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Ocean Engineering

journal homepage: www.elsevier.com/locate/oceaneng

A numerical model for fully coupled aero-hydrodynamic analysis of floatingoffshore wind turbine

Ping Cheng, Yang Huang, Decheng Wan∗

State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Collaborative Innovation Centre forAdvanced Ship and Deep-Sea Exploration, Shanghai, 200240, China

A R T I C L E I N F O

Keywords:Unsteady actuator line modelCoupled aero-hydrodynamicsFOWT-UALM-SJTU solvernaoe-FOAM-SJTU solverFloating offshore wind turbine

A B S T R A C T

Designing floating offshore wind turbine system is a quite challenging task because of the complex environ-mental loading and complicated coupling effects. In the present study, the fully coupled aero-hydrodynamicmodel for numerical simulation of floating offshore wind turbine (FOWT) is established with open source toolOpenFOAM. The coupled FOWT-UALM-SJTU solver is developed using the open source CFD packageOpenFOAM, in which the unsteady actuator line model (UALM) is introduced into OpenFOAM for the aero-dynamic simulation of wind turbine, while the hydrodynamic computation of floating platform is carried outwith a two-phase CFD solver naoe-FOAM-SJTU. In the coupled model, the three-dimensional Reynolds-AveragedNavier-Stokes (RANS) equations are solved with the turbulence model k-ω SST employed for closure of RANSequations, and the Pressure-Implicit with Splitting of Operations (PISO) algorithm is applied to solve thepressure-velocity coupling equations. The coupled responses of a FOWT with NREL-5MW baseline wind turbinemounted on a semi-submersible platform are investigated. From the simulation, aerodynamic forces includingthe unsteady aerodynamic power and thrust can be obtained, and hydrodynamic responses such as the six-degree-of-freedom motions of the floating platform and the mooring tensions are also available. The impact ofdynamic motions of floating platform on the aerodynamic performance of wind turbine is analyzed, and theeffect of the aerodynamic forces on the hydrodynamic response of the floating platform is also studied.

1. Introduction

Excessive exploitation of conventional fossil fuels has intensified theenergy crisis and environmental pollution problem, which makes it animmediate issue to find clean and renewable energy resource to replacethe traditional energy. As one of the most promising non-polluting re-newable energy sources, wind energy has shown great potential andattracted the global attention. Exploitation of wind energy has experi-enced rapid growth since last few decades. According to the statistics,the global reserves of wind energy is up to 2.74×109MW and2×107MW are utilizable (Zhang et al., 2010), which is about 10 timesof the available water energy. The offshore wind resource has lots ofparticular advantages over onshore wind energy. For instance, theaverage speed of offshore wind is about 90% larger than that of onshoreone (Archer and Jacobson, 2005). Wind turbines, as wind energy har-vesting devices, has developed from onshore to offshore wind farms inrecent years.

Installing wind turbines in offshore wind farms far away from landcan reduce the visual pollution and noise compared with those onshore

or near land offshore ones (Bae et al., 2011). Water depth increasesrapidly with the distance from the land, while cost of the traditionalgravity-based or jacket type foundations grow sharply with waterdepth. Floating offshore wind turbines (Sørensen and Shen, 2002) aremore cost effective choice for offshore wind farms with water depthexceeding 50m (Butterfield et al., 2005). In June 2009, the first multi-megawatt FOWT in the world, Hywind Demo equipped with a 2.3-MWwind turbine, was installed at the west coast of Norway, and its powerproduction has been quite promising (Skaare et al., 2015). And thesuccess of Hywind Demo has inspired the development on FOWT. TheScottish government granted installation of a floating offshore windfarm with five 6-MW FOWTs in the North Sea off the Peterhead coast(BBC, 2015; Liu et al., 2017), where the water depth is over 100m.

However, designing FOWT system is a quite challenging task due tothe complicated structure, the complex environmental loading and thecoupling effects (Luo et al., 2012). Compared with conventional on-shore wind turbine or fixed-bottom wind turbine working in shallowwater, a FOWT suffers much more complicated environmental loads:the aerodynamic forces on turbine rotor, the hydrodynamic loads on

https://doi.org/10.1016/j.oceaneng.2018.12.021Received 26 July 2018; Received in revised form 30 October 2018; Accepted 5 December 2018

∗ Corresponding author.E-mail address: dcwan@sjtu.edu.cn (D. Wan).

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0029-8018/ © 2018 Elsevier Ltd. All rights reserved.

T

floating support platform and the mooring forces, etc. Furthermore, theaerodynamic forces on turbine rotor transmitted to the floating supportplatform via the tower, which affects the dynamic responses of theplatform; the mooring lines provide restoring forces on supportingplatform to restrict the movement of the system; and on the otherround, the motion of platform influences the aerodynamic performanceof the turbine blades by changing the relative flow velocity experiencedby turbine blades. Complex interaction between the components makescoupling prediction of FOWT a quite challenging task.

Experimental test, as an indispensable tool for research, plays animportant role in study on FOWT. A couple of intermediate-scale FOWTmodels have been deployed on ocean coast (Viselli et al., 2015). Ex-periencing the offshore wind-wave environment, the intermediate-scaleexperiments provide reliable reference data for further design of com-mercial-scale devices. However, the high cost and the difficulties inoperational control make intermediate-scale experiment an inadvisablechoice. Meanwhile, a number of scaled-down FOWT with differentdesigning concepts have been carried out in wave basin under variousexperimental conditions (Martin, 2011; Koo et al., 2014; MyhrANygaard, 2014; Sandner et al., 2015). These scaled-down experimentsalso show practical results and reference data for validation and de-signing of FOWT. But there still underlies a problem that the Froudescaling law and the Reynolds similarity law cannot be guaranteed at thesame time.

