NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Challenges in Simulation of 

Aerodynamics, Hydrodynamics, 

and Mooring-Line Dynamics of

Floating Offshore Wind 

Turbines

D. Matha and M. Schlipf

Universität Stuttgart

A. Cordle

Garrad Hassan and Partners Ltd.

R. Pereira

Germanischer Lloyd Industrial Services

J. Jonkman

National Renewable Energy Laboratory

Presented at the 21st Offshore and Polar Engineering Conference

Maui, Hawaii

June 19-24, 2011

Conference Paper

NREL/CP-5000-50544

October 2011
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1 

Challenges in Simulation of Aerodynamics, Hydrodynamics, and Mooring-Line Dynamics of 

Floating Offshore Wind Turbines 

Denis Matha, Markus Schlipf

Endowed Chair of Wind Energy, Universität Stuttgart

Stuttgart, Germany

Andrew Cordle

Garrad Hassan and Partners Ltd. 

Bristol, United Kingdom

Ricardo Pereira 

Germanischer Lloyd Industrial Services, Renewables Certification

Hamburg, Germany

Jason Jonkman

National Renewable Energy Laboratory

Golden, Colorado, USA

ABSTRACT

This paper presents the current major modeling challenges for floating 

offshore wind turbine design tools. It also describes aerodynamic and 

hydrodynamic effects due to rotor and platform motions and usage of 

non-slender support structures. The applicability of advanced potential 

flow and computational fluid dynamics–based aerodynamic and 

hydrodynamic simulation methods to represent these effects—

exceeding state-of-the-art design tool capabilities—is analyzed and the 

results are presented. Different techniques for the representation of 

mooring-line dynamics, including quasi-static, finite element, and 

multibody methods, and their impact on global system loads are 

investigated. Conclusions are drawn about the importance of the 

relevant effects, strengths and weaknesses of the different methods are 

discussed, and development needs of future tools are described.

KEY WORDS: Offshore; floating wind turbine; integrated design 

tools; mooring system; aerodynamics; hydrodynamics; potential flow; 

computational fluid dynamics; CFD; multibody simulation; MBS.

INTRODUCTION

Combined aerodynamic, hydrodynamic, and mooring-system dynamic 

effects on floating offshore wind turbines (FOWT) create unique 

operating and failure design conditions which have not yet been studied 

in great detail. The large rotor and platform motions and the use of nonslender support structures potentially render state-of-the-art techniques 

applied for modeling fixed-bottom offshore wind turbines—for 

example the blade element momentum (BEM) method for rotor 

aerodynamics and Morison’s equation for hydrodynamics—insufficient 

for accurately describing the dynamics of floating wind turbines. 

Addressing these limitations and effectively designing and analyzing 

wind turbines on offshore floating support structures requires advanced 

modeling methods and techniques.

Dedicated hydrodynamic and mooring-system codes and techniques 

developed for the oil and gas industry for analysis of ships and oil 

platforms, as well as advanced aerodynamic methods used in the 

aircraft and helicopter industry, which are capable of addressing most 

effects relevant for FOWTs are not readily applicable for integrated 

FOWT simulations. The specific coupled aero-servo-hydro-elastic 

dynamics of FOWT and the requirements of the International 

Electrotechnical Commission (IEC) standard and certification 

guidelines (2009) to run large numbers of design load simulations must 

be considered when analyzing the application of existing and novel 

methodologies.

In sum, this paper describes the important physical effects unique for 

FOWTs in theory and the current major modeling challenges in FOWT 

design codes. It introduces techniques and methodologies to overcome 

the limitations of current integrated simulation tools, discusses their 

applicability for the simulation and analysis of FOWTs, and presents 

first indicative results of new approaches, including computational fluid 

dynamics (CFD) aerodynamic models and multibody system (MBS) 

mooring-line representations. This work also draws conclusions about

the importance of the relevant effects, strengths, and weaknesses of the 

different methods and notes the development needed.

AERODYNAMICS

Aerodynamic Effects on Floating Wind Turbines

All of the design codes currently capable of performing integrated 

modeling of floating wind turbines (Cordle and Jonkman, 2011) use the 

Blade Element Momentum (BEM) theory to calculate the aerodynamic 
2

forces on the wind turbine blades. The significant low-frequency 

platform motions experienced by floating offshore wind turbines, 

however, result in flow conditions which are considerably different and 

more complex than those experienced by conventional onshore or 

fixed-bottom offshore wind turbines. Extensive load-case simulations 

performed by Jonkman, Matha, and Robertson (Jonkman, 2007; Matha, 

2009; Jonkman and Matha, 2011; Robertson and Jonkman, 2011) have 

shown that, particularly for a catenary moored floating wind turbine, 

significant rotational pitch motions occur at approximately the incidentwave frequency.

For the investigated OC3-Hywind spar buoy featuring the NREL 

5-MW baseline wind turbine, pitch motions of up to 8° for production 

design load cases (DLCs) and 14° for extreme DLCs have been found. 

In addition to significant pitch motions, large lower-frequency translational surge motions also are predicted. These rotational and translational motions often cause the rotor to operate in non-axial flow 

conditions, and lead to a change in the interaction between the rotor and 

wake with the rotor potentially traversing back over its own wake. The 

transitions between windmill and propeller states where the rotor 

interacts with its own wake cannot be accurately modeled using 

traditional BEM theory with common corrections, as Sebastian and 

Lackner (2010; 2011) have shown. A BEM theory cannot model the 

resulting development of a turbulent region behind the rotor, leading to 

toroidal recirculation normal to the rotor blade which is expected to be 

most significant at the blade tips in below-rated wind conditions. 

