Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T22:25:23.758Z Has data issue: false hasContentIssue false

Cavitation Bubble in Compressible Fluid Near the Rigid Wall Subjected to the Acoustic Wave with Arbitrary Incidence Angle in Three-Dimensional

Published online by Cambridge University Press:  21 October 2014

X. Ye*
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China
X.-L. Yao
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China
L.-Q. Sun
Affiliation:
College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China
B. Wang
Affiliation:
National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang, China
*
* Corresponding author (yexi0527@gmail.com
Get access

Abstract

A balanced cavitation bubble is released near the rigid wall in the sound field generated by the incidence plane wave and its reflecting wave. With the modified boundary integral equation, the dynamics of bubble is solved considering the compressibility of fluid in this paper. Also the Bernoulli equation as the boundary condition for cavitation bubble in sound field is deduced using Euler equation. Since the arbitrary incidence angle of acoustic wave, the three-dimensional model is utilized. The bubble will expand or contract at first according to the initial phase of acting acoustic pressure on bubble surface. And during the contraction phase, the liquid jet with high speed will be generated pointing to rigid wall but be deflected to the incidence direction of acoustic wave. The oblique degree of jet will be affected by the incidence angle and initial distance between bubble center and rigid wall. The oscillation amplitude of bubble will be affected by the incidence amplitude and incidence frequency, but be limited by the rigid wall. Since the compressibility of fluid, the perturbation will propagate to the far-field. Thus the oscillation amplitude of bubble will be reduced.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Crum, L. A. and Reynolds, G. T., “Sonolumines-cence Produced by ‘Stable’ Cavitation,” Journal of the Acoustical Society of America, 78, pp. 137139 (1985).Google Scholar
2.Gaitan, D. F. and Crum, L. A., Frontiers of Nonlinear Acoustics, Hamilton, M. F., Blackstock, D. T. Eds., New York: Elsevier Applied Science, US (1990).Google Scholar
3.Gaitan, D. F., Crum, L. A., Church, C. C. and Roy, R. A., “Sonoluminescence and Bubble Dynamics for a Single, Stable, Cavitation Bubble,” Journal of the Acoustical Society of America, 91, pp. 31663183 (1992).CrossRefGoogle Scholar
4.Prosperetti, A. and Lezzi, A., “Bubble Dynamics in a Compressible Liquid. Part I. First-Order Theory,” Journal of Fluid Mechanics, 168, pp. 457478 (1986).Google Scholar
5.Lezzi, A. and Prosperetti, A., “Bubble Dynamics in a Compressible Liquid. Part II. Second-Order Theory,” Journal of Fluid Mechanics, 185, pp. 289321 (1987).CrossRefGoogle Scholar
6.Rayleigh, J. W., “On the Pressure Developed in a Liquid During the Collapse of a Spherical Cavity,” Philosophical Magazine, 34, pp. 9498 (1917).Google Scholar
7.Krller, J. B. and Miksis, M. J., “Bubble Oscillations of Large Amplitude,” Journal of the Acoustical Society of America, 68, pp. 628633 (1980).CrossRefGoogle Scholar
8.Matula, T. J., “Inertial Cavitation and Single-Bubble Sonoluminescence,” Philosophical Transactions of the Royal Society, 357, pp. 225249 (1999).Google Scholar
9.Zhang, A. M., Cui, P. and Wang, Y., “Experiments on Bubble Dynamics Between a Free Surface and a Rigid Wall,” Experiments in Fluids, 54, p. 1602 (2013).Google Scholar
10.Zhang, A. M., Xiao, W. and Wang, S. P., “Experimental Investigation of the Interaction Between a Pulsating Bubble and a Rigid Cylinder,” Acta Me-chanica Sinica, 29, pp. 503512 (2013).Google Scholar
11.Wang, C. and Khoo, B. C., “An Indirect Boundary Element Method for Three-Dimensional Explosion Bubbles,” Journal of Computational Physics, 194, pp. 451480 (2004).Google Scholar
12.Zhang, A. M. and Ni, B. Y., “Influence of Different Forces on the Bubble Entrainment Into a Stationary Gaussian Vortex,” Science China Physics, Mechanics & Astronomy, 56, pp. 21622169 (2013).Google Scholar
13.Rungsiyaphornrat, S., Klaseboer, E., Khoo, B. C. and Yeo, K. S., “The Merging of Two Gaseous Bubbles with an Application to Underwater Explosions,” Computers & Fluids, 32, pp. 10491074 (2003).CrossRefGoogle Scholar
