 350 mm thickness is robust enough to resist environmental loads. Furthermore, in order to increase the structural stiffness and separate watertight compartments, stiffeners and bulkheads are arranged inside the platform and considered during the calculation of structural properties, which are summarized in Table 1.

## 3. Setup of the Model Tests

#### 3.1. Test Facility

#### 3.2. Experimental Models

_{d}is the drag coefficient which is set to 1.9 according to the DNV rule [40]; ρ is the air density; v is the wind speed at hub height; A is the area of the disc. The wind thrust force was calibrated in the small test section of the wind tunnel. An ATI force balance mounted at the tower base was employed for the wind turbine thrust measurement. The diameters of the discs were adjusted by trial and error to match the target wind thrust forces. Finally, the thrust force comparison between the model and the prototype and the equivalent wind turbine model for the rated wind condition are presented in Figure 3. Note that the prototype data was derived from the wind turbine simulator Bladed. It is shown that the averaged measured values agree quite well with the targets. The diameter of the disc 110 cm.

^{4}N/m in prototype), which was determined by linear least-squares fitting of the displacement-restoring force/moment curve of the prototype catenary mooring lines. The comparisons of the surge-restoring force curves and the pitch-restoring moment curves between the catenary and the spring mooring system in three load directions are illustrated in Figure 5. Except slight discrepancies in the large surge displacements, the horizontal restoring stiffness of the spring mooring system agrees fairly well with the prototype catenary mooring system. The figure also indicates that the restoring stiffness of three load directions is basically consistent with each other. In addition, in order to examine the surge-pitch coupling effects on the restoring force/moment of the mooring lines, surge-restoring force curves with pitch motion and pitch-restoring moment curves with surge motion are plotted in Figure 6. Obviously, the platform pitch motion is less influential on the mooring restoring forces according to Figure 6a–c. In term of the restoring moments, the impact of platform surge motion is significant. Compared with the prototype, the spring mooring lines tend to provide larger restoring moments with the increase of surge motion along the positive direction of wind/wave loads. However, on the whole, it is feasible to emulate the catenary mooring system by horizontal spring mooring lines in the flume model tests.

#### 3.3. Measuring Instruments

#### 3.4. Wind and Wave Environment Calibration Tests

_{s}and spectral peak period T

_{p}are 11.5 m/s, 2.23 m and 6.74 s respectively, which are determined on the basis of long-term met-ocean data from the south-eastern coast of China.

#### 3.5. Test Matrix

## 4. Numerical Simulations

**M**is the structure mass matrix;

**A**(∞) is the added mass matrix at infinite frequency; $\mathbf{q}\left(t\right)$, $\dot{\mathbf{q}}\left(t\right)$ and $\ddot{\mathbf{q}}\left(t\right)$ are the platform displacement, velocity and acceleration vectors respectively;

**K**(τ) is the wave-radiation-retardation kernel which depends on the added mass and radiation damping matrix;

**C**is hydrostatic restoring matrix;

**B**

_{add}is the user-defined additional quadratic damping matrix;

**F**

_{wave}(t) is the excitation load from incident waves;

**F**

_{Aero}(t) is the aerodynamic load from wind turbine;

**F**

_{Lines}(t) is the load from the mooring lines. The hydrodynamic, aerodynamic and mooring loads applied in the numerical models will be discussed in the following subsections.

#### 4.1. Hydrodynamics Modeling

**F**

_{wave}(t) in Equation (1). It relies on the body form and wave headings. The third term,

**Cq**(t), represents the restoring force/moment resulting from the effects of waterplane area and the gravitational-buoyancy as the displacements of the platform (heave, roll and pitch) take place. The hydrodynamic coefficients of these three terms can be obtained by solving the boundary-value problem using panel method [45].

**B**

_{add}is available in FAST, helping to tune the numerical model to match damping to experimental results, such as free decay tests.

