预混合火焰传播特征值的一种简单计算方法

H. Iizuka, K. Kuwana, S. Yazaki
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引用次数: 0

摘要

路易斯数是热扩散系数与分子扩散系数之比,它对预混火焰传播的影响一直是燃烧研究的热点。扩散热模型忽略了燃烧引起的温度升高引起的密度变化,已被广泛用于研究路易斯数的影响。扩散热模型的主要优点是它允许在给定的流场下进行计算,并且可以研究路易斯数的唯一影响。扩散热模型包含一个无因次参数,后记为(cid:1993),它对应于反应速率常数的指前因子。它的值必须确定,这样才能得到正确的燃烧速度。尽管许多研究使用最低阶渐近表达式来评估(cid:1993)的值,但根据条件的不同,该表达式会导致多达数十个百分点的误差。在本研究中,(cid:1993)的值是通过在一维运动坐标系中求行波解来数值确定的。该方法非常简单,可以在Microsoft Excel中使用其解算器插件实现。发现(cid:1993)的两项渐近展开式在某些情况下误差大于10%。因此,建议在每个感兴趣的条件下对(cid:1993)的值进行数值计算。作为一种替代方法,本文提出了一个经验公式,该公式在本研究中测试的大多数情况下误差小于1%(所有情况下误差小于2%),得出(cid:1993)的值。
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A simple method to evaluate the eigenvalue of premixed flame propagation
The Lewis number is the ratio of thermal diffusivity to molecular diffusion coefficient, and its influence on premixed-flame propagation has been a topic of extensive combustion research. Diffusive-thermal model, which neglects density variation caused by temperature increase due to combustion, has been frequently used to examine the effect of the Lewis number. Major advantages of the diffusive-thermal model are that it allows computation with a given flow field and that the sole effect of the Lewis number can be investigated. The diffusive-thermal model includes a dimensionless parameter, hereafter denoted by (cid:1993) , which corresponds to the pre-exponential factor of reaction rate constant. Its value must be determined such that the correct burning velocity can be reproduced. Although a number of studies use the lowest-order asymptotic expression for evaluating the value of (cid:1993) , the expression causes errors as much as several tens of percent depending on the condition. In this study, the value of (cid:1993) is numerically determined by seeking a traveling wave solution in a one-dimensional moving coordinate system. The method is simple enough to be implemented in Microsoft Excel using its solver add-in. It was found that even two-term asymptotic expansion of (cid:1993) resulted in errors more than 10% in some cases. It is therefore recommended to numerically evaluate the value of (cid:1993) under every condition of interest. As an alternative means, