Abstract We proceed to examine the stability of the adiabatic and non-adiabatic structures of forward smolder waves elaborated in Part (I) of this series. The dispersion relation for adiabatic forward smolder waves with a reaction trailing structure turns out to take a form similar to that for premixed flames, thereby strengthening the analogy of the reaction trailing structure with the premixed flame regime of diffusion flames. According to the dispersion relation, corresponding to each Damkohler number there exists a marginal oxygen Lewis number, below which cellular instability occurs. In particular, similar to the Burke–Schumann limit of diffusion flames, the stoichiometric limit at infinite Damkohler number is unconditionally stable. Such unconditional stability is found to further extend to the entire Damkohler number range for adiabatic forward smolder waves with a reaction leading structure. Linear stability analysis of non-adiabatic forward smolder waves indicates that, for both reaction trailing and reaction leading structures, the low smolder temperature (or high reactant leakage) solution branch is physically unrealistic, whereas on the high smolder temperature (or low reactant leakage) branch different kinds of instabilities may develop near the quenching limit. Under a fixed Damkohler number, the range of the heat loss coefficient corresponding to these instabilities shows a trend to grow with decreasing oxygen Lewis number. 2-D time-dependent numerical simulations of unstable non-adiabatic forward smolder waves confirm that fingering or cellular instability occurs exclusively for the reaction trailing structure, whereas traveling wave instability prevails for the reaction leading structure. A comparison is made between the current stability analysis results of non-adiabatic forward smolder waves and results from a concurrent flame spread experiment. Agreement is achieved not only on the existence of reaction front instabilities near the quenching limit, but also on the conditions determining the type of these instabilities.

中文翻译：

---

前向阴燃波的扩散火焰模拟：（II）稳定性分析

摘要 我们继续研究本系列第 (I) 部分中阐述的正向阴燃波的绝热和非绝热结构的稳定性。具有反应拖尾结构的绝热前向阴燃波的色散关系与预混火焰的形式相似，从而加强了反应拖尾结构与扩散火焰预混火焰状态的类比。根据色散关系，每一个Damkohler数对应存在一个边际氧路易斯数，低于这个数就会发生细胞不稳定。特别是，类似于扩散火焰的伯克-舒曼极限，无穷大丹科勒数下的化学计量极限是无条件稳定的。发现这种无条件稳定性进一步扩展到具有反应引导结构的绝热正向阴燃波的整个 Damkohler 数范围。非绝热正向闷烧波的线性稳定性分析表明，对于反应拖尾和反应引导结构，低闷烧温度（或高反应物泄漏）溶液分支在物理上是不现实的，而在高闷烧温度（或低反应物泄漏）上不同种类的不稳定性可能在淬火极限附近发展。在固定的 Damkohler 数下，与这些不稳定性对应的热损失系数的范围显示出随着氧路易斯数的减少而增加的趋势。不稳定的非绝热正向闷烧波的二维时间相关数值模拟证实，指法或细胞不稳定性仅发生在反应拖尾结构中，而行波不稳定性则主要发生在反应引导结构中。对非绝热正向阴燃波的当前稳定性分析结果与同时进行的火焰蔓延实验的结果进行了比较。不仅在淬火极限附近反应前沿不稳定性的存在上达成一致，而且在决定这些不稳定性类型的条件上达成一致。对非绝热正向阴燃波的当前稳定性分析结果与同时进行的火焰蔓延实验的结果进行了比较。不仅在淬火极限附近反应前沿不稳定性的存在上达成一致，而且在决定这些不稳定性类型的条件上达成一致。对非绝热正向阴燃波的当前稳定性分析结果与同时进行的火焰蔓延实验的结果进行了比较。不仅在淬火极限附近反应前沿不稳定性的存在上达成一致，而且在决定这些不稳定性类型的条件上达成一致。