Quantifying the impact of modeling fidelity on different substructure concepts for floating offshore wind turbines – Part 1: Validation of the hydrodynamic module QBlade-Ocean [original]

Wind Energ. Sci., 9, 623–649, 2024

https://doi.org/10.5194/wes-9-623-2024

the Creative Commons Attribution 4.0 License.

Quantifying the impact of modeling fidelity

on different substructure concepts for floating

offshore wind turbines – Part 1: Validation

of the hydrodynamic module QBlade-Ocean

Robert Behrens de Luna1, Sebastian Perez-Becker1, Joseph Saverin1, David Marten1, Francesco Papi2,

Marie-Laure Ducasse3, Félicien Bonnefoy4, Alessandro Bianchini2, and Christian-Oliver Paschereit1

1Chair of Fluid Dynamics, Hermann Föttinger Institute, Technische Universität Berlin,

Müller-Breslau-Straße 8, 10623 Berlin, Germany

2Department of Industrial Engineering, University of Florence, via di Santa Marta 3, 50139 Firenze, Italy

3Saipem, 7 Av. de San Fernando, 78180 Montigny-le-Bretonneux, France

4CNRS – École Centrale Nantes, 1 rue de la Noë, 44321 Nantes CEDEX 3, France

Correspondence: Robert Behrens de Luna (r[email protected])

Received: 9 September 2023 – Discussion started: 19 September 2023

Revised: 19 December 2023 – Accepted: 30 January 2024 – Published: 14 March 2024

Abstract. To realize the projected increase in worldwide demand for floating offshore wind, numerical sim-

ulation tools must capture the relevant physics with a high level of detail while being numerically efficient.

This allows engineers to have better designs based on more accurate predictions of the design driving loads,

potentially enabling an economic breakthrough. The existing generation of offshore wind turbines is reaching a

juncture, where traditional approaches, such as the blade element momentum theory, are becoming inadequate

due to the increasing occurrence of substantial blade deflections. QBlade is a tool that includes a higher-fidelity

aerodynamic model based on lifting-line theory, capable of accurately modeling such scenarios. In order to en-

able the simulation of offshore conditions in QBlade and to make use of this aerodynamic capability for novel

offshore wind turbine designs, a hydrodynamic module called QBlade-Ocean was developed. In the present

work, this module is validated and verified with two experimental campaigns and two state-of-the-art simulation

frameworks on three distinct floating offshore wind turbine concepts. The results confirm the implementation

work and fully verify QBlade as a tool to be applied in offshore wind turbine simulations. Moreover, a method

aimed to improve the prediction of non-linear motions and loads under irregular wave excitation is analyzed

in various conditions. This method results in a significant improvement in the surge and pitch degrees of free-

dom in irregular wave cases. Once wind loads are included, the method remains accurate in the pitch degree of

freedom, while the improvements in the surge degree of freedom are reduced. A code-to-code comparison with

the industry-designed Hexafloat concept highlights the coupled interactions on floating turbines that can lead to

large differences in motion and load responses in otherwise identically behaving simulation frameworks.

Published by Copernicus Publications on behalf of the European Academy of Wind Energy e.V.

624 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

1 Introduction

In recent years, wind turbine technology has seen a dynamic

development, characterized by the continuous trend towards

increasing tower heights and rotor sizes. This growth has

challenged the modeling assumptions of current wind tur-

bine simulation tools. The unfavorable square–cube law scal-

ing (Burton et al., 2001, p. 329) that is characteristic of the

scaling of blade lengths has already led to innovative slender

blade designs which are notably more flexible (Veers et al.,

2019). These developments have required wind turbine sim-

ulation tools to move on from the assumption of rigid com-

ponents and include structural dynamics that enable the anal-

ysis of aeroelastic effects and its influence on loads and sub-

sequently designs.

As a consequence, aerodynamic assumptions inherent to

the blade element momentum (BEM) method require several

corrections to make them viable for modern wind turbines

(Perez-Becker et al., 2020; Li et al., 2022). An alternative

approach could involve a shift towards physically more ac-

curate models such as a lifting line coupled with a free vor-

tex wake model. A shift towards higher-fidelity aerodynamic

methods may be accelerated as wind turbines are placed fur-

ther offshore, on floating structures that are excited by waves

and currents, introducing additional complexity and requir-

ing more accurate models within the wind turbine simulation

tools. These capabilities are essential for economic evalua-

tion and optimized engineering solutions of such systems.

To enable economically viable floating offshore wind tur-

bines (FOWTs), simulation tools also require hydrodynamic

capabilities to capture the coupled dynamics of aero-hydro-

servo-elastic problems and solve the mooring system dy-

namics. The added degrees of freedom (DOFs) inherent to

FOWTs may accelerate the change in how aerodynamic

loads and wake aerodynamics are modeled in these increas-

ingly complex scenarios. A floating turbine, unlike its fixed-

bottom or land-based counter parts, may also interact with its

own wake. Modeling this phenomenon accurately requires

resolving the wake explicitly.

At present, FOWTs still rely to a large extent on the BEM

method to calculate aerodynamic loads on a wind turbine.

This method, while efficient, includes several simplifying as-

sumptions that require empirical corrections. In particular,

the rotor is assumed to behave like a planar actuator disk

that extracts energy from the stream tube by causing a pres-

sure drop when air flows through it. This assumption inher-

ently omits the finite number of blades on a wind turbine.

Moreover, it implies that rotor blades do not deflect outside

the rotor plane. Additionally, the momentum theory breaks

down for high induction factors, and uniform aerodynamic

conditions across the rotor plane are assumed (Burton et al.,

2001; Perez-Becker et al., 2020; Li et al., 2022). Given the

shortcomings of this method and the empirical nature of its

corrections, as detailed and explained by Perez-Becker et al.

(2020), current BEM methods might not be sufficient in cer-

tain circumstances. Ramos-García et al. (2022) analyzed the

effects of floating motion on the aerodynamic loads predicted

by a BEM and a lifting-line solver. The result of this study

was that the BEM method can lead to an increased motion

response of up 50 % at high wave frequencies. Moreover,

it was shown that the BEM method notably underestimates

thrust during large backwards oscillations, where the turbine

interacts with its own wake.

One particular area in which BEM methods need to im-

prove if they are to maintain their applicability in the fu-

ture alongside other, more advanced methods is their mod-

eling of dynamic inflow conditions (Jeon et al., 2014). In

FOWT modeling in particular, dynamic inflow plays an im-

portant role due to the wave-induced motion of the floating

structures. Vortex wake models do not have such shortcom-

ings as the wake is modeled explicitly by the trailing and

shed vorticity caused by spacial and temporal gradients in

the blade-bound vortex. Hence, the wake develops over time

and includes the transient effects that, e.g., pitch actuation

or gusts have on the induction in the rotor plane (Mancini

et al., 2023). The fact that the most recent release of the Aero-

Dyn module (v15) (Murray et al., 2017) of the widely used

code OpenFAST (Jonkman et al., 2019) includes a lifting-

line aerodynamic method named OLAF (Shaler et al., 2020)

may be seen as confirmation that higher-fidelity methods

than BEM are a requirement for certain conditions. HAWC2

(Larsen and Hansen, 2007), another well-established state-

of-the-art simulation framework, also features multiple aero-

dynamic solvers based on lifting-line theory.

Another relevant topic for the simulation of FOWTs, on

which the community has focused in the past and which re-

mains a major focus of research today, is the accurate predic-

tion of hydrodynamic excitation and floater response below

the linear wave excitation frequency range (Pegalajar Jurado

and Bredmose, 2019; Gueydon et al., 2014; Azcona et al.,

2019). Accurately capturing the excitation at these slow-drift

frequencies is important because the natural frequencies of

floating structures with catenary mooring systems typically

lie below the linear frequency range, and resonance can oc-

cur. The current generation of simulation tools often under-

estimates this non-linear response, as is discussed in detail

in the Offshore Code Comparison, Collaboration, Contin-

ued, with Correlation (OC5) project (Robertson et al., 2017).

Their analysis shows that the inclusion of second-order dif-

ference frequency forces leads to a response at the accu-

rate frequency. However, the response at these low frequen-

cies is small compared to experimental results. In the OC6

project (Robertson, 2019), phases Ia and Ib aim for a better

understanding of the cause of this underestimation. Robert-

son et al. (2020) and Souza do Carmo et al. (2020) indicate

that the addition of linear damping coefficients during the

tuning process is one reason. These coefficients are often

added in mid-fidelity tools to better align the decaying be-

havior with an experimental reference. However, they lead

to a restricted response during wave excitation. In addition,

Wind Energ. Sci., 9, 623–649, 2024 https://doi.org/10.5194/wes-9-623-2024

R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 625

both argue that the excitation forces outside the linear wave

frequency range are underpredicted. To address the underpre-

diction of excitation forces, Li and Bachynski-Poli´

c (2021)

propose a method to tune the difference-frequency quadratic

transfer function (QTF) based on the results of a high-fidelity

computational fluid dynamics simulation. Another attempt

to formulate a methodology that improves the prediction of

the floater surge and pitch responses is given by Wang et al.

(2022). They identified erroneous viscous excitation, a third-

order effect, as the possible source for the underprediction at

the natural frequency and suggest a varying treatment of the

transversal drag of members close to the mean sea level and

a frequency-dependent treatment of the axial drag on heave

plates.

QBlade is a tool that includes a numerically optimized free

wake method (Marten, 2020). With its hydrodynamic exten-

sion QBlade-Ocean, the tool gains the ability to model all

required domains to simulate the dynamics of floating wind

turbines. Thereby, QBlade addresses a need in the commu-

nity to provide a numerically efficient code with more accu-

rate aerodynamic and structural models in open access. The

development work was carried out within the Horizon 2020

project (FLOATECH, 2020) and was identified as a key out-

come. Additionally, to improve the accuracy of the non-linear

motion response, the method proposed by Wang et al. (2022)

is adopted in QBlade-Ocean, thus allowing an analysis of

its improvement in the prediction of non-linear motion re-

sponses for two distinct floater types in varying conditions,

including irregular wind and wave excitation.

The aim of this two-part study is to analyze the influence

of higher-fidelity methods on design driving loads. Part 1

lays the groundwork by validating and verifying the develop-

ment of QBlade-Ocean. This is done on three different float-

ing offshore wind turbine designs. The designs of the float-

ing substructures deviate strongly from each other regard-

ing their stabilization concept, water plane area, and struc-

tural complexity. These characteristics require modeling ap-

proaches appropriate for each design and therefore allow for

a verification of the various models that are combined to

capture the full turbine response to environmental loading.

The first FOWT model is the 5 MW Maritime Research In-

stitute Netherlands (MARIN) stock wind turbine (MSWT)

experimental turbine which is mounted on the DeepCwind

substructure (Robertson, 2017) and was built and tested

thoroughly within the OC5 code collaboration (Robertson

et al., 2014). The second FOWT that is used for verifica-

tion purposes is a spar-buoy-type platform on which the Soft-

wind software-in-the-loop (SIL) experiments focused (Arnal,

2020). For both FOWTs, an OpenFAST model that serves

as a comparison and a reference to analyze QBlade’s results

with respect to the experiment was built. The third and final

model considered in this work is the Hexafloat concept de-

signed by the company Saipem. This final part documents a

code-to-code comparison between QBlade and the industrial

software DeepLines WindTM (Principia, 2023). DeepLines

WindTM was the main tool used during the design process of

this substructure. This work is continued with Part 2 (Papi

et al., 2023), which focuses on the analysis of the influence

of increased model fidelity on design driving loads in an ex-

haustive number of simulations that represent more realistic

met-ocean conditions.