To meet the requirement of predicting coupled aero-hydrodynamicperformances of a FOWT system, the numerical method stands out,which is much more economical than experimental tests either in in-termediate-scale or scaled-down models and without limitation of thescaling laws. Since onshore wind turbines have developed for decades,there exist a couple of numerical tools for aerodynamic analysis. Themost commonly used numerical methods are the blade element mo-mentum (BEM) method (Glauert, 1963), the vortex methods (Voutsinaset al., 1995), the potential flow theory (Van Bussel, 1995), the actuatorline model (Shen and Sørensen, 2002), the computational fluid dy-namics (CFD) methods (Zhou and Wan, 2015), etc. BEM method issimple and very time-saving during computing, and most of the com-mercial numerical tools are developed based on BEM method(Jonkman, 2007). However, the assumptions in this model and thedependency on 2D aerodynamic experimental data of airfoils exposedthe limitation and the inaccuracy of BEM model. To gain the descriptionof 3D flow information around turbine blades, the vortex methods andpotential flow theory are developed. As is known to all, these twomethods are based on the inviscid flow assumption, so the viscous ef-fects are neglected, which may result in significant inaccuracy. Besides,the vortex method has a potential risk for stability while vortex ele-ments getting close to each other (Hansen et al., 2006). With rapiddevelopment of computational technology, the CFD method is be-coming popular in aerodynamics study (Cheng et al., 2016). With directcalculation by solving Navier-Stokes (N-S) equations, CFD simulationsprovide much more precise results including detailed flow informationfor in-depth discuss on the physical mechanism. On the other side, thedirect calculation method requires higher computing performance andtakes much longer time. Using the actuator line model (ALM) is aneffective way to reduce computational cost by replacing the real bladestructure with virtual actuator lines, and guarantee considerable pre-cision by solving the Navier-Stokes equations in flow field (Troldborget al., 2007).

However, the aerodynamics analysis of FOWTs is significantly dif-ferent from the conventional fixed wind turbines due to the additionalmotion caused by platform dynamic responses (Sebastian and Lackner,2012). In some previous research works, the unsteady aerodynamics ofFOWT blades is investigated by considering the typical motions ofsupport platform. Tran (Tran and Dong, 2015; Tran and Kim, 2016a)has done a series of calculations on unsteady aerodynamic predictionsof turbine blades by considering platform motion with periodic surge,pitch or yaw using unsteady CFD methods with a dynamic moving grid

technique. Besides the oscillating regularity of both aerodynamic thrustand power, the flow interaction phenomena between the turbine bladeswith oscillating motions and the generated blade-tip vortices were ob-served. Wu (Wu and Nguyen, 2017) has developed a CFD model forunsteady and non-linear aerodynamic simulations of rotor underfloating platform-induced motions with arbitrary mesh interface (AMI).

Recently, fully coupled aero-hydrodynamic simulations of FOWTshave been conducted under combined wind-wave conditions, and thecoupling effects between the aerodynamics of wind turbine and thehydrodynamics of floating platform are studied. The NationalRenewable Energy Laboratory (NREL) developed a fully coupled aero-hydro-servo-elastic tool named FAST (Jonkman, 2009), which is basedon BEM and potential flow theory, to implement the coupled simulationof FOWTs. However, utility of FAST is dependent on data-inputtingfrom an external potential-flow-based hydrodynamic solver, such asWAMIT, which restricts its usage for more accurate predictions as theviscous effect is ignored in potential flow theories. There are othernumerical tools for coupling simulation of FOWT based on BEMmethod, such as HAWC2, 3Dfloat, bladed, etc. (Cordle, 2010). As BEMis an empirical method with various correction models (such as Glauertcorrection, skewed wake correction, etc.), Sebastian (Sebastian andLackner, 2013) indicated that the BEM is still questionable in unsteadyaerodynamic prediction for FOWTs. Therefore, benefitting from therapid development of high-performance computing (HPC) technique,the CFD method has shown great potential for accurate numerical si-mulation for FOWT. In recent years, studies on fully coupled analysis ofFOWTs have been conducted with CFD method. Tran conducted thefully coupled aero-hydrodynamic analysis of a semi-submersible FOWTusing a dynamic fluid body interaction approach (Tran and Kim,2016b). Liu (Liu et al., 2017) established a fully coupled CFD analysistool for FOWTs based on OpenFOAM package and the coupling effect ofthe OC4 DeepCWind semi-submersible FOWT was studied. CFD simu-lations achieve accurate results and enable detailed quantitative ana-lysis of flow field. However, a full structure CFD simulation is quitecomputational costly.

Based on the open source platform OpenFOAM, our research teamdeveloped the CFD solver naoe-FOAM-SJTU to investigate hydro-dynamic problems in the field of ship and ocean engineering, and theunsteady actuator line model (UALM) (Li et al., 2015) was introducedinto OpenFOAM for aerodynamic simulation of wind turbine. By com-bining these two solvers, the fully coupled aero-hydrodynamic modelfor simulation of a floating offshore wind turbine is established. Byusing the solver, the validation of unsteady aerodynamic loads wasconducted compared to different numerical methods. Moreover, thecoupled aero-hydrodynamic simulation for a FOWT was also completedcompared to the simplified method (Karimirad and Moan, 2012). In thepresent study, the coupled aero-hydrodynamic responses of Phase II ofOC4, which is a semisubmersible-supported wind turbine system, areinvestigated. The three-dimensional Reynolds-Averaged Navier-Stokes(RANS) equations coupled with the k-ω SST turbulence model aresolved. The Pressure-Implicit with Splitting of Operations algorithm(PISO) is employed to solve the pressure-velocity coupling equations.The effect of turbine aerodynamics on floating platform response isinvestigated with proper comparison between the fully coupled simu-lation of FOWT system and the hydrodynamic results of pure platform.Similarly, the influence of platform hydrodynamics on turbine dy-namics is examined by comparing the fully coupled simulation of FOWTsystem and the aerodynamic results of pure wind turbine. In addition,the impact of incoming wave condition on the system performance isanalyzed by varying the wave conditions.

In this paper, the numerical model utilized in this present work isintroduced firstly; validations for both aerodynamic and hydrodynamicmodels are conducted and presented in the following part; and thedescriptions of the physical model employed in the present study, thePhase II of OC4 floating offshore wind turbine system, are shown; si-mulation results and discussions are interpreted; and finally, proper

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conclusions are stated.

