一种精确的含可溶性表面活性剂两相流动相场方法  

An Accurate Phase Field Method for 2-Phase Flow With Soluble Surfactants

作　　者：陈黎明 张良奇[1] 王小双 肖姚 曾忠[1] CHEN Liming;ZHANG Liangqi;WANG Xiaoshuang;XIAO Yao;ZENG Zong(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：《应用数学和力学》2024年第12期1455-1472,共18页Applied Mathematics and Mechanics

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

摘　　要：基于相场理论,该文提出了一种精确的考虑可溶性表面活性剂作用的两相流相场方法.为保证相界面处动量输运的守恒性,引入一致性的质量通量以考虑相变量扩散对质量守恒的影响,应用有限体积方法离散守恒形式的控制方程;选择五阶WENO格式处理控制方程的对流项,改善界面处理的精度和稳定性.此外,还构造了多组二维差分模板以进一步改善表面张力项中的梯度离散,并证实了对应格子Boltzmann D2Q9模型的模板能够显著降低伪势速度,改善表面活性剂浓度的计算精度.通过对静态液滴、双液滴融合、大密度比气泡上升以及剪切流中的单液滴变形与破裂等问题进行数值研究,充分验证了所提出的两相流相场方法的精度、守恒性与鲁棒性.An accurate phase field method for 2-phase flow with soluble surfactants was developed based on the phase field theory.The key point of this method was the utilization of consistent and conservative mass flux to ensure the conservation of momentum transport across the interface.The finite-volume method was used to discretize the governing equations in their conservative form.The 5th-order WENO scheme was chosen to effectively handle the convective terms,aimed to enhance accuracy and robustness in addressing steep variations in the interfacial region.Furthermore,various 2D difference templates were designed to optimize gradient discretization in the surface tension term.Particularly,with the template corresponding to the lattice Boltzmann D2Q9 model,a notable reduction of the spurious velocity and a significant improvement of the accuracy of surfactant concentration prediction were achieved.Various examples such as static droplets,fusion of 2 droplets,bubble rise with a large density ratio,deformation and breakage of individual droplets in shear flow demonstrate the accuracy,conservative properties,and robustness of the proposed method.

关 键 词：两相流 相场方法 可溶性表面活性剂 连续表面力模型 

分 类 号：O359[理学—流体力学]