Proceedings of the ASME nd International Conference on Ocean, Offshore and Arctic Engineering OMAE2013 June 9-14, 2013, Nantes, France

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1 Proceedings of the ASME 23 32nd International Conference on Ocean, Offshore and Arctic Engineering OMAE23 June 9-4, 23, Nantes, France OMAE A METHOD FOR MODELING OF FLOATING VERTICAL AXIS WIND TURBINE Kai Wang NOWITECH/CeSOS, NTNU Trondheim, Norway Torgeir Moan CeSOS,NTNU Trondheim, Norway Martin Otto Laver Hansen DTU Wind Energy /CeSOS Lyngby, Denmark ABSTRACT It is of interest to investigate the potential advantages of floating vertical axis wind turbine (FVAWT) due to its economical installation and maintenance. A novel 5MW vertical axis wind turbine concept with a Darrieus rotor mounted on a semi-submersible support structure is proposed in this paper. In order to assess the technical and economic feasibility of this novel concept, a comprehensive simulation tool for modeling of the floating vertical axis wind turbine is needed. This work presents the development of a coupled method for modeling of the dynamics of a floating vertical axis wind turbine. This integrated dynamic model takes into account the wind inflow, aerodynamics, hydrodynamics, structural dynamics (wind turbine, floating platform and the mooring lines) and a generator control. This approach calculates dynamic equilibrium at each time step and takes account of the interaction between the rotor dynamics, platform motion and mooring dynamics. Verification of this method is made through model-to-model comparisons. Finally, some dynamic response results for the platform motion are presented as an example for application of this method. KEY WORDS: FVAWT; Coupled method; semi-submersible support structure INTRODUCTION Ever-increasing demand for energy and associated service boost various renewable energies. Wind turbines are considered one of energy devices with the highest potential and placing them on a floating platform is very attractive for the utilization of wind power in deep water. The vertical axis wind turbine (VAWT) has lost ground in the past 2 years compared to horizontal axis wind turbines (HAWT). However, it is of importance also to investigate the potential of floating vertical axis wind turbines (FVAWT) when great efforts have been invested to develop floating horizontal axis wind turbines (FHAWT). From an economic aspect and possible smaller motion, the floating vertical axis wind turbine combined to an effective mooring system, seems to be well fitted for floating offshore application. Recently two popular concepts have been proposed by Risø DTU and France respectively as shown in Figure. The former is DeepWind Concept [-3] which is designed to be 2MW with the rotor height of 75m and rotor diameter of 67m under European project-fp7 and the latter is called VertiWind concept [4] of 2MW with rotor height of 5m. A larger size of DeepWind concept with a generator of 5WM [5] is also designed to be the baseline model. However, they are still on the way to be validated and optimized. Many different challenges arise when the FVAWT is subjected to the wave, wind and current. The wind turbine experiences periodic aerodynamic loads even under the steady wind condition and the floating support structure undergoes first order wave loads and second order wave drift. The slow drift motion of the platform and yaw motion will be withstood by mooring lines. Therefore a fully coupled method for modeling of the floating vertical axis wind turbine needs to be established in order to carry out dynamic analysis of platform motion and structural response as well as power estimation and system design. The interaction between the platform motion and mooring line, as well as between the wind turbine motion and aerodynamic loads can be taken into account. Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

2 A variety of methods have been developed from frequency domain techniques [6-] to the fully coupled aero-hydroservo-elastic model [-6] for conceptual assessment and dynamic analysis of FHAWTs. Moreover, the code-to-code verification activities of the Offshore Code Comparison Collaboration (OC3) based on the existing models are carried out under the Subtask 2 of the International Energy Agency Wind Task 23 [7]. Among the latter, the model (FAST [8] with Aerodyn [9] and Hydrodyn) developed by J.M.Jonkman [2] is widely used. A more recent model that integrates AeroDyn and SIMO/RIFLEX is developed and verified through a benchmark study [2], which aims to overcome some inherent limitations of the other models. However, the available simulation tool to model the floating vertical axis wind turbine is limited. Subsequently the corresponding feasibility assessment and dynamic loads analysis are not easily implemented. A simplified model to represent the DeepWind concept is made by Karl Merz [2] and a corresponding control strategy [22] is designed to carry out the dynamic analysis of 5MW floating vertical axis wind turbine for the