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Asymptotic analysis of flame propagation in weakly-strained mixing layers under a reversible chemical reaction

机译：可逆化学反应下弱应变混合层中火焰传播的渐近分析

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We present an asymptotic study of triple-flames in a strained mixing layer under a reversible reaction, which extends analytical descriptions of these flames beyond the common framework of a single irreversible Arrhenius reaction and constitutes a first step towards accounting for real chemistry effects. The study is carried out in the two-dimensional counterflow configuration and adopts a constant-density assumption along with a generalization of the near-equidiffusional flame (NEF) approximation to the case of a reversible reaction. This generalization involves a convenient and physically motivated distinguished limit comprising a specific scaling of the difference in the activation energies of the forward and backward reactions and of the degree of reversibility. The resulting model yields an extensive set of results for weakly strained triple-flames characterizing the combined influence of the stoichiometry and reversibility of the reaction, the strain rate, and the Lewis numbers of the reactants. The findings include the determination of the local burning speed, temperature and Markstein length along the flame-front, the shape, leading edge and curvature of the latter, and the propagation speed of the triple-flame. In particular, it is found that the Markstein length is affected by the reversibility parameter and the local coordinate along the flame-front whenever the Lewis numbers of the fuel and oxidizer are unequal and is independent of them otherwise; in all cases, however, its value at the leading-edge, which features in the formula derived for the propagation speed, is found to be unaffected by the reversibility. Several features of triple-flames specifically associated with the reversibility of the reaction are described analytically, including the decrease in the propagation speed and flame-front curvature and the increased shift of the location of the leading edge away from the stoichiometric surface with increased reversibility. Some of these features have no counterparts in the irreversible case. For example, whereas the maximum temperature of the triple-flame front occurs at the stoichiometric location in the irreversible case, irrespective of the location of the leading edge, it is typically found to be sandwiched between these two locations in the reversible case.
机译：我们提出了在可逆反应下应变混合层中三重火焰的渐近研究，该分析将对这些火焰的分析描述扩展到单个不可逆阿伦尼乌斯反应的通用框架之外，并构成了考虑真实化学作用的第一步。该研究是在二维逆流构型中进行的，并采用了恒定密度假设以及对可逆反应情况的近似等扩散火焰（NEF）近似的推广。这种概括涉及便利的和有物理动机的区别极限，该界限包括正向和反向反应的活化能之差和可逆性程度的特定比例。所得模型为弱应变三重火焰产生了广泛的结果集，表征了化学计量和反应的可逆性，应变速率和反应物的Lewis数的综合影响。研究结果包括确定局部燃烧速度，温度和沿火焰前沿的马克斯坦长度，火焰的形状，前沿和曲率，以及三重火焰的传播速度。特别是，发现当燃料和氧化剂的路易斯数不相等时，Markstein的长度受可逆性参数和沿火焰前沿的局部坐标的影响，否则与它们无关。但是，在所有情况下，都发现其在前沿的值不受可逆性影响，该值在为传播速度而导出的公式中具有特征。分析性地描述了与反应的可逆性特别相关的三重火焰的几个特征，包括传播速度的降低和火焰前曲率的降低以及前缘位置远离化学计量表面的位移的增加以及可逆性的增加。在不可逆转的情况下，其中某些功能没有对应的功能。例如，尽管在不可逆的情况下三火焰锋的最高温度发生在化学计量位置，而不管前缘的位置如何，但通常发现在可逆的情况下它夹在这两个位置之间。

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