Numerical Validation of Floating Offshore Wind Turbine Scaled ... - MDPI

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Numerical Validation of Floating Offshore Wind Turbine Scaled Rotors for Surge Motion Krishnamoorthi Sivalingam 1, *, Steven Martin 2 and Abdulqadir Aziz Singapore Wala 1 1 2

*

Lloyd’s Register Singapore Pte Ltd., 1 Fusionopolis Place, #09-11 Galaxis, Singapore 138522, Singapore; [email protected] Wind Energy Systems Centre for Doctoral Training, University of Strathclyde, Glasgow G1 1XQ, UK; [email protected] Correspondence: [email protected]; Tel.: +65-3163-0614

Received: 29 August 2018; Accepted: 26 September 2018; Published: 27 September 2018

Abstract: Aerodynamic performance of a floating offshore wind turbine (FOWT) is significantly influenced by platform surging motions. Accurate prediction of the unsteady aerodynamic loads is imperative for determining the fatigue life, ultimate loads on key components such as FOWT rotor blades, gearbox and power converter. The current study examines the predictions of numerical codes by comparing with unsteady experimental results of 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 influences the windmill operating state due to strong flow interaction between the rotating blades and generated blade-tip vortices. Almost in all frequencies and amplitudes, CFD, LR-BEM and LR-uBEM predictions of mean thrust shows a good correlation with experimental results. Keywords: CFD; unsteady BEM; floating offshore wind turbine; scaled wind turbine rotor

1. Introduction This paper is an extension and continuation of earlier work presented at the 2018 2nd International Conference on Green Energy and Applications of IEEE (ICGEA) [1]. The insatiable demand for the energy and the rising greenhouse gas emissions is pushing the energy sector towards renewable energy utilization. Among the various renewable energy sources, wind energy is one popular form of energy due to its reliability and cost competitiveness. The wind industry has seen a tremendous growth in the past decades [2], leading to the addition of 52.6 GW of power to an existing 539 GW as of 2017. Hence, the wind sector is motivated to explore technologies on the far side of conventional land-based installations to meet the projected energy demand. Due to the consistent and steadier wind, offshore wind turbine is one amongst the known potential solutions for substantial annual energy output. Offshore wind technologies are continuously improved by myriad experimental, numerical and field studies. Beyond a certain depth, the standard monopile or gravity-based foundations are not economically profitable. Hence floating wind turbines are proposed as an alternative solution in terms of cost and reliability [3]. Innovative floating wind turbine concepts aiming to curtail the installation and maintenance costs are an active research topic in recent years. Some feasibility studies are in progress with a few floater types at a prototype level to demonstrate the techno-economic viability for deep sea use.

Energies 2018, 11, 2578; doi:10.3390/en11102578

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To wind andand other conventional power sectors, it is essential for the floating Tocompete competewith withonshore onshore wind other conventional power sectors, it is essential for the wind sector to explore the ways to reduce the capital and operation and maintenance (O&M) cost. floating wind sector to explore the ways to reduce the capital and operation and maintenance (O&M) The such as theasselection of right platforms and access to thetoassets in thein deep cost.challenges The challenges such the selection of floating right floating platforms and access the assets the sea along with the offshore environment conditions are the main reasons that increase the O&M costs deep sea along with the offshore environment conditions are the main reasons that increase the O&M of theof floating wind wind sector.sector. Due to these reasons, the floating windwind sector is expected to meet the costs the floating Due to these reasons, the floating sector is expected to meet stringent requirement of reliability criteriacriteria against against the strong loads and loads environmental conditions. the stringent requirement of reliability thewind strong wind and environmental These demand an accurate prediction of various forces with combined environmental loading for the conditions. These demand an accurate prediction of various forces with combined environmental floating wind turbine systems design. systems design. loading offshore for the floating offshore wind turbine Numerical simulations play an important role in every stage of the turbine product life cycle Numerical simulations play an important role in every stage of wind the wind turbine product life development, from conceptual design to operation, maintenance and decommissioning to optimize cycle development, from conceptual design to operation, maintenance and decommissioning to CAPEX OPEXand (O&M). In(O&M). additionIntoaddition their significant in predicting wind loads optimizeand CAPEX OPEX to their contribution significant contribution inthe predicting the on the turbine, numerical simulations also help to develop radically new designs. During the During design wind loads on the turbine, numerical simulations also help to develop radically new designs. review, compliance certification process, thousands of simulations areofnormally performed. Hence, the design review,and compliance and certification process, thousands simulations are normally the typical engineering code like NREL FAST,code is often to assess performance behaviors performed. Hence, the analytic typical engineering analytic likeused NREL FAST,the is often used to assess the of the turbine. To compute aerodynamics loads, AeroDyn sub module is integrated with FAST modular performance behaviors of the turbine. To compute aerodynamics loads, AeroDyn sub module is framework. Blade Element Momentum (BEM) and Generalized Wake Dynamic (GDW) methods are integrated with FAST modular framework. Blade Element Momentum (BEM) and Generalized Wake implemented in AeroDyn. Dynamic (GDW) methods are implemented in AeroDyn. The wind industry has adopted variousvarious mathematical models to models computeto thecompute aerodynamic The windturbine turbine industry has adopted mathematical the loads on the onshore turbine rotor. Among the prescribed or free-wake vortex method, acceleration aerodynamic loads on the onshore turbine rotor. Among the prescribed or free-wake vortex method, potential method, NREL FASTNREL with AeroDyn module, BEM model is preferred their low acceleration potential method, FAST withsub AeroDyn sub module, BEM model is for preferred for computational requirements and well understood [4]. Although BEM codes include corrections their low computational requirements and well understood [4].the Although the BEM codes include for wake expansion, pressure due wake rotation improved accuracy by accounting for the corrections for wakethe expansion, the topressure due toand wake rotation and improved accuracy by losses at blade root and tip sections, they are developed for wind turbines with static foundations. accounting for the losses at blade root and tip sections, they are developed for wind turbines with Hence the assumptions in the BEM are not applicable floating offshore turbines where the pitching static foundations. Hence assumptions in BEM[5] arefor not applicable [5] for floating offshore turbines and surging motions [6] of the platform leads to the turbine rotor going through different wake states where the pitching and surging motions [6] of the platform leads to the turbine rotor going through as shown in Figure 1. Various non-linear effects like rotor-wake interactions, wake-wake interactions, different wake states as shown in Figure 1. Various non-linear effects like rotor-wake interactions, wake meandering etc., arewake not accounted in etc., BEMare theory. wake-wake interactions, meandering not accounted in BEM theory.

Figure 1. 1. Hypothetical Hypothetical floating floating wind wind turbine turbine motions motions [1]. [1]. Figure

Lloyds Register (LR) has been actively actively involved involved in the the development development of of numerical numerical models models and and experimental onon scaled rotorrotor provides an insight on the on aerodynamic loading experimental modelling. modelling.Experiments Experiments scaled provides an insight the aerodynamic loading of the and to the validate the non-linear models. As platform motions has greater of the rotor androtor to validate non-linear models. As platform motions of FOWT of hasFOWT greater influence influence on theaerodynamic unsteady aerodynamic a scaled of the rotor was designed to study on the unsteady response, a response, scaled model of themodel rotor was designed to study the effect [7]. the effect [7]. The platform motions significantly affect the power and thrust characteristics of the rotor almost to the same order as the effect of tip speed ratio (TSR) and the blade angle. A scaled

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The platform motions significantly affect the power and thrust characteristics of the rotor almost to the same order as the effect of tip speed ratio (TSR) and the blade angle. A scaled down model of the NREL 5 MW rotor was designed and tested in the wave tank (immersed in the water) to match the Reynolds number Re, as in field operation. The experiments are conducted with the focus on surge motion [8] and its effects on aerodynamic performances. The BEM-based AeroDyn model was modified (LR AeroDyn) to predict the hydrodynamic load on to the scaled rotor. LR has enhanced the BEM code (LR-uBEM) to simulate the unsteady aerodynamic behavior of the rotors. The LR-uBEM model implements the dynamic inflow model based on the elemental aerodynamic loads prediction of individual blades. To gauge the accuracy of engineering numerical codes LR AeroDyn and LR-uBEM, high fidelity CFD model was developed and validated against the experimental simulation. 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 [9–12]. It is highly challenging to match the performance of the scaled rotor for the coefficients such as coefficient of power (Cp), coefficient of torque (Cq), and the coefficient of thrust (Ct), to a full scale reference rotor due to the incompatibility of the three primary scaling criteria, the maintenance of geometric, kinematic, and dynamic similarity between model and full scale. Geometric and kinematic similarity are readily achieved by the application of constant geometric scale factor and the maintenance of the tip speed ratio, respectively. However, in doing so the dynamic similarity criteria, defined principally as the maintenance of the Reynolds number for the flow over the blade at model and full scale, is typically not met. In order to address this, a number of researchers have proposed a global performance matching approach for the design of model scale wind turbine rotors where the primarily objective was not the study of the rotor in normal operating conditions [9–12]. Examples of such are the MARIN Stock Wind Turbine for the evaluation of the performance of floating wind turbine foundations scaled down under wind and wave action and the evaluation of advanced control strategies under unsteady operating conditions. In both cases, the design objective was to match the coefficients of the model scale to their respective full scales for a range of operating tip speed ratios. This is achieved by changing the aerofoil profile in the scaled down model along the length of the blade so as to increase the lift coefficient, increasing the chord distribution along the length of the blade by a constant factor, and altering the twist distribution to maximize the lift to drag ratio for the tip speed ratios of primary interest. The criteria for geometric similarity is abandoned, kinematic similarity is maintained, the deficit in the dynamic similitude is corrected for. As is the case for the two rotor designs discussed, the objective of the experiments in this case was the evaluation of the rotor performance subjected to external influence relative to the normal operating state. Specifically, the quantification of the time varying coefficient of thrust resulting from the periodic motion of a rotor at a number of frequencies and amplitudes typical of floating wind turbine system. As such a similar approach to the scaling criteria has been taken. However, in this case, in addition to the global performance matching model scale rotor design objective, additional objectives have been defined in attempt to maintain the critical local performance measures. The model scale rotor requirements are defined as follows: 1. 2. 3. 4.

