An Eulerian/Lagrangian computational procedure was developed for the prediction of cavitation inception by event rate. The carrier-phase flow field was computed using an Eulerian Reynolds-averaged Navier-Stokes (RANS) solver. The Lagrangian analysis was one-way coupled to the RANS solution, since at inception, the contributions of mass, momentum, and energy of the microbubbles to the carrier flow are negligible. The trajectories were computed using Newton’s second law with models for various forces acting on the bubble. The growth was modeled using the Rayleigh-Plesset equation. The important effect of turbulence was included by adding a random velocity component to the mean flow velocity and by reducing the local static pressure. Simulation results for the Schiebe body indicate agreement with experimentally observed trends and a significant event rate at cavitation indices above visual inception.

1.
McCormick
,
B. W.
,
1962
, “
On Cavitation Produced by a Vortex Trailing from a Lifting Surface
,”
ASME J. Basic Eng.
,
84
, pp.
369
379
.
2.
Farrell
,
K. J.
, and
Billet
,
M. L.
,
1994
, “
A Correlation of Leakage Vortex Cavitation in Axial-Flow Pumps
,”
ASME J. Fluids Eng.
,
116
, pp.
551
557
.
3.
Meyer
,
R. S.
,
Billet
,
M. L.
, and
Holl
,
J. W.
,
1992
, “
Freestream Nuclei and Traveling Bubble Cavitation
,”
ASME J. Fluids Eng.
,
114
, pp.
672
679
.
4.
Hsiao
,
C.-T.
, and
Pauley
,
L. L.
,
1999
, “
Study of Tip Vortex Cavitation Inception using Navier-Stokes Computation and Bubble Dynamics Model
,”
ASME J. Fluids Eng.
,
121
(
1
), pp.
198
204
.
5.
Johnson, J. E., Jr., and Hsieh, T., 1966, “The Influence of the Trajectories of the Gas Nuclei on Cavitation Inception,” Sixth Naval Hydrodynamics Symposium, pp. 163–182.
6.
Chahine, G. L., 1995, “Bubble Interactions With Vortices,” Fluid Vortices, S. I. Green, ed., Kluwer, Dordrecht, The Netherlands, pp. 783–828.
7.
Schiebe, F. R., 1972, “Measurement of the Cavitation Susceptibility of Water Using Standard Bodies,” University of Minnesota, St. Anthony Falls Hydraulic Laboratory, Report No. 188.
8.
Gates, E. M., Billet, M. L., Katz, J., Ooi, K. K., Holl, J. W., and Acosta, A. J., 1979, “Cavitation Inception and Nuclei Distributions Joint ARL/CIT Experiments,” CalTech, Division of Eng. and Applied Science, Report E244.1.
9.
Hamilton, M. F., Thompson, D. E., and Billet, M. L., 1982, “An Experimental Study of Traveling Bubble Cavitation Noise,” ASME International Symposium on Cavitation Noise, ASME, New York, pp. 25–33.
10.
Holl, J. W., and Carroll, J. A., 1979, “Observations of the Various Types of Limited Cavitation on Axisymmetric Bodies,” Proceedings of ASME International Symposium on Cavitation Inception, pp. 87–99.
11.
Ceccio
,
S. L.
, and
Brennen
,
C. E.
,
1991
, “
Observations of the Dynamics and Acoustics of Traveling Bubble Cavitation
,”
J. Fluid Mech.
,
233
, pp.
633
660
.
12.
Kuhn de Chizelle
,
Y.
,
Ceccio
,
S. L.
, and
Brennen
,
C. E.
,
1995
, “
Observations and Scaling of Traveling Bubble Cavitation
,”
J. Fluid Mech.
,
292
, pp.
99
126
.
13.
Liu
,
Z.
, and
Brennen
,
C. E.
,
1998
, “
Cavitation Nuclei Population and Event Rates
,”
ASME J. Fluids Eng.
,
120
, pp.
728
737
.
14.
Taylor, L. K., and Whitfield, D. L., 1991, “Unsteady Three-Dimensional Incompressible Euler and Navier-Stokes Solver for Stationary and Dynamic Grids,” AIAA Paper No. 91-1650.
15.
Whitfield, D. L., 1995, “Perspective on Applied CFD,” AIAA Paper No. 95-0349.
16.
Roe
,
P. L.
,
1981
, “
Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes
,”
J. Comput. Phys.
,
43
, pp.
357
372
.
17.
