圆射流零阶色散关系式的线性稳定性理论推导

Derivation on linear stability theory of zero order dispersion relation in liquid jets

为了研究粘性圆射流喷射进入不可压缩气体介质中的碎裂过程,利用线性化的纳维-斯托克斯控制方程组与线性化的运动学和动力学边界条件,采用流函数方法,对碎裂过程进行线性稳定性分析。结果表明:可推导出圆射流零阶对称波形的量纲一色散准则关系式,且该色散准则关系式只与量纲一参数——维伯数We、雷诺数Re、欧拉数Eu、马赫数Ma、气液流速比U、气液压力比P等有关。

In order to study the disintegrated process of a viscous liquid jet moving in an incompressible gas medium,a linear stability analysis was carried out using the linearized Navier-Stokes equations,the linearized kinematic and dynamic boundary conditions,and employing the stream function method.The results indicate that：the dimensionless dispersion relation of the zero-order varicose waves in circular liquid jets can be derivated,which is related to some dimensionless parameters,they are Weber number We;Reynolds number Re;Euler number Eu;Mach number Ma,gas-liquid velocity ratio U and gas-liquid pressure ratio P.2 figs,6 refs.