PSI - Issue 28

Daniel Mella et al. / Procedia Structural Integrity 28 (2020) 511–516 Mel la D. A. et al. / Structural Integrity Procedia 00 (2020) 000–000 5 increased with U r . Figure 2a and 2b show the maximum oscillatory response in the streamwise A ∗ osc,x and crossflow A ∗ osc,y directions, respectively. The maximum oscillatory response in a given direction was defined as the mean value of the highest 10% of the recorded response, as in Hover et al. (1998). Vertical bars correspond to one standard deviation (SD) around the maximum value. The cylinder response increased with U r , except for an initial reduction of A ∗ osc,x at U r = 3 . 24 . The maximum observed responses were A ∗ osc,x = 0 . 28 D and A ∗ osc,y = 0 . 89 D at the maximum tested flow velocity. Figure 2c shows the cylinder main oscillation frequency in the crossflow direction f y . Dashed-dotted lines represent the ratio between the main streamwise and crossflow oscillation frequency, f y /f x . Dashed lines enclose f nw and f na . The crossflow oscillation frequency varied between 0 . 63 f nw and 1 . 17 f nw . The ratio f y /f x was equal to 0.5 throughout the tested flow velocities, except at the initial U r = 2 . 67 . 4.2. Maximum stresses 515

0 . 4

200

200

− 1 . 2 − 0 . 8 − 0 . 4 0

100

100

σ x + σ ∗ osc,x

− 200 − 100 0

R

σ ∗ osc,y

0

3 4 5 6

3 4 5 6

3 4 5 6

U r

U r

U r

(c)

: σ x + σ ∗ osc,x .

: σ ∗ osc,x .

:

(a)

: Maximum/minimum σ x ± σ ∗ osc,x .

(b)

: Maximum/minimum ± σ ∗ osc,y .

: mean σ x

σ ∗ osc,y Fig. 4: Bending stresses associated to the maximum responses and stress ratio. a) Streamwise stress, error bars: σ x ± SD x . b) Crossflow stress, error bars: σ y ± SD y . c) Stress ratio Same as in Section 4.1, the stresses in a given direction were decomposed as the sum of a cyclic and mean stresses, σ = σ osc + σ . σ y ≈ 0 , whereas σ x increased with U r . Figure 4a and 4b show the maximum total stresses in the streamwise ( σ x + σ ∗ osc,x ) and crossflow ( σ ∗ osc,y ) direction. Here, σ ∗ osc,x and σ ∗ osc,y are the stresses associated with A ∗ osc,x and A ∗ osc,y , respectively. The maximum σ ∗ osc,x was 52.3 Mpa at the maximum tested U r . On the other hand, the maximum σ ∗ osc,y was 171 Mpa. Considering the influence of σ x , the maximum and minimum total stresses in the streamwise direction were 53.4 and 158 Mpa, respectively. These results showed that, despite having a dominant crossflow response ( A ∗ osc,y /A ∗ osc,x ≈ 3 . 1 ), the maximum total stress in the streamwise direction was on average only 11% lower than its crossflow counterpart for U r ≥ 4 . 39 . The stress ratio, defined as the quotient between the minimum and maximum stress, is shown in Figure 4c. As expected, R ≈ − 1 across U r for σ ∗ osc,x and σ ∗ osc,y . Considering the total streamwise stresses, the stress ratio varied between 0.18 and 0.33 for U r ≥ 3 . 28 . 5. Conclusion This work employed a non-contact measurement system to determine the cyclic (i.e. fatigue) stresses on a pivoted cylinder subjected to VIV. The structural configuration allowed to transfer the complex fluid structure interaction forces to a bottom-fixed stainless steel rod through a single rigid connection. Thus, a direct relationship between the cylinder motion and the maximum stresses on the rod was established. The results showed a crescent-shape trajectory as the flow velocity increased. The maximum observed responses were 0.28D and 0.89D in the streamwise and crossflow direction, respectively. The main oscillation frequency