耦合界面张力的三维流体界面不稳定性的格子Boltzmann模拟

采用介观格子Boltzmann方法模拟界面张力作用下三维流体界面的Rayleigh-Taylor (RT)不稳定性的增长过程,主要分析表面张力对流体界面动力学行为及尖钉和气泡后期增长的影响机制.首先发现三维RT不稳定性的发生存在临界表面张力(σ_c),其值随着流体Atwood数的增大而增大,且数值预测值与理论分析结果σ_c=(ρ_h-ρ₁)g/k~2一致.另外,随着表面张力的增大,不稳定性演化过程中界面卷吸程度和结构复杂性逐渐减弱,系统中界面破裂形成离散液滴的数目也显著减少.相界面的后期动力学行为也从非对称发展转向始终保持关于中轴线对称.尖钉与气泡振幅在表面张力较小时对其变化不显著,当表面张力增大到一定值后,可以有效地抑制尖钉与气泡振幅的增长.进一步发现,高雷诺数三维RT不稳定性在不同表面张力下均经历4个不同的发展阶段:线性阶段、饱和速度阶段、重加速和混沌混合阶段.尖钉与气泡在饱和速度阶段以近似恒定的速度增长,其渐进速度的值与修正的势流理论模型结果一致.受非线性Kelvin-Helmholtz旋涡的剪切作...

Lattice Boltzmann simulation of three-dimensional fluid interfacial instability coupled with surface tension

In this paper,the development of three-dimensional fluid interfacial Rayleigh-Taylor(RT)instability coupled with the surface tension was numerically studied using the mesoscopic lattice Boltzmann method.We mainly analyzed the influence of surface tension on fluid interfacial dynamics and spike/bubble late-time growth.The numerical experiments show that there exists the critical surface tension(σc)in the three-dimensional RT instability,above which the RT phenomenon does not appear and below which it would take place.It is found that the critical surface tension increases with the fluid Atwood number and the corresponding numerical predictions show good agreements with those of the theoretical analysisσc=(ρh?ρl)g/k².In addition,we can find that increasing surface tension reduces the roll-up of the interface and the complexity of interfacial structure,also preventing the breakup of the interface into the individual droplets.The late-time dynamics of phase interface change from the asymmetric development to the symmetry with respect to the middle axis.When the surface tension is sufficiently low,the spike and bubble amplitudes almost no longer change with it,and further increasing the surface tension can slow down the growth of the spike and bubble amplitudes.Furthermore,we can observe that the development of the high-Reynolds-number RT instability under different surface tensions can also be divided into four distinct stages,including the linear growth,saturated velocity growth,reacceleration,and chaotic mixing.The spike and bubble grow with approximately constant velocities at the saturated stage and their asymptotic values are consistent with those of the modified potential flow theory.In the following,the spike and bubble driven by the increasing Kelvin-Helmholtz vortices are accelerated such that their evolutional velocities exceed the solutions of the potential flow model at the reacceleration stage.The reacceleration stage cannot last infinitely and the spike and bubble velocities at the late time fluctuate with time,implying that the growth of the RT instability enters into the chaotic mixing stage.By numerical analysis,we demonstrate that the three-dimensional RT instability at the chaotic mixing stage has a quadratic growth and also report that the spike and bubble growth rates decrease with the surface tension in general.