6 Verification of the optimized design
6.2 Verification of Results
6.2.1 ULS Verification
It should be noted that the main purpose of the verification step is not to fully document the concept, but to demonstrate the viability of the optimization approach. For the ULS results, an accuracy of ±15 % is assumed, due to lack of seed variation.
6.2 Verification of Results
One of the most potentially problematic aspects of the TLB system is that the mooring loads are relatively high. Thus, these loads are focal points of the ULS verification. Local buckling is not assessed at ULS as mooring pad eyes, equipment fixation, secondary structures and J-tube are not assessed at this stage.
6.2.1 ULS Verification
The ULS verification results are shown in Table 17 to Table 18. The extremals in each category are highlighted.
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Table 17: Translations and rotations at the tower top during the verification ULS DLCs
vDLC Heave [m] Surge [m] Sway [m] Pitch [deg] Roll [deg] Yaw [deg]
Mean Max Mean Max Mean Max Mean Max Mean Max Mean Max ULS01 -0.20 0.21 0.40 0.70 -0.04 0.24 0.23 0.40 -0.03 0.14 0.01 0.23 ULS02 -0.20 0.21 0.23 1.04 -0.05 0.29 0.13 0.61 -0.03 0.16 0.01 0.37 ULS03 -0.20 0.21 0.21 1.05 -0.06 0.30 0.12 0.58 -0.04 0.18 0.02 0.49 ULS04 -0.20 0.21 0.24 0.47 0.32 0.66 0.14 0.26 0.18 0.35 0.01 0.23 ULS05 -0.20 0.21 0.16 0.65 0.17 0.99 0.09 0.37 0.10 0.55 0.01 0.36 ULS06 -0.20 0.21 0.15 0.57 0.15 0.81 0.09 0.32 0.08 0.47 0.02 0.50 ULS07 -0.20 0.22 0.21 0.79 -0.06 0.33 0.12 0.49 -0.04 0.19 0.02 0.48 ULS08 -0.20 0.22 0.15 0.52 0.15 0.68 0.09 0.30 0.08 0.40 0.02 0.50 ULS09 -0.18 0.20 0.08 0.91 0.00 0.35 0.04 0.53 0.00 0.20 0.00 0.08 ULS10 -0.18 0.20 0.02 0.48 0.04 0.62 0.01 0.26 0.02 0.31 -0.01 0.08
Table 18: Accelerations at the tower top during the verification ULS DLCs
vDLC Heave [m/s2] Surge [m/s2] Sway [m/s2]
Mean Max Mean Max Mean Max
ULS01 0.00 0.20 0.00 1.12 0.00 0.69
ULS02 0.00 0.31 0.00 1.76 0.00 0.89
ULS03 0.00 0.46 0.00 1.48 0.00 1.59
ULS04 0.00 0.21 0.00 0.75 0.00 1.34
ULS05 0.00 0.32 0.00 0.89 0.00 1.45
ULS06 0.00 0.46 0.00 2.36 0.00 1.27
ULS07 0.00 0.48 0.00 1.76 0.00 1.61
ULS08 0.00 0.46 0.00 1.58 0.00 1.40
ULS09 0.00 0.19 0.00 2.47 0.00 0.92
ULS10 0.00 0.18 0.00 1.20 0.00 1.45
These values are considered well within acceptable limits. The maximum horizontal acceleration is 2.47 m/s2, within the targeted upper limit of 2.5 m/s2. The rotations and translation are similar to levels of onshore turbines. Maximum heave occurs during interactions with the largest waves, and the surge and sway responses are similar, but peak at rated wind speeds in ULS03. It should be noted that the results are based on one three-hour seed, thus the values should be expected to have ± 20 % variation. A Gumbel distribution generated with several seeds is suggested to estimate 50-year extreme ULS responses accurately.
For the mooring lines, OS-E301 (DNV-OS-E301, 2010) states the following:
𝑆𝑐− 𝑇𝑐,𝑚𝑒𝑎𝑛− 𝑇𝑐,𝑑𝑦𝑛≥ 0 Equation 12
Where:
𝑆𝑐= 𝐶ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑇𝑐,𝑚𝑒𝑎𝑛= 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑠𝑎𝑓𝑒𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑛 𝑚𝑒𝑎𝑛 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 ∙ 𝑚𝑒𝑎𝑛 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 𝑇𝑐,𝑑𝑦𝑛= 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑠𝑎𝑓𝑒𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 𝑜𝑛 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑡𝑒𝑛𝑠𝑖𝑜𝑛 ∙ 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑡𝑒𝑛𝑠𝑖𝑜𝑛
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The required stiffness (EA) according to the optimization is approximately 1.37E6 kN for the upper mooring lines. According to (BEXCO, 2015) this corresponds to a stock DeepRope of 187 diameter with a Minimum Breaking Load (MBL) of 24812 kN. OS-E301 requires the characteristic strength 𝑆𝑐 to be considered as 95 % of the minimum break strength, which equals 23571 kN.
For the lower mooring lines, a stiffness of approximately 1.20 kN is required. This corresponds to a diameter of 177 mm and result in a characteristic strength of 20798 kN.