#### 4.2. Aerodynamics Modeling

_{wi}(t) is the wind speed at the height of the i-th component at time t; v

_{i}(t) is the motion velocity of the ith component along the incoming wind direction at time t; A

_{i}is the projected area of the i-th component along the incoming wind direction. Before the dynamic simulations of the FOWT system started, the hydrodynamics module was switched off and the wind drag coefficients of the blades and tower were tuned to match the average tower base forces/moments measured in the wind turbine calibration test.

#### 4.3. Mooring Line Modeling

#### 4.4. Structural Modeling of the Tower

## 5. Results and Discussion

#### 5.1. Free Decay Tests

#### 5.2. Regular Wave Tests

^{5}for the low-period waves, whereas 10

^{4}for the long-period waves. Correspondingly, the drag coefficients for circular section in the former circumstance (below 1.0) are smaller than the latter (over 1.1) according to Schewe’s study [51]. Since flow-separation-induced drag is a large component of the total hydrodynamic damping [11], the viscous damping effects tend to be more significant in the long-period waves than those in the low-period waves. The quadratic damping coefficients of the numerical models are determined based on free decay tests. Figure 12a,c imply that these damping values are applicable in the low-period wave cases. For that reason, the numerical models are inclined to overestimate the motion responses in the long-period waves. Nevertheless, this study mainly focuses on the rated operational sea state whose wave periods are less than 10 s. Therefore, the selected quadratic damping coefficients meet the requirement of the study.

#### 5.3. Steady Wind Tests

#### 5.4. Irregular Wave Tests

_{1}is one of the frequency pairs which makes $\left|{f}_{1}-{f}_{2}\right|$ equal to the surge/pitch natural frequency. Figure 18a shows that the second-order surging forces for the 90° wave are remarkably larger than those for the other two wave headings between 0.15 and 0.18 Hz, which belong to the prominent range of the rated operational wave condition. Beyond that range, the QTF values for 90° drop down rapidly and the local maximum values tend to occur in the 60° wave. However, the wave energy in such a high frequency range is less influential. Figure 18b demonstrates that the floating platform is more likely to suffer from the largest pitching moment under the 60° wave attack.

_{d}is the difference frequency;

**QTF**

^{F}(ω

_{d}) and

**QTF**

^{M}(ω

_{d}) are the load and motion QTF vector respectively;

**B**is the radiation damping matrix.

_{mn}is the phase of motion QTFs; φ

_{m}and φ

_{n}are the random phases of stochastic waves at the frequency of ω

_{m}and ω

_{n}, respectively, which are assumed to uniformly distribute between 0 and 2π [49]. It is worth noting that the magnitudes of motion response differ from different wave phase values. To get an overall impression of the differences between the three wave directions, the summation is done for 300 different wave seeds. For comparative purpose, identical wave phase values are taken between the three wave headings for each wave seed. The second-order motion responses along with different wave seeds are presented in Figure 19. In accordance with the phenomena observed in the tests, larger surge motion tends to occur in the 90° wave, while larger pitch motion more likely to be seen in the 60° wave. For clarity, the response values are averaged and plotted by the dash lines in the figures. This analysis verifies the inference that the wave load directionality effects are attributable to the second-order hydrodynamic loads.

_{twr}and nacelle acceleration a

_{ncl}are also investigated and the simulation results are shown in Figure 20. The wind turbine is excited in three frequency components, i.e., the platform pitch natural frequency, the incident wave frequency and the fundamental tower-bending frequency. Thereinto, the wave-frequency excitation, which is induced by the first-order hydrodynamic loads, is the most significant component for the wind turbine dynamic responses. The largest and smallest M

_{twr}and a

_{ncl}PSD values are seen in the 60° and 90° wave respectively. This trend is consistent with the RAO results shown in Figure 12e,f and it is fundamentally correlated to the first-order wave loads in the surge DOF (as Figure 13 shows). Figure 20 also shows that M

_{twr}is more sensitive to the platform pitch motion compared with a

_{ncl}. Large M

_{twr}PSD values are predicted in the pitch natural frequency, which can be explained by the larger moments induced by the gravitational loads as the wind turbine tilts. Once again, the dynamic responses for 60° are larger than the other two directions. Based on the above analysis, it can be appreciated that this part of the difference originates from the second-order hydrodynamic loads. As a whole, both the first- and second-order hydrodynamic loads contribute to the differences of M

_{twr}and a

_{ncl}between wave directions. It seems that the former is more influential.

