通过数值方法研究了窄通道中近可燃极限预混火焰的结构和稳定性. 窄通道由上、下两个圆形平行平板构成, 燃气和氧气组成的混合气体充满窄通道内部, 点燃后形成的预混火焰在一定条件下有可能稳定在窄通道内. 采用基于Arrhenius单步反应的反应-扩散火焰模型, 考察了平板间距、平板材料和平板半径对火焰的影响. 结果表明, 一定的平板间距下主要有两个火焰的稳态解: 一个对应较大的火焰半径, 另一个对应较小的火焰半径. 通过线性稳定性分析发现, 窄通道中存在一维稳定的火焰, 但不存在二维稳定的火焰. 对一维稳定但二维不稳定的火焰的失稳进行数值模拟可以发现, 失稳主要表现为火焰整体向边界漂移, 或者一个火焰分裂成两个新的火焰后分别沿相反方向向边界漂移.
Structure and dynamics of near-limit premixed flames in narrow channels are numerically studied. The channel consists of two circular parallel plates, one of which is upward and another is downward. It is possible that the premixed flame is stable when the mixture of fuel gas and oxygen in the channel is ignited. A reaction-diffusion model is used based on the Arrhenius-type chemistry, and attention is focused on the influence of distance between two plates as well as the plate’s material and radius. There are mainly two steady solutions for a given distance between the plates, a small flame and a large flame. Linear stability analysis shows that 1D stable flames may exist in the narrow channel, but 2D stable flames do not exist. The dynamical evolution processes of 1D stable, but 2D unstable flames are studied by direct numerical simulations. It is shown that the flame drifts to the boundary as a whole or an old one splits into two new flames that drift to the boundary along the opposite direction.
[1] Fernandez-Pello A C. Micropower generation using combustion: issues and approaches [J]. Proceedings of the Combustion Institute, 2002, 29(1): 883-899.
[2] Maruta K. Micro and mesoscale combustion [J]. Proceedings of the Combustion Institute, 2011, 33(1): 125-150.
[3] Ju Y, Maruta K. Microscale combustion: technology development and fundamental research [J]. Progress in Energy and Combustion Science, 2011, 37(6): 669-715.
[4] Zeldovich Y B, Barenblatt G I, Librovich V B, et al. The mathematical theory of combustion and explosions [M]. New York: Consultants Bureau, 1985: 327.
[5] Ronney P D. Near-limit flame structures at low Lewis number [J]. Combustion and Flame, 1990, 82(1): 1-14.
[6] Buckmaster J, Joulin G, Ronney P. The structure and stability of nonadiabatic flame balls [J]. Combustion and Flame, 1990, 79(3/4): 381-392.
[7] Buckmaster J D, Joulin G, Ronney P D. The structure and stability of nonadiabatic flame balls: Ⅱ. Effects of far-field losses [J]. Combustion and Flame, 1991, 84(3/4): 411-422.
[8] Buckmaster J, Smooke M, Giovangigli V. Analytical and numerical modeling of flame-balls in hydrogen-air mixtures [J]. Combustion and Flame, 1993, 94(1/2): 113-124.
[9] Ronney P D, Wu M S, Pearlman H G, et al. Structure of flame balls at low Lewis-number (SOFBALL): preliminary results from the STS-83 space flight experiments [J]. AIAA J, 1998,
36: 1361-1368.
[10] Lu Z, Buckmaster J. Interactions of flame balls [J]. Combustion Theory and Modelling, 2008, 12(4): 699-715.
[11] Shah A A, Thatcher R W, Dold J W. Stability of a spherical flame ball in a porous medium [J]. Combustion Theory and Modelling, 2000, 4(4): 511-534.
[12] Spalding D. A theory of inflammability limits and flame-quenching [J]. Proceedings of the Royal Society of London: Series A—Mathematical and Physical Sciences, 1957, 240(1220): 83-100.
[13] Rheinboldt W C, Burkardt J V. A locally parameterized continuation process [J]. ACM Transactions on Mathematical Software, 1983, 9(2): 215-235.
