# Response-Based Assessment of Operational Limits for Mating Blades on Monopile-Type Offshore Wind Turbines

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## Abstract

**:**

## 1. Introduction

## 2. Wind-Turbine Blade-Mating Process

#### 2.1. Procedure

#### 2.2. Critical Event and Limiting Response Parameter

## 3. Methodology

**Global response assessment of the mating system**: Here, the installation system characterizing the mating process is numerically modelled using multibody simulations. Software from SIMO [44], HAWC2 [32], Ren et al. [34,45] etc. can be used. Time-domain stochastic analyses for various sea states, characterized by different combinations of ${H}_{s},{T}_{p},{U}_{w},{\beta}_{wave}$ is performed. Furthermore, response statistics for limiting response parameters (${V}_{x}^{imp},{V}_{y}^{imp}$) are analyzed and extreme value distributions (${F}_{{V}_{x}}\left({V}_{x}^{imp}\right)$ and ${F}_{{V}_{y}}\left({V}_{y}^{imp}\right)$) are derived for each sea state and for reference duration of the mating task which is considered to be 10 min. Finally, a characteristic value (${V}_{x}^{cha},{V}_{y}^{cha}$) for a target probability of exceedance is evaluated for each sea state. Please note that in this study, ${10}^{-2}$ exceedance level is considered, and it corresponds to practical reported incident data in the industry [25] including an acceptable consequence level for the installation task in case of such an event. The categorization of different safety levels and corresponding consequences can be found in [26], and is also discussed briefly in Section 6.5 of this paper.

**Impact analysis of the blade root with the hub**: Here, finite element method (FEM) is used to investigate damages developed at the root connection because of impact with the hub. Standard FEM solvers such as Abaqus [46], Ansys [47], or other user defined solvers with explicit or implicit integration scheme can be used. Both impact scenarios are numerically modelled, and allowable levels of impact velocities in x and y direction (${V}_{x}^{allow},{V}_{y}^{allow}$) are established. These values correspond to the threshold level of impact velocity below which there are no damages in the composite root laminate [26]. These values were already determined in the previous work [19,42] and were reported in Figure 4.

**Assessment of allowable sea states**: In the final step, the characteristic values of impact velocities (${V}_{x}^{cha},{V}_{y}^{cha}$) obtained in step 1 for different sea states are compared individually with the allowable impact velocities (${V}_{x}^{allow},{V}_{y}^{allow}$) obtained from finite element analysis in step 2. The sea states in which the characteristic values in both the impact scenarios are less than the allowable responses are considered acceptable for the mating task, otherwise the sea states are not acceptable. Therefore, the overall criteria for estimating allowable sea states in this study is given by:

## 4. Modelling of Installation System

#### 4.1. Preassembled Monopile Sub-System

#### 4.2. Single Blade-Lift Sub-System

## 5. Environmental Conditions

## 6. Results and Discussion

#### 6.1. Hub Motions

#### 6.2. Blade-Root Motions

#### 6.3. Impact Velocities between Root and Hub

#### 6.4. Extreme Value Analysis of Limiting Response Parameter

#### 6.5. Characteristic Extreme Responses and Determination of Limiting Sea States

## 7. Conclusions

## 8. Limitations and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | Acceptable sea state representing safe domain for the mating task |

CDF | Cumulative Distribution Function |

CFD | Computational Fluid Dynamics |

DNV-GL | Det Norske Veritas-Germanischer Lloyd |

DTU | Technical University of Denmark |

EC | Environmental Cases |

FEM | Finite Element Method |

FFT | Fast Fourier Transformation |

GW | Gigawatt |

HAWC2 | Horizontal Axis Wind-Turbine Simulation Code 2nd generation |

Hz | Hertz |

MW | Megawatt |

NA | Not Acceptable sea state representing unsafe domain for the mating task |

NREL | National Renewable Energy Laboratory |

OWT | Offshore Wind-Turbine |

OWTs | Offshore Wind Turbines |

Probability Density Function | |

QRAs | Qualitative Risk Analyses |

RMSE | Root Mean Square Error |

RSM | Response Surface Method |

SFI MOVE | Centre for Research-based Innovation of Marine Operations |

SIMO | Simulation of Marine Operation- time-domain simulation program |

STD | Standard Deviation |

2D | Two-dimensional |

## Nomenclature

${H}_{s}$ | Significant wave height (m) |

${T}_{p}$ | Wave spectral peak period (s) |

${U}_{w}$ | Mean wind speed (m/s) |

${\beta}_{wind}$ | Direction of mean wind speed (degree) |

${\beta}_{wave}$ | Degree of wind–wave misalignment (degree) |

${x}_{global}$, ${y}_{global}$, ${z}_{global}$ | Earth fixed global coordinate system used in HAWC2 simulations |