Sebastian and Lackner identify this transitional aerodynamic 

phenomenon as vortex ring state (VRS), and conclude that momentum 

equations used in typical BEM analysis methods yield unrealistic 

results for the axial and the rotational motion of the rotor.

Wind turbine airfoils in production up to rated power usually operate 

close to their maximum lift coefficient to generate maximum power, 

therefore the described pitch motions also cause the airfoil to operate in 

stalled condition more often, increasing the importance of dynamic stall 

models. Common dynamic stall models such as Beddoes-Leishman are 

semi-empirical and their applicability for the dynamic-stall effects 

occurring on floating wind turbines has yet to be investigated.

For floating support platform designs with relatively little yaw stiffness, 

yawed inflow conditions also occur more often. Yawed inflow also 

likely will occur frequently for proposed downwind floating concepts 

that don’t include a tower-top mounted yaw drive (such as Sway’s 

concept). The BEM theory as originally developed assumed flow 

perpendicular to the rotor plane, and commonly introduced skewedwake correction models have yielded unreliable load predictions, with 

deviations increasing with greater yaw errors. The aforementioned 

proposed downwind FOWT configurations combined with the 

increased wind turbine motions also increase the importance of tower 

dam and shadow models, as well as improved models for aerodynamic 

blade and tower interaction.

The expected large ratings (10 MW and greater) of FOWT will lead to 

longer blades and greater tip speeds, due to (likely) reduced noiseemission regulations far offshore. Although beyond the scope of this 

paper, the aeroelastic representation of such large rotors also is 

important when investigating the aforementioned effects, and has 

significant influence (Matha, Hauptmann, Hecquet, and Kühn, 2010) on 

the general capability to predict some of these effects and the resulting 

loads, deflections, and instabilities (e.g., flutter).

Computational Fluid Dynamics

Several possibilities exist for modelling the described aerodynamic 

effects. The approach that computationally is most demanding, but 

physically is most accurate, is to solve the Navier-Stokes Equations 

(NSE) with a CFD solver. In CFD, to model turbulent flows with their 

large range of length scales, three basic approaches exist.

Direct numerical simulation (DNS), in which the full Navier-Stokes 

Equations are solved, requires all relevant length scales to be resolved 

by the computational grid. This method results in extremely large grids. 

Therefore, with current available computational power, DNS is not 

applicable to structures such as wind turbines with large Reynolds 

numbers.

Large eddy simulation (LES), in which only the equations for larger 

turbulent structures are resolved, is applicable for the turbine wake. In 

the boundary layer of the blades, LES also currently is very difficult to 

apply due to the great number of necessary grid cells.

The least computationally expensive method to model turbulent flows 

in CFD is the Unsteady Reynolds Averaged Navier-Stokes (URANS) 

method. The URANS method uses a time-average formulation of the 

Navier-Stokes Equations. The occurring nonlinear Reynolds stress term 

requires the introduction of turbulence models (for example, twoequation models such as k-ω) to close the URANS equations. These 

turbulence models can have great effects on the CFD solution and must 

be selected carefully. A combination of URANS and LES, using 

URANS for the flow around the blades and LES for the wake, also is 

possible and could provide a good solution for floating wind turbine 

CFD modeling.

Regardless of the specific CFD method used, due to very long resulting 

simulation times it can be applied only to very specific load situations. 

The primary application of CFD is to investigate and analyze the 

aerodynamic flow phenomena occurring in the situations noted above 

and help quantify their influence on loads. This knowledge can help in 

deciding whether current models still are sufficient and, more 

importantly, the significance of their errors and in what load situations 

these errors become most significant. Based on that knowledge, simpler 

aerodynamic codes suitable for integrated design codes—such as 

correction models for BEM—could be introduced, correction factors be 

derived, or new additions to the IEC standard (including novel load 

case definitions unique for floating turbines) be defined.

The studies by Jonkman (2007) and Matha (2009) also show that, for 

extreme DLCs with occurrence of failures (such as in DLC6.2) where 

the rotor is idling, all blades are pitched to feather, and great yaw errors 

occur, severe instabilities can be identified. The particular DLC6.2 

instability is caused by negatively damped modes due to the blade 

aerodynamics, which are, for idling or stand-still conditions, being 

calculated with no induction factor (airfoil data look-up table). In this 

case, the aerodynamic lift and drag forces on the blade segments are 

computed without taking into account the blade’s influence on the flow. 

To investigate this effect—as well as other observed instabilities for 

floating turbines—more closely, CFD also can provide valuable insight.

CFD methods already are used in wind turbine blade design and also 

can be applied to develop floating offshore–specific blades. Although, 

to date, no dedicated research on FOWT-specific blade design using a 

CFD process chain has been published, the European KIC (Knowledge 

& Innovation Community) work package, “Offshore Blades,” of the 

InnoEnergy research project Offwindtech (started at the end of 2010) 

will address this issue.

