# Dynamic Response Analysis of Floating Wind Turbines with Emphasis on Vertical Axis Rotors

## Abstract

Large floating wind turbines are feasible for offshore application. Due to the commercial success onshore and nearshore, floating horizontal axis wind turbines (HAWTs) are now being widely studied. However, floating vertical axis wind turbines (VAWTs) have an excellent potential in the cost of energy reduction compared with floating HAWTs. This paper deals with the integrated modeling and dynamic response analysis of typical floating VAWT concepts. A fully coupled aero-hydro-servo-elastic method is presented for numerical modeling and dynamic response analysis of floating wind turbine systems. Considering a two-bladed 5 MW Darrieus rotor, the dynamic response characteristics of typical floating VAWT concepts are studied. In addition, comparative studies of floating HAWTs and VAWTs are performed.

## Keywords

Wind Turbine Mooring Line Aerodynamic Load Vertical Axis Wind Turbine Horizontal Axis Wind Turbine## 12.1 Introduction

During the 1970s and 1980s, a large amount of efforts was devoted to develop VAWTs, particularly in the United States and Canada. However, the VAWTs gradually lost the competition with the horizontal axis wind turbines (HAWTs) due to low efficiency and fatigue problems within the bearings and blades. In recent years, offshore wind farms are moving towards deeper waters where floating wind turbines are required in countries such as the Japan, Norway and United States. Due to the commercial success onshore and nearshore, floating HAWTs are now being widely studied and prototypes have been developed and tested, such as the Hywind demo in Norway, the WindFloat demo in Portugal and the floating wind turbines off the Fukushima coast of northeast Japan.

The interest in the development of VAWTs for offshore application has also been resurging. Compared with floating HAWTs, floating VAWTs have lower centers of gravity, are independent of wind direction, can provide reduced machine complexity and have the potential of achieving more than 20 % cost of energy reductions (Paquette and Barone 2012). Moreover, floating platforms can help to mitigate the fatigue damage suffered by the onshore VAWTs (Wang et al. 2016). In addition, floating VAWTs are more suitable for deploying as wind farms than floating HAWTs (Dabiri 2011). Thus, more and more efforts are devoted to the development of floating VAWTs.

In order to assess the technical feasibility of floating VAWTs, a numerical simulation tool is required to conduct the fully coupled aero-hydro-servo-elastic analysis. To date the available simulation tools that can model the floating VAWTs in a fully-coupled way are limited, but are emerging, such as the FloVAWT code by Cranfield University (Collu et al. 2013), the OWENS toolkit by Sandia National Laboratories (Brian et al. 2013), the HAWC2 by DTU Wind Energy (Larsen and Madsen 2013), the SIMO-RIFLEX-DMS (Wang et al. 2013) and SIMO-RIFLEX-AC (Cheng et al. 2016b) code by NTNU. Among these codes, the aerodynamic loads are mainly computed using the double multi-streamtube (DMS) model (Paraschivoiu 2002) or actuator cylinder (AC) flow model (Madsen 1982), which are capable of predicting the aerodynamic loads accurate at a small computational cost. These two models are validated using experimental data by Wang et al. (2015b) and Cheng et al. (2016a). Code-to-code comparisons between these codes were also conducted to verify each code, such as the comparison of FloVAWT and SIMO-RIFLEX-DMS by Borg et al. (2014c), and the comparison of three codes SIMO-RIFLEX-DMS, SIMO-RIFLEX-AC and HAWC2 by Cheng et al. (2016b).

Considerable efforts have been made to study the floating VAWTs by many researchers using the aforementioned codes. Using the code HAWC2, Paulsen et al. (2013) performed a design optimization of the proposed DeepWind concept. An improved design has been obtained with an optimized blade profile with less weight and higher stiffness than the 1st baseline design. Based on the code FloVAWT, Borg et al. (2014a, b) presented a review on the dynamic modeling of floating VAWTs, used a wave energy converter as a motion suppression device for floating wind turbines (Borg et al. 2013) and further performed a comparison on the dynamics of floating VAWTs with three different floating support structures (Borg and Collu 2014). A floating VAWT concept with a 5 MW Darrieus rotor mounted on a semi-submersible was proposed by Wang et al. (2013) and fully coupled aero-hydro-servo-elastic simulations were carried out with emphasis on stochastic dynamic responses (Wang et al. 2016), effects of second order difference-frequency forces and wind-wave misalignment (Wang et al. 2015a), and emergency shutdown process with consideration of faults (Wang et al. 2014a).

