Numerical Validation of Floating Offshore Wind Turbine Scaled Rotor for Surge Motion

Transcription

1 Numerical Validation of Floating Offshore Wind Turbine Scaled Rotor for Surge Motion Krishnamoorthi Sivalingam 1, Steven Martin 2 and Abdulqadir Aziz Singapore Wala 3, * 1 Lloyd s Register Singapore Pte Ltd, 1 Fusionopolis Place, #09-11 Galaxis, Singapore ; krishnamoorthi001@suss.edu.sg 2 Wind Energy Systems Centre for Doctoral Training, University of Strathclyde, Glasgow, United Kingdom; steven.martin@strath.ac.uk 3 Lloyd s Register Singapore Pte Ltd, 1 Fusionopolis Place, #09-11 Galaxis, Singapore ; Qadir.SingaporeWala@lr.org * Correspondence: krishnamoorthi001@suss.edu.sg ; Tel.: Abstract: Aerodynamic performances of a floating offshore wind turbine (FOWT) is significantly influenced by platform surging motion. Accurate prediction of the unsteady aerodynamic loads is imperative for determining the fatigue life and ultimate loads of FOWT rotor blades and the other key components such as gearbox and power converter. The current study examines the predictions of numerical codes by comparing with unsteady experimental results on a scaled floating wind turbine rotor. The influence of platform surge amplitude together with the tip speed ratio on the unsteady aerodynamic loading has been simulated through unsteady CFD. It is shown that the unsteady aerodynamic loads of FOWT are highly sensitive to the changes in frequency and amplitude of the platform motion. Also, the surging motion significantly influence the windmill operating state due to strong flow interaction between the rotating blades and generated blade-tip vortices. At low frequencies and low amplitudes, CFD, BEM and ubem predictions have good consistency with experimental results. Keywords: CFD, unsteady BEM, Floating Offshore Wind Turbine, Scaled Wind Turbine Rotor; 1. Introduction This paper is an extension of work originally presented in nd International Conference on Green Energy and Applications of IEEE (ICGEA) [1]. The insatiable demand for the energy together with the rising greenhouse gas emissions push for a dramatic shift towards renewable energy. Among the various renewable energy sources, wind energy is one popular form of the energy due to its reliability and cost competitiveness. The wind industry has seen a tremendous growth in the past decades leading to the addition of 52.6 GW of power to an existing 539 GW as of 2017 [2]. To meet the projected energy demand, the wind industries are pushed to explore technologies beyond conventional land-based installations. Offshore wind turbine is one of the identified potential solutions with significant annual energy output due to high wind speed. Offshore wind technologies are continuously improved by myriad experimental, numerical and field studies. As the water depth increases, the conventional monopile foundation or gravity-based foundation is not feasible economically. Hence floating wind turbines are projected as an alternative solution in terms of cost and reliability [3]. Floating wind turbines are an active research topic in the recent days and myriad concepts are put forward with the objective of curtailing the cost of installation and to bolster the reliability. A few concepts have been implemented in prototype turbines in deep waters to demonstrate the feasibility of the concept. The floating offshore wind turbine s capital, Operation and Maintenance (O&M) cost should be significantly reduced in order to be competitive to fixed bottom wind machines and conventional 2018 by the author(s). Distributed under a Creative Commons CC BY license.

2 power sources. Apart from the design considerations of offshore environment, floating offshore wind turbine technology is impaired with other challenges such as application of right floating platform technology and increased O&M cost due to the accessibility of the assets in deep waters. Hence the offshore wind turbines are expected to have improved reliability and should be able to with stand high wind loads to reduce the maintenance cost. Accurate prediction of various forces and total loading are the important aspects of floating offshore wind turbine systems design. Numerical simulation becomes an inevitable part in every stages of the wind turbine product life cycle development from conceptual design to operation, maintenance and decommissioning. In addition to their significant contribution in predicting the wind loads on the turbine, radically new designs can be attempted. In order for a real-world physical system to be represented in a numerical system precisely, it has to be validated against the experimental results. The current study aims to validate one such numerical system representing the floating offshore wind turbine with the scaled rotor design for surge motion as it is predominant in the floating motions [4-5]. The experimental results obtained through the tow tank tests, yield valuable data on the unsteady aerodynamics responses which are then compared with the numerical predictions. Floating platform motions have significant influence on the power and thrust characteristics of floating wind turbine in addition to tip speed ratio (TSR) and blade angle. A scaled rotor was designed and developed at Strathclyde University to investigate the unsteady aerodynamic response. The designed rotor is scaled both globally and locally matching the aerodynamic performance of the full scale 5MW NREL turbine. The details of the scaling methodology have been discussed in [6]. In addition, the [6] investigates the scaled rotor experimental results by comparing with high fidelity CFD simulation models and LR-AeroDyn and LR- ubem code computations. 2. Scaled Rotor for unsteady aerodynamic experiments To predict the global loads in well-ordered experimental conditions by scaling down the wind turbine rotor is challenging. This can be attributed to the complexities involved in accomplishing the three scaling laws, which has to be followed to design a scaled rotor that matches the performance of full scale reference rotor [7-10]. The scaled rotor model is derived from the open literature, available for 126m diameter 5MW NREL virtual wind turbine rotor. A geometric scaling factor of is used to obtain 1.0 m diameter scaled rotor matching the full-scale aerodynamics coefficients at the Reynolds Number, Re= 1x10 5. As aerodynamic coefficients largely influence the rotor performance, a new methodology has been adopted to match the scaled airfoil Re to the full-scale airfoil Re [6]. Significant effort has been dedicated to optimize the airfoil profile in order to match the lift curves even in low Re [6], by retaining the twist of 5 MW NREL rotor blade. Considering the blade length of the scaled rotor, three significant airfoil profiles are employed in comparison to the six profiles in full scale model. The following Table.1 indicates the full-scale rotor airfoils and the corresponding airfoils of the scaled rotor. The shape of SMA series airfoils are shown in comparison to the full-scale model airfoils in Fig. 1. Scaled rotor parameters are shown in Table 1. The designed scaled rotor blades are similar to full scale rotor following the procedure of Froude-scaled model. Table 1. Scaled rotor details Element *Cross-sectional profile Element center Node center Twist(o) chord(m) radius(m) Cylinder Cylinder Cylinder DU40 (SMA3540)