DeepWind concept. Vita Luca used HAWC2 to make some investigations for the DeepWind concept. When the spar rotates under water it produces Magnus effect on the spar. However the research is still at the early stage for this concept due to its complexity and unique challenges. WIND TURBINE AND FLOATING PLATFORM MODEL DESCRIPTION The DeepWind 5MW wind turbine is preliminarily designed as a baseline model of floating vertical axis wind turbine by DTU as a part of the FP7 European project DeepWind (2-24). Table below summarizes the important parameters. Table : Wind turbine Properties Rotor radius [m] Rotor height [m] Chord [m] 7.45 Rated power [MW] 5 Rated rotational speed [rad/s] 5.26 Rated wind speed [m/s] 4 Figure : (a) DeepWind (b)vertiwind In this paper a novel concept with the DeepWind rotor mounted on a semi-submersible is proposed. The DeepCwind floater initiated from a U.S. based project aimed at validating floating offshore wind turbine modeling tools is employed for the floating structure. The coupled method for modeling the novel floating concept is inspired by the simulation tool integrating AeroDyn and SIMO/RIFLEX for FHAWT. The AeroDyn code is replaced by the Double Multiple Streamtube model (DMS) which is an exclusive aerodynamic code for VAWTs and implemented as an external Dynamic Link Library (DLL). Moreover, an appropriate controller for VAWT is to be properly designed. Figure 2: Visualization of the FVAWT with a simplified structure layout The OC4 DeepCwind semisubmersible is designed to support the NREL 5MW turbine. The detailed information and definition of the platform designed for NREL 5MW turbine can be found in [23]. When the vertical axis wind turbine is mounted on the platform, the tower is connected to the main column of the platform with multiple bearings in order to release the relative rotational restraint between tower and the platform, as shown in Figure 2. Furthermore, the generator is 2 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

3 installed on the platform, which differs from the horizontal axis wind turbine. In order to maintain the same draft for the floating vertical axis wind turbine as for the floating horizontal axis wind turbine, the ballast is rearranged. The main parameters of the platform for the vertical axis wind turbine after correction are listed in Table 2. Table 2: Geometry, Structural and hydrodynamic properties of platform configurations Depth of platform base below 2 m SWL (total draft) Elevation of main column (tower m base) above SWL Elevation of offset columns above 2 m SWL Spacing between offset columns Platform mass, including ballast and generator CM location below SWL 5 m t -3.69m Buoyancy in undisplaced position t CM location below SWL 3.5m Hydrostatic restoring in heave Hydrostatic C ) ( 33 Hydrostatic restoring in roll Hydrostatic C ) ( E+6 N/m 9.E+8 N m/rad Methods Aerodynamics Aerodynamic loads on the vertical axis wind turbine (VAWT) is calculated based on the Double Multiple Stream-tube model (DMS) [3], which can be implemented as external loads through DLL routine. The code was validated through comparison between numerical results and experimental results for the Sandia 5m and 7m Darrieus rotor. More detailed verification of the code can be found in [24] and the dynamic stall model is not included in this study. Power coefficient Sandia 5m-diameter wind turbine-5rpm 3blades Cp-exp Cp Figure 3: Comparison of Cp curve between simulation model and experimental data for the Sandia 5 meter Darrieus rotor Sandia 7m-diameter wind turbine-5.6rpm 2blades Cp-exp Cp Hydrostatic restoring in pitch Hydrostatic C ) ( 55 9.E+8 N m/rad Power coefficient OVERVIEW OF SIMULATION TOOL DEVELOPMENT The developed simulation tool based on a fully coupled method has the capability to compute the dynamic motion of the FVAWT in the time domain. The aerodynamics is modeled by the Double Multiple StreamTube method including the effect of Reynolds number variation. The Simo&Riflex codes can compute the hydrodynamic loads at the actually displaced position of the structure and carries out full equilibrium iteration at each time step. Viscous drag forces from the Morison s equation and mooring line forces are also included. Moreover a control strategy is contained in this integrated system and the PI controller is designed for the generator speed. In this way a fully integrated analysis tool is established including aerodynamic blade loads, hydrodynamic loads on the floating support structure and mooring lines Figure 4: Comparison of Cp curve between simulation model and experimental data for the Sandia 7 meter Darrieus rotor. Structural dynamics The wind turbine (tower and curved blades) and mooring lines are modeled as flexible elements in the non-linear finite element code Riflex developed by MARINTEK. Hydrodynamics The motion of the floating support structure is simulated according to the linear hydrodynamic theory in Simo with the 3 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

