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Research Papers: Multiphase Flows

Study of Quantitative Numerical Prediction of Cavitation Erosion in Cavitating Flow

[+] Author and Article Information
Naoya Ochiai

e-mail: ochiai@cfs.ifs.tohoku.ac.jp

Yuka Iga, Toshiaki Ikohagi

Institute of Fluid Science,
Tohoku University,
2-1-1, Katahira,
Aoba-ku, Sendai,
Miyagi, 980-8577, Japan

Motohiko Nohmi

EBARA Corporation,
78-1 Shintomi, Futtsu,
Chiba, 293-0011, Japan

Manuscript received March 21, 2012; final manuscript received July 2, 2012; published online December 21, 2012. Assoc. Editor: Frank C. Visser.

J. Fluids Eng 135(1), 011302 (Dec 21, 2012) (10 pages) Paper No: FE-12-1139; doi: 10.1115/1.4023072 History: Received March 21, 2012; Revised July 02, 2012

Cavitation erosion is a material damage phenomenon caused by the repeated application of impulsive pressure on a material surface induced by bubble collapse, and the establishment of a method by which to numerically predict cavitation erosion is desired. In the present study, a numerical quantitative prediction method of cavitation erosion in a cavitating flow is proposed. In the present method, a one-way coupled analysis of a cavitating flow field based on a gas-liquid two-phase Navier–Stokes equation (Eulerian) and bubbles in the cavitating flow by bubble dynamics (Lagrangian) is used to treat temporally and spatially different scale phenomena, such as the macroscopic phenomenon of a cavitating flow and the microscopic phenomenon of bubble collapse. Impulsive pressures acting on a material surface are evaluated based on the bubble collapse position, time, and intensity, and the erosion rate is quantitatively predicted using an existing material-dependent relationship between the impulsive energy (square of the impulsive force) and the maximum erosion rate. The erosion rate on a NACA0015 hydrofoil surface in an unsteady transient cavitating flow is predicted by the proposed method. The distribution of the predicted erosion rate corresponds qualitatively to the distribution of an experimental surface roughness increment of the same hydrofoil. Furthermore, the predicted erosion rate considering the bubble nuclei distribution is found to be of the same order of magnitude as the actual erosion rate, which indicates that considering bubble nuclei distribution is important for the prediction of cavitation erosion and that the present prediction method is valid to some degree.

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Figures

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Fig. 1

Schematic diagram of the numerical prediction method of cavitation erosion

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Fig. 2

Schematic diagram of calculation of impulsive force

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Fig. 3

Spatial distribution of the number of high impulsive pressure events on the hydrofoil surface for four different time intervals during one cycle of a transient cavitating flow and the representative aspects of the flow field (pressure distribution, isoline of the void fraction of 10%, and bubbles) at these times (NACA0015, αin = 4 deg, σ = 0.92, Re  = 1.8×106, R∞ = 100μm)

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Fig. 4

First and second collapses of single bubble (the initial bubble shape is an ellipsoid, γ = 1.4, (i ), (ii ), (iii ): the first collapse, (iv ), (v ), (vi ): the second collapse)

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Fig. 5

Maximum wall pressure (a dashed line shows pmm/pspher = 1)

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Fig. 7

Position of maximum wall pressure during second collapse

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Fig. 8

Spatial distribution along the chord direction of erosion rate for a standard radius until 50 ms (NACA0015, αin = 4 deg, σ = 0.92, Re  = 1.8 × 106)

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Fig. 9

Bubble number density

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Fig. 10

Spatial distribution along the chord direction of average erosion rate for a standard radius until 50 ms, weighted based on bubble number density (NACA0015, αin = 4 deg, σ = 0.92, Re  = 1.8×106)

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Fig. 11

Spatial distribution along the chord direction of the average erosion rate considering the bubble nuclei distribution until 50 ms (NACA0015, αin = 4 deg, σ = 0.92, Re = 1.8×106, 10 μm≤R∞≤ 110 μm) and experimental surface roughness increment [18] (NACA0015, αin = 4 deg, σ = 0.92)

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