3 DU35 (SMA3540) DU35 (SMA3540) DU30 (SMA2130) DU25 (SMA2130) DU25 (SMA2130) DU21 (SMA2130) DU21 (SMA2130) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) Note: * The name in the bracket is Strathclyde Scaled Rotor airfoil corresponding airfoil of 5 MW NREL Rotor airfoils Figure 1 Strathclyde model and reference airfoil shapes [1] Lift coefficient for the SMA airfoils are computed through Xfoil for the model Re, while for the full-scale airfoils, the generated lift coefficients from Xfoil is verified through wind tunnel test. The Xfoil follows the experimental curve at lower AoA, but at higher AoA it over predicts. This can be attributed to the earlier onset of flow separation in the experimentation [6]. The Fig.2 shows the 3D model of the scaled rotor Figure 2. 3D Model of the scaled rotor.

4 During the designing stage, the global model rotor performance was compared to the full scale reference for non-dimensional thrust and torque [6]. The thrust force on the rotor is primarily influenced by the aerofoil lift and as such the match between the model and reference for this property is favorable. The increased aerofoil drag at the experimental Reynolds number results in a reduced model rotor non-dimensional torque as compared to the reference. This was an expected result of implementing this scaling methodology. The local blade performance is assessed for the model scale rotor by comparing the axial and tangential Induction factors and the angle attack along the non-dimensional length of the blade for different tip speed ratios (TSR) by the authors [6]. The scaled rotor with its surge motion rig is as shown in Fig Figure 3. Physical scaled rotor with a rig setup (for surge motion unsteady effects) on the carriage of the towing tank Scaled model experiments were conducted in the tow-tank at Kelvin Hydrodynamics Laboratory, University of Strathclyde. The tow tank is 76 m length, 2.5 m depth and 4.6 m in width as shown in Fig 4. The cross-sectional area of the tow tank is sufficiently large compared to the rotor diameter under investigation assuring minimum blockage. Hence the data obtained from the experiments are not blockage corrected. The motions in 6 degrees of freedom are induced by using a dual-carriage system allowing for sinusoidal surge motions of the scaled rotor. The carriage is maneuvered at constant rate to represent the water flow. Resistive torque was applied through a brake disc to measure the rotor torque along with the thrust and the rotor rpm Figure 4. The tow tank at the Kelvin Hydrodynamics Laboratory Experimental Design of Surge Motion The surge motion of the rotor does not represent a specific floating wind turbine system, but rather a generalized matrix of operating points, from which conclusions can be drawn regarding the rotor thrust loading. The three variables under investigation are the rotor tip speed ratio, the surge amplitude, and the surge frequency. Similar to the steady state analysis of the rotor, the tow speed is