The coefficient of thrust of the model rotor must be similar to the full scale reference for a range of tip speed ratios, The chord must be scaled by the same geometric scale factor as the diameter of the rotor, The twist distribution along the non-dimensional length of the model blade must be same as full scale reference, The axial induction factor along the non-dimensional length of the model blade must be same as the full scale reference for a range of tip speed ratios.

a new methodology has been adopted to match the scaled airfoil Re to the full-scale airfoil Re. Significant effort has been dedicated to optimize the airfoil profile in order to match the lift curves even in low Re [7], by retaining the twist of 5 MW NREL rotor blade. As the lift coefficient heavily influences the2018, non-dimensional rotor thrust and the axial induction factor, the primary objective is to Energies 11, 2578 4 of 25 achieve the required lift coefficients of airfoil sections and in turn complying the design requirements 1 and 4. Considering the blade length of the scaled rotor, three significant airfoil profiles are The full scale reference rotor used for this study is the NREL 5 MW Reference wind turbine [13], employed the six profiles in full scale model. following Table 1 indicates the thisin hascomparison been studied to extensively and has been extensively reportedThe in literature. This was also the full-scale rotor airfoils corresponding airfoilsThe of diameter the scaled basis for the design and of thethe MARIN Stock Wind Turbine. of therotor. scaled The modelshape of the of SMA rotor has been chosen to be 1.0 m in order to minimize experimental blockage effects resulting in a model (Strathclyde Model rotor Airfoil) series airfoils are shown in comparison to the full-scale geometric scale factor of 126.0. As aerodynamic coefficients largely influence the rotor performance, airfoils in Figure 2. The methodology followed to accomplish the airfoil profiles and further analysis a new methodology has been adopted to match the scaled airfoil Re to the full-scale airfoil Re. on the scaled rotor model performances are described in more detail in [7,14]. Scaled rotor parameters Significant effort has been dedicated to optimize the airfoil profile in order to match the lift curves are shown designed are similar full rotorheavily following the evenin inTable low Re1. [7],The by retaining thescaled twist ofrotor 5 MWblades NREL rotor blade. Astothe liftscale coefficient procedure of Froude scaling. A comparison rotor model and full scale airfoil influences the non-dimensional rotor thrust of andthe the scaled axial induction factor, the primary objective is togeometry achieve the required lift coefficients of airfoil sections and in turn complying the design requirements 1 is shown in Figure 2. and 4. Considering the blade length of the scaled rotor, three significant airfoil profiles are employed in comparison to the six profiles in full1.scale model. following Table Scaled rotorThe airfoil details.Table 1 indicates the full-scale rotor airfoils and the corresponding airfoils of the scaled rotor. The shape of SMA (Strathclyde Model rotor Airfoil) series airfoils are shown in comparison to the full-scale model airfoils*in Figure 2. Cross-Sectional Element/ Element Center Chord (m) Element Center Radius (m) Twist (o) The methodology followed to accomplish the airfoil profiles and further analysis on the scaled rotor Node Profile are described in more detail in [7,14]. Scaled rotor parameters are shown in 1 model performances 0.023 13.308 0.028 Cylinder Table 1. The designed scaled rotor blades are similar to full scale rotor following the procedure of 2 0.044 13.308 0.031 Cylinder Froude scaling. A comparison of the scaled rotor model and full scale airfoil geometry is shown 3 0.066 13.308 0.033 Cylinder in Figure 2.

4 5 6 7 8 9 10 11 12 13 14 15 16 17

Element/Node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.093 13.308 0.036 0.126 11.48rotor airfoil details. 0.037 Table 1. Scaled 0.158 10.162 0.035 Element Center Radius (m) Twist (o ) Element Center Chord (m) 0.191 9.011 0.034 0.023 13.308 0.028 0.223 0.044 7.795 13.308 0.031 0.032 0.066 13.308 0.033 0.03 0.256 6.544 0.093 13.308 0.036 0.288 0.126 5.361 11.48 0.037 0.028 0.158 10.162 0.035 0.321 0.191 4.188 0.026 9.011 0.034 7.795 0.032 0.024 0.354 0.223 3.125 6.544 0.03 0.386 0.256 2.319 0.022 0.288 5.361 0.028 4.188 0.026 0.02 0.419 0.321 1.526 0.354 3.125 0.024 0.446 0.386 0.863 2.319 0.022 0.018 1.526 0.02 0.017 0.467 0.419 0.37 0.446 0.863 0.018 0.489 0.467 0.106 0.37 0.017 0.011 0.489

0.106

0.011

DU40 (SMA3540) DU35 (SMA3540) DU35 (SMA3540) * Cross-Sectional Profile DU30 (SMA2130) Cylinder CylinderDU25 (SMA2130) CylinderDU25 (SMA2130) DU40 (SMA3540) DU21 (SMA2130) DU35 (SMA3540) DU35 (SMA3540) DU21 (SMA2130) DU30 (SMA2130) DU25 (SMA2130) NACA64 (SMA64) DU25 (SMA2130) NACA64 (SMA64) DU21 (SMA2130) DU21 (SMA2130) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64) NACA64 (SMA64)

Note: * The name in the bracket is scaled rotor airfoil with corresponding airfoil of 5 MW NREL rotor Note: * The name in the bracket is scaled rotor airfoil with corresponding airfoil of 5 MW NREL rotor airfoils. airfoils.

Figure 2. Scaled rotor model airfoil shapes in comparison with reference [1].

Figure 2. Scaled rotor model airfoil shapes in comparison with reference [1].

Lift coefficient for the SMA airfoils are computed using Xfoil for the model Re, while for the fullscale airfoils, the generated lift coefficients from Xfoil are verified through wind tunnel tests. The

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airfoils are computed using Xfoil for the model Re, while for 5 ofthe 26 full-scale airfoils, the generated lift coefficients from Xfoil are verified through wind tunnel tests. The result compare with experimental curves lowerAoA, AoA,but butatat higher higher AoA AoA Xfoil XfoilXfoil result compare wellwell with thethe experimental curves at at lower This can can be be attributed attributed to to the the earlier earlier onset onset of of flow separation in the overpredicts the coefficients. This experimentation. A A 3D 3D rendering rendering of of the the fully fully assembled assembled rotor is shown in Figure 3. The blades are experimentation. ◦ the hub hub at ataafixed fixedpitch pitchangle angleofof0°0 using usinga aflange flange machined root end of the blades; fixed to the machined in in thethe root end of the blades; as as a result the accuracy of the pitch angle is defined by the machining tolerance of the stainless a result the accuracy of the pitch angle is defined by the machining tolerance of the stainless steel steel components and notofthat of the measurement of the pitch angle itself asbewould beifthe case if components and not that the measurement of the pitch angle itself as would the case a locking a lockingtype bearing typewas fixture was used.this Using this approach the model scaleishub is bearing fixture used. Using approach requiresrequires that thethat model scale hub nonnon-dimensionally larger than the full scale reference to allow for the sufficient space to make the dimensionally larger than the full scale reference to allow for the sufficient space to make from the theblade bladetotohub huband and hub shaft. However, the increased diameter thedoes hub connection from hub to to shaft. However, the increased diameter of theofhub doesrequire not require that thegeometry blade geometry is in altered in anyother section than that defined with a not that the blade is altered any section thanother that defined with a cylindrical cylindrical section Table 1 andwill as such noon impact on the aerodynamic performance section detailed indetailed Table 1 in and as such havewill no have impact the aerodynamic performance of the of the blades. blades.

Figure Figure 3. 3. 3D 3D Model Model of of the the scaled scaled rotor. rotor.

During the design stage, the global model rotor performance was compared to the full scale reference for non-dimensional thrust and torque. The thrust force on the rotor is primarily influenced by the theaerofoil aerofoilliftlift and as such the match between the model and reference for this is property is and as such the match between the model and reference for this property favorable. favorable. The aerofoil increased aerofoil at the experimental Reynoldsresults number in atorque reduced The increased drag at thedrag experimental Reynolds number in aresults reduced as torque as compared to therotor. full scale rotor. was an expected result of implementing this scaling compared to the full scale This was anThis expected result of implementing this scaling methodology. methodology. The local blade performance was assessed for the model scale rotor by comparing the axial and The local blade performance was assessed for along the model scale rotor by comparing tangential Induction factors and the angle of attack the non-dimensional length of the the axial bladeand for tangential Induction factors and of attack along therotor non-dimensional of dual the blade for different tip speed ratios (TSR) bythe theangle authors [7]. The scaled with its surgelength motion carriage different tip in speed ratios is as shown Figure 4. (TSR) by the authors [7]. The scaled rotor with its surge motion dual carriage is as shown 4. Reynold number similarity the model was tested under water at the University In orderintoFigure achieve In order toKelvin achieve Reynold number similarity the tank model tested2.5under water of Strathclyde’s Hydrodynamics Laboratory towing (76 was m length, m depth andat4.6the m University of Strathclyde’s Kelvin Hydrodynamics Laboratory towing tank (76 m length, 2.5 m depth in width). When compared to the scaled rotor, the cross-sectional area of the tow tank was adequately and in width). When the scaled theflow cross-sectional of the tow was large4.6 formleast blockage. Thecompared prescribedtosteady and rotor, periodic speeds werearea imparted into tank the rotor adequately large forthrough least blockage. The prescribed steady andcarriage periodic flow speeds were imparted by pulling the rotor the stationary water using a dual system (primary carriage was into the rotormotion by pulling rotor through thefor stationary water using aas dual carriage (primary for constant andthe secondary carriage surge cyclic motion) in Figure 5. system The rotor speed carriage was for constant andPID secondary carriage forcoupled surge cyclic as in Figure The was controlled using a DCmotion motor and controller directly to themotion) rotor through a shaft5.fixed rotor speed was controlled using a DC motor and PID controller directly to the rotor through to a stiff bedplate using three low-friction bearings. The torque and thrustcoupled forces are measured in-line a shaft a stiff bedplate using three low-friction bearings. The torque with thefixed shaftto using a bi-directional force transducer at a frequency of 137 Hz. and thrust forces are measured in-line with the shaft using a bi-directional force transducer at a frequency of 137 Hz.

