黏性液滴变形过程的核梯度修正光滑粒子动力学模拟

蒋涛; 欧阳洁; 赵晓凯; 任金莲

doi:10.7498/aps.60.054701

摘要

本文提出了一种核梯度改进光滑粒子动力学(KGC-SPH)方法,模拟了黏性液滴形变自由表面问题.首先,通过模拟等温黏性液滴拉伸和旋转变形,验证了KGC-SPH法较SPH法具有较高精度和更好稳定性,且能很好地保持总角动量守恒.其次,基于非等温van der Waals模型对平衡态圆形液滴的形成过程进行数值研究,观察到小幅度振荡现象,并给出了一种新的克服张力不稳定性的方法和一种适合KGC-SPH方法的新的表面张力处理技术.最后,研究了van der Waals液滴的周期性振荡现象,讨论了初始椭圆形液滴长短半轴比

关键词:

Abstract

In this paper, a kernel gradient corrected smoothed particle hydrodynamics (KGC-SPH) method is proposed to simulate the deformation process of a viscous liquid drop. The KGC-SPH method has higher accuracy and better stability than the SPH method, which is verified by simulating the stretching and rotating process of an isothermal viscous liquid drop, and the property of preservation of total angular momentum of the present method is also checked. And then, the formation of a stable spherical liquid drop based on van der Waals model is investigated, and a phenomenon of periodic oscillation with small amplitude is observed. Meanwhile, a new variable smoothing length is presented to remove the unstable phenomenon and a new surface tension technique is adopted in the simulation. Subsequently, the phenomenon of periodic oscillation of a van der Waals model liquid drop is simulated using KGC-SPH method, in which the influence of the elongation and Reynolds number on the amplitude and oscillation period is discussed.

Keywords:

作者及机构信息

1.
西北工业大学理学院应用数学系,西安 710129

基金项目: 国家自然科学基金(批准号:10871159),国家重点基础研究发展计划(973)项目(批准号:2005CB321704 )资助的课题.

Authors and contacts

1.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710129, China

参考文献

[1]	Zhang L, Zhang L F, Wu H Y, Wang J P 2009 Acta Phys. Sin. 58 703 (in Chinese)[张亮、张立凤、吴海燕、王骥鹏 2009 物理学报 58 703]
[2]	Zhang A M, Yao X L, Li J 2008 Acta Phys. Sin. 57 1672 (in Chinese) [张阿漫、姚熊亮、李佳 2008 物理学报 57 1672]
[3]	Zhang A M 2008 Chin. Phys. B 17 927
[4]	Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫、姚熊亮 2008 物理学报 57 339]
[5]	Harlow F H 1957 Journal of the Association for Computing Machinery 4 137
[6]	Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵颖、季仲贞、冯涛 2004 物理学报 53 671]
[7]	Zhong C W,Xie J F,Zhuo C S,Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[8]	Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[9]	Cheng R J,Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[10]	Wang X D, Ouyang J, Su J 2010 Acta Phys. Sin. 59 6361(in Chinese) [王晓东、欧阳洁、苏进 2010 物理学报59 6361]
[11]	Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[12]	Monaghan J J 1994 J. Comp. Phys. 110 399
[13]	Morris J P, Fox P J, Zhu Y 1997 J. Comp. Phys. 136 214
[14]	Watkins S J, Bhattal A S, Francis N, Turner J A, Whitworth A P 1996 Astron. Astrophys. Suppl. Ser. 119 177
[15]	Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[16]	Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[17]	Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[18]	Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[19]	Fang J, Parriaux A, Rentschler M, Ancey C 2009 Appl. Num. Math. 59 251
[20]	Bonet J, Lok T S L 1999 Comput. Meth. Appl. Mech. Eng. 180 97
[21]	Apfel R E, Tian Y, Jankovshy J, Shi T, Chen X, Holt R G, Trinh E, Croonquist A, Thornton K C, Sacco A, Jr, Coleman C, Leslie F W, Matthiesen D H 1997 Phys. Rev. Let. 78 1912
[22]	Melean Y, Singalotti L D G, Hasmy A 2004 Comp. Phys. Comm. 157 191
[23]	Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[24]	Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[25]	Monaghan J J, Lattanzio J C 1985 Astron. Astrophys. 149 135
[26]	Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌、常建忠 2010 物理学报 59 3654]
[27]	Liu M B, Liu G R 2006 Appl. Num. Math. 56 19
[28]	Silverman B W 1986 Statistics and Applied Probability (London: Chapman and Hall)
[29]	Schussler M, Schmitt D 1981 Astron. Astrophys. 97 373
[30]	Gray J P, Monaghan J J, Swift R P 2001 Comp. Meth. Appl. Mech. Eng. 190 6641
[31]	Monaghan J J 2000 J. Comp. Phys. 159 290
[32]	Tang B, Li J F, Wang T S 2008 Acta Phys. Sin. 57 6722 (in Chinese) [汤波、李俊峰、王天舒 2008 物理学报 57 6722]
[33]	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]
[34]	Wang X L, Chen S 2010 Acta Phys. Sin. 59 6778 (in Chinese) [王晓亮、陈硕 2010 物理学报 59 6778]
[35]	Trinh E, Wang T G 1982 J. Fluid Mech. 122 315