Potential Flow Methods

More suitable for integrated load simulation in terms of simulation time 

are aerodynamic codes based on vortex theory. In potential flow theory, 
3

the fluid is considered to be incompressible, inviscid, and irrotational, 

and surface-tension effects are neglected. The flow field around the 

airfoil generally is described through the distribution of discrete sources 

and vortices, with several possible implementations, for example lifting 

line, lifting surface, or vortex lattice methods. In these time-accurate 

aerodynamic codes, the shape and strength of the wake of the blades 

will develop in time (e.g., free wake particle method). To reduce 

simulation time, the shape of the wake also can be prescribed. This 

approach, like BEM, is based on measured profile data. That is, the 

aerodynamic lift- , drag- , and pitching-moment characteristics of the 

blade cross-sections are assumed to be known and corrected for the 

effects of blade rotation. In comparison to the currently used BEMbased codes, more accurate predictions are expected in situations where 

local aerodynamic characteristics strongly vary with time—such as in 

yawed flow—and where dynamic wake effects play a significant role; 

effects which are increasingly important for floating wind turbines.

Currently there are several potential flow aerodynamic codes for wind 

turbine application in development. Specific analyses with these codes 

addressing the above-mentioned aerodynamic problems regarding 

floating wind turbines currently are performed by Sebastian and 

Lackner (2011) using an in-house free-wake code, and by Matha and 

others at University Stuttgart.

Rotor-Only Computational Fluid Dynamics Study

To investigate the aerodynamic effects occurring on a rotor of a FOWT, 

a full three-dimensional (3D) CFD model of a generic multi-megawatt 

rotor has been set up in the URANS code FLOWer (a URANS/LES 

CFD solver for structured meshes, developed by the German 

Aeronautical and Aerospace Centre DLR). Figure 1 presents the mesh 

used and the prescribed motion of the rotor. Note that the spinning 

direction of this particular rotor is counterclockwise when looking 

downwind. The prescribed motion was selected from the IEC load 

simulations of the OC3-Hywind FOWT conducted by Matha and 

Jonkman (Matha, 2009) in the design code FAST with AeroDyn and 

HydroDyn. A representative extreme platform-pitch motion occurring 

in wind turbine production mode in DLC 1.6 was chosen. The selected 

specific DLC 1.6 simulation run featured 12.0 m/s hub-height wind 

speed (close to rated, or maximum rotor thrust) and, using the extreme 

sea state (ESS) model, a significant wave height of 15.0 m and a peak 

spectral period of 19.2 s. One pitch motion was selected, where the 

rotor first is pitching 11.5° in downwind direction and then 4° in 

upwind direction before reaching 0° again. This motion has been 

approximated by two appended sine functions, as presented in Fig. 1 

and also incorporates the associated surge motion (rotation is defined 

around an horizontal axis 90m vertically below rotor hub).

Following the work of Streiner (Streiner, Hauptmann, Kühn and 

Krämer, 2008), a sufficient timestep size corresponding to an azimuth 

movement of ΔΨ = 5° per timestep was chosen. Before starting the 

CFD calculation of the prescribed floating motion, four rotor rotations 

were pre-calculated to ensure that transients had decayed and the wake 

behind the rotor was developed in the background grid when the 

motion starts. Due to good experiences in former studies by Streiner, 

the k-ω SST turbulence model was used. A uniform inflow velocity of 

10 m/s was applied.

The computational grid consists of the components blade, hub, and 

background grid, equaling a total number of ~10 million grid points. 

Refined grids around each blade (Fig. 1, green grid), with a 

dimensionless grid distance y+

-value between 0.1 and 2 are embedded 

in a cylindrical grid around the hub (Fig. 1, red grid), which is rotating 

within a coarser background grid (Fig. 1, blue grid). The grid has the 

total in-plane dimension of 3 rotor diameters in each direction, centered 

at the hub, and a total out-of-plane dimension of 3.5 diameters upwind 

and downwind, respectively. FLOWer features the Chimera 

technique (DLR Braunschweig, 2007), allowing for arbitrary relative 

motion of aerodynamic bodies. Applying the Chimera technique, the 

previously described pitch motion was prescribed as a rigid-body 

motion on the rotor and hub grids, which are moving within the 

background meshes. Chimera also is applied for modeling the rotor 

rotation.

Fig. 1. Prescribed rotor motion for CFD study and CFD mesh

In this study, no elastic deformation of the blade is introduced, but 

fluid-structure coupled simulations are planned for subsequent 

analyses. Further studies also will include the tower and nacelle, as 

performed by Meister and others using FLOWer for a 5-MW onshore 

turbine under unsteady inflow conditions, but without prescribed 

floating motions (Meister, Lutz and Krämer, 2010).

The presented CFD results showed good numerical convergence, 

therefore it is assumed that the presented flow field is realistically 

representing the actual aerodynamic conditions during such a motion. 

Nevertheless, the results presented are from a preliminary study on a 

relatively coarse mesh and require further validation from CFD and 

potential flow calculations and, ultimately, experimental data.

Fig. 2. Pressure contours of rotor during prescribed motion

The dimensionless pressure distribution over the blades is presented in 

Fig. 2. Motion (1) corresponds to the first half of the downwind swing 

(c.f. Fig. 1), which is 4/3 rotor rotations. Motion (2) corresponds to the 

second half of the downwind swing and the first half of the upwind 

swing, or from 5/3 to 4 rotor rotations. Motion (3) represents the last 

half of the upwind swing, 13/3 to 5 rotor rotations. During motion (1), 

the pressure on the pressure side of the blades decreases due to the 

backward motion and the increased turbulence in the wake. When the 

turbine is pitching upwind again, motion (2), the pressure on the blades 

increases until the rotor returns to its vertical position and then slightly 
4 

decreases until the end of motion (2). The pressure increase is due to 

the increased inflow velocity, and also possibly due to rotor wake interactions. In the last part of the period, motion (3), the pressure again is 

decreasing, but to a lesser extent than in the first downwind motion (1). 