In Sect. 2, QBlade and the other simulation tools are

presented briefly. Section 3 introduces the models utilized

throughout the verification process and highlights the model-

ing differences between the simulation tools. Section 4 shows

the main results of this study, and the conclusions are drawn

in Sect. 5, which is then followed by an outlook on the in-

tended applications of the fully verified QBlade framework.

2 Compared simulation frameworks

2.1 QBlade

QBlade is an openly available simulation tool developed

to calculate wind turbine response in the time domain.

It has been under development at Technische Universität

Berlin (TUB) since 2010, where it started as a coupling be-

tween the open-source panel code XFOIL (Drela, 1989), the

graphical user interface (GUI) XFLR5 (Deperrois, 2023),

and an in-house-developed steady BEM solver. The code has

been expanded in its capabilities ever since. Today, QBlade

features two time domain aerodynamic solvers. The lower-

fidelity one is a BEM method that makes use of a po-

lar grid for the azimuthal discretization of the induction

factors, following the approach laid out by Madsen et al.

(2020). The higher-fidelity method, the lifting-line free vor-

tex wake (LLFVW) solver, applies the Lagrangian vortex

theory and follows the implementation of van Garrel (2003).

The structural model used in QBlade relies on the finite el-

ement analysis (FEA) module of the PROJECTCHRONO

multi-physics engine (Tasora et al., 2016). The application in

QBlade is such that the structural model of the turbine con-

sists of multiple body objects for the blades and the tower.

Each body is modeled as an Euler–Bernoulli beam using

a co-rotational formulation with a floating reference frame

(Marten, 2020). The full FEA model of a wind turbine is gen-

erated by constraining the different bodies in a multi-body

formulation. The aero-elastic coupling of the LLFVW and

polar-BEM solvers with the structural solver has been vali-

dated against different aero-elastic couplings of the simula-

tion tool HAWC2 by Behrens de Luna et al. (2022).

In the FLOATECH project, QBlade has been extended

by a hydrodynamic module that expands its capabilities to

offshore conditions. Moreover, the structural model was ex-

panded so that arbitrary substructure geometries can be mod-

eled. Thus, fixed-bottom and floating offshore wind turbines

can be designed and analyzed in the simulation suite. More

specifically, the hydrodynamic module features the follow-

ing:

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626 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

1. a wave generator with the capability to generate waves

from several energy spectra but also read prescribed

wave amplitude time series;

2. a hydrodynamic solver that calculates radiation damp-

ing forces, first-order excitation forces, and second-

order excitation forces (sum and difference frequency)

from pre-computed potential flow coefficients;

3. a Morison equation approach (Morison et al., 1950)

to account for viscous drag, added mass, and Froude–

Krylov forces for arbitrary geometries (Faltinsen,

1990);

4. an enhanced model, following the description of Wang

et al. (2022), to improve the non-linear motion response

under irregular wave excitation (described in detail be-

low Sect. 3.4);

5. a soil model that captures the restoring forces with a

distributed spring with non-linear coefficients.

Readers interested in detailed information about the im-

plementation work of QBlade-Ocean are referred to Saverin

et al. (2021) and the online documentation (QBlade Docu-

mentation, 2022).

2.2 OpenFAST

OpenFAST is a widely known open-source multi-physics

simulation tool developed by the National Renewable En-

ergy Laboratory (NREL) (Jonkman et al., 2019). OpenFAST

builds on a highly modularized framework that couples mod-

ules from various physics disciplines with each other to

model the behavior of a wind turbine and the environment

around it. All OpenFAST results shown in this study were

run with OpenFAST v3.0.0 and the BEM solvers imple-

mented in versions 14 (Jonkman et al., 2023) and 15 (Mur-

ray et al., 2017) of the AeroDyn module (depending on the

model). The Beddoes–Leishman dynamic stall model and the

Øye dynamic wake effects were used. The ElastoDyn mod-

ule (ElastoDyn, 2023) was utilized to resolve the structural

dynamics, employing Euler–Bernoulli beam theory with pre-

scribed modes that allow only edge- and flapwise bending of

the blades and neglect blade torsion (Rinker et al., 2020).

Moreover, the HydroDyn (HydroDyn, 2023) module is used

to account for the interaction between the floater and marine

environment. The mooring lines are modeled using Moor-

Dyn (Wendt et al., 2016).

2.3 DeepLines WindTM

DeepLines WindTM (Principia, 2023) is a module of the

commercial integrated software solution DeepLinesTM de-

veloped by Principia and IFP Energies Nouvelles. It is pri-

marily known as a software solution to calculate in-place and

installation analyses for offshore structures such as flexible

risers, power cables, and mooring systems. The DeepLines

WindTM module was developed in 2011 due to the increased

market share of wind energy in the offshore environment and

is now able to carry out fully coupled dynamic finite element

analysis. Multiple BEM models are implemented and can be

chosen from an external .dll library. Like QBlade, DeepLines

WindTM can model horizontal- and vertical-axis wind tur-

bines. Within this study, a dynamic inflow model was acti-

vated while no unsteady blade aerodynamics were applied.

A validation study on DeepLines WindTM was carried out by

Perdrizet et al. (2013).

3 Simulation models and modeling approaches

This section briefly introduces the three simulation models

used for the validation and verification of QBlade. First, the

properties and characteristics of each of the three FOWTs

are discussed together with their respective modeling ap-

proaches. Second, the areas where the three simulation suites

differ from each other in the representation of the physics are

highlighted and discussed regarding their possible influence

on results. Third, the chosen test cases for validation and

verification purposes are introduced. A more extensive de-

scription of the three QBlade model definitions can be found

in Perez-Becker and Behrens de Luna (2022). Additionally,

each turbine database is available on the Zenodo online plat-

form. The corresponding DOIs are provided at the end of this

work. To allow for a fair comparison with regard to experi-

mental results (relevant for OC5 and Softwind), each numer-

ical model was tuned independently to reproduce the natural

system response of the reference. Details on this matter are

specified by Perez-Becker et al. (2022). Figure 1 displays the

three FOWT models with their mooring systems in still wa-

ter. The locations of the load sensors consistently used in this

work to validate and verify the mooring tensions are labeled

in Fig. 2. For the Softwind model, the loads are exported at

the delta connector of the mooring system.

3.1 OC5 model

The first model of a floating offshore wind turbine used for

the verification and validation is the MARIN stock wind tur-

bine mounted on the DeepCwind substructure, henceforth re-

ferred to as the OC5 model. This FOWT was thoroughly in-

vestigated within the Offshore Code Comparison, Collabora-

tion, Continued, with Correlation (OC5) project (Robertson

et al., 2014). The OC5 project was operated under the Inter-

national Energy Agency Wind Task 30 and builds on previ-

ous code-to-code comparison efforts (OC3 and OC4). In the

OC5 collaboration, a large number of participants applied

various modeling tools with the goal to simulate test cases

that were carried out experimentally and relate differences to

certain modeling approaches. The experiments were carried

out at the Maritime Research Institute Netherlands (MARIN)

offshore wave basin. The model on which the experiments

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 627

Figure 1. Renders of the (a) OC5, (b) Softwind, and (c) Hexafloat models exported from the QBlade GUI.

Figure 2. Top view of the FOWT models. The incoming wind and wave propagation direction goes from left to right for all considered cases

in this study. (a) OC5, (b) Softwind, and (c) Hexafloat.

were conducted consists of the 1/50th scale model of the

NREL 5 MW research wind turbine (RWT) turbine mounted

on top of the floating semi-submersible substructure. The

flexible tower is made out of two aluminum rods that are in-

terconnected and matches the reference turbine’s first fore–

aft and side–side natural frequencies. The substructure, as

mentioned before, is a three-pillar design semi-submersible

known as the DeepCwind platform. It consists of a central

column, on which the turbine is mounted, and three addi-

tional buoyancy-providing columns that connect to the cen-

tral column through braces. The scaled platform is moored to

the ground with three catenary mooring lines, one attached to

each buoyancy column. The QBlade model of the OC5 plat-

form can be seen in Fig. 1a. A more precise description of

the FOWT is provided by Robertson et al. (2014). Similar

to the approach undertaken in the OC5 project, the numeri-

cal models are formulated utilizing properties that have been

upscaled to match the dimensions of the full-scale size. To

compare the numerical results with the experimental ones,

the latter are also scaled to a full-scale equivalent via Froude

scaling. The OC5 model is particularly well suited for this

study as simulation results from a wide variety of simulation

codes are openly available for validation purposes, and, even

more importantly, experimental data can serve as a reference,

thus allowing for a full validation of QBlade. A comprehen-

sive analysis of the OC5 results is provided by Robertson

et al. (2017). Moreover, an equivalent model was built in

OpenFAST in order to have full oversight of the subtleties

of the model and to have the ability to compare test cases not

considered in the OC5 collaboration.

3.1.1 OC5 model – turbine modeling choices

The rotor blades of the model-scale NREL 5 MW turbine

predominantly consist of MARIN-modified Drela AG04 air-

foil sections. The modification was made to reproduce the

scaled thrust and torque loads of the reference turbine in

a low-Reynolds-number environment. The three most inner

stations, which amount to roughly 13 % of the radius, are

blended with a cylindrical airfoil. Due to the minor influence

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628 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

of the root region on aerodynamic performance, the lift co-

efficient of the inner stations is neglected, and an angle-of-

attack-independent drag coefficient of 0.5 is assigned. Due

to the favorable scaling of the structural properties towards

full scale, the blades are assumed to be rigid. These choices

are in line with the description found in Goupee et al. (2015),

where additional information on the MSWT blade, such as

chord and twist distribution as well as the modified polars,

may be found. In both QBlade and OpenFAST, the Øye dy-

namic stall and the tower shadow models are activated. A

tower drag coefficient of 0.5 was used.

3.1.2 OC5 model – substructure modeling choices

The popularity of the DeepCwind substructure within the re-

search community has led to the open availability of hydro-

dynamic coefficient files that were generated with the bound-

ary element solver WAMIT (WAMIT Inc., 2024). This en-

ables a hydrodynamic treatment that relies on solving the

diffraction and radiation problems as well as the calculation

of non-linear excitation forces through fully populated sum

and difference quadratic transfer functions (Faltinsen, 1990).

To account for viscous forces, non-linear drag is resolved via

application of Morison drag applied to strip theory, where

drag coefficients are assigned to the cylindrical elements.

Henceforth, this combination is referred to as the potential

flow plus Morison drag (PFMD) approach. The required in-

put files for radiation damping, excitation, and second-order

wave forces are adopted from the OpenFAST GitHub repos-

itory (Jonkman et al., 2019) and are used in the respective

OpenFAST and QBlade models.

3.2 Softwind model

Instead of deploying a scaled experimental wind turbine that

includes a rotor-nacelle assembly (RNA), as was done in the

OC5 campaign, the Softwind experiments rely on a software-

in-the-loop setup to capture the fully coupled dynamics of a

FOWT. The campaign was carried out at the Research Lab-

oratory in Hydrodynamics, Energetics and Atmospheric En-

vironment department of the École Centrale de Nantes. The

SIL setup includes a digital twin of the Softwind FOWT that

runs parallel to the experiment and gets information, such as

floater displacements and velocities, as an input. The aerody-

namics are subsequently solved in the numerical code (Open-

FAST), which calculates the rotor’s power and thrust force.

