Amrit Shankar Verma ·Zhiyu Jiang·Zhengru Ren·Zhen Gao·Nils Petter Vedvik

Abstract Most wind turbine blades are assembled piece-by-piece onto the hub of a monopile-type offshore wind turbine using jack-up crane vessels.Despite the stable foundation of the lifting cranes,the mating process exhibits substantial relative responses amidst blade root and hub.These relative motions are combined effects of wave-induced monopile motions and wind-induced blade root motions,which can cause impact loads at the blade root’s guide pin in the course of alignment procedure.Environmental parameters including the wind-wave misalignments play an important role for the safety of the installation tasks and govern the impact scenarios. The present study investigates the effects of wind-wave misalignments on the blade root mating process on a monopile-type offshore wind turbine.The dynamic responses including the impact velocities between root and hub in selected wind-wave misalignment conditions are investigated using multibody simulations.Furthermore,based on a finite element study,different impact-induced failure modes at the blade root for sideways and head-on impact scenarios, developed due to wind-wave misalignment conditions, are investigated. Finally, based on extreme value analyses of critical responses,safe domain for the mating task under different wind-wave misalignments is compared.The results show that although misaligned wind-wave conditions develop substantial relative motions between root and hub,aligned wind-wave conditions induce largest impact velocities and develop critical failure modes at a relatively low threshold velocity of impact.

Keywords Wind turbine blade . Wind-wave misalignment . Monopile . Marine operation . Finite element analysis . T-bolt connections

1 Introduction

In order to resolve the issues related to global warming and climate change, there is a continuous demand for renewable sources of energy. In Europe, wind energy ranks second in terms of power generation (Wind Europe 2017a), and immense political and scientific interest is placed on the growth of offshore wind turbines(OWTs).Monopile-type OWTs are the most popular choice of turbines in shallow waters, and currently account for more than 87% of the market share(Wind Europe 2017b). One of the main challenges in the industry includes high installation and assembly cost (Molla 2015)associated with the project cycle of OWTs,and therefore, recent trends involve deploying large size OWTs. This facilitates having less number of turbine units at an offshore farm, thus reducing the overall installation cost. However,several safety issues are inevitably present during the installation of bigger and heavier turbine components.For example,components like blades and nacelle are structurally delicate and demand absolute precision during transportation and installation.

Generally, blades of a monopile-type offshore wind turbine are installed using jack-up crane vessels (Verma et al. 2017; Verma et al. 2019a; Ren et al. 2018a)(Figure 1a). Individual pieces are hoisted to the hub, and blade root consisting of several bolted connections, together with the guide pin, is mated with the hub’s flange holes (Verma et al. 2019b). The guide pins are long-sized bolts (Figure 1b-c) and are inserted in the blade root to visually aid the offshore crew (present in the nacelle)while performing the mating task.

Figure 1 Blade root mating process (https://orsted.com/en) (https://vessels.offshorewind.biz/vessels/sea challenger) (https://www.siemens.com)

Despite the stable foundation of the jack-up crane vessels, the mating process suffers substantial relative responses amidst blade root and hub (Jiang et al. 2018;Ren et al.2018b;Ren et al.2019).The blade root motions are a result of wind-induced loads on the lifted blade,whereas the hub responses are caused by wave actions on the preassembled monopile structures. Note that monopiles are large diameter structures fixed to the seabed and have low damping characteristics (Jiang 2018).For example, the monopiles have deficient structural, hydrodynamic and soil-damping attributes. The damping is even more critical during the installation phase as the aerodynamic damping from the rotating blades is missing.Thus, large dynamic amplification of tower top responses develops and contributes to excessive relative motions while performing the mating task. This can induce impact loads at the guide pin during the alignment process, causing critical damages at the blade root and thus, failure of installation task. Verma et al. (2019a) investigated impact assessment of wind turbine blade root during offshore mating process where relative responses under aligned wind-wave conditions were investigated.Furthermore, damage assessment at the blade root was studied, and bending of guide pin and delamination of root laminate were found as failure modes. Nevertheless,mating operations under misaligned wind-wave conditions were not considered,and damages for such scenarios were not assessed. In practice, for an offshore site,wind-wave misalignments are present for all ranges of wind speeds, and therefore, it is important to investigate such effects for the success of the wind turbine blade mating process. Wind-wave misalignment is the measure of temporal difference between the wind direction and mean wave directions (Van Vledder 2013), where highest degree of misalignments is found at low wind speeds, and minor misalignments are found at high wind speeds (Li et al. 2015; Van Vledder 2013; Bachynski et al. 2014).