Figure 3 presents the axial velocities in the near wake of the rotor in a 

vertical plane through the hub center. The single plots display the flow 

field after consecutive full rotor revolutions during the pitching motion, 

therefore covering the full movement from Fig. 1. Blade one in these 

plots always points upward and the axial flow velocity is directed to the 

right. In Fig. 3(1) the downwind motion reduced velocity at the blade 

tip, blade root, and hub region (compared to Fig. 3(0)) can be identified 

and the wake starts to expand further in vertical direction from the 

blade tip. During the upwind move in Fig. 3(2), (3), and (4), regions 

with very low and even negative velocities are enlarging on the suction 

side of the blade and behind the hub. 

Fig. 3. Axial velocity contours of rotor and near wake 

Although single vortices cannot be identified due to the coarse 

background grid used in this preliminary study (the vortices dissipate 

and are “blurred”), the global effects from vortices being shed from the 

blade tips and the inner blade region are visible. These include the 

further expansion of the wake and the “rippled” boundary region at the 

top of the wake in Fig. 3(3) and (4). When comparing the beginning 

(Fig. 3(0)) and end (Fig. 3(5)) of the motion, a changed flow field with 

a larger lower-velocity region in front of the rotor can be identified, as 

well as the expansion of the wake in the vertical and horizontal 

directions and the disappearance of the hub-shadow region in Fig. 3(0). 

The velocity at the tip also decreased. Because the single vortices are 

not resolved with the used-mesh resolution, the vortex ring state, as 

described by Sebastian and Lackner (2010; 2011), cannot be 

demonstrated with this study. 

HYDRODYNAMICS 

Morison Equation Limitations 

Current integrated wind turbine design codes model the loads on fixedbottom offshore structures by applying Morison’s equation. Morison’s 

equation is valid for slender cylinders and is a function of the diameter 

of the cylinder, fluid particle velocity and acceleration, and the 

hydrodynamic drag and inertia coefficients CD and CM. The drag and 

inertia coefficients are functions of Reynold’s number, KeuleganCarpenter number, and surface roughness, as well as a number of other 

factors. To calculate the applied hydrodynamic loads acting over the 

length of the structure, the cylinder can be divided into a number of 

elements in a manner similar to that of BEM theory. The total applied 

load is determined by integrating the loads acting on each element. The 

relative form of Morison’s equation (Eq. 1) accounts for the relative 

motion between the cylinder and the fluid, and includes added mass 

effects from the movement of the water. 

Östergaard and Schellin (1987) describe this variation for slender 

hydrodynamic transparent cylindrical structures with arbitrary 

orientation to the current of the surrounding fluid. In Eq. 1 v denotes 

the fluid’s velocity vector, ur is the relative velocity vector between 

structure and fluid, and index n is the normal direction to the segment. 

The drag and inertia coefficients Cd and Ca are chosen empirically. 

When it comes to modeling floating support structures, however, 

Morison’s equation also has disadvantages. For support structures with 

a small diameter relative to the wavelength of the incident waves—that 

is, when the member diameter is less than 0.2 times the wavelength—

diffraction effects can be neglected. This comes from G.I. Taylor’s 

long-wavelength approximation. It states that, for surface-piercing 

bodies with a small diameter relative to the wavelength, the wave 

potential can be assumed to be constant across the body and 

calculations therefore can be performed at the centre of the body. 

Morison’s equation uses this approximation to simplify the diffraction 

problem. When the submerged body has a diameter large enough for 

the waves to be disturbed by the presence of the structure, however, 

wave diffraction effects must be included for correct determination of 

the local pressure force and global wave loads. This often is the case for 

floating platforms, in particular for those stabilized by buoyancy, which 

means that Morison’s equation cannot be used. 

Morison’s equation also assumes that viscous drag dominates the drag 

loading, and that wave radiation damping therefore can be ignored. 

This assumption is valid for slender structures and when the motions of 

the support structure are very small, which is usually the case for fixedbottom support structures with soft-stiff characteristics. For floating 

platforms with sizeable volume and with low-frequency rigid modes, 

however, the support structure can experience significant movement, 

which means that wave radiation forces should be taken into account. 

Morison’s equation is used only for axisymmetric cylindrical structures, therefore it does not take account of any added mass-induced 

coupling between hydrodynamic force and support structure acceleration in all degrees of freedom present in nonaxisymmetric structures. 

Morison’s equation also neglects hydrostatic restoring forces; however, 

additional terms can be added to account for this. 

 F= ׬ ቀρ πD2

4

∂vn

∂t +Caρ πD24

∂urn

∂t +Cdρ D

2 |urn|urnቁ ds, ls⁄2

-ls⁄2 (1) 
5

Linear Hydrodynamics Limitations

The most complete linear method of accounting for the different 

sources of hydrodynamic loading is to divide them into separate 

problems and solve them independently. To divide the hydrodynamics 

problem in this manner, the assumption of hydrodynamic linearity is 

required. This assumption also necessitates the use of linear Airy wave 

theory for the calculation of wave-particle kinematics. This approach is 

most commonly used in the oil and gas industry.