This information is communicated to a Schübeler high static

thrust (HST) thruster sitting atop the tower (Arnal, 2020),

which applies the thrust force of the turbine rotor with close

to no time lag. The FOWT model is scaled to a 1/40th scale,

and the turbine is based on the DTU 10 MW RWT (Bak

et al., 2013) design, appropriately scaled. Accordingly, the

RNA mass distribution aligns with the reference wind tur-

bine. Similarly, the tower properties were scaled down from

the DTU 10MW RWT to match the natural frequency of

the first fore–aft and side–side modes, the amplitude of de-

formation, and the mode shape. The substructure is a spar-

type foundation which was dimensioned based on existing

geometries such as the OC3 Hywind platform (Jonkman,

2010). Finally, the mooring system has been designed with

three catenary lines that split up into two lines just before

the substructure to form a delta connection for increased yaw

stability (see Fig. 2b). The SIL setup and the Softwind model

are described more precisely by Arnal (2020). Figure 1b dis-

plays the QBlade model of the Softwind FOWT. Throughout

the following sections, this FOWT is referred to as the Soft-

wind model.

3.2.1 Softwind model – turbine modeling choices

As mentioned previously, the rotor of the turbine is, due to

the SIL approach, modeled numerically in the experiment

as well. Hence, there is no need for re-adjusting the airfoil

polars towards a low-Reynolds-number environment. There-

fore, the blade definition, along with the airfoil characteris-

tics as outlined in Bak et al. (2013), is utilized to set up the

turbine models in QBlade and OpenFAST, respectively. In

contrast to the OC5 model, this includes the structural def-

inition of the blades and the tower. Both are assumed to be

flexible bodies. For servo dynamics, the DTU baseline con-

troller (Hansen and Henriksen, 2013) with the corresponding

parameters was selected for this turbine. It should be pointed

out that the SIL setup included the AeroDyn v14 (Jonkman

et al., 2023) module. Hence, the OpenFAST calculations for

this turbine also deploy the AeroDyn v14 module.

3.2.2 Softwind model – substructure modeling choices

The hydrodynamic loads on the spar-type substructure are

modeled with the PFMD approach with first-order forces

relying on potential flow theory. Even though second-order

forces are generally small in relation to first-order forces on

spar-buoy-type platforms, they can cause notable excitation

at the resonant natural frequencies of the platform (Roald

et al., 2013). For this platform, only the main diagonal terms

of the difference-frequency QTF were available. This in turn

yields the opportunity to verify the implementation of New-

man’s approximation of the slowly varying drift forces (New-

man, 1974) within QBlade against experimental results. Vis-

cous forces are modeled through the application of Morison

drag coefficients to the cylindrical elements of the spar. The

potential flow coefficients were calculated in a previous step

in the open-source software NEMOH (Kurnia and Ducrozet,

2023; Babarit and Delhommeau, 2015) and converted into

the WAMIT format.

3.3 Hexafloat model

The Hexafloat concept has been designed by the company

Saipem to provide a cost-efficient substructure with favor-

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 629

able hydrodynamic characteristics. It consists of a hexag-

onally shaped structure composed of cylindrical members.

Twelve braces extend from the six corners inwards, two per

corner with varying angles, and converge in a single column.

This column is the only member that breaks the water sur-

face in a neutral position, and it connects to the tower of the

turbine coaxially. The stability of the platform is provided by

a counterweight that connects with six tendons to the corners

of the hexagonal structure. The QBlade model of the Hex-

afloat model is displayed in Fig. 1c. Through this design, the

benefits of a shallow draft are merged with the characteristics

of a spar-type floater, including a small water plane area and

gravity stabilization. The turbine atop the floater is the DTU

10 MW RWT and equals the definition provided by Bak et al.

(2013).

3.3.1 Hexafloat model – substructure modeling choices

The Hexafloat structure is modeled with a full-Morison

strip theory approach. Accordingly, added mass forces, drag

forces, and the Froude–Krylov forces are all resolved in an

implicit manner using empirical added mass and drag coef-

ficients for the cylindrical elements. This treatment implies

that no linear damping is inherent to the system. Diffrac-

tion forces are modeled by the application of the MacCamy–

Fuchs correction, and non-linear hydrodynamic excitation is

captured, to some extent, by the application of the hydro-

dynamic loads at the instantaneous position of the floating

structure and by using kinematic wave stretching (Robertson

et al., 2017).

3.4 Treatment of non-linear excitation

Non-linear excitation is modeled with the approach pro-

posed by Wang et al. (2022). In this approach, the transver-

sal drag coefficients of the substructure members are treated

as depth dependent. Hence, to improve the response within

the surge DOF, the transversal drag coefficient of the mem-

bers near sea level (until –4m below sea level) is increased

to CD,tr =1.6. The reason for this is that there is a greater ef-

fective drag near the surface (Clement, 2021). In addition, the

extrapolation stretching method is applied since this method

leads to larger wave-induced velocities near the water sur-

face (Fig. A1 demonstrates the impact of stretching methods

on the non-linear response). To improve the response within

the pitch DOF, Wang et al. (2022) suggest focusing on the

axial drag of the heave plates. They argue that the Morison

drag for hybrid members (PFMD treatment) should only be

applied on the face of the heave plates that experience neg-

ative flow. The reason is that only the flow separation phe-

nomenon is not already accounted for in the potential flow

solution. Furthermore, it is argued that one single drag coeffi-

cient for heave plates cannot satisfy the appropriate damping

and excitation requirements in both the heave DOFs and the

pitch DOFs. Flow separation is largely caused by the higher-

frequency flow in the heave mode and not by the lower-

frequency pitch mode; i.e., the viscous drag influencing the

pitch DOF should be lower. This, however, as pointed out

by Böhm et al. (2020), leads to a trade-off between an accu-

rate non-linear response in heave and pitch. The proposed ap-

proach by Wang et al. (2022) is to high-pass filter the normal

velocity at the heave plate faces and to compute the resulting

axial drag force applied through the Morison equation with

the following:

FDax =αFDax +(1 −α)FDax,f.(1)

In this weighted sum, αis the scaling factor between the ax-

ial drag force calculated with the unfiltered and filtered ve-

locities FDax and FDax,f. To filter the velocity components, a

simple first-order high-pass filter is recommended to prevent

phase shift effects. With α=0.5 and fc=0.07 Hz, Wang

et al. (2022) weigh both terms equally and use a cutoff fre-

quency that is towards the lower end of the linear wave fre-

quency with good results.

The implementation of the method proposed by Wang

et al. (2022) in QBlade-Ocean required different parameter

settings in order to achieve good agreement with the exper-

imental results for the test cases considered in this work. In

the case of the OC5 model, the near-surface transversal drag

coefficients had to be increased to CD,tr =2.21to match the

non-linear surge response of the experiment. For the corre-

sponding response in pitch, a weight factor α=0.2 and a

cutoff frequency fc=0.04Hz were required together with

an axial drag coefficient of CD,ax =3.52on the heave plates.

A parameter study showing the influence of the respective

parameters on the non-linear heave and pitch motion peaks

and an exemplary velocity time signal with the applied filter

is provided in the Appendix (see Figs. A2 and A3) to pro-

vide some guidance for researchers looking to implement or

fine-tune such an approach. Despite high-pass filtering the

axial velocity components, additional damping was required

in the heave DOF to prevent overestimation in the heave re-

sponse. In addition, the approach was tested on the Softwind

model in order to gain information on its efficacy for spar-

type platforms. For this model, the near-surface transversal

drag coefficient is increased from previously CD,tr =0.3 to

CD,tr =0.6. Due to the lack of heave plates on this structure,

the approach making use of Eq. (1) is not applied.

3.5 Modeling approaches and test cases

Even though QBlade, OpenFAST, and DeepLines WindTM

are simulation frameworks with similar capabilities on a

broader scale, decisions made by the developers regarding

the representation of specific physical problems (such as

wake induction) can cause smaller-scale deviations. In a fully

1Previously, CD,tr =0.61 and CD,tr =0.68 had been used for

the main columns and the offset columns, respectively.

2Previously, CD,ax =3.85 had been used.

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630 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

coupled, non-linear system like a FOWT, these deviations

may affect overall system dynamics and result in growing

deviations throughout the runtime of a full simulation. To

help interpret differences in the results between the compared

simulation codes, it is important to discuss these modules and

their distinctions. Therefore, an overview of the main differ-

ences between the three simulation codes is given in the fol-

lowing.

Table 1 summarizes the modeling capabilities of the main

physical models of each tool. It can be seen that distinctions

are present in various modeling approaches: QBlade deviates

from both of the other codes with its LLFVW method com-

pared to the lower-fidelity unsteady BEM approach. Struc-

turally, OpenFAST deviates in the formulation with its Elas-

toDyn model, which uses a linear modal representation of

the blades and the tower, which requires the user to provide

previously generated mode shapes. QBlade and DeepLines

WindTM both use a non-linear beam FEA representation

to model the structure of the blades and the tower. Hy-

drodynamically, the OpenFAST version used (v3.0.0) lacks

the kinematic stretching option available in QBlade and

DeepLines WindTM. OpenFAST furthermore relies on lin-

ear hydrostatics, whereas both of the other tools explicitly

compute the buoyancy and restoring forces caused by the

displaced water mass through the submerged volume. Ad-

ditionally, the formulation described in Sect. 3.4 to capture

non-linear excitation was used in a separate QBlade model

(referred to as the enhanced model in the following). Finally,

the mooring dynamics are resolved explicitly in each of the

three tools; however only QBlade and DeepLines WindTM

employ FEA cable elements, while OpenFAST follows a

lumped-mass approach. Readers interested in greater detail

in the modeling formulations are referred to Marten (2020)

and QBlade Documentation (2022) for QBlade, Jonkman

and Buhl (2005) and OpenFAST Documentation (2023)

for OpenFAST, and Perdrizet et al. (2013) for DeepLines

WindTM.

The authors acknowledge that OpenFAST includes the

OLAF solver in its newest AeroDyn v15 release. OLAF is a

higher-fidelity lifting-line solver for aerodynamics similar to

the one implemented in QBlade (Shaler et al., 2020). More-

over, OpenFAST includes the BeamDyn structural model

that allows for the computation of full geometric non-

linearity and large deflections of the blades due to its exact

beam theory formulation. The application of both modules

was not included in this study. The number of simulations

for the different turbine designs was large, and the simula-

tions were performed on desktop workstations. Using OLAF

and BeamDyn for the OpenFAST calculations would have

rendered an unacceptably long evaluation time for these sim-

ulations. Finally, NREL released OpenFAST v3.5.0, which

includes kinematic wave stretching and explicit buoyancy

calculation features, after the underlying simulations for this

study were completed.

4 Results

This section presents the main results of the validation test

cases. They are intended to validate individual components

and models that influence the FOWT dynamics in isolation.

