中文摘要：

采用两股互相冲击的圆射流可以形成环形的液体薄膜,液膜在径向扩展到一定的临界半径距离会破碎.数值模拟了液膜在周围气体中形成和破碎的非定常过程.考虑了液体和气体都是不可压缩Newton流体的轴对称问题.液体和气体的界面采用Levelset函数来跟踪,Navier-Stokes控制方程和物理边界条件采用有限差分格式离散求解.计算结果给出了环形液体薄膜形成并在其环形边缘处破碎,并缓慢运动的过程.液膜的厚度随着液膜在轴向的扩展会逐渐变薄,因此定义的局部Weber数会在径向逐渐减小,这里的局部Weber数定义为ρu2h/σ,其中ρ和σ分别为液体的密度和界面的张力,u和h分别为在径向某个位置的液膜的平均径向速度和半液膜厚度.数值结果表明就像实验中所观察到的那样,液膜径向扩展的过程的确会在局部Weber数趋向于1的时候终结而停止扩张.根据空间-时间线性稳定性理论,液膜的破碎最初是由正弦模式在临界局部Weber数Wec=1引起的,在临界局部Weber数小于1时会发生绝对不稳定性.在线性理论中另一个独立的模式,所谓的余弦模式,则增长比正弦模式要慢,从而会推测到正弦模式主导破碎的结论.然而,这里的数值结果却表明,余弦模式在界面波的非线性发展阶段实质的超越了正弦模式的增长,并对液膜的最终阶段的破碎起主导作用.这验证了线性理论只能够对触发时扰动波的性质进行预测,而对失稳后情况和结果的预测则不一定正确.

英文摘要：

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 was simulated numerically. Both liquid and gas were treated as incompressible Newtonian fluids. The flow considered was axi-symmetric. The liquid-gas interface was modeled with a level set function. A finite difference scheme was 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 broken 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 as ρu2h/σ,where ρ and σ are respectively the liquid density and the surface tension,and u and h are,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 number Wec=1 below which Absolute instability occurs. The other independent mode called 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 instability,but cannot predict the exact consequence of the instability.