_{twr}and a

_{ncl}varies a lot with wave directions. The maximum values of M

_{twr}and a

_{ncl}in the 60° wave are nearly two times larger than those of the 90° wave, demonstrating the great impact of the wave load directionality effects on the wind turbine dynamics.

#### 5.5. Combined Wind and Waves Tests

_{twr}and a

_{ncl}under the rated combined wind and wave condition are also examined and the PSD diagrams are presented in Figure 24. By comparing the results shown in Figure 20 and Figure 24, the influence of wind loads on the dynamic characteristics of the wind turbine can be summed up as follows: firstly, the responses in pitch natural frequency are suppressed into a very small level; secondly, the components in incident wave frequencies are augmented. As mentioned above, the former is related to the second-order pitch motion which is suppressed by the quasi-static wind loads, while the latter is correlated with the first-order surge motion which is slightly amplified by the wind loads, eventually leading to such M

_{twr}and a

_{ncl}responses under the rated combined wind and wave condition. In this case, the M

_{twr}and a

_{ncl}distinctions between load directions mainly attribute to the first-order wave loads. However, it is worth noting that these conclusions are restricted to the equivalent irrotational wind turbine model and the steady wind conditions used in the tests.

_{twr}and a

_{ncl}is shown in Figure 25. The mean M

_{twr}depends on average wind loads. As Figure 15 shows, the platform motions are independent of wind load directions. Hence, it can be appreciated that the mean M

_{twr}values are identical between load directions. The directionality differences in the maximum and standard deviation values once again demonstrate the importance of load directions for the Y-shape semi-submersible floating wind turbine.

