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中文核心期刊

横向交流电场下液膜参数不稳定性分析

PARAMETRIC INSTABILITY OF LIQUID SHEETS SUBJECTED TO A TRANSVERSE AC ELECTRIC FIELD

  • 摘要: 当将运动的平面液膜置于横向的交流电场之间时会产生参数振荡现象.为了得到交流电场下平面液膜的色散关系并为液膜的破碎行为分析提供理论基础,本文基于漏电介质模型对液体的电学特性进行假设,对平面液膜在直流和交流电场下的参数不稳定性进行了分析.由于主流是基于时间的流动, 在稳定性分析中引入了Floquet理论. 在文中,将电场定义为部分交流电场和部分直流电场共同耦合后的混合型电场. 最后,波数和不稳定增长率之间的无量纲色散方程可由矩阵的形式表示.本文考虑了多种参数对不稳定的影响, 包括气液密度比、韦伯数、雷诺数、欧拉数、 松弛时间以及衡量交流电场占比的参数及频率参数,并得知欧拉数同时影响毛细不稳定性及参数不稳定性,交流电场占比对不稳定性的影响体现在恒定电场力上, 而交流电场频率主要影响参数不稳定性. 为了在实验中更容易地寻求参数振荡现象,增大电欧拉数及减小交流电场频率是有效的方法.

     

    Abstract: Parametric resonance occurs at the gas-liquid interface when a liquid sheet moving in a transverse AC electrical field. In order to obtain the dispersion relation of liquid sheet under AC electric field and to provide the theoretical basis for the analysis of the breaking behavior of liquid sheet, in this paper, the temporal parametric instability under DC and AC electric field were both analyzed in the leaky dielectric model. The leaky dielectric model is used to characterize the electrical properties of liquid. Since the mean flow is time-dependent function, the Floquet theory is used to solve the stability problem. In this paper, the electric field is defined as a mixed electric field coupled by part of an ac electric field and part of a DC electric field. The dimensionless dispersion relation between wave number and temporal growth rate can be derived as a matrix. According to this relationship, the influence of various liquid properties on the parametric instability were discussed. The effects of the ratio of gas-to-liquid density (\rho ), the Weber number (We), the Reynolds number (Re), the electrical Euler number (Eu), the relative relaxation time (\tau ) and the characteristic of the proportion of AC electric field (Pr) and the frequency of the electric field (\varOmega ) was concluded in this paper. As a conclusion, the electrical Euler number (Eu) influence the instability of both capillary unstable and parametric unstable region, the proportion of electric field (Pr) effects as a constant electric field force, the frequency of the AC electric field (\varOmega ) mainly influence the parametric instability region. In the experiment, in order to obtain parameter oscillation phenomenon more easily, increasing electrical Euler number (Eu) and reducing the frequency of AC electric field (\varOmega ) are founded as effective methods.

     

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