重庆工商大学学报（自然科学版）

引用本文:	杨钧翔，温茂茜.剪切流作用下三维液滴变形的相场法数值模拟(J/M/D/N,J:杂志，M：书，D：论文，N：报纸).期刊名称,2020，37（4）：74-82
	CHEN X. Adap tive slidingmode contr ol for discrete2ti me multi2inputmulti2 out put systems[ J ]. Aut omatica, 2006, 42(6): 4272-435

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剪切流作用下三维液滴变形的相场法数值模拟
杨钧翔，温茂茜^1,2
1.高丽大学数学系，首尔 02841;2.重庆交通大学数学与统计学院，重庆400074

摘要:

液滴动力学在工业和自然科学领域有着广泛的应用和科研价值，其中最为典型的代表便是剪切流作用下的液滴变形特性。针对剪切流作用下三维液滴变形的动力学特性，利用相场方法进行了数值模拟。为了准确地描述表面张力作用下的两相不可压缩流动，采用了改进的Navier Stokes Cahn Hilliard 方程组，表面张力项和浓度对流项被添加于方程中来实现Navier Stokes方程与Cahn Hilliard方程的耦合;在数值求解方面，Chorin的投影方法被用于求解Navier Stokes 方程，并且Eyre的非条件稳定方法被用于求解Cahn Hilliard方程。数值模拟结果表明小Weber数条件下液滴更快达到稳定形态并且会随流动产生回转运动，更大的Weber数使得液滴呈现持续拉长变形。相同Weber数条件下，较大的Reynolds数会使液滴产生明显回转运动趋势。此外，液滴的变形程度也受到计算域上下边界的位置和速度的影响，边界距离液滴越近或者边界速度越大，液滴的变形程度越大。

关键词: 液滴变形相场方法投影法非条件稳定方法

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Phase field Numerical Simulation for Three dimensional Droplet Deformation in Shear Flow

YANG Jun-xiang, WEN Mao-qian^1,2

1.Department of Mathematics, Korea University, Seoul 02841, Korea;2.2.School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China

Abstract:

The dynamics of droplet has extensive applications and scientific values in natural and industrial fields, and the most typical example is the droplet deformation in shear flow. According to dynamics properties of three dimensional droplet deformation in shear flow, phase field method is used to make numerical simulation.In order to accurately describe two phase and incompressible flow with surface tension, the modified Navier Stokes Cahn Hilliard equation set is used, and the coupling of Navier stoles equation with Cahn Hilliard equation is realized by adding surface tension term and concentration convection term into the equation. For numerical solution, Chorin projection method is used to solve Navier Stokes equation, and Eyre’s unconditionally stable scheme is used for solving Cahn Hilliard equation. Numerical simulation results show that the droplet reaches a stable state faster as the Weber number is small and then rotates with the motion of flow field while a larger Weber number makes the droplet keep constantly tensile deformation. Under the same Weber number condition, the droplet shows an obvious twist deformation in a larger Reynolds number. Moreover, the droplet deformation degree is affected by the positions and velocities of up and down boundaries, the closer the distance between the droplet and the boundaries is or the larger the boundary velocities are, the larger the deformation degree of the droplet is.

Key words: droplet deformation phase field method projection method unconditionally stable scheme