4 hydrodynamic coefficients from HydroD. Viscous drag forces from Morison s equation and mooring line forces are also included. Control model The objective of the control model is to enable variable speed operation maximizing power capture below rated operation point and maintaining generator speed above the rated operation point. In addition, damping the 2p variations is also a challenging objective. Because the axis of rotation is not parallel to the wind direction and the angle of attack of blades varies with azimuthal position during operation, the aerodynamic loads vary within one revolution. For a two-blade wind turbine, the variation of torque occurs twice per revolution, 2p variations. It has large effects on the generator torque and gird, which experience severe fatigue problem. The control strategy is modeled as shown in figure 5 from [22] and is also used in this study. The relevant controller parameters are set the same as those in [22]. In order to eliminate the instability problem the notch filter is switched off for the analysis in this work. (( M A )() x t ( t)() x d( K (()) x t K )() x t F () t () m h exc where M is the body mass matrix, A is the added mass at high frequencies, x(t) is the displacement of motion, ( t ) is retardation function accounting for frequency-dependent added mass and damping, K m (x(t)) is the non-linear restoring matrix from the mooring system, F exc (t) is the excitation forces. In this study it includes the Froude-Krylov force F FK, diffraction force F D, aerodynamic force F Aero and viscous drag F Drag, shown in Eq.(2): FK D Aero Drag F () t F F F F (2) exc The aerodynamic force F Aero is calculated from the aerodynamic model and transferred from the wind turbine to the generator. The viscous drag is calculated approximately based on the drag coefficient C q according to the Eq.(3) Drag F C ux ( ux ) (3) q Then the equations are solved with aerodynamic loads and viscous drag included at each time step through Simo-Riflex- DMS simulation tool. The wave environmental condition is assumed to be 3m for the wave height, 8s for the wave peak period in the direction of positive x-axis for the subsequent simulations. Furthermore, the wind speed is assumed to be steady without turbulence and varies from 5 m/s to 25m/s to simplify the process of verification and analysis. Figure 5: Control diagram. Finally, all the models are integrated to enable coupled time domain simulation. Time domain simulation In the time-domain analysis, the floating vertical axis wind turbine is modeled by the previously described method. In the numerical process the complete system of equations accounting for the rigid body model of the floater (Simo) as well as the slender body model for mooring lines and wind turbine (Riflex) under the external wind loads through DLL, wave loads and current are solved simultaneously using a non-linear time domain approach for dynamic analyses. The equations of motion of the platform can be formulated by Eq.(): Frequency domain simulation The frequency domain method has been widely used in the analysis of offshore structure as a simplified method due to its low computation cost compared to time-domain fully coupled method. In this study the system including the wind turbine and platform is considered as a rigid body to calculate the motions of the platform. The external loads on the platform take into account the hydrostatic forces, hydrodynamic forces and mooring line loads. The hydrostatic forces is simplified as a hydrostatic stiffness matrix K h and the mooring line loads are modeled by a mooring system stiffness matrix K m obtained from the linearization analysis about the undisplaced position of platform. The hydrodynamic added mass, damping and excitation forces are calculated from the panel model in HydroD. Then the equations of motion for the rigid body system (Eq.(4)) are solved at the different wave frequencies in MATLAB to obtain the response amplitude operators (RAOs). The RAO is the transfer function between the wave amplitude and the platform displacements, depending on the wave frequency and direction. 2 ( ( Mij Aij( )) ibij( ) Kh, ij Km, ij) ij( ) Fij( ) (4) 4 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

5 The aerodynamic damping, wind excitation, additional stiffness from mean drift and second order hydrodynamic effects are neglected in the frequency domain analysis. OVERVIEW OF THE SIMULATION VERIFICATION Verification is carried out through model-to-model comparisons. The aerodynamic module within the integrated simulation tool in the time domain is verified by comparing with the stand-alone aerodynamic code which has been verified through comparisons between numerical results and experiment test data. The wind turbine control is also verified by comparison with the designed reference. The results from this coupled time-domain aero-hydro-servo-elastic simulation are compared to those from frequency domain models. Therefore the following verifications are carried out one by one: Verification of Aerodynamic model Verification of Eigen modes