There are a number of important limitations introduced with the 

assumption of linearity. The use of Airy wave theory means that steepsided or breaking waves found in shallow water cannot be modeled 

together with the resulting slap and slam loading. Additionally, the 

potential-flow theories used in a number of floating wind turbine design 

tools to calculate hydrodynamic loads were developed for stationary 

bodies, and only are valid when the support structure translational 

motion is small relative to the wavelength and the rotational motion is 

less than the wave steepness. Many floating configurations, however, 

experience large translational displacements relative to the length of the 

platform, for instance catenary moored systems where there is low 

resistance to surge and sway. This means that these potential-flow 

theories no longer are valid.

Second-Order Hydrodynamics

Linear wave theories also do not take into account second-order or 

higher order hydrodynamic effects, which are necessary for the analysis 

of platforms which are subject to steep-sided or very large waves. 

Second-order hydrodynamic loads are proportional to the square of the 

wave amplitude, and have frequencies equal to both the sum and the 

difference of the multiple-incident wave frequencies of an irregular sea 

state. This means that, although the natural frequencies of the structure 

are designed to be outside the wave energy spectrum, the second-order 

forces can excite these frequencies. Therefore, despite the forces 

normally being small in magnitude, the resonant effect can be 

important. The three components of second-order hydrodynamic forces 

for the diffraction problem are described below.

Mean drift forces. These forces result in a mean offset of the body 

relative to its undisplaced position, and typically are an order of 

magnitude less than first-order wave excitation forces. The mean drift 

force is a combination of second-order hydrodynamic pressure due to 

first-order waves and the interaction between first-order motion and the 

first-order wave field. The viscous drag could add to this force 

significantly when a current is present. The mooring-line tension often 

is related non-linearly to platform displacement, therefore the mean 

drift forces can have an important effect.

Slowly varying drift forces. These forces persist much longer than the 

main wave energy spectrum but still are within the range of horizontal 

platform motion. They result from non-linear interactions between 

multiple waves having different frequencies. Again, the forces resulting 

from slowly varying drift generally are small as compared to forces at 

the wave frequency, but they can cause large displacements in moored 

floating wind turbines which can in turn lead to high loads in the 

mooring lines. These forces also can excite the large amplitude 

resonant translational motion of the floating platform.

Sum frequency forces. These forces have a frequency which is higher 

than the wave frequency and also generally are small in amplitude. 

They arise from the same source as low-frequency drift forces, that is, 

from interactions between multiple waves of varying frequency. The 

contribution from these forces can be particularly important when 

analyzing “ringing” behavior for floating wind turbine configurations 

such as TLP concepts, which typically have high natural frequencies in 

heave, roll, and pitch. They also potentially can excite vibration modes 

of the supported wind turbine.

A recent study performed by Lucas (2011) on the comparison of firstand second-order hydrodynamics confirms the importance of secondorder effects for an FOWT. The detailed comparison between the 

solution of first-order (linear) and second-order potential flow 

hydrodynamic models has been performed with regard to the 

characterization of the wave-induced loading and motion response 

under both regular and irregular waves. More specifically, the 

hydrodynamic quantities compared were the first- and second-order 

excitation force and the first- and second-order response amplitude 

operator (RAO) for unconstrained motions, analyzed for three distinct 

monochromatic waves and three unidirectional Pierson-Moskowitz 

spectra.

Two FOWT concepts featuring a 5-MW wind turbine were considered, 

the OC3-Hywind spar-buoy (Jonkman and Musial, 2010) and a semisubmersible platform with geometric dimensions similar to Principle 

Power’s WindFloat platform concept, which comprises three 

equidistant columns and a wind turbine centered in one of the columns. 

For the WindFloat, hexagonal water-entrapment plates are installed at 

the bottom of each column to provide high heave added-mass and 

viscous damping to decrease the motions in this mode. The commercial 

software WAMIT, which solves the hydrodynamic problem in the 

frequency domain, was used to compute both the first-order (linear) and 

second-order (weakly nonlinear) hydrodynamic loads and unrestrained 

motions for the two structures considered in this study. Second-order 

excitations forces in Lucas’ analysis are obtained as the sum of the 

force quadratic transfer functions (QTF) in the sum-frequency and 

difference-frequency. For a monochromatic wave, the second-order 

excitation force is expressed as the sum of only two components of the 

force QTF in the double and zero frequency. Note that, for the 

computation of the second-order hydrodynamic quantities, in addition 

to the platform itself, the free-surface also must be discretized.

In summary, for the OC3-Hywind, the second-order excitation force in 

stochastic waves is important in surge and pitch modes, although it still 

is smaller than the first-order excitation force. For the semi-submersible 

platform, the second-order excitation force is dominant over the first 

order for less-steep waves and lower significant wave heights for all 

modes except heave. The importance of the second-order excitation 

force decreases for the steeper waves and higher significant wave 

heights. The study shows that second-order effects prove to be more 

important for the semi-submersible concept than the OC3-Hywind, 

whose geometry is more hydrodynamically transparent. A detailed 

description of the investigation and results are given in Lucas (2011).

Even with second-order hydrodynamic terms included, however, the 

hydrodynamic theory might not completely apply to floating wind 

turbine platforms. This is because the theory was derived for use in the 

offshore oil and gas industry in which floating platforms typically have 

much smaller displacements than what is conventional for floating 

wind turbines.

