搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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

Comparative study on the spatial evolution of liquid jet under linear and nonlinear stability theories

Lü Ming, Ning Zhi, Yan Kai
PDF
导出引用
  • 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.
    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.
      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.
      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).
    [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

  • [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

  • [1] 邱海舰, 胡玉禄, 胡权, 朱小芳, 李斌. 考虑谐波互作用的行波管欧拉非线性理论模型. 物理学报, 2018, 67(8): 088401. doi: 10.7498/aps.67.20180024
    [2] 沙莎, 陈志华, 张庆兵. 激波与SF6球形气泡相互作用的数值研究. 物理学报, 2015, 64(1): 015201. doi: 10.7498/aps.64.015201
    [3] 谷云庆, 牟介刚, 代东顺, 郑水华, 蒋兰芳, 吴登昊, 任芸, 刘福庆. 基于蚯蚓背孔射流的仿生射流表面减阻性能研究. 物理学报, 2015, 64(2): 024701. doi: 10.7498/aps.64.024701
    [4] 刘云龙, 张阿漫, 王诗平, 田昭丽. 基于边界元法的近平板圆孔气泡动力学行为研究. 物理学报, 2013, 62(14): 144703. doi: 10.7498/aps.62.144703
    [5] 王诗平, 张阿漫, 刘云龙, 吴超. 圆形破口附近气泡动态特性实验研究. 物理学报, 2013, 62(6): 064703. doi: 10.7498/aps.62.064703
    [6] 张阿漫, 肖巍, 王诗平, 程潇欧. 不同沙粒底面下气泡脉动特性实验研究. 物理学报, 2013, 62(1): 014703. doi: 10.7498/aps.62.014703
    [7] 沙莎, 陈志华, 薛大文. 激波冲击R22重气柱所导致的射流与混合研究. 物理学报, 2013, 62(14): 144701. doi: 10.7498/aps.62.144701
    [8] 梁刚涛, 郭亚丽, 沈胜强. 液滴撞击液膜的射流与水花形成机理分析. 物理学报, 2013, 62(2): 024705. doi: 10.7498/aps.62.024705
    [9] 白春江, 李建清, 胡玉禄, 杨中海, 李斌. 利用等效电路模型计算耦合腔行波管注-波互作用. 物理学报, 2012, 61(17): 178401. doi: 10.7498/aps.61.178401
    [10] 马俊建, 朱小芳, 金晓林, 胡玉禄, 李建清, 杨中海, 李斌. 回旋速调管放大器时域非线性理论与模拟. 物理学报, 2012, 61(20): 208402. doi: 10.7498/aps.61.208402
    [11] 郭建华, 喻胜, 李宏福, 张天钟, 雷朝军, 李想, 张颜颜. 回旋速调管注波互作用瞬态非线性理论与模型研究. 物理学报, 2011, 60(9): 090301. doi: 10.7498/aps.60.090301
    [12] 刘静, 舒挺, 李志强. 电子束空间极限电流的非线性理论研究. 物理学报, 2010, 59(4): 2622-2628. doi: 10.7498/aps.59.2622
    [13] 杜朝海, 刘濮鲲, 薛谦忠. 基于损耗介质加载波导的回旋行波管放大器的互作用分析. 物理学报, 2010, 59(7): 4612-4619. doi: 10.7498/aps.59.4612
    [14] 张阿漫, 姚熊亮, 李 佳. 气泡群的动态物理特性研究. 物理学报, 2008, 57(3): 1672-1682. doi: 10.7498/aps.57.1672
    [15] 王 琛, 方智恒, 孙今人, 王 伟, 熊 俊, 叶君建, 傅思祖, 顾 援, 王世绩, 郑无敌, 叶文华, 乔秀梅, 张国平. 利用X射线激光进行激光等离子体射流的诊断. 物理学报, 2008, 57(12): 7770-7775. doi: 10.7498/aps.57.7770
    [16] 张雅鑫, 祝大军, 刘盛纲, 王峨锋. 内开槽螺纹回旋行波管线性理论研究. 物理学报, 2006, 55(9): 4535-4541. doi: 10.7498/aps.55.4535
    [17] 唐昌建, 钱尚介. 离子通道回旋电子注受激辐射非线性理论. 物理学报, 2002, 51(6): 1256-1261. doi: 10.7498/aps.51.1256
    [18] 杨中海, 彭良福, 刘盛纲. 改型wiggler高次谐波自由电子激光的非线性理论分析. 物理学报, 1995, 44(7): 1064-1072. doi: 10.7498/aps.44.1064
    [19] 杨光参. q振子光场模型的光与物质相互作用的非线性理论. 物理学报, 1994, 43(4): 521-529. doi: 10.7498/aps.43.521
    [20] 胡宁海, 刘永盛, 周清廉, 郭东耀. ∑关系线性理论的应用(Ⅱ)——∑7关系的应用问题. 物理学报, 1987, 36(2): 140-148. doi: 10.7498/aps.36.140
计量
  • 文章访问数:  4772
  • PDF下载量:  192
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-03-15
  • 修回日期:  2016-06-06
  • 刊出日期:  2016-08-05

/

返回文章
返回