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Figure 4. 4. Physical Physical scaled scaled rotor rotor with with aaa rig rig setup setup (for (for surge surge motion motion unsteady unsteady effects) effects) on on the the carriage carriage of of Figure Figure 4. Physical scaled rotor with rig setup (for surge motion unsteady effects) on the carriage of the towing tank. the towing tank. the towing tank.

Figure 5. 5. The The tow tow tank tank at at the the Kelvin Kelvin Hydrodynamics Hydrodynamics Laboratory and carriage Hydrodynamics Laboratory Laboratory and and carriage carriage systems. systems. Figure systems.

Experimental Design of Surge Motion Experimental Design Design of of Surge Surge Motion Motion Experimental The surge motion of the rotor does not represent a specific floating wind turbine system, but rather The surge surge motion motion of of the the rotor rotor does does not not represent represent aa specific specific floating floating wind wind turbine turbine system, system, but but The a generalized matrix of operating points, from which conclusions can be drawn regarding the rotor rather aa generalized generalized matrix matrix of of operating operating points, points, from from which which conclusions conclusions can can be be drawn drawn regarding regarding the the rather thrust loading. The three variables under investigation were the rotor tip speed ratio, the surge rotor thrust loading. The three variables under investigation were the rotor tip speed ratio, the surge rotor thrust loading. The three variables under investigation were the rotor tip speed ratio, the surge amplitude, and the surge frequency. Similar to the static analysis of the rotor, the tow speed was amplitude, and and the the surge surge frequency. frequency. Similar Similar to to the the static static analysis analysis of of the the rotor, rotor, the the tow tow speed speed was was amplitude, constant and the rotor speed was varied to alter the tip speed ratio. The operating range of values for constant and and the the rotor rotor speed speed was was varied varied to to alter alter the the tip tip speed speed ratio. ratio. The The operating operating range range of of values values for for constant these parameters were specified such that they mimic the full-scale rotor operating conditions limited these parameters were specified such that they mimic the full-scale rotor operating conditions limited these parameters were specified such that they mimic the full-scale rotor operating conditions limited to the experimental setup and surge carrier motion. to the the experimental experimental setup setup and and surge surge carrier carrier motion. motion. to Three prior studies have been conducted with the objective of studying the aerodynamic Three prior prior studies studies have have been been conducted conducted with with the the objective objective of of studying studying the the aerodynamic aerodynamic Three performance with the surge motion. The initial values for the parameters were set according to performance with the surge motion. The initial values for the parameters were set according to these these performance with the surge motion. The initial values for the parameters were set according to these studies for the current unsteady experimentation of the model scale rotor. Liu et al. [8] studied studies for for the the current current unsteady unsteady experimentation experimentation of of the the model model scale scale rotor. rotor. Liu Liu et et al. al. [8] [8] studied studied the the studies the NREL 5 MW baseline wind turbine at three different wind speeds, surge velocities, and surge NREL 5 MW baseline wind turbine at three different wind speeds, surge velocities, and surge NREL 5 MW 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. frequencies numerically numerically using using aa BEM BEM based based aerodynamic aerodynamic model model with with aa dynamic dynamic inflow inflow correction. correction. frequencies DeVaal et al. [15] compared the aerodynamic performance of the NREL 5 MW turbine subjected to the DeVaal et et al. al. [15] [15] compared compared the the aerodynamic aerodynamic performance performance of of the the NREL NREL 55 MW MW turbine turbine subjected subjected to to DeVaal a surging motion using four different numerical approaches; a quasi-static BEM model, a BEM model the a surging motion using four different numerical approaches; a quasi-static BEM model, a BEM the a surging motion using four different numerical approaches; a quasi-static BEM model, a BEM with an integrated Pit-Peters dynamic inflow correction, a BEM model with an integrated Stig Oye model with with an an integrated integrated Pit-Peters Pit-Peters dynamic dynamic inflow inflow correction, correction, aa BEM BEM model model with with an an integrated integrated Stig Stig model dynamic inflow correction, and a CFD based actuator disc model. Similarly, Micallef and Sant [16] Oye dynamic dynamic inflow inflow correction, correction, and and aa CFD CFD based based actuator actuator disc disc model. model. Similarly, Similarly, Micallef Micallef and and Sant Sant [16] [16] Oye studied the NREL 5 MW rotor in surge using a quasi-static BEM model, a generalised dynamic wake studied the NREL 5 MW rotor in surge using a quasi-static BEM model, a generalised dynamic wake studied the NREL 5 MW 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 model, and and aa CFD CFD based based actuator actuator disk disk model. model. The The valuable valuable conclusion conclusion that that has has been been arrived arrived from from model, these studies is that the wake induced effects of the rotor thrust as a result of the rotor surging into the these studies is that the wake induced effects of the rotor thrust as a result of the rotor surging into these studies is that the wake induced effects of the rotor thrust as a result of the rotor surging into flow depends upon the tip speed ratio, surge frequency, and surge displacement amplitude. the flow depends upon the tip speed ratio, surge frequency, and surge displacement amplitude. the flow depends upon the tip speed ratio, surge frequency, and surge displacement amplitude. The experimental experimental surge surge operational operational points points considered considered are are drawn drawn primarily primarily from from the the work work of of Liu Liu The et al. [8] and deVaal et al. [15], the surge frequency considered by Micallef and Sant [16], although et al. [8] and deVaal et al. [15], the surge frequency considered by Micallef and Sant [16], although representative of of aa full full scale scale operational operational condition condition which which would would be be experienced experienced by by aa floating floating wind wind representative

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The experimental surge operational points considered are drawn primarily from the work of Liu et al. [8] and deVaal et al. [15], the surge frequency considered by Micallef and Sant [16], 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. were 0.1, 0.2, and 0.3 rad/s, and between 0.127 and 1.0 rad/s, respectively; the corresponding surge displacement amplitudes were, 3.0, 6.0, and 9.0 m, and between 2.0 and 16.0 m. deVaal considers only the rotor operating at its rated wind speed (V = 11.2 m/s), Liu et al. and Micallef and Sant both consider this same rotor operation in addition to off 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, were 8.0, 11.2 and 16.0 m/s and 4.0, 7.0, and 11.0. The tip speed ratio of the NREL 5 MW Baseline Wind Turbine at its rated wind speed of 11.2 m/s, as defined by Jonkman et al. [13], is 7.0. The model scale surge motion displacement and frequency were derived from the studies discussed by Liu et al. [8] and deVaal et al. [15] by applying a suitable scaling methodology. This was achieved by following the scaling relationships defined by Jain et al. [17] for the experimental analysis of the combined effect of aerodynamic 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 were scaled following the relationships defined in Equations (1) and (2), respectively: ω (surge, model ) = ω (surge, f ull ) ∗ A(surge, model ) =

√ λ

A(surge, f ull ) √ λ

(1) (2)

where A is amplitude, ω is the angular frequency and λ is the geometric scaling factor, 126.0 for the present set of experiments. A comprehensive static and unsteady test matrix was performed. The dimensionless parameters Ct and Cq that determine the amount of momentum and energy extracted from the water was computed for static cases. The coefficient of thrust is defined by Equation (3): Ct =

T = 4a (1 − a) 0.5 ρAV 2

(3)

where T is the rotor thrust force, ρ is the fluid density, A is the rotor plane area and V is the fluid velocity. The coefficient of torque is defined by Equation (4): Cq =

Q 0.5 π ρR3 V 2

(4)

where Q is the torque and R is rotor radius. The torque is measured when the scaled rotor is at constant rotational speed, constant tow speed of primary carriage for the static test as in Table 2. Time history of thrust and torque are captured in unsteady surge motion test scenario cases (as in Table 3). During the unsteady test scenario, secondary carriage oscillates while primary carriage is at constant speed. Table 2. Static state test condition. Tow Speed (m/s)

TSR

Rotational Speed (rad/s)

1.000 0.931 1.000 0.822 0.735

3.000 4.500 7.000 8.519 9.522

6 9 14 14 14

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Table 3. Unsteady experimental test case scenarios chosen for numerical validation at the rotor rotational speed of 14 rad/sec. TSR

8.5

7.0

6.0

Tow Speed, m/s

Surge Frequency (f), rad/s

Amplitude(A), M

Scenario Name for Reference

0.824

1.12 (0.18 Hz) 1.12 (0.18 Hz) 3.37 (0.54 Hz) 3.37 (0.54 Hz) 5.61 (0.89 Hz) 5.61 (0.89 Hz)

0.0238 0.1190 0.0238 0.1190 0.0238 0.0952

SFA1 SFA2 SFA3 SFA4 SFA5 SFA6

1.000

1.12 (0.18 Hz) 1.12 (0.18 Hz) 3.37(0.54 Hz) 3.37 (0.54 Hz) 5.61 (0.89 Hz) 5.61 (0.89 Hz)

0.0238 0.1190 0.0238 0.1190 0.0238 0.0952


1.167

1.12 (0.18 Hz) 1.12 (0.18 Hz) 3.37 (0.54 Hz) 3.37 (0.54 Hz) 5.61 (0.89 Hz) 5.61 (0.89 Hz)

0.0238 0.1190 0.0238 0.1190 0.0238 0.0714


3. Numerical Methodology Due to wind shear between the ground or sea level to the tip of the rotor blade, gust, turbulence, flow field around the rotor and near wake regions are highly complex, even in land-based installations. In FOWT, the complexity is further compounded by the additional motions at the rotor plane induced by the floating platform subjected to the three translational (heave, sway, and surge) and three rotational (yaw, pitch, and roll) motions as shown in the Figure 6. Among these six motions, surge motion and pitch motion are responsible for pushing the rotor to interact with its own wake. This interaction significantly modifies the wind turbine’s operating state and in turn varying the axial induction velocity field and unsteadiness. As the BEM theory is constructed based on the axial induction factor range, it has to be validated to gain sufficient confidence before applying to FOWT. In the current study, Energies 11, surge x FOR PEER REVIEW 8 of 26 scaled2018, rotor motion experimental results were exploited for validating the numerical codes.