In this study, dynamic response characteristics of typical floating VAWTs are addressed. The development and verification of fully coupled numerical simulation tools SIMO-RIFLEX-DMS and SIMO-RIFLEX-AC are presented. Using a two-bladed 5 MW Darrieus rotor, dynamic responses of three floating VAWT concepts (Cheng et al. 2015a, 2015c) are studied by fully coupled nonlinear time domain simulations. In addition, comparative studies of the dynamic responses of floating HAWTs with the NREL 5 MW wind turbine (Jonkman et al. 2009) and VAWTs with the 5 MW Darrieus rotor (Vita 2011) are also performed to assess the merits and disadvantages of each concept.

## 12.2 Typical Floating VAWT Concepts

Currently several floating VAWT concepts have been proposed, including the DeepWind (Vita 2011), VertiWind (Cahay et al. 2011) and floating tilted axis (Akimoto et al. 2011) concepts. They are comprised of a vertical axis rotor, a floater and a mooring system. The rotor can be straight-bladed H-type rotor, curve-bladed Darrieus rotor, helical-bladed rotor and V-type rotor, while the floater could be a spar, semi-submersible or TLP.

Specifications of the Darrieus 5 MW wind turbine

Darrieus rotor | |
---|---|

Rated power [MW] | 5 |

Rotor radius [m] | 63.74 |

Rotor height, root-to-root [m] | 129.56 |

Chord length [m] | 7.45 |

Cut-in, rated, cut-out wind speed [m/s] | 5, 14, 25 |

Rated rotor rotational speed [rpm] | 5.26 |

Total mass, including rotor, shaft and tower [kg] | 754,226 |

Location of overall center of mass [m] | (0, 0, 75.6) |

Properties of the three floating wind turbine systems

Floater | Spar | Semi-submersible | TLP |
---|---|---|---|

Water depth [m] | 320 | 200 | 150 |

Draft [m] | 120 | 20 | 22 |

Diameter at mean water line [m] | 6.5 | 12.0/6.5 | 14.0 |

Platform mass, including ballast & generator [ton] | 7308.3 | 13353.7 | 2771.9 |

Center of mass for platform [m] | (0, 0, −89.76) | (0, 0, −15.38) | (0, 0, −13.42) |

Buoyancy in undisplaced position [kN] | 80,710 | 139,816 | 56,804 |

Center of buoyancy [m] | (0, 0, −62.07) | (0, 0, −13.15) | (0, 0, −14.20) |

Surge/Sway natural period [s] | 130.8 | 114.0 | 45.3 |

Heave natural period [s] | 27.3 | 17.1 | 0.6 |

Roll/Pitch natural period [s] | 34.5 | 31.0 | 4.5/4.9 |

Yaw natural period [s] | 8.5 | 79.7 | 19.3 |

Since the difference in mass between the 5 MW Darrieus rotor and the NREL 5 MW wind turbine was small compared to the displacements of these three concepts, it was assumed that such modifications would not alter the hydrostatic performance of each platform significantly, which was verified by the following simulations. After these modifications, these substructures supporting the 5 MW Darrieus rotor may not be optimal from an economical point of view, but they are sufficient to demonstrate the inherent motion and structural response characteristics of each concept.

## 12.3 Integrated Modeling of a Floating VAWT System

A floating wind turbine system is usually comprised of a rotor harvesting wind energy, a floater supporting the rotor and a mooring system keeping the floater in position. To evaluate its performance, a fully coupled aero-hydro-servo-elastic simulation tool is required to carry out the time domain simulations similar as those used for analysis of floating HAWTs. This coupled code should account for the aerodynamics, hydrodynamics, structural dynamics, controller dynamics and mooring line dynamics. Currently, two fully coupled codes, namely SIMO-RIFLEX-DMS and SIMO-RIFLEX-AC, are developed in NTNU to conduct such fully integrated modeling and analysis for floating VAWTs. These two codes are based on the codes SIMO (MARINTEK 2012b) and RIFLEX (MARINTEK 2012a), which are originally developed and are now widely used in the offshore oil & gas industry. The SIMO-RIFLEX wind turbine module has previously been verified (Luxcey et al. 2011; Ormberg et al. 2011).