#### 5.6. Simulations with a Fully Operational Wind Turbine and Realistic Wind and Waves

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Breton, S.; Moe, G. Status, plans and technologies for offshore wind turbines in Europe and North America. Renew. Energy
**2009**, 34, 646–654. [Google Scholar] [CrossRef] - Ederer, N. The market value and impact of offshore wind on the electricity spot market: Evidence from Germany. Appl. Energy
**2015**, 154, 805–814. [Google Scholar] [CrossRef] - Esteban, M.; Leary, D. Current developments and future prospects of offshore wind and ocean energy. Appl. Energy
**2012**, 90, 128–136. [Google Scholar] [CrossRef] - Musial, W.; Butterfield, S.; Boone, A. Feasibility of floating platform systems for wind turbines. In Proceedings of the 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 5–8 January 2004; The American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2004. [Google Scholar]
- Stiesdal, H. Hywind: The world’s first floating MW-scale wind turbine. Wind Dir.
**2009**, 52, 1–9. [Google Scholar] - Roddier, D.; Cermelli, C.; Aubault, A.; Weinstein, A. WindFloat: A floating foundation for offshore wind turbines. J. Renew. Sustain. Energy
**2010**, 2, 33104. [Google Scholar] [CrossRef] - Fukushima Offshore Wind Consortium. Fukushima Floating Offshore Wind Farm Demonstration Project (Fukushima FORWARD). Available online: http://www.fukushima-forward.jp/pdf/pamphlet3.pdf (accessed on 8 December 2017).
- Karimirad, M.; Michailides, C. V-shaped semisubmersible offshore wind turbine: An alternative concept for offshore wind technology. Renew. Energy
**2015**, 83, 126–143. [Google Scholar] [CrossRef] - Bruinsma, N. Validation and Application of a Fully Nonlinear Numerical Wave Tank. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2016. [Google Scholar]
- Liu, Y.; Li, S.; Yi, Q.; Chen, D. Developments in semi-submersible floating foundations supporting wind turbines: A comprehensive review. Renew. Sustain. Energy Rev.
**2016**, 83, 433–449. [Google Scholar] [CrossRef] - Coulling, A.J.; Goupee, A.J.; Robertson, A.N.; Jonkman, J.M.; Dagher, H.J. Validation of a FAST semi-submersible floating wind turbine numerical model with DeepCwind test data. J. Renew. Sustain. Energy
**2013**, 5, 023116. [Google Scholar] [CrossRef] - Robertson, A.; Jonkman, J.M.; Masciola, M.; Song, H.; Goupee, A.; Coulling, A.; Luan, C. Definition of the Semisubmersible Floating System for Phase II of OC4; Report No. NREL/TP-5000-60601; Contract No. DE-AC36-08-GO28308; National Renewable Energy Laboratory: Golden, CO, USA, 2014.
- Jonkman, J.M.; Buhl, M.L., Jr. FAST User’s Guide; Report No. NREL/EL-500-38230; Contract No. DE-AC36-99-GO10337; National Renewable Energy Laboratory: Golden, CO, USA, 2005.
- Michailides, C.; Gao, Z.; Moan, T. Experimental study of the functionality of a semisubmersible wind turbine combined with flap-type Wave Energy Converters. Renew. Energy
**2016**, 93, 675–690. [Google Scholar] [CrossRef] - Gao, Z.; Moan, T.; Wan, L.; Michailides, C. Comparative numerical and experimental study of two combined wind and wave energy concepts. J. Ocean Eng. Sci.
**2016**, 1, 36–51. [Google Scholar] [CrossRef] - Chen, J.; Hu, Z. Experimental investigation of aerodynamic effect–induced dynamic characteristics of an OC4 semi-submersible floating wind turbine. Proc. Inst. Mech. Eng. Part M
**2017**. [Google Scholar] [CrossRef] - Bachynski, E.E.; Thys, M.; Sauder, T.; Chabaud, V.; Sæther, L.O. Real-Time Hybrid Model Testing of a Braceless Semi-Submersible Wind Turbine: Part II—Experimental Results. In Proceedings of the 35th International Conference on Ocean, Offshore and Arctic Engineering, Busan, Korea, 19–24 June 2016; American Society of Mechanical Engineers: New York, NY, USA, 2016. [Google Scholar]
- Naess, A.; Moan, T. Stochastic Dynamics of Marine Structures; Cambridge University Press: Cambridge, UK, 2012. [Google Scholar]
