Abstract: Multiple bubbles rising and interaction in a quiescent viscous incompressible fluid was simulated with three-dimensional lattice Boltzmann free energy model with a large density ratio.In order to avoid numerical instability caused by a large density ratio, eight-point and eighteen-point difference schemes were used to calculate the first and the second order derivative 1586Φ and 1586²Φ, respectively.The results of simulation presented the effects of initial bubble size and location on the flow field induced by rising bubbles and on the evolution of bubble shape.For multiple rising bubbles with the same size, the trailing bubble was influenced by the wake of the leading bubble.The strength of influence depended on both the distance between bubbles and the relative position.With the increase of distance, the strength decreased gradually.For multiple bubbles with different sizes, however, the larger bubble always strongly affected the smaller one at any initial size and location.

Key words: three-dimensional numerical simulation, lattice Boltzmann method, multiple bubbles, interactions

摘要： 应用格子Boltzmann自由能模型,在三维空间里模拟了大密度比气泡群在静止的黏性不可压缩流体中上升过程以及它们之间的相互作用。为了避免气液密度比过大造成数值不稳定问题,采用八点差分和十八点差分格式分别求解一阶1586Φ和二阶1586²Φ。模拟结果表明,气泡的初始大小和初始位置影响上升气泡周围的流场以及形状变化。当直径相同的气泡群上升时,位置靠下的气泡会受到位置靠上气泡尾迹的影响,并有很明显的形状变化。气泡之间的影响程度取决于两气泡之间的距离及相对位置,并且随着距离增加而逐渐减小。然而直径不同的气泡群上升时,不管初始位置如何,大气泡总会对小气泡造成强烈的影响。

关键词: 三维数值模拟, 格子Boltzmann方法, 气泡群, 相互作用