Once this initial validation is achieved, the study will move

to more complex test cases where all components interact

simultaneously. Although not identical, due to the constraint

of resembling the experiments, the set of test cases follows a

similar approach for each FOWT model:

1. static cases for assessment of the isolated mooring

loads;

2. system properties, including decay cases in still condi-

tions for assessment of the natural system properties;

3. aerodynamic loads, including wind-only cases with a

fixed floater for assessment of the isolated aerodynamic

loads;

4. hydrodynamic loads, including wave-only excitation

cases (regular and irregular) for assessment of the iso-

lated hydrodynamics;

5. combined aero- and hydrodynamic wind and wave

cases for assessment of the combined aero-hydro-servo-

elastic dynamics.

Following this procedure, the results of all three models are

discussed and presented for one set of cases before moving

to the next set. The respective test cases are defined in the

tables at the beginning of the associated subsections.

4.1 Static displacement

The static displacement test case aims to confirm the static

loads caused by the restoring forces of the mooring system

which result from displacement of the FOWT model from

its neutral position. In the presented case, the substructure

is traversed from positive towards negative surge and sway

positions. A close alignment of the results, with both the ex-

periment and the other simulation codes, verifies a proper

definition of the mooring properties and, subsequently, the

static loads calculated by the mooring model of QBlade.

The static displacement tests were only performed for the

OC5 model, since experimental data of these tests were read-

ily available. The mooring tensions on the other models were

confirmed in still conditions at the neutral position. The an-

alyzed load sensors are located at the fairlead positions. For

easier visualization, the fairlead tensions are cumulated to

one value in the global surge and sway DOFs and displayed

over the displacement direction. Figure 3 shows the results

from the OC5 model. The excellent agreement that is dis-

played by both QBlade and OpenFAST with the experiment,

even under significant displacements, allows for the conclu-

sion of a correctly defined mooring system and reliable load

estimates of QBlade’s mooring model in static conditions.

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 631

Table 1. Key differences between the simulation frameworks regarding the respective model.

Model Code Aero Structure Hydrodynamics Mooring

OC5 MSWT

QBlade LLFVW Non-linear beams Whe stretch Explicit buoy – Cable elements

QBlade LLFVW Non-linear beams Ext stretch Explicit buoy Sect. 3.4 method Cable elements

OpenFAST UBEM Linear modal – Linear buoy – Lumped mass

Softwind

QBlade LLFVW Non-linear beams Whe stretch Explicit buoy – Cable elements

QBlade LLFVW Non-linear beams Ext stretch Explicit buoy Sect. 3.4 method Cable elements

OpenFAST UBEM Linear modal – Linear buoy – Lumped mass

Hexafloat QBlade LLFVW Non-linear beams Whe stretch Explicit buoy – Cable elements

DLW UBEM Non-linear beams Whe stretch Explicit buoy – Cable elements

Figure 3. Cumulated fairlead tensions on the OC5 model obtained from static displacement tests in surge (a) and sway (b). Positive xvalues

indicate a displacement in the downwind direction.

4.2 System properties – decay tests

The dynamic response of a FOWT when it is displaced from

its neutral position is affected by several factors, such as sys-

tem mass and inertia, center of gravity position, and restor-

ing forces and moments originating from the mooring sys-

tem and buoyancy. Such decay tests determine the natural

frequency and damping of the eigenmodes for the different

degrees of freedom. Thereby, these tests are very useful for

confirming a correct model setup and give the opportunity to

improve alignment of the numerical models with a reference

through additional tuning. This subsection presents and dis-

cusses the results extracted from the decay time series of the

three FOWT models. The time series and damping charac-

teristics are provided by Perez-Becker and Behrens de Luna

(2022) and Perez-Becker et al. (2022).

Table 2 shows the natural frequencies as they are extracted

from the time series of the decay test for the three FOWT

models. The blank spaces indicate that no results of the cor-

responding test were obtainable. By and large, very good

alignment between the numerical codes and, where avail-

able, the experiments has been achieved. Minor deviations

can be pointed out for (i) the OC5 model, where OpenFAST

deviates with a lower surge natural frequency compared to

QBlade and the experiment, and (ii) the Softwind model,

where the same observation also applies. In both instances,

attention has been paid to corresponding masses and inertias

between the models. Moreover, the added mass coefficients

are adopted from the WAMIT output files. Hence, a possi-

ble cause for the small discrepancy could lie in the dynamics

predicted by the mooring system, even though in steady con-

ditions very good alignment is observed in Fig. 3. As noted

in Table 1, OpenFAST relies on a simplified lumped-mass

approach that neglects bending stiffness (Hall and Goupee,

2015). QBlade-Ocean instead models the lines as cable el-

ements with the absolute nodal coordinate transformation

in Chrono (QBlade Documentation, 2022), which is a non-

linear finite element formulation that includes bending, tor-

sion, and shear deformation.

4.3 Aerodynamic loads

The next set of test cases considered in this study focuses

on isolated aerodynamic excitation. Aerodynamic loads af-

fect the dynamics of FOWTs through changes in rotor thrust.

This can lead to strong excitation in the substructure surge

and pitch DOFs. The test cases follow the setup defined in

the first two aerodynamic cases of the OC5 phase II collabo-

ration (Robertson et al., 2014) to be able to compare it to the

experimental reference model. This was done for two dif-

ferent rotors: the one used in the OC5 experiment and the

DTU 10MW RWT rotor, used on the Softwind and Hexafloat

models, respectively. For the OC5 model, two rotor charac-

teristic curves are recorded with a rotor speed sweep over

the same wind field, one representing close to rated and the

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632 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

Table 2. Natural frequencies in hertz extracted from the dominant degrees of freedom of each decay time series.

Model Code Surge Sway Heave Roll Pitch Yaw

OC5

QBlade 0.00944 0.00875 0.05777 0.03083 0.03028 0.01222

OpenFAST 0.00917 0.00931 0.05777 0.03111 0.03067 0.01208

Experiment 0.00944 – – – 0.03027 –

Softwind

QBlade 0.00844 – 0.03283 – 0.03083 –

OpenFAST 0.00833 – 0.03250 – 0.03116 –

Experiment 0.00858 – 0.03264 – 0.03079 –

Hexafloat QBlade 0.00417 0.00417 0.02694 0.02139 0.02139 0.01750

DeepLines WindTM 0.00431 0.00430 0.02694 0.02138 0.02138 0.01500

other one above-rated conditions of the OC5 turbine model.

Meanwhile, the substructure is constrained at its neutral po-

sition and hence does not respond dynamically to the exci-

tation. The second rotor that was tested is the one from the

DTU 10 MW RWT. The Softwind experiment, following a

SIL setup, applies the aerodynamic loads that are calculated

in real time along the experiment by AeroDyn v14. Accord-

ingly, a verification with OpenFAST using AeroDyn v14 as-

sures alignment with the experiment. To isolate aerodynamic

loads, the comparison was carried out on a simplified geome-

try of the DTU 10 MW turbine that has a rigid tower, no shaft

tilt, and also no coning angle. The shape of the blades and

their flexibility were not modified. The aerodynamic thruster

installed in the SIL experiments only applies the thrust force

at a single point on top of the tower. Hence, for this turbine,

the thrust coefficient was the main point in the comparison. In

each software package, the thrust force applied on the rotor

shaft was used to calculate the thrust coefficient. A descrip-

tion of the test cases can be found in Table 3.

The average value for Cpand Ctfor each rotor speed of the

OC5 turbine sweep is displayed in Fig. 4. The reference re-

sults that are displayed stem from the study of Goupee et al.

(2015), in which the polars of an OpenFAST model were cal-

ibrated to resemble the aerodynamic behavior of the OC5

turbine. Two curves can be seen for each coefficient. Test

case 2.1 ranges from a tip speed ratio (TSR) of 2.8 up to

close to 9 and represents a rotor speed sweep at constant,

close to rated wind speed with a 0.89° blade pitch angle.

Test case 2.2 ranges from a TSR of 1.7 up to 5.3 at wind

speeds representing an above-rated condition. Focusing on

the power coefficient first, little deviation between both nu-

merical tools is visible, even though different aerodynamic

models are deployed. Bearing in mind that the blades of the

OC5 turbine are modeled as rigid structures and are almost

perfectly straight, the planar rotor assumption underlying the

BEM method is not violated. Hence, good alignment is to

be expected. Small deviations from the experiment are visi-

ble above a TSR of 6.5, which is in alignment with Goupee

et al. (2015). According to them, this is a side effect probably

caused by the primary objective during the polar tuning pro-

cess, which was carried out with the objective to match the

experiment’s thrust behavior. The turbine’s operating point

during the experiment will be just below TSR 6, where good

agreement is present between both the codes and the exper-

iment. The thrust coefficient shows excellent agreement be-

tween QBlade, OpenFAST, and the experiment.

Figure 5 shows the thrust coefficient of the DTU 10 MW

RWT for two rotor speed sweeps at a just-below-rated con-

dition (test case 2.1, Fig. 5a) and well above (test case 2.2,

Fig. 5b). Inspecting the below-rated case first, it can be seen

that for lower TSRs, close agreement between the numerical

codes exists. In the region above a TSR of 10, which is rep-

resentative of cut-in and below-rated conditions, DeepLines

WindTM shows increasing deviation from OpenFAST and

QBlade. The latter two continue to show good agreement in

that region. In rated and below-rated conditions (TSR =8),

excellent agreement is present between all codes. In the sec-

ond sweep, where blades are collectively pitched to 15° and

above-rated wind speeds are present, DeepLines WindTM un-

derpredicts thrust compared to QBlade and OpenFAST in the

TSR range between 3 and 5. Below this region, good agree-

ment is achieved. The conditions analyzed later in this paper

will resemble states at a TSR approximately equal to 8 in

test case 2.1 and a TSR equal to 6 in test case 2.2. In both,

acceptable agreement is found in steady conditions.

4.4 Hydrodynamic loads

The isolated hydrodynamic (wave-only) test cases consid-

ered in the following amount to one regular wave and one

irregular wave case for each of the models. After the con-

firmation of the mooring loads and the decaying behavior

(see Sect. 4.1 and 4.2), the excitation by solely waves with-

out considering aerodynamic effects allows for the validation

of the hydrodynamic loads computed by QBlade. Thanks to

the distinct nature of the hydrodynamic modeling character-

istics of the three models, i.e., PFMD for OC5 and Softwind

and full Morison for Hexafloat, the implementation of hy-

drodynamic theory in QBlade can be validated in a general

sense. When using the PFMD approach in regular wave test

cases, the first-order excitation forces calculated via excita-

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 633

Table 3. Description of test cases 2.1 and 2.2. Isolated aerodynamic excitation with a constrained substructure at its neutral position.

Test Turbine Rotor Blade Wind Turbulence Length

case speed pitch speed [min]

[min−1]β u∞

[°] [m s−1]

2.1 OC5 MSWT 5.5–17.0 0.86° 12.91 5 % 20

2.1 DTU 10 MW RWT 3.0–13.0 0° 8 0 % until converged

2.2 OC5 MSWT 5.5–17.0 15° 21.19 5 % 20

2.2 DTU 10 MW RWT 2.5–9.0 15° 15 0 % until converged

Figure 4. OC5 turbine power (a) and thrust (b) coefficients for test case 2.1 (β=0.86°, u∞=12.91 m s−1) and test case 2.2 (β=15°,

u∞=21.19 m s−1).

