等直径微液滴碰撞过程的改进光滑粒子动力学模拟

蒋涛; 陆林广; 陆伟刚

doi:10.7498/aps.62.224701

摘要

运用一种改进光滑粒子动力学(SPH)方法模拟了相溶和不相溶两种情况下的等直径微液滴碰撞动力学过程. 为提高传统SPH方法的数值精度和稳定性, 采用一种不涉及核导数计算的核梯度改进形式; 为处理液滴界面张力采用修正的van der Waals表面张力模型. 通过模拟牛顿液滴碰撞聚并变形过程并与相关文献或试验结果进行对比, 验证了改进SPH 方法模拟微液滴碰撞过程的可靠性. 随后, 研究了基于van der Waals模型相溶聚合物微液滴碰撞聚并变形过程及不相溶微液滴碰撞后的反弹、分离过程, 讨论了碰撞过程中碰撞速度、碰撞角度、密度比等参数对碰撞变形过程的影响, 分析了流体桥、旋转角度等因素的变化情况.

关键词:

Abstract

In this work, the dynamical collision process between two miscible/immiscible micro-droplets is simulated by a modified smoothed particle hydrodynamics (C-SPH) method. In order to improve the numerical accuracy and stability of traditional SPH method, a kernel gradient modified scheme without kernel derivative is considered. Meanwhile, an improved surface tension technique based on the van der Waals model is adopted to deal with the moving interface. The reliability of C-SPH method of simulating the deformation process between two droplet collisions is tested through the numerical simulations of coalescence process between two miscible Newtonian droplet collisions. Subsequently, the coalescence process of miscible polymer droplet collision and the deformation process of bouncing and separation between two immiscible droplet collisions are investigated, in which the control equations of droplets are all based on the van der Waals model. The influences of the collision velocity, collision angle and the density ratio on the deformation process of collision are discussed, and the changes of liquid bridge and rotation angle are analyzed.

Keywords:

作者及机构信息

1.
扬州大学数学科学学院, 扬州大学水利科学与工程学院, 扬州 225002;

2.
西北工业大学应用数学系, 西安 710129

基金项目: 江苏省高校自然科学研究项目(批准号: 12KJD570001)和江苏省青年科学基金(批准号: BK20130436) 资助的课题.

Authors and contacts

1.
Department of Mathematics, College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225002, China;

2.
Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129, China

Funds: Project supported by the Natural Science Fundamental Research Project of Jiangsu Colleges and Universities, China (Grant No. 12KJD570001) and the Young Scholars Foundation of Jiangsu Province, China (Grant No. BK20130436).

参考文献

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[4]	Mashayek F, Ashgriz N, Minkowycz W J, Shotorban B 2003 Int. J. Heat Mass Transfer 46 77
[5]	Bach G A, Koch D L, Gopinath A 2004 J. Fluid Mech. 518 157
[6]	Chen R H, Chen C T 2006 Experim. Fluids 41 453
[7]	Gao T C, Chen R H, Pu J Y, Lin T H 2005 Experim. Fluids 38 731
[8]	Lyu S P, Bates F S, Macosko C W 2002 Fluid Mech. Transport Phenomena 48 7
[9]	Eggers J, Lister J, Stone H A 1999 J. Fluid Mech. 401 293
[10]	Yao W, Maris H J, Pennington P, Seidel G M 2005 Phys. Rev. E 71 016309
[11]	Dai M Z, Schmidt D P 2005 Phys. Fluids 17 041701
[12]	Qian J, Law C K 1997 J. Fluid Mech. 331 59
[13]	Jiang X, James A J 2007 J. Engineer. Math. 59 99
[14]	Motzigemba M, Roth N, Bothe D, Warnecke H J, Pruss J, Wielage K, Weigand B 2002 Proceedings of the 18th Annual Conference Liquid Atomization Spray Systems (ILASS Europe) Zaragoza, Spain September 9–11, 2002 p559
[15]	Ashgriz N 2011 Handbook of Atomization and Sprays Theory and Applications (New York: Springer) p157
[16]	Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵颖, 季仲贞, 冯涛 2004 53 671]
[17]	Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[18]	Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[19]	Cheng R J, Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[20]	Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[21]	Monaghan J J 1994 J. Comp. Phys. 110 399
[22]	Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[23]	Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[24]	Ellero M, Kröger M, Hess S 2002 J. Non-Newtonian Fluid Mech. 105 35
[25]	Fang J, Owens R G, Tacher L, Parriaux A 2006 J. Non-Newtonian Fluid Mech. 13 68
[26]	Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 59 3654]
[27]	Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[28]	Yang X Y, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 61 224701]
[29]	Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 096206 (in Chinese) [蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲2011 60 096206]
[30]	Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[31]	Jiang T, Ouyang J, 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 60 054701]
[32]	Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[33]	Hopper R W 1990 J. Fluid Mech. 213 349
[34]	Jiang Y J, Umemura A, Law C K 1992 J. Fluid Mech. 234 171
[35]	Qian J, Law C K 1997 J. Fluid Mech. 331 59