2. Numerical method

2.1. Governing equations

In the fully coupled numerical simulation model for FOWT system,the three-dimensional (3D) Reynolds-Averaged Navier-Stokes (RANS)equations for transient, incompressible and viscous Newtonian fluid aresolved, which contain the continuity and momentum equations:

∇⋅ =U 0 (1)

∂∂

+ ∇⋅ − = −∇ − ⋅ ∇ + ∇⋅ ∇ + ∇

⋅∇ +

ρt

ρ p ρ μ

μ

UU U U g x U U

f

( )( ( )) ( ) ( )g d eff

eff s (2)

Where, U represents velocity of flow field; Ug is the velocity of gridnodes; pd = p-ρg·x is the dynamic pressure by subtracting hydrostaticcomponent ρg·xfrom total pressure p; g is the acceleration vector ofgravity; ρ is the mixture density with two phases (water and air);

= +μ ρ ( υ υ )eff t is μeff =ρ(ν+νt) effective dynamic viscosity, in which νand νt are the kinematic viscosity and eddy viscosity respectively; fs isthe source term. With introduction of the time-averaged terms, theabove RANS equations are not closed as they contain more variablesthan equations. In order to meet the closure requirement and solveRANS equations, the two-equation turbulence model k-ω SST (Menter,1994) is employed, where the turbulent kinetic energy k and the tur-bulent dissipation rate ω can be described as:

∂∂

+ ∇⋅ = ∇⋅ ∇ + − +ρkt

ρ k Γ k G Y SU( ) ( )k k k k (3)

∂∂

+ ∇⋅ = ∇⋅ ∇ + − + +ρωt

ρ ω Γ ω G Y D SU( ) ( )ω ω ω ω ω (4)

Where, Гk and Гω are the effective diffusion coefficients for the turbu-lent kinetic energy k and the turbulent dissipation rate ω, respectively,Gk and Gω are turbulence generation terms for k and ω, Yk and Yω areturbulent dissipation terms for k and ω, Sk and Sω are the source termsfor k and ω, Dω is the cross-diffusion terms for ω.

2.2. Unsteady actuator line model

In this present study, the actuator line model (ALM) is utilized toimplement the aerodynamic prediction of FOWT. The ALM is an ef-fective way to reduce computational cost by displacing the real bladessurfaces with virtual actuator lines and not being required to solve theblade geometry layer. The wind turbine blades are simplified into ac-tuator lines withstanding body forces in ALM, which are divided into aseries of discrete actuator points (Sørensen and Shen, 2002).

In this study, modifications are made to the initial ALM so that it canbe used to simulate the FOWT. This is accomplished by accounting forthe influence of the platform motion on the blades. When the ALM isapplied to the simulation of the FOWTs, the velocity vector UM inducedby the motions of the floating platform is added into the velocity tri-angle (as shown in Fig. 1), which will lead to complex interactionsbetween the rotor and its wake. So the ALM needs to be modified tosolve the unsteady problem caused by the dynamic motion responses offloating platform. The unsteady actuator line model considering theeffect of six-degree-of-freedom motions is used in this paper.

In order to determine the aerodynamic forces acting on rotor blades,a blade element method combined with two-dimensional (2D) airfoilcharacteristics is used. Fig. 1 shows a cross-sectional element at radius rwhich defines the airfoil in the xOy plane. The figure shows the integralvelocity vectors relationship described as:

= + × + +U U Ω r U Urel in rot M (5)

Where, Uin represents the inflow velocity vector, Urot is the flow

velocity induced by the rotating blade, Ω×r is the speed of airfoilcauses by the blades rotation, UM is the additional airfoil velocity vectorinduced by the motions of the floating platform. And the magnitude ofthe local velocity relative to the rotating blade is given as:

= − + × − +U U U Ω r U U( ) ( )rel in M in rot M rot,2

,2 (6)

The angle of attack α which determines the airfoil aerodynamic datais defined as:

⎜ ⎟= − = ⎛⎝

−× − +

⎞⎠

−α ϕ θ ϕU U

Ω r U U, tant

in M in

rot M rot

1 ,

, (7)

Where, φis the inflow angle;θt is the local airfoil twist angle; and theaerodynamic lift and drag forces can be given by the following equa-tion:

= = +ρ U cN

rdθdzC Cf L D e e( , )

2( )rel b

L L D D

2

(8)

Where, c is the chord length of the airfoil, Nb is the total number ofblades; CL and CD CL and CD are the lift and drag coefficient respectively,eL and eD denote the unit vectors in the directions of the lift and thedrag respectively. The lift and drag coefficient are determined frommeasured or computed 2D airfoil data which are corrected with 3Deffects.

The aerodynamic lift and drag forces are acting as body force in theflow field after smooth treatment to avoid singular behavior.

= ⊗ ηf fε ε (9)

and,

= −⎛⎝

⎞⎠η d

ε πe( ) 1

ε

dε

3 3/2

i2

(10)

Here, diis the distance between the measured point in flow field and theactuator points on the rotor. ε is a constant width parameter to adjustthe strength of regularization function, and the parameter ε is suggestedto be determined according to the length of grid near turbine blades orthe chord length of airfoil (Sørensen et al., 1998). And the body forceadded onto the right side of the momentum equations as a source termcan be written as:

==

−⎛⎝

⎞⎠x y z t Σ x y z t

ε πef f( , , , ) ( , , , ) 1

εi

Ni i i

dε

1 3 3/2

i2

(11)

Then the UALM is programmed as a C++ class based on theOpenFOAM.

2.3. Six-degree-of-freedom (6DOF) motions

The fully coupled aero-hydrodynamic solver is established bycombining the aerodynamic UALM module and the hydrodynamiccode. And the hydrodynamic solver employed in this paper is our in-house code naoe-FOAM-SJTU (Shen et al., 2012a). naoe-FOAM-SJTU isdeveloped based on the OpenFOAM, which is an open source toolpackage. In this solver, the two-phase incompressible RANS equationsare solved, which are discretized by the finite volume method (FVM),and the volume of fluid (VOF) method is utilized to capture the freesurface and the dynamic deformation mesh approach is employed tohandle structure motions (Shen et al., 2012b). Based on fundamentalcodes in OpenFOAM, several modules are developed: a numerical tanksystem including the wave generation and damping module, the six-Degree of Freedom (6DOF) motion module and the mooring systemmodule. As validations, hydrodynamic simulation of floating platformcoupled with mooring system was conducted by Cao using naoe-FOAM-SJTU (Cao et al., 2013), and some verification was made in previouswork (Zhao and Wan, 2015), which proved that naoe-FOAM_SJTU is agood choice to deal with this kind of problems.

