Formation of radially expanding liquid sheet by impinging two round jets

作     者：王志亮 S．P．LIN 周哲玮 

作者机构：Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P. R. China Department of Mechanical and Aeronautical Engineering Clarkson University Potsdam NY 13699 USA 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2010年第31卷第8期

页      面：937-946页

核心收录：

学科分类：08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 10702038 and10772107) the National Science Foundation of USA (No. CTS-0138057) the Foundation of Science and Technology Commission of Shanghai Municipality (No. 09DZ1141502) the ShanghaiLeading Academic Discipline Project (No. Y0103) 

主　　题：flow instability level set method interfacial flow liquid jet 

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 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 as ρu 2 h/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 We c =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.