- Wan, L.; Greco, M.; Lugni, C.; Gao, Z.; Moan, T. A combined wind and wave energy-converter concept in survival mode: Numerical and experimental study in regular waves with a focus on water entry and exit. Appl. Ocean Res.
**2017**, 63, 200–216. [Google Scholar] [CrossRef] - Moriarty, P.J.; Hansen, A.C. AeroDyn Theory Manual; National Renewable Energy Laboratory: Golden, CO, USA, 2005.
- Jonkman, J.M. Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine. Ph.D. Thesis, University of Colorado, Golden, CO, USA, 2007. [Google Scholar]
- Hall, M.; Goupee, A. Validation of a lumped-mass mooring line model with DeepCwind semisubmersible model test data. Ocean Eng.
**2015**, 104, 590–603. [Google Scholar] [CrossRef] - Wang, L.; Sweetman, B. Multibody dynamics of floating wind turbines with large-amplitude motion. Appl. Ocean Res.
**2013**, 43, 1–10. [Google Scholar] [CrossRef] - Ormberg, H.; Bachynski, E.E. Global analysis of floating wind turbines: Code development, model sensitivity and benchmark study. In Proceedings of the 21st International Offshore and Polar Engineering Conference, Rhodes, Greece, 17–22 June 2012; International Society of Offshore and Polar Engineers: Mountain View, CA, USA, 2012. [Google Scholar]
- Philippe, M.; Babarit, A.; Ferrand, P. Effect of wave direction relative to wind on the motions of offshore floating wind turbine systems. In Proceedings of the 3rd International Conference and Exhibition on Ocean Energy, Bilbao, Spain, 6–8 October 2010; Ocean Energy Systems: Lisbon, Spain, 2010. [Google Scholar]
- Philippe, M.; Babarit, A.; Ferrant, P. Modes of response of an offshore wind turbine with directional wind and waves. Renew. Energy
**2013**, 49, 151–155. [Google Scholar] [CrossRef] - Wayman, E.N. Coupled Dynamics and Economic Analysis of Floating Wind Turbine Systems. Master’s Thesis, Massachusetts Institute of Technology, Cambridge, MA, USA, 2006. [Google Scholar]
- Ramachandran, G.K.V.; Bredmose, H.; Sorensen, J.N.; Jensen, J.J. Fully Coupled Three-Dimensional Dynamic Response of a Tension-Leg Platform Floating Wind Turbine in Waves and Wind. J. Offshore Mech. Arct. Eng.
**2014**, 136, 020901. [Google Scholar] [CrossRef] - Barj, L. Influence of Met-Ocean Conditions on the Loads Analysis of a Floating Wind Turbine. Master’s Thesis, The Pennsylvania State University, State College, PA, USA, 2013. [Google Scholar]
- Barj, L.; Stewart, S.; Stewart, G.; Lackner, M.; Jonkman, J.; Robertson, A.; Matha, D. Wind/wave misalignment in the loads analysis of a floating offshore wind turbine. In Proceedings of the 32nd ASME Wind Energy Symposium, National Harbor, MD, USA, 13–17 January 2014; The American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2014. [Google Scholar]
- Bachynski, E.E.; Kvittem, M.I.; Luan, C.; Moan, T. Wind-wave misalignment effects on floating wind turbines: Motions and tower load effects. J. Offshore Mech. Arct. Eng.
**2014**, 136, 0419024. [Google Scholar] [CrossRef] - Karimirad, M.; Michailides, C. V-shaped semisubmersible offshore wind turbine subjected to misaligned wave and wind. J. Renew. Sustain. Energy
**2016**, 83, 126–143. [Google Scholar] [CrossRef] - Jonkman, J.; Butterfield, S.; Musial, W.; Scott, G. Definition of a 5-MW Reference Wind Turbine for Offshore System Development; Report No. NREL/TP-500-38060; Contract No. DE-AC36-08-GO28308; National Renewable Energy Laboratory: Golden, CO, USA, 2009.
- Martin, H.R. Development of a Scale Model Wind Turbine for Testing of Offshore Floating Wind Turbine Systems. Master’s Thesis, University of Maine, Orono, ME, USA, 2011. [Google Scholar]
- Martin, H.R.; Kimball, R.W.; Viselli, A.M.; Goupee, A.J. Methodology for wind/wave basin testing of floating offshore wind turbines. J. Offshore Mech. Arct. Eng.
