Validation of a panel method with full-scale FOWT measurements and verification with engineering models

The present paper gives insights into the verification of different models of the Floatgen demonstrator by BW Ideol. This floating offshore wind turbine (FOWT) is based on a barge type-floater with moonpool. The moonpool shall dampen the platform’s motion and is challenging to model due to the increased complexity of the hydrodynamic behaviour. For the verification purposes, the results of two engineering methods (OrcaFlex, OpenFAST) equipped with frequency-dependent hydrodynamic solver and the nonlinear time-domain boundary element method panMARE are compared. The OrcaFlex model designed by BW Ideol is regarded as a reference because of a preceding calibration with measurement data. All models show fairly good agreement in most cases. Only in heave there are significant differences between engineering and the nonlinear models which is caused by different modelling of the moonpool hydrodynamics. In addition, a hybrid simulation approach with prescribed motion and constrained wind field based on motion sensors and LIDAR measurements on the Floatgen demonstrator was applied for an aerodynamic and load validation of panMARE. The validation shows good agreement based on time-domain comparison regarding the tower top loads and turbine operation.


Introduction
The ongoing development of offshore wind energy towards floating systems requires comprehensive modelling capabilities to estimate the motion behaviour and loads.Engineering methods based on bladeelement-momentum-theory (BEMT) have been extended to cover the new field of floating foundations, e.g.OpenFAST [1].In addition to others, frequency-domain based methods were often used to estimate the hydrodynamic forces on the platform [2,3].These methods rely on frequency-dependent coefficients which are calculated in advance on the basis of linearized boundary element methods (BEM).Additional drag components are usually added to consider viscous effects not captured by BEM.Overall these engineering methods are fast and reliable tools in the design process of a floating offshore wind turbine.In neither method, aerodynamic BEMT and hydrodynamics based on linearized BEM, is the flow field around the structure available.Only the loads on blade section respectively the total platform hull are determined.In contrary, a nonlinear BEM method resolves the flow field in time-domain.This approach can be applied on both -the aerodynamic flow around the wind turbine rotor and the hydrodynamic problem of the floating platform in waves.It enables an analysis of the flow field around the structure and is capable of estimating the pressure distribution on the blade and the hull of the floating structure.On the aerodynamic side it captures the time history of the wake due to rotor motions and changes of the incoming wind.On the hydrodynamic side it is capable of estimating the instantaneous wetted surface in the presence of waves and change of floating condition.This is accompanied by an increased computational effort, but allows a compromise between computationally expensive RANS simulations and simplified engineering models.The present study gives an insight into the verification of the nonlinear BEM panMARE [4] with different engineering methods.The floatgen demonstrator from BW Ideol is used as a case study.Furthermore, full-scale measurement data of the tower top loads and turbine operation are considered for the validation of a novel hybrid simulation approach, where the platform motions and incoming wind are prescribed specified based on on-site measurement data.

Simulation methods
Results of three different numerical models of the Floatgen platform by BW Ideol were employed in the verification study.Two of them were engineering tools, OpenFAST [1] used by University of Stuttgart (USTUTT) and OrcaFlex [5] coupled with OpenFAST used by BW IDEOL.These models were based on frequency-dependent hydrodynamic coefficients and had a related underlying theory for time-domain simulations.Since the theory is extensively documented in numerous publications, it is not described in further detail.The model of BW Ideol was applied in hydrodynamic cases only and is therefore simply named OrcaFlex.The third software was panMARE developed by TUHH, based on a time-domain BEM.This method is less known and described briefly below.

