液滴撞击圆柱内表面的数值研究
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摘要
针对液滴撞击圆柱内表面的过程,利用基于相场的格子Boltzmann方法模拟液滴以不同初速度、从不同初始高度、撞击不同大小的圆柱内表面时液滴的形态变化,分析了液滴自身物性(如密度和黏性等)和圆柱内表面润湿性等因素对撞击现象的具体影响.研究发现:撞击韦伯数、密度比及动力黏性比、圆柱半径等对液滴撞击后沿圆柱内表面的铺展均有一定影响,较高的韦伯数下液滴可能会发生分裂;液滴初始高度对大密度比和动力黏性比的撞击影响较小;液滴反弹现象可能出现在接触角较大时;重力作用会抑制撞击后液滴的振荡.
Droplet impact on a solid surface is ubiquitous in daily life and various engineering fields such as ink-jet printing and surface coating. Most of existing studies focused on the droplet impact on flat or convex surface whereas the droplet impact on a concave surface has been less investigated. The purpose of this paper is to investigate the dynamic process of droplet impact on the inner surface of a cylinder numerically by using the phase-field-based lattice Boltzmann method.This method combines the finite-difference solution of the Cahn-Hilliard equation to capture the interface dynamics and the lattice Boltzmann method for the hydrodynamics of the flow. Besides, a recently proposed method is employed to deal with the wetting boundary condition on the curved wall. The method is first verified through the study of the equilibrium contact angle of a droplet on the inner surface of a cylinder and the droplet impact on a thin film, for which good agreement is obtained with theoretical results or other numerical solutions in the literature. Then, different droplet impact velocity, initial height of the droplet, surface wettability and radius of the cylinder are considered for the main problem and their effects on the evolution of the droplet shape are investigated. The physical properties of the droplet including the density and viscosity are also varied to assess their effects on the impact outcome. It is found that the impact Weber number, the liquid/gas density and dynamic viscosity ratios, the wettability of the inner surface of the cylinder, and the radius of the cylinder may have significant effects on the deformation and spreading of the droplet.At low Weber numbers, when the density and dynamic viscosity ratios are sufficiently high, their variations have little effect on the droplet impact process. At high Weber numbers, changes of these two ratios have more noticeable effects.When the Weber number is high enough, droplet splashing appears. When the density and dynamic viscosity ratios are high, the initial height of the droplet only has a minor effect on the impact results. The increment of the cylinder radius not only increases the maximum spreading radius but also enlarges the oscillation period of the droplet after its impact.Rebound of the droplet may be observed when the contact angle of the inner surface of the cylinder is large enough.Besides, the gravity force is found to suppress the oscillation of the droplet on the cylinder's inner surface. This work may broaden our understanding of the droplet impact on curved surfaces.
Droplet impact on a solid surface is ubiquitous in daily life and various engineering fields such as ink-jet printing and surface coating. Most of existing studies focused on the droplet impact on flat or convex surface whereas the droplet impact on a concave surface has been less investigated. The purpose of this paper is to investigate the dynamic process of droplet impact on the inner surface of a cylinder numerically by using the phase-field-based lattice Boltzmann method.This method combines the finite-difference solution of the Cahn-Hilliard equation to capture the interface dynamics and the lattice Boltzmann method for the hydrodynamics of the flow. Besides, a recently proposed method is employed to deal with the wetting boundary condition on the curved wall. The method is first verified through the study of the equilibrium contact angle of a droplet on the inner surface of a cylinder and the droplet impact on a thin film, for which good agreement is obtained with theoretical results or other numerical solutions in the literature. Then, different droplet impact velocity, initial height of the droplet, surface wettability and radius of the cylinder are considered for the main problem and their effects on the evolution of the droplet shape are investigated. The physical properties of the droplet including the density and viscosity are also varied to assess their effects on the impact outcome. It is found that the impact Weber number, the liquid/gas density and dynamic viscosity ratios, the wettability of the inner surface of the cylinder, and the radius of the cylinder may have significant effects on the deformation and spreading of the droplet.At low Weber numbers, when the density and dynamic viscosity ratios are sufficiently high, their variations have little effect on the droplet impact process. At high Weber numbers, changes of these two ratios have more noticeable effects.When the Weber number is high enough, droplet splashing appears. When the density and dynamic viscosity ratios are high, the initial height of the droplet only has a minor effect on the impact results. The increment of the cylinder radius not only increases the maximum spreading radius but also enlarges the oscillation period of the droplet after its impact.Rebound of the droplet may be observed when the contact angle of the inner surface of the cylinder is large enough.Besides, the gravity force is found to suppress the oscillation of the droplet on the cylinder's inner surface. This work may broaden our understanding of the droplet impact on curved surfaces.