5 constant and the rotor speed is varied to alter the tip speed ratio. The operating range of values for these parameters are specified such that they mimic the full-scale rotor operating conditions limited to the experimental setup and surge carrier motion. Three prior studies have been conducted with the objective of studying the aerodynamic performance in response to the surge motion. The initial values for the parameters are set according to these studies for the current unsteady experimentation of the model scale rotor. Liu et al [11] study the NREL 5MW baseline wind turbine at three different wind speeds, surge velocities, and surge frequencies numerically using a BEM based aerodynamic model with a dynamic inflow correction. DeVaal et al [12] compared the aerodynamic performance of the NREL 5MW turbine subjected to the a surging motion using four different numerical approaches; a quasi-static BEM model, a BEM model with an integrated Pit-Peters dynamic inflow correction, a BEM model with an integrated Stig Oye dynamic inflow correction, and a CFD based actuator disc model. Similarly, Micallef and Sant [13] study the NREL 5MW rotor in surge using a quasi-static BEM model, a generalised dynamic wake model, and a CFD based actuator disk model. The valuable conclusion that has been arrived from these studies is that the wake induced effects of the rotor thrust as a result of the rotor surging into the flow, the degree of which is dependent upon the tip speed ratio, surge frequency, and surge displacement amplitude. The experimental surge operational points considered are drawn primarily from the work of Liu et al [11] and devaal et al [12], the surge frequency considered by Micallef and Sant [13], although representative of a full scale operational condition which would be experienced by a floating wind turbine system, is out with the operational envelope of the experimental apparatus when scaled to the model scale. The surge frequencies studied by Liu at al and devaal et al are 0.1, 0.2, and 0.3rad/s, and between and 1.0rad/s, respectively; the correspond surge displacement amplitudes are, 3.0, 6.0, and 9.0m, and between 2.0 and 16.0m. devaal considers only the rotor operating at its rated wind speed (V = 11.2m/s), Liu et al and Micallef and Sant both consider this same rotor operation in addition to o_ design points. The investigated rotor operational states, defined by Liu et al and Micallef and Sant in terms of inflow wind speed and tip speed ratio, respectively, are 8.0, 11.2 and 16.0m/s and 4.0, 7.0, and The tip speed ratio of the NREL 5MW Baseline Wind Turbine at its rated wind speed of 11.2m/s, as defined by Jonkman et al [14], is 7.0. The model scale surge motion displacement and frequency is derived from the studies discussed by Liu et al [11] and devaal et al [12] by applying a suitable scaling methodology. This is achieved by following the scaling relationships defined by Jain et al [15] for the experimental analysis of the combined effect of hydrodynamic and hydrodynamic force components on a model floating wind turbine rotor and foundation in a wind and wave basin. The model scale surge frequency and displacement are scaled following the relationships defined in Equations 1 and 2, respectively. 165 ( ) ω surge,mod el = ω( surge, full)* λ (1) 166 Asurge (,mod el) = A( surge, full) λ (2) where A is amplitude, ω is the angular frequency and λ is the geometric scaling factor, for the present set of experiments Computational Fluid Dynamics (CFD) Method As a first part of the numerical validation activity, high fidelity mesh sensitivity study is carried as the thrust force is very sensitive to the mesh cluster around the scaled rotor. The level of fine clustering is determined by the y+ value, which is a non-dimensional wall distance for wall bounded flow [1]. The blade geometry was generated in ANSYS ICEM CFD (Version 16.2) by sweeping

6 various cross sections of the scaled rotor airfoil. A hexahedral structured mesh around the scaled rotor of one blade and the surrounding water of turbine rotor was generated and for other blades mesh generated using periodicity option. The 3D model of the scaled rotor model and three kinds of mesh clustering methods (log scale change in near wall and linear towards perpendicular direction) around the rotor used in the mesh sensitivity study are shown in Fig. 5 and 6 respectively Figure 5. 3D model generation of University of Strathclyde scaled rotor Figure 6. Three types of mesh clustering around the blade cross section (a. coarse with 0.59million nodes; b. medium with 1.65million nodes; c. fine with 2.38million nodes-from left to right). The blade geometry is generated through Ansys ICEM CFD (Version 16.2) by sweeping various cross section of the scaled rotor aero profiles derived from full scale NREL 5MW rotor. The modelled rotor along with the computational domain is shown in Fig 7. The hub is modelled to the dimensions used in the tow tank to eliminate any inaccuracies introduced due to the flow variation near the blade root. The computational domain is 4.5 m in width and 2.5 m in depth following the dimensions of the towing tank size and has been divided into 12 sub domains. In comparison with the blade length, the domain extends by four-fold in radial direction and nine-fold in axial direction with sub domains comprising of individual components. A multi-block meshing strategy has been employed to create hexahedral mesh in

7 the outer domain. O-grid type mesh is chosen for the blade domain. The blade geometry mesh and the rotating rotor domain are shown in Fig. 8 and Fig. 9 respectively. The entire computational domain is shown in Fig. 9. The mesh is sufficiently discretized to capture the near wake and far wake field. The scaled rotor is refined to yield an y+ of ~1 near the tip and less than 2 for the rest of the domain as shown in Fig Figure 7. A blade mesh domain of the scaled rotor (medium) Figure 8. Internal rotating domain of the scaled rotor (medium).

8 Figure 9. A complete CFD mesh model of the scaled rotor including internal rotating domain (with total mesh size of 7.32million nodes) The K-Omega SST (Shear Stress Transport) turbulence scheme is employed through Ansys 16.2 CFD solver.. A high order advection scheme and first order numerical method is chosen for turbulence modelling. The k-ω based SST model employs the k-ω model for the near surface treatment and the k-ε model in the free-shear layers. A blending function is adopted to bridge these two models. The SST k-ω model accounts the transportation of the turbulent shear stress and capable of accurately predicting the onset and the magnitude of flow separation under adverse pressure gradients. For the aforementioned reasons, the two-equation SST k-ω model is widely exploited in wind industry for their accurate predictions of flow over blunt body. The K-Omega SST model has a similar form to the standard K-Omega model: And (ρқ) + (ρқu ) = қ Г қ + G қ Y қ +S қ (3) (ρω) + (ρωu ) = Г + G Y +D +DS (4) Gk in the Eq. (3) and Eq. (4) represents the generation of turbulence kinetic energy due to mean velocity gradients. Gw represents the generation of ω. Гk and Гw represents the effective diffusivity of қ and ω respectively. Yk and Yω represent the dissipation of k and ω due to turbulence. Dω represents the cross-diffusion term. Sk and Sω are user-defined source terms. The CFD simulations were carried out with uniform water velocity at the inlet boundary for the third case scenario as shown in Table 2. For mesh sensitive study, the rotor thrust co-efficient is