Figure 5. DTU 10 MW RWT thrust coefficients for test case 2.1 (a) (β=0°, u∞=8.0 m s−1) and test case 2.2 (b) (β=15°, u∞=

15.0 m s−1).

tion force coefficients drive the floater response. In the full-

Morison case, the wave excitation is captured by the instanta-

neous wave elevation (Froude–Krylov force) combined with

diffraction effects captured with the MacCamy–Fuchs cor-

rection. As viscous effects are represented through the inclu-

sion of the drag term in the Morison equation in both ap-

proaches, additional damping and excitation effects are cap-

tured through drag forces (Lemmer et al., 2018). This ef-

fect is significant for models with structural members close

to mean sea level. In an irregular wave field, the floater re-

sponse to the linear wave excitation spectrum is validated.

In this subsection, the linear response along with non-linear

excitation due to slowly varying drift forces is validated on

the OC5 and Softwind models. In addition, an analysis of the

efficacy of the enhanced model in capturing non-linear exci-

tation that is implemented in QBlade can be compared to the

conventional approaches for both FOWTs. Furthermore, the

application of hydrodynamic loads at the instantaneous po-

sition (Hexafloat) can be validated. A detailed description of

the test cases can be found in Table 4.

4.4.1 Regular wave excitation

Figure 6 displays the response amplitude operators (RAOs)

of the OC5, Softwind, and Hexafloat FOWTs in the three

mainly excited motion DOFs. The RAO provides a quantita-

tive value of the FOWT’s response under regular wave exci-

tation. It can be understood as a transfer function that quanti-

fies the motion response for a given excitation. As is done by

Robertson et al. (2017), the RAO is defined as the ratio of the

amplitude of the rigid-body motion to the amplitude of the

wave frequency. RAOs are effective at validating the linear-

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634 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

Table 4. Description of test cases 3.1 and 3.2. Hydrodynamic excitation applied to the free-floating substructure without aerodynamic loads.

Test Model Wave Wave characteristics Length

case condition [min]

3.1 OC5 Regular wave Hs=9.41 m, Tp=14.3 s 20

3.1 Softwind Regular wave Hs=9 m, Tp=18 s 5

3.1 Hexafloat Regular wave Hs=9 m, Tp=18 s 10

3.2 OC5 Irregular wave Hs=7.1 m, Tp=12.1 s, JONSWAP 176

3.2 Softwind Irregular wave Hs=9.4 m, Tp=14 s, JONSWAP 60

3.2 Hexafloat Irregular wave Hs=9.4 m, Tp=14 s, JONSWAP 20

Figure 6. RAOs extracted from the time series corresponding to TC 3.1 for the (a) OC5, (b) Softwind, and (c) Hexafloat models.

wave-induced excitation of the model, which is the objec-

tive of this section. Across the three models, excellent agree-

ment is present. QBlade demonstrates good agreement with

the experiments and OpenFAST in the case of the OC5 and

Softwind platforms (Fig. 6a and b). When compared to the

large database from the OC5 collaboration, QBlade falls in

line with the superior-performing simulation codes (Robert-

son et al., 2017). For the Hexafloat model, good agreement

with DeepLines WindTM is found (Fig. 6c). The modifica-

tion of the near-sea-level transversal drag coefficient in the

enhanced model has a negligible influence on the surge and

pitch RAOs for OC5 and Softwind. However, in the heave

DOF there is a noticeable reduction in the corresponding

RAO. Both the decreased axial drag on the heave plates and

the additionally imposed linear damping affect this only to

a minor degree. The driving cause of the discrepancy is the

weighted sum displayed in Eq. (1) that now applies the high-

pass filter to the local velocities present at the heave plates

and weights the corresponding axial drag with 80 % in the

present model. With a wave frequency of 0.07 Hz in the OC5

test case 3.1, it lies above the cutoff frequency.

Because floating offshore wind turbines are coupled sys-

tems, non-linear responses may occur even under regular

wave excitation, especially since we compare them to ex-

perimental setups that can only approximate an ideal regu-

lar wave with only a single frequency component. Hence,

in addition to the RAOs, the analysis of several load sensor

time series can provide additional information. In Fig. 7, the

time series corresponding to the tower top force and the tower

base moment (fore–aft) of the OC5 model are shown along

with the fairlead tension. Interestingly, the tower-related sen-

sors show a reduced amplitude at the main wave frequency

in QBlade and OpenFAST compared to the experimental re-

sults. In contrast, the enhanced model (indicated with QB2)

with modified treatment of the heave plate viscous drag

shows better alignment with the experiment. Moreover, the

tower force and moment in the fore–aft direction show a

more irregular pattern compared to the fairlead tensions.

A plausible explanation could be the existence of multiple

wave components (e.g., through reflection) in the experi-

ment, which result in a wave field that includes additional

wave components into the dominant wave frequency that ex-

cite the tower modes. This phenomenon is only captured by

numerical codes when the wave elevation time series of the

experiment is used as a direct input.

4.4.2 Irregular wave excitation

Continuing with the isolated hydrodynamic excitation cases,

the complexity is increased by considering excitation from ir-

regular wave spectra in this subsection. Figure 8 displays the

two load-driving motion DOFs (surge and pitch) next to the

fore–aft tower base moment and fairlead tension of line 2. As

for the regular wave case, good visual agreement is present

in the dynamics between all compared instances. QBlade and

OpenFAST show almost identical results, while the experi-

ment shows differences mainly in the surge and, to a lesser

extent, the pitch DOF. A low-frequency component is present

in the time signal that matches the surge natural frequency of

the floater with approximately 0.01 Hz (see Table 2). With

the enhanced model, this low-frequency component of the

experiment (visible in Fig. 8a between 750 and 850s) is very

well captured, while the higher-frequency dynamics remain

accurate. The fore–aft tower base moment demonstrates a

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 635

Figure 7. OC5 model response to TC 3.1 – regular wave excitation in the (a) tower top force in x,(b) tower base fore–aft moment, (c) fairlead

tension in line 2, and (d) wave elevation.

Figure 8. OC5 model response to TC 3.2 – irregular wave excitation in (a) surge, (b) pitch, (c) tower base fore–aft moment, and (d) fairlead

tension in line 2.

higher-frequency component caused by an excitation of the

tower eigenmode. These are captured to varying degrees by

the two structural solvers of QBlade and OpenFAST and are

analyzed in more detail in the frequency domain. Besides

higher frequencies in the tower response, the wave excita-

tion frequency can be made out and displays good alignment

between the three numerical results and the experiment. The

tension in fairlead 2 correlates closely with the surge motion,

given that it provides the main restoring force. As a result,

the enhanced model shows closer alignment with the experi-

ment.

The evaluation of the full test case on a statistical basis

is presented in Fig. 9, where the PSD of selected sensors

along with their distribution visualized with box–whisker

plots is displayed. The PSD can be categorized into several

regions: linear wave excitation between 0.05 and 0.3 Hz, the

platform’s natural frequencies in surge (0.01Hz) and pitch

(0.03 Hz) below the wave frequency range, and the tower nat-

ural frequency at about 0.32–0.34Hz. Focusing on the plat-

form motions first, QBlade shows excellent agreement with

the reference results from the experiment and agrees with

OpenFAST regarding the linear wave excitation frequencies.

Below the wave frequency spectrum, peaks in the natural fre-

quency of each motion DOF are visible. Within these fre-

quencies, QBlade modestly predicts more energy compared

to OpenFAST, which can be attributed to the presence of

Wheeler stretching.

The experimental results, in contrast, show a much higher

energy within the natural frequencies of the surge DOF and,

to a lesser extent, the pitch DOF. As shown by the time se-

ries in Fig. 8a, the enhanced model achieves much closer

alignment with the experiment in the surge natural frequency,

while maintaining good agreement in the linear wave range.

In the pitch DOF, QBlade and OpenFAST show almost-

identical energy spectra, again underestimating the response

in the pitch natural frequency. This underestimation of low-

frequency response is visible in the load sensors as well. The

tower bottom and fairlead load PSDs both show a reduced

response in the pitch (tower base) or surge (fairlead 2) natu-

ral frequencies compared to the experiment. As was the case

in surge, the enhanced model demonstrates good agreement

with the experiment in the pitch natural frequency. The more

accurate representation of motion response in both DOFs

translates to more accurate tower base moments and fair-

lead estimations at the corresponding natural frequencies but

also an overprediction in the response within the fairlead ten-

sion at wave frequency. Above the linear wave excitation fre-

quency, the natural fore–aft frequency of the tower is evident

in the tower base moment PSD. Here, the different structural

representations of the tower between QBlade and OpenFAST

are evident. Even though both tools predict similar natural

frequencies (Perez-Becker et al., 2022), the shape of the peak

is resembled more closely in OpenFAST, while the excitation

frequency itself is matched better by QBlade.

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636 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

Figure 9. OC5 model response to TC 3.2 – irregular wave excitation. PSD of (a) surge motion, (b) pitch motion, (c) tower base fore–aft

moment, and (d) fairlead tension in line 2 and the corresponding box–whisker plots (e)–(h). The qualitative wave spectrum is displayed with

the transparent blue color in the background for reference.

For a statistical evaluation of the data, the platform mo-

tions and load sensors are shown in boxplots in the second

row of Fig. 9. The boxplots categorize the data into five quan-

tities: the 1st and 99th percentile thresholds (outer whiskers),

the 1st and 3rd quartiles (height of the box), and the me-

dian (black line inside the box). Outside the whiskers lie flier

values that are considered extreme outliers. First, the plat-

form motion is analyzed. The surge and pitch interquartile

ranges (IQRs) predicted by QBlade amount to a decrease of

28 % and 22 %, respectively, compared to the experiment.

This is an improvement compared to the respective Open-

FAST values of −32% in surge and −23% in pitch (Fig. 9a

and b). The median position of the experiment is matched

more closely by OpenFAST in surge and by QBlade in pitch.

As was noted before, both numerical tools did not capture

certain frequency responses that were visible in the experi-

mental data, mainly in surge but also in the pitch degree of

freedom. This low-frequency component leads to the larger

IQR and spread of the whiskers in the corresponding ex-

perimental boxplot and to a more skewed distribution in

surge. This is confirmed by the much closer alignment in

IQR achieved by the enhanced model, which deviates by

only 6 % increase in surge IQR compared to the experiment,

and a similarly skewed distribution, albeit with a slightly

shifted median position. Moreover, a 2 % increase in pitch

compared to the experiment can be seen. With regard to the

tower loads (Fig. 9g), a few systemic distinctions can be iden-

tified, indicating a similar distribution and good alignment of

data from QBlade, OpenFAST, and the experiment. Never-

theless, a slightly more accurate IQR is visible for the en-

hanced model. In the fairlead tension (Fig. 9h), the response

at the linear wave range dominates the IQR compared to the

non-linear peak as QBlade almost matches the experimental

IQR (−3 %), OpenFAST underpredicts it by 20 %, and the

enhanced model overestimates it by 16%.

To facilitate a more focused discussion, the time series

data of the Softwind model are omitted, as only very lim-

ited additional insight is contained. The main observations

are similar to the ones seen in Fig. 8, with more pronounced

long-period responses in the surge and pitch DOFs, which

translate into the response of the tower and mooring load sen-

sors. As is shown in the boxplot analysis, an offset in moor-

ing loads that amounts to an approximately 8% difference in

mean tension was present.

In Fig. 10, the Softwind model response to an equivalent

test case is analyzed with the same quantitative methods.

