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Ocean Engineering

# Extreme Dynamic Structural Response Analysis of Catenary Moored Spar Wind Turbine in Harsh Environmental Conditions

[+] Author and Article Information

Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, N-7491 Trondheim, Norwaymadjid.karimirad@ntnu.no

Torgeir Moan

Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, N-7491 Trondheim, Norwaytorgeir.moan@ntnu.no

J. Offshore Mech. Arct. Eng 133(4), 041103 (Apr 12, 2011) (14 pages) doi:10.1115/1.4003393 History: Received April 24, 2010; Revised November 17, 2010; Published April 12, 2011; Online April 12, 2011

## Abstract

Proper performance of structures requires among other things that their failure probability is sufficiently small. This would imply design for survival in extreme conditions. The failure of a system can occur when the ultimate strength is exceeded (ultimate limit state (ULS)) or fatigue limit (fatigue limit state) is exhausted. The focus in this paper is on the determination of extreme responses for ULS design checks, considering coupled wave and wind induced motion and structural response in harsh condition up to 14.4 m significant wave height and 49 m/s 10 min average wind speed (at the top of the tower, 90 m) for a parked floating wind turbine of a spar type concept. In the survival condition, the wind induced resonant responses (mainly platform pitch resonance) are dominant. Due to the platform resonant motion responses, the structural responses are close to Gaussian, but wide banded. The critical structural responses are determined by coupled aerohydro-elastic time domain simulation. Based on different simulations (20 1 h, 20 2 h, 20 3 h, and 20 5 h), the mean up-crossing rate has been found in order to predict the extreme structural responses. The most probable maximum of the bending moment and the bending moment having an up-crossing rate of $10−4$ are found to be close in the present research. The minimum total simulation time in order to get accurate results is highly correlated with the needed up-crossing rate. The 1 h and 2 h raw data cannot provide any information for $10−4$ up-crossing rate. Comparison of different simulation periods shows that the 20 1 h simulations can be used in order to investigate the 3 h extreme bending moment if the proper extrapolation of up-crossing rate is used.

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## Figures

Figure 1

Forces on a blade element (18)

Figure 2

100 year return period contour lines for 1 h mean wind speed versus 3 h significant wave height (22)

Figure 3

Contour surface of the joint distribution for mean wind speed and waves (100 year return period) (22)

Figure 4

Turbulence intensity (26)

Figure 5

Mooring system layout

Figure 6

Surge and sway mooring line stiffness

Figure 7

Yaw mooring line stiffness

Figure 8

Catenary moored spar floating wind turbine

Figure 9

First and second elastic modes (based on a shell model in ABAQUS )

Figure 11

Nacelle surge spectrum based on a 1 h time domain simulation, spectrum smoothed based on a Parzen window method

Figure 12

Maximum bending moment in each section along the structure in 1 h analysis

Figure 13

Maximum shear force in each section along the structure in 1 h analysis. There is a big mass at the bottom of spar, which needs very fine modeling to capture the accurate shear force; the dashed line means that the model at that region has not enough accuracy.

Figure 14

Bending moment time history at z=−20 m based on a 1 h time domain simulation considering wave and wind induced loads

Figure 15

Bending moment spectrum at z=−20 m based on a 1 h time domain simulation considering wave and wind induced loads, spectrum smoothed based on a Parzen window method

Figure 16

Thrust force (shear force at the top of the tower) time series realization for a parked wind turbine in a harsh environmental condition (considering simultaneous wave and wind loading)

Figure 17

Extreme value in the sample, standard deviation, and mean value of maximum bending moment (kN m) for individual simulations (20 2 h case)

Figure 20

Coefficient of variation (σ/μ) of bending moment for an up-crossing rate of 10−3 versus simulation time

Figure 21

Coefficient of variation (σ/μ) of bending moment for an up-crossing rate of 10−4 versus simulation time

Figure 22

Poisson probability density function (PDF) for the largest normalized bending moment in a 3 h period based on 20 1 h simulations

Figure 10

Nacelle surge time history based on a 1 h time domain simulation, wave, and wind induced responses

Figure 18

Skewness and kurtosis of the bending moment (kN m) for individual simulations (20 2 h case)

Figure 19

Up-crossing rate for 20 2 h simulations and the average up-crossing rate (40 h)

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