9 compared against the chosen case of 14 rad/s with 7 TSR and 1 m/s water speed, which is the representative of 1m/s tow speed of the carriage mounted with scaled physical rotor as in Table 2 and the results were published [1]. The water temperature is set at 15 o C for the current study Table 2. Chosen Static Test Cases from University of Strathclyde Test Matrix for CFD Validation TSR Tow Speed (m/s) Rotational Speed (rad/s) Medium size mesh model used in CFD for the validation purposes of static and unsteady test experimental cases. Thrust force alone is considered for comparison as the scaled rotor was developed based on the thrust force related parameter function used in the optimization function [6]. The overall domain mesh size model is with 7.32 million nodes. The chosen mesh model yields the y+ of less than 1 near the tip and less than 2 everywhere else as shown in Fig. 10. Multiple Reference Frame (MRF) and sliding mesh simulation methodology was used in the CFD simulations to validate the thrust and torque predictions of the scaled rotor model. The CFD predicted values are then validated against the measured values of the experiments as in the Table Figure 10. y+ contour of the scaled rotor. A test matrix is developed for both static and unsteady runs. The static runs were carried out to obtain the Ct and Cq in relation to TSR as benchmark values to compare the rotor subjected to unsteady motions. The unsteady runs include sinusoidal surging motions of the rotor from low to extreme frequencies and amplitudes, to demonstrate the effect on the rotor unsteady aerodynamics In order to allow the rotor to rotate at different TSR, the rotor was subjected to various tow 251 speeds and rotational speeds (rad/s) facilitating a smooth distribution over the operating range. The 252 TSR of the rotor was allowed to vary from 3 to 9.5 though a constant TSR should be achieved for 253 static scaling. The model rotational speed of 14 rad/s corresponds to the rated rotational speed of the 254 NREL 5MW of rpm. Other model rotational speeds linearly correspond to full-scale rpm. Thus, for a model rotational speed of Ω m in rad/s, the full scale rotational speedωf in rpm is 256 given by

10 257 Ωm Ω f = *12.1( rpm) 14( rad / s) (5) 258 The full-scale wind speed, Vf, is found from the TSR of the experiment: 259 Vf 63 π * Ωf = 30* TSR (6) since the rotor radius is 63m. The rated conditions of RPM and 11.4m/s wind speed are modelled at a rotational speed of 14.0 rad/s and a tow speed of 1m/s. The boundary conditions for the CFD models are derived from the experimental values and scaled rotor parameters. The objective is to predict the thrust and the drag coefficient in steady cases first for the first level of validation. In the case of a steady or static case, the inlet boundary condition is set with constant water velocity same as the tow speed of the rotor from the experiment. The coefficient of thrust ( Ct ) and the coefficient of torque ( Cq ) in relation to the tip speed ratio are computed analytically, numerically and experimentally. The results are plotted as shown in the Fig. 11. The thrust coefficients from all the three methods are comparable, while the torque coefficient displays a notable difference in analytical prediction (design values) from the well correlated experimental and CFD results. Xfoil predictions of lift coefficient ( Cl ) and drag coefficient ( Cd ) would have contributed significantly to the deviation. It was experimentally verified that the Xfoil over predicts the drag in the low Re range as the flow over the airfoil is extremely complex and nonlinear to compute the drag by panel method. The over prediction is exacerbated by the extrapolation for higher angle of attack from the initial set of lift and drag coefficients computed at lower angle of attack. A possible way of curtailing the error is to experimentally obtain the initial set of Cl and Cd from the wind tunnel test and extrapolate by Viterna or Montgomerie method. Considerable effort has been dedicated in refining the mesh for improved near wall treatment to compute the boundary layer separation and to achieve accurate rotor drag. Since optimization of the airfoil for the operating Re of the scaled rotor is not in the scope of the current study, the effect of low Re are anticipated. The discrepancies due to drag is inevitable especially for the scaled prototype due to premature flow separation on airfoils induced by low Re because of smaller chord length. 283

11 Figure 11. Scenario SFA1: Comparison of thrust co-efficient of static cases; Comparison of torque co-efficient of static cases The Ct and Cq are important dimensionless parameters that determine the amount of momentum and energy extracted from the wind. The coefficient of thrust is defined by T Ct = 0.5ρ AV where T is the rotor thrust force, ρ is the fluid density, A is the rotor plane area and V is the 2 (6) fluid velocity. The coefficient of torque is defined by Q Cq = 0.5πρRV 3 2 (8) where Q is the torque and R is rotor radius As per the Table 3, the complete surge motions of unsteady cases of experimental test cases were carried out in CFD, LR-AeroDyn and LR-uBEM codes. Table 3. Unsteady experimental test case scenarios chosen for numerical validation at the rotor rotational speed of 14 rad/sec. TSR Tow speed, m/s Surge frequency, rad/s Amplitude, m Scenario name for reference 1.12 (0.18Hz) SFA1 1.12(0.18Hz) SFA (0.54Hz) SFA3 3.37(0.54Hz) SFA4 5.61(0.89Hz) SFA5 5.61(0.89Hz) SFA6 1.12(0.18Hz) SFA7 1.12(0.18Hz) SFA8 3.37(0.54Hz) SFA (0.54Hz) SFA (0.89Hz) SFA (0.89Hz) SFA (0.18Hz) SFA (0.18Hz) SFA (0.54Hz) SFA (0.54Hz) SFA (0.89Hz) SFA (0.89Hz) SFA18 For unsteady test cases, the sinusoidal surging motions for the model rotor were designed to be based on the work by [11] and [12]. As the surge motion is predominant in floating offshore wind