**2012**, 136, 020905. [Google Scholar] - Fowler, M.J.; Kimball, R.W.; Thomas, I.D.A.; Goupee, A.J. Design and testing of scale model wind turbines for use in wind/wave basin model tests of floating offshore wind turbines. In Proceedings of the 32nd International Conference on Ocean, Offshore and Arctic Engineering, Nantes, France, 9–14 June 2013; American Society of Mechanical Engineers: New York, NY, USA, 2013. [Google Scholar]
- Wan, L.; Gao, Z.; Moan, T. Experimental and numerical study of hydrodynamic responses of a combined wind and wave energy converter concept in survival modes. Coast. Eng.
**2015**, 104, 151–169. [Google Scholar] [CrossRef] - Wan, L.; Gao, Z.; Moan, T.; Lugni, C. Experimental and numerical comparisons of hydrodynamic responses for a combined wind and wave energy converter concept under operational conditions. Renew. Energy
**2016**, 93, 87–100. [Google Scholar] [CrossRef] - Wan, L.; Gao, Z.; Moan, T.; Lugni, C. Comparative experimental study of the survivability of a combined wind and wave energy converter in two testing facilities. Ocean Eng.
**2016**, 111, 82–94. [Google Scholar] [CrossRef] - Det Norske Veritas. Recommended practice dnv-rp-c205. In Environmental Conditions and Environmental Loads; Det Norske Veritas: Oslo, Norway, 2010. [Google Scholar]
- Ishihara, T.; Phuc, P.V.; Sukegawa, H.; Shimada, K.; Ohyama, T. A study on the dynamic response of a semi-submersible floating offshore wind turbine system Part 1: A water tank test. In Proceedings of the 12th International Conference on Wind Engineering, Gairns, Australia, 1–6 July 2007; Australasian Wind Engineering Society: Gairns, Australia, 2007. [Google Scholar]
- Shan, B.; Zheng, S.; Ou, J. Free vibration monitoring experiment of a stayed-cable model based on stereovision. Measurement
**2015**, 76, 228–239. [Google Scholar] [CrossRef] - Shan, B.; Zheng, S.; Ou, J. A stereovision-based crack width detection approach for concrete surface assessment. KSCE J. Civ. Eng.
**2016**, 20, 803–812. [Google Scholar] [CrossRef] - Faltinsen, O. Sea Loads on Ships and Offshore Structures; Cambridge University Press: Cambridge, UK, 1993. [Google Scholar]
- Lee, C. WAMIT Theory Manual; Massachusetts Institute of Technology: Cambridge, MA, USA, 1995. [Google Scholar]
- Duarte, T.; Sarmento, A.; Jonkman, J. Effects of second-order hydrodynamic forces on floating offshore wind turbines. In Proceedings of the 32nd ASME Wind Energy Symposium, National Harbor, MD, USA, 13–17 January 2014; The American Institute of Aeronautics and Astronautics: Reston, VA, USA, 2014. [Google Scholar]
- Bayati, I.; Jonkman, J.; Robertson, A.; Platt, A. The Effects of Second-Order Hydrodynamics on a Semisubmersible Floating Offshore Wind Turbine; Report No. NREL/CP-5000-61752; Contract No. DE-AC36-08-GO28308; National Renewable Energy Laboratory: Golden, CO, USA, 2014.
- Coulling, A.J.; Goupee, A.J.; Robertson, A.N.; Jonkman, J.M. Importance of second-order difference-frequency wave-diffraction forces in the validation of a fast semi-submersible floating wind turbine model. In Proceedings of the 32nd International Conference on Ocean, Offshore and Arctic Engineering, Nantes, France, 9–14 June 2013; American Society of Mechanical Engineers: New York, NY, USA, 2013. [Google Scholar]
- Roald, L.; Jonkman, J.; Robertson, A.; Chokani, N. The effect of second-order hydrodynamics on floating offshore wind turbines. Energy Procedia
**2013**, 35, 253–264. [Google Scholar] [CrossRef] - Bir, G. User’s Guide to BModes (Software for Computing Rotating Beam-Coupled Modes); Report No. NREL/TP-500-39133; Contract No. DE-AC36-99-GO10337; National Renewable Energy Laboratory: Golden, CO, USA, 2005.
- Schewe, G. On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers. J. Fluid Mech.
**1983**, 133, 265–285. [Google Scholar] [CrossRef] - Kelley, N.D.; Jonkman, B.J. Overview of the TurbSim Stochastic Inflow Turbulence Simulator; Report No. NREL/TP-500-41137; Contract No. DE-AC36-99-GO10337; National Renewable Energy Laboratory: Golden, CO, USA, 2007.
- International Electrotechnical Commission. Wind Turbines—Part 1: Design Requirements; IEC61400-1; International Electrotechnical Commission: Geneva, Switzerland, 2005. [Google Scholar]

