NI Bao-yu, ZHANG A-man, YAO Xiong-liang, WANG Bin. Numerical Simulation of Trajectory and Deformation of a Bubble in a Tip Vortex[J]. Applied Mathematics and Mechanics, 2012, 33(6): 663-677. doi: 10.3879/j.issn.1000-0887.2012.06.003
 Citation: NI Bao-yu, ZHANG A-man, YAO Xiong-liang, WANG Bin. Numerical Simulation of Trajectory and Deformation of a Bubble in a Tip Vortex[J]. Applied Mathematics and Mechanics, 2012, 33(6): 663-677.

# Numerical Simulation of Trajectory and Deformation of a Bubble in a Tip Vortex

##### doi: 10.3879/j.issn.1000-0887.2012.06.003
• Rev Recd Date: 2012-03-01
• Publish Date: 2012-06-15
• According to the behavior of a bubble in the ship wake flow, the numerical simulation was divided into two stages: quasi-spherical motion and non-spherical motion, based on whether the bubble was captured by the vortex or not. Oneway coupled particle tracking method (PTM) and boundary element method (BEM) were adopted to simulate these two stages respectively. Meanwhile, the initial condition of the second stage was taken as the output of the first one and the whole simulation was connected and completed therefore. Based on the numerical results and experimental data published, the cavitation inception was studied and the wake bubble was tracked. Besides, the split of the bubble captured by the vortex and the following sub-bubbles were simulated, including the motion, deformation and collapse as well. It is aimed that the results would provide some insight into the control on wake bubbles and optimization of the wake flow.
•  [1] Carrica M, Bonetto F, Drew D A, Lahey R T. A polydisperse model for bubbly two-phase flow around a surface ship[J]. International Journal of Multiphase Flow,1999, 25(2): 257-305. [2] Hsiao C T, Pauley L L. Numerical computation of the tip vortex flow generated by a marine propeller[J]. Journal of Fluids Engineering, 1999, 121(3): 638-645. [3] Johnson V E, Hsieh T. The influence of the trajectories of gas nuclei on cavitation inception[C]Sixth Symposium on Naval Hydrodynamics. Washington, USA, 1996: 163-179. [4] Hsiao C T, Pauley L L. Study of tip vortex cavitation inception using Navier-Stokes computation and bubble dynamics model[J]. Journal of Fluids Engineering, 1999, l21(1): 198-204. [5] Hsiao C T, Chahine G L. Scaling effect on prediction of cavitation inception in a line vortex flow[J]. Journal of Fluid Engineering, 2003, 125(1): 53-60. [6] Hsiao C T, Chahine G L. Prediction of tip vortex cavitation inception using coupled spherical and nonspherical bubble models and Navier-Stokes computations[J]. Journal of Marine Science Technology, 2004, 8(3): 99-108. [7] Hsiao C T, Jain A, Chahine G L. Effect of gas diffusion on bubble entrainment and dynamics around a propeller[C]26th Symposium on Naval Hydrodynamics. Rome, Italy, September, 17-22, 2006. [8] Rebow M, Choi J, Choi J K, Chahine G L, Ceccio S L. Experimental validation of BEM code analysis of bubble splitting in a tip vortex flow[C]11th International Symposium on Flow Visualization. Indiana, USA, August, 9-12, 2004. [9] Oweis G F, Choi J, Ceccio S L. Dynamics and noise emission of laser induced cavitation bubbles in a vortical flow field[J]. Acoustical Society of America, 2004, 115(3): 1049-1058. [10] Choi J, Hsiao C T, Chahine G L, Ceccio S L. Growth, oscillation and collapse of vortex cavitation bubbles[J]. Journal of Fluid Mechanics, 2009, 624: 255-279. [11] Saffman P G. Vortex Dynamics[M]. Cambridge: Cambridge University Press, 1992. [12] Park K, Seol H, Choi W, Lee S. Numerical prediction of tip vortex cavitation behavior and noise considering nuclei size and distribution[J]. Applied Acoustics, 2009, 70(5): 674-680. [13] Rayleigh J W. On the pressure developed in a liquid during the collapse of a spherical cavity[J]. Philosophical Magazine, 1917, 34: 94-98. [14] Plesset M S, Chapman R B. Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary[J]. Journal of Fluid Mechanics, 1971, 47: 283-290. [15] Cole R H. Underwater Explosion[M]. USA: Princeton University Press, 1948. [16] Gilmore F R. The growth and collapse of a spherical bubble in a viscous compressible liquid[J]. Hydro Lab California Institute Technical Report, 1952, 26(4): 117-125. [17] Maxey M R, Riley J J. Equation of motion for a small rigid sphere in a nonuniform flow[J]. Physics of Fluids, 1983, 26(4): 883-889. [18] Haberman W L, Morton R K. An experimental investigation of the drag and shape of air bubbles rising in various liquids [19] [R]. DTMB Report 802, USA, 1953. [20] Oweis G F, Hout I E, Iyer C, Tryggvason G, Ceccio S L. Capture and inception of bubbles near line vortices[J]. Physics of Fluids, 2005, 17(2): 1-14. [21] Borse G J.Numerical Methods With MATLAB[M]. Boston, USA: PWS, 1997. [22] Choi J K, Chahine G L. Non-spherical bubble behavior in vortex flow fields[C]International Association for Boundary Element Method. Austin, TX, USA, 2002. [23] Chahine G L, Sarkar K, Duraiswami R. Strong bubble/flow interaction and cavitation inception [24] [R]. Technical Report 94003-1ONR, USA: Dynaflow, Inc, 1997. [25] Best J P, Kucera A. A numerical investigation of non-spherical rebounding bubbles[J]. Journal of Fluid Mechanics, 1992, 245: 137-154. [26] Bronshtein I N, Semendyayev K A. Handbook of Mathematics[M]. 3rd ed. Berlin, Germany: Springer Publication, 1997. [27] Oguz H, Zeng J. Axisymmetric and three-dimensional boundary integral simulations of bubble growth from an underwater orifice[J]. Engineering Analysis With Boundary Elements, 1997, 19(4): 319-330. [28] Klaseboer E, Khoo B C. Boundary integral equations as applied to an oscillating bubble near a fluid-fluid interface[J]. Computational Mechanics, 2004, 33(2): 129-138. [29] 张阿漫, 姚熊亮.近自由面水下爆炸气泡的运动规律研究[J].物理学报, 2008, 57(1): 339-353.(ZHANG A-man, YAO Xiong-liang. The law of the underwater explosion bubble motion near free surface[J]. Acta Physics Sinica, 2008, 57(1):339-353.(in Chinese)) [30] 张阿漫, 倪宝玉, 宋炳月, 姚熊亮.狭窄流域内气泡破裂现象数值模拟[J].应用数学和力学, 2010, 31(4):420-432.(ZHANG A-man, NI Bao-yu, SONG Bing-yue, YAO Xiong-liang. Numerical simulation of the bubble breakup phenomena in the narrow flow field[J]. Applied Mathematics and Mechanics(English Edition), 2010, 31(4): 449-460.)

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142