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Numerical simulation of two- and three-dimensional two-phase fluid motion by lattice Boltzmann method

机译：二维玻尔兹曼方法对二维和三维两相流体运动的数值模拟

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This study describes the numerical simulations of two-phase fluid motions under gravity by the lattice Boltzmann method (LBM), in which the fluid motions result from collision and translation of mesoscopic particles and the interface interaction in multiphase fluids can be reproduced in a self-organizing way. Our aims are to examine the applicability of LBM to the numerical analysis of bubble motions in comparison with the two-dimensional results by the Volume Of Fluid (VOF) method based on the Navier-Stokes and the liquid-volume convective equations, and to develop the three-dimensional binary fluids model, consisting of two sets of distribution functions to represent the total fluid density and the density difference, which introduces the repulsive interaction consistent with a free energy function between fluid particles. We included the buoyancy terms due to the density difference between two phases in the lattice Boltzmann equations, and simulated the motions of single bubble and two bubbles rising in a duct, calculating the surface tension from the Laplace's law represented by the non-dimensional numbers, Eotvos and Morton numbers. In the two-dimensional simulations, the results by LBM agree with those by the VOF method. The three-dimensional simulation of two bubble interaction shows that the upper bubble takes a shape of skirt as the lower bubble approaches due to the wake formation, and they coalesce into a single bubble eventually, These results prove the validity of the buoyancy model proposed here and the applicability of LBM to the quantitative numerical analysis of two-phase fluid motions.
机译：这项研究描述了通过格子Boltzmann方法（LBM）在重力作用下进行的两相流体运动的数值模拟，其中流体运动是由介观粒子的碰撞和平移产生的，并且多相流体中的界面相互作用可以在自组织方式。我们的目的是与基于Navier-Stokes和液体体积对流方程的流体体积（VOF）方法的二维结果进行比较，以检验LBM在气泡运动数值分析中的适用性，并发展三维二元流体模型，由两组分布函数组成，分别代表总流体密度和密度差，它引入了与流体粒子之间的自由能函数一致的排斥相互作用。我们将由于两相之间密度差异而产生的浮力项包括在格子Boltzmann方程中，并模拟了单个气泡和两个气泡在管道中上升的运动，并根据由无量纲数字表示的拉普拉斯定律计算了表面张力， Eotvos和Morton数。在二维仿真中，LBM的结果与VOF方法的结果一致。两种气泡相互作用的三维模拟表明，由于尾流的形成，上部气泡随着下部气泡的接近而呈裙状，并最终合并为单个气泡，这些结果证明了本文提出的浮力模型的有效性。以及LBM在两相流体运动定量数值分析中的适用性。

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