Nonlinear hydrodynamic theories. Ongoing research at the University 

of Hamburg is the proposal of a nonlinear seakeeping simulation 

technique by using a Rankine-Airy panel method (Söding, 2010). The 

base flows from which the flow around the moving body is 

superimposed are not only source (and possibly vortex) flows, but also 

are Airy waves. Nonlinear boundary conditions at the free surface 

(constant pressure, no flux through the surface) are satisfied 

numerically in each time step by superimposing Airy waves of different 

wave numbers and propagation directions. The amplitudes and phase 
6

angles of the Airy waves are not constant over time, but must be 

computed from evolution equations. These are derived from the 

kinematic and dynamic free-surface conditions. The method is suitable 

for arbitrary geometries, and can handle most of the aforementioned 

nonlinear effects in steep waves. This method can be applied 

effectively for the estimation of extreme behavior of floating offshore 

wind turbines in survival conditions.

Vortex-Induced Vibrations

Another effect currently not accounted for in hydrodynamic analysis 

for floating wind turbines is vortex-induced vibration (VIV). This effect 

is caused by steady currents or by the velocities associated with longperiod waves. It refers to the dynamic loading that occurs as a result of 

fluctuations in pressure due to the motion of vortices in the wake of a 

body. If the frequency of excitation is near a natural frequency of the 

structure, then the interaction between the flow and the motion of the 

structure can cause the two frequencies to resonate. This can result in 

large amplitudes of oscillation. The forces due to vortex shedding are 

complex, and predictions of loading and response are not well 

understood. The frequencies at which oscillations can occur, however, 

can be predicted with more confidence. Vortex-induced vibrations 

generally are not seen in conventional fixed-bottom offshore support 

structures, but are more likely to be experienced in mooring lines and 

can be critical for the stability of some designs.

MOORING-LINE DYNAMICS

Overview

Floating offshore wind turbine structures are held in position by means 

of mooring systems which, depending on the type of the structure and 

the water depth where it is to be moored, can have different levels of 

complexity. For floating wind turbine applications, a general distinction 

must be made between slack catenary, taut catenary, and taut tensionleg mooring systems. In slack catenary designs, the lower part of the 

line often rests on the seabed, which adds more complexity to the 

system. In the oil and gas industry, large floating drilling platforms are 

restored by up to 20 mooring lines with different geometrical and 

material properties. The lines consist of a combination of chains and 

cables made of natural or synthetic fibers (e.g., polyester, aramid, 

polyamide, polypropylene fibers). Submerged buoyancy tanks located 

along the mooring lines also are common. Such complex mooring 

solutions likely will be implemented and specially adapted for future 

floating wind turbines as well, thus requiring the codes to have 

adequate capabilities.

In addition to station-keeping, the mooring system also provides 

stability. For some platform designs, such as the tension-leg platform 

(TLP), the mooring system is the main contributor to the system’s 

stability—meaning that a failure in this component would likely cause 

the destruction of the complete system. The mooring system of floating 

wind turbine platforms therefore is one of the most important 

components for the stability and the dynamic behavior of floating 

offshore wind turbines, making appropriate modeling of the mooring 

system highly critical during the design process.

The central issue with regard to mooring-line behavior is whether it is 

acceptable to neglect the dynamic effects of mooring lines for floating 

wind turbines. For shallow mooring systems the total mass of the lines 

is negligible and the motion is small. Therefore, even though the drag 

force of the lines through the fluid still might be significant, it generally 

is accepted that dynamics can be neglected. For deeper-water configurations, however, mooring-line dynamics become increasingly 

important. The conclusion drawn from studies performed for oil 

platforms and vessels was that line dynamic analysis should be conducted when the wave frequency response of the vessel is large, when 

the water depth exceeds 150 m, or when the mooring line includes large 

drag elements such as chain moorings.

To date, however, no studies have been dedicated to the dynamics of 

mooring lines for floating wind turbines. It is proposed that a study be 

performed specifically for floating wind turbines. It should investigate 

which aspects of mooring-line behavior are important, and determine 

the depth at which dynamic mooring-line effects become nonnegligible for floating wind turbines, and which types of mooring 

system have the most dynamic effect on floating wind turbine platforms 

(and therefore must be designed using a full dynamic analysis). This 

study could incorporate a comparison between the different methods 

for calculating mooring-line tension forces for floating wind turbines.

The restoring forces on a floating wind turbine platform due to mooring 

lines can be approximated using force-displacement or quasi-static 

methods. These methods, however, do not account for mooring-line 

dynamic effects, such as line inertia, the drag of the line through fluid, 

and vortex shedding. For some configurations, these effects can have a 

significant contribution to the overall response of the system. A number 

of programs exist which can model the dynamics of mooring lines. 

These programs, however, generally do not allow for the detailed 

modeling of an integrated wind turbine system, including aeroelastic 

and aerodynamic forces, which make a significant contribution to the 

response of the whole system. Consequently, it is difficult to 

simultaneously account for the dynamic response of the mooring lines 

and the wind turbine in a single coupled analysis.

One approach is to use a dynamic line analysis code to derive a forcedisplacement relationship and apply this as a non-linear spring at the 

fairlead position. This method would give similar results as a quasistatic implementation. Another approach is to couple together dedicated 

mooring-line and wind turbine analysis codes. An attempt has been 

made by Jonkman and others to couple the dynamic mooring-line 

system LINES of SML with the aeroelastic wind turbine codes FAST 

and ADAMS. This attempt was abandoned after it was found that 

LINES encountered numerical instabilities when modeling the slack 

catenary mooring lines of interest. The most fruitful attempt to date is 

the coupling between offshore floating structures code SIMO/RIFLEX 

and the multibody wind turbine code HAWC2, described by Cordle and 

Jonkman (2011). This approach still is limited, however, in that the 

floating wind turbine cannot be modeled as a single integrated dynamic 

structure. The two problems must be solved in separate programs and 

information exchanged between the programs at a single interface 

point. This interface was known to be quite unstable numerically.