In the surge PSD (Fig. 10a), the response within the linear

wave spectrum is equivalent between the three results. In

the peak of the surge natural frequency, the formerly seen

shortcoming regarding non-linear excitation is also visible

in both simulation codes on this spar-type FOWT. QBlade

and OpenFAST demonstrate equivalent energy within this

frequency, indicating that Newman’s approximation imple-

mented in QBlade performs similarly to the implementa-

tion in OpenFAST. Furthermore, it implies a lesser influ-

ence of Wheeler stretching on this model. The correspond-

ing boxplot confirms this with no deviation in the IQR be-

tween QBlade and OpenFAST. Both tools underpredict the

IQR in surge by 29 % (Fig. 10e). Again, the increased non-

linear response seen in the experiment PSD is seemingly the

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 637

Figure 10. Softwind model response to TC 3.2 – irregular wave excitation. PSD of (a) surge motion, (b) pitch motion, (c) tower base fore–aft

moment, (d) fairlead tension in line 2, and the corresponding box–whisker plots (e)–(h). The qualitative wave spectrum is displayed with the

transparent blue color in the background for reference.

cause. Compared to the conventional models, the enhanced

model shows close alignment with the experimental peak at

the natural surge frequency and underestimates the IQR by

only 14 %. The median value is shifted slightly as a result

of different neutral positions in both numerical tools with re-

spect to the experiment. The pitch DOF (Fig. 10b) shows an

increased response within the linear frequency range in the

experiment. Here, OpenFAST displays closer agreement to

the reference compared to QBlade. However, it should be

noted that the amplitudes within the linear wave range are

small, and therefore small absolute deviations – of the order

of a 10th of a degree – cause this relatively large appear-

ing deviation between QBlade and OpenFAST that is seen

in the PSD. In the non-linear excitation below the wave fre-

quency range, QBlade and OpenFAST accurately determine

the excitation frequency. In contrast to what is observed in

Fig. 9f, the underprediction at the natural frequency of this

DOF is less severe for the spar-type platform. Since this plat-

form does not include heave plates, the filtered velocity treat-

ment in the enhanced model is not applicable. Nevertheless,

the modification of the near-surface transversal drag coef-

ficients demonstrates an improvement in the pitch DOF as

well, showing exact alignment with the experimental result.

The boxplot (Fig. 10f) shows good alignment among the

compared instances and highlights the occurrence of small

amplitudes in the pitch response. QBlade and OpenFAST un-

derestimate the IQR by 16 % and 10 %, respectively, while

the enhanced model underestimates it by 13 %. The tower

base loads (Fig. 10c and g) reproduce observations from the

pitch PSD to some degree, albeit with different relative mag-

nitudes between the non-linear and the linear frequency re-

sponse range, with the former barely visible. The enhanced

model matches the baseline QBlade result exactly. Close

agreement prevails in the boxplot with similar distribution

of data between the 1st and the 99th percentiles between the

compared results. Finally, the tension in fairlead 2 (Fig. 10d)

also shows a considerable response in the non-linear surge

natural frequency, directly related to the increased surge mo-

tion at that frequency. In the linear frequency range, the ex-

periment’s PSD reveals an increased response that is not fully

reproduced by the numerical tools. While it is difficult to

pinpoint a definite cause, it is likely to be due to an incor-

rect estimation of the hydrodynamic damping of the mooring

lines, which can be sea-state dependent. Interestingly, this

discrepancy does not translate to the response in the linear

wave range of the surge DOF (Fig. 10a). Given that the nat-

ural frequency lies significantly below the linear frequency

range of the wave field, the response in this range is pre-

dominantly driven by forcing and the system inertia (Chopra,

2014, p. 79). Thus, the effect of (mooring) stiffness on the

surge response in this range is negligible. In the correspond-

ing box–whisker plot in Fig. 10h, QBlade overestimates the

median tension by 6.3% and OpenFAST by 5 % compared

to the experiment, while the enhanced model shows an im-

provement in the IQR by about 15% compared to QBlade

and OpenFAST.

To conclude the isolated wave excitation test cases, the

Hexafloat model is analyzed. As for the Softwind model,

the time series result is only briefly summarized. The mo-

tion sensors demonstrate very close alignment with regard

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638 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

to the dynamic response. A mean offset in the surge posi-

tion of approximately 0.75 m upstream is visible in QBlade,

which can be attributed to minor differences in the mooring

tension. Notably, the amplitudes of the pitch motion were

slightly increased in QBlade, which causes a minor increase

in the tower base moment response as a result.

Figure 11 illustrates a high degree of similarity between

the responses of both tools in the degrees of freedom within

the linear excitation frequency range of the wave spectrum,

as well as in the non-linear response within the surge and

pitch natural frequencies below the wave spectrum (Fig. 11a

and b). Notably, no QTFs were available for this model, pro-

viding an opportunity to validate the weak, non-linear exci-

tation caused by the application of hydrodynamic loads at

the instantaneous floater position combined with kinematic

stretching. Both the tower fore–aft moment and fairlead ten-

sion in line 2 show good agreement in the excited frequen-

cies, with QBlade predicting moderately higher peaks at the

relevant frequencies (Fig. 11c and d). This can be attributed

to a slightly larger surge and pitch response within the lin-

ear wave spectrum, visible in the corresponding PSDs. The

boxplot results show the effect of the increased response

throughout the linear frequency range in QBlade: in surge,

the IQR is 14 % larger in QBlade, while the median is shifted

in a negative xdirection (Fig. 11e). The platform pitch and

tower base moment data are in good agreement with regard

to their median value. Their IQR range is again larger in

QBlade (Fig. 11f and g) with 19 % increased spread in pitch

that translates to a 10 % increase in the tower base moment

spread. Finally, the boxplot of the tension in line 2 (Fig. 11h)

displays a mirrored pattern compared to the surge boxplot,

indicating their close dependency. QBlade predicts a 30 %

larger IQR compared to DeepLines WindTM.

4.5 Combined aero- and hydrodynamic loads

The final test case, which concludes this verification and val-

idation study, combines the fully coupled aero-servo-hydro-

elastic dynamics exhibited by a floating offshore wind tur-

bine throughout its lifetime. As before, we perform qualita-

tive analysis of cut-out time series for one exemplary model,

in this case Softwind, at the beginning of this section. Sub-

sequently, quantitative statistics are used for each model to

assess the predicted responses by QBlade and to compare

them to the numerical counterparts and experimental refer-

ence cases. Table 5 showcases the three test cases considered,

one for each FOWT assembly. To cover three different opera-

tional states, varied environmental conditions are selected for

each FOWT. The Softwind model is simulated in conditions

beyond the rated regime, where the controller constantly ac-

tuates the blade pitch to not exceed rated power output. Con-

versely, the simulation of the OC5 model approximates con-

ditions that are near to rated power. This is done with a con-

stant prescribed value for the blade pitch angle and rotor

speed (as was done in the OC5 collaboration). In the case of

the Hexafloat model, below-rated conditions are discussed.

Here, the controller gradually adjusts the rotational speed to

operate at the optimal tip speed ratio to maximize power gen-

eration. For the servo control of the DTU 10 MW turbine atop

the Softwind platform, the DTU baseline controller (Hansen

and Henriksen, 2013) is used, replicating conditions from the

experiment. The control parameters correspond to those of

the reference turbine, except for the proportional and integral

gains of the pitch controller and the linear and quadratic aero-

dynamic gain scheduling coefficients. These were adjusted

to prevent negative damping that originates from the cou-

pling between blade pitch actuation and the floater pitching

motion. The PI parameters of the OO-Star 10 MW FWT are

used, since the pitch natural frequency between both the OO-

Star and the Softwind platforms is nearly identical (Yu et al.,

2018). In the case of the Hexafloat model, the ROSCO v2.4.1

controller (NREL, 2021) was selected due to its ability to

include a velocity feedback damping loop designed to re-

duce pitching motion and thereby increase stability of the

floating substructure. Unfortunately, this feature had to be

disabled for this code-to-code comparison after difficulties

were found in the communication between the ROSCO con-

troller and DeepLines WindTM. Leaving this feature active

in QBlade alone would have impeded a consistent compari-

son. Therefore, the controller gains were de-rated to prevent

negative damping effects instead.

The Softwind model is analyzed at above-rated conditions,

with a mean wind speed of 18 m s−1that requires contin-

uous blade pitch actuation by the DTU wind turbine con-

troller. The blade pitch actuation is based on the power out-

put of the wind turbine, which depends on the velocity in

the rotor plane. Hence, blade pitch actuation depends on the

motion-induced velocities and the wake-induced velocities

in the rotor plane of the system. Considering this, the wake

model (lifting line vs. BEM) and the hydrodynamic model

(buoyancy modeling, wave kinematics) in a given simulation

collectively influence the pitch actuation process and sub-

sequently the overall system dynamics. Figure 12 shows a

cut-out of the time series displaying the same sensors that

were chosen in TC 3.2 to analyze the system response of

the Softwind model. What stands out is that even after more

than 10 min into the time series, good qualitative agreement

between the three compared results is present. The surge

time trace demonstrates a long-period cycle at the natural

frequency of this DOF. OpenFAST demonstrates a slightly

closer agreement with the experiment in the surge response

compared to QBlade, which only slightly underestimates the

surge amplitude. This is unsurprising as the SIL experiment

and OpenFAST both utilize the same aerodynamic models.

The enhanced model, in contrast to the results shown in

Fig. 8a without wind loading, shows only minor deviation

from the baseline QBlade result. The aerodynamic thrust

combined with the mean drift force causes a mean surge dis-

placement around 0.5 m that is accurately reflected in the nu-

merical tools. The mean pitch angle enforced by the thrust

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 639

Figure 11. Hexafloat model response to TC 3.2 – irregular wave excitation. PSD of (a) surge motion, (b) pitch motion, (c) tower base

fore–aft moment, (d) fairlead tension in line 2, and the corresponding box–whisker plots (e)–(h). The qualitative wave spectrum is displayed

with the transparent blue color in the background for reference.

Figure 12. Softwind model motion and load response to TC 4.1 – combined irregular wave and wind excitation in (a) surge CoG motion,

(b) pitch motion, (c) tower base fore–aft moment, and (d) fairlead tension in line 2.

force amounts to approximately 2°. The pitch response is

very similar in all three numerical models, showing good

alignment with the experiment. As a result, the tower base

moment is in good alignment too, indicating that the aero-

dynamic thrust predicted by the LLFVW method is similar

to the one of the SIL experiment (AeroDyn v14) in unsteady

conditions as well. Given that the mean TSR of the test cases

is 5, such close agreement could be expected from Fig. 5. The

observed offset in the fairlead tension to the experiment that

was pointed out in the Softwind response to TCs 3.1 and 3.2

is reduced once aerodynamic thrust is included. The exper-

iment validates the alignment between QBlade and Open-

FAST, showing only slightly lower tensions. Regarding the

dynamics, good agreement is found.

Continuing the analysis with Fig. 13, a severe response

within the natural frequencies of the different degrees of mo-

tion becomes evident. In fact, the response in the surge nat-

ural frequency (Fig. 13a) at around 0.01Hz dominates the

spectrum to an extent that the linear wave response is only

observable in the zoomed-in frame. In addition to the wave

spectrum, the scaled wind spectrum is displayed as an indica-

tor of the excited frequencies by the turbulent wind field. The

peak of the wind spectrum aligns with the frequency at Soft-

wind’s natural frequency. The energy in that frequency is pre-

dicted slightly more accurately by the enhanced model com-

pared to the baseline QBlade model. In the magnified frame,

the surge response shows excellent agreement between the

numerical tools and the experiment. The corresponding box-

plot for the surge direction (Fig. 13e) reveals good alignment

between QBlade and the experiment regarding the median

and IQR at −11 % difference. The OpenFAST result is off-

set towards a larger surge displacement and yields an IQR of

−16 %. No significant improvement of the enhanced model

can be found with an IQR of −13 %. Figure 13b and f shows

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640 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

Table 5. Description of test case 4.1. Combined aero-hydrodynamic-servo-dynamic conditions applied to the FOWT models.