引文
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[3]Han F H,Zhang C M,Wang Y X 1995 J.Beijing Univ.Aeron.Astron.21 16(in Chinese)[韩凤华,张朝民,王跃欣1995北京航空航天大学学报21 16]
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[5]Fan Y 2016 M.S.Thesis(Chongqing:University of Chongqing)(in Chinese)[范瑶2016硕士学位论文(重庆:重庆大学)]
[6]Wang Y E,Zhou J H,Qin Y L,Li P L,Yang M M,Han Q,Wang Y B,Wei S M 2012 J.Vib.Shock 31 51(in Chinese)[汪焰恩,周金华,秦琰磊,李鹏林,杨明明,韩琴,王月波,魏生民2012振动与冲击31 51]
[7]Li Y P,Wang H R 2009 J.Xi’an Jiaotong Univ.43 21(in Chinese)[李彦鹏,王焕然2009西安交通大学学报4321]
[8]Huang J J,Wu J,Huang H 2018 Eur.Phys.J.E 41 17
[9]Shen S Q,Bi F F,Guo Y L 2012 Int.J.Heat Mass Tran.55 6938
[10]Song Y C,Ning Z,Sun C H,LüM,Yan K,Fu J 2013T.CSICE 31 531(in Chinese)[宋云超,宁智,孙春华,吕明,阎凯,付娟2013内燃机学报31 531]
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[12]Ling J 2016 M.S.Thesis(Dalian:Dalian University of Technology)(in Chinese)[凌俊2016硕士学位论文(大连:大连理工大学)]
[13]Huang J J,Huang H B,Shu C,Chew Y T,Wang S L2013 J.Phys.A:Math.Theor.46 55501
[14]Lee T 2009 Compu.Math.Appl.58 987
[15]Lee T,Liu L 2010 J.Comput.Phys.229 8045
[16]Lallemand P,Luo L S 2000 Phys.Rev.E 61 6546
[17]Lee H G,Kim J 2011 Comput.Fluids 44 178
[18]Ding H,Spelt P D M 2007 Phys.Rev.E 75 046708
[19]Huang J J,Huang H B,Wang X Z 2015 Int.J.Numer.Meth.Fluids 77 123
[20]Gao Y J,Jiang H Q,Li J J,Zhao Y Y,Hu J C,Chang Y H 2017 Acta Phys.Sin.66 024702(in Chinese)[高亚军,姜汉桥,李俊键,赵玉云,胡锦川,常元昊2017物理学报66 024702]
[21]Shen S Q,Yu H,Guo Y L,Liang G T 2013 J.Therm.Sci.Technol.12 20(in Chinese)[沈胜强,于欢,郭亚丽,梁刚涛2013热科学与技术12 20]
[22]Yue P T,Zhou C F,Feng J J 2010 J.Fluid Mech.645279
[23]Wen B H,Zhang C Y,Fang H P 2017 Sci.Sin.:Phys.Mech.Astron.47 070012(in Chinese)[闻炳海,张超英,方海平2017中国科学:物理学力学天文学47 070012]
[24]Shao J Y,Shu C,Huang H B,Chew Y T 2014 Phys.Rev.E 89 033309
[25]Prosperetti A 1981 Phys.Fluids 24 1217
[26]Liu Y,Tan P,Xu L 2015 PNAS 112 3280
[27]Yue P,Zhou C,Feng J J 2007 J.Comput.Phys.223 1