Figure6.6.Floating Floating platform motions(3(3linear linearand and3 3rotational). rotational). Figure platform motions

CFD, LR-AeroDyn and LR-uBEM has been chosen for the validation study. CFD simulations are CFD, LR-AeroDyn and LR-uBEM has been chosen for the validation study. CFD simulations are carried out with reasonable accuracy to gain insight on surge motion’s flow field and wake interactions. carried out with reasonable accuracy to gain insight on surge motion’s flow field and wake As AeroDyn is widely employed in industry for its accuracy, Marine and Hydrokinetic code is modified interactions. As AeroDyn is widely employed in industry for its accuracy, Marine and Hydrokinetic to incorporate the surge motion scenarios (LR-AeroDyn). LR’s research on unsteady aerodynamics of code is modified to incorporate the surge motion scenarios (LR-AeroDyn). LR’s research on unsteady FOWT resulted in the development of LR-uBEM code accounting dynamic in flow model with other aerodynamics of FOWT resulted in the development of LR-uBEM code accounting dynamic in flow unique features. The following sections discuss in detail on these methodologies. model with other unique features. The following sections discuss in detail on these methodologies.

3.1. CFD Model The tow tank is defined in the CFD numerical environment as in Figure 7 to solve the unsteadiness on the rotor due to surge motion. The primary or main carriage motion (constant) of the

carried out with reasonable accuracy to gain insight on surge motion’s flow field and wake interactions. As AeroDyn is widely employed in industry for its accuracy, Marine and Hydrokinetic code is modified to incorporate the surge motion scenarios (LR-AeroDyn). LR’s research on unsteady aerodynamics of FOWT resulted in the development of LR-uBEM code accounting dynamic in flow model with other unique features. The following sections discuss in detail on these methodologies. Energies 2018, 11, 2578 9 of 25 3.1. CFD Model 3.1. CFD Model The tow tank is defined in the CFD numerical environment as in Figure 7 to solve the unsteadiness on the rotor due The primary or as main carriage (constant) of the The tow tank is defined in to thesurge CFD motion. numerical environment in Figure 7 tomotion solve the unsteadiness rotor represented as uniform boundary condition the secondary carriage surge on theisrotor due to surge motion.inlet Thewater primary or main carriageand motion (constant) of the rotor is motion is represented as multiple reference frame (MRF) and sliding mesh motion on the rotor represented as uniform inlet water boundary condition and the secondary carriage surge motion is domain. represented as multiple reference frame (MRF) and sliding mesh motion on the rotor domain.

Figure Figure7.7. Schematic Schematic representation representationof oftow towtank tankin inCFD CFDcomputational computationaldomain. domain.

3.1.1. CFD Mesh Model 3.1.1. CFD Mesh Model As shown in Figure 8, the scaled rigid 3D rotor blade geometry was generated through commercial As shown in Figure 8, the scaled rigid 3D rotor blade geometry was generated through meshing software Ansys ICEM CFD (Version 16.2) by sweeping through all the 17 aero profiles of commercial meshing software Ansys ICEM CFD (Version 16.2) by sweeping through all the 17 aero the scaled model. The hub is modelled to the dimensions used in the tow tank to eliminate any profiles of the scaled model. The hub is modelled to the dimensions used in the tow tank to eliminate inaccuracies introduced to the flow variation near the blade root. Energies 2018, 11, x FOR PEERdue REVIEW 9 of 26 any inaccuracies introduced due to the flow variation near the blade root.

Figure Figure8.8.Scaled Scaledrotor rotor3D 3Dmodel modelgenerated generatedininAnsys AnsysICEM ICEMCFD CFDenvironment. environment.

The was with hexahedral mesh created by multi-block meshing strategy. The blade Theouter outerdomain domain was with hexahedral mesh created by multi-block meshing strategy. The domain is meshed with ‘O-grid’ One rotor One bladerotor of the scaled is meshed hexahedral blade domain is meshed with topology. ‘O-grid’ topology. blade ofrotor the scaled rotorwith is meshed with structured mesh around itmesh and the surrounding of turbine rotor bladeofwas generated. hexahedral structured around it and water the surrounding water turbine rotor Periodicity blade was option was used for other blades mesh make theblades rotor plane mesh region. As shown in Figures 9 generated. Periodicity option was usedtofor other mesh to make the rotor plane mesh region. and 10, the3D model of the scaled rotor model and three kinds of mesh clustering methods (log scale As shown in Figures 9 and 10, the3D model of the scaled rotor model and three kinds of mesh change in near wall and linearchange towards perpendicular direction) around the rotor were used around in the clustering methods (log scale in near wall and linear towards perpendicular direction) mesh sensitivity studyinasthe themesh thrustsensitivity force is more sensitive to method the rotor were used study as the thrust forceofismesh moreclustering. sensitive to method of

mesh clustering.

hexahedral structured mesh around it and the surrounding water of turbine rotor blade was generated. Periodicity option was used for other blades mesh to make the rotor plane mesh region. As shown in Figures 9 and 10, the3D 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 were used in the mesh sensitivity study as the thrust force is more sensitive to method of Energies 2018, 11, 2578 10 of 25 mesh clustering.

Figure 9. 9. Scaled mesh model model and and 1/3rd 1/3rd Scaled rotor 1/3rd model model of rotating domain with single rotor. Figure rotor mesh model of of rotating rotating domain domain with with single single rotor. rotor.

independent study study (a) Figure Figure 10. 10. Mesh Mesh independent independent study (a) 0.59 0.59 million million nodes nodes with with coarse coarse mesh mesh (b) (b) 1.65 1.65 million million nodes nodes with medium mesh size (c) 2.38 million nodes with fine mesh. Energies 2018, 11, x FOR PEER 10 of 26 with medium mesh sizeREVIEW (c) 2.38 million nodes nodes with with fine fine mesh. mesh.

The domain is is shown in in Figure 11.11. TheThe mesh waswas sufficiently discretized to Theentire entirecomputational computational domain shown Figure mesh sufficiently discretized capture the near wakewake and far field field reasonably. The scaled rotor was to yieldtoan y+ of to capture the near andwake far wake reasonably. The scaled rotorrefined was refined yield an~1 y+ near the tip and less than 2 for the rest of the domain as shown in Figure 12. of ~1 near the tip and less than 2 for the rest of the domain as shown in Figure 12.

(a)

(b)

Figure11. 11.CFD CFDcomputational computationaldomain domain(a) (a)1/3rd 1/3rd rotor rotormodel modelisisswept sweptfor for360 360deg degwith withnear nearwake wake Figure domain(b) (b)the thecomplete completenear nearwake wakeregion regionmesh meshmodel modelinside insidethe theglobal globalmodel. model. domain

(a)

(b)

Figure 11. CFD computational domain (a) 1/3rd rotor model is swept for 360 deg with near wake 11 of 25 domain (b) the complete near wake region mesh model inside the global model.

Energies 2018, 11, 2578

Figure Figure 12. 12. Scaled Scaled rotor–y+ rotor–y+ contour. contour.

3.1.2. CFD Numerical Solver 3.1.2. CFD Numerical Solver The mesh mathematical model is imported in to Ansys CFX CFD solver (Version 16.2) to simulate The mesh mathematical model is imported in to Ansys CFX CFD solver (Version 16.2) to experimental scenario cases of the rigid 3D scaled rotor. The k-ω Shear Stress Transport (SST) simulate experimental scenario cases of the rigid 3D scaled rotor. The k-ω Shear Stress Transport turbulence scheme was employed without transition modeling. A high order advection scheme (SST) turbulence scheme was employed without transition modeling. A high order advection scheme and first order numerical method were chosen for turbulence modelling. The k-ω based SST model and first order numerical method were 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. In this employs the k-ω model for the near surface treatment and the k-ε model in the free-shear layers. In methodology a blending function is adopted to bridge these two models. The SST k-ω model accounts this methodology a blending function is adopted to bridge these two models. The SST k-ω model the transportation of the turbulent shear stress and capable of accurately predicting the onset and the accounts the transportation of the turbulent shear stress and capable of accurately predicting the magnitude of flow separation under adverse pressure gradients in the rotor blade, near wake and far onset and the magnitude of flow separation under adverse pressure gradients in the rotor blade, near wake regions. wake and far wake regions. For the aforementioned reasons, the two-equation SST k-ω model is widely exploited in wind 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. industry for their accurate predictions of flow over blunt body. The k-ω SST model has a similar form to the standard k-ω model: The k-ω SST model has a similar form to the standard k-ω model: ! ∂ 𝜕 ∂ 𝜕 ∂ 𝜕 ∂κ𝜕қ eκ − Yκ + Sκ ) ΓκГ ++G (5) (ρκ) + + (ρκu i ) =) = (𝜌қ𝑢 𝐺қ − 𝑌қ + 𝑆қ ) (5) ∂x 𝜕𝑥 (𝜌қ) ∂x ∂x𝜕𝑥 ∂x қ j i j 𝜕𝑥 𝜕𝑥 and: and: ∂ ∂ ∂ (ρω ) + (ρωui ) = ∂x ∂xi ∂x j

∂ω Γω ∂x j

! eω − Yω + Dω + DSω +G

(6)

eκ in the Equations (5) and (6) represents the generation of turbulence kinetic energy due to mean G eω represents the generation of ω. Γκ and Γω represents the effective diffusivity of velocity gradients. G κ and ω respectively. Yκ and Yω represent the dissipation of κ and ω due to turbulence. Dω represents the cross-diffusion term. Sκ and Sω are user-defined source terms. 3.1.3. Mesh Sensitivity Study, Static Case Simulation and Validation The CFD simulations were performed with constant water velocity at the inlet boundary for the static scenarios (without surge cyclic motion) as shown in Table 2 before carrying out the unsteady test case simulations. Being aimed at mesh independent results, the Ct of the scaled rotor was compared against the selected scenario at primary carriage speed of 1 m/s (with 14 rad/s rotor rotational speed for 7 TSR), which is 1 m/s constant water inlet velocity BC in CFD simulations. The results were published by the authors [1] already. For the validation with reasonable accuracy, medium size mesh model was used in CFD model for static and unsteady experimental scenario. As the thrust force used for scaled airfoil optimization function [7], it is primarily considered for the comparison and validation with numerical scaled rotor simulations. The medium size mesh CFD model domain was with 7.32 million cells. This mesh model is considered to be acceptable aerodynamically as y+ value is below 1 close to critical area of the rotor and below 2 in the rest of the scaled rotor area. To validate

