PSI - Issue 27

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Muhammad Yusvika et al. / Procedia Structural Integrity 27 (2020) 109–116 Yusvika et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 3. Comparison of pressure fluctuation and pressure amplitudes at design and ballast draught conditions (Paik et al., 2013).

5. Numerical investigation to the cavitation erosion Cavitation erosion is caused when several cavitation bubbles are collapse in the vicinity near the solid surface. Noak and Vogel stated in their research that shock waves of an initial pressure magnitude of 10 GPa are damped by roughly two orders of magnitudes when traveling over a distance of 100 μ m through liquid water (Noack and Vogel, 1998). Peters et al. have conducted a numerical simulation to predict the cavitation erosion on the propeller blades (Peters et al., 2018). Numerical prediction of the cavitation erosion was used as an assumption that shock wave generation and large scales structures propagation are neglected. Only one collapse of a single bubble near the solid surface is considered for modeling. To modeling cavitation erosion impact, a single erosion impact can be predicted once per time step on the face of a boundary considered. The erosion distinguishes between impact and no impact in a Boolean manner. The surface damage is proposes caused by the collapse of the bubble near the surface forming microjet. The microjet velocity (see Eq. 5) depends on the pressure of the surrounding side of the bubble wall. To predict the erosion, Peters et al. apply a relation of the microjet and the critical velocity formula (see Eq. 6) by Chihane (2014). v jet ≈ c y + √ P - P v ρ l (5) Lush has proposed a relation for the critical velocity by considering the impact of a liquid mass on the propeller surface (Lush, 1983). He stated that compression of the stationary fluid at the wall by microjet lead to shock impact and generates a high amplitudes pressure wave that travels perpendicularly from the wall. When the pressure exceeds the yield strength of the material, it may allow deformation plastically. Supposedly this happens when the microjet velocity exceeds a critical value (Lush, 1983). v crit = √ P y P l ( 1- ( 1+ P y B ) -1 n ⁄ ) (6) where B = 300 MPa, and n = 7 is standard coefficients for liquid water in the Tait equation of state relating pressure and density. Peters et al. (2018) have numerically predicted overall cavitation erosion behavior compared with the experimental results for the case condition of σ n = 0.963 and J = 0.8208, as the considered material cannot be specified for the experimental erosion prediction, which uses an erosive coating. Although the experimental prediction has shown is a valid method to predict the area of erosion qualitatively. To define the critical velocity for numerical simulation and conduct reasonable erosion prediction, yield strength of 200 x 10 6 N/mm 2 is applied for commonly standard cast copper alloy for the propeller material. Based on the results, erosion predicted at an area above the root of the propeller blade. As shown in Fig. 4, the numerical prediction result has a similar pattern of cavitation erosion with the