### 12.3.1 Aerodynamics

Among the aerodynamic models for VAWTs, the Double Multiple-Streamtube (DMS) model (Paraschivoiu 2002) and Actuator Cylinder (AC) flow method (Madsen 1982) are two favorable methods that are suitable for fully coupled modeling and analysis for floating VAWTs. Based on these two methods, two aerodynamic codes are developed for fully coupled modeling and analysis of floating VAWTs by Wang et al. (2015b) and Cheng et al. (2016a), respectively.

The AC method is a 2D quasi-steady flow model developed by Madsen (1982). The model extends the actuator disc concept to an actuator surface coinciding with the swept area of the 2D VAWT. In the AC model, the normal and tangential forces resulting from the blade forces are applied on the flow as volume force perpendicular and tangential to the rotor plane, respectively. The induced velocities are thus related to the volume force based on the continuity equation and Euler equation. The induced velocity includes a linear part and a nonlinear part; the linear part can be computed analytically given the normal and tangential loads. However, it’s to some extent time-consuming to compute the nonlinear solution directly. A simple correction is therefore introduced to make the final solution in better agreement with the fully nonlinear solution. The developed AC model (Cheng et al. 2016a) is verified by comparison with other numerical models and experimental data, as demonstrated in Fig. 12.4. The AC model implemented in Cheng et al. (2016b) includes the effects of wind shear and turbulence, and dynamic inflow. The effect of dynamic stall is also incorporated using the Beddoes-Leishman dynamic stall model.

### 12.3.2 Hydrodynamics

The hydrodynamic loads are computed using a combination of the potential flow theory and Morison’s equation. For large volume structures, the added mass, radiation damping and first order wave forces were obtained from a potential flow model and applied in the time domain using the convolution technique (Faltinsen 1995). When the second-order wave force becomes important for structures with natural frequencies that either very low or near twice the wave frequency, the second-order potential flow theory is applied to account for the mean drift, difference-frequency and sum-frequency wave forces using the Newman approximation or quadratic transfer function (QTF). Regarding the slender structures where the diameter D is small compared to the wavelength λ (roughly, D/λ < 1/5), the Morison equation is applied to calculate the inertial load and viscous drag load (Faltinsen 1995). In addition, viscous forces on large volume structures can also be incorporated through the Morison’s equation by considering only the quadratic viscous drag term.

### 12.3.3 Structural Dynamics

In the structural model, the blades are modeled as flexible beam elements with two symmetric planes to differ the flapwise stiffness and edgewise stiffness. The tower and shaft are modeled as axisymmetric beam elements while the mooring lines are considered as nonlinear bar element, as shown in Fig. 12.3. A flexible joint is used to connect the rotating part and non-rotating part within the shaft. The electric torque from the generator is also applied at this joint to regulate the rotor rotational speed according to the prescribed control strategy. Moreover, master–slave connections are applied to integrate the motions between the tower base and fairleads.

In RIFLEX, the dynamic equilibrium equations can be solved in the time domain using the Newmark-β numerical integration (β = 0.256, γ = 0.505). Structural damping is included through global proportional Rayleigh damping terms for all beam elements.

### 12.3.4 Control System

Considering a typical floating VAWT that operates at a fixed blade pitch angle, a generator torque controller can be used to regulate the rotational speed (Cheng et al. 2016b). The controller aims to minimize the error between the measured and filtered rotational speed Ω_{mea} and the reference rotational speed Ω_{ref} by adjusting the generator torque through a PI control algorithm.

_{in}to V

_{ΩN}, the rotor operates at the optimal tip speed ratio so as to achieve the highest power coefficient. In region II, the rotor operates at a moderate tip speed ratio and holds the rotational speed constant at the rated one. The control targets in region I and II aim to maximize the power capture and at the same time keep the rotational speed not larger than the rated one. However, the control targets in region III shift to limit the aerodynamic loads acting on the rotor by limiting the rotational speed. In this case, the rotor rotates at relatively low tip speed ratios and two control strategies, as illustrated in Fig. 12.5, are considered here.

Based on these two control strategies, two controller were developed, namely i.e. the baseline controller and improved controller. This baseline controller is capable of maximizing the power capture for wind speeds below V_{ΩN} and maintaining the rotational speed for wind speeds above V_{ΩN}, while the improved controller aims to maximize the power capture for wind speeds below V_{N} and maintain the power capture approximately constant for the above rated wind speeds.