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thrust force and torque predictions, the CFD scaled rotor model was employed with sliding mesh with MRF (Multiple Reference Frame) methodologies for computations. The CFD model predictions were Energies 2018,against 11, x FOR PEER REVIEW 12 of 26 validated the tow tank experimental values for the specified cases in Table 2. The CFD model was simulated for the static test scenario to obtain the Ct and Cq for different TSR. as the full-scale rotor diameter is 126 m. The primary tow speedspeed) of 1 m/s (for the The results werereference bench marked. By the combination of tow speedcarriage (primary carriage and scaled full-scale reference rated winditspeed of 11.4 m/s) and scaled rotoratrotational speed of 14.0 rad/sit (for rotor rotational speed (rad/s), was possible to operate the rotor different TSR. Even though was full-scale reference rotor rotational speed of 12.1 RPM) were modeled in CFD environment to validate meant for static scaling at constant TSR, the TSR was varied in the range of 3 to 9.5 in the experiments the experimentalThe conditions. the Ct reference and the NREL Cq were predicted analytically andstatic CFD simulations. rotationalHenceforth, speed of full-scale 5 MW rated RPM is 12.10 (designed values) and then experimental numerical simulations Plotted which is 14 rad/sinitially for the scaled model. All otherand full-scale 5 MW rotor RPMwere is inperformed. linear relationship results are depicted in the Figure 13. with scaled rotor. Therefore, a simple correlation between the scaled model rotational speed of Ωm The thrust coefficients from all the three methods were comparable and difference was within in rad/s and the full-scale NREL 5 MW reference rotor rotational speed Ωf in rpm, is derived by 10%, while the Ct exhibits a prominent variation with analytical prediction (design values) from the Equation (7): well-correlated CFD and experimental predictions. Ωm It was expected that the significant contribution ∗ 12.1 rpm Ω f = (7) of deviation could come from Xfoil calculations rad of Cl (lift coefficient) and Cd (drag coefficient) due 14 s to the fact that Xfoil over predicts the drag for the low Re ranges and the same was experimentally confirmed. This is mainly to the inability the panel account the effect non-linear The full-scale NREL due 5 MW wind speedof (Vf ) can be method derivedtofrom the TSR of theofscaled rotor flow on the drag force prediction. As the first set of Cl and Cd were derived for low angle of attack, experiment: 63πΩ f extrapolation of values for higher angle of attack V f =make the situation for the model to over predict the (8) 30error TSR from the above problem is to obtain the Cl Cl and Cd values. A possible solution to reduce the as the reference is 126 primary carriage tow speed of 1suggested m/s (for the and Cdfull-scale experimentally (byrotor winddiameter tunnel) for firstm.setThe of Cl and Cd and thereafter it was to full-scale reference rated wind speed for of 11.4 m/s) and scaled rotor the rotational speed of 14.0 rad/s (for use Viterna or Montgomerie method extrapolation. To predict drag force very accurately by full-scale the reference rotorlayer rotational speed of a 12.1 RPM) were in CFD environment to validate resolving boundary flow properly, great effort hasmodeled been made in fine-tuning the CFD mesh thearound static experimental conditions. Henceforth, Ctwall and the Cq wereinpredicted analytically (designed all the wall boundary to get very goodthe near treatment the calculation. The error due values) initially then experimental numerical simulations were performed. Plotted results are to low Re effectsand were inevitable as the and scaled rotor airfoil optimization was not under the operating depicted the Figure 13. Re and theinearly flow separation due to smaller chord length.

(a)

(b)

Figure Figure13. 13.Static Staticstate statevalidation validationcurves curvesfor forCFD CFD(a) (a)Comparison Comparisonof ofthrust thrustco-efficient co-efficient(b) (b)Comparison Comparison of oftorque torque co-efficient. co-efficient.

from all the threeScenarios methods were comparable and difference was within 3.1.4. The CFDthrust Modelcoefficients for Unsteady Experimental 10%, while the Ct exhibits a prominent variation with analytical prediction (design values) from the The surge cyclic motion method was implemented in Ansys-CFX (Version 16.2) software well-correlated CFD and experimental predictions. It was expected that the significant contribution environment. Medium size with 7.32 million node mesh model was used for the unsteady of deviation could come from Xfoil calculations of Cl (lift coefficient) and Cd (drag coefficient) due simulations. The unsteady runs include sinusoidal surging motions of the rotor from low to extreme to the fact that Xfoil over predicts the drag for the low Re ranges and the same was experimentally frequencies (3–low, medium, and high) and amplitudes (2–lower and higher), to demonstrate the confirmed. This is mainly due to the inability of the panel method to account the effect of non-linear effect on the rotor unsteady aerodynamics as experimentally simulated. Simulations were carried out flow on the drag force prediction. As the first set of Cl and Cd were derived for low angle of attack, with MRF and deforming mesh setup in the CFD environment, constant water velocity from the inlet extrapolation of values for higher angle of attack make the situation for the model to over predict the (with a turbulence intensity of 5%) of the computational domain represented constant primary Cl and Cd values. A possible solution to reduce the error from the above problem is to obtain the Cl carriage motion. The deforming mesh was setup up such that the mesh in the blade and near-wake and Cd experimentally (by wind tunnel) for first set of Cl and Cd and thereafter it was suggested to regions was given a high rigidity, so that deformation is limited to the outer region with bigger cells, use Viterna or Montgomerie method for extrapolation. To predict the drag force very accurately by so negative volumes would not occur. A high resolution scheme was used for advection and turbulence numerics, a second order backward Euler scheme was used for time stepping. Pressurevelocity coupling was solved using a fourth order Rhie-Chow interpolation. The surge motion is defined by the Equation (9):

−𝐴 + 𝐴 𝑐𝑜𝑠 2𝜋𝑓

(9)

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resolving the boundary layer flow properly, a great effort has been made in fine-tuning the CFD mesh all around the wall boundary to get very good near wall treatment in the calculation. The error due to low Re effects were inevitable as the scaled rotor airfoil optimization was not under the operating Re and the early flow separation due to smaller chord length. 3.1.4. CFD Model for Unsteady Experimental Scenarios The surge cyclic motion method was implemented in Ansys-CFX (Version 16.2) software environment. Medium size with 7.32 million node mesh model was used for the unsteady simulations. The unsteady runs include sinusoidal surging motions of the rotor from low to extreme frequencies (3–low, medium, and high) and amplitudes (2–lower and higher), to demonstrate the effect on the rotor unsteady aerodynamics as experimentally simulated. Simulations were carried out with MRF and deforming mesh setup in the CFD environment, constant water velocity from the inlet (with a turbulence intensity of 5%) of the computational domain represented constant primary carriage motion. The deforming mesh was setup up such that the mesh in the blade and near-wake regions was given a high rigidity, so that deformation is limited to the outer region with bigger cells, so negative volumes would not occur. A high resolution scheme was used for advection and turbulence numerics, a second order backward Euler scheme was used for time stepping. Pressure-velocity coupling was solved using a fourth order Rhie-Chow interpolation. The surge motion is defined by the Equation (9):

− A + A cos 2π f

(9)

where A is the amplitude of motion and f is the frequency. The entire blade and near-wake regions were set to oscillate as defined by Equation (9). The equation assumes that the mesh starts at the forward-most position, since there are more cells downstream of the rotor, thus it would facilitate smoother deformation. As per the Table 3, simulations are carried out to compare against the experimental values. The sinusoidal surge cyclic motions for the scaled rotor were designed based on the work by [15,16] for the unsteady test scenario. As in [17], one of the predominant motions is surge motion, a detailed surge motion experiments were designed to carry out for the scaled rotor. The scenarios were chosen carefully to validate the effects of unsteadiness by the various numerical simulations. Mean thrust and torque values were considered for validation purposes initially. For each of the three different TSRs, three different surge frequencies and two amplitudes (minimum and maximum) were chosen to capture the unsteady behavior. The steady state MRF simulations were first performed with the rotational speed of the rotor and primary carriage speed as water inlet velocity boundary condition in CFD simulations for the designed scenarios as given in the Table 2. For unsteady transient surge motion study, the static or steady state simulation results were used to initialize the solutions of all the designed unsteady scenario cases. The CFD computational domains were well organized in such a way that both the blade rotations and rotor surging motions could be handled smoothly by the solver. The rotor domain had a sliding mesh interface for blade rotations and the mesh motion (deforming mesh) applied for surging motion 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+ ~ 1. 3.2. LR–AeroDyn Model for Unsteady Experimental Scenario AeroDyn (V15.04) is an open source (NREL) time-domain wind turbine aerodynamics module [18] that has been tailored for marine hydrokinetic turbines (MHTs). 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 the whole scenario. FAST model settings:

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AeroDyn calculates aerodynamic loads on both the blades and tower. The AeroDyn’s aerodynamic computations are based on actuator lines methodology. In this methodology, two-dimensional (2D) flows at 17 cross section (node) are used to approximate the three-dimensional (3D) flow around a body. The lift forces, drag forces and pitching moments are lumped at the nodes which enables the algorithm to approximate the distributed pressure and shear stresses. 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. The MHK-based model is customized for the scaled rotor to compute the effect of wake based on the derivation of induction factors by quasi-steady BEM theory. An iterative Brent’s methodology is employed for nonlinear equations. Reaction to the immediate load changes on the induction is captured by quasi-steady or equilibrium wake (EQUIL) model. 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). The time lag is not implemented in this method which means no dynamic inflow. For high induction factors of linear momentum theory, the Glauert’s empirical correction with Buhl’s modification is normally used. In the BEM methodology, Prandtl hub-loss and Prandtl tip-loss models are implemented. Angle-of-attack calculations in AeroDyn assume that the axial induction factor (a) 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: Vrel = Vα (1 − a) + Vrotor (10) Vrotor , is the structural velocity of the blade element normal to the disc (measured positive when pointing upwind). The assumption 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: Vrel = (Vα + Vrotor )(1 − a)

(11)

3.3. LR–u BEM Model for Unsteady Experimental Scenario The LR uBEM code was developed to address the issue of uncertainty in predicting the aerodynamics of floating offshore wind turbines. The development of the uBEM code included several features vital to an accurate assessment of floating offshore wind turbine aerodynamics. These include: 1. 2. 3. 4. 5.