14.Park, J., “A Coupled Runge-Kutta Discontinuous Galerkin-Direct Ghost Fluid (RKDG-DGF) Method to Near-Field Early Time Underwater Explosion (UNDEX) Simulations,” Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Virginia, US (2008).Google Scholar
15.Qiu, J. X., Liu, T. G. and Khoo, B. C., “Simulations of Compressible Two-Medium Flow by Runge-Kutta Discontinuous Galerkin Methods with the Ghost Fluid Method,” Communications in Computational Physics, 3, pp. 479504 (2008).Google Scholar
16.Blake, J. R. and Gibson, D. C., “Growth and Collapse of a Vapour Cavity Near a Free Surface,” Journal of Fluid Mechanics, 111, pp. 123140 (1981).Google Scholar
17.Wang, Q. X., “Unstructured MEL Modeling of Unsteady Nonlinear Ship Waves,” Journal of Computational Physics, 210, pp. 183224 (2005).CrossRefGoogle Scholar
18.Zhang, A. M., Yang, W. S., Huang, C. and Ming, F. R., “Numerical Simulation of Column Charge Underwater Explosion Based on SPH and BEM Combination,” Computers and Fluids, 71, pp. 169178 (2013)Google Scholar
19.Jamaluddin, A. R. and Ball, G. J., “The Collapse of Singal Bubbles and Approximation of the Far-Field Acoustic Emissions for Cavitation Induced by Shock Wave Lithotripsy,” Journal of Fluid Mechanics, 677, pp. 305341 (2011).Google Scholar
20.Turangan, C. K. and Jamaluddin, A. R., “Free-Lagrange Simulations of the Expansion and Jetting Collapse of Air Bubbles in Water,” Journal of Fluid Mechanics, 598, pp. 125 (2008).Google Scholar
21.Michael, L. C., Lindau, O., Blake, J. R. and Szeri, A. J., “Shape Stability and Violent Collapse of Microbubbles in Acoustic Traveling Waves,” Physics of Fluids, 19, p. 047101 (2007).Google Scholar
22.Curtiss, G. A., Leppinen, D. M., Wang, Q. X. and Blake, J. R., “Ultrasonic Cavitation Near a Tissue Layer,” Journal of Fluid Mechanics, 730, pp. 245272 (2013).Google Scholar
23.Wang, Q. X. and Blake, J. R., “Non-Spherical Bubble Dynamics in a Compressible Liquid Part 1: Travelling Acoustic Wave,” Journal of Fluid Mechanics, 659, pp. 191224 (2010).Google Scholar
24.Wang, Q. X. and Blake, J. R., “Non-Spherical Bubble Dynamics in a Compressible Liquid Part 2: Acoustic Standing Wave,” Journal of Fluid Mechanics, 679, pp. 559581 (2010).Google Scholar
25.Wang, Q. X., “Underwater Explosion Bubble Dynamics in a Compressible Liquid,” Physics of Fluids, 25, p. 072104 (2013).Google Scholar
26.Wang, Q. X., “Multi-Oscillations of a Bubble in a Compressible Liquid Near a Rigid Boundary,” Journal of Fluid Mechanics, 745, pp. 509536 (2014).Google Scholar
27.Yao, X. L., Ye, X. and Zhang, A. M., “Cavitation Bubble in Compressible Free Fluid Subjected to the Travelling Wave,” Acta Physica Sinica, 62, p. 244701 (2013).Google Scholar
28.Ye, X., Zhang, A. M. and Yao, X. L., “The Motion Characteristics of Cavitation Bubble Near the Rigid Wall with the Driving of Vertical-Incidence Acoustic Wave,” China Ocean Engineering, accepted (2014).Google Scholar
29.Zhang, A. M., Wang, S. P. and Wu, G. X., “Simulation of Bubble Motion in a Compressible Liquid Based on the Three Dimensional Wave Equation,” Engineerging Analysis with Boundary Elements, 37, pp. 11791188 (2013).Google Scholar
30.Morse, P. M. and Ingard, K. U., Theoretical Acoustics, McGray-Hill Book Company, New York, US (1968).Google Scholar
31.Wang, C., Khoo, B. C. and Yeo, K. S., “Elastic Mesh Technique for 3D BIM Simulation with an Application to Underwater Explosion Bubbles,” Computers & Fluids, 32, pp. 11951212 (2003).Google Scholar
32.Sun, H., “A Boundary Element Method Applied to Strongly Nonlinear Wave-Body Interaction Problems,” Ph.D. Dissertation, Norwegian University of Science and Technology, Trondheim, Norway (2007).Google Scholar
33.Zhang, A. M., Wang, S. P., Bai, Z. H. and Huang, C., “Experimental Study on Bubble Pulse Features Under Different Circumstances,” Chinese Journal of Theoretical and Applied Mechanics, 43, pp. 7183 (2011).Google Scholar
34.Bjerknes, , Fields of Force, Columbia University Press, New York, US (1966).Google Scholar
35.Philipp, A. and Lauterborn, W., “Cavitation Erosion by Single Laser-Produced Bubbles,” Journal of Fluid Mechanics, 361, pp. 75116 (1997).Google Scholar