12 turbine applications [13], a detailed surge motion experiments were carried out with scaled rotor. The scaling methodology employed is found in [7] and can be described as in equation [1-2]. The chosen unsteady experimental test cases scenarios are given in the Table 3 for CFD model validation. The scenarios are chosen carefully to validate the effects of unsteadiness by the various numerical simulations. For each of three different TSRs, three different surge frequencies and two amplitudes (minimum and maximum) are chosen to capture the unsteady effect behavior. For the scenarios given in the Table 2, the steady state MRF simulations were first carried out with the rotational speed of the rotor and towing speed as water inlet velocity in CFD simulations. The results of the steady state calculations were used to initialize the solutions for a complete transient case involving the surge motion of the scaled rotor unsteady test case scenario. The surge motion methodology was developed in Ansys-CFX (Version 16.2) software. The domains were structured in such a way that both the blade rotations and rotor pitching motions could be handled smoothly by the solver. The rotor domain had a sliding mesh interface for blade rotations and the mesh motion applied for pitching had an extremely high stiffness in this domain which was relaxed gradually towards the outer domain to preserve the fine boundary layer mesh. This high stiffness ensured that the mesh in the rotor domain had almost no relative nodal displacement, as the mesh on the blade had the first node on the order of microns to yield a y+ ~ LR AeroDyn Model AeroDyn (V15.04) is a open source (NREL) time-domain wind turbine aerodynamics module [16] that has been tailored for Marine Hydorkinetic Turbines (MHT). MHT AeroDyn module is customized for scaled rotor performance prediction of unsteady experimental test case runs as shown in Table 3 as the model was refined to cover whole scenario. FAST model settings. AeroDyn calculates aerodynamic loads on both the blades and tower. Aerodynamic calculations within AeroDyn are based on the principles of actuator lines, where the three-dimensional (3D) flow around a body is approximated by local two-dimensional (2D) flow at 17 cross sections, and the distributed pressure and shear stresses are approximated by lift forces, drag forces, and pitching moments lumped at a node in a 2D cross section. Analysis of 17 nodes are distributed along the length of each blade, the 2D forces and moment at each node are computed as distributed loads per unit length, and the total 3D aerodynamic loads are found by integrating the 2D distributed loads along the length. For the MHK based model customized for scaled rotor of Strathclyde University Rotor turbine, calculates the influence of the wake via induction factors based on the quasi-steady Blade-Element/Momentum (BEM) theory, which requires an iterative Brent s method to nonlinear equation. By quasi-steady or equilibrium wake (EQUIL) model, it is meant that the induction reacts instantaneously to loading changes. The induction calculation, and resulting inflow velocities and angles, are based on flow local to each analysis node of each blade, based on the relative velocity between the fluid and structure (including the effects of local inflow skew, shear, and turbulence). This method has no time log which means no dynamic inflow. The Glauert s empirical correction (with Buhl s modification) is used the linear momentum balance at high axial induction factors. In the BEM solution, Prandtl tip-loss, Prandtl hub-loss models are applied. Angle-of-attack calculations in AeroDyn assume that the axial induction factor only applies to the free-stream wind velocity(vα). To calculate the total relative wind speed(vrel) normal to the rotor disc, each blade element s structural velocity is added to the free-stream wind velocity at the rotor disc, as shown below. V =V (1 a) + V ( 9)

13 Vrotor, where is the structural velocity of the blade element normal to the disc (measured positive when pointing upwind). The assumption made in AeroDyn is that the structural velocities are the product of structural vibrations at high frequencies, which would results in relatively small induced velocities. However, when considering floating offshore wind turbines (FOWT), low-frequency motions, particularly, in surge, pitch and yaw degrees of freedom, which induce change in the free-stream velocity, could lead to high induced velocities. In low-frequency motion, a better way of expressing the relative wind speed normal to the rotor disc would be: V rel =(V α +V rotor )(1 a) (10) LR Unsteady BEM(uBEM) Model The unsteady blade element momentum method (ubem) used in the present study, is based on the method presented in [17]. The relative velocity vector is given by: 0 V =V +W+ Ωr cos(θ ) (11) 0 where V0 is the blade-specific wind speed at the blade element including relative speed due to rotor motion, is the rotor rotational speed in rad/s, r is the local blade segment radius. The flow angle, φ, is the angle between the relative velocity and the normal of the rotor plane. φ = arctan V rel,y V rel,z (12) The normal (z) and tangential (y) induced velocities are then given by: W z = W y = V rel 2 C l cos(φ)cb 0 8F (V 0 A) f g 0 πr W z V rel 2 C l sin(φ)cb 0 8F (V 0 A) f g 0 πr W z (13) (14) where B is the number of blades, F is the tip-loss factor, fg is the Glauert correction for high axial induction factors and Cl is the coefficient of lift computed using the Du & Selig stall-delay model [18] and the shape-specific modified Beddoes-Leishman model of Singapore Wala et al [19] the angle of attack equal to the flow angle less the blade twist. Wx is set to 0. At every time step, for each blade element in each blade, equations (1) to (2) are iterated until there is no change in the induced velocity vector. When the steady-state induced velocity vector is computed, it is corrected for the dynamic wake effect using the dynamic wake model of Singapore Wala et al [20]. The force coefficients are then recomputed to determine the unsteady forces at each blade element. 3. Results and discussion of unsteady test cases For the unsteady case of numerical simulation, the last two cycles of six cycle surge motion simulation results are extracted for comparison and further analysis. This is to ensure that all the