Test Model Wind Control Wave characteristics Length

case condition [min]

[m s−1]

4.1 Softwind 18, TI =17 % DTU controller Hs=5.8 m, Tp=11 s, 60

Bretschneider

4.1 OC5 12.91, TI =5 % pitch =°Hs=7.1 m, Tp=12.1 s 176

rotor speed =12.1 min−1JONSWAP

4.1 Hexafloat 7.0, TI =32.6 % ROSCO v2.4.1 Hs=6.0 m, Tp=12.0 s, 20

JONSWAP

Figure 13. Softwind response to TC 4.1 – irregular wave and wind excitation. PSD of the (a) surge CoG motion, (b) pitch motion, (c) tower

base fore–aft moment, and (d) fairlead tension in line 2 and the corresponding box–whisker plots (e)–(h). The qualitative wave (blue) and

wind (red) spectra are displayed with the transparent color in the background for reference.

the PSD and boxplot corresponding to the pitch DOF. The

former demonstrates only minor excitation within the linear

wave frequency range, in contrast to a strong response in the

pitch natural frequency. As continuously stated throughout

this work, this excitation frequency matches the experiment

response albeit at a reduced scale. This leads to an increased

spread of the IQR of the box corresponding to the experiment

compared to QBlade (−28 %) and OpenFAST (−18 %). The

enhanced model matches the baseline QBlade result exactly.

The tower base moment (Fig. 13c and g), being closely re-

lated to the pitch motion of the FOWT system, matches the

observations for the pitch sensor with more aligned IQRs be-

tween QBlade and OpenFAST. Excitation peaks correspond-

ing to the natural frequencies of the coupled surge and pitch

DOFs can be seen in the PSD of the tension at the delta

connection point of the Softwind platform (Fig. 13d). The

boxplots of the mooring tension yet again show the consis-

tent difference in the mooring tensions that was observed

throughout the analysis of the Softwind platform. To sum up

this load case, it can be stated that, compared to TC 3.2 in

Fig. 10, the enhanced model only leads to modest improve-

ment with regard to the motion and load responses when

wind loads were included.

The corresponding PSD and boxplot of the OC5 model for

TC 4.1 are shown in Fig. 14. The PSD can still be categorized

into the system’s natural frequencies, the linear wave fre-

quency range, and the range above, which is most visible in

the tower loads. Comparing to the PSD from TC 3.2 in Fig. 9,

an outstanding effect is the damping visible in the surge and

pitch DOFs (Fig. 14a and b) when aerodynamic loads are in-

cluded. The aerodynamic damping comes into effect by an

increased thrust force that acts on the tower top when the

relative wind velocity in the rotor plane is increased during

forward motion and reduced during backwards motion. This

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 641

Figure 14. OC5 model response to TC 4.1 – irregular wave and wind excitation. PSD of the (a) surge motion, (b) pitch motion, (c) tower

base fore–aft moment, and (d) fairlead tension in line 2 and the corresponding box–whisker plots (e)–(h). The qualitative wave (blue) and

wind (red) spectra are displayed with the transparent color in the background for reference.

leads to a more dampened response within the resonant fre-

quencies of the floater. Thereby, the peak in the surge natural

frequency is reduced by about 40%. In contrast, the response

within the linear wave range is not changed. As was the case

for the Softwind model, when compared to the wave-only

test case, the enhanced model shows only slight improvement

compared to the baseline QBlade and OpenFAST models.

This can be explained by an overall more constrained FOWT

as soon as wind is included compared to only hydrodynamic

excitation. The aerodynamic thrust force and the increased

mooring force that result from a shift in the mean surge posi-

tion dampen the oscillation at the system’s natural frequency.

As a result of this, the approach of increasing the near-surface

drag coefficient that is followed by the enhanced method is

less effective. The impact of aerodynamics also becomes vis-

ible in the boxplot (Fig. 14e), where the difference in the in-

terquartile range corresponding to the experiment in surge

compared to the one seen for the numerical codes is reduced

(−20 % in QBlade, −23 % in OpenFAST). The smaller rel-

ative difference between them within the oscillation in natu-

ral frequency leads to a closer alignment in data distribution.

The same trend can be observed in the pitch PSD (Fig. 14b)

with a reduction in the energy within the pitch natural fre-

quency of close to 50% compared to TC 3.2. The linear

response at higher frequencies remains largely unchanged.

QBlade and OpenFAST show good agreement with one an-

other, with a slight underestimation of the linear response

visible in the QBlade results. The response in the pitch nat-

ural period is underestimated by both numerical tools. Com-

pared to them, the enhanced model demonstrates significant

improvement in the pitch DOF. Looking at Fig. 14f, the rel-

ative differences in the quantile ranges between the exper-

iment and the numerical tools are similar to the ones ob-

served for wave-only excitation, despite the reduced relative

difference in the pitch motion at low frequencies (QBlade

−23 %, OpenFAST −20%, and enhanced model −15 %).

QBlade shows good alignment with the median position of

the experiment, while OpenFAST exhibits a slight underesti-

mation of this position. Moving on to the tower base moment

(Fig. 14c), two peaks lie within the linear wave spectrum, one

at 0.07Hz, aligning with the dominant wave frequency, and

a larger one at 0.14 Hz that does not. According to Robertson

et al. (2017), these two peaks inside the linear wave spec-

trum are caused by the motion of the structure with respect

to the wave. QBlade and OpenFAST capture both peaks sim-

ilarly, but both underestimate the response compared to the

experiment. The underestimation of the response in this fre-

quency is in line with the participants of the OC5 collabora-

tion that deployed a PFMD approach. Furthermore, the tower

fore–aft moment PSD shows peaks in the pitch natural fre-

quency and in the tower fore–aft natural frequency. Here, in

contrast to Fig. 9, the shape of the peak predicted by QBlade

aligns closely with the OC5 experiment, while OpenFAST

overestimates the response at an accurate tower frequency.

Even though the enhanced model improves the estimation of

the peak in the pitch natural frequency, its predicted IQR is

with −20 % similar to the other numerical models (−23 %

for QBlade and −18 % for OpenFAST). This is a result of

the increased response at 0.14Hz seen only in the experiment

(Fig. 14g). The tension within fairlead 2 (Fig. 14d and h) re-

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642 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

flects the increased loads on the mooring system caused by

the aerodynamic loads compared to TC 3.2. Good alignment

is present within the linear frequency range. The increased

response of the experimental model in the surge natural pe-

riod is reflected again in the tension of this line.

The final case that is discussed in this study is the com-

bined wind and wave excitation case for the Hexafloat model.

As is shown in Table 5, below-rated conditions are assumed.

Consequently, the ROSCO v2.4.1 controller follows the ob-

jective of maximizing power by adjusting rotational speed

to operate at the optimal TSR of 8.06. According to Fig. 5,

the aerodynamic models of DeepLines WindTM and QBlade

demonstrate close agreement with regard to the thrust coeffi-

cient in this condition. Hence, similar responses on the mo-

tion DOFs and loads are to be expected with similarly behav-

ing hydrodynamic models. A time series comparison of the

motion and load sensors (not shown here for brevity) con-

firms this with very good agreement between both simulation

tools in the surge and pitch degrees of freedom. In the plat-

form pitch response, QBlade demonstrates slightly increased

amplitudes in frequencies that appeared to be within the lin-

ear frequency range of the wave field.

The PSDs in Fig. 15 are dominated by the resonant re-

sponse in the natural surge and pitch frequencies. The re-

sponse within the linear frequency range only becomes vis-

ible within the magnified cut-outs, where good alignment

in the time series is confirmed. In contrast to the other two

FOWT models that rely on a PFMD approach, the buoyancy

calculation at the instantaneous position and submerged vol-

ume, the viscous excitation, and the MacCamy–Fuchs cor-

rection model the wave excitation in this Morison represen-

tation. The boxplots show a closely matched distribution of

the data, with the most prominent difference being visible in

the surge DOF and in the 99 % quantile of the fairlead ten-

sion in line 2 (Fig. 15e and h). However, this is not caused

by hydrodynamic treatment but is due to the coupled effects

that the servo-dynamics have on the overall response of the

turbine, as is discussed next.

The small deviation described above in the floater pitch

response can partially be traced back to the rotational speed

that is controlled by the ROSCO controller. Figure 16 dis-

plays for reference the floater pitch along with the rotational

speed which contains a high-frequency component in the

QBlade results that is not captured in DeepLines WindTM

(Fig. 16a and b).

As a result of the small spikes visible in the rotational

speed time series, the thrust force will follow this behavior in

QBlade and thus causes the slightly increased pitch motion

of the floating platform. Following the causal chain further,

this deviation is visible in the generator torque (Fig. 16c),

where DeepLines WindTM predicts a calmer torque control

response compared to QBlade. Since the turbine is operat-

ing in a below-rated condition, the blade pitch is only acti-

vated temporarily when the rotor speed briefly exceeds rated

speed. One example of this can be seen at 1350s of simula-

tion time, where the increase in rotor speed causes the con-

troller to pitch the blades (Fig. 16d). The controller response

in QBlade is more dynamic, and it triggers the controller to

activate the blade pitch at a few, much shorter instances. Even

though the differences in drivetrain dynamics and the follow-

ing pitch controller actuation seem to have only a minor in-

fluence on overall dynamics, this picture changes drastically

when the FOWT operates in regimes with above-rated wind

speed. Figure 17 shows an example of this. The turbulent

wind in this figure contains velocities above rated between

700 and 1100 s. Here, the rotational speed once again fluctu-

ates more in QBlade compared to DeepLines WindTM, and

this leads to larger blade pitch actuation (Fig. 17a and b).

The drastic influence on system dynamics is visible in the

surge and pitch DOFs. The QBlade model undergoes much

larger oscillations with amplitudes of 5.5 m in surge and 4.5°

in pitch compared to 1.5 m and 1.2° in DeepLines WindTM.

When the wind speed dips below rated and the blade pitch

actuation is not required (above 1100s), the platform surge

and pitch responses quickly align (Fig. 16c and d).

We do not yet fully understand the large differences seen

for this model when above-rated conditions are present, es-

pecially given the accuracy of the QBlade results compared

to OpenFAST and the Softwind experiment in above-rated

conditions, which also include a controller. Further research

must be carried out to better understand this phenomenon and

isolate whether it emerges from differences between QBlade

and DeepLines WindTM in the aerodynamic treatment or the

controller interface.

5 Conclusion and outlook

In this work, the hydrodynamic module QBlade-Ocean, de-

veloped to expand the capabilities of the wind turbine sim-

ulation tool QBlade for offshore simulations, is verified and

validated on three floating offshore wind turbine models. The

three models encompass a variety of different substructure

concepts. They are the semi-submersible OC5, Softwind, and

Hexafloat FOWTs. In the case of the former two, an exper-

imental campaign was used to validate the results produced

within QBlade. Furthermore, equivalent models were built in

OpenFAST to verify the results with state-of-the-art code. In

the case of the Hexafloat model, a code-to-code comparison

with the simulation tool DeepLines WindTM was carried out.