Verification of Controls model Time Domain versus Frequency Domain verification Verification of Aerodynamic model The aerodynamic coefficients and aerodynamic loads are computed through three different methods which are the standalone aerodynamic code, the fully coupled method for integrated system with bottom fixed and mounted on a floating semi-submersible. The first uses the Double Multiple Streamtube model to calculate aerodynamic loads where the rotor speed and wind speed are given constant at the same time without control model, blade flexibility and platform motion. The normal force coefficient Cn and tangential force coefficient Ct at the center of blade span from three different methods as a function of azimuthal angle θ at the rated wind speed of 4m/s are plotted in Figure 6 and Figure 7, respectively. Figure 6 shows that the difference of Cn between the different models is very small. The difference of Ct using the three different models is also very small except the zone near 3 degree. Here the tangential force coefficient has abrupt change because the change of angle of attack is induced by the platform motion that contributes to the relative velocity. In Figure 8 the rotor torque is shown as a function of the azimuthal angle θ at the rated wind speed of 4m/s for the DeepWind turbine using pure DMS model and using the coupled method. The results obtained from the different models match quite well although a small difference exists in some points. This is reasonable because the influence from blade flexibility, platform motion and small oscillation of rotor rotational speed are not included in the pure DMS model. The blade flexibility can decrease the torque slightly at most azimuthal positions compared to rigid blades while the platform motion can increase the torque somewhat at some azimuthal positions. Therefore the torque of the floating wind turbine seems to match the result from pure DMS model better than that from a bottom fixed wind turbine. Normal force coefficient Cn Stand-alone DMS Bottom fixed Floating Azimuthal angle Figure 6: The normal force coefficient Cn at the center of blade span at the rated wind speed of 4m/s. Tangential force coefficient Ct Stand-alone DMS Bottom fixed Floating Azimuthal angle Figure 7: The tangential force coefficient Ct at the center of blade span at the rated wind speed of 4m/s. Rotor Torque, KN Stand-alone DMS Bottom fixed Floating Azimuthal angle Figure 8: The Rotor torque as function of azimuthal blade position at the rated wind speed of 4m/s. 5 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

6 Based on the above comparison of normal force coefficient Cn, tangential force coefficient Ct and rotor torque, it is concluded that the aerodynamic module of the coupled method to model the complete floating vertical axis wind turbine seems to work properly. Verification of eigen modes To give some structural information of the dynamics of the VAWT rotor, the natural frequencies and corresponding eigen modes of the equivalent land-based version of the 5MW turbine excluding the transmission and generator components are calculated using both Riflex and Abaqus. The Lanczos s method is used for both of these two models. To avoid the rigid body mode, the wind turbine is considered in a stationary configuration with the rotating shaft brake engaged and represented by flex join between the rotating shaft and generator. Table 3 lists results for the first natural frequencies. The agreement between Riflex and Abaqus is quite good. Table 3: Natural frequencies of VAWT in Hertz Relative Mode Description Riflex Abaqus error st tower side-toside % 2 st tower fore-aft % 3 st blade collective flatwise % 4 st blade asymmetric flatwise % 5 st blade twist % 6 st blade butterfly (Edgewise) % 7 2nd blade asymmetric flatwise % 8 2nd blade collective flatwise % 9 3rd blade asymmetric flatwise % 3rd blade collective flatwise % The flatwise modes are the motion perpendicular to the chord of the blade whereas the edgewise modes are the motion parallel to the chord of the blade. The edgewise modes can be divided in to butterfly modes and twist modes. The butterfly modes are associated with both blades moving in the same direction, like butterfly wings flapping while the twist modes involve motion of both blades in the opposite direction, like rotation of blades around tower. However, the natural frequencies shift due to centrifugal stiffening and gyroscopic effects when the blades rotate. The effect of centrifugal stiffening is most prominent in flatwise bending because the increase in stiffness is a much greater percentage of the total stiffness than in the edgewise case. The gyroscopic effects make significant frequency shifts on tower modes and edgewise modes. In addition a significant amount of modal cross-talk may occur for dynamic responses. Verification of Control model The control model described in the previous section is compiled in Java code and implemented along with the Simo&Riflex. Firstly the optimized curve of torque versus rotational