基于格子玻尔兹曼多相流通量求解和分形理论的微尺度瑞利-泰勒不稳定性

Micro-scale Rayleigh-Taylor Instability Based on MLBFS and Fractal Theory

采用MLBFS(multiphase lattice Boltzmann flux solver)方法对两种不相混溶、不可压缩流体的微尺度下瑞利-泰勒(R-T)不稳定性进行数值模拟。通过分析R-T不稳定性初期线性阶段的漩涡发展来比较不同粘度的影响。当该过程进入非线性阶段,界面会呈现一定的分形特性;在高雷诺数情况下尤其明显。结合分形理论,运用盒维数法对界面图像进行处理,得到不同情况下界面分形维数的发展情况。研究表明当雷诺数较小时,界面分形维数呈现近似线性的增长;随着雷诺数增大,界面扰动不断加剧界面分形维数增长呈现明显的非线性状态,当雷诺数足够大时,界面的分形维数增长呈现相似性并且趋于饱和。同时,也对比了重力作用恒定时表面张力对R-T不稳定性的影响。当Bo数稍大时,表面张力的变化对界面的发展几乎没有影响;但是当Bo数极小时,表面张力对界面不稳定抑制作用明显,界面分形维数也明显小于Bo稍大的情形。

Numerical simulation of Rayleigh-Taylor( R-T) instability of two immiscible and incompressible fluids was carried out by MLBFS( multiphase lattice Boltzmann flux solver). The effects of different viscosities were compared by analyzing the vortex development of the initial linear phase of R-T instability. When the process enters the nonlinear phase,the interface will exhibit some fractal characteristics,especially in the case of high Reynolds number. Based on the fractal theory,this paper uses the Box-dimension method to deal with the interface image,and obtains the development of the fractal dimension of the interface under different conditions. The results show that when the Reynolds number is small,the fractal dimension of the interface increases linearly. With the increase of the Reynolds number,the interface perturbation increases and the fractal dimension increases obviously. When the Reynolds number is large,the interface fractal dimension growth is similar and tends to be saturated. At the same time,the effect of surface tension on the R-T instability was also compared when the gravity effect is constant.When the Bo number is slightly larger,the change of the surface tension has little effect on the development of the interface. However,when the Bo number is very small,the surface tension has obvious effect on the interface instability,and the fractal dimension of the interface is obviously smaller than that of Bo number.