PSI - Issue 80

Francisco J.G. de Oliveira et al. / Procedia Structural Integrity 80 (2026) 1–10 Author name / Structural Integrity Procedia 00 (2023) 000–000

9

9

γ f

γ e

2000

1000

0

1

2

3

4

5

6

1

2

3

4

5

6

λ

λ

ROOT

MIDSPAN

TIP

Fig. 8. Evolution of the experienced flapwise and edgewise root bending moment for the tested conditions.

ROOT

MIDSPAN

TIP

12 . 5

10 . 0

RMS( ε )

7 . 5

5 . 0

1 2 3 3 . 5 4 5 6 . 5 λ

1 2 3 3 . 5 4 5 6 . 5 λ

1 2 3 3 . 5 4 5 6 . 5 λ

Fig. 9. Spanwise evolution of RMS( ε ′ ), for the di ff erent operational conditions tested. Error bars represent the standard deviation of the statistic in between results.

Figure 8 presents the root bending moment surrogates γ f and γ e evolution across λ and FST. These are computed as: γ i = s 1 s 0 ⟨ ε i ⟩ d s , (5) where s 0 and s 1 correspond to the spatial limits associated with the ROOT region of the blade. Flapwise and edgewise contributions to the root bending moment (respectively γ f and γ e ) increase with λ .However, edgewise contributions are more sensitive to λ than flapwise ones. These results underline the spanwise heterogeneity of the structural response: the root dominated by cyclic bending, the mid-span by transitional loads, and the tip by vortex-driven excitation. To complement these observations, the RMS of the magnitude of strain fluctuations provides a measure of the cyclic loading acting on the blade. Figure 9 highlights the evolution of these fluctuations at the 3 regions of the blade under analysis. The results clearly show a strong dependence of induced fluctuating strain dynamics with λ . Above design conditions ( λ > λ r ), the turbine At λ < λ r , the ROOT presents the largest magnitude of RMS( ε ′ ), while at λ > λ r , the magnitude of the fluctuating dynamics induced at the TIP grow. This is especially true for λ = λ r , where tip vortices forming at the edge of the blade are expected to be the strongest, and most spatially coherent. the MIDSPAN emerges as a transition region between the two extreme regions of the blade. As λ increases up to λ r , the flow becomes progressively attached to the blade towards the tip. This is evidenced by the evolution of RMS( ε ′ ) for the 3 regions under analysis. Furthermore, the TIP experiences the largest standard deviation of magnitudes of RMS( ε ′ ), across λ ≈ λ r as the tip vortices become more intense, and their corresponding interaction with the blade becomes relatively stronger.