'Lumping' of Fatigue Load Cases

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Garrad Hassan & Partners Ltd. Mungo Morris Inverse SN slope 4 6 8 10 Blade 1 Root My 228.34 348.69 465.42 571.40 Blade 1 Root Fx 12.09 17.88 23.44 28.61 Blade 1 Flapwise moment 234.48 358.66 475.99 582.70 Blade 1 Flapwise force 13.10 19.47 25.08 30.08 Rotating hub Fx 22.36 35.61 46.59 55.88 Tower Base My 2419.55 3550.89 4590.65 5508.01 Tower Base Fx 189.26 285.18 387.43 495.88 Tower Top My 246.41 336.75 429.09 517.14 Tower Top Fx 25.09 40.11 53.11 64.55 Table 3: Series 1 - Fatigue loads for wave height and period bin sizes of 0.5m and 0.5s respectively (in kNm) Inverse SN slope 4 6 8 10 Blade 1 Root My 228.38 348.74 465.46 571.41 Blade 1 Root Fx 12.09 17.88 23.45 28.62 Blade 1 Flapwise moment 234.47 358.66 476.02 582.74 Blade 1 Flapwise force 13.10 19.47 25.08 30.08 Rotating hub Fx 22.36 35.60 46.56 55.84 Tower Base My 2424.67 3544.61 4566.12 5468.30 Tower Base Fx 191.04 285.12 382.86 486.14 Tower Top My 246.42 336.76 429.06 517.10 Tower Top Fx 25.10 40.12 53.13 64.61 Table 4: Series 2 - Fatigue loads for wave height and period bin sizes of 2.5m and 2.5s respectively (in kNm) Inverse SN slope 4 6 8 10 Blade 1 Root My 228.35 348.70 465.43 571.40 Blade 1 Root Fx 12.09 17.88 23.44 28.60 Blade 1 Flapwise moment 234.45 358.62 475.96 582.67 Blade 1 Flapwise force 13.10 19.47 25.08 30.07 Rotating hub Fx 22.35 35.60 46.56 55.85 Tower Base My 2411.54 3541.25 4595.88 5543.22 Tower Base Fx 192.69 282.88 372.23 461.06 Tower Top My 246.49 336.83 429.06 516.94 Tower Top Fx 25.04 40.03 53.01 64.45 Table 5: Series 3 - Fatigue loads for wave height and period bin sizes of 7.0m and 8.0s respectively (in kNm) Table 6 shows the percentage changes between results for series 2 and series 1, and between series 3 and series 1. The applicable values of inverse SN slope for each load are highlighted. It can be seen that the variation in DEL, even when all the wave heights and periods are
Garrad Hassan & Partners Ltd. Mungo Morris condensed into single values at each wind speed, never exceeds 2% (Tower Base Fx), and many other loads are almost unaffected. Series 2 Series 3 4 6 8 10 4 6 8 10 Blade 1 Root My 0.02 0.02 0.01 0.00 0.00 0.00 0.00 0.00 Blade 1 Root Fx -0.01 0.01 0.03 0.04 -0.01 -0.02 -0.02 -0.01 Blade 1 Flap moment 0.00 0.00 0.01 0.01 -0.01 -0.01 0.00 -0.01 Blade 1 Flap force 0.00 0.00 -0.01 -0.01 0.00 -0.02 -0.02 -0.02 Rotating hub Fx 0.00 -0.04 -0.06 -0.06 -0.02 -0.04 -0.05 -0.05 Tower Base My 0.21 -0.18 -0.53 -0.72 -0.33 -0.27 0.11 0.64 Tower Base Fx 0.94 -0.02 -1.18 -1.96 1.81 -0.81 -3.92 -7.02 Tower Top My 0.01 0.00 -0.01 -0.01 0.03 0.02 -0.01 -0.04 Tower Top Fx 0.03 0.02 0.04 0.09 -0.19 -0.20 -0.19 -0.16 Table 6: Variation in load from original base-line case (percent) A possible explanation for the very small changes in fatigue loads is that the wave loading itself makes a very small contribution to the total fatigue loading. To check this possibility, two simulations, one with waves present and one without waves, were run and damage equivalent loads calculated. If there was negligible difference between the loads generated by both runs then this would be evidence that the wave action had an insignificant affect on the fatigue loads. These simulations were performed at a wind speed of 6.56m/s (the mode of the wind speed distribution) and, in one case, with a significant wave height of 1.0m and a peak spectral period of 3.9s. The percentage increases in tower loads due to the inclusion of the waves is presented in table 7. Inverse SN slope 4 6 8 10 Tower Base My 8.11% 9.83% 10.11% 10.19% Tower Base Fx 279.64% 270.51% 243.94% 229.54% Tower Top My 0.02% 0.01% 0.00% 0.00% Tower Top Fx -0.12% -0.04% -0.01% 0.00% Table 7: Fatigue load increase due to presence of wave It can be seen from Table 7 that, although all tower top loads are little affected by the presence of the wave in the simulation, the tower base loads are strongly affected – the foreaft tower base force in particular. From Table 6 one can see that this is the same load that varied by only 1.8% when all 204 initial simulations were ‘lumped’ into 1 value of wave height and period for all simulations. One must therefore conclude that, despite having a strong influence on the fatigue loading of the turbine, the effect of waves can be simply and accurately modelled by using large bin size means of the wave height and period in all simulations.
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'Lumping' of Fatigue Load Cases

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