### 12.3.5 Verification of the Fully Coupled Codes

In addition, the semi VAWT described in Sect. 12.2 is used to verify the capability of the codes SIMO-RIFLEX-DMS and SIMO-RIFLEX-AC in modeling and dynamic analysis of floating VAWTs. Figure 12.9 demonstrates the mean value and standard deviation of the tower base fore-aft and side-side bending moment for the semi VAWT. It is found that the code SIMO-RIFLEX-AC can to some extent predict more accurate dynamic responses than the code SIMO-RIFLEX-DMS.

## 12.4 Dynamic Response Characteristics of Three Floating VAWTs

Figure 12.10 shows the mean values of the generator power production of the three floating VAWT concepts. The error bar indicates the standard deviation from the mean value. It can be observed that the mean generator powers increase as the wind speed increases. At rated wind speed of 14 m/s, the mean generator powers slightly exceed the rated power of 5 MW, since the Beddoes-Leishman dynamic stall model is included in the DMS model. The rotor considered can achieve a rated power of 5 MW when excluding the dynamic stall effect. In addition, the mean generator power of the three floating VAWT concepts is very close to each other, except at high wind speeds where the mean generator power of the semi VAWT begins to differ from that of the spar VAWT. The difference results from the different rotational speed and increases as the wind speed increases. The different rotational speeds for the three concepts are due to the implemented controller. The controller regulates the rotational speed by adjusting the generator torque, but fails to keep the rotational speed at above rated wind speed exactly constant. The variations of the generator power for the three floating VAWT concepts are very close to each other as well.

The global platform motions of the three floating VAWT concepts present significant differences. The mean values of platform motions increase as the wind speed increases, since the mean values are mainly wind-induced. For each load case, the spar VAWT suffers the considerable larger platform motions in surge and pitch. But the standard deviations of the spar VAWT and semi VAWT in pitch motions are very close to each other. Regarding the yaw motion, the mean yaw motions of the three floating VAWT concepts are fairly close. However, the standard deviation of the yaw motion of the semi VAWT is relatively larger than that of the spar VAWT, this is due to the resonant yaw motions excited by the turbulent wind.

_{FA}and side-side bending moment M

_{SS}are chosen as the primary structural performance parameters. The tower base was assumed to be located below the bearings between the rotating shaft and the drive train shaft. Since the aerodynamic loads of each blade varies with the azimuthal angle, not only M

_{FA}but also M

_{SS}have great variations, which is quite different from the horizontal axis wind turbine. These variations of bending moments can cause large stress fluctuations, thus leading to great fatigue damage. Figure 12.11 compares the power spectra of M

_{FA}and M

_{SS}under the turbulent wind and irregular wave condition. The turbulent winds excite the certain low-frequency response of M

_{FA}, but the wind-induced response is much smaller than the 2P response in both M

_{FA}and M

_{SS}. Furthermore, since the taut tendons cannot absorb the 2P aerodynamic excitations for the TLP VAWT, the 2P responses in M

_{FA}and M

_{SS}of the spar VAWT and semi VAWT are much smaller than that of the TLP VAWT, which implies that the catenary mooring system can greatly mitigate the 2P effects on structural dynamic responses. Eigen-frequency analysis has been carried out for this rotor and states that the natural frequencies of the first and second tower base bending modes are far away from the 1P and 2P excitations (Wang et al. 2013). As a consequence, the standard deviations of M

_{FA}and M

_{SS}for the spar VAWT and the semi VAWT are smaller than those of the TLP VAWT.

## 12.5 Comparative Study of Floating HAWTs and VAWTs

In this section, comparative studies on the dynamic responses of floating HAWTs and VAWTs are briefly discussed. The rotors considered are the NREL 5 MW wind turbine (Jonkman et al. 2009) and the 5 MW Darrieus rotor (Vita 2011). The code SIMO-RIFLEX-DMS and SIMO-RIFLEX-AeroDyn are used to conduct the fully coupled analysis for the floating VAWTs and HAWTs, respectively.

### 12.5.1 Semi HAWT vs. Semi VAWT

Wang et al. (2014b) studied the dynamics of the semi-type HAWT and VAWT with the OC4 semi-submersible supporting the NREL 5 MW wind turbine (Jonkman et al. 2009) and the 5 MW Darrieus rotor (Vita 2011). Regarding the semi VAWT, the baseline controller described in Sect. 12.3.4 was adopted in the simulations. Thus the generator power production of the semi VAWT exceeds 5 MW and is much larger than that of the semi HAWT above the rated wind speed. Other details with respect to the floating wind turbine systems and load cases can be found in Wang et al. (2014b).

