Diffuse interface model for incompressible two-phase flows with large density ratios
Diffuse interface model for incompressible two-phase flows with large density ratios
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DOI：
10.1016/j.jcp.2007.06.028
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发表时间：
2007-10-01
影响因子：
4.1
通讯作者：
Shu, Chang
中科院分区：
文献类型：
--
作者：
Ding, Hang;Spelt, Peter D. M.;Shu, Chang
我们研究了不可压缩扩散界面模型对具有大粘度和密度差的两相不可压缩流体流动的适用性。扩散界面模型以前主要用于密度匹配的流体，目前尚不清楚这种模型在多大程度上可以用于不同密度的流体，从而潜在地限制了这些模型的应用。本文从二元混合物的质量守恒定律出发，对于大密度、大粘度的流体，直接导出了对流Cahn-Hilliard方程和速度场无散度的条件。运动方程与以前导出的准不可压缩模型的不同是由于对两个物种的扩散通量之间的关系所作的各自假设的结果。在密度比较大的情况下，研究了模型的收敛性质。与前人的研究结果进行了定量比较，以验证该模型及其数值实现。试验表明，计算过程中体积的变化是机器精度的量级，这与我们对Cahn-Hilliard方程使用的保守离散格式(有限体积方法)是一致的。对上升气泡的拓扑变化和Rayleigh-Taylor不稳定性进行了计算，并与前人的结果进行了比较。文中还给出了分层流中液滴迎头碰撞和液滴卷吸的其他结果。(C)2007 Elsevier Inc.保留所有权利。
We investigate the applicability of an incompressible diffuse interface model for two-phase incompressible fluid flows with large viscosity and density contrasts. Diffuse-interface models have been used previously primarily for density-matched fluids, and it remains unclear to what extent such models can be used for fluids of different density, thereby potentially limiting the application of these models. In this paper, the convective Cahn-Hilliard equation and the condition that the velocity field is divergence-free are derived from the conservation law of mass of binary mixtures in a straightforward way, for fluids with large density and viscosity ratios. Differences in the equations of motion with a previously derived quasi-incompressible model are shown to result from the respective assumptions made regarding the relationship between the diffuse fluxes of two species. The convergence properties of the model are investigated for cases with large density ratio. Quantitative comparisons are made with results from previous studies to validate the model and its numerical implementation. Tests show that the variation in volume during the computation is of the order of machine accuracy, which is consistent with our use of a conservative discretization scheme (finite volume methods) for the Cahn-Hilliard equation. Results of the method are compared with previous work for the change in topology of rising bubbles and Rayleigh-Taylor instability. Additional results are presented for head-on droplet collision and the onset of droplet entrainment in stratified flows. (c) 2007 Elsevier Inc. All rights reserved.