14 startup transient factors are eliminated. Results of CFD, LR-AeroDyn and LR-uBEM model computations are compared against the experimental results to comprehend their ability in predicting the forces due to unsteady effects. The variation in mean and standard deviation of thrust and torque values of different numerical simulation methods would determine its capability and limitations to predict the unsteady aerodynamic loads on the scaled rotor. Albeit, thrust is the only imperative parameter for the comparison between the numerical methods in this case (as the scaled rotor is designed against lift curve or thrust of full scale reference rotor), torque comparisons will further establish their capabilities Figure 12. Scenario SFA1: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 13. Scenario SFA1: Torque comparison; Torque comparison in box plot with 25 and 75% Figure 14. Scenario SFA2: Thrust comparison; Thrust comparison in box plot with 25 and 75%.

15 Figure 15. Scenario SFA2: Torque comparison; Torque comparison in box plot with 25 and 75%. Poring over the Fig [12-15] of 0.18 Hz surge motion with 8.5 TSR, it is evident that the mean thrust is inversely proportional to the surge amplitude, whereas the torque increases marginally. For the same scenario as in the Fig [48-55], the thrust predicted by the numerical simulation varies within 10 % of the experimental results. Another interesting finding is that the cyclical variation of thrust and torque (standard deviation) computation between the numerical models is diminutive Figure 16. Scenario SFA3: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 17. Scenario SFA3: Torque comparison; Torque comparison in box plot with 25 and 75%.

16 Figure 18. Scenario SFA4: Thrust comparison; Thrust comparison box plot with 25 and 75% Figure 19. Scenario SFA4: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [16-19] and Fig [48-55] for the scenario 0.54 Hz surge motion with 8.5 TSR, mean thrust reduces as the surge amplitude increases in both experiments and LR-AeroDyn model predictions, whereas it reduces in CFD and LR-uBEM computations. There is a substantial increase in torque for all numerical computations with minimal variation between the predicted values. Prediction of cyclical thrust variation (standard deviation) by LR-uBEM model is well correlated with experimental results when compared to other two numerical method predictions for the increased amplitude of 0.54Hz surge motion Figure 20. Scenario SFA5: Thrust comparison; Thrust comparison in box plot with 25 and 75%. 431

17 Figure 21. Scenario SFA5: Torque comparison; Torque comparison in box plot with 25 and 75% Figure 22. Scenario SFA6: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 23. Scenario SFA6: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [20-23] and Fig [48-55] of the scenario 0.89 Hz surge motion with 8.5 TSR, mean thrust increases as the surge amplitude increases for the experiments and LR-uBEM model predictions, whereas it reduces in CFD and LR-AeroDyn model predictions. LR-uBEM mean thrust error exceeds 10%. Torque reduces drastically in all the numerical methods as surge amplitude increases. Prediction of thrust cyclic variation (standard deviation) by LR-uBEM model is well correlated with experimental results.

18 Figure 24. Scenario SFA7: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 25. Scenario SFA7: Torque comparison; Torque comparison in box plot with 25 and 75% Figure 26. Scenario SFA8: Thrust comparison; Thrust comparison in box plot with 25 and 75%. 460

19 Figure 27. Scenario SFA8: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [24-27] and Fig [48-55] of the scenario 0.18 Hz surge motion with 7 TSR, mean thrust does not vary significantly when the surge amplitude increases for experiments, LR-AeroDyn and LR-uBEM model predictions, whereas it increases in CFD model predictions. Mean torque also exhibit minimal variation in all the numerical method predictions as the surge amplitude increases and the values are almost same. Predictions of cyclical thrust variation (standard deviation) between the numerical models is minimum Figure 28. Scenario SFA9: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 29. Scenario SFA9: Torque comparison; Torque comparison in box plot with 25 and 75%.

20 Figure 30. Scenario SFA10: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 31. Scenario SFA10: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [28-31] and Fig [48-55] of the scenario 0.54 Hz surge motion with 7 TSR, mean thrust is inversely proportional to surge amplitude for experiments, LR-AeroDyn and CFD model predictions, whereas it increases in LR-uBEM model predictions. Mean torque increases in experiments and all numerical predictions as the surge amplitude increases Figure 32. Scenario SFA11: Thrust comparison; Thrust comparison in box plot with 25 and 75%.

