Small pre-detonators have potential applications in practical pulse detonation engines or rotating detonation engines. The effects of detonation stability parameter and area divergence on flame propagation in capillary tubes are experimentally analyzed using high-speed cinematography. The four mixtures (namely, stoichiometric methane/oxygen, ethylene/oxygen, propane/oxygen and stoichiometric acetylene/oxygen/50% Ar mixtures) used have different values of stability parameter. The inner diameters of the tubes (namely, 0.5, 1.0, 2.0, and 4.0 mm) investigated provide a variation in area divergence at initial pressures $p_0$ ranging from 5 to 100 kPa. The results show that stability parameter and area divergence play positive and inhibitory roles, respectively, in the process of flame propagation. Five propagation modes are observed (namely, steady detonation, stuttering detonation, galloping detonation, deflagration, and no flame), among which the stuttering detonations have three different forms, depending on the product of stability parameter and area divergence. For the most-unstable mixture (stoichiometric methane/oxygen, with the largest values of stability parameter), the range of the product of stability parameter and area divergence in which steady detonation can occur is the narrowest. The results also indicate that the stoichiometric ethylene/oxygen and stoichiometric propane/oxygen, with similar values of the product of stability parameter and area divergence, have the same propagation modes. Further analysis suggests that the Chapman–Jouguet deflagration-to-detonation transition (DDT) distance L decreases with increasing of stability parameter and area divergence for all four mixtures. Compared with the other three mixtures, stoichiometric methane/oxygen, which has the smallest values of L because it is the most unstable mixture with the greatest propensity for hotspot formation, is most likely to undergo DDT under the same initial and boundary conditions. These conclusions agree well with the various characteristics of L obtained for larger tubes.

小型预雷管在实际脉冲爆震发动机或旋转爆震发动机中具有潜在应用。使用高速摄影实验分析了爆轰稳定性参数和面积散度对毛细管中火焰传播的影响。使用的四种混合物（即化学计量甲烷/氧气、乙烯/氧气、丙烷/氧气和化学计量乙炔/氧气/50% Ar 混合物）具有不同的稳定性参数值。所研究的管的内径（即 0.5、1.0、2.0 和 4.0 毫米）提供了初始压力下面积发散的变化$p_0$范围从 5 到 100 kPa。结果表明，稳定性参数和面积散度在火焰传播过程中分别起到正向和抑制作用。观察到五种传播模式（即稳态爆轰、断续爆轰、疾驰爆轰、爆燃和无火焰），其中断续爆轰具有三种不同的形式，具体取决于稳定性参数和面积散度的乘积。对于最不稳定的混合物（化学计量的甲烷/氧气，具有最大的稳定参数值），稳定参数与面积散度的乘积可发生稳定爆轰的范围最窄。结果还表明，化学计量的乙烯/氧气和化学计量的丙烷/氧气，稳定参数与面积散度的乘积具有相似的值，具有相同的传播模式。进一步分析表明，Chapman–Jouguet 爆燃到爆轰转变 (DDT) 距离对于所有四种混合物， L随着稳定性参数和面积散度的增加而减小。与其他三种混合物相比，化学计量的甲烷/氧气具有最小的L值，因为它是最不稳定的混合物，具有最大的热点形成倾向，最有可能在相同的初始和边界条件下进行 DDT。这些结论与大管获得的L的各种特性非常吻合。