PSI - Issue 8

N. Di Domenico et al. / Procedia Structural Integrity 8 (2018) 422–432 N. Di Domenico et al. / Structural Integrity Procedia 00 (2017) 000–000

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In figure 2 the hydrofoil geometry and setup is shown. The blunt geometry, built in steel with density ρ = 7850 Kg / m 3 and submerged in water, is clamped by one side and embedded in a pivot leaving free tip rotation. These particular boundary conditions are necessary to amplify the torsional vibration modes induced by the water flow. The trailing edge is truncated in order to obtain the blunt shape where the flow separation occurs.

(a) First bending mode 1133.8 Hz

(b) First torsional mode 1587.1 Hz

(c) Second torsional mode 3630.9 Hz

(d) Second bending mode 3917.7 Hz

(e) Third bending mode 5936.6 Hz

(f) Third torsional mode 6789.6 Hz

Fig. 3: Hydrofoil natural modes

The first six modal shapes, obtained in ANSYS Mechanical, were extracted and are shown in figure 3. Nodal displacements associated to modal shapes have been exported and employed to set up the RBF problems in RBF Morph, obtaining a shape modification parameter for each mode. Embedding the modal shapes using RBF Morph was then possible to start the transient FSI analysis. As boundary conditions a 101325 Pa pressure, 288 . 15 K temperature, 10 − 6 mm 2 / s kinematic viscosity and 998 Kg / m 3 density were applied. Simulation was carried for 10000 time steps of 2 e − 5 s . Five inner iterations per time step were carried. Simulations were accomplished with two flow velocities values, 16 m / s and 22 m / s , in order to catch the lock-in and lock-o ff (Ausoni et al. (2012)). Choosing a point in the trailing edge was extracted its time-velocity amplitude and FFT.

200

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| P ( f ) |

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800 1 , 000 1 , 200 1 , 400

0 0 . 02 0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14 0 . 16 0 . 18 0 . 2

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Fig. 4: Time-Velocity Amplitude and Spectral Analysis for 16 m / s

In figure 4 the time-velocity amplitude and the FFT are shown for the case with a 16 m / s velocity flow. The FFT of the output data shows a good sync between the shedding of the vortices and the body oscillation: this particular condition is the Lock-In and it depicts the resonance phenomenon. The frequency of the vortex shedding is really