21 Figure 33. Scenario SFA11: Torque comparison; Torque comparison in box plot with 25 and 75% Figure 34. Scenario SFA12: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 35. Scenario SFA12: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [32-35] and Fig [48-55] of the scenario 0.89 Hz surge motion with 7 TSR, mean thrust reduces with increase in surge amplitude, which is similar to the experimental results, LR-AeroDyn and CFD model predictions, whereas it exhibits an increasing trend in LR-uBEM model predictions. Error in mean thrust exceeds 10% in LR-uBEM model predictions. Mean torque increases in experiments and all numerical predictions as the surge amplitude increases. Prediction of thrust cyclic variation (standard deviation) by LR-uBEM is accurate compared to other numerical methods.

22 Figure 36. Scenario SFA13: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 37. Scenario SFA13: Torque comparison; Torque comparison in box plot with 25 and 75% Figure 38. Scenario SFA14: Thrust comparison; Thrust comparison in box plot with 25 and 75%. 515

23 Figure 39. Scenario SFA14: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [36-39] and Fig [48-55] of the scenario 0.18 Hz surge motion with 6 TSR, mean thrust slightly reduces when the amplitude increases in CFD and LR-AeroDyn model predictions, whereas increases moderately in experiments and LR-uBEM model predictions. Mean torque increases marginally in experiments and all numerical predictions as the amplitude increase. Prediction of thrust cyclic variation (by standard deviation) by all numerical methods are almost equal Figure 40. Scenario SFA15: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 41. Scenario SFA15: Torque comparison; Torque comparison in box plot with 25 and 75% Figure 42. Scenario SFA16: Thrust comparison; Thrust comparison in box plot with 25 and 75%.

24 Figure 43. Scenario SFA16: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [40-43] and Fig [48-55] of the scenario 0.54 Hz surge motion with 6 TSR, mean thrust reduces when the surge amplitude increases in CFD and LR-AeroDyn model predictions which is in line with experimental results, whereas the thrust increases in LR-uBEM model prediction. Mean torque increases marginally in experiments and all numerical predictions except for the CFD model prediction when the surge amplitude increases. Computation of cyclical thrust variation (standard deviation) by all numerical methods is marginally different with each other Figure 44. Scenario SFA17: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 45. Scenario SFA17: Torque comparison; Torque comparison in box plot with 25 and 75%. 549

25 Figure 46. Scenario SFA18: Thrust comparison; Thrust comparison in box plot with 25 and 75% Figure 47. Scenario SFA18: Torque comparison; Torque comparison in box plot with 25 and 75%. As in Fig [44-47] and Fig [48-55] of the scenario 0.89 Hz surge motion with 6 TSR, mean thrust reduces with increase in surge amplitude for experiments and LR-AeroDyn model predictions, whereas it increases in LR-uBEM and CFD model predictions. Mean torque increases as surge amplitude increases for experiments and all numerical predictions except for CFD model prediction. Prediction of thrust cyclic variation (standard deviation) by all numerical methods is marginally different from each other.

26 Figure 48. Mean thrust comparison for all 18 scenarios Almost all numerical methods over predict the mean thrust values against experiments when TSR is 8.5, whereas TSR 6 under predicts the mean thrust values. LR-uBEM over predicts the mean thrust at very high surge frequencies and amplitudes in all the TSR values Figure 49. Mean torque comparison for all 18 scenarios Almost all the numerical methods over predicts the mean torque values in comparison with experimental results for most of the TSR scenarios except TSR 6.

27 Figure 50. Mean thrust comparison: Percentage (%) error with respect to experiment Almost all numerical methods predicts the mean torque within 10% error except LR-uBEM model at higher surge amplitude scenarios Figure 51. Mean torque comparison: Percentage (%) error with respect to experiment The percentage error in torque prediction is higher when compared to experimental results with notable change at 8.5 TSR than 7 and 6 TSR scenarios.

28 Figure 52. Comparison of standard deviation of thrust with changes in amplitude in surging cycles As expected, the standard deviation of thrust value is higher as the surge motion frequency increases. The standard deviation of thrust values is lower in lower amplitudes of each cyclic surge motion frequencies. Moreover, all the numerical models are able to predict accurately at lower amplitude surge motion irrespective of surge frequencies. At higher amplitude and higher frequencies, LR-uBEM predicts closer to experimental values Figure 53. Comparison of standard deviation of torque with changes in amplitude in surging cycles 591

29 Figure 54. Comparison of standard deviation of thrust with changes in amplitude in surging cycles: in percentage (%) error The error range of thrust cyclic variation (in standard deviation) is from 0-40% for TSR 8.5 and TSR 7 Scenarios, whereas -30 to 50% at 6 TSR Figure 55. Comparison of standard deviation of torque with changes in amplitude in surging cycles: in percentage (%) error The error range of torque cyclic variation (in standard deviation) is from 0-35% for TSR 8.5 and TSR 7 Scenarios, whereas 0 to 55% at 6 TSR.

