二维Rayleigh-Taylor不稳定性组分剖面与Atwood数相关性

由Rayleigh-Taylor不稳定性引起的湍流混合广泛存在于自然现象和工程应用中.在重力场作用下,将重流体置于轻流体之上,系统处于平衡状态.此时,在轻重流体界面处添加微小扰动,重流体向下形成尖钉,轻流体向上形成气泡,轻重流体进入湍流混合状态,系统失去稳定状态,进入失稳过程.组分剖面揭示了流场在任意时刻任意高度上的成分,从而揭示了Rayleigh-Taylor不稳定性的发展过程.利用计算流体力学软件CFD2模拟常加速度场下二维多模Rayleigh-Taylor不稳定性的发展,研究了重流体组分剖面随Atwood数的变化.文章对比了Atwood数为0.1,0.5,0.9这3种情况下质量分数剖面.在利用气泡高度hb和尖钉深度hs对高度做归一化之后,质量分数剖面不依赖于密度比.在不同密度比下,质量分数曲线都满足fm^1/2erf4(y-hs/hb-hs-1/2)]+1/2.

Invariance of Two-Dimensional Rayleigh-Taylor Instability Species Profile on Atwood Number

The turbulent mixing induced by Rayleigh-Taylor instability exists widely in nature and engineering applications. When a light fluid is on a heavy fluid under gravity acceleration, the system is balanced but unstable. However, when there are perturbations at the interface, the heavy fluid penetrates into the light fluid (spikes) and the light fluid penetrates into the heavy fluid (bubbles). The system loses its balance. This process is called Rayleigh-Taylor instability. The species profile shows the composition of fluid at any time and at any height. With the computational fluid dynamics software CFD2, the dependence of mass fraction profile of heavy fluid on Atwood number was studied by two-dimensional numerical simulations at different density ratios (i.e., Atwood number=0.1, 0.5, 0.9). The normalized mass fraction profiles with the height of bubbles and spikes show that the mass fraction profile of heavy fluid is independent on Atwood number. At different density ratios, the mass fraction profile follows the same law:f_m~$\frac{1}{2}{\mathop{\rm erf}\nolimits} \left( {4\left( {\frac{{y-{h_{\rm{s}}}}}{{{h_{\rm{b}}}-{h_{\rm{s}}}}}-\frac{1}{2}} \right)} \right) + \frac{1}{2}$.