Figure 2a-d present the relative frequency of wind direction, mean wave directions and misalignment between wind and waves for the North Sea centre. It can be clearly seen that though the wind and waves are spread out in all directions, the misalignment between wind-wave is mostly concentrated between 0° and 90°. Majority of the misalignment occurs till 30°, with frequency being less than 5% for wind-wave misalignment greater than 60°(Bachynski et al. 2014). Currently, there are limited published literature sources (Jiang et al. 2018; Verma et al.2019c; Verma et al. 2019d; Verma et al. 2020a; Verma et al. 2020b) dealing with the effects of wind-wave misalignment on the installation phases of OWTs, although several studies in the past emphasised operational and parked conditions of OWTs for design purposes. Barj et al. (2014), Bachynski et al. (2014) and Zhou et al.(2017) investigated the effect of misalignment on the operational loads for floating OWTs, whereas Fischer et al.(2011) investigated the effect of misalignment on monopile-type OWTs.The response parameters of interest for such assessments were tower top motions, bending moments and fatigue damages. On the other hand, in this study, the mating process of blade is studied, and therefore, the response parameters of interest are related to the critical event that can cause failure of the installation task.These include (1) impact velocity between root and hub during mating, (2) impact-induced damages at the blade root and (3) structural safety assessment of the mating task for a given wind-wave misalignment condition.

The present paper investigates the effect of wind-wave misalignment for the blade root mating process where dynamic responses including the impact velocities in selected wind-wave misalignment conditions are investigated using multibody simulations in HAWC2 (Larsen and Hansen 2007). Furthermore, based on a finite element study in Abaqus/explicit (Hibbitt et al. 2016), impact-induced failure modes at the blade root are discussed.Finally,safe domain for the mating task is compared for different wind-wave misalignment conditions.The remainder of the paper proceeds as follows.Section 2 presents the analysis procedure and identifies relevant response parameter for investigating effects of wind-wave misalignment. Section 3 presents the material and modelling methods.Section 4 presents and discusses the results.Finally,Section 5 concludes the paper.

2 Response Parameters and Analysis Procedure

There are three response parameters identified in this paper to investigate the effects of wind-wave misalignment on the wind turbine blade mating process and are described below:

Figure 2 Different wind and wave directions(wind and wave direction corresponds to a compass—0°represents East,90°North,180°West and 270°represents South)

2.1 Impact Velocity between Root and Hub

2.2 Damage Assessment for a Critical Location at the Blade Root

2.3 Structural Safety Assessment of the Mating Task for a Sea State with Given Wind-Wave Misalignment

Analysis Procedure

Figure 3 Illustration of impact scenarios during the blade mating process

Figure 4 Position of interest at the blade root for assessment

3 Material and Modelling Methods

The mating process of DTU 10 MW wind turbine blade(Bak et al. 2013) is considered in this article,and thus, all the parameters used for modelling are derived from DTU 10 MW report (Bak et al. 2013). Here, the modelling details of the installation system using multibody dynamics are described first. Then, the finite element modelling information for impact analysis between blade root and hub for different scenarios are addressed.

Figure 5 Analysis procedure considered in this study

3.1 Numerical Modelling of Installation System

The installation system is modelled in HAWC2 numerical code (Larsen and Hansen 2007). The code can simulate dynamics of the wind turbines in the time domain considering various effects such as wind and waves.The installation system consists of two independent sub-systems—(1)preassembled monopile sub-system, and (2) single-blade lift sub-system (Figure 6). Different modelling aspects are considered in HAWC2 and are discussed below.

Structural Model

In the HAWC2 code, the structural formulation of the turbine components depends upon multibody dynamics.The first structural system, i.e.(1)preassembled monopile system consists of a monopile,along with a turbine tower,a nacelle and a hub. The components of this sub-system are grouped into several flexible bodies, and are modelled with Timoshenko beam elements linked through a coupling joint. Large rotations and large displacements are permissible at these joints; however, only small deflections are allowed within each body.