With establishment of the 6DOF motion module, the naoe-FOAM-

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SJTU solver is able to predict the motion responses of floating struc-tures. Two coordinate systems (as shown in Fig. 2) are set up in theprocedure of solving 6DOF motion equations: the body-fixed coordinatesystem and the earth-fixed coordinate system. At each time step simu-lation, the motion equations are solved in platform-fixed coordinatesystem while the forces are calculated in earth-fixed coordinate system.Therefore, a transformation between the data in these two systems isessential. The added velocity induced by the dynamic motions of thesupporting platform is updated by the following equation:

= + × −U J U ω x x[ ]( ( ))motion i C i CC. (12)

Where, [J] represents the transformation matrix defined from thebody-fixed coordinate to earth-fixed coordinate; Uc and ωc donate thetranslational velocity and the angular velocity of the rotating center; xcis the location the rotating center.

2.4. Volume of fluid (VOF) method

For capturing the free surface, the VOF method (Hirt and Nichols,1981) with bounded compression technique (Rusche, 2003) is appliedin our solver. The VOF transport equation is defined as:

∂∂

+ ∇⋅ − + ∇⋅ − =αt

α α αU U U[( ) ] [ (1 ) ] 0g r (13)

Where, U is the velocity of flow field, Ug is the velocity of grid nodes,and α is the volume fraction representing the relative proportion offluid in each cell which is defined as:

⎧⎨⎩

==

< <

αα

α

01

0 1

airwater

interface (14)

And the fluid density ρ and the dynamic viscosity μ can be describedwith the volume fraction as:

= + −ρ αρ α ρ(1 )l g (15)

= + −μ αμ α μ(1 )l g (16)

Where, ρl and μl are the density and dynamic viscosity of the liquid(water), while ρl and μl are the density and dynamic viscosity of the gas(air).

2.5. Wave generation and absorption module

For hydrodynamic simulation of a floating platform, the work ofwave generation must be implemented. In naoe-FOAM-SJTU solver, thewave generation and absorption module is capable of generating var-ious types of waves such as linear wave, high order (2nd to 5th) Stokeswaves, irregular waves (Shen and Wan, 2016), focusing waves (Cao andWan, 2014), etc. The linear regular waves will be adopted in the fol-lowing paper. The surface elevation for the linear regular wave and thehorizontal and vertical components of fluid velocity distribution aredescribed as:

= −η A kx ωtcos( ) (17)

⎧⎨⎩

= −

= −

+

+

u kx ωt

w kx ωt

cos( )

sin( )

πHT

k z dkd

πHT

k z dkd

cosh ( )sinh

sinh ( )sinh (18)

Where, A and H=2A denote the wave amplitude and wave height; kand ω are wave number and wave circular frequency; z is the verticalcoordinate and d represents the water depth.

Once the wave is generated and propagates from inlet towardsoutlet boundary, reflection is non-negligible which travels in an oppo-site direction and may interfere with the incident wave, so that thewave damping module is developed (Larsen and Dancy, 1983). In thewave damping module, sponge layer takes effect by adding an addi-tional artificial viscous term as a source term on the right side of themomentum equation in RANS. The new term is expressed as:

Fig. 1. Cross-sectional airfoil element.

Fig. 2. Coordinate system.

Fig. 3. Overlooking of the calculation domain and sponge layer.

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186

= −ρμf Us s (19)

Where, μs is the artificial viscosity determined by the following equa-tion:

=⎧⎨⎩

>

≤

−( )μ x α x x

x x( ) ,

0,s

sx x

L

20

0

s0

(20)

Where, αs is a dimensionless quantity defining damping strength for thesponge layer. Ls represents the length of sponge layer, and x0 is the startof the sponge layer (see Fig. 3).

2.6. Mooring system modelling

To simulate the interaction between the mooring lines and floatingplatform, the code of mooring system module (Liu, 2014) is developed.Here, the piecewise extrapolating method (PEM) which is a quasi-staticmodel is implemented to calculate the mooring forces. In this method, amooring line is divided into a number of segments (Fan et al., 2012). Atypical example is shown in Fig. 4. Equations of static equilibrium areestablished in both horizontal and vertical directions:

⎧⎨⎩

= + ++ = + +

+ + +

+ + +

T T F ds φ D ds φT D ds φ T F ds φ w dl

cos sincos sin

xi xi i i i i

zi i i zi i i i

1 1 1

1 1 1 (21)

Where Tx and Tz represent horizontal and vertical components of totalmooring line tension at a cross section of one segment, φ is the anglebetween total tension force vector and horizontal plane; dl and ds arethe segment length before and after elongation respectively; wi is netsubmerged weight of lines per unit length; D and F denote normal andtangential components of drag force acting on the segment which arecalculated by Morison's equation; and the subscript i represents the ithnode lies on the ith segment.

2.7. Coupled aero-hydrodynamic analysis model

A fully coupled aero-hydrodynamic analysis model FOWT-UALM-SJTU for numerical simulation of floating wind turbine was establishedby combing the UALM and naoe-FOAM-SJTU. The coupled dynamicresponses of the FOWTs include the aerodynamics of wind turbine, thehydrodynamics of floating platform and the performance of mooringsystem. Fig. 5 shows the coupled analysis module of this coupled model,where the aerodynamic simulations are conducted with the UALM, andthe 6DOF motions and the mooring forces are predicted by the naoe-FOAM-SJTU.

As introduced above, the body force on flow field smoothed fromaerodynamic force obtained with UALM module are added as a sourceterm fε on the right side of the momentum equations. In addition, the

effect of sponge layer is also considered as a source term fs. So themomentum equation in RANS is modified as:

∂∂

+ ∇⋅ − = −∇ − ⋅ ∇ + ∇⋅ ∇ + ∇

⋅∇ + + +

ρt

ρ p ρ μ

μ

UU U U g x U U

f f f

( )( ( )) ( ) ( )g d eff

eff σ s ε (22)

Where, fσ is the surface tension term in two phases model and takeseffect only on the liquid free surface.