An improved tip-loss model which accounts for changes in tip speed ratio and changes in loss distributions in different wake states. An unsteady airfoil model including a modified Beddoes-Leishman model which models the unsteady circulation using the suction surface shape-dependent time constants A combined unsteady airfoil and stall delay model, accounting for changes in stall delay due to changes in wind and rotational velocities in real-time. An extension of the Gluaert correction by Buhl to the propeller and propeller-brake wake states. A dynamic wake model to account for the time-lag between aerodynamic forces on the rotor and wake velocities.

In addition, uBEM predicts the forces on each blade section separately, taking into account local velocity changes at any position on each blade. The development of the code was based on CFD

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simulations of the NREL 5 MW virtual wind turbine, used for code comparison studies in OC3, OC4, and OC5. The CFD simulations were carried out for a static wind turbine and for a surging wind turbine under various surge conditions, with a fixed rotor RPM. The code was developed completely in MATLAB, and is modularized to allow for changes to the various corrective models implemented. The unsteady blade element momentum method (uBEM) used in the present study, is based on the method presented in [19]. The relative velocity vector is given by: 

Vrel

 0   = V0 + W +  −Ωr cos(θc )  0

(12)

where V 0 is the blade-specific wind speed at the blade element including relative speed due to rotor motion, Ω 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

Vrel, y Vrel,z

(13)

The normal (z) and tangential (y) induced velocities are then given by: Wz =

Wy =

−|Vrel |2 Cl cos(φ)cB   0   8F (V0 + A) + f g  0  πr Wz −|Vrel |2 Cl sin(φ)cB   0   8F (V0 + A) + f g  0  πr Wz

(14)

(15)

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 [20] and the shape-specific modified Beddoes-Leishman model with the angle of attack equal to the flow angle less the blade twist [21]. Wx is set to 0. At every time step, for each blade element in each blade, Equations (1) and (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 [22]. The force coefficients are then recomputed to determine the unsteady forces at each blade element. The LR-uBEM model is customized and simulated for scaled rotor model unsteady simulations as per the experimental scenarios. 4. Results and Discussion of Unsteady Test Cases Comprehensive static and unsteady experimental scenarios were performed and results were obtained for numerical evaluation and validation. For the unsteady experimental scenario cases, the last two cycles of six cycle surge motion simulation results were extracted for comparison and further analysis. This is to ensure that all the initial transient factors were eliminated. Results of CFD, LR-AeroDyn and LR-uBEM model computations were compared against the experimental results to comprehend their ability in predicting the aerodynamic forces due to unsteady effects. The variation in time mean thrust values of different numerical simulation methods would determine the capability and limitation to predict the unsteady aerodynamic loads on the scaled rotor. Albeit, thrust is the only significant parameter for the comparison between the numerical methods in this case (as the scaled

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rotor is designed against lift curve or thrust of full scale reference rotor), torque comparisons will further establish their capabilities. 4.1. Hydrodynamic Thrust One of the main aerodynamic performance parameters is thrust force which is used for axial induction factor computation in BEM and unsteady based BEM methodologies. Hence, thrust force was chosen for the model evaluation and validation purposes. Moreover, the axial induction factor was used to predict the type of the wind turbine operating wakes states as well. Validity of BEM models are pretty much depending on wind turbine operating wake states and appropriate correction factors involved. A detailed investigation on thrust force prediction by numerical codes and comparison is made against the experimental prediction for 8.5, 7.0 and 6.0 TSR unsteady scenarios. For numerical simulation of the unsteady scenarios with LR-AeroDyn and LR-uBEM are typically taking a few minutes to complete each scenario, whereas it take 34 h for the each CFD simulation cases with 36 core parallel processing computing workstation. 4.1.1. TSR 8.5 Scenario Energies 2018, 11, x FOR PEER REVIEW

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involved. A the detailed investigation on thrust force prediction numerical In orderfactors to understand unsteady flow behavior at the below by rated wind codes speedand which is about comparison is made againstspeed the experimental prediction for scale 8.5, 7.0 FOWT, and 6.0 TSR unsteady scenarios. 16% lower than the rated wind (11.4 m/s) of full scaled rotor was subjected to For numerical simulation of the unsteady scenarios with LR-AeroDyn and LR-uBEM are typically experimental anda numerical 8.5 TSR. With a constant of 14 rad/s for taking few minutes tosimulations complete each at scenario, whereas it take 34 h for theangular each CFDspeed simulation with 36 core parallelamplitude processing computing workstation. the differentcases prescribed surge frequency motions the experiments were carried out at a constant primary carriage motion of 0.824 m/s. Owing to the unsteadiness triggered by prescribed 4.1.1. TSR 8.5 Scenario surge motion, both thrust and torque fluctuate with time. Lower amplitude surge motion based In order to understand the unsteady flow behavior at the below rated wind speed which is about numerical models were predicting mean within error against experimental results 16% lower thanover the rated wind speed (11.4thrust m/s) of force full scale FOWT,5% scaled rotor was subjected to experimental and numerical simulations at 8.5motion TSR. With a constant angular speed of 14 rad/s the as shown Figure 14h. Higher amplitude surge based numerical models wereforpredicting mean different prescribed surge amplitude frequency motions the experiments were carried out at a thrust within 10% error except at the high surge frequency motion. Mean thrust slightly increases constant primary carriage motion of 0.824 m/s. Owing to the unsteadiness triggered by prescribed as surge motion frequency and and amplitude increases. AsLower in Figure 14a–f, surge motion, both thrust torque fluctuate with time. amplitude surge backward motion basedand forward numerical models were over predicting mean thrust forceto within erroralmost against 8–100% experimental motions in surge oscillations causing the maximum thrust vary5% from higher than the Figure 14h. Higher amplitude surge motion based numerical models were mean value results while as theshown minimum thrust is about 8–100% lower at TSR 8.5. Its essential to consider the predicting mean thrust within 10% error except at the high surge frequency motion. Mean thrust large difference between extremes for structural stressincreases. and related fatigue issues during full scale slightly increasesthe as surge motion frequency and amplitude As in Figure 14a–f, backward and forward motions surgeits oscillations causing the maximum thrustapplications. to vary from almost design of wind turbines rotorinand pitching control for floating The8–100% possible source of higher than the mean value while the minimum thrust is about 8–100% lower at TSR 8.5. Its essential errors: (1) Experiments—It is estimated to be around 2–4% error from various sources of uncertainties to consider the large difference between the extremes for structural stress and related fatigue issues from measurement random error and systematic model is veryThe similar to [23] during fullsystem, scale design of wind turbines rotor and its pitchingerror controlas forthe floating applications. source of Experiments—It is estimated to be around 2–4% error from and yet to bepossible quantified inerrors: detail(1)(2) CFD—numerical discretization, error due to various mesh deformation sources of uncertainties from measurement system, random error and systematic error as the model techniques and time step selection for high frequency and larger amplitude motions (3) LR-AeroDyn is very similar to [23] and yet to be quantified in detail (2) CFD—numerical discretization, error due and LR-uBEM—Load computations are completely basedfor onhigh thefrequency design data of scaled 2D airfoil airfoil to mesh deformation techniques and time step selection and larger amplitude (3) LR-AeroDyn and 2D LR-uBEM—Load computationsdata are completely based on the design lift and dragmotions data, not with scaled airfoil experimental and 3D correction errors. A detailed scaled 2D airfoil airfoil lift and drag data, not with scaled 2D airfoil experimental data and 3D investigationdata is of needed to quantify the uncertainties of these methods. correction errors. A detailed investigation is needed to quantify the uncertainties of these methods.

(a)

(b)

Figure 14. Cont.

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14. TSR 8.5 Cases: (a) SFA1-Low f & lower A; (b) SFA2-Low f & higher A; (c) SFA3-Medium f Figure 14.Figure TSR 8.5 Cases: (a) SFA1-Low f & lower A; (b) SFA2-Low f & higher A; (c) SFA3-Medium f & lower A; (d) SFA4-Medium f & higher A; (e) SFA5-High f & lower A; (f) SFA6-High f & higher A; & lower A; (d) SFA4-Medium f & higher A; (e) SFA5-High f & lower A; (f) SFA6-High f & higher A; (g) Mean trust-comparison for all TSR 8.5 cases; (h) Mean trust-percentage error comparison for all (g) Mean trust-comparison for all TSR 8.5 cases; (h) Mean trust-percentage error comparison for all TSR 8.5 cases. TSR 8.5 cases.

4.1.2. TSR 7 Scenario

4.1.2. TSR 7 Scenario In order to understand the unsteady flow behavior at the rated wind speed of full scale FOWT, scaled rotor is subjected to different prescribed surge amplitude frequency motions at 7.0 TSR, 14

In order to understand the unsteady flow behavior at the rated wind speed of full scale FOWT, rad/s inside the tow tank water experimentally when the primarily carriage constant motion is 1 m/s. scaled rotor subjected toisdifferent frequency motions 7.0 TSR, 14 rad/s Theissame scenario simulatedprescribed for all threesurge chosenamplitude numerical simulation tools. Lower at amplitude motion based numerical models mean thrust force within 5% error is 1 m/s. inside thesurge towfrequency tank water experimentally whenwere the predicting primarily carriage constant motion against experimental results as shown Figure 15h. Higher amplitude surge frequency motion based The same scenario is simulated for all three chosen numerical simulation tools. Lower amplitude numerical models were predicting mean thrust within 5% error except at the high frequency surge surge frequency motion based numerical models were predicting mean thrust force within 5% error against experimental results as shown Figure 15h. Higher amplitude surge frequency motion based numerical models were predicting mean thrust within 5% error except at the high frequency surge motion and close to 10% error at higher amplitude scenario. In experiments, mean thrust gradually reduces as surge motion frequency and amplitude increases whereas mean thrust gradually increases in LR-uBEM. Mixed trend is found in both LR-AeroDyn and CFD. As in Figure 15a–f, backward and forward motions in surge oscillations causing the maximum thrust to vary between 4–110% higher than the mean value while the minimum thrust is about 4–110% lower at TSR 7.0.


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motion and close to 10% error at higher amplitude scenario. In experiments, mean thrust gradually reduces as surge motion frequency and amplitude increases whereas mean thrust gradually increases in 2578 LR-uBEM. Mixed trend is found in both LR-AeroDyn and CFD. As in Figure 15a–f, backward and Energies 2018, 11, forward motions in surge oscillations causing the maximum thrust to vary between 4–110% higher than the mean value while the minimum thrust is about 4–110% lower at TSR 7.0.