施引文献

[1]	Zhang L, Zhang L F, Wu H Y, Wang J P 2009 Acta Phys. Sin. 58 703 (in Chinese)[张亮、张立凤、吴海燕、王骥鹏 2009 物理学报 58 703]
[2]	Zhang A M, Yao X L, Li J 2008 Acta Phys. Sin. 57 1672 (in Chinese) [张阿漫、姚熊亮、李佳 2008 物理学报 57 1672]
[3]	Zhang A M 2008 Chin. Phys. B 17 927
[4]	Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫、姚熊亮 2008 物理学报 57 339]
[5]	Harlow F H 1957 Journal of the Association for Computing Machinery 4 137
[6]	Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵颖、季仲贞、冯涛 2004 物理学报 53 671]
[7]	Zhong C W,Xie J F,Zhuo C S,Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[8]	Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[9]	Cheng R J,Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[10]	Wang X D, Ouyang J, Su J 2010 Acta Phys. Sin. 59 6361(in Chinese) [王晓东、欧阳洁、苏进 2010 物理学报59 6361]
[11]	Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[12]	Monaghan J J 1994 J. Comp. Phys. 110 399
[13]	Morris J P, Fox P J, Zhu Y 1997 J. Comp. Phys. 136 214
[14]	Watkins S J, Bhattal A S, Francis N, Turner J A, Whitworth A P 1996 Astron. Astrophys. Suppl. Ser. 119 177
[15]	Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[16]	Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[17]	Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[18]	Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[19]	Fang J, Parriaux A, Rentschler M, Ancey C 2009 Appl. Num. Math. 59 251
[20]	Bonet J, Lok T S L 1999 Comput. Meth. Appl. Mech. Eng. 180 97
[21]	Apfel R E, Tian Y, Jankovshy J, Shi T, Chen X, Holt R G, Trinh E, Croonquist A, Thornton K C, Sacco A, Jr, Coleman C, Leslie F W, Matthiesen D H 1997 Phys. Rev. Let. 78 1912
[22]	Melean Y, Singalotti L D G, Hasmy A 2004 Comp. Phys. Comm. 157 191
[23]	Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[24]	Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[25]	Monaghan J J, Lattanzio J C 1985 Astron. Astrophys. 149 135
[26]	Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌、常建忠 2010 物理学报 59 3654]
[27]	Liu M B, Liu G R 2006 Appl. Num. Math. 56 19
[28]	Silverman B W 1986 Statistics and Applied Probability (London: Chapman and Hall)
[29]	Schussler M, Schmitt D 1981 Astron. Astrophys. 97 373
[30]	Gray J P, Monaghan J J, Swift R P 2001 Comp. Meth. Appl. Mech. Eng. 190 6641
[31]	Monaghan J J 2000 J. Comp. Phys. 159 290
[32]	Tang B, Li J F, Wang T S 2008 Acta Phys. Sin. 57 6722 (in Chinese) [汤波、李俊峰、王天舒 2008 物理学报 57 6722]
[33]	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]
[34]	Wang X L, Chen S 2010 Acta Phys. Sin. 59 6778 (in Chinese) [王晓亮、陈硕 2010 物理学报 59 6778]
[35]	Trinh E, Wang T G 1982 J. Fluid Mech. 122 315