The solving procedure of coupled aero-hydrodynamic simulation forthe FOWTs is shown in Fig. 6. The main program loop is based on naoe-FOAM-SJTU. At the start of the simulation for each time step, theaerodynamics, hydrodynamics, and the mooring systems are calculatedsimultaneously with corresponding modules since the mesh grid andfluid field information are updated according to the motions calculatedin last time step. Then the volume forces calculated with the UALMmodule are transferred to the main program to solve the RANS equa-tions (Eqn. (22)) with PISO loops for the whole fluid field, where 2–6PISO loops are required to reach convergence of the fluid field simu-lation. And when the 6DOF motion equations are solved, the turbineaerodynamic forces calculated with UALM module, as well as themooring forces simulated with the mooring module are transferred tothe main program, so the motion of FOWT is calculated and the meshdeforming information is updated.

3. Validation for the numerical models

3.1. Validation for aerodynamics with UALM module

In our previous study with ALM, the validation against “Blind Test1” is conducted (Li, 2016). Fig. 7 illustrates the thrust and powercomparisons of the numerical results and the experimental ones. Boththe numerical power and thrust show quite good agreement with thetest data, which confirms ALM a powerful and reliable tool in aero-dynamic simulation.

The UALM module is employed for the aerodynamic simulation ofNREL-5MW baseline wind turbine (detailed description can be found inthe following section). The aerodynamic forces and powers on theNREL-5MW wind turbine with various steady uniform wind speed arefirst obtained with ALM model. The results of power and thrust arecompared with results obtained with previous results in Fig. 8, whichshows quite good agreement with other results and certifies that theFOWT-UALM-SJTU solver is reliable in basic aerodynamic simulation.

Considering the wind turbine in the whole FOWT system experi-ences 6DOF motion, the unsteady aerodynamic simulation for turbinerotor experiencing periodic surge motion is also conducted for valida-tion of UALM module. The surge motion is determined with a sinusoidalfunction s= 8sin(0.246t), where the amplitude and the circular fre-quency of oscillating surge motion are 8m and 0.246, respectively. Theperiodic surge motion causes the variation of the relative wind speednearby the turbine blades, and brings about the oscillation of theaerodynamic forces on turbine. The aerodynamic thrust and power arecompared with those calculated with overset grid technique (Tran andKim, 2016a), and the curves in Fig. 9 show good agreement in boththrust and power of the wind turbine. The range between the maximumand the minimum of both the aerodynamic power and thrust resultedfrom UALM are a little smaller than that from simulations using full-structured CFD method with overset grid technique but the difference isno more than 7%. It is also well proved that the FOWT-UALM-SJTUsolver is a reliable solver for both unsteady aerodynamic calculations.

3.2. Validation for wave generation and absorption module

The 3D numerical wave tank including wave generation and ab-sorbing is employed. The wave properties used for validation and thefollowing coupled simulation in the present work are listed in Table .1.

Fig. 4. Force analysis of a mooring line segment for PEM.

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Fig. 5. Coupled analysis modules.

Fig. 6. Solving procedure of coupled simulation.

Fig. 7. Comparison of numerical thrust and power coefficient with “Blind test 1” result (Krogstad and Lund, 2012; Li, 2016).

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The simulation domain is set as a rectangular region with longituderange of−150m–300m which is about three times of the wave length, arange of −150m–150m in landscape direction, and the distance frombottom to the initial water surface is 100m to guarantee the linear wavecondition requirement. To validate the wave generation and absorbing,four wave gauges are set along wave propagating direction in the nu-merical wave tank (x=−50m, 0m, 100m, 279m) to monitor waveelevation at different position.

The numerical results are compared with the theoretical data. Thefirst three pictures in Fig. 10 show the comparison results of waveelevation at the position of the three wave gauges, and the fourth showsresult at the end of the damping area. The figures indicate that thenumerical simulation results agree quite well with the theoretical so-lutions. In the last figure, the wave height has been significantly re-duced over 90% with the sponge layer effect, in which case the wavereflection effect is neglected. Therefore, the wave generation and ab-sorbing module for naoe-FOAM-SJTU solver utilized in this paper isaccurate and reliable.

3.3. Validation for naoe-FOAM-SJTU with hydrodynamic response ofplatform in regular wave

The hydrodynamic response of the semi-submersible floating

platform is also investigated under a regular heading wave condition asintroduced above. Three main degrees of freedoms of the floatingplatform with the most significant responses in heading wave condi-tions, surge, heave and pitch, are analyzed. Fig. 11 shows the ResponseAmplitude Operators (RAOs) for surge, pitch and heave motions of thefloating platform. The numerical results of this present work are com-pared with the experimental data and numerical results with FAST(Coulling et al., 2013) and other CFD solvers (Liu et al., 2017; Tran andKim, 2016b). To get the RAOs of the platform motions, the motionamplitudes of surge, pitch and heave are normalized by the amplitudeof the regular wave (3.79m). Fig. 11 shows that the hydrodynamicprediction of the platform motion in this regular heading wave condi-tion agrees quite well with the experimental data as well as the nu-merical results using other simulation solvers.

3.4. Validation for naoe-FOAM-SJTU solver with free-decay motion of theplatform

Free-decay test is an efficient way to predict the natural frequencyof a floating structure, which is one of the main hydrodynamic coeffi-cients. Since the surging, pitching, heaving motion responses are moresignificant than others in heading waves, the free-decay motion analysisof the OC4 DeepCWind semi-submersible floating platform utilized inthe present study is performed for each of the three DOFs (surge, heave,pitch) using naoe-FOAM-SJTU solver. The platform model and simu-lation domain are shown in Fig. 12, while detailed structural para-meters are described in the following section. Free-decay tests arecarried out in calm water without wind/wave/current. Herein, theplatform is initially perturbed with a prescribed displacement, and re-leased to move freely as oscillating back to the equilibrium position.The perturbed displacements in the numerical simulation are de-termined with experimental data.

Table .2 presents the natural periods for these three DOFs comparedwith experimental and numerical results. The natural period obtainedin the present simulations show good agreement with those from othernumerical tools with potential-flow panel method or CFD method, andmatches quite well with the experimental results by MARIN (Coullinget al., 2013). Fig. 13 illustrates the dynamic responses of free-decaysurge and pitch motions. The dynamic motion results are comparedwith the previous studies (Tran and Kim, 2015; Luan et al., 2013;Krogstad and Lund, 2012) in both CFD method and potential-flow

Fig. 8. Aerodynamic simulation results with different numerical methods.

Fig. 9. Aerodynamic thrust and power of the NREL-5MW wind turbine with periodic surge motion ( =s sin t8 (0.246 )) of platform.

Table 1Wave properties.

