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 引用本文: 李游, 李贵, 李桥忠, 代安定, 牛小东. 正则化相场格子玻尔兹曼两相流模型. 力学学报, 2024, 56(7): 1-12.
Li You, Li Gui, Li Qiaozhong, Dai Anding, Niu Xiaodong. A regularized phase-field lattice boltzmann model for two-phase flows. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 1-12.
 Citation: Li You, Li Gui, Li Qiaozhong, Dai Anding, Niu Xiaodong. A regularized phase-field lattice boltzmann model for two-phase flows. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(7): 1-12.

## A REGULARIZED PHASE-FIELD LATTICE BOLTZMANN MODEL FOR TWO-PHASE FLOWS

• 摘要: 目前, 基于相场理论的格子Boltzmann(lattice Boltzmann, LB)模型已经被广泛应用于气-液两相流流动问题中. 为了提高已有相场LB模型的数值稳定性, 提出了一种新型的正则化相场格子玻尔兹曼模型(regularized lattice Boltzmann model, RLBM)用于模拟大密度比和大黏度比的气液两相流动. 该模型由界面追踪和流场求解两个核心模块构成, 其中界面变化采用守恒型Allen-Cahn(A-C)相场方程控制, 流场演化则通过不可压Navier-Stokes(N-S)方程控制. 首先, 构建了两个正则化格子Boltzmann方程(lattice Boltzmann equation, LBE)分别获取流场信息和相场信息. 与标准的单松弛模型不同的是, 提出的模型在演化方程的碰撞项中引入了非平衡态的预前碰撞函数, 且该预前碰撞项仅与宏观量有关. 通过Chapman-Enskog(C-E)多尺度展开分析, 证实了所提出的模型能够准确地恢复到宏观流场控制方程和相场控制方程. 进一步地, 为了验证本模型的有效性, 模拟了4个两相流典型算例, 包括静态液滴、Rayleigh-Taylor(R-T)不稳定性问题、气泡上升和单个液滴撞击液膜. 数值结果证实了提出的模型能够准确地模拟大密度比、大黏度比、大雷诺数下的气液两相流流动问题. 更重要的是, 相较于传统的相场单松弛模型在小的迁移率( \theta _M < 2.0 \times 10^ - 2 )下就会诱发数值方法不收敛的问题, 提出的模型在模拟迁移率较小( \theta _M = 1.0 \times 10^ - 6 )的复杂两相流动时表现出更好的稳定性, 能够更准确地刻画界面流动, 捕捉界面形态.

Abstract: At present, the lattice Boltzmann (LB) model based on the phase field theory has been widely applied in gas-liquid two-phase flow problems. In order to improve the numerical stability of the existing phase field LB models, a new regularized phase-field lattice Boltzmann model (RLBM) is proposed for simulating gas-liquid two-phase flows with large density ratio and high viscosity ratio in this work. The proposed model consists of two core modules, namely interface tracking and flow field solver, where the interface is governed by the conservating Allen-Cahn (A-C) phase-field equation, and the flow field is governed by the incompressible Navier-Stokes (N-S) equations. Firstly, two regularized lattice Boltzmann equations (LBE) have been constructed to obtain flow field and phase field information, respectively. Unlike the standard Single-Relation-Time (SRT) model, a non-equilibrium pre-collision function, which is only related to the macroscopic variables, have been introduced into the collision term of the evolution equation in the proposed model. It has been confirmed that this model can accurately recover to the macroscopic flow field and phase filed governing equations by the multi-scale Chapman-Enskog (C-E) analysis. Furthermore, to verify the effectiveness of the present model, four typical two-phase flow cases were simulated in this paper, including static droplet, Rayleigh-Taylor (R-T) instability problems, bubble rising and a single droplet impacting on the liquid film. The obtained numerical results of these typical examples demonstrate that the proposed model can accurately simulate gas-liquid two-phase flow problems under large density ratio, high viscosity ratio and high Reynolds number. More importantly, compared to the traditional phase field SRT model, which could cause non-convergence issues at low mobility ( \theta _M < 2.0 \times 10^ - 2 ), it has been found that the model proposed in this paper exhibits better stability in simulating complex two-phase flow with low mobility ( \theta _M = 1.0*10^ - 6 ), and can more accurately characterize interface flow and capture interface morphology.

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