The (2) single-blade lift-sub-system on the other hand consists of the wind turbine blade, yoke, tugger lines, lift and sling wires connected to a fixed crane tip. The wind turbine blade is discretised with Timoshenko beam elements, and is defined as one single body. The yoke is added as a concentrated rigid body defined at the mass centre of the blade. The tugger lines are 10 m long and consist of cable bodies joined by spherical joints (Verma et al. 2019a). It is to be noted that the effect of jack-up crane vessel is ignored in this study as the vessel is generally stable due to load bearing legs, and thus has a minor contribution to crane tip responses. The structural characteristics of components used in the modelling of installation system are also mentioned in Table 1.

Figure 6 Description of numerical modelling of installation system

Table 1 Modelling parameters of installation system used in HAWC2

Pile-Soil Interaction Model

The monopile support structure along with the characteristics of soil layers used in this study is based on the work of Velarde (2016), where the foundation for DTU 10 MW reference turbine was designed. In Velarde(2016), only the non-linear p-y curve corresponding to soil lateral stiffness was reported and this makes the basis for pile-soil interaction model in our study.The pile diameter is around 9 m and has a penetration depth of 45 m. The distributed springs model is utilised,which considers the pile as a flexible component having lateral springs spread around the soil layer.

Wave-Induced Hydrodynamic Model

Morison equation (Morison et al. 1950) is used to calculate hydrodynamic wave-induced loads exerted on the monopile.The equation consists of inertial as well as drag-associated terms and is given by:

where ρ is defined as the density of sea water, D is the monopile diameter,and Cmand Cdin the above equation are the inertial and drag coefficient and is assumed as 2.0 and 1.0,respectively(Jiang 2018).Furthermore, ˙xwin the above equation describes the velocity,whereas..xwdescribes the acceleration of water particles at the strip centre.

Wind and Aerodynamic Model

Cross-flow principles are used,which assume the wind flow as 2D,and neglect the wind flow in the span-wise direction of the blade. As the blade is non-rotating, steady lift and drag coefficients are utilised(Bak et al.2013;Verma et al.2019b)to calculate aerodynamic loads exerted on blade sections.The Mann’s turbulence (Mann 1994) module available in HAWC2 code is utilised to generate inflow turbulent field in this study. This module is defined by three parameters—turbulence length scale factor,eddy lifetime and spectral multiplier.The details of these parameters can be found in Jiang et al.(2018).

3.2 Environmental Load Cases for Time Domain Analysis

In this study, North Sea centre is considered for studying the effect of wind-wave misalignment during offshore blade mating task. The offshore site has a water depth of 29 m, which nears the water depth of 30 m considered for the monopile foundation in this study. Figure 7a and b present the histogram of Hsand Tp, respectively, from 10 years of hindcast data (2001-2010). It can be clearly seen that bulk of Hsfor the site is less than 6m, whereas Tplies in the range of 2-16s.

Figure 7 Histogram data at North Sea centre

Table 2 Description of environmental load cases

Given that the mating task is expected to give very high responses for Hs＞3m, the present paper only considers time domain analysis for Hsin the range 1m ≤Hs≤3m where Hsvaries with a step of 0.5m. Again, the analysis considers Tpin the range 4s ≤Tp≤12s, where Tpvaries with a step of 2s. Also, since the site has wind-wave misalignments varying between 0° and 90°(as discussed in Section 1), four cases of wind-wave misalignments (βwave=0°, 30°, 60° and 90°) are considered for each load case. For simplicity, only one case of mean wind speed (Uw=10m/s) is considered in this paper and corresponds to turbulence intensity of 0.12 selected from IEC standard (IEC 2005). Figure 8 presents the bird view of the installation process, where different wind-wave misalignments taken in the paper are illustrated. The details of environmental load cases are mentioned in Table 2.

Figure 8 Bird view of mating process with considered wind-wave misalignment

3.3 Time Domain Analyses

Time domain analyses are performed at a time step of 0.01s with each environmental load case analysed for 20 seeds for stochastic variability.Therefore,a total sum of 2000 environmental cases are considered for the time domain analysis.Each case has a total time duration of 1000 s, where first 400 s are removed during post-processing to avoid any transient effects.