Wave Length 228.7m

Wave Period 12.1sWave Height 7.58m

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method. The present CFD approach (black solid curve) is capable toconsider the viscous effect of floating platform, which shows improvedhydrodynamic damping of CFD results than those potential based ap-proach.

4. Description of Geometry Model

4.1. Phase II of OC4 floating offshore wind turbine system

In the present simulation work, a semi-submersible floating offshorewind turbine (FOWT) system, Phase II of OC4 project (Robertson et al.,2012), is adopted. The Offshore Code Comparison Collaboration Con-tinuation (OC4) project, which was formed in 2010 under the Inter-national Energy Agency Wind Task 30, is a project to verify the accu-racy of the simulation tools and codes for offshore wind turbines(Robertson et al., 2013). The FOWT contains several main parts: a windturbine (the NREL-5MW baseline wind turbine), a tower supporting theturbine, a supporting floating platform (the semi-submersible platform)on which the tower is mounted, and the mooring system to restrict themotion of platform. Fig. 14 shows the sketch of this FOWT system.

4.2. NREL-5MW baseline wind turbine

The wind turbine in Phase II of OC4 FOWT system is NREL-5MWbaseline line wind turbine, which is a conventional three-bladed, up-wind, variable-speed and blade-pitch-to-feather controlled wind tur-bine. This 5-MW wind turbine is a large scaled turbine with bladelength of 63m, and the center of rotor is 90m above the still water level(SWL). The specification of the prototype is listed in Table .3 (Jonkmanet al., 2009).

4.3. The semi-submersible platform

As shown in Fig. 15, the semi-submersible floating system consistsof a main column attached to the tower, three offset columns coveringsignificant portion of buoyancy, a couple of smaller diameter pontoonsand cross braces to link the main column and offset columns and tostrengthen the structure. Detailed properties are listed in Table .4.

Fig. 10. Comparison of numerical and wave theory results.

Fig. 11. Comparison of RAOs for platform hydrodynamic responses.

Fig. 12. Geometry model and simulation domain for free decay simulation.

Table 2Comparison of natural periods of the platform.

DOF Experiment (Coullinget al., 2013)

FAST (Coullinget al., 2013)

Simo/Riflex+ TDHMILL (Luan et al.,2013)

AQWA (Tran andKim, 2015)

Unsteady CFD (Krogstadand Lund, 2012)

naoe-FOAM-SJTU(present work)

Surge 107.0 107.0 115.9 112.5 108.1 108.3Heave 17.5 17.3 17.1 17.3 17.8 17.58Pitch 26.8 26.8 25.8 25.4 25.2 25.8

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4.4. Mooring system

The semi-submersible floating system for Phase Ⅱ of OC4 is mooredwith three catenary lines spread symmetrically about the platformcenter (Robertson et al., 2012). Fig. 16 shows the arrangement of themooring system. Table .5 lists the mooring system properties used inthis paper.

4.5. Determination of the rotating center

The Phase II of OC4 Floating Wind Turbine System is shown inFig. 14. Besides the floating support platform, the FOWT system alsocontains the wind turbine and the tower above the supporting system.

So the wind turbine and the tower should be counted when analyzingthe mass distribution and the inertia of the whole system. The massdistribution and the structural of the whole system are listed in Table .6and Table .7.

4.6. Simulation domain and grid structure

The entire hexahedral simulation domain is set as750(x)× 320(y)× 400(z), as shown in Fig. 17. In Fig. 17, the para-meter λ represents for the wave length which changes in the cases, sothe length of simulation domain is not set exactly according to the wave

Fig. 13. Dynamic comparison of free-decay motions of OC4 platform.

Fig. 14. Phase II of OC4 floating offshore wind turbine system.

Table 3Specification of NERL 5-MW turbine.

Rating 5MW

Rotor Orientation, Configuration Upwind, 3 BladesControl Variable Speed, Collective PitchDrivetrain High Speed, Multiple-Stage GearboxRotor, Hub Diameter 126m, 3mHub Height 90mCut-in, Rated, Cut-out Wind Speed 3m/s, 11.4 m/s, 25m/sCut-in, Rated Rotor Speed 6.9 rpm, 12.1 rpmRated Tip Speed 80m/sOverhang, Shaft Tilt, Precone Angle 5m, 5°,2.5°Rotor Mass 110,000 kgNacelle Mass 240,000 kgTower Mass 347,460 kgCoordinate Location of Overall CM (−0.2 m, 0.0m, 64.0 m)

Fig. 15. The semi-submersible floating system.

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length. The distance between the inlet boundary and the center thefloating offshore wind turbine system is 200m, and a sponge layer re-gion with 180m length is set for wave absorption near the outlet

boundary. Here, the water depth is set as 200m, and the distance be-tween the bottom of computational domain and the initial still watersurface is 10m, where d is the water depth. And the height of domainabove the water surface is set as 4D≈ 260m, where D is the diameter ofrotating turbine. The right figure shows the grid structure on a crosssection. The refine region around the platform and the wake flow areawith second-order refinement is illustrated in the right figure in Fig. 17.

As ALM is an efficiency model with simplified actuator model in-stead of the real blades structure in the aerodynamic simulation, muchhigher level refinement along the blades surface layer is saved. Thus thetotal number of grid cells in this simulation is about 3.5M. Both simu-lations are running in parallel with 40 processors, and time consump-tion for each time step with 6 inner PISO loops is about 20s.

5. Results and discussions

5.1. Aerodynamics of NREL-5MW wind turbine

The fully coupled aero-hydrodynamic numerical simulations of thephase II of OC4 semi-submersible FOWT are conducted with two dif-ferent regular incoming waves under same inflow wind condition. Aslisted in Table .8, the inflow wind speed for both fully coupled simu-lations are set as the rated wind speed 11.4m/s, while regular incomingwaves with different wave period and wave height are adopted. InCASE#1, the wave period is 9.7s and the wave height which is twotimes of the wave amplitude is 3.66m, while the wave period and waveheight in CASE#2 are 12.1s and 7.58m, respectively.