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Figure 15. TSR 7(a) Cases: (a) SFA7-Low f & lower A; SFA8-Low (b) SFA8-Low f &higher higher A; f & f & lower Figure 15. TSR 7 Cases: SFA7-Low f & lower A; (b) f& A;(c) (c)SFA9-Medium SFA9-Medium lower A; (d) SFA10-Medium f & higher A; (e) SFA11-High f & lower A; (f) SFA12-High f & higher A; A; (d) SFA10-Medium f & higher A; (e) SFA11-High f & lower A; (f) SFA12-High f & higher A; (g) Mean (g) Mean trust-comparison for all TSR 7 cases; (h) Mean trust-percentage error comparison for all TSR trust-comparison 7 cases. for all TSR 7 cases; (h) Mean trust-percentage error comparison for all TSR 7 cases.

4.1.3. TSR 64.1.3. Scenario TSR 6 Scenario order to understand the unsteady flow behavior above rated wind speedspeed (13.2 m/s), which In order toInunderstand the unsteady flow behavior abovethe the rated wind (13.2 m/s), which is 16% higher than the rated wind speed of full scale FOWT, scaled rotor is subjected to experimental is 16% higher than the rated wind speed of full scale FOWT, scaled rotor is subjected to experimental and numerical simulations at 6.0 TSR, 14 rad/s for the different prescribed surge amplitude frequency and numerical simulations at 6.0 TSR, 14velocity rad/s for them/s. different prescribed surge amplitude motions when the primary carriage is 1.167 As shown Figure 16h, all surge frequencyfrequency motions under carriage predicting velocity the mean thrust force within error against experimental resultsfrequency motions when thewere primary is 1.167 m/s. As8% shown Figure 16h, all surge except at the high frequency motion for thrust higher amplitude scenario. thrust slightly increases as results motions were under predicting the mean force within 8%Mean error against experimental surge motion frequency and amplitude increases. As in Figure 16a–f, backward and forward motions except at the high frequency motion for higher amplitude scenario. Mean thrust slightly increases as in surge oscillations causing the maximum thrust to vary between 5–60% higher than the mean value while the minimum thrust is about 5–60% lower at TSR 6.0.

7 cases.

4.1.3. TSR 6 Scenario In order to understand the unsteady flow behavior above the rated wind speed (13.2 m/s), which is 16% higher than the rated wind speed of full scale FOWT, scaled rotor is subjected to experimental and simulations at 6.0 TSR, 14 rad/s for the different prescribed surge amplitude frequency Energies 2018, 11,numerical 2578 19 of 25 motions when the primary carriage velocity is 1.167 m/s. As shown Figure 16h, all surge frequency motions were under predicting the mean thrust force within 8% error against experimental results except at the high and frequency motion for higher amplitude scenario. Mean backward thrust slightly increases as motions surge motion frequency amplitude increases. As in Figure 16a–f, and forward surge motion frequency and amplitude increases. As in Figure 16a–f, backward and forward motions in surge oscillations causing the maximum thrust to vary between 5–60% higher than the mean value in surge oscillations causing the maximum thrust to vary between 5–60% higher than the mean value while the minimum thrustthrust is about 5–60% lower TSR6.0. 6.0. while the minimum is about 5–60% lower at at TSR

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Figure 16. TSR 6 Cases: (a) SFA13-Low f & lower A; (b) SFA14-Low f & higher A; (c) SFA15-Medium

Figure 16. TSR 6 Cases: (a) SFA13-Low f & lower A; (b) SFA14-Low f & higher A; (c) SFA15-Medium f & lower A; (d) SFA16-Medium f & higher A; (e) SFA17-High f & lower A; (f) SFA18-High f & higher f & lower A; A;(g)(d) SFA16-Medium f & (e) SFA17-High f & lowererror A; (f) SFA18-High Mean trust-comparison for higher all TSR 6A; cases; (h) Mean trust-percentage comparison for all f & higher A; (g) Mean trust-comparison for all TSR 6 cases; (h) Mean trust-percentage error comparison for all TSR TSR 6 cases. 6 cases. 4.2. Hydrodynamic Torque Comparison

As power is calculated from the torque values, the torque predictions are compared between the numerical models, though the scaled rotor design is based on the lift curve. In order to understand the torque characteristics at the operating wind speed (11.4 m/s) of full scale FOWT, scaled rotor experimental and numerical model results were compared for the prescribed surge amplitude frequency motions at 7.0 TSR, 14 rad/s rotational speed at primary carriage constant motion of 1 m/s. Mean torque value predictions by all numerical models are close to each other, but differs by maximum of 45% error compared with experimental measurement. As in Figure 17a–f, backward

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4.2. Hydrodynamic Torque Comparison As power is calculated from the torque values, the torque predictions are compared between the numerical models, though the scaled rotor design is based on the lift curve. In order to understand the torque characteristics at the operating wind speed (11.4 m/s) of full scale FOWT, scaled rotor experimental and numerical model results were compared for the prescribed surge amplitude frequency motions at 7.0 TSR, 14 rad/s rotational speed at primary carriage constant motion of 1 m/s. Mean torque value predictions by all numerical models are close to each other, but differs by Energies of 2018, 11, xerror FOR PEER REVIEW with experimental measurement. As in Figure 17a–f, backward 21 of 26 and maximum 45% compared forward motions in surge oscillations causing the maximum torque to vary between 10–150% higher and forward motions in surge oscillations causing the maximum torque to vary between 10–150% than higher the mean while thewhile minimum torque is about lowerlower at TSR 7.0. 7.0. thanvalue the mean value the minimum torque is 10–150% about 10–150% at TSR

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Figure 17. Cont.

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(h) (h)

Figure17. 17.TSR TSR777Cases: Cases:(a) (a)SFA7-Low SFA7-Lowfff& (b)SFA8-Low SFA8-Lowfff& (c)SFA9-Medium SFA9-Mediumfff& Figure Figure 17. TSR Cases: (a) SFA7-Low &lower lowerA; A;(b) (b) SFA8-Low &higher higherA; A;(c) (c) SFA9-Medium & lowerA; A;(d) (d)SFA10-Medium SFA10-Mediumfff& &higher higherA; A;(e) (e)SFA11-High SFA11-Highfff& &lower lowerA; A;(f) (f)SFA12-High SFA12-Highfff& higherA; A; lower lower A; (d) SFA10-Medium & higher A; (e) SFA11-High & lower A; (f) SFA12-High &higher higher A; (g)Mean Meantorque-comparison torque-comparisonfor forall allTSR TSR777cases; cases;(h) (h)Mean Meantorque-percentage torque-percentageerror errorcomparison comparisonfor forall all (g) Mean torque-comparison for all TSR cases; (h) Mean torque-percentage error comparison for all (g) TSR777cases. cases. TSR cases. TSR

4.3. Evaluation of Wind Turbine Operating State 4.3.Evaluation Evaluationof ofWind WindTurbine TurbineOperating OperatingState State 4.3. As shown in Figure 18, when the axial induction factor exceeds 0.4, the turbine rotor will no As shown shownin inFigure Figure18, 18, when when the the axial axialinduction induction factor factor exceeds exceeds0.4, 0.4, the the turbine turbine rotor rotor will willno no As longer be in wind mill state and will be operating in turbulent wake state until the induction factor longerbe bein inwind windmill millstate stateand andwill willbe beoperating operatingin inturbulent turbulentwake wakestate stateuntil untilthe theinduction inductionfactor factor longer exceeds states areare predominantly developed during normal windwind turbine operation based exceeds1. Twowake wake states are predominantly developed during normal wind turbine operation exceeds 1.1.Two Two wake states predominantly developed during normal turbine operation on the drop of the wind speed in the wake. The primary state is the windmill state during medium to based on on the thedrop drop of of the the wind wind speed speed in in the the wake. wake.The The primary primarystate state isis the the windmill windmill state stateduring during based high winds, in which the rotor follows the momentum theory with coefficient of thrust as indicated in mediumto tohigh highwinds, winds,in inwhich whichthe therotor rotorfollows followsthe themomentum momentumtheory theorywith withcoefficient coefficientof ofthrust thrustas as medium the Equation (9). indicatedin inthe theEquation Equation(9). (9). indicated

Figure18. 18.Axial Axialinduction inductionfactor factorVs VsThrust/thrust Thrust/thrustco coefficient efficient[24]. [24]. Figure Figure 18. Axial induction factor Vs Thrust/thrust co efficient [24].

Atlower lowerwind windspeeds, speeds,the thewind windvelocity velocitydiffers differsbetween betweenthe thefreestream freestreamwind windand andthe thewake wakeby by At lower wind speeds, the wind velocity differs between the freestream wind and the wake by At highermagnitude. magnitude.This lowenergy energywake wakewith withrecirculation recirculationleading leadingto tothe theturbulent turbulent higher magnitude. Thisleads leadsto to the the low low energy wake with recirculation leading to the turbulent aaahigher wakestate. state.The Thefree freeshear shearlayer layerbetween betweenthe thewake wakeand andfreestream freestreamis isunstable, unstable,producing producingeddies eddiesthat that wake state. The free shear layer between the wake and freestream is unstable, producing eddies that wake carrymomentum momentumfrom fromthe thefreestream freestreaminto intothe thewake. wake.Hence Hencethe theBEM BEMtheory theoryfollowing followingthe theidealized idealized carry momentum from the freestream into the wake. Hence the BEM theory following the idealized carry momentumprinciple principleis notable ableto topredict predict the drop in the thrust force. As rated wind speed differs momentum the drop inin the thrust force. AsAs rated wind speed differs for momentum isisnot not able to predict the drop the thrust force. rated wind speed differs for each each turbine, the occurrence occurrence of the turbulent turbulent wake state can be be represented represented by using usinginduction an axial axial each turbine, the occurrence of theof turbulent wake state can be represented by usingby an axial for turbine, the the wake state can an induction factor. factor. Based Based on on the the experimental experimental data data shown shown in in Figure Figure 18, 18, Glauert Glauert recommended recommended an an induction equation to model the relationship between Ct and axial induction factor in the turbulent wake state: equation to model the relationship between Ct and axial induction factor in the turbulent wake state:

