Final report for WP4.3: Enhancement of design methods ... - Upwind

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UPWIND WP4: Offshore Support Structures and Foundations The results of the convergence in the present study are evaluated through the error norm defined by: The grid converge ratio (R) is a useful quantity to identify the behaviour of the convergence. This quantity defined by: And the solution is classified in terms of the value of R as: • Oscillatory divergence, if R < -1 • Oscillatory convergence, if -1 < R < 0 • Monotonic convergence, if 0 1. The uncertainty (Uk) associated with the computations finer discretisation ( ) is given by: where Fs is a safety factor which may vary between 1 and 3. The present study considers a very conservative approach and takes Fs = 3. Convergence studies for the OC3-Hywind platform The geometry of OC3-Hywind spar buoy was discretised for three grid sizes shown in Figure 8.4. Following Cruz in [113], the grid cell size (hi) is related to the WAMIT higher order panel size parameter associated to an automatic discretisation of the geometry. Panel sizes equal to 10 m, 5.0 m and 2.5m were considered and the hydrodynamic quantities were evaluated for five wave periods selected randomly between 3 s to 16 s. Figure 8.4: Three discretisations of the geometry of the OC3-Hywind used for the convergence tests. The panel size parameter equal to (a) 10.0 m, (b) 5.0 m and (c) 2.5m. The convergence ratio (R) (Equation 3-6) associated with the discretisation triplet used in this study computed for the linear excitation forces is shown in Table 8.4. The values of (R) depend on the hydrodynamic quantity being evaluated and on the frequency. Most of the values are between -1 and 1 and the solution for the majority of evaluated cases can be classified as convergent. 96 [8-4] [8-5] [8-6] [8-7]
UPWIND WP4: Offshore Support Structures and Foundations Table 8.4: Convergence ratio (R) associated with the absolute value of the linear excitation force for a discretisation triplet with panel sizes equal to 10.0 m, 5.0 m and 2.5 m for the OC3-Hywind geometry. T (s) | FX1 | | FX2 | | FX3 | | FX4 | | FX5 | | FX6 | 3.9 -1.86 0.25 0.48 0.25 -2.10 -0.12 7.1 0.07 0.03 0.33 -0.09 -0.05 0.09 7.9 0.1 0.13 0.33 0.06 -0.02 0.11 8.5 0.18 0.20 0.33 0.11 0.03 0.12 14.4 0.41 0.37 0.22 0.31 0.28 0.23 An estimation of the exact solution for the linear excitation force associated with the incident wave periods considered in this study is presented in Table 8.5. The uncertainty associated with the finer mesh (panel size equal to 2.5m) for the linear excitation forces is presented in Table 8.6. The evolution of the convergence for four different discretisations is presented in terms of the error norm defined by Equation 3.5 for the linear excitation forces in Figure 8.5. WAMIT does not provide the solution on each panel, and it also does not output the total number of panels. Throughout the study the number of equations (N) in the linear system (which corresponds to the number of unknowns) is used as a measure of the total number of panels. The relationship between N and the panel size is presented in Table 8.7. Overall the uncertainty estimates are relatively small when compared to the absolute value of the excitation force for all tested wave frequencies. A panel size equal to 2.5m was chosen for the computations of the hydrodynamic quantities associated with the OC3-Hywind. Table 8.5: Estimations of the exact value associated with the linear excitation force for the incident wave periods considered in this study. T (s) | FX1 | | FX2 | | FX3 | | FX4 | | FX5 | | FX6 | 3.9 5.80E+1 1.40E-6 3.60E+0 1.20E-4 4.90E+3 1.50E-13 7.1 1.10E+2 2.60E-6 1.80E+1 1.90E-4 7.90E+3 7.10E-14 7.9 1.10E+2 2.70E-6 2.10E+1 1.90E-4 7.90E+3 6.10E-14 8.5 1.10E+2 2.80E-6 2.30E+1 1.90E-4 7.90E+3 5.30E-14 14.4 1.10E+2 2.80E-6 2.50E+1 1.30E-4 5.50E+3 1.40E-14 Table 8.6: Uncertainty associated with the computations for the finer mesh (panel size 2.5) for the linear excitation force at the incident wave periods considered in this study. T (s) | FX1 | | FX2 | | FX3 | | FX4 | | FX5 | | FX6 | 3.9 1.50E-2 3.30E-10 5.70E-3 1.50E-8 1.32E+0 2.49E-14 7.1 2.10E-4 9.30E-13 3.30E-3 1.89E-10 6.60E-3 1.08E-14 7.9 4.50E-4 7.80E-12 2.91E-3 1.20E-10 7.50E-4 1.29E-14 8.5 1.41E-3 2.55E-11 2.64E-3 6.00E-10 2.01E-3 1.44E-14 14.4 8.10E-3 1.59E-10 4.20E-4 5.40E-9 1.68E-1 2.25E-14 Table 8.7: Relation between panel size parameter and the number of unknowns in the equations in WAMIT for the OC3- Hywind discretisations of the geometry. Panel Size (m) 2.5 5.0 7.5 10 Number of Unknowns 300 136 81 66 97
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Project UpWind Contract No.: 019945
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Acknowledgement The presented work
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Summary The overall aim of the UpWi
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Table of Contents Acknowledgement..
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Task 4.1 Integration of support str
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Sequential coupling The sequential
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analysis. In the new multibody code
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Figure 2.4: 2nd global bending mode
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3.2 Comparison of deterministic loa
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Figure 3.5: Time series of axial fo
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• Time domain simulation in ADCoS
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• A supplementary load vector for
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The following results are found: Fi
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Figure 4.5: Output positions in the
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It is directly visible that there i
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ated eigenfrequency is shifted into
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Water levels For the calculation of
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guidelines for the inclusion of cli
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damaging if the frequency of the ex
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uncertain parameters carefully. Thr
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Table 5.3 shows annual reliability
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Steel substructure for offshore win
Page 46 and 47: Table 5.16 shows the required FDF v
Page 48 and 49: A Fracture Mechanical (FM) modellin
Page 50 and 51: Figure 5.4: Annual reliability indi
Page 52 and 53: Further, the effect of possible ins
Page 54 and 55: Rainflow evaluation The load cases
Page 56 and 57: For DLC 7.2 it has to be considered
Page 58 and 59: Guideline, DLC 1.5). Furthermore, t
Page 60 and 61: Table 5.28: Output locations for da
Page 62 and 63: From these results it can be clearl
Page 64 and 65: Figure 5.11: Normalised DELs with v
Page 66 and 67: Figure 5.14 presents normalized DEL
Page 68 and 69: Figure 5.16: Output locations for e
Page 70 and 71: UPWIND WP4: Offshore Support Struct
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Final report for WP4.3: Enhancement of design methods ... - Upwind

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