Aerodynamic forces and power of the FOWT are recorded duringsimulation, and time history of aerodynamic thrust and power areplotted in Fig. 18. Different from the conventional steady aerodynamicsimulations for centre fixed wind turbines, both aerodynamic thrust andpower of FOWT show significantly unsteady characteristics with thecoupling interaction between aerodynamic loads on turbine and thehydrodynamic responses of floating platform. The time history of thrustcurves of CASE#1 and CASE#2 both fluctuate periodically, while theperiods of differs from each other. Due to the computational start-upfluctuation, the quasi-static periodic results are achieved sincet= 200s, and curves in Fig. 18 are drawn with data in time range of(340s–356s), which covers fluctuation periods of both cases.

The fluctuation periods of both thrust and power in CASE#1 areabout 9.7s, which is the same with the wave period adopted in CASE#1.Similarly, the fluctuation period of aerodynamic loads in CASE#2 areabout 12.1s same with the wave period in CASE#2. Wave does not acton the turbine blades directly but on the floating platform, whichcauses periodic hydrodynamic motion responses of the platform. Herein the present work, the platform, wind turbine and tower are all re-garded as rigid bodies. Amounted on the floating platform through rigidtower, the wind turbine gains an additional motion from the platform'shydrodynamic response.

Compared with the thrust and power data obtained from steadyaerodynamic simulations conducted in the above Validation section,the averaged value of both thrust and power of FOWT are decreased.The difference between the averaged values of CASE#1 and CASE#2 isnegligible, but the oscillating amplitude of both thrust and power inCASE#2 is significantly larger than that in CASE#1. Thus a preliminaryconclusion indicates that the growth of incoming wave amplitude

Table 4Floating platform geometry.

Depth of platform base below SWL (total draft) 20m

Elevation of main column (tower base) above SWL 10mElevation of offset columns above SWL 12mSpacing between offset columns 50mLength of upper columns 26mLength of base columns 6mDepth to top of base columns below SWL 14mDiameter of main column 6.5mDiameter of offset (upper) columns 12mDiameter of base columns 24mDiameter of pontoons and cross braces 1.6m

Fig. 16. Arrangement of the mooring system.

Table 5Mooring system properties.

Number of Mooring Lines 3

Angle Between Adjacent Lines 120°Depth to Anchors Below SWL(Water Depth) 200mDepth to Fairleads Below SWL 14mRadius to Anchors from Platform Centerline 837.6mRadius to Fairleads from Platform Centerline 40.868mUnstretched Mooring Line Length 835.5mMooring Line Diameter 0.0766mEquivalent Mooring Line Mass Density 113.35 kg/mEquivalent Mooring Line Mass in Water 108.63 kg/mEquivalent Mooring Line Extensional Stiffness 7.536E+8NHydrodynamic Drag Coefficient for Mooring Lines 1.1Hydrodynamic Added-Mass Coefficient for Mooring Lines 1.0

Table 6Mass distribution of the FOWT system.

Mass(kg) CM Location above SWL (m)

Rotor 1.1E5 87.6Nacelle 2.4E5 87.6Tower 2.497E5 43.4Platform 1.347E7 −13.46Total 1.407E7 −9.9376

Table 7Structural properties of the system.

Structural mass 1.407E7kg

CM location below SWL 9.9376mTotal structure roll inertia about CM 1.1E10 kg*m2

Total structure pitch inertia about CM 1.1E10 kg*m2

Total structure yaw inertia about CM 1.226E10 kg*m2

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causes the increase of fluctuation amplitude, but has tiny influence onthe averaged value of the turbine aerodynamic loads.

5.2. Hydrodynamic responses of the semi-submersible platform

As is well known, an incoming regular wave induces periodic mo-tion responses of the structures floating on the free surface (Cheng andWan, 2015), where the first-order wave force causes the periodic mo-tion around the initial position with the same period as incoming wave,while the higher-order hydrodynamic wave load drives the structuretowards the wave marching direction. With restriction of mooringsystem, the floating structure will finally oscillates around an equili-brium position after a period of evolution. A FOWT naturally is amoored floating structure with additional wind turbine, so the basicoscillating regulation is observed in the hydrodynamic motions re-corded during fully coupled simulation. And the motions time history ofthree main DOFs in heading waves (surge, heave and pitch) are plottedin Fig. 19.

The impact of wind turbine on platform is equivalent to externaldynamic forces transformed through tower. Since the tower is ignoredin the structure model, the force approximates to the aerodynamicforces by integrating the aerodynamic forces on actuator points alongturbine blades, and the moments is determined as cross product of the

aerodynamic forces and the moment arm vector pointing from turbinerotating centre to the FOWT rotating centre. Previous studies (Chengand Wan, 2015) indicated that the distance from equilibrium positionof hydrodynamic oscillating motion to the initial centre is no more than0.5m with same wave condition as CASE#1, while the equilibriumposition for coupled system in CASE#1 is about 14.2m as shown assurge motion in Fig. 19 (a), which is significantly increased with theaerodynamic impacts of the wind turbine. With growth of wave am-plitude and wave length, the averaged surge motion is increased fromCASE#1 to CASE#2. The averaged surge motion is driven by two mainfactors: high-order drift forces with incoming wave and the externalforces from the wind turbine. As discussed above, the aerodynamicforces of wind turbine in CASE#1 and CASE#2 have similar averagedvalue, so it can be demonstrated preliminarily that the increase ofaveraged surge motion from CASE#1 to CASE#2 is mainly resultedfrom the growth of drift forces. On the other hand, the oscillatingamplitudes of the motions are quite similar to that from previous cal-culation (Cheng and Wan, 2015). However, as larger-amplitude wave inCASE#2 causes stronger oscillating forces which induces greater peri-odic motion, the increase of oscillating amplitude is observed for allthree DOFs in Fig. 19.

5.3. Coupled aero-hydrodynamic analysis

As discussed above, the oscillating motion of floating platform hassignificant influence on the aerodynamic loading of the wind turbine,and the aerodynamic forces also strongly affects the hydrodynamicresponses of supporting platform. Eqn. (8) illustrates that the de-termining factor for the aerodynamic loads is the relative velocity nearthe actuator points, which has taken the platform motion into account.When rotor blade moves towards inflow wind marching direction, therelative velocity of air flow is lower compared to the fixed rotating

Fig. 17. The sketch of computational domain and the refined grid structure.

Table 8Environmental description.

CASE# 1 2

Inflow Wind Speed (m/s) 11.4Rotor Speed (rpm) 12.1Wave Period (s) 9.7 12.1Wave Height (m) 3.66 7.58

Fig. 18. Aerodynamic Forces and Power of the floating wind turbine.

