AN ASYMPTOTIC THEORY OF CONDENSED TWO‐PHASE FLAME PROPAGATION
AN ASYMPTOTIC THEORY OF CONDENSED TWO‐PHASE FLAME PROPAGATION
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凝聚两相火焰传播的渐近理论
DOI：
10.1111/j.1749-6632.1983.tb19465.x
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
S. Margolis
中科院分区：
文献类型：
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作者：
S. Margolis
本文提出了一种通过冷凝可燃混合物的火焰传播模型，在该模型中，混合物的限制组分在反应过程中熔化。一个渐近分析，有效的大活化能，推导出一个稳定的，平面绝热火焰速度的两项扩展。然后使用线性稳定性分析表明，对于足够大的值的活化能和/或一组特殊的熔化参数，稳定的，平面的解决方案失去稳定的各种类型的平面和非平面的脉动模式。熔化的效果被发现是不稳定的意义上，这些脉动模式发生的活化能比严格的固体燃料燃烧的情况下，较低的值。1.导论.凝聚相燃烧中反应前沿的传播发生在各种冶金和烟火应用中。例如，在放热金属合金化过程中，两种金属被研磨成细粉混合物。当点燃时，建立反应前沿，其通过混合物传播，将金属反应物转化为合金产物。虽然这种现象通常被称为固体燃料燃烧，但为了维持燃烧过程，认为至少一种反应物的熔化是必要的（参见图1）。Hardt和Phung（1973））。对此的一个明显的解释是，当两种反应物都是固体时，由于固体颗粒之间的有限量的表面与表面接触，决定局部反应速率的微观物质扩散很小。当一种反应物熔化时，熔化的反应物可以覆盖未熔化的颗粒，从而显著提高局部反应速率。凝聚相燃烧的一个迷人的特点是证实存在的非稳态，非平面传播模式的反应前沿。Merzhanov等人（1973）和Maksimov等人（1979）的实验研究表明，除了通常的定常平面传播模式外，还存在着可观察到“自动振荡”和旋转燃烧锋的参数区域。在前一种情况下，反应前沿以脉动的方式传播，并且燃烧的样品具有层状外观。在后一种情况下，前端具有不均匀的结构，其中观察到一个或多个热点随着前端传播而围绕圆柱形燃料样品的表面旋转。在凝聚单相系统中这些现象的数值预测（即，Shkadinsky等人（1971年）和Ivleva等人（1978年）报道了这种情况。前一篇文章指出，活化能是决定稳定传播和脉动溶液之间的过渡的关键参数。此外，由于出现二次和高阶分叉，脉动模式可以是多周期的。也就是说，一个完整的周期可以由几个脉动组成。马戈利斯（1980）曾预言在气体燃烧中也有类似的现象.最近的几项分析研究（Matkowsky和Sivashinsky（1978），Sivashinsky（1981），Kaper，Leaf和Matkowsky（1982））已经很好地阐明了这些不同传播模式的性质和过渡特征。使用由气体火焰的渐近（大活化能）模型（Sivashinsky（1977），Matkowsky和Sivashinsky（1979））提出的单相模型，
A model is presented for flame propagation though a condensed combustible mixture in which the limiting component of the mixture melts during the reaction process. An asymptotic analysis, valid for large activation energies, is employed to derive a two-term expansion for the steady, planar adiabatic flame speed. A linear stability analysis is then used to show that for sufficiently large values of the activation energy and/or a special group of melting parameters, the steady, planar solution loses stability to various types of planar and nonplanar pulsating modes. The effect of melting is found to be destabilizing in the sense that these pulsating modes occur for lower values of the activation energy than would be the case for strictly solid fuel combustion. 1. Introduction. The propagation of reaction fronts in condensed phase combus- tion occurs in various metallurgical and pyrotechnical applications. In exothermic metal alloying processes, for example, two metals are ground into a fine powdered mixture. When ignited, a reaction front is established which propagates through the mixture, converting the metal reactants into an alloy product. Although this phenomenon is often referred to as solid fuel combustion, melting of at least one of the reactants is thought to be necessary in order to sustain the combustion process (cf. Hardt and Phung (1973)). An obvious explanation for this is that microscopic species diffusion, which determines the local reaction rate, is small when both reactants are solid due to the limited amount of surface-to-surface contact between the solid particles. When one of the reactants melts, the melted reactant can coat the unmelted particles, thereby significantly increasing the local reaction rate. One fascinating feature of condensed phase combustion is the confirmed existence of nonsteady, nonplanar modes of propagation of the reaction front. Experimental studies due to Merzhanov et al. (1973) and Maksimov et al. (1979) show that in addition to the usual steady, planar mode of propagation, there exist parameter regimes for which "auto-oscillatory" and spinning combustion fronts are observed. In the former case, the reaction front propagates in a pulsating fashion and the burned samples have a layered appearance. In the latter situation, the front has a nonuniform structure in which one or more hot spots are observed to rotate about the surface of the cylindrical fuel sample as the front propagates. Numerical predictions of these phenomena in condensed single-phase systems (i.e., no melting) have been reported by Shkadinsky et al. (1971) and Ivleva et al. (1978). The former paper showed that the activation energy is a critical parameter in determining the transition between the steadily propagating and pulsating solutions. In addition, due to what appears to be secondary and higher order bifurcations, the pulsating modes can be multiply periodic. That is, a complete cycle can consist of several pulsations. A similar phenomenon in gaseous combustion was predicted by Margolis (1980). The nature and transition characteristics of these various modes of propagation have been greatly clarified by several recent analytical studies (Matkowsky and Sivashinsky (1978), Sivashinsky (1981), Kaper, Leaf and Matkowsky (1982)). Using a single-phase model suggested by the asymptotic (large activation energy) models derived for gaseous flames (Sivashinsky (1977), Matkowsky and Sivashinsky (1979)),