Zierke, W. C., ed., 1997, “A Physics-Based Means of Computing the Flow around a Maneuvering Underwater Vehicle,” Applied Research Laboratory Penn State, Technical Report No. TR 97-002.
18.
Maxey
,
M. R.
, and
Riley
,
J. J.
,
1983
, “
Equation of Motion of a Small Rigid Sphere in a Non-uniform Flow
,”
Phys. Fluids
,
26
, pp.
883
889
.
19.
Sirignana
,
W. A.
,
1993
, “
Fluid Dynamics of Sprays
,”
ASME J. Fluids Eng.
,
115
, pp.
345
378
.
20.
Stock
,
D. E.
,
1996
, “
Particle Dispersion in Flowing Gases
,”
ASME J. Fluids Eng.
,
118
, pp.
4
17
.
21.
Mei
,
R.
,
1996
, “
Velocity Fidelity of Flow Tracer Particles
,”
Exp. Fluids
,
22
, pp.
1
13
.
22.
Michaelides
,
E. E.
,
1997
, “
Review—The Transient Equation of Motion for Particles, Bubbles, and Droplets
,”
ASME J. Fluids Eng.
,
119
, pp.
233
247
.
23.
Crowe, C., Sommerfeld, M., and Tsuji, Y., 1998, Multiphase Flows with Droplets and Particles, CRC Press, Boca Raton, FL, pp. 113–146.
24.
Gore
,
R. A.
, and
Crowe
,
C. T.
,
1989
, “
Effect of Particle Size on Modulating Turbulence Intensity
,”
Int. J. Multiphase Flow
,
15
, pp.
279
285
.
25.
Yarin
,
L. P.
, and
Hetsroni
,
G.
,
1994
, “
Turbulent Intensity in Dilute Two-Phase Flows
,”
Int. J. Multiphase Flow
,
20
, pp.
27
44
.
26.
Yuu
,
S.
,
Yasukouchi
,
N.
,
Hirowawa
,
Y.
, and
Jotaki
,
T.
,
1878
, “
Particle Turbulent Diffusion in a Duct Laden Jet
,”
AIChE J.
,
24
, pp.
509
519
.
27.
Dukowicz
,
J. K.
,
1980
, “
A Particle-Fluid Model for Liquid Sprays
,”
J. Comput. Phys.
,
35
, pp.
229
253
.
28.
Lockwood
,
F. C.
,
Salooga
,
A. P.
, and
Syed
,
S. A.
,
1980
, “
A Prediction Method for Coal-Fired Furnaces
,”
Combust. Flame
,
38
, pp.
1
15
.
29.
Jurewicz, J. T., and Stock, D. E., 1976, “Numerical Model for Turbulent Diffusion in Gas-Particle Flows,” ASME Paper No. 76-WA/FE-33.
30.
Smith, P. J., Fletcher, T. J., and Smoot, L. D., 1981, “Model for Pulverized Coal Fired Reactors,” 18th International Symposium on Combustion, pp. 1285–1293.
31.
Gosman
,
A. D.
, and
Ioannides
,
E.
,
1983
, “
Aspects of Computer Simulation of Liquid-Fueled Combustors
,”
J. Energy
,
7
, pp.
482
490
.
32.
Crowe
,
C. T.
,
Troutt
,
T. R.
, and
Chung
,
J. N.
,
1996
, “
Numerical Models for Two-Phase Turbulent Flows
,”
Annu. Rev. Fluid Mech.
,
28
, pp.
11
43
.
33.
de Jong, F. J., Meyyappan, M., and Choi, S.-K., 1994, “An Eulerian-Lagrangian Analysis for Liquid Flows With Vapor Bubbles,” Scientific Research Associates, SBI Phase II Final Report R94-9085-F, NASA Marshall Space Flight Center.
34.
Hinze, J. O., 1975, Turbulence, Second Ed., McGraw-Hill, New York.
35.
Billet, M. L., 1985, “Cavitation Nuclei Measurements—A Review,” ASME Cavitation and Multiphase Flow Forum—1985, ASME, New York, FED-Vol. 23, pp. 31–38.
36.
O’Hern, T. J., Katz, J., and Acosta, A. J., “Holographic Measurements of Cavitation Nuclei in the Sea,” ASME Cavitation and Multiphase Flow Forum—1985, ASME, New York, FED-Vol. 23, pp. 39–42.
37.
Meyer, R. S., 1989, “An Investigation of the Relation Between Free-Stream Nuclei and Traveling-Bubble Cavitation,” M.S. thesis, Penn State University, State College, PA.
You do not currently have access to this content.