3.4 Modelling and Analysis of Blade Root Impact with Hub

The main purpose of the impact analysis is to relate the impact velocity obtained for a given wind-wave misalignment condition with the damages obtained at the blade root. In this way, allowable impact velocities in fore-aft() and side-side () direction are obtained.Here, the details for structural modelling and analysis of blade root impact with hub are discussed for sideways and head-on impact scenarios. It is assumed that for both the scenarios,single guide pin at root suffers impact,and thus,any distribution of contact forces among adjacent bolts is neglected. It is to be noted that a detailed finite element modelling technique describing sideways’impact scenario was thoroughly presented in Verma et al. (2019a). In this study,the same model is used for head-on impact but with a different direction for impact loads, and thus, the details of finite element model are described only briefly.

Abaqus/explicit (Hibbitt et al. 2016) environment is chosen as the solver environment for impact analysis given that it is suited for non-linear problems involving large rotation, large displacements and complex interaction(Verma et al. 2019e). The DTU 10 MW blade, which is based on shell-element is considered for impact assessment.The parent blade model has a span of 86.4 m with a root radius of 2.7 m and has no detailed connections or joint descriptions at its root (Verma et al. 2019f). For the purpose of impact assessment, a high-fidelity 3D finite element model for T-bolt connection is separately developed and is coupled with remaining region of the blade using shell-to-solid coupling constraint feature in Abaqus(Figure 9). The components of the T-bolt connections—steel guide pin, steel barrel nut and root laminate with Triaxial layup [+45/-45/0] (see dimensions in Figure 9)—are modelled with eight noded linear brick elements with reduced integration (C3D8R) elements. The remaining region of the blade is discretised with four noded thick conventional shell (S4R) elements. The details of the element size, mesh sensitivity study and contact formulations between the components of T-bolt connection can be found in Verma et al. (2019a, 2020).

A simplified structural representation of hub is considered for impact assessment. The hub is defined as a rigid body, discretised with four noded bilinear (R3D4) elements, and is constrained in all degrees of freedom.General contact attribute together with suitable tangential and mechanical interaction properties available in Abaqus/explicit is used to define contact between impact surface of the guide pin and hub. For the case of sideways’ impact, the initial impact surface is transverse to the guide pin (red arrows, Figure 9), whereas for head-on impact,the initial impact surface is along its axial direction (blue arrows, Figure 9). Maximum stress failure criterion is used as failure prediction model for root laminate, whereas von-Mises equivalent plastic strain criterion is used for damage assessment at barrel nut and guide pin. The details of these criteria along with corresponding material properties can also be found in Verma et al.(2019a, 2020).

Figure 9 Finite element modelling of guide pin impact with hub for sideways and head-on impact scenarios

4 Results and Discussion

In this section,response time histories,spectral densities and corresponding standard deviations are considered for discussing the effect of wind-wave misalignment on the wind turbine blade mating process.First,an individual description of hub-centre and blade root motions are presented,followed by discussion of impact velocity between root and hub for different wind-wave misalignment.Then,the damage assessment results for blade root impact with hub are discussed,where allowable impact velocities for sideways and head-on impact scenarios are estimated. Finally, a safe domain for performing mating task under different wind-wave misalignment conditions is compared.

4.1 Hub Motions

Figure 10 Response time histories and spectral density curve for load case Hs=2.5 m, Tp=4 s, Uw=10 m/s and for βwave=0°, 30°, 60°,and 90°

Figure 11 Motion of hub-centre in xy-plane and comparison of standard deviations for load case Hs=2.5 m, Tp=4 s, 6 s, 8 s, 10s, 12 s, Uw=10 m/s and βwave=0°,30°,60°and 90°

4.2 Blade Root Motions

Figure 12a presents the displacement of blade root in global x- and y-direction of the installation system for environmental condition with Uw=10m/s. The blade root responses in y-direction are dominant compared with its motion in x-direction which is negligible. This is due to the action of tugger lines which constrains the blade root motions in x-direction. Figure 12b presents the spectral density curve for the blade root displacement in global y-direction, where peak frequency is observed at approximately 0.08Hz, and corresponds to fr1.