Time-domain BEM -panMARE
The nonlinear boundary element method panMARE was initially designed to simulate flow fields around ship propellers [6,7].Since then it has been further developed to be used for various offshore applications, including wave-body interaction [8], landing manoeuvres of service vessels on monopiles [9], and underwater radiated noise [10,11].Another growing field of application is floating wind turbines [12,13,14,15], including validation within the OC6 project [16,17].The core of panMARE is a three-dimensional low-order panel method which is extended by various supplementing techniques.In case of a floating wind turbine, two simulation domains are required: the aerodynamic flow around the rotor and tower and the hydrodynamic flow around the platform.The flow field is solved based on potential theory, hence an incompressible, irrotational and inviscid flow is assumed.It is then possible to describe the velocity field by a potential function Φ.The continuity equation can then be reduced to the Laplace equation: (1) The induced potential Φ ind represents the influence of all panels in the domain.The wave potential Φ wave is only present in the hydrodynamic domain.The absolute fluid velocity results from the gradient of the potential plus an additional wind velocity within the aerodynamic domain: Panels on platform, free surface, tower and rotor have source strength  and doublet strength .The potential inside the closed bodies is assumed to be Φ = 0.In this case, Dirichlet boundary condition can be applied on the body panel centre to obtain two conditions for each panel: with all doublet panels dp, all source panels sp, the panel normal  ⃗⃗ pointing into the fluid, distance  between the evaluation point and the panel centre, the panel area  and the panel motion velocity  ⃗ m .It is now possible to obtain a closed set of linear equations, which can be solved to calculate the doublet strength of each panel, see [18, p. 237-249].The pressure  on each panel can then be calculated using Bernoulli's equation for the unsteady potential flow with the gravitational acceleration  and the density .
Rotor aerodynamics: In the aerodynamic domain a wake is necessary on the rotor blades to consider the circulation around the lifting body.The wake panels are shed from the trailing edges and transported downstream by the local fluid velocity.Combined with the rotational speed of the rotor they form a helix.Wake panels have a doublet strength which is constant in time and set when they are shed from the trailing edge using the Kutta condition and the upper and lower panels at the trailing edge.
wake panel =  upper −  lower The wind velocity  ⃗ wind is either constant or determined by evaluating a wind field, based on the approach given by Greve et al. [19].A wind field is used when turbulent wind fields are applied.The wind velocity is then evaluated based on a given turbulent input spanning over the rotor area and for a certain time analogous to the procedure described by Jonkman and Kilcher [20, p. 11].