### 12.5.2 Spar HAWT vs. Spar VAWT

Comparative study of floating HAWTs and VAWTs was further extended to the spar-type concepts by Cheng et al. (2015b, 2016c). The OC3 spar buoy was used to support the aforementioned two rotors. Cheng et al. (2015b) conducted the comparative study using the baseline control strategy for the spar VAWT. To make the comparative study more reasonable, an improved control strategy was employed, as described in Sect. 12.3.4 (Cheng et al. 2016c). A series of numerical simulations were carried out under the turbulent wind and irregular wave conditions.

The spar HAWT and VAWT also differ in the platform motions due to the different aerodynamic loads and control strategies. For both the spar HAWT and VAWT, the trends in the mean values of the surge, heave and pitch are very similar to those of the mean thrust acting on the rotors, since the mean values of the platform motions are mainly related to wind thrust force. The mean values of the sway, roll and yaw motions of the spar HAWT are very small, because the aerodynamic lateral force and yaw moment are small due to symmetry. However, the spar VAWT has much larger mean values in sway, roll and yaw motions, especially at high wind speed.

The structural responses of the spar HAWT and VAWT illustrate significant differences as well. Figure 12.14 shows the power spectra of the tower base fore-aft and side-side bending moment for the spar HAWT and VAWT in turbulent wind and irregular wave condition with Uw = 14 m/s, Hs = 3.62 m, Tp = 10.29 s. Obviously the response corresponding to the 2P frequency is considerably dominating in the tower base fore-aft and side-side bending moments for the spar VAWT. Moreover, the tower base fore-aft bending moment for the spar VAWT also includes prominent low-frequency turbulent wind induced response and wave frequency response. With respect to the spar HAWT, the tower base fore-aft bending moment consists of significant low-frequency turbulent wind induced response, pitch resonant response and wave frequency response. The pitch resonant response mainly results from the relatively large platform pitch motion. In addition, the tower base of the spar HAWT is mainly affected by the fore-aft bending moment, while the side-to-side bending moment can be neglected.

## 12.6 Conclusions

This paper deals with the integrated modeling methodology for a floating vertical axis wind turbine (VAWT) system and reveals the dynamic response characteristics of representative floating VAWTs.

Firstly two fully coupled simulation tools, namely SIMO-RIFLEX-DMS and SIMO-RIFLEX-AC, are briefly introduced so as to assess the dynamic performance of typical floating VAWT concepts. These two simulation tools are based on the double multi-streamtube (DMS) method and actuator cylinder (AC) flow method, respectively. Moreover, they are capable of accounting for the turbulent inflow, aerodynamics, hydrodynamics, structural elasticity and controller dynamics. Validations of the aerodynamic module using experimental data and verifications of the fully coupled tools using a series of code-to-code comparisons are also presented.

The dynamic responses of three floating VAWT concepts are then studied. A spar, semi-submersible and TLP floater is used to support a two-bladed Darrieus rotor, respectively. Stochastic dynamic response analysis reveals that 2P effects resulting from the 2P aerodynamic loads are prominent in the dynamic responses of these concepts. Due to the compliant catenary mooring systems, the spar and the semi-submersible can help to mitigate the 2P effects on structural loads and mooring line tensions as compared to the TLP concept, at the cost of larger platform motions. The TLP is not a good substructure for vertical axis wind turbine unless the cyclic variation of aerodynamic loads is significantly reduced.

Comparative studies on the dynamics of floating VAWTs and HAWTs are also demonstrated. Due to different aerodynamic load characteristics and control strategies, the spar VAWT results in larger mean tower base bending moments and mooring line tensions above the rated wind speed. Because significant 2P aerodynamic loads act on the spar VAWT, the generator power, tower base bending moments and delta line tensions show prominent 2P variation. Consequently the spar VAWT suffers severe fatigue damage at the tower bottom. The semi VAWT shows significant 2P variations in structural responses as well.

## Notes

### Acknowledgments

The authors would like to acknowledge the financial support from the EU FP7 project MARE WINT (project NO. 309395) and Research Council of Norway through the Centre for Ships and Ocean Structures (CeSOS) and Centre for Autonomous Marine Operations and Systems (AMOS) at the Department of Marine Technology, Norwegian University of Science and Technology (NTNU), Trondheim, Norway. The first author would also thank Dr. Kai Wang from Aker Solutions for his valuable comments and discussions.

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