基于WENO格式有限体积法的铁磁流体两相流相场方法  

A finite volume-based phase field method for two-phase ferrofluid flows

作　　者：张少松 张良奇[1] 陈黎明 王小双 肖姚 曾忠[1] ZHANG Shaosong;ZHANG Liangqi;CHENG Liming;WANG Xiaoshuang;XIAO Yao;ZENG Zhong(College of Aerospace Engineering,Chongqing University,Chongqing 400044,P.R.China;Shanghai-Chongqing Institute of Artificial Intelligence,Chongqing 401332,P.R.China)

机构地区：[1]重庆大学航空航天学院,重庆400044 [2]沪渝人工智能研究院,重庆401332

出　　处：《重庆大学学报》2025年第4期67-83,共17页Journal of Chongqing University

基　　金：国家自然科学基金资助项目(12102071,12172070);重庆市博士直通车资助项目(CSTB2022BSXM-JCX0086)。

摘　　要：采用基于WENO格式的有限体积法,发展了包括铁磁流体的两相流相场方法。采用不可压缩Navier-Stokes方程描述流体流动,利用Cahn-Hilliard方程捕捉两相流界面运动,并采用Maxwell方程描述磁场分布。同时,在流体流动控制方程中加入开尔文力和表面张力以实现磁场对界面动力学行为的描述。将四阶Cahn-Hilliard方程拆分为2个Helmholtz类型方程,从而克服四阶非线性项的离散和高精度计算带来的难题。采用五阶WENO格式对控制方程的对流项进行统一离散处理,从而提高数值计算的精度性,同时避免产生数值振荡。Zalesak’s圆盘问题数值模拟的结果表明,本文方法的相界面捕捉精度高于参考文献中所报道的离散方法,与高精度相场方法的精度相当;对剪切流中的液滴变形问题的数值模拟揭示本文数值方法可以更真实地捕捉到更多个卫星液滴。此外,针对磁场影响下,较低毛细数条件的铁磁流体液滴剪切变形研究显示,当外加磁场方向与液滴水动力学变形方向一致时,磁场的作用会放大液滴变形,进一步增加磁场强度会诱发液滴分裂;而当外加磁场方向与液滴水动力学变形方向垂直时,较低强度的磁场作用能够改变液滴变形方向,而较高强度的磁场则会使液滴直接呈现出沿磁场方向变形。This paper presents a finite volume method based on the weighted essentially non-oscillatory(WENO)Stokes equations is used to describe fluide flow,the Cahn-Hilliard equation is adopted to capture interfacial motion of two-phase flow,and the Maxwell equation is used to describe external magnetic field distribution.At the same time,adding Kelvin force and surface tension to the fluid flow control equation to achieve the description of interface dynamic behavior by magnetic field.To address the challenges posed by the fourth-order nonlinear diffusion terms,the Cahn-Hilliard equation is decomposed into two Helmholtz equations.The fifthorder WENO scheme is employed to handle the convection term,enhancing computational accuracy and mitigating numerical oscillations.Validation through Zalesak’s disk problem shows that the proposed method achieves higher phase interface capture accuracy compared to existing references,while maintaining performance comparable to high-precision phase field methods.The method is applied to investigate droplet shear deformation,revealing its capability to capture more satellite droplets.Moreover,research on the shear deformation of ferromagnetic fluid droplets under the influence of magnetic fields and with lower capillary numbers indicates that the magnetic interfacial force favors droplet deformation when the external magnetic field direction aligns with the hydrodynamic deformation.Furthermore,increasing the magnetic field intensity leads to droplet splitting.Conversely,when the magnetic field is nearly perpendicular to the deformation direction,a low-intensity field alters the deformation trajectory,while a high intensity magnetic field enforces deformation along the magnetic field direction.

关 键 词：相场法 有限体积法 铁磁流体液滴 磁场控制 

分 类 号：O359.1[理学—流体力学]