4.3 Impact Velocity Between Blade Root and Hub

Figure 12 Blade root responses for Uw=10 m/s

Figure 13 Response time histories and spectral density curve for load case Hs=2.5 m,Tp=4 s,Uw=10 m/s and for different wind-wave misalignment βwave=0°,30°,60°and 90°

Figure 14 Comparison of standard deviations for load case Hs=2.5 m,Tp=4 s, 6 s, 8 s, 10s, 12 s, Uw=10 m/s and for different wind-wave misalignment βwave=0°,30°,60°and 90°

4.4 Damage Assessment at the Blade Root

Figure 15 Allowable impact velocities

4.5 Structural Safety Assessment of Mating Task for Sea States with Given Wind-Wave Misalignment

Figure 16 Comparison of failure modes for impact in sideways and head-on impact scenarios

Figure 17 Gumbel fitting of extreme responses and corresponding extreme value distribution for load case Hs=2.5 m, Tp=4 s, Uw=10 m/s and βwave=0°,30°,60°and 90°

Figure 18 Characteristic extreme responses for load case: Hs=2.5 m,Uw=10 m/s and for βwave=0°,30°,60°and 90°

Figure 19 Comparison of safe domain for different wind-wave misalignment

wind-wave misalignments. Note that the area lying below the line corresponding to a particular wind-wave misalignment is considered safe for the mating task.It can be clearly seen that the collinear wind-wave condition has the least percentage of safe domain,whereas βwave=90°has highest percentage of safe sea states for the mating task. This is because of the fact that aligned wind-wave conditions cause sideways’impact that are critical and cause damages to the root laminate at relatively less impact velocity.Overall, it can be said that, although both, aligned and misaligned wind-wave conditions can induce large responses between root and hub during the blade mating process; it is the aligned wind-wave conditions that are the most critical as far as the structural safety of the blade root mating process is concerned.

5 Conclusion

The present paper investigated the effects of wind-wave misalignment on the wind turbine blade mating process. Three distinct response parameters:(1)impact velocity between root and hub during mating, (2) impact-induced damages at the blade root and(3)safety assessment of the mating task for a given wind-wave misalignment condition, were considered for discussion.The mating process was numerically modelled in HAWC2 numerical code, and time domain analyses were performed for load cases representing environmental conditions for the North Sea centre.Four cases of wind-wave misalignments(βwave=0°,30°,60°and 90°)were considered for each load case.Additionally,the impact scenarios—sideways and head-on impact of the guide pin with the hub—were also numerically modelled using Abaqus/explicit,and corresponding allowable impact velocities in the fore-aft and side-side directions were obtained.The following are the main conclusions from this study:

2) The load cases with largest degree of wind-wave misalignment have the largest impact velocity in the side-side direction,and thus for such cases,head-on impact between guide pin and hub are dominant. On the contrary,aligned wind-wave cases induce largest impact velocity in the fore-aft direction,and thus cause impact of the guide pin with the hub in sideways scenario.

3) The sideways’impact of the guide pin with hub is more critical than the head-on impact,and the failure criteria in the root laminate are met at a relatively low velocity of impact. This is because sideways’ impact scenario involves impact loads along the transverse direction of the guide pin causing bending of the bolt.On the other hand,for the case of head-on impact,impact loads are caused in the axial direction of guide pin,where the bolt has high strength and stiffness.This causes impact-induced buckling of guide pin,but at a large impact energy.Therefore,impact scenarios for aligned wind-wave conditions are more critical for the wind turbine blade mating process.

4) The safety assessment of the mating task was also compared for load cases with different wind-wave misalignment conditions. It was found that βwave=90° has the largest domain for safe installation of wind turbine blades, which reduces with shift in the degree of misalignment. Also, for collinear wind-wave condition(βwave=0°), lowest percentage of safe domain for mating task was obtained.The reason for this is that aligned wind-wave conditions cause sideways impact, which,from a structural perspective, is more critical than a head-on impact scenario, developed due to misaligned wind-wave conditions.

Funding Information The study is a part of SFI MOVE projects funded by the Research Council of Norway,NFR project number 237929.

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