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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Soyama, H., and Kumano, H., 2002, “The Fundamental Threshold Level—A New Parameter for Predicting Cavitation Erosion Resistance,” J. Test Eval., 30(5), pp. 421–431. [CrossRef]
Hattori, S., Hirose, T., and Sugiyama, K., 2010, “Prediction Method for Cavitation Erosion Based on Measurement of Bubble Collapse Impact Loads,” Wear, 269, pp. 507–514. [CrossRef]
Franc, J. P., 2009, “Incubation Time and Cavitation Erosion Rate of Work-Hardening Materials,” ASME J. Fluids Eng., 131(2), p. 021303. [CrossRef]
Fortes-Patella, R., Challier, R., and Reboud, J. L., 2001, “Cavitation Erosion Mechanism: Numerical Simulation of the Interaction Between Pressure Wave and Solid Boundaries,” Proceedings of 4th International Symposium on Cavitation (CAV2001), Pasadena, CA.
Fukaya, M., Tamura, Y., and Matsumoto, Y., 2010, “Prediction of Cavitation Intensity and Erosion Area in Centrifugal Pump by Using Cavitating Flow Simulation With Bubble Flow Model,” J. Fluid Sci. Technol., 5(2), pp. 305–316. [CrossRef]
Dular, M., Stoffel, B., and Sirok, B., 2006, “Development of a Cavitation Erosion Model,” Wear, 261, pp. 642–655. [CrossRef]
Ochiai, N., Iga, Y., Nohmi, M., and Ikohagi, T., 2010, “Numerical Prediction of Cavitation Erosion Intensity in Cavitating Flows Around a Clark Y 11.7% Hydrofoil,” J. Fluid Sci. Technol., 5(3), pp. 416–431. [CrossRef]
Okuda, K., and Ikohagi, T., 1996, “Numerical Simulation of Collapsing Behavior of Bubble Cloud,” Trans. JSME Ser. B, 62(603), pp. 3792–3797 (in Japanese). [CrossRef]
Ochiai, N., 2011, “Study of Numerical Prediction of Cavitation Erosion Based on Bubble Collapse Intensity,” Ph.D. thesis, Graduate School of Engineering, Tohoku University, Japan.
Shima, E., and Jounouchi, T., 1994, “Role of Computational Fluid Dynamics in Aeronautical Engineering (No. 12)—Formulation and Verification of Uni-Particle Upwind Schemes for the Euler Equations,” Proceedings of 12th NAL Symposium on Aircraft Computational Aerodynamics, pp. 255–260.
Anderson, W. K., Thomas, J. L., and van Leer, B., 1986, “Comparison of Finite Volume Flux Vector Splittings for the Euler Equations,” AIAA J., 24(9), pp. 1453–1460. [CrossRef]
Degani, D., and Schiff, L., 1986, “Computation of Turbulent Supersonic Flows Around Pointed Bodies Having Crossflow Separation,” J. Comput. Phys., 66, pp. 173–196. [CrossRef]
Maxey, M. R., and Riley, J. J., 1983, “Equation of Motion for a Small Rigid Sphere in a Nonuniform Flow,” Phys. Fluids, 26(4), pp. 883–889. [CrossRef]
Tomiyama, A., Kataoka, I., Zun, I., and Sakaguchi, T., 1998, “Drag Coefficients of Single Bubble Under Normal and Micro Gravity Conditions,” JSME Int. J. Ser. B, 41(2), pp. 472–479. [CrossRef]
Keller, J. B., and Kolodner, I. I., 1956, “Damping of Underwater Explosion Bubble Oscillations,” J. Appl. Phys., 27(10), pp. 1152–1161. [CrossRef]
Yasui, K., 1996, “Variation of Liquid Temperature at Bubble Wall Near the Sonoluminescence Threshold,” J. Phys. Soc. Jpn., 65(9), pp. 2830–2840. [CrossRef]
Philipp, A., and Lauterborn, W., 1998, “Cavitation Erosion by Single Laser-Produced Bubbles,” J. Fluid Mech., 361, pp. 75–116. [CrossRef]
Nakashima, Y., Kato, H., and Maeda, S., 1981, “A Comparison of New Cavitation Erosion Test Methods and Their Application to Foil Sections,” J. Soc. Nav. Archit. Jpn., 149, pp. 73–79 (in Japanese). [CrossRef]
Ochiai, N., Iga, Y., Nohmi, M., and Ikohagi, T., 2011, “Numerical Analysis of Nonspherical Bubble Collapse Behavior and Induced Impulsive Pressure During First and Second Collaspes Near the Wall Boundary,” J. Fluid Sci. Technol., 6(6), pp. 860–874. [CrossRef]
Matsumoto, Y., Okudaira, T., Wada, M., Enomoto, H., and Ichikawa, Y., 1985, “Influence of Cavitation on the Nuclei Distribution,” Trans. JSME B, 51(472), pp. 3844–3851 (in Japanese). [CrossRef]
Franc, J. P., and Michel, J.-M., 1997, “Cavitation Erosion Research in France: The State of the Art,” J. Mar. Sci. Technol., 2(4), pp. 233–244. [CrossRef]


Grahic Jump Location
Fig. 1

Schematic diagram of the numerical prediction method of cavitation erosion

Grahic Jump Location
Fig. 2

Schematic diagram of calculation of impulsive force

Grahic Jump Location
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)

Grahic Jump Location
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)

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 7

Position of maximum wall pressure during second collapse

Grahic Jump Location
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)

Grahic Jump Location
Fig. 9

Bubble number density

Grahic Jump Location
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)

Grahic Jump Location
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)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In