An approach for modeling mooring lines within integrated wind turbine 

design codes is to divide the mooring line into rigid (or flexible, modal 

reduced) multibody elements connected by spring-damper elements, 

originally described by Kreuzer and Wilke (2002) for oil platforms. 

The line-seabed interaction is modeled with a coulombic friction 

element including spring and hysteresis characteristics as a function of 

the translational forces. This MBS approach currently is being 

investigated by Matha and others, in which a multi-purpose commercial 

multibody code (SIMPACK, 2010; Matha, Hauptmann, Hecquet and 

Kühn, 2010) is extended to model offshore floating wind turbines. An 

originally implemented quasi-static mooring line model (within 

NREL’s HydroDyn module) was replaced by an MBS-based model. 

With this approach, no interface between separate programs is 

necessary because the turbine’s structure and mooring lines are 

modeled within one code using the same mathematical MBS formulation. This MBS formulation is numerically stable, integrated, and 

allows for a simple implementation of line-seabed interaction required 
7

for catenary systems. Following this MBS approach, the mooring 

system of the OC3-Hywind spar buoy in 320-meter deep water is 

modeled. The topology of the model of one mooring line is presented in 

Fig. 4.

Fig. 4. Topology of MBS mooring-line model

Each of the spar buoy’s three mooring lines is discretized into separate 

rigid bodies. Every single body is modeled as a cylindrical structure 

and has the gross properties of the particular part of the mooring line it 

represents, allowing modeling of different sectional mooring line 

configurations. The segments are connected by spring-damper elements 

to simulate the extensional (ct) and rotational (cr) stiffness and the 

accordant damping (dt, dr). Although this is a significant simplification 

of the structural arrangement of the line’s fibers, it is necessary to 

reduce the model’s complexity and simulation time. If using chain 

mooring lines, then this stiffness and damping could be neglected.

The degrees of freedom (DOF) relative to a prior body are reduced to a 

minimum of one translational (uy) and two rotational (φx, φz) directions: 

To enable the simulation of the line’s elongation, the DOF in cylinder’s 

longitudinal direction must be maintained. The transverse rotational 

movements also must be enabled. The line’s twist DOF was eliminated 

because there is no significant structural mooring-line torsion expected, 

and torsion only introduces minor hydrodynamic loads.

The very complex behavior of the seabed is reduced to a unilateral 

spring-damper model with high stiffness (cs) and damping (ds) to 

represent a rigid floor. The lateral friction is modeled by a coulombic 

element with an empiric friction coefficient.

The hydrodynamic effects on the mooring line are represented by a 

variation of the Morison Equation (Eq. 1), considering hydrodynamic 

drag and inertia, but neglecting effects based on dissipative flow, such 

as vortex induced vibrations.

Investigations of the discretization show only small effects on the 

results when increasing the number of elements beyond a certain 

number of elements. This model-specific number must be identified by 

a sensitivity analysis. Following this procedure enables the determination of a moderate discretization and limited simulation time, and 

retains the accuracy of the results.

Fig. 5.Time series of OC3-Hywind platform translation in surge 

direction for OC3 DLC 1.4 surge

Fig. 6. Time series of OC3-Hywind tower-base fore-aft bending 

moment for OC3 DLC 1.4 surge

Comparisons of the MBS to quasi-static model in Fig. 5 for the 

platform’s surge motion show differences caused by the non-linear 

additional hydrodynamic damping of the MBS model. Here, the 

platform initially is displaced 21 m in surge direction in still water 

(setup equals OC3 DLC 1.4 Surge) and then released, displaying the 

damped sine-shaped motion. The amplitudes of the motion are lower 

for the non-linear model and the periods are increased. Accordingly, 

similar differences in the fore-aft bending moment at the tower base 

can be identified in Fig. 6. Studies with stochastic sea states also show 

similar behavior.

CONCLUSIONS

State-of-the-art design tools for floating offshore wind turbines that can 

simulate such systems in an integrated way have already reached a 

viable level of sophistication. Nevertheless, the unique aerodynamics, 

hydrodynamics, and mooring-line dynamic effects occurring on 

floating offshore wind turbines due to large rotor and platform motions 

and the use of non-slender support structures require the further 

improvement of current modeling techniques to reach a greater 

confidence in simulated results. This paper presents the current 

challenges in simulation of FOWT. It examines both the important 

physical effects not yet addressed by current simulation codes, and the 

potential simulation developments and methodologies required to 

model these effects more accurately. Conclusions are drawn about the 

importance of the relevant effects, strengths, and weaknesses of the 
8

different methods and the development needed. Also analyzed is the 

applicability of the methods in FOWT design codes.

Regarding aerodynamics, the large low-frequency platform motions 

experienced by floating offshore wind turbines result in flow conditions 

that can be considerably more complex than those experienced by 

conventional onshore or fixed-bottom offshore wind turbines, and 

which are not captured by BEM. Significant pitch and surge motions 

lead to a change in the interaction between the rotor and wake. 

