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本文基于具有守恒性与相容性的N相相场模型，发展了一种用于高效模拟N相非混溶不可压流体流动的正则化格子Boltzmann方法。通过设计辅助矩，该方法能够精确恢复二阶Allen-Cahn方程与修正的动量方程。通过数值模拟三相液滴透镜铺展与三相Kelvin-Helmholtz不稳定性现象，验证了所发展的N相正则化格子Boltzmann方法的正确性与有效性。最后，对三相Rayleigh-Taylor不稳定性进行了数值模拟与分析，重点探究了雷诺数在500 ≤Re≤ 20000范围内（特别是高雷诺数Re=20000工况下）相界面的演化过程，定量分析了两个界面处气泡与尖钉的振幅以及无量纲化速度的变化规律。
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关键词:
- 相场模型 /
- N相不可压流体 /
- 格子Boltzmann方法 /
- Rayleigh-Taylor不稳定性
This paper develops a regularized lattice Boltzmann method for efficiently simulating the flow of N-phase immiscible incompressible fluids based on the phase field model that satisfies conservation and compatibility. By designing auxiliary moments, this method can accurately recover the second-order Allen-Cahn equation and the modified momentum equation. The correctness and effectiveness of the developed N-phase regularized lattice Boltzmann method are validated through numerical simulations of three-phase liquid lens spreading and Kelvin-Helmholtz instability phenomena. Finally, numerical simulations and analyses of three-phase Rayleigh-Taylor instabilities (RTI) were conducted, focusing on the evolution of the phase interface within the Reynolds number range of 500 ≤ Re ≤ 20000 (particularly under high Reynolds number condition of Re = 20000). Quantitative analyses were performed on the amplitude variations of bubbles and spikes at the two interfaces, as well as the changes in dimensionless velocity. We found that as the Reynolds number increases, the phase interface curls up at multiple locations due to Kelvin-Helmholtz instability, making the fluid more prone to dispersion and fragmentation. This study also simulated the evolution of RTI under different interface perturbations. The results indicate that RTI first develops at the perturbed interface, and its evolution gradually triggers instability at another interface.-
Keywords:
- Phase field model /
- N-phase incompressible fluid /
- lattice Boltzmann method /
- Rayleigh-Taylor instability
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