[论文解读] Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio

Hong Liang, Yang Li+2 more|arXiv (Cornell University)|Oct 22, 2018

Lattice Boltzmann Simulation Studies参考文献 38被引用 4

一句话总结

本文提出了一种基于Allen-Cahn相场方法的新型轴对称格子Boltzmann模型，用于模拟大密度比的多相流——这一能力在现有轴对称LB模型中此前无法实现。该模型采用两个独立的格子Boltzmann方程：一个用于界面追踪，配备定制的源项和平衡分布函数；另一个用于流体动力学，采用强迫分布函数。模型实现了高精度和极低的虚假速度，与广泛密度比范围内的解析解和实验数据高度一致。

ABSTRACT

In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows. The most striking feature of the model is that it enables to handle multiphase flows with large density ratio, which are unavailable in all previous axisymmetric LB models. The present model utilizes two LB evolution equations, one of which is used to solve fluid interface, and another is adopted to solve hydrodynamic properties. To simulate axisymmetric multiphase flows effectively, the appropriate source term and equilibrium distribution function are introduced into the LB equation for interface tracking, and simultaneously, a simple and efficient forcing distribution function is also delicately designed in the LB equation for hydrodynamic properties. Unlike many existing LB models, the source and forcing terms of the model arising from the axisymmetric effect include no additional gradients, and consequently, the present model contains only one non-local phase field variable, which in this regard is much simpler. We further conducted the Chapman-Enskog analysis to demonstrate the consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn equation and hydrodynamic equations. A series of numerical examples, including static droplet, oscillation of a viscous droplet, breakup of a liquid thread, and bubble rising in a continuous phase, are used to test the performance of the proposed model. It is found that the present model can generate relatively small spurious velocities and can capture interfacial dynamics with higher accuracy than the previously improved axisymmetric LB model. Besides, it is also found that our present numerical results show excellent agreement with analytical solutions or available experimental data for a wide range of density ratios, which highlights the strengths of the proposed model.

研究动机与目标

• 开发一种能够模拟大密度比轴对称多相流的格子Boltzmann模型，此类问题在现有模型中仍具挑战性。
• 克服先前轴对称LB模型因数值不稳定性和界面动力学不准确而无法处理大密度对比的局限性。
• 通过引入先进的多重松弛时间（MRT）碰撞模型并最小化非局部依赖关系，确保数值稳定性和准确性。
• 通过Chapman-Enskog分析，实现轴对称流体动力学和相场方程的一致恢复。

提出的方法

• 该模型使用两个不同的格子Boltzmann方程：一个用于相场演化（界面追踪），另一个用于流体动力学属性（流体运动）。
• 为界面追踪方程专门设计了源项和平衡分布函数，以考虑轴对称效应，而无需引入额外梯度项。
• 在流体动力学方程中引入一种简单高效的强迫分布函数，以模拟轴对称效应，避免了复杂的梯度项。
• 在碰撞算子中应用多重松弛时间（MRT）格式，以增强数值稳定性并减少黏度相关的人工误差。
• 通过Chapman-Enskog分析推导出该模型，证明其在不可压缩流条件下能正确恢复轴对称Cahn-Hilliard方程和Navier-Stokes方程。
• 通过包含松弛参数和速度项的推导表达式，从分布函数的零阶矩重构流体压力。

实验结果

研究问题

• RQ1 能否开发一种格子Boltzmann模型，准确模拟超出先前轴对称LB模型能力范围的大密度比轴对称多相流？
• RQ2 如何在格子Boltzmann框架中引入轴对称效应，而无需引入额外梯度项或非局部项？
• RQ3 MRT碰撞模型对大密度比流动中界面动力学的数值稳定性和准确性有何影响？
• RQ4 与现有轴对称LB模型相比，该模型在多大程度上降低了虚假速度？
• RQ5 该模型在广泛密度比范围内，对解析解和实验数据的重现能力如何？

主要发现

• 所提出的模型成功实现了大密度比多相流的模拟——这是此前轴对称格子Boltzmann模型无法实现的，充分体现了其新颖性和强大能力。
• 与先前改进的轴对称LB模型相比，该模型产生的虚假速度显著更小，从而提升了界面追踪的准确性。
• 静态液滴、振荡液滴、液丝断裂和气泡上浮等数值结果，与广泛密度比范围内的解析解和实验数据高度一致。
• Chapman-Enskog分析证实，在不可压缩流假设下，MRT-LB模型能正确恢复轴对称流体动力学和相场方程。
• 该模型的设计仅包含一个非局部相场变量，且避免了额外梯度项，相比先前方法更为简洁且鲁棒。
• 基于分布函数零阶矩的压力计算方法提供了稳定且准确的流体压力，经渐近分析验证。