[1]	张超, 布龙祥, 张智超, 樊朝霞, 凡凤仙. 丁二酸-水纳米气溶胶液滴表面张力的分子动力学研究. 物理学报, 2023, 72(11): 114701. doi: 10.7498/aps.72.20222371
[2]	周浩, 李毅, 刘海, 陈鸿, 任磊生. 最优输运无网格方法及其在液滴表面张力效应模拟中的应用. 物理学报, 2021, 70(24): 240203. doi: 10.7498/aps.70.20211078
[3]	张旋, 张天赐, 葛际江, 蒋平, 张贵才. 表面活性剂对气-液界面纳米颗粒吸附规律的影响. 物理学报, 2020, 69(2): 026801. doi: 10.7498/aps.69.20190756
[4]	蒋涛, 黄金晶, 陆林广, 任金莲. 非线性薛定谔方程的高阶分裂改进光滑粒子动力学算法. 物理学报, 2019, 68(9): 090203. doi: 10.7498/aps.68.20190169
[5]	沈婉萍, 尤仕佳, 毛鸿. 夸克介子模型的相图和表面张力. 物理学报, 2019, 68(18): 181101. doi: 10.7498/aps.68.20190798
[6]	艾旭鹏, 倪宝玉. 流体黏性及表面张力对气泡运动特性的影响. 物理学报, 2017, 66(23): 234702. doi: 10.7498/aps.66.234702
[7]	孙鹏楠, 李云波, 明付仁. 自由上浮气泡运动特性的光滑粒子流体动力学模拟. 物理学报, 2015, 64(17): 174701. doi: 10.7498/aps.64.174701
[8]	刘虎, 强洪夫, 陈福振, 韩亚伟, 范树佳. 一种新型光滑粒子动力学固壁边界施加模型. 物理学报, 2015, 64(9): 094701. doi: 10.7498/aps.64.094701
[9]	白玲, 李大鸣, 李彦卿, 王志超, 李杨杨. 基于范德瓦尔斯表面张力模式液滴撞击疏水壁面过程的研究. 物理学报, 2015, 64(11): 114701. doi: 10.7498/aps.64.114701
[10]	马理强, 苏铁熊, 刘汉涛, 孟青. 微液滴振荡过程的光滑粒子动力学方法数值模拟. 物理学报, 2015, 64(13): 134702. doi: 10.7498/aps.64.134702
[11]	李源, 罗喜胜. 黏性、表面张力和磁场对Rayleigh-Taylor不稳定性气泡演化影响的理论分析. 物理学报, 2014, 63(8): 085203. doi: 10.7498/aps.63.085203
[12]	蒋涛, 任金莲, 徐磊, 陆林广. 非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟. 物理学报, 2014, 63(21): 210203. doi: 10.7498/aps.63.210203
[13]	蒋涛, 陆林广, 陆伟刚. 等直径微液滴碰撞过程的改进光滑粒子动力学模拟. 物理学报, 2013, 62(22): 224701. doi: 10.7498/aps.62.224701
[14]	邱流潮. 基于不可压缩光滑粒子动力学的黏性液滴变形过程仿真. 物理学报, 2013, 62(12): 124702. doi: 10.7498/aps.62.124702
[15]	苏铁熊, 马理强, 刘谋斌, 常建忠. 基于光滑粒子动力学方法的液滴冲击固壁面问题数值模拟. 物理学报, 2013, 62(6): 064702. doi: 10.7498/aps.62.064702
[16]	毕菲菲, 郭亚丽, 沈胜强, 陈觉先, 李熠桥. 液滴撞击固体表面铺展特性的实验研究. 物理学报, 2012, 61(18): 184702. doi: 10.7498/aps.61.184702
[17]	马理强, 刘谋斌, 常建忠, 苏铁熊, 刘汉涛. 液滴冲击液膜问题的光滑粒子动力学模拟. 物理学报, 2012, 61(24): 244701. doi: 10.7498/aps.61.244701
[18]	马理强, 常建忠, 刘汉涛, 刘谋斌. 液滴溅落问题的光滑粒子动力学模拟. 物理学报, 2012, 61(5): 054701. doi: 10.7498/aps.61.054701
[19]	刘谋斌, 常建忠. 光滑粒子动力学方法中粒子分布与数值稳定性分析. 物理学报, 2010, 59(6): 3654-3662. doi: 10.7498/aps.59.3654
[20]	王晓亮, 陈硕. 液气共存的耗散粒子动力学模拟. 物理学报, 2010, 59(10): 6778-6785. doi: 10.7498/aps.59.6778

计量

文章访问数: 9019
PDF下载量: 884
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板