Hydrodynamics:
The hydrodynamic domain includes waves and free surface around the platform grid.
The wave potential is given by a linear potential depending on the position  ⃗ = [, , ]  and time .
The wave is described by its amplitude  a , angular wave frequency , wave number  and phase shift .The horizontal distance ̅ is the length of  ⃗ in wave propagation direction.A superposition of multiple waves is used to model irregular seaway.In the following cases, only regular waves or a superposition of linear waves were used.Second-order effects of wave-wave interaction were neglected.The free-surface elevation is divided into the wave elevation and the induced elevation  fs =  ind +  wave , as described by Ferreira-Gonzalez et al. [21].Two further boundary conditions are applied on the free surface.First, the kinematic boundary ensures that it follows the fluid velocity: Second, the dynamic boundary condition defines the dynamic pressure equal to the environmental pressure  0 with d d ⁄ ≡   ⁄ +  ⃗ fs : A gap between the hull panels and free-surface panels allows for a fixed panel distribution on the platform hull.This procedure has shown good agreement with results of RANS simulations [9] and avoids linking of hull and free surface panels which involves a deformation of hull panels.A split factor specifies the wetting area of a panel.Emerged panels are neglected at the instantaneous step and the influence of partially immersed panels is reduced accordingly.An additional acceleration potential is solved in the hydrodynamic domain to improve the quality of the acceleration dependent pressure and hydrodynamic mass calculation.It requires an additional solving step, which is described by Sichermann [22].Special handling is required to model the flow behaviour in the moonpool.The piston resonance affects the free surface elevation as well as the body motion.Its frequency can be calculated depending on the dimensions of the moonpool and the platform draft [23].A damping term can be applied, similar to the pressure reduction due to flow separation at the moonpool opening [24,25].
The damping factor  is dependent on the piston frequency and must be tuned for the specific model [25, p. 6].
Additions to the hydrodynamic modelling: Viscous effects can be of major importance on the damping, especially on heave plates.Additional drag elements are implemented to account for viscous effects as they cannot be captured by potential flow simulations.These elements are part of the platform and evaluate the relative fluid velocity at their centre point.The drag term of Morison's equation is then applied to estimate the drag force.
A lumped-mass mooring model is implemented to account for line loads [26].The model considers the axial elasticity and models synthetic fibre ropes by applying the static-dynamic stiffness model [27, p. 10].Hydrodynamic loads are applied using Morison's equation.A verification of the mooring model was provided in a previous publication [12] by agreement with other results of the OC4 project.
Coupling: A six-degrees-of-freedom (6DOF) solver is implemented for the coupling of the aerodynamic and the hydrodynamic domain as well as the mooring model.The motion solver sums up the forces of each model and integrates the equation of motion for a rigid body.A fourth-order Runge-Kutta method is applied to integrate the acceleration into body motion.Motions of all models are synchronised during the sub-steps of the integration scheme.For further information can be found in previous publication [12].
The rotor itself has an additional degree-of-freedom for a free rotation around its axis with a counter torque provided by the generator controller.The controller is also able to set the blade pitch angle to control the power output of the turbine.The entire structure, including blades and tower, is treated as rigid due to the lack of a structural solver.The platform hull was discretised by 1836 panels with a refinement near the water line area, see Figure 2. A gap between the platform panels and free surface panels was considered to avoid deformations of the platform panels due to the change of shape of the waterline, see Figure 4. Inside the moonpool a grid with 16x16 panels was applied.On the outer side 1600 panels have been used.This resolution was selected as it provided stable simulations and satisfying computational time.Each blade had 1300 panels and 2950 wake panels, see Figure 3. 160 panels were used for the tower.This results in a total number of 16602 panels of the model.12 additional drag elements were placed around the platform at the heave plates to calculate forces based on a drag coefficient.The mooring of the Floatgen platform has two long fore lines pointing in the main wave direction and two by two additional lines on the opposite side, see Figure 1.All lines consist of catenary and fibre rope parts and are equipped with buoys and clump weights.The lumped-mass-model resolved all these parts and a static-dynamic stiffness characteristic was used to represent the fibre ropes.In total 318 nodes were employed with a refinement near the platform were the largest deformations in the lines were presumed.

Model setup in panMARE
A global time step of 0.1 s was used in all simulations using a fourth-order Runge-Kutta method.

Results
Results of two different sets of simulations are presented in the following.First, a verification was carried out using the results of all three simulation tools introduced above.The second set is a validation with full scale measurement data using the hybrid simulation approach in panMARE.A focus is on time-series comparison.