${V}_{x}^{imp}$ | Impact velocity in side-side direction (head-on impact)-(m/s) |

${V}_{y}^{imp}$ | Impact velocity in fore-aft direction (sideways impact)-(m/s) |

${V}_{x}^{allow}$ | Allowable impact velocity in side-side direction (head-on impact)-(m/s) |

${V}_{y}^{allow}$ | Allowable impact velocity in fore-aft direction (sideways impact)-(m/s) |

${I}_{z}({S}_{33})$ | Failure index in the transverse normal tensile stress |

${F}_{{V}_{x}}({V}_{x}^{imp})$ | Extreme value distribution in side-side direction |

${F}_{{V}_{y}}({V}_{y}^{imp})$ | Extreme value distribution in fore-aft direction |

${V}_{x}^{char}$ | Characteristic impact velocity in side-side direction-(m/s) |

${V}_{y}^{char}$ | Characteristic impact velocity in fore-aft direction-(m/s) |

x | Given a sea state consisting of a particular combination of ${H}_{s}$, ${T}_{p}$, ${U}_{w}$, ${\beta}_{wave}$ |

X | A set of load cases for which time-domain analysis of marine operation is performed |

$p-y$ curves | Pile–soil interaction curve representing lateral stiffness |

${f}_{{U}_{w}}\left(u\right)$ | Probability density function of mean wind speed |

${U}_{x}^{hub}$ | Displacement of hub-center in side-side direction (m) |

${U}_{y}^{hub}$ | Displacement of hub-center in fore-aft direction (m) |

$\mu $ | Location parameter of Gumbel distribution |

$\beta $ | Shape parameter of Gumbel distribution |

${\mu}_{y}^{imp}$ | Location parameter of impact velocity in fore-aft direction for Gumbel distribution |

${\beta}_{y}^{imp}$ | Shape parameter of impact velocity in fore-aft direction for Gumbel distribution |

${H}_{o}$ | Null hypothesis for hypothesis testing |

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**Figure 4.**Critical event of blade-root impact with hub during mating: (

**a**) impact scenarios, (

**b**) failure modes at the blade root and (

**c**) allowable impact velocities [42].

**Figure 7.**Description of North sea center offshore site (

**a**) marginal PDF of mean wind speed (${f}_{{U}_{w}}\left(u\right)$) (

**b**) 2D-contour surface for ${H}_{s}$-${T}_{p}$ for different ranges of wind speeds (

**c**) wind–wave misalignment (${\beta}_{wave}$) (

**d**) bird view of wind-turbine blade-root mating task.

**Figure 8.**Displacement of the hub-center in side-side (${U}_{x}^{hub}$) and fore-aft directions (${U}_{y}^{hub}$) for ${H}_{s}=2$ m, ${U}_{w}=8$ m/s, ${T}_{p}=4$ s (

**a**) ${\beta}_{wave}=0$° (

**b**) ${\beta}_{wave}=30$° (

**c**) ${\beta}_{wave}=60$°.

**Figure 9.**(

**a**) Displacement hub-center y displacement (${U}_{y}^{hub}$) (

**b**) Spectral densities (

**c**) Blade root y displacement (

**d**) Spectral densities.

**Figure 10.**Response-time histories for ${V}_{x}^{imp}$ and ${V}_{y}^{imp}$ for load case ${H}_{s}=2$ m, ${T}_{p}=4$ s, ${U}_{w}=8$ m/s and for different wind–wave misalignment (

**a**) ${\beta}_{wave}=0$° (

**b**) ${\beta}_{wave}=30$° (

**c**) ${\beta}_{wave}=60$° (

**d**) comparison of standard deviations for ${V}_{y}^{imp}$ for different ${T}_{p}=4$ s, 6 s, 8 s, 10 s, and 12 s.

**Figure 11.**Spectral density curve for ${V}_{x}^{imp}$ and ${V}_{y}^{imp}$ for load case ${H}_{s}=2$ m, ${T}_{p}=4$ s, ${U}_{w}=8$ m/s and for different wind–wave misalignment (

**a**) ${\beta}_{wave}=0$° (

**b**) ${\beta}_{wave}=30$° (

**c**) ${\beta}_{wave}=60$°.

**Figure 12.**Fitting of the extreme (

**a**) ${V}_{x}^{imp}$ (

**b**) ${V}_{y}^{imp}$ to the Gumbel probability paper; (

**c**) (${F}_{{V}_{x}}({V}_{x}^{imp})$ (

**d**) ${F}_{{V}_{y}}({V}_{y}^{imp})$) for ${H}_{s}=2$ m, ${T}_{p}=4$ s, ${U}_{w}=8$ m/s and for different wind–wave misalignment ${\beta}_{wave}=0$°, 30° and 60°.

