对于射流的动力学边界条件,学术界一直没有全面、系统地论述过。线性和非线性动力学边界条件之间存在相互对应的关联关系,即线性动力学边界条件应该通过对非线性动力学边界条件的线性化得到,而现有文献中并未明确。本文从动力学边界条件的普适性原始表达式入手,对平面液膜、圆射流和环状液膜气液交界面三维扰动瑞利和瑞利-泰勒表面波的线性动力学边界条件和一维扰动多级瑞利表面波的非线性动力学边界条件进行详细的推导。
Dynamic boundary conditions of the liquid jets are not comprehensive and systematic studied by researchers. It is correlated between linear and nonlinear dynamic boundary conditions. Linear dynamic boundary conditions can be obtained by linearizing nonlinear dynamic boundary conditions, which is not cleared in the references. Started with the general and universal initial expression of the dynamic boundary condition, the linear dynamic boundary conditions of three dimensional R and R-T surface waves between liquid and gas interfaces and nonlinear dynamic boundary conditions of multi-order, one dimensional R surface waves for plane liquid film, liquid jet, and annular liquid film, were derived in detail.
[1] 曹建明. 液体喷雾学[M]. 北京: 北京大学出版社, 2013.
[2] 曹建明. 射流表面波理论的研究进展[J]. 新能源进展, 2014, 2(3): 165-172. DOI: 10.3969/j.issn.2095-560X.2014. 03.001.
[3] 林建忠, 阮晓东, 陈邦国, 等. 流体力学[M]. 北京: 清华大学出版社, 2005.
[4] 周光坰, 严宗毅, 许世雄, 等. 流体力学[M]. 2版. 北京: 高等教育出版社, 2000.
[5] FRANK M W.Fluid mechanics[M]. 5th ed. New York: McGraw-Hill Press, 2004.
[6] JEAN P.F., GREGORY L. N. TSOU S. T. Classical Mechanics; Fluid Dynamics[M]. 北京: 科学出版社, 2008.
[7] LEFEBVRE A H.Atomization and sprays[M]. New York: Hemisphere Pub. Corp., 1989.
[8] LI X G.Spatial instability of plane liquid sheets[J]. Chemical engineering science, 1993, 48(16): 2973-2981. DOI: 10.1016/0009-2509(93)80042-O.
[9] LI X G.On the instability of plane liquid sheets in two gas streams of unequal velocities[J]. Acta mechanica, 1994, 106(3/4): 137-156. DOI: 10.1007/BF01213559.
[10] CAO J M, LI X G.Stability of plane liquid sheets in compressible gas streams[J]. Journal of propulsion and power, 2000, 16(4): 623-627. DOI: 10.2514/2.5618.
[11] 曹建明, 熊玮, 李雯霖, 等. 粘性平面液膜喷入可压缩气流中的线性稳定性分析[J]. 新能源进展, 2018, 6(6): 490-497. DOI: 10.3969/j.issn.2095-560X.2018.06.005.
[12] LI X G.Mechanism of atomization of a liquid jet[J]. Atomization and sprays, 1995, 5(1): 89-105. DOI: 10.1615/AtomizSpr.v5.i1.50.
[13] LI X G, CHEN T B.Liquid jet atomization in a compressible gas stream[J]. Journal of propulsion and power, 1999, 15(3): 369-376. DOI: 10.2514/2.5445.
[14] SHI S X, XI D G, QIN J R, et al.Unstable asymmetric modes of a liquid jet[J]. Journal of fluids engineering, 1999, 121(2): 379-383. DOI: 10.1115/1.2822217.
[15] 侯婕, 曹建明, 李跟宝, 等. 圆射流零阶色散关系式的线性稳定性理论推导[J]. 长安大学学报(自然科学版), 2011, 31(4): 94-97. DOI: 10.19721/j.cnki.1671-8879.2011. 04.018.
[16] 曹建明, 侯婕. 孔式喷嘴油束碎裂的线性稳定性理论研究[J]. 动力学与控制学报, 2018, 16(4): 356-360. DOI: 10.6052/1672-6553-2017-086.
[17] SHEN J H, LI X G.Breakup of annular viscous liquid jets in two gas streams[J]. Journal of propulsion and power, 1996, 12(4): 752-759. DOI: 10.2514/3.24098.
[18] CAO J M.Theoretical and experimental study of atomization from an annular liquid sheet[J]. Proceedings of the institution of mechanical engineers, part D: journal of automobile engineering, 2003, 217(8): 735-743. DOI: 10.1243/09544070360692122.
[19] JAZAYERI S A, LI X G.Nonlinear instability of plane liquid sheets[J]. Journal of fluid mechanics, 2000, 406: 281-308. DOI: 10.1017/S0022112099007491.
[20] NAYFEH A H.Nonlinear stability of a liquid jet[J]. The physics of fluids, 1970, 13(4): 841-847. DOI: 10.1063/ 1.1693025.