Dynamic stall and yawed inflow models also have increased 

importance for FOWTs. This paper discusses the limitations of BEM 

and the capabilities of computational fluid dynamics and potential flow 

methods (PFM) for FOWT simulation. Computational fluid dynamics 

results which show the complex flow conditions at the rotor occurring 

during a representative platform pitch motion are presented for the first 

time.

For modeling of non-slender floating platforms, hydrodynamic wave 

diffraction effects must be accounted for to correctly determine the 

local pressure force and global wave loads. Significant platform movements require inclusion of wave radiation forces; non-cylindrical 

elements demand modeling of added mass-induced coupling between 

hydrodynamic force and support structure acceleration. Their significance as well as the importance of second-order linear hydrodynamics

and vortex-induced vibrations for FOWT simulation are discussed.

Different techniques for the representation of mooring-line dynamics, 

including quasi-static, look-up table, FEM and MBS methods, and their 

impact on global system loads are investigated. A MBS methodology is 

introduced and initial results are presented, indicating the importance of 

advanced non-linear mooring system models. Dedicated studies of the 

dynamics of mooring lines, including VIV effects, but specifically 

focusing on floating wind turbines are necessary.

Beyond theoretical and numerical analysis, validation of advanced 

modeling techniques with measurement data from full-scale prototypes 

is of great importance and is necessary to resolve the challenges 

discussed in this paper; especially when considering a potential new 

standard for the design of floating offshore wind turbines. The IEA 

Wind Task 30 Offshore Code Comparison Collaboration Continuation 

(OC4) project, which started in 2010, also will address some of these 

modeling challenges. In the future, advanced FOWT simulation tools 

will enable more reliable motion, load, and deflection predictions and 

ultimately will lead to improved designs to utilize the vast amount of 

wind resource located in deep waters.

ACKNOWLEDGEMENTS

The work presented here was funded partially by the Commission of 

the European Communities, Research Directorate-General within the 

scope of the Integrated Project “UpWind—Integrated Wind Turbine 

Design” (Project No. 019945 (SES6).

REFERENCES

Cordle, A, and Jonkman, J (2011). State of the Art in Floating Wind 

Turbine Design Tools. GL Garrad Hassan, ISOPE 2011.

DLR Braunschweig (2007). FLOWer: Installation and User Manual of 

FLOWer MAIN version FLOWer 1-2007.1.

International Electrotechnical Commission (2009). IEC 61400-3, Wind 

Turbines—Part 3: Design Requirements for Offshore Wind 

Turbines.

Jonkman, J (November 2007). Dynamics Modeling and Loads Analysis 

of an Offshore Floating Wind Turbine. NREL/TP-500-41958. 

Golden, CO.

Jonkman, J, and Matha, D (2011). “Dynamics of offshore floating wind 

turbines - analysis of three concepts,” NREL, Wind Energy 

Journal, DOI: 10.1002/we.442 2011.

Jonkman, J, and Musial, W (2010). Final Technical Report, IEA Wind 

Task 23, Subtask 2, Offshore Code Comparison Collaboration 

(OC3), International Energy Agency (IEA), IEA Wind Task 23, 

Offshore Wind Technology and Deployment.

Kreuzer, E, and Wilke, U (2002). “Mooring Systems—A Multibody 

Dynamic Approach,” Technical University Hamburg-Harburg, 

Multibody System Dynamics, Vol 8.

Lucas, J (January 2011). Comparison of First and Second-Order 

Hydrodynamic Results for Floating Offshore Wind Structures, 

GL Garrad Hassan, Report Ref: 11594br02a.

Matha, D (2009). Model Development and Loads Analysis of an 

Offshore Wind Turbine on a Tension Leg Platform, with a 

Comparison to Other Floating Turbine Concepts. NREL/TP-500-

45891. Golden, CO.

Matha, D, Hauptmann, S, Hecquet, T, and Kühn, M (2010). 

Methodology and Results of Loads Analysis of Wind Turbines with 

Advanced Aeroelastic Multi-Body Simulation, DEWEK, Bremen, 

Germany.

Meister, K, Lutz, T, and Krämer, E (2010). Consideration of Unsteady 

Inflow Conditions in Wind Turbine CFD Simulations, DEWEK, 

Bremen, Germany, 2010.

Östergaard and Schellin (1987). “Comparison of experimental and 

theoretical wave actions on floating compliant offshore 

structures,” Applied Ocean Research 9, pp 192-213

Robertson, A, and Jonkman, J (2011). Loads Analysis of Several 

Offshore Floating Wind Turbine Concepts. NREL, ISOPE 2011.

Sebastian, T, and Lackner, M (2010). A Comparison of First-Order 

Aerodynamic Analysis Methods for Floating Wind Turbines, 48th 

AIAA Aerospace Sciences Meeting, Orlando, Florida, 2010.

Sebastian, T, and Lackner, M (2011). Offshore Foating Wind Turbines 

- An Aerodynamic Perspective, 49th AIAA Aerospace Sciences 

Meeting, Orlando, Florida, 2011.

SIMPACK (2010). “SIMPACK Reference Guide,” SIMDOC v8.904.

Söding, H (2010). “Boundary Element Methods for Seakeeping,” 

Technical University Hamburg-Harburg, Duisburg, Contribution 

to the Lectures on Seakeeping and Sea Loads.

Streiner, S, Hauptmann, S, Kühn, M, and Krämer, E (2008). Coupled 

Fluid-Structure Simulations of a Wind Turbine Rotor, University 

Stuttgart, DEWEK