The OC5 and Softwind models were simulated using poten-

tial flow theory combined with Morison drag, whereas the

Hexafloat model was simulated using a strip-theory-based

full-Morison approach. Additionally, an enhanced method to

improve the prediction of excitation within the resonant fre-

quencies developed by Wang et al. (2022) has been tested

in various conditions, including turbulent wind and irregu-

lar waves. The influence of the wave stretching type on the

method’s efficacy and a parameter study indicating its sensi-

tivity have been shown.

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 643

Figure 15. Hexafloat model response to TC 4.1 – irregular wave and wind excitation. PSD of the (a) surge CoG motion, (b) pitch motion,

(c) tower base fore–aft moment, and (d) fairlead tension in line 2 and the corresponding box–whisker plots (e)–(h). The qualitative wave

(blue) and wind (red) spectra are displayed with the transparent color in the background for reference.

Figure 16. Hexafloat model controller actuation (ROSCO v2.4.1)

– combined irregular wave and wind excitation: (a) platform

pitch, (b) rotor speed, (c) generator torque (high-speed shaft), and

(d) blade pitch.

In the decay tests, both QBlade and OpenFAST aligned

well with the experimental results, thus validating the imple-

mentation of the radiation forces and Morison drag. As is

common practice, both tools required minor tuning of damp-

ing and stiffness parameters to fully align with the reference.

Regular wave excitation cases validated the implemen-

tation of diffraction effects and Froude–Krylov forces. In

QBlade they can be modeled either through potential flow

Figure 17. Hexafloat model controller actuation and motion re-

sponse – combined irregular wave and wind excitation: (a) rotor

speed, (b) blade pitch, (c) platform surge, and (d) platform pitch.

Wind with 11.4 m s−1, 15 % TI, and wave field with JONSWAP

spectrum with H=7.7 m and T=12.4 s.

theory (OC5 and Softwind) or through the use of the full-

Morison equation with the MacCamy–Fuchs correction com-

bined with explicitly calculating the buoyancy based on the

instantaneous submerged volume (Hexafloat). The RAOs

in relation to the reference experimental results and to

DeepLines WindTM validated and verified both approaches

in QBlade. The observed differences in the experiments were

comparable to those of OpenFAST and amounted to less than

https://doi.org/10.5194/wes-9-623-2024 Wind Energ. Sci., 9, 623–649, 2024

644 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

3 % in surge, 6% in heave, and 12 % in pitch. The enhanced

model showed a 50 % reduction in the heave RAO of the OC5

model, revealing shortcomings in its applicability in regular

wave regimes. However, it was the only one to capture non-

linear excitation effects from the regular wave field generated

during the experiment and accurately predicted its influence

on the tower load amplitudes at regular wave frequency.

In the next step, QBlade’s ability to capture non-linear

excitation and more complex system dynamics was veri-

fied with irregular wave excitation. For the FOWTs modeled

with PFMD, sum and difference frequency quadratic trans-

fer functions (OC5) and Newman’s approximation (Soft-

wind) were applied to capture the mean drift and non-linear

forces. For the full-Morison treatment, weak, non-linear ex-

citation was calculated through the application of hydrody-

namic loads at the instantaneous position. The analysis of

the conventional numerical models in the spectral space con-

firmed the observations made throughout the OC5 and OC6

collaborations; non-linear excitation frequencies were cap-

tured accurately but with a considerably dampened response

compared to experiments. QBlade underestimated the IQR in

surge and pitch by 28 % and 22 %, respectively – a slight im-

provement compared to OpenFAST (32 % and 23 %), which

can be attributed to the Wheeler stretching method. The main

cause for this deviation lies in the underprediction of the non-

linear response, which is significantly improved with the en-

hanced model. Consequently, the IQR in surge and pitch is

overpredicted by only 6 % and 2 %, respectively. The anal-

ysis of the PSDs for the Softwind model showed similar

responses between the QBlade and OpenFAST models in

the linear wave frequency range for platform motions and

loads. Again, the enhanced model demonstrated significant

improvements in the non-linear motion response in the surge

DOF and the corresponding load sensors. Specifically, the

enhanced model resulted in a 14% underestimation of the

surge IQR, compared to the 29 % underestimation observed

for the baseline QBlade and OpenFAST models. Compared

to the OC5 semi-submersible, both baseline models demon-

strated better accuracy in capturing the non-linear pitch re-

sponse for the Softwind spar. Nevertheless, the improved

model still demonstrated better alignment with the experi-

ment. The comparison to DeepLines WindTM, based on the

Hexafloat model, showed good accordance in the frequency

domain, with modestly increased energy within the several

peaks predicted by QBlade. In terms of interquartile ranges,

this led to an increase in the spread by 14 % in surge and

19 % in pitch motions.

The final test case validated and verified the fully coupled

aero-hydro-servo-elastic response predicted by QBlade for

the three FOWTs. The discrepancy within the non-linear ex-

citation in the natural frequencies of the PFMD models con-

tinued to be noticeable for the conventional methods, albeit

less significantly due to aerodynamic damping. QBlade pro-

duced improvements of 3 and 5 percentage points over Open-

FAST in the surge interquartile range for the OC5 and Soft-

wind models, respectively, due to Wheeler stretching. In con-

trast to the wave-only cases, the enhanced model produced

only modest improvements over the baseline QBlade model

in the surge DOF that amounted to 4 percentage points for the

OC5 platform and no improvement for Softwind. The cause

of the reduced efficacy in surge is the constrained floater

movement under wind loads, which leads to reduced viscous

excitation. However, in the pitch DOF, the treatment of the

axial heave plate drag remained effective with a 9 percentage

point improvement concerning the IQR of the OC5 platform

over the baseline model. The code-to-code comparison on

Hexafloat demonstrated the influence of minor differences in

the controller actuation on the overall system dynamics. It

was found that the combination of an extremely slack moor-

ing system, a minor increase in the motion response to the

linear wave spectrum in QBlade, and a more inert behavior

of the drivetrain dynamics in DeepLines WindTM led to dif-

ferences in the dynamics of the platform pitch. These differ-

ences between QBlade and DeepLines WindTM were vastly

amplified when operating conditions above-rated wind speed

were analyzed. Here, amplitudes in the substructure pitch os-

cillations of up to 4.5° were seen in QBlade compared to 1.2°

in DeepLines WindTM.

Concluding this study, the simulation suite QBlade was

expanded by a hydrodynamic module called QBlade-Ocean.

The flexible framework of QBlade allows for the combina-

tion of different modeling approaches. The PFMD and full-

Morison approaches were validated with two experimental

campaigns and verified against the state-of-the-art simula-

tion tools OpenFAST and DeepLines WindTM. The results of

QBlade-Ocean showed good agreement with both tools and

the experimental results. The largest differences that were

seen were related to the application of distinct aerodynamic

and structural models on the Hexafloat FOWT. In the case

of QBlade, these models have been validated in previous

studies. Since a floating offshore wind turbine is a complex,

tightly coupled multi-disciplinary system, differences in the

modeling approaches will influence the overall dynamics and

loads of the system. Moreover, the inclusion of an enhanced

hydrodynamic model, developed by Wang et al. (2022), to

capture viscous excitation improved the prediction of non-

linear floater response significantly under hydrodynamic ex-

citation. However, when aerodynamic loads were included,

the enhanced model demonstrated less effectiveness.

In Part 2 of this work (Papi et al., 2023), a quantita-

tive analysis to determine the effects of using higher-fidelity

modeling methods (LLFVW, structural dynamics) during

FOWT simulations on design driving loads during realistic

environmental conditions is carried out. Future work will

focus on the integration of QBlade with optimization algo-

rithms, where the increased fidelity in the structural and aero-

dynamic methods could be leveraged to facilitate the devel-

opment of more accurate surrogate models, which in turn can

be included efficiently in optimization problems.

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R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1 645

Appendix A: Nomenclature

BEM Blade element momentum theory

DOF Degree of freedom

DLW DeepLines WindTM

Ext stretch Extrapolation stretching

FEA Finite element analysis

FOWT Floating offshore wind turbine

GUI Graphical user interface

HST High static thrust

LLFVW Lifting-line free vortex wake

MARIN Maritime Research Institute Netherlands

MSWT MARIN stock wind turbine

NREL National Renewable Energy Laboratory

PFMD Potential flow approach with the addition of Morison drag

PSD Power spectral density

QTF Quadratic transfer function

RNA Rotor-nacelle assembly

RWT Research wind turbine

SIL Software in the loop

TSR Tip speed ratio

TUB Technische Universität Berlin

Whe stretch Wheeler stretching

Figure A1. Influence of kinematic wave stretching on the OC5 model motion response in the surge DOF. JONSWAP spectrum with Hs=

8.1 m and Tp=12.7 s. Panel (a) shows an excerpt of the time series, (b) the non-linear response, and (c) the response within the linear wave

frequency range.

Figure A2. Influence of the (a) axial drag coefficient, (b) cutoff frequency, and (c) weight factor on the integral of the non-linear PSD peak

in the heave and pitch DOFs of the OC5 model (integral from 0–0.066Hz).

https://doi.org/10.5194/wes-9-623-2024 Wind Energ. Sci., 9, 623–649, 2024

646 R. Behrens de Luna et al.: Quantifying the impact of modeling fidelity on different substructure concepts – Part 1

Figure A3. High-pass filter, as defined by Wang et al. (2022), applied on a velocity signal in a global zdirection. Cutoff frequency fc=

0.04 Hz. Displayed is the time signal (a) and the corresponding PSD (b).

Code and data availability. The three QBlade models that are

used in this study can be accessed under the following DOIs:

i. OC5 – https://doi.org/10.5281/zenodo.10634206 (Behrens

de Luna, 2024),

ii. Softwind – https://doi.org/10.5281/zenodo.10634540 (Perez-

Becker et al., 2024), and

iii. Hexafloat – https://doi.org/10.5281/zenodo.10634616 (Perez-

Becker and Behrens de Luna, 2024).

Author contributions. All authors contributed to this work. In

particular, the numerical models in QBlade, OpenFAST, and

DeepLines WindTM were built and simulated by the groups at TUB,

the University of Florence, and MLD, respectively. FB provided

the necessary information to accurately build and tune the Softwind

FOWT and offered consultation on the interpretation of the corre-

sponding experimental results.

Competing interests. At least one of the (co-)authors is a mem-

ber of the editorial board of Wind Energy Science. The peer-review

process was guided by an independent editor, and the authors also

have no other competing interests to declare.

Disclaimer. Publisher’s note: Copernicus Publications remains

neutral with regard to jurisdictional claims made in the text, pub-

lished maps, institutional affiliations, or any other geographical rep-

resentation in this paper. While Copernicus Publications makes ev-

ery effort to include appropriate place names, the final responsibility

lies with the authors.

Acknowledgements. This work has received funding from the

European Union’s Horizon 2020 research and innovation program

under grant agreement no. 101007142.

Financial support. This research has been supported by the

Horizon 2020 (grant no. 101007142).

This open-access publication was funded

by Technische Universität Berlin.

Review statement. This paper was edited by Erin Bachynski-

Poli´

c and reviewed by three anonymous referees.

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