N种不互溶不可压缩流体的多相流：守恒型艾伦-卡恩方程与格子玻尔兹曼方程方法

Multiphase flows of N immiscible incompressible fluids: Conservative Allen-Cahn equation and lattice Boltzmann equation method.

作者信息

Zheng Lin, Zheng Song, Zhai Qinglan

机构信息

MIIT Key Laboratory of Thermal Control of Electronic Equipment, School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China.

School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, People's Republic of China.

出版信息

Phys Rev E. 2020 Jan;101(1-1):013305. doi: 10.1103/PhysRevE.101.013305.

DOI:10.1103/PhysRevE.101.013305

PMID:32069624

Abstract

In this paper, we develop a conservative phase-field method for interface-capturing among N (N≥2) immiscible fluids, the evolution of the fluid-fluid interface is captured by conservative Allen-Cahn equation (CACE), and the interface force of N immiscible fluids is incorporated to Navier-Stokes equation (NSE) by chemical potential form. Accordingly, we propose a lattice Boltzmann equation (LBE) method for solving N (N≥2) immiscible incompressible NSE and CACE at high density and viscosity contrasts. Numerical simulations including stationary droplets, Rayleigh-Taylor instability, spreading of liquid lenses, and spinodal decompositions are carried out to show the accuracy and capability of present LBE, and the results show that the predictions by use of the present LBE agree well with the analytical solutions and/or other numerical results.

摘要

在本文中，我们开发了一种用于N（N≥2）种不混溶流体间界面捕捉的守恒相场方法，流体-流体界面的演化通过守恒的艾伦-卡恩方程（CACE）来捕捉，并且N种不混溶流体的界面力通过化学势形式被纳入到纳维-斯托克斯方程（NSE）中。相应地，我们提出了一种格子玻尔兹曼方程（LBE）方法，用于在高密度和高粘度对比情况下求解N（N≥2）种不混溶不可压缩的NSE和CACE。进行了包括静态液滴、瑞利-泰勒不稳定性、液体透镜扩展以及旋节线分解等数值模拟，以展示当前LBE的准确性和能力，结果表明使用当前LBE的预测与解析解和/或其他数值结果吻合良好。