speed is calculated using the aerodynamic model. The result is shown in figure 9. To investigate the effectiveness of the control model, the power output is computed at different wind speeds for both the bottom fixed wind turbine and floating wind turbine. Figure shows the comparison of power output of the wind turbine between the two configurations and the theoretical reference. The power curve is based on mean value of simulated power within 6s length of simulation time. The variability of power output is indicated by error bars showing standard deviation from the mean value. Neglecting the small difference due to the blade flexibility and platform motion, the power output is well controlled to be close to the theoretical curve. Therefore it can be concluded that the wind turbine with the suggested controller model is able to meet the desired objective. Rotor Torque (KN) V=5m/s V=6.5m/s V=7.8m/s V=8.m/s V=8.2m/s V=m/s V=2m/s V=4m/s Cpmax rad/s Figure 9: Optimized torque-speed curve. An assortment of variables including the generator speed, the aerodynamic torque and the generator torque at the rated wind speed of 4m/s are selected to investigate the difference between a bottom fixed wind turbine and a floating wind turbine and effectiveness of the control for generator torque. Figure shows that the generator speed for both the floating wind turbine and the bottom fixed wind turbine oscillate around the desired generator speed which is set to be the reference by controls model. The generator speed for the bottom fixed wind turbine reaches steady state condition while the generator speed for the floating wind turbine has a little deviation from steady state condition between different periods 6 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

7 due to the platform motion. However both of them are reasonably well controlled to follow the reference point. Figure 2 shows that the generator torque can be controlled to have much smaller oscillation amplitude compared to the large oscillation amplitude of the aerodynamic torque for both of the wind turbines. It also shows the mean value of generator torque of floating wind turbine is larger slightly than that of bottom fixed wind turbine at the rated wind speed. Power(KW) Power curve of Deepwind turbine-5.26rpm Floating Bottom fixed Theoretical power curve V(m/s) Figure : Simulated mean power output versus wind speed with error bar indicating variability for bottom fixed and floating configuration. motion are estimated, as shown in Table 4, by considering the added mass from a panel model in HydroD. The spectra from time domain simulation are derived from time series of computed responses by using Fourier transformation technique excluding the transient part. For the time domain simulation, 6 different 3-minute simulations were performed to give a total simulation of 3-hour for specified environment condition. Three different simulations (listed below) are compared to each other for surge, heave and pitch motion.. Frequency-domain 6 DOF rigid turbine model (Linear wave only) 2. Time-domain fully coupled model without Wind (Nonlinear wave only) 3. Time-domain fully coupled model with Wind (Nonlinear wave + wind) Torque(KN*m) Generator-Floating Generator-Bottom fixed Aero-Floating Aero-Bottom fixed Generator speed(rad/s) Floating Bottom fixed Reference Simulation time(s) Figure : Generator speed of bottom fixed wind turbine and floating wind turbine at the rated wind speed of 4m/s. Time Domain versus Frequency Domain verification To verify the results from this coupled model, a comparison in terms of spectra between time- and frequency-domain simulations was conducted. The spectra from frequency domain simulation are derived from the RAO. Thus the spectral responses are computed from the RAOs and input wave spectra. The natural periods and frequencies of the platform Simulation time(s) Figure 2: Aerodynamic torque and generator torque of bottom fixed wind turbine and floating wind turbine at the rated wind speed of 4m/s. Table 4: Natural periods and natural frequency Natural period (s) Natural frequency (rad/s) Surge Sway Heave Roll Pitch Yaw The results from the three different simulations and the corresponding comparisons are plotted in figure 3. When only the wave is present, the spectra of surge and heave from time domain simulation are similar to those from frequency domain simulation while the amplitude of spectra of pitch motion within wave frequency range from time domain simulation is 7 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

