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本文对传统的光滑粒子动力学方法进行了改进, 改进的光滑粒子动力学方法对传统粒子方法中的核梯度进行了修正, 采用了一种新型的核函数和离散格式, 应用改进的光滑粒子动力学方法对微液滴振荡过程进行了数值研究. 研究了不同纵横比和雷诺数(Re)下振荡阻尼与振荡的周期、振幅与Re数的关系. 研究表明: 对于纵横比λ≤ 4时的微液滴振荡过程, 其他参数恒定不变的前提下, Re数越大, 液滴形状变化越剧烈, 波的阻尼作用越弱, 液滴振荡周期变长; 在Re数一定的前提下, 随着液滴初始的纵横比的增大, 液滴振动的振幅增大, 液滴振荡的周期变长.In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. SPH is a Lagrangian meshfree particle method, and it is attractive in dealing with free surfaces, moving interfaces, and deformable boundaries. The improved SPH method modifies the kernel gradient in the traditional SPH method with a new kernel function and a modified SPH discrete form. Use of improved smoothed particle hydrodynamics is made to carry out numerical analysis on micro liquid drop oscillation process. The study focuses on the relation between the micro liquid drop oscillation damping and the oscillating period and amplitude in different aspect ratio and Re number. It is shown that for the micro liquid drop oscillation process with aspect ratio λ≤ 4, under the circumstance of constancy of other parameters, the larger the Re number, the more intense the change of liquid drop's shapes, the weaker the damping effect, and the longer the period of liquid drop's oscillation. Under the circumstance of constancy of Re number, as the initial aspect ratio of liquid drop increases, the amplitude of liquid drop oscillation is stronger, and the period of liquid drop's oscillation is longer.
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Keywords:
- liquid drop oscillation /
- surface tension /
- smoothed particle hydrodynamics /
- numerical simulation
[1] Melean Y, Sigalotti L D, Hasmy A 2006 Rev. Mex. Fis. 52 38
[2] Rayleigh L 1879 Proc. Roy. Soc. London 29 71
[3] Apfel R E, Tian Y, Jankovsky J, Shi T, Chen X, et al 1997 Phys. Rev. Lett. 78 1912
[4] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[5] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛 2008 物理学报 57 3954]
[6] Jiang T, Jie O Y, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲 2011 物理学报 60 054701]
[7] Chen Q, Yu W, Zhou C X 2007 Acta Mech Sinica 39 528 (in Chinese) [陈全, 俞炜, 周持兴 2007 力学学报 39 528]
[8] Qiu L C 2013 Acta Phys. Sin. 62 124702 (in Chinese) [邱流潮 2013 物理学报 62 124702]
[9] Shen C L, Xie W J, Wei B 2010 Phys. Rev. E 81 046305
[10] Shen C L, Xie W J, Wei B 2010 Phys. Lett. A 374 2301
[11] Yan Z L, Xie W J, Shen C L, Wei B B 2011 Acta Phys. Sin. 60 064302 (in Chinese) [鄢振麟, 解文军, 沈昌乐, 魏炳波 2011 物理学报 60 064302]
[12] Ma L Q, Liu M B, Chang J Z 2012 Acta Phys. Sin. 61 244701 (in Chinese) [马理强, 刘谋斌, 常建忠 2012 物理学报 61 244701]
[13] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[14] Fu X J, Qiang H F, Yang Y C 2007 Advances in Mech. 37 375 (in Chinese) [傅学金, 强洪夫, 杨月诚 2007 力学进展 37 375]
[15] Swegle J W, Hicks D L, Attaway S W 1995 J. Comput. Phys. 116 123
[16] Morris J P 1996 Ph. D. Dissertation (Melbourne: Monash University)
[17] Liu M B, Liu G R, Lam K Y 2003 J. Comput. Appl. Math. 155 263
[18] Xiao S P, Belytschko T 2005 Adv. Comput. Math. 23 171
[19] Hicks D L, Liebrock L M 2004 Appl. Math. Ccmput. 150 213
[20] Yang X F, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 物理学报 61 224701]
[21] Lopez H, Sigalotti L 2006 Phys. Rev. E 73 051201
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[1] Melean Y, Sigalotti L D, Hasmy A 2006 Rev. Mex. Fis. 52 38
[2] Rayleigh L 1879 Proc. Roy. Soc. London 29 71
[3] Apfel R E, Tian Y, Jankovsky J, Shi T, Chen X, et al 1997 Phys. Rev. Lett. 78 1912
[4] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[5] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛 2008 物理学报 57 3954]
[6] Jiang T, Jie O Y, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲 2011 物理学报 60 054701]
[7] Chen Q, Yu W, Zhou C X 2007 Acta Mech Sinica 39 528 (in Chinese) [陈全, 俞炜, 周持兴 2007 力学学报 39 528]
[8] Qiu L C 2013 Acta Phys. Sin. 62 124702 (in Chinese) [邱流潮 2013 物理学报 62 124702]
[9] Shen C L, Xie W J, Wei B 2010 Phys. Rev. E 81 046305
[10] Shen C L, Xie W J, Wei B 2010 Phys. Lett. A 374 2301
[11] Yan Z L, Xie W J, Shen C L, Wei B B 2011 Acta Phys. Sin. 60 064302 (in Chinese) [鄢振麟, 解文军, 沈昌乐, 魏炳波 2011 物理学报 60 064302]
[12] Ma L Q, Liu M B, Chang J Z 2012 Acta Phys. Sin. 61 244701 (in Chinese) [马理强, 刘谋斌, 常建忠 2012 物理学报 61 244701]
[13] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[14] Fu X J, Qiang H F, Yang Y C 2007 Advances in Mech. 37 375 (in Chinese) [傅学金, 强洪夫, 杨月诚 2007 力学进展 37 375]
[15] Swegle J W, Hicks D L, Attaway S W 1995 J. Comput. Phys. 116 123
[16] Morris J P 1996 Ph. D. Dissertation (Melbourne: Monash University)
[17] Liu M B, Liu G R, Lam K Y 2003 J. Comput. Appl. Math. 155 263
[18] Xiao S P, Belytschko T 2005 Adv. Comput. Math. 23 171
[19] Hicks D L, Liebrock L M 2004 Appl. Math. Ccmput. 150 213
[20] Yang X F, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 物理学报 61 224701]
[21] Lopez H, Sigalotti L 2006 Phys. Rev. E 73 051201
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