**Figure 13.**2D-response surface contour plot for Gumbel parameters (${\mu}_{y}^{imp}$, ${\beta}_{y}^{imp}$) for load case ${H}_{s}=2$ m, ${T}_{p}=4$ s, ${U}_{w}=6$ m/s: ${\mu}_{y}^{imp}$: (

**a**) ${\beta}_{wave}=0$°(

**b**) ${\beta}_{wave}=30$°(

**c**) ${\beta}_{wave}=60$°; ${\beta}_{y}^{imp}$: (

**d**) ${\beta}_{wave}=0$°; (

**e**) ${\beta}_{wave}=30$°; (

**f**) ${\beta}_{wave}=60$°

**Figure 14.**Estimation and comparison of (

**a**) ${V}_{x}^{char}$ (

**b**) ${V}_{y}^{char}$ with ${V}_{x,y}^{allow}$ for ${H}_{s}=2$ m, ${T}_{p}=4$ s, ${U}_{w}=8$ m/s and ${\beta}_{wave}=0$°, 30° and 60°; Estimation and comparison of (

**c**) ${V}_{x}^{char}$ (

**d**) ${V}_{y}^{char}$ with ${V}_{x,y}^{allow}$ for ${H}_{s}=2$ m, ${T}_{p}=12$ s, ${U}_{w}=8$ m/s and ${\beta}_{wave}=0$°, 30° and 60° (green dots: ${V}_{x,y}^{char}\le {V}_{x,y}^{allow}$ and red dots: ${V}_{x,y}^{char}\ge {V}_{x,y}^{allow}$).

**Figure 15.**Response surface for (

**a**) ${V}_{x}^{char}$ and (

**b**) ${V}_{y}^{char}$ for different ${H}_{s},{T}_{p}$, ${\beta}_{wave}=0$°, 30°, 60° and ${U}_{w}=6$ m/s.

**Figure 16.**Operational limiting sea state curves for different ${H}_{s}$, ${T}_{p}$, ${U}_{w}$, ${\beta}_{wave}=0$°, 30°, 60° with specific: (

**a**) ${U}_{w}=6$ m/s (

**b**) ${U}_{w}=10$ m/s (

**c**) ${U}_{w}=14$ m/s (A: Acceptable domain and NA: Not acceptable domain for the mating task).

Parameter | Notation | Value |
---|---|---|

Diameter of monopile (m) | ${\varphi}_{D}$ | 9 |

Monopile penetration depth (m) | ${P}_{m}$ | 45 |

Water depth (m) | ${d}_{w}$ | 30 |

Natural period of first-fore aft mode (s) | ${T}_{FA}$ | 4.2 |

Damping ratio of first-fore aft mode | ${\zeta}_{FA}$ | 1% |

Blade mass (ton) | ${M}_{bd}$ | 41.7 |

Blade length (m) | ${L}_{bd}$ | 86.4 |

Blade-root diameter (m) | ${D}_{bd}$ | 3.54 |

Yoke weight (ton) | ${W}_{yk}$ | 50 |

Tugger line length (m) | ${L}_{tl}$ | 10 |

1st rotational mode of blade about y-axis (Hz) | ${f}_{r1}$ | 0.08 |

EC | ${\mathit{\beta}}_{\mathit{wave}}$ | ${\mathit{H}}_{\mathit{s}}$ (m) | ${\mathit{T}}_{\mathit{p}}$ (s) | ${\mathit{U}}_{\mathit{w}}$ (m/s) |
---|---|---|---|---|

1 | 0° | 1, 1.5, …, 3.0 | 4, 6, …, 12 | 6, 8, 10, 12, 14 |

2 | 30° | 1, 1.5, …, 3.0 | 4, 6, …, 12 | 6, 8, 10, 12, 14 |

3 | 60° | 1, 1.5, …, 3.0 | 4, 6, …, 12 | 6, 8, 10, 12, 14 |

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## Share and Cite

**MDPI and ACS Style**

Verma, A.S.; Jiang, Z.; Ren, Z.; Gao, Z.; Vedvik, N.P.
Response-Based Assessment of Operational Limits for Mating Blades on Monopile-Type Offshore Wind Turbines. *Energies* **2019**, *12*, 1867.
https://doi.org/10.3390/en12101867

**AMA Style**

Verma AS, Jiang Z, Ren Z, Gao Z, Vedvik NP.
Response-Based Assessment of Operational Limits for Mating Blades on Monopile-Type Offshore Wind Turbines. *Energies*. 2019; 12(10):1867.
https://doi.org/10.3390/en12101867

**Chicago/Turabian Style**

Verma, Amrit Shankar, Zhiyu Jiang, Zhengru Ren, Zhen Gao, and Nils Petter Vedvik.
2019. "Response-Based Assessment of Operational Limits for Mating Blades on Monopile-Type Offshore Wind Turbines" *Energies* 12, no. 10: 1867.
https://doi.org/10.3390/en12101867