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factor. Based on the experimental data shown in Figure 18, Glauert recommended an equation to model the relationship between Ct and axial induction factor in the turbulent wake state:


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1 1 Ct = 4aF 1 − (5 − 3a) a , a > 1 3 41

𝐶𝑡 = 4𝑎𝐹 1 −

4

(5 − 3𝑎)𝑎 , 𝑎

3

(16) (16)

where F is the tip-loss factor. where F is the tip-loss factor. Even with the inclusion of F in (16), discontinuities nonetheless existed at a = 0.4 between the Even with the inclusion of F in (16), discontinuities nonetheless existed at a = 0.4 between the momentum theory and Glauert equation, at values of F other than 1. Correction has to be introduced momentum theory and Glauert equation, at values of F other than 1. Correction has to be introduced as suggested by Buhl [25], in an equation 16, that can eliminate the discontinuities at a = 0.4 and have a as suggested by Buhl [25], in an equation 16, that can eliminate the discontinuities at a = 0.4 and have value of Ct = 2 when a = 1, for all values of F: a value of Ct = 2 when a = 1, for all values of F: 88 40 50 40 50 Ct𝐶𝑡== + (4F − a+ − 4F a ∗ a (17) (17) 99 + (4𝐹 − 99 𝑎 + 9 9− 4𝐹 𝑎 ∗ 𝑎

The The current current study study bolsters bolsters the the fact fact that that the the surge surge cyclic cyclic motions motions are are pushing pushing the the rotor rotor under under investigation scenario as as depicted 19. From investigation to to the the turbulent turbulent wake wake state state of of SFA10 SFA10 scenario depicted in in Figure Figure 19. From the the scaled scaled rotor rotor blade blade element element number number 14 14 to to 17 17 (the (the last last four four elements elements upto upto scaled scaled rotor rotor tip tip of of total total 17 17 elements elements as in Table 1), the turbulent wake state is clearly identified by the axial induction factor, a. CFD as in Table 1), the turbulent wake state is clearly identified by the axial induction factor, a. based CFD induction factor factor derivation [6] is obtained at 1.25ats1.25 of the cycles and compared against LRbased induction derivation [6] is obtained s oflast the2last 2 cycles and compared against AeroDyn model prediction as shown in Figure 19. LR-AeroDyn prediction is within 6% error on these LR-AeroDyn model prediction as shown in Figure 19. LR-AeroDyn prediction is within 6% error on elemental nodes nodes when compared to CFDto predictions. Hence, Hence, BEM based models like LRthese elemental when compared CFD predictions. BEMengineering based engineering models AeroDyn and LR-uBEM are able predict the surge the motion responses the rotoronloading reasonably like LR-AeroDyn and LR-uBEM are able predict surge motion on responses the rotor loading well. reasonably well.

Figure element 14–17 of of thethe scaled rotor for for the the SFA10 scenario withwith LRFigure 19. 19. Axial Axialinduction inductionfactor factorofof element 14–17 scaled rotor SFA10 scenario AeroDyn model simulation and corresponding point wise CFD based axial induction factor LR-AeroDyn model simulation and corresponding point wise CFD based axial induction factor comparison comparison at at 1.25 1.25 s. s.

CFD simulation results are exported to Ansys CFD Post (V16.2) to visualize the velocity and vorticity contour profiles. These profiles are plotted in Matlab, which clearly demonstrates how the scaled rotor is interacting with its own wake and the near wake distortion by surge motion frequencies. The Figures 20 and 21 show the velocity contour profiles. In addition, these contours display the surge oscillations behavior and corresponding rotor loading.

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CFD simulation results are exported to Ansys CFD Post (V16.2) to visualize the velocity and vorticity contour profiles. These profiles are plotted in Matlab, which clearly demonstrates how the scaled rotor is interacting with its own wake and the near wake distortion by surge motion frequencies. Energies 2018, 11, x FOR PEER REVIEW 24 of 26 The Figures 20 and 21 show the velocity contour profiles. In addition, these contours display the surge Energies 2018, 11, x FOR PEER 24 of 26 oscillations behavior andREVIEW corresponding rotor loading.

(a)

(b)

Figure 20. SFA10 mean rotor (a) position at the end of 6th cycle of surge motion, (b) velocity (a) Line plot; (b) contour plot showing tip vertices and compressed and elongated wake in the near wake field by Figure 20. 20. SFA10 SFA10mean meanrotor rotorposition positionatatthe the end cycle surge motion, velocity (a) Line Figure end of of 6th6th cycle of of surge motion, velocity (a) Line plot;plot; (b) CFD. (b) contour showing tip vertices and compressed and elongated thewake near wake field by contour plot plot showing tip vertices and compressed and elongated wake wake in thein near field by CFD. CFD.

Figure 21.21.SFA10 mean rotor position atat the end ofof6th Figure SFA10 mean rotor position the end 6thcycle cycleofofsurge surgemotion, motion,near nearwake wakefield fieldvelocity velocity contour plots atat 0.50.5 mm intervals from rotor plane inin thethe rotating domain byby CFD. contour plots intervals from rotor plane rotating domain CFD. Figure 21. SFA10 mean rotor position at the end of 6th cycle of surge motion, near wake field velocity 5. Conclusions contour plots at 0.5 m intervals from rotor plane in the rotating domain by CFD.

5. Conclusions The flow characteristics on a FOWT are a highly complex phenomenon as it is simultaneously The flow characteristics on a FOWT are a highly complex phenomenon as it is simultaneously 5. Conclusions subjected to aerodynamic and hydrodynamic forces from wind and ocean waves. The study on subjected to aerodynamic and hydrodynamic forces from wind and ocean waves. The study on The flow on a FOWT are a highly complex as it isissimultaneously sensitivity of thecharacteristics aerodynamic behavior with respect to the changesphenomenon in platform motion indispensable, sensitivity of the aerodynamic behavior with respect to the changes in platform motion is subjected to aerodynamic and hydrodynamic forces from wind and ocean waves. The study on as small changes in platform motion will be amplified due to the tower height. The current study indispensable, as small changes in platform motion will be amplified due to the tower height. The sensitivity of investigation the aerodynamic behavior with respect to the in platform motion is focused on the of unsteady aerodynamic loading due changes to surge motion through various current study focused on the investigation of unsteady aerodynamic loading due to surge motion indispensable, as small changes in platform motion will be amplified due to the tower height. The through various numerical codes. A scaled floating rotor has been successfully designed with current study focused on the investigation of unsteady aerodynamic loading due to surge motion necessary instrumentation and imparted with hydrodynamic motions, similar to a FOWT operating through various numerical codes. A scaled floating rotor has been successfully designed with conditions. The experimental outcome is compared with CFD model results in addition to the necessary instrumentation and imparted with hydrodynamic motions, similar to a FOWT operating selected engineering simulation codes, LR-AeroDyn and LR-uBEM. Almost in all the selected conditions. The experimental outcome is compared with CFD model results in addition to the

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numerical codes. A scaled floating rotor has been successfully designed with necessary instrumentation and imparted with hydrodynamic motions, similar to a FOWT operating conditions. The experimental outcome is compared with CFD model results in addition to the selected engineering simulation codes, LR-AeroDyn and LR-uBEM. Almost in all the selected unsteady scenarios, numerical codes predict mean thrust values within 10% error level against the experimental results. Backward and forward motions in surge oscillations leading to the maximum and minimum thrust variation in the range of 4% to 110% from mean thrust. The detailed CFD visualization of complex flow field around the rotor 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. Though LR-AeroDyn is equipped with quasi-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. Turbulent wake state of wind turbine operation is identified and compared against CFD based induction factor derivation. 6. Future Work The computational mesh quality will be further refined around near wake regions with smaller time steps for accurate predictions of unsteady rotor loading results at higher frequency surge motions. Time history of velocity and vorticity data from CFD will be exported to Matlab for enhanced visualization of wake interactions. Lift and drag co-efficient of scaled rotor airfoils will be experimentally obtained to improve the LR-AeroDyn and LR-uBEM model accuracy. A detailed investigation will be performed to quantify the uncertainty analysis for these methods. The numerical models will be further refined for full scale 5 MW NREL turbine at its operating conditions of TSR, surge frequencies and amplitude and will be compared with scaled rotor results. The computed results will be used in digital twin approach, in which the remaining useful life of key components such as power converters will be predicted. The proposed approach will curtail the maintenance and inventory cost especially for FOWT. Author Contributions: CFD and LR-AeorDyn, K.S.; Scaled Rotor Design, Development and Tow Tank Steady and Unsteady Experiments, S.M.; LR-uBEM, A.A.S.W. 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: The authors declare no conflict of interest.

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2. 3. 4. 5.

6.

Sivalingam, K.; Davies, P.; Singapore Wala, A.A.; Day, S. CFD Validation of Scaled Floating Offshore Wind Turbine Rotor. In Proceedings of the 2nd International Conference on Green Energy and Applications (ICGEA), Singapore, 24–26 March 2018. [CrossRef] World Wind Energy Association. 2013 Half-Year Report; Technical Report; World Wind Energy Association: Bonn, Germany, 2013. Musial, W.; Butterfield, S.; Boone, A. Feasibility of Floating Platform Systems for Wind Turbines. In Proceedings of the 23rd ASME Wind Energy Symposium, Reno, NV, USA, 5–8 January 2004. Burton, T.; Jerkins, N.; Sharpe, D.; Bossanyi, E. Wind Energy Handbook; John Wiley & Sons: Hoboken, NJ, USA, 2011; ISBN 13:978-0-471-48997-9. Matha, D.; Schlipf, M.; Cordle, A.; Pereira, R.; Jankman, J. Challenges in Simulation of Aerodynamics, Hydrodynamics, and Mooring-Line Dynamics of Floating Offshore Wind Turbines. In Proceedings of the 21st International Offshore and Polar Engineering Conference, Maui, HI, USA, 19–24 June 2011. Sivalingam, K.; Bahuguni, A.; Gullman-Strand, J.; Davies, P.; Nguyen, V.T. Effects of Platform Pitching Motion on Floating Offshore Wind Turbine (FOWT) Rotor. In Proceedings of the Offshore Technology Conference, Houston, TX, USA, 4–7 May 2015.

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