**Figure 1.**The ConFloat semi-submersible platform: (

**a**) 3D model; (

**b**) Dimensions of the platform; (

**c**) Side view of the platform; (

**d**) Definition of wind/wave load directions.

**Figure 2.**The wind tunnel and wave flume joint laboratory: (

**a**) Plane diagram; (

**b**) Small test section; (

**c**) large test section.

**Figure 3.**Wind turbine calibration test: (

**a**) Thrust force comparison between the model and the prototype; (

**b**) Simplified wind turbine model for rated operational condition.

**Figure 4.**Arrangement of the spring mooring system (under 0° load direction) in (

**a**) lateral view (

**b**) top view and its (

**c**) components.

**Figure 5.**Comparison of (

**a**) the surge-restoring force curves and (

**b**) the pitch-restoring moment curves between the catenary mooring system and the spring mooring system in three load directions.

**Figure 6.**Surge-restoring force curves with pitch motion: (

**a**) pitch= −2 deg; (

**b**) pitch = 2 deg; (

**c**) pitch = 4 deg and pitch-restoring moment curves with surge motion: (

**d**) surge = −2 m; (

**e**) surge = 2 m; (

**f**) surge = 4 m.

**Figure 7.**Measuring instruments: (

**a**) A micromanometer installed onto a lifting frame; (

**b**) Three wave probes; (

**c**) The stereo vision measurement system.

**Figure 8.**The measured wind and wave fields: (

**a**) Average wind speed profile; (

**b**) Turbulence intensity profile; (

**c**) Stochastic wave spectrum.

**Figure 9.**Grids for the hydrodynamics computation: (

**a**) Panel model for the ConFloat semi-submersible platform; (

**b**) Free surface grids.

**Figure 10.**Load-displacement relationships for the horizontal spring mooring system (under 0° load direction).

**Figure 12.**Comparisons of RAOs in three wave headings: (

**a**) Surge; (

**b**) Heave; (

**c**) Pitch; (

**d**) Tower base shear force; (

**e**) Tower base bending moment; (

**f**) Nacelle fore-aft acceleration.

**Figure 14.**Time series of (

**a**) surge; (

**b**) tower base bending moment and (

**c**) nacelle acceleration under the 5-s regular wave.

**Figure 17.**Statistical comparisons of the FAST simulation and model test data in three wave headings: (

**a**) Surge motion; (

**b**) Pitch motion.

**Figure 18.**Comparisons of load and motion QTFs between three wave directions: (

**a**) Surging force QTF; (

**b**) Pitch moment QTF; (

**c**) Surge QTF; (

**d**) Pitch QTF.

**Figure 19.**Second-order (

**a**) surge and (

**b**) pitch motion responses under the rated operational wave condition.

**Figure 20.**Comparisons of (

**a**) tower base fore-aft bending and (

**b**) nacelle acceleration PSD in three wave headings.

**Figure 21.**Statistical comparisons of (

**a**) tower base bending moment and (

**b**) nacelle acceleration between three wave headings.

**Figure 23.**Statistical comparisons of the FAST simulation and model test data between three aligned wind/wave directions: (

**a**) Surge response; (

**b**) Pitch response.

**Figure 24.**Comparisons of (

**a**) tower base fore-aft bending and (

**b**) nacelle acceleration PSD between three aligned wind and wave directions.

**Figure 25.**Statistical comparisons of (

**a**) tower base bending moment and (

**b**) nacelle acceleration between three aligned wind/wave directions.

**Figure 28.**PSD plot of fore-aft (

**a**) tower base bending moment, (

**b**) nacelle acceleration and (

**c**) wind thrust.

**Figure 29.**Statistical data of fore-aft (

**a**) tower base bending moment; (

**b**) nacelle acceleration and (

**c**) wind thrust.

Structural Properties | Value without Wind Turbine | Value with Wind Turbine |
---|---|---|

