横向交流电场下液膜参数不稳定性分析

王铁晗; 富庆飞; 杨立军

doi:10.6052/0459-1879-20-300

横向交流电场下液膜参数不稳定性分析

doi: 10.6052/0459-1879-20-300

王铁晗^*,
富庆飞^*,†,2), ,,
杨立军^*,†

^*北京航空航天大学宇航学院, 北京 100191
^†北京航空航天大学大数据精准医疗高精尖创新中心, 北京 100191

基金项目: 1) 国家自然科学基金资助项目(11922201)

详细信息

作者简介:
2) 富庆飞, 研究员, 主要研究方向: 火箭发动机喷雾燃烧. E-mail: fuqingfei@buaa.edu.cn

通讯作者:
富庆飞

中图分类号: O35
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- 被引次数: 0
出版历程
- 收稿日期: 2020-08-25
- 刊出日期: 2021-02-10

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

Wang Tiehan^*,
Fu Qingfei^{*,†,2)
, ,},
Yang Lijun^*,†

^*School of Astronautics, Beihang University, Beijing 100191, China
^†Beijing Advanced Innovation Center for Big Date-based Precision Medicine, Beihang University, Beijing 100191, China

摘要

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.
- 参数不稳定性 /
- 平面液膜 /
- 电场 /
- 漏电介质模型
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.
- parametric instability /
- liquid sheet /
- electric field /
- leaky dielectric model

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参考文献(35)

