对粘性平面液膜射流喷射进入可压缩气体环境的线性稳定性进行了理论分析。应用纳维-斯托克斯控制方程组,代入运动学和动力学边界条件,推导得到了线性化和量纲一化的色散关系式。编制Fortran语言数值计算程序,运用穆勒方法求得液膜射流表面波增长率随表面波数变化关系的数值解。分析了气液流速比之差、韦伯数、雷诺数、欧拉数、马赫数等量纲一参数对液膜射流碎裂过程的影响。结果表明,上述量纲一参数均是液膜碎裂的促进因素。
Viscous plane liquid film injected into compressible gas environment was theoretically analyzed by linear stability theory. A linearization and dimensionless dispersion relation was derived by using Navier-Stocks control equations, and kinematic & dynamic boundary conditions. A Fortran language numerical computation program was developed for getting a liquid film surface wave relation between wave growth rate and wave number by Muller method. The effects of some dimensionless parameters, difference between gas/liquid velocity ratios , Weber number We, Reynolds number Re, Euler number Eu, and Mach number Ma, on the liquid film breakup process were analyzed. The results showed that all of above dimensionless parameters were promotion factors for liquid film breakup.
[1] 曹建明. 液体喷雾学[M]. 北京: 北京大学出版社, 2013.
[2] SQUIRE H B.Investigation of the instability of a moving liquid film[J]. British journal of applied physics, 1953, 4(6): 167-169. DOI: 10.1088/0508-3443/4/6/302.
[3] HAGERTY W W.A study of the stability of plane fluid sheets[J]. Journal of applied physics, 1955, 22: 509-514.
[4] LIN S P, LIAN Z W, CREIGHTON B J.Absolute and convective instability of a liquid sheet[J]. Journal of fluid mechanics, 1990, 220: 673-689. DOI: 10.1017/ S0022112090003421.
[5] MANSOUR A, CHIGIER N.Disintegration of liquid sheets[J]. Physics of fluids A: fluid dynamics, 1990, 2(5): 706-719. DOI: 10.1063/1.857724.
[6] HASHIMOTO H, SUZUKI T.Experimental and theoretical study of fine interfacial waves on thin liquid sheet[J]. JSME international journal, 1991, 34(3): 277-283. DOI: 10.1299/jsmeb1988.34.3_277.
[7] LI X G, TANKIN R S.On the temporal instability of a two- dimensional viscous liquid sheet[J]. Journal of fluid mechanics, 1991, 226: 425-443. DOI: 10.1017/S0022112091002458.
[8] LI X G.Spatial instability of plane liquid sheets[J]. Chemical engineering science, 1993, 48(6): 2973-2981. DOI: 10.1016/0009-2509(93)80042-O.
[9] LI X.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.Derivation on the linear stability theory of plane liquid sheets spray in two compressible gas streams[J]. Journal of combustion science and technology, 1999, 5(4): 349-355.
[11] CAO J M, LI X.Liquid sheet breakup in compressible gas streams[C]//Proceedings of the ASME Energy Sources Technology Conference, 1999: 1-6.
[12] CAO J M, LI X G.Stability of plane liquid sheets in compressible gas streams[J]. AIAA journal of propulsion and power, 2000, 16(4): 623-627. DOI: 10.2514/2.5618.
[13] 陈志伟. 静止空气环境中粘性平面液膜的非线性稳定性分析[D]. 西安: 长安大学, 2008: 11.
[14] 张秋霞. 静止空气环境中粘性液膜碎裂的试验研究[D]. 西安: 长安大学, 2008: 11.
[15] 丁宁, 杜青, 郗大光, 等. 加热条件下液膜射流破碎尺度影响因素的研究[J]. 内燃机学报, 2003, 21(1): 53-56. DOI: 10.3321/j.issn:1000-0909.2003.01.011.
[16] 杜青, 丁宁, 郗大光, 等. 射流参数对加热条件下液膜射流破碎不稳定性的影响(1)?射流参数对液膜反对称模式破碎的影响[J]. 内燃机学报, 2003, 21(2): 145-149. DOI: 10.3321/j.issn:1000-0909.2003.02.010.
[17] 杜青, 丁宁, 郗大光, 等. 射流参数对加热条件下液膜射流破碎不稳定性的影响(2)?射流参数对液膜对称模式破碎的影响[J]. 内燃机学报, 2003, 21(2): 150-154. DOI: 10.3321/j.issn:1000-0909.2003.02.011.
[18] MULLER D E.A method for solving algebraic equations using an automatic computer[J]. Mathematical tables and other aids to computation, 1956, 10(56): 208-215. DOI: 10.2307/2001916.