The partial safety factors for mean and dynamic tension of a mooring line in consequence class 1 assessed by dynamic analyses are 1.1 and 1.5, respectively. However, amendment D203 is used, multiplying the values by 1.2, as the redundant mooring line system has not been fully verified at this point. The resulting partial safety factors used for the ULS evaluation of the mooring lines are therefore set to 1.32 and 1.8 for mean and dynamic tension, respectively.
Table 19: Mooring line utilization during the verification ULS DLCs
vDLC Lower mooring lines (worst) Upper mooring lines (worst)
Mean [kN] Dynamic [kN] Utilization [%] Mean [kN] Dynamic [kN] Utilization [%]
ULS01 5269 4125 40 3190 2205 23
ULS02 4719 4395 39 3509 2985 28
ULS03 4664 4725 40 3564 2730 27
ULS04 4620 2310 29 2420 4830 31
ULS05 4367 2775 30 2992 4740 33
ULS06 4367 2790 30 3058 4260 31
ULS07 4686 5505 43 3553 3195 29
ULS08 4378 2925 31 3036 6150 39
ULS09 4422 6060 44 3630 3870 32
ULS10 4103 4830 38 3421 6780 43
As expected, the mooring lines’ utilization, shown in The partial safety factors for mean and dynamic tension of a mooring line in consequence class 1 assessed by dynamic analyses are 1.1 and 1.5, respectively. However, amendment D203 is used, multiplying the values by 1.2, as the redundant mooring line system has not been fully verified at this point. The resulting partial safety factors used for the ULS evaluation of the mooring lines are therefore set to 1.32 and 1.8 for mean and dynamic tension, respectively.
Table 19, increases with the sea state, but there is also a local peak around rated wind speed for production. Elements such as marine growth and additional forces from secondary structures have not been assessed, but are considered less significant for the mooring line response as the utilization is low. One can also conclude that stiffness rather than loads drive the mooring design as the utilization is low.
Reducing the anchor loads has been an important design driver for the continued development of the TLB concept. Characteristic anchor load results are presented in Table 20. The maximum vertical resultant (occurring when wave heights are most severe) is about 7 500 kN and anchor resultant forces peak when the worst wave conditions coincide with a production state at winds speeds close to cut-out. The utilization is based on a Vryhof Vertical Load Anchor (VLA) type
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anchor with an ultimate holding capacity of 20 000 kN, excluding the computation of soil capabilities. Both the anchor and mooring line loads are now well within loads considered typical for offshore installations.
Table 20: Anchor vertical lift and resultant force during ULS verification
vDLC Anchor vertical force Anchor resultant force Utilization Mean [kN] Max [kN] Mean [kN] Max [kN] [%]
ULS01 4650 5440 8730 13500 84
ULS02 4280 5440 8430 13900 87
ULS03 4250 5440 8430 13600 85
ULS04 4200 5530 7050 12000 76
ULS05 3080 5810 7340 11900 75
ULS06 3120 5690 7350 11900 75
ULS07 4270 5440 8470 14600 93
ULS08 3100 6900 7320 13800 89
ULS09 4110 5440 8460 14600 93
ULS10 3340 7440 7400 14100 91
With respect to directions, the 60 degree production cases result in approximately 10 % lower peak mooring line and anchor forces, but the total translation is somewhat larger. This implies that the system is slightly softer in this direction. Parked cases produce similar anchor forces, and as waves alone account for more of the forces in the system the lack seed variation increase the uncertainty of the results. For the lower mooring lines, no temporary slack events occurred during any of the simulations with the six-line configuration. For the upper lines, slack events occurred during some of the cases with wind speeds around cut-out and the turbine in production state.
Traditionally slack lines are known to produce snapping loads, but no snapping loads appeared in the time series. An example from ULS07 is shown in Figure 17.
Figure 17: Force plots over time for the waves (left) and lower mooring lines (right) during the ULS07 DLC
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A shell integrity control was performed based on DNV RP-C202. Shell, panel ring and column buckling was checked. The dimensioning moment and axial stress was checked for all the time series. The governing load case and the resulting utilization is shown in Table 21 .
Table 21: Buckling utilization
Position [m] Governing DLC Utilization
-37.8 ULS07 91%
-20.1 ULS07 67%
-12.5 ULS07 62%
0.0 ULS07 67%
10.0 ULS02 56%
10.0 ULS02 69%
24.6 ULS02 77%
24.6 ULS02 77%
37.0 ULS02 70%
50.0 ULS02 63%
62.0 ULS02 52%
75.0 ALS01 43%
86.0 ALS01 43%
Overall, the buckling utilization is relatively low. For the lower part of the substructure, wave loads are dominating. Above the water line, typically high turbulence loads on the wind turbine result in extreme moments that produce the highest utilization.
The lowest section produce a high utilization, in general, due to a simplified approach, as no support from the bottom end cap structure is included, but a simple distribution of ring stiffeners was included. The vertical spacing was 3 m, and a generic stiffener with a height of 0.3 m and an average thickness of 0.025 m was assumed. No vertical stiffeners was assumed, although this might be beneficial for the submerged tapered section in the substructure. The resulting mass of the ring stiffener system was 26.1 tons.