WANG Zhi-liang, S. P. Lin, ZHOU Zhe-wei. Formation of Radially Expanding Liquid Sheet by Impinging Two Round Jets[J]. Applied Mathematics and Mechanics, 2010, 31(8): 891-900. doi: 10.3879/j.issn.1000-0887.2010.08.001
 Citation: WANG Zhi-liang, S. P. Lin, ZHOU Zhe-wei. Formation of Radially Expanding Liquid Sheet by Impinging Two Round Jets[J]. Applied Mathematics and Mechanics, 2010, 31(8): 891-900.

# Formation of Radially Expanding Liquid Sheet by Impinging Two Round Jets

##### doi: 10.3879/j.issn.1000-0887.2010.08.001
• Rev Recd Date: 2010-06-01
• Publish Date: 2010-08-15
• A thin circular liquid sheet can be formed by impinging two identicalround 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 smiulated num erically. Both liquid and gas were treated as incompressible Newtonian fluids. The flow considered was axi-symm etric. 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 rad ially. The Weber number is defined asu2h/, where and 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 num erical results show that the sheet indeed terminates at a radial location where the Weber num ber reaches one as observed in experiments. The spatio-tem poral linear theory predicts that the breakup is initiated by the sinuousm ode at the critical Weber number Wec=1 be low which absolute instability occurs. The other independentmode called varicose mode grow smore slowly than the sinuousmode according to the linear theory. However our numerical results show that the varicose mode actually overtakes the sinuous mode during the non linear evolution, and is respon sible for the final breakup. The linear theory predicts the nature of disturbance waves correctly only at the onset of instability, but cannotpredict the exact consequence of the instability.
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