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centre condition. On the contrary, the relative velocity increases as thewind turbine moving to the reverse. Note that the platform motioncomponent which makes a difference in the rotor blades motion is notonly the surging motion but also pitching motion. Comparing Fig. 19(a)with Fig. 19(c), the platform surging motion has an opposite variationlaw with pitching motion. Namely, when the platform surge motiondrives the rotor blade towards the Ox direction, the blade motioncaused by the platform pitching motion points to the -Ox direction.There is another notable phenomenon, the aerodynamic forces ofCASE#1 and CASE#2 meet the maximum value at the same time aboutt= 342.2s in Fig. 18, but both surge and pitch in these two caseschange on the opposite way at t= 342.2s. This is comprehensible bycombining the surging effect and the pitching effect on the bladesmotion. In CASE#1, the oscillating amplitude of surge is 0.7m while theoscillating amplitude of pitch is about 0.8deg. Multiplying pith anglewith the distance between blade points to the rotational centre of wholeFOWT system (100m), the amplitude of equilibrium motion induced byplatform pitching motion is up to 1.4m, so the pitching motion plays theleading role in affecting the relative flow velocity at turbine blade. Theplatform motion speed is determined with the time derivative of surge

displacement or pitch angle, and it's clear to see that pitching motionmeets the minus maximum speed around t= 342.2s, therefore the re-lative flow speed achieve the maximum value, and so does the aero-dynamic loads. The same principle applies to CASE#2 with surge os-cillating amplitude 2.3m and pitch oscillating amplitude 1.05deg, inwhich case the surging motion acts as the leading factor. Thus CASE#2meets the maximum aerodynamic forces when platform surging withthe minus maximum surging speed.

The aerodynamic forces also cause significant increase of averagedsurge and pitch motion on hydrodynamic responses of floating plat-form, and the fluctuation of aerodynamic forces also influences theoscillating amplitude of surge and pitch. Nevertheless, the aerodynamicforces and moments transmitted to floating platform are negligiblysmall compared with the hydrodynamic loads.

With the coupling interaction, the wake flow is also disturbed. Theevolution of wake vortex structure of CASE#1 is illustrated during arepresentative period in Fig. 20. The wake vortex of the rotor is vi-sualized with the iso-surface of the second-order invariant of velocitygradient Q (Digraskar, 2010), and the wave free surface is contoured bysurface elevation. Three clear and stable spiral vortexes are generatedat the tip of the blades then march downstream with positive speeds ofair flow. With additional motions transmitted from platform, the rotorblades moves into and out of its wake flow, which results the differ-ences of the distance between two neighbour vortex tubes. And thisadditional motion also disturbs the wake flow and results in the quickdissipation of vortexes.

6. Conclusions

The actuator line model (ALM) is introduced into OpenFOAM foraerodynamic simulation of wind turbine. To take the platform motioninto consideration in the aerodynamic simulation of wind turbine, theunsteady actuator line model (UALM) is established. By implementingthe UALM as an aerodynamic simulation module into our in-house CFDcode naoe-FOAM-SJTU, the fully coupled aero-hydrodynamic modelFOWT-UALM-SJTU is developed for the fully coupled aero-hydro-dynamic analysis of FOWTs. Since the complex blades structures aresimplified as actuator line model and only structured background gridsare requested for aerodynamic simulations, this numerical model isquite time-saving comparing with other conventional CFD tools.Besides, by solving the N-S equations in the entire flow filed, this si-mulation model provides more detailed and more accurate flow in-formation over traditional BEM and potential flow theory.

Proper fundamental validations for the FOWT-UALM-SJTU solverare carried out, which shows good capability and reliability on bothaerodynamic prediction of wind turbine and the hydrodynamic calcu-lation of floating platform. Then fully coupled aero-hydrodynamic si-mulation of Phase II of OC4 semi-submersible FOWT is conducted withthis coupled model.

Compared with aerodynamic loads in fixed centre simulations, bothaerodynamic thrust and power decrease in fully coupled FOWT system.From the coupled aero-hydrodynamic simulation results, oscillatingregularity on aerodynamic loads of wind turbine is observed with thesame oscillating period as the incoming wave. With growth of the waveamplitude, the fluctuation amplitude of aerodynamic loads increasesobviously, but wave condition has tiny influence on the averaged valueof the turbine aerodynamic loads. The fluctuation of aerodynamic loadresults from the oscillation of platform motions, and meets the max-imum value when the blade actuator points moves with the maximumspeed in the opposite direction with inflow wind. Both surging andpitching motions play important roles in the influence on the relativeflow velocity, and the maximum of aerodynamic loads are achievedwhen the leading motion reaches the minus maximum speed. With ef-fect of turbine aerodynamics as an external load on the supportingplatform, the platform motion shows significant increase on the aver-aged value, while the influence of turbine loads on the fluctuation of

Fig. 19. Comparison of platform 6DOF motion responses.

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platform is negligible. Nevertheless, the wave amplitude affects thefluctuation amplitude of platform a lot. Besides, the oscillating motionof the FOWT disturbs the flow wake of turbine and speeds up the dis-sipation of wake vortex.

The coupling interactions between the turbine aerodynamics andthe platform hydrodynamics is much more complicated, and more re-search work need to be done for further study on the complex coupledfloating offshore wind turbine system. In the preliminary stage, themodel studies herein limited in steady wind and regular wave condi-tions with rigid blade structures, where the flexibility of the structures,the pitch-control effect, as well as the tower-blades interaction areomitted. Thus in our near future work, the numerical model will beimproved to take these practical factors. This numerical model showsgreat potential in aero-hydrodynamic simulations of floating offshorewind turbines.

Acknowledgements

This work is supported by the National Natural Science Foundationof China (51879159, 51490675, 11432009, 51579145), Chang JiangScholars Program (T2014099), Shanghai Excellent Academic LeadersProgram (17XD1402300), Program for Professor of SpecialAppointment (Eastern Scholar) at Shanghai Institutions of HigherLearning (2013022), Innovative Special Project of Numerical Tank ofMinistry of Industry and Information Technology of China (2016-23/09) and Lloyd's Register Foundation for doctoral student, to which theauthors are most grateful.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.oceaneng.2018.12.021.

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