Verification
A large set of verification load cases were defined as part of the underlying project.They range from steady state over decay and coupled simulations.A selection is shown in the present publication.
Frequency-dependent coefficients for the engineering methods were estimated using Ansys AQWA [28], a commercial hydrodynamic software.The OrcaFlex model was calibrated with measurement data in advance in a conservative manner [2], [3].Unfortunately these data were not available for the calibration of the other two models.Thus, the results of the OrcaFlex model can be seen as a reference but do not necessarily correspond with the measured values.The OpenFAST model was set up using the same frequency-based coefficients.Additionally, the calibration of linear and quadratic damping as well as Morison element drag coefficient was carried out.
The steady state has demonstrated good agreement between all methods.This ensures a consistent modelling of buoyancy and masses as well as static mooring forces.The decay tests have shown good compliance in most cases, however, also indicated differences especially in heave where the moonpool effects had strong influence.The method panMARE estimated a larger natural period in heave, see Figure 5, which likely was caused by a higher hydrodynamic mass.Free surface parameters of the moonpool had major influence on the damping and natural period due to their effect on the water motions inside the moonpool.The selected setup showed closest agreement with OrcaFlex and OpenFAST while reduced artificial damping impacts at the same time.The two methods showed favourable compliance, with regard to period and damping alike.Quite good agreement was reached in pitch decay.All methods applied predicted the same natural period.Only panMARE determined a bit larger damping.A PQ analysis [17, p. 14] related this to a higher quadratic damping while linear damping was relatively low.This is consistent with results of panMARE in the OC6 CFD validation [17].The comparison of the RAO's had a similar outcome.Heave and pitch RAO's have been estimated for regular waves and different wave heights (H1 < H2 < H3), see Figure 7 and Figure 8. Larger differences between panMARE and the other two methods were found in heave.Again, the results of panMARE were dependent on the free surface parameters.The peak in the RAO appears at a higher period, which is consistent with the heave decay.The higher hydrodynamic mass leads directly to an increase in the natural period.Furthermore a larger dependency on the wave height indicates nonlinear effects in heave.The differences between OrcaFlex and OpenFAST likely originate from different handling of the irregular frequencies which exist in the frequency-dependent coefficients.The pitch RAO show overall good agreement.At higher periods, panMARE predicted slightly larger motions which recurs in the coupled cases later.Coupled Simulation: A snapshot of the time-series of a coupled load case is shown as part of the verification.Seaway and the turbulent wind field were specified precisely to ensure equal wave elevations and turbulent wind field in all models.Unfortunately, only results of OpenFAST and  panMARE can be displayed here.The load case is modelled in accordance with the average conditions of the Floatgen platform at a wind speed of 11 m/s: A wave height of 1.5 m with peak period of 11.5 s.The wind direction was aligned with the front mooring lines and the wave direction was set with a slight offset.Heave and pitch motions as well as tower top bending moments are shown in Figure 9.Consistent with the RAOs, panMARE predicted slightly higher pitch motions than the OpenFAST model.Larger deviations occurred in the heave motions, but these should have less influence on the loads and turbine operation.Tower top moments agreed fairly well.They were mostly induced by inertia loads with fluctuations from the blade-tower interaction and incoming wind.Some turbine parameters are shown in Figure 10.The aerodynamic model in panMARE predicted slightly different load conditions and, combined with the slightly larger pitch motions, resulted in more active blade pitch control.These effects concern the rotor speed, power and thrust accordingly.

Hybrid Simulation
Full-scale measurement data of the Floatgen platform were provided by BW Ideol.The data included time-series of selected time windows from motion sensors, load measurements, and turbine operation parameters.LIDAR measurements were performed by the University of Stuttgart to estimate the incoming wind.The LIDAR was placed on top of the nacelle and measured the incoming wind in a distance of 200 m.A wind field was then reconstructed based on the measurement [29].In addition to the method referred, the platform motion was extracted during the reconstruction process.The reconstructed wind field had a low frequency coherence, but high frequency turbulences were added in a statistical manner.Unfortunately information on wave elevations at the platform position were not available.The wave elevation could also not be determined from measurement data of wave buoy located in a distance of around 1 km.Therefore it was not possible to perform a coupled validation in time domain.Instead, a hybrid simulation model was used under which the measured platform motion was used as input data to the simulation model.The motion data was filtered to remove high-frequency noise in all directions to prevent high accelerations in the simulation model.The reconstructed wind field completed the input data for a validation of the turbine model.A time-series with above-rated wind conditions is shown in the following.All values are normalised with a constant reference value to maintain a minimum amount of confidentiality.The roll and pitch motion and corresponding tower top moments are shown in Figure 11.A matching motion is predefined by the simulation model.The tower top bending moments are dominated by the inertia loads of the tower head.The aerodynamic loads increased the amplitude and contributed higher frequency fluctuations especially in the region of the blade frequency due to the tower shadow and wind profile, see power    spectral density in Figure 12.The side-to-side bending moment was a little underestimated while foreaft was slightly overestimated.The tower eigenfrequency was not visible in the simulation data due to the neglected structural deformation.
Figure 13 shows the time-series of rotor speed, torque and blade pitch.They mostly exhibit the same characteristic, however, larger deviations occur.More agreement was achieved for conditions below the rated turbine wind speed where the blade pitch was constantly 0°, see Figure 14.
One reason for the difference can be explained by the turbine controller.The controller of the real turbine differs from the simulation controller which may likely have caused overshoots in the rotor speed and higher torque values at above-rated conditions.Additional deviations might result from the wind field reconstruction or discrepancies in the synchronization of applied motions and wind field.

