Formation of radially expanding liquid sheet by impinging two round jets
Formation of radially expanding liquid sheet by impinging two round jets
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DOI：
10.1007/s10483-010-1328-x
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发表时间：
2010-07
影响因子：
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通讯作者：
Zhi-Liang Wang;S. P. Lin;Zhe-wei Zhou
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文献类型：
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作者：
Zhi-Liang Wang;S. P. Lin;Zhe-wei Zhou
通过使两个相同的圆形射流彼此撞击，可以形成薄的圆形液体片。液体层膨胀到一定的临界径向距离并破裂。数值模拟了环境气体中液膜的形成和破碎的非定常过程。液体和气体都被视为不可压缩的牛顿流体。所考虑的流动是轴对称的。气液界面采用水平集函数建模。采用有限差分法求解带物理边界条件的Navier-Stokes方程。数值结果显示了一个薄的圆形片可以形成和打破在其圆形边缘在缓慢运动。当它径向膨胀时，薄片继续变薄。因此，韦伯数径向减小。韦伯数定义为ρ u ~ 2 h/σ，其中ρ和σ分别为液体密度和表面张力，ρ和σ分别为液体层中局部径向位置的平均速度和半层厚度。数值计算结果表明，薄片确实终止于一个径向位置，在那里韦伯数达到实验中观察到的1。时空线性理论预测，在临界Weber数Wec =1时，破裂由弯曲模引发，低于此值时，出现绝对不稳定性。根据线性理论，称为静脉曲张模式的另一个独立模式比弯曲模式增长得更慢。然而，我们的数值计算结果表明，在非线性演化过程中，实际上是静脉曲张模式超过了蜿蜒模式，并负责最终破碎。线性理论只能在不稳定性开始时正确地预测扰动波的性质，但不能准确地预测不稳定性的后果。
A thin circular liquid sheet can be formed by impinging two identical round jets against each other. The liquid sheet expands to a certain critical radial distance and breaks. The unsteady process of the formation and breakup of the liquid sheet in the ambient gas is simulated numerically. Both liquid and gas are treated as incompressible Newtonian fluids. The flow considered is axisymmetric. The liquid-gas interface is modeled with a level set function. A finite difference scheme is used to solve the governing Navier-Stokes equations with physical boundary conditions. The numerical results show how a thin circular sheet can be formed and break at its circular edge in slow motion. The sheet continues to thin as it expands radially. Hence, the Weber number decreases radially. The Weber number is defined asρu2h/σ, whereρandσare, respectively, the liquid density and the surface tension, anduandhare, respectively, the average velocity and the half sheet thickness at a local radial location in the liquid sheet. The numerical results show that the sheet indeed terminates at a radial location, where the Weber number reaches one as observed in experiments. The spatio-temporal linear theory predicts that the breakup is initiated by the sinuous mode at the critical Weber numberWec=1, below which the absolute instability occurs. The other independent mode called the varicose mode grows more slowly than the sinuous mode according to the linear theory. However, our numerical results show that the varicose mode actually overtakes the sinuous mode during the nonlinear evolution, and is responsible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of the instability, but cannot predict the exact consequence of the instability.