[1]	Squire HB. Investigation of the instability of a moving liquid film. British Journal of Applied Physics, 2002,4(6):167-169
[2]	Jones AR, Thong KC. The production of charged monodisperse fuel droplets by electrical dispersion. Journal of Physics D: Applied Physics, 1971,4(8):1159-1166
[3]	Tomita Y, Ishibashi Y, Yokoyama T. Fundamental studies on an electrostatic ink jet printer: 1st report, electrostatic drop formation. Transactions of the Japan Society of Mechanical Engineers Part B, 1986,29(257):3737-3743
[4]	Hagerty WW. A study of the stability of plane fluid sheets. Journal of Applied Mechanics, 1955,22:509-514
[5]	Lin SP. Stability of a viscous liquid curtain. Journal of Fluid Mechanics, 2006,104:111-118
[6]	Li X. Spatial instability of plane liquid sheets. Chemical Engineering Science, 1993,48(16):2973-2981
[7]	Li HS, Kelly RE. The instability of a liquid jet in a compressible airstream. Physics of Fluids A Fluid Dynamics, 1992,4(10):2162-2168
[8]	Cao J, Li X. Stability of plane liquid sheets in compressible gas streams. Journal of Propulsion & Power, 2011,16(4):623-627
[9]	张鹏, 俞刚. 高Bond数下黏性液滴的Rayleigh-Taylor不稳定性. 力学学报, 2006,38(3):289-295 (Zhang Peng, Yu Gang. Rayleigh-Taylor instability of viscous droplets with high Bond numbers. Chinese Journal of Theoretical and Applied Mechanics. 2006,38(3):289-295 (in Chinese))
[10]	El-Sayed MF. Three-dimensional electrohydrodynamic temporal instability of a moving dielectric liquid sheet emanated into a gas medium. The European Physical Journal E, 2004,15(4):443-455
[11]	李广滨, 司廷, 尹协振. 电场作用下无黏聚焦射流的时间不稳定性研究. 力学学报, 2012,44(5):876-883 (Li Guangbin, Si Ting, Yin Xiezhen. Temporal instability study of inviscid focused jets under an electric field. Chinese Journal of Theoretical and Applied Mechanics. 2012,44(5):876-883 (in Chinese))
[12]	李帅兵, 杨睿, 罗喜胜等. 气流作用下同轴带电射流的不稳定性研究. 力学学报, 2017,49(5):997-1007 (Li Shuaibing, Yang Rui, Luo Xisheng, et al. Instability study of an electrified coaxial jet in a coflowing gas stream. Chinese Journal of Theoretical and Applied Mechanics. 2017,49(5):997-1007 (in Chinese))
[13]	Yang LJ, Liu YX, Fu QF. et al. Linear stability analysis of electrified viscoelastic liquid sheets. Atomization & Sprays, 2012,22(11):951-982
[14]	Taylor GI, McEwan AD. The stability of a horizontal fluid interface in a vertical electric field. Journal of Fluid Mechanics, 1965,22(1):1-15
[15]	Melcher JR, Warren EP. Electrohydrodynamics of a current-carrying semi-insulating jet. Journal of Fluid Mechanics, 1971,47(1):127-145
[16]	Taylor GI. Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proceedings of the Royal Society A, 1966,291(1425):159-166
[17]	Fish BR. Electrical generation of natural aerosols from vegetation. Science, 1972,175(4027):1239-1240
[18]	Saville DA. Electrohydrodynamics: The Taylor-Melcher leaky dielectric model. Annual Review of Fluid Mechanics, 2003,29(1):27-64
[19]	Montanero, José M, Alfonso M, et al. Dripping, jetting and tip streaming. Reports on Progress in Physics, 2020,83(9):1-60
[20]	Gamero-Casta?o M, Magnani M. Numerical simulation of electrospraying in the cone-jet mode. Journal of Fluid Mechanics, 2019,859:247-267
[21]	Gamero-Casta?o M, Manuel, Magnani M. The minimum flow rate of electrosprays in the cone-jet mode. Journal of Fluid Mechanics, 2019,876:553-572
[22]	Carroll CP, Joo YL. Electrospinning of viscoelastic boger fluids: Modeling and experiments. Physics of Fluids, 2006,18(5):053102
[23]	Reneker DH, Yarin AL. Electrospinning jets and polymer nanofibers. Polymer, 2008,49(10):2387-2425
[24]	Demekhin E, Polyanskikh S, Ramos A. Taylor cones in a leaky dielectric liquid under an AC electric field. Physical Review E Statal Nonlinear & Soft Matter Physics, 2011,84(3):035301
[25]	Yeo LY, Lastochkin D, Wang SC. et al. A new AC electrospray mechanism by Maxwell-Wagner polarization and capillary resonance. Physical Review Letters, 2004,92(13):133902
[26]	Demekhin EA, Polyanskikh SV. Stability of a viscous liquid jet in a high-frequency alternating electric field. Journal of Applied Mechanics & Technical Physics, 2010,51(1):31-43
[27]	Yang W, Duan H, Li C. et al. Crossover of varicose and whipping instabilities in electrified microjets. Physical Review Letters, 2014,112(5):054501
[28]	Ward K, Matsumoto S, Narayanan R. The electrostatically forced Faraday instability: Theory and experiments. Journal of Fluid Mechanics, 2019,862:696-731
[29]	Cui X, Fu QF, Yang LJ. et al. Linear instability of liquid sheets subjected to a transverse electric field. Journal of Fluids Engineering, 2020,142(1):011203
[30]	Jia BQ, Xie L, Yang LJ. et al. Linear instability of viscoelastic planar liquid sheets in the presence of gas velocity oscillations. Journal of Non-Newtonian Fluid Mechanics, 2019,273:104169
[31]	Jia BQ, Xie L, Cui X et al. Linear stability of confined coaxial jets in the presence of gas velocity oscillations with heat and mass transfer. Physics of Fluids, 2019,31:092101
[32]	谢络. 静/交变电场作用下黏性圆柱射流的稳定性分析. [博士论文]. 北京: 北京航空航天大学, 2020 (Xie L. Instability analysis of cylindrical viscous liquid jets under DC and AC electric fields. [PhD Thesis]. Beijing: Beihang University, 2020 (in Chinese))
[33]	Benjamin TB, Ursell FJ. The stability of the plane free surface of a liquid in vertical periodic motion. Proceedings of the Royal Society of London, 1954,225(1163):505-515
[34]	姚慕伟, 贾伯琦, 杨立军等. 气流速度振荡场中幂律液膜不稳定性分析. 航空学报, 2020,41(11):123873 (Yao Muwei, Jia Boqi, Yang Lijun, et al. Instability of power-law liquid sheets in the presence of gas velocity oscillations. Acta Aeronautica et Astronautica Sinica. 2020,41(11):123873 (in Chinese))
[35]	谢络, 杨立军. 径向交流电场作用下的射流稳定性分析//第十届全国流体力学学术会议论文摘要集, 2018,115:92 (Xie Luo, Yang Lijun. The instability of liquid jet under radial AC electric field//The 10th Chinese Congress of Theoretical and Applied Mechanics, 2018,115:92 (in Chinese))