8 less than that from frequency domain simulation because the viscous drag force is only included in the time-domain fully coupled model. The effect of the wind on the heave motion is negligible, but the surge and pitch motion are both excited at high frequency by 2p excitation due to aerodynamic thrust. Furthermore, the presence of wind also excites some motion at the first pitch natural frequency. Therefore the coupled method in the time domain has the ability to calculate the dynamic responses with fair improvement compared to those from frequency time domain. S( ), m 2 s S( 3 ), m 2 s, m 2 s S( 5 ), deg 2 s.5.5 H s 3m, T p 8s, U 4m/s Linear Nonlinear Nonlinear Wave + Wind , rad/s Figure 3: Wave, surge, heave and pitch spectra for floating vertical axis wind turbine under the specified environmental condition. much even if the wind is present. In the same way, the simulation results for different combinations of wave and wind can also be obtained by the fully coupled method in the time domain simulation., m Wave + Wind 4m/s Figure 4: Time series of surge motion for wave only condition and combined wave and wind conditions. 2, m Wave + Wind 4m/s Figure 5: Time series of sway motion for wave only condition and combined wave and wind conditions. RESULTS In order to investigate the dynamic responses of the FVAWT the simulation results of the motions of platform are plotted in Figures 4-9 both for wave only condition and combined wave and wind condition. When only the wave is present, the sway, roll and yaw motions are negligible while the surge, heave and pitch motions oscillate around the mean water plane. The latter motions are mainly excited by wave and thus the oscillatory frequencies are mainly within the wave frequency range. Whereas the latter motions can take place and it is found that they oscillate around nonzero mean values when the wind at the rated wind speed of 4m/s is combined with the wave. In addition, the surge and pitch motions have similar oscillatory trajectory to the wave only condition, but the mean values are increased and the amplitude within the transient range is enlarged. However the heave motion does not change 3, m Wave + Wind 4m/s Figure 6: Time series of heave motion for wave only condition and combined wave and wind conditions. 8 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

9 4, deg Wave + Wind 4m/s Figure 7: Time series of roll motion for wave only condition and combined wave and wind conditions. 5, deg Wave + Wind 4m/s Figure 8: Time series of pitch motion for wave only condition and combined wave and wind conditions. 6, deg Wave + Wind 4m/s Figure 9: Time series of yaw motion for wave only condition and combined wave and wind conditions. CONCLUSIONS The concept of a 5MW Darrieus type vertical axis wind turbine mounted on the OC4 DeepCwind semi-submersible support structure has been presented. A coupled method for modeling the floating vertical axis wind turbine in the time domain was established. This model solves the equations of motion taking into account an aerodynamic model, a hydrodynamic model, a control model and mooring system into a complete system which can be represented by equations of motion in the time domain. The aerodynamic loads are calculated using a DMS model and the hydrodynamic loads are calculated using linear diffraction/radiation theory with viscous drag included. Verification of this coupled method has been carried out through model-to-model comparison. The aerodynamic model imbedded in the integrated system is well verified by comparing with the stand-alone aerodynamic code which was already verified by experimental data. The results of the bottom fixed wind turbine and floating wind turbine are all very close to the results from stand-alone aerodynamic code. The structural modeling of the wind turbine in Riflex is verified by comparing the eigen frequencies from Riflex with those calculated using the commercial software Abaqus. The power curve, aerodynamic torque, generator torque and generator speed have been presented to prove the effectiveness of the controller. Furthermore, the results from frequency domain simulation have been computed for the linear rigid boy motion of the platform with vertical axis wind turbine included. Then the results from the coupled method in time domain simulation were compared with the results from frequency domain simulation, showing a good agreement. The 2p response and first natural pitch motion from wind can be observed when the wind is combined with wave. However, it should be noted that the second order hydrodynamics effects were not included in the analysis of time domain simulation so far. This study highlights the development of the coupled method for modeling a floating vertical axis wind turbine. Based on the verified method the complete system of equations accounting for the rigid body model of the platform (Simo) and the slender body model for mooring lines and wind turbine (Riflex) under the combined wind and wave condition are solved simultaneously using a non-linear time domain approach. Then dynamic response analysis of platform motion and structure can be carried out for the further study. ACKNOWLEDGMENTS The authors wish to acknowledge the financial support from the Research Council of Norway through NOWITECH and the Centre for Ships and Ocean Structures at the Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway. 9 Copyright 23 by ASME Downloaded From: on /26/24 Terms of Use:

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