Mass, including ballast (kg) | 1.4560 × 10^{7} | 1.5237 × 10^{7} |

Center of mass (CM) location below MSL (m) | 16.063 | 11.797 |

Roll inertia around CM (kg·m^{2}) | 5.780 × 10^{9} | 1.109 × 10^{10} |

Pitch inertia around CM (kg·m^{2}) | 5.780 × 10^{9} | 1.109 × 10^{10} |

Yaw inertia around CM (kg·m^{2}) | 9.630 × 10^{9} | 9.970 × 10^{9} |

Properties | Value |
---|---|

Number of mooring lines | 3 |

Depth of fairleads below MSL (m) | 18 |

Depth of anchors below MSL (m) | 90 |

Horizontal distance between anchors and the z-axis (m) | 424.8 |

Unstretched length of mooring line (m) | 392 |

Diameter of mooring line (m) | 0.08 |

Equivalent apparent mass in fluid per unit length (kg/m) | 136.248 |

Equivalent extensional stiffness (MN) | 50 |

Category | Closed Return Wind Tunnel with Two Test Sections |
---|---|

Sizes of the small test section | 4.0 m (W) × 3.0 m (H) × 25 m (L) |

Sizes of the large test section | 6.0 m (W) × 3.6 m (H) × 50 m (L) |

Sizes of the wave flume | 5.0 m (W) × 4.5 m (H) × 50 m (L) |

Maximum wind speed | 50 m/s for the small test section |

30 m/s for the large test section | |

Maximum wave height | 0.4 m |

Range of wave periods | 0.5 s to 5 s |

Tests | Wind Speed at Hub Height (m/s) | Wave Period (s) | Wave Height (m) | Wind/Wave Headings |
---|---|---|---|---|

Free decay tests | - | - | - | - |

Regular wave tests | - | 5:2:15 | 1.8 | 0°/60°/90° |

- | 17:2:25 | 2 | ||

Wind-only tests | 11.5 | - | - | 0°/60°/90° |

Irregular wave tests | - | 6.74 | 2.23 | 0°/60°/90° |

Combined wind and wave tests | 11.5 | 6.74 | 2.23 | 0°/60°/90° |

DOF | Tests | Simulations | Relative Errors |
---|---|---|---|

Surge | 80.5 s | 79.9 s | −0.7% |

Sway | 79.7 s | 78.6 s | −1.4% |

Heave | 17.7 s | 17.6 s | −0.6% |

Roll | 25.8 s | 26.0 s | 0.8% |

Pitch | 26.0 s | 26.0 s | 0% |

Yaw | 79.0 s | 79.7 s | 0.9% |

DOF | Global Quadratic Coefficient |
---|---|

Surge | 4.0 × 10^{6} N·s^{2}/m^{2} |

Sway | 4.0 × 10^{6} N·s^{2}/m^{2} |

Heave | 1.0 × 10^{6} N·s^{2}/m^{2} |

Roll | 2.0 × 10^{9} N·m·s^{2}/rad^{2} |

Pitch | 2.0 × 10^{9} N·m·s^{2}/rad^{2} |

Yaw | 4.0 × 10^{9} N·m·s^{2}/rad^{2} |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhou, S.; Shan, B.; Xiao, Y.; Li, C.; Hu, G.; Song, X.; Liu, Y.; Hu, Y.
Directionality Effects of Aligned Wind and Wave Loads on a Y-Shape Semi-Submersible Floating Wind Turbine under Rated Operational Conditions. *Energies* **2017**, *10*, 2097.
https://doi.org/10.3390/en10122097

**AMA Style**

Zhou S, Shan B, Xiao Y, Li C, Hu G, Song X, Liu Y, Hu Y.
Directionality Effects of Aligned Wind and Wave Loads on a Y-Shape Semi-Submersible Floating Wind Turbine under Rated Operational Conditions. *Energies*. 2017; 10(12):2097.
https://doi.org/10.3390/en10122097

**Chicago/Turabian Style**

Zhou, Shengtao, Baohua Shan, Yiqing Xiao, Chao Li, Gang Hu, Xiaoping Song, Yongqing Liu, and Yimin Hu.
2017. "Directionality Effects of Aligned Wind and Wave Loads on a Y-Shape Semi-Submersible Floating Wind Turbine under Rated Operational Conditions" *Energies* 10, no. 12: 2097.
https://doi.org/10.3390/en10122097