30 Figure 56. SFA2 mean rotor position velocity contour plots: Line plots showing tip vertices; contour plot Figure 57. SFA2: near wake to far wake filed velocity contour plots at 0.5m intervals from rotor plane in the rotating domain The 2D velocity contour profiles and near wake contour profiles are given in Fig. 56 and Fig. 57 respectively for the scenario of SFA2 at the end of 6th surge motion cycle. As shown in Fig.58 extracted from [21], when the axial induction factor exceeds 0.5, the turbine rotor will no longer be in wind mill state and will be operating in turbulent wake state until the induction factor is less than 1. The current study bolsters the fact that the surge cyclic motions are pushing the rotor under investigation to the turbulent wake state as depicted in Fig. 59 of SFA10 scenario.

31 Figure 58. Axial induction factor Vs Thrust/thrust co efficient (Eggleston and Stoddard,1987) Figure 59. Axial induction factor of node of the scaled rotor for the SFA10 scenario with LR-AeroDyn model simulation. 4. Conclusion The flow characteristics around a FOWT is a highly complex phenomena as it is simultaneously subjected to aerodynamic and hydrodynamic forces from wind and ocean waves. The study on sensitivity of the aerodynamic behavior with respect to the changes in platform motion is inevitable, as small changes in platform motion will be amplified due to the tower height. The current study focused on the investigation of unsteady aerodynamic loading through various numerical codes. A scaled floating rotor has been successfully constructed with necessary instrumentation and induced with hydrodynamic motions, similar to a FOWT operating conditions. The experimental outcome is compared with the selected numerical codes, LR-AeroDyn and LR-uBE. An unsteady CFD has been performed to assess the accuracy of the simulation. All the numerical

32 codes together with the CFD are compared with each other and also with the experimental result. It is evident from the comparison that, the CFD and other numerical models also can predict the mean thrust values close to the experimental results (within 7.5%) especially in the lower surge frequency of 0.18Hz (or less) irrespective of TSR. Other numerical codes exhibit a variation of 15 % from the experimental results for other surge frequencies and amplitudes. The complex flow field around the rotor and the blade tip vortices has been visualized. The computational mesh quality should be further improved with refined mesh around near wake regions and smaller time steps for accurate results. The detailed CFD visualization unfolded the fact that the windmill changes its operating state due to the strong interaction of rotor with its own wake instantaneously at higher amplitudes and surge frequencies. The wake strength during the surge motion has to be accurately resolved in CFD simulation for the better predictions of unsteady rotor loading. Though LR-AeroDyn is equipped with qasi-steady state BEM method, utmost care has to be dedicated when using for higher surge frequencies and amplitudes. LR-uBEM code predicts comparatively well at higher surge frequencies and amplitudes as it is based on dynamic in flow modeling methods, yet variation of 10-15% do exist in some cases. 5. Future work The numerical models will be further refined based on their strength for full scale 5MW NREL turbine at its operating conditions of TSR, surge frequencies and amplitude. The computed results are employed for digital twin approach in which the remaining useful life of key components such as power converters are predicted. The proposed approach will curtail the maintenance and inventory cost especially for FOWT. The CFD mesh will be enhanced to improve the predictions especially during the extreme operating conditions such as high waves and gust. Author Contributions: CFD and LR-AeorDyn, Krishnamoorthi Sivalingam; Scaled Rotor Design, Development and Tow Tank Steady and Unsteady Experiments, Steven Martin.; LR-uBEM, Abdulqadir Aziz Singapore Wala. Acknowledgments: Authors gratefully acknowledges the great support of Lloyds Register and University of Strathclyde University for the numerical simulation and experiments. This research was supported by Lloyds Register. Conflicts of Interest: Declare References 1. Krishnamoorthi Sivalingam, Peter Davies, Abdulqadir Aziz Singapore Wala, Sandy Day; CFD Validation of Scaled Floating Offshore Wind Turbine Rotor. 2nd International Conference on Green Energy and Applications (ICGEA) 2018, DOI: /ICGEA Half-Year Report. Technical report, World Wind Energy Association, Bonn, Germany, 3. Musial, W et al (2004), Feasibility of Floating Platform Systems for Wind Turbines, 23rd ASME Wind Energy Symposium 4. Anand Bahuguni, Krishnamoorthi Sivalingam and Peter Davies (2014), Implementation of Computational Methods to Obtain Accurate Induction Factors for Offshore Wind Turbines Volume 9B: Ocean Renewable Energy, ASME rd International Conference on Ocean, Offshore and Arctic Engineering 5. Krishnamoorthi Sivalingam et al (2015), Effects Of Platform Pitching Motion On Floating Offshore Wind Turbine (FOWT) Rotor, Offshore Technology Conference, Houston, Texas, USA 6. Steven Martin, Sandy Day, and Conor B. Gilmour, Rotor Scaling Methodologies for Small Scale Testing of Floating Wind Turbine Systems, Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering 7. E-J de Ridder, W Otto, G-J Zondervan, F Huijs, and G Vaz. Development of a Scaled-Down Floating Wind Turbine for Offshore Basin Testing. In Proceedings of the ASME rd In- ternational Conference on Ocean, Offshore and Arctic Engineering, pages 1{11, San Francisco, California, American Society of Mechanical Engineers.