施引文献

[1]	Pan Y, Suga K 2005 Phys. Fluids 17 082105
[2]	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 57 3954]
[3]	Willis K D, Orme M E 2000 Experim. Fluids 29 347
[4]	Mashayek F, Ashgriz N, Minkowycz W J, Shotorban B 2003 Int. J. Heat Mass Transfer 46 77
[5]	Bach G A, Koch D L, Gopinath A 2004 J. Fluid Mech. 518 157
[6]	Chen R H, Chen C T 2006 Experim. Fluids 41 453
[7]	Gao T C, Chen R H, Pu J Y, Lin T H 2005 Experim. Fluids 38 731
[8]	Lyu S P, Bates F S, Macosko C W 2002 Fluid Mech. Transport Phenomena 48 7
[9]	Eggers J, Lister J, Stone H A 1999 J. Fluid Mech. 401 293
[10]	Yao W, Maris H J, Pennington P, Seidel G M 2005 Phys. Rev. E 71 016309
[11]	Dai M Z, Schmidt D P 2005 Phys. Fluids 17 041701
[12]	Qian J, Law C K 1997 J. Fluid Mech. 331 59
[13]	Jiang X, James A J 2007 J. Engineer. Math. 59 99
[14]	Motzigemba M, Roth N, Bothe D, Warnecke H J, Pruss J, Wielage K, Weigand B 2002 Proceedings of the 18th Annual Conference Liquid Atomization Spray Systems (ILASS Europe) Zaragoza, Spain September 9–11, 2002 p559
[15]	Ashgriz N 2011 Handbook of Atomization and Sprays Theory and Applications (New York: Springer) p157
[16]	Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵颖, 季仲贞, 冯涛 2004 53 671]
[17]	Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[18]	Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[19]	Cheng R J, Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[20]	Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[21]	Monaghan J J 1994 J. Comp. Phys. 110 399
[22]	Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[23]	Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[24]	Ellero M, Kröger M, Hess S 2002 J. Non-Newtonian Fluid Mech. 105 35
[25]	Fang J, Owens R G, Tacher L, Parriaux A 2006 J. Non-Newtonian Fluid Mech. 13 68
[26]	Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 59 3654]
[27]	Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[28]	Yang X Y, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 61 224701]
[29]	Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 096206 (in Chinese) [蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲2011 60 096206]
[30]	Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[31]	Jiang T, Ouyang J, 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 60 054701]
[32]	Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[33]	Hopper R W 1990 J. Fluid Mech. 213 349
[34]	Jiang Y J, Umemura A, Law C K 1992 J. Fluid Mech. 234 171
[35]	Qian J, Law C K 1997 J. Fluid Mech. 331 59

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