线性与非线性稳定性理论下液体射流空间发展的对比研究

吕明; 宁智; 阎凯

doi:10.7498/aps.65.166801

摘要

分别基于线性和非线性稳定性理论，建立了描述同轴旋转可压缩气体中含空泡液体射流稳定性的一阶与二阶色散方程，并对色散方程进行验证分析；在此基础上，进行了射流表面一阶与二阶扰动及其发展的分析，线性与非线性稳定性理论下射流空间发展的对比研究. 研究结果表明，二阶扰动波的波长和振幅明显小于一阶扰动波；沿射流方向，射流表面的扰动发展主要由一阶扰动波的发展所主导；随着轴向距离的增大，二阶扰动波才开始逐渐对扰动的发展起一定的作用. 两种稳定性理论下射流表面的占优扰动模式不会发生改变；采用非线性稳定性理论时，可以反映一些实验中发现的射流表面出现’’卫星液滴’’的现象，由于考虑了射流表面的二阶扰动，射流界面振荡程度加剧.

关键词:

Abstract

In the injecting process of liquid jet, the disturbance wave on jet interface will grow continually, leading to the spatial development and atomization of liquid jet. Studying the spatial evolution of liquid jet will help to deepen the understanding of the mechanism of jet breakup and atomization. In this paper, based on the linear and nonlinear stability theories, the first-order and second-order dispersion equations describing the stability of liquid jet with cavitation bubbles in a coaxial swirling compressible airstream are built, respectively, and the dispersion equation and its solving method are verified by the data in the literature. On this basis, the developments of first-order and second-order disturbance are analyzed, and the spatial evolutions of liquid jet are compared under linear and nonlinear stability theories. The results show that the wavelength and amplitude of the second-order disturbance are much smaller than those of the first-order disturbance. The disturbance development on jet surface is mainly dominated by the development of the first-order disturbance along the axial direction. With the increasing of axial distance, the second-order disturbance gradually begins to play a role in the developing of disturbance. The role of second-order disturbance is mainly reflected in three aspects, i. e., obviously increasing the disturbance amplitude at wave crest, reducing the disturbance amplitude at wave trough (sometimes ups and downs occur), and changing the waveform to a certain degree. The dominant disturbance mode on jet surface will not change under two kinds of theories. By using the nonlinear stability theory, satellite droplets which are found on jet surface in experiments can be reflected, and the shape of main droplet changes obviously from the ellipsoid to sphere. Also, the change of dimensionless radius of liquid jet is greater by nonlinear stability theory than by linear stability theory, which indicates that the oscillation extent of jet surface increases due to considering the second-order disturbance. Therefore, compared with the linear stability theory, the nonlinear stability theory has the advantage that it considers the effects of high-order disturbance on the spatial evolution of liquid jet in addition to the first-order disturbance on jet surface. The nonlinear stability theory can predict the spatial development of liquid jet in more detail than the linear stability theory.

Keywords:

作者及机构信息

1.
北京交通大学机械与电子控制工程学院, 北京 100044

通信作者: 宁智, zhining@bjtu.edu.cn

基金项目: 国家自然科学基金（批准号：51276011）、北京市自然科学基金（批准号：3132016）、中国博士后科学基金（批准号：2016M591061）和中央高校基本科研业务费（批准号：2016JBM049）资助的课题.

Authors and contacts

1.
School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China

Corresponding author: Ning Zhi, zhining@bjtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51276011), the Natural Science Foundation of Beijing, China (Grant No. 3132016), the China Postdoctoral Science Foundation (Grant No. 2016M591061), and the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant No. 2016JBM049).

参考文献

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[9]	Yuen M C 1968 J. Fluid Mech. 33 151
[10]	Nayfeh A H 1970 Phys. Fluids 13 841
[11]	Lafrance P 1975 Phys. Fluids 18 428
[12]	Ibrahim A A, Jog M A 2006 Phys. Fluids 18 114101
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[16]	Ibrahim E A, Lin S P 1992 J. Appl. Mech. 59 291
[17]	Tharakan T J, Ramamurthi K, Balakrishnan M 2002 Acta Mech. 156 29
[18]	Ibrahim A A 2006 Ph. D. Dissertation (Cincinnati: University of Cincinnati)
[19]	Yan K, Jog M A, Ning Z 2013 Acta Mech. 224 3071
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施引文献

[1]	Yi S J 1996 Ph. D. Dissertation (Dalian: Dalian University of Technology) (in Chinese) [易世君 1996 博士学位论文(大连: 大连理工大学)]
[2]	Zhou Z W, Lin S P 1992 J. Propul. Power 8 736
[3]	Ozgen S, Uzol O 2012 J. Fluid Eng. 134 1
[4]	Turner M R, Sazhin S S, Healey J J 2012 Fuel 97 288
[5]	Liang X, Deng D S, Nave J C 2011 J. Fluid Mech. 683 235
[6]	Cao J M 2014 J. Circ. Syst. 2 165 (in Chinese) [曹建明 2014 新能源进展 2 165]
[7]	Jazayeri S A, Li X G 2000 J. Fluid Mech. 406 281
[8]	Yang L J, Wang C, Fu Q F 2013 J. Fluid Mech. 735 249
[9]	Yuen M C 1968 J. Fluid Mech. 33 151
[10]	Nayfeh A H 1970 Phys. Fluids 13 841
[11]	Lafrance P 1975 Phys. Fluids 18 428
[12]	Ibrahim A A, Jog M A 2006 Phys. Fluids 18 114101
[13]	Ibrahim A A, Jog M A 2008 Int. J. Multiphase Flow 34 647
[14]	Rangel R H, Sirignano W A 1988 Phys. Fluids 31 1845
[15]	Lozano A, Olivares A G, Dopazo C 1998 Phys. Fluids 10 2188
[16]	Ibrahim E A, Lin S P 1992 J. Appl. Mech. 59 291
[17]	Tharakan T J, Ramamurthi K, Balakrishnan M 2002 Acta Mech. 156 29
[18]	Ibrahim A A 2006 Ph. D. Dissertation (Cincinnati: University of Cincinnati)
[19]	Yan K, Jog M A, Ning Z 2013 Acta Mech. 224 3071
[20]	Hadji L, Schreiber W 2007 J. Phys. Nat. Sci. 1 1
[21]	Potter M C, Wiggert D C 2009 Mechanics of Fluids (3rd Ed.) (Stamford: Cengage Learning) p213
[22]	Lin S P 2003 Breakup of Liquid Sheets and Jets (Cambridge: Cambridge University Press) p109
[23]	Zhou H, Zhao G F 2004 Hydrodynamic Stability (Beijing: National Defence Industry Press) p23 (in Chinese) [周恒, 赵耕夫 2004 流动稳定性 (北京: 国防工业出版社) 第23页]
[24]	Li Q Y, Wang N C, Yi D Y 2008 Numerical Analysis (Beijing: Tsinghua University Press) p228 (in Chinese) [李庆扬, 王能超, 易大义 2008 数值分析 (第5版) (北京: 清华大学出版社) 第228页]
[25]	Lin S P, Lian Z W 1990 AIAA J. 28 120
[26]	Sallam K A, Dai Z, Faeth G M 2002 Int. J. Multiphase Flow 28 427

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