Conclusion
The verification shows good agreement between the models in OrcaFlex, OpenFAST and panMARE in most cases.Differences occurred in heave motion which was heavily affected by the dynamics of the moonpool.For methods based on the frequency domain, there are several approaches to deal with irregular frequencies due to moonpool modelling (e.g.cut-off frequency, external lid).The coefficients can be tuned based on model tests if available.Modelling in panMARE requires different procedures to capture the considerable influence of viscous effects caused by the moonpool.The damping parameter introduced by Faltinsen and Timokha [24] provides a good approach.Further development might be necessary to imbed this approach directly into the solving procedure of panMARE.Finally it is inevitable to perform a step-by-step validation with measurement data to evaluate panMARE's capability of moonpool simulations.The hybrid simulation method with prescribed motion and wind field allows the conducting of a precious time-series validation with measurement data.Tower loads and turbine operation shows good agreement of full-scale measurement data and panMARE in most cases.

Acknowledgments
The present investigations were carried out within the framework of the VAMOS project (grant no.03EE2004A and 03EE2004C) funded by the German Federal Ministry for Economic Affairs and Climate Action (BMWK).The installation of the nacelle-based LIDAR was supported by the European Union's Horizon 2020 research and innovation program under grant agreement number 731084 (MaRINET2) at the SEM-REV test infrastructure.

Author contributions
SN contributed to the development of the load case sets, performed the panel method simulations, overtook major parts of the analysis of numerical results, performed the hybrid simulations and wrote the manuscript.UÖ contributed to the development of the load case sets and the analysis of the numerical results, performed OpenFAST simulations and reviewed the manuscript.CWS set up the aerodynamic numerical model in panMARE, contributed to the analysis of the numerical results, supported the hybrid simulations and reviewed the manuscript.RA performed OrcaFlex simulations, contributed to the analysis of the numerical results and provided measurement data.TC supported the works of RA, provided measurement data and coordinated the collaboration on BW Ideol's side.PWC contributed to the theoretical discussions, supervised the works of UÖ and acquired funding.MM contributed to the theoretical discussions, supervised all works of CWS and SN, reviewed the manuscript and acquired funding.

References
A global view on the panMARE simulation model is shown Figure 1.Domains are indicated by colouring.Tower and rotor including its wake were part of the aerodynamic domain (red).Platform hull including drag elements and free surface and mooring were within the hydrodynamic domain (blue).The platform has a draft of 7 m at a water depth of around 35 m and the turbine has a nominated power of 2 MW.The overall centre of gravity of the structure is located close to the centre of the moonpool in the region of the water plane area.

Figure 1 .
Figure 1.Global view on the model.

Figure 9 .
Figure 9. Platform motions and tower loads at 11 m/s wind and random seaway.

Figure 10 .
Figure 10.Turbine operation parameter at 11 m/s wind and random seaway

Figure 11 .
Figure 11.Motions and tower top moments in hybrid simulation with conditions above rated.

Figure 12 .
Figure 12.PSD of the tower top moments.Figure 13.Turbine parameters above rated.

Figure 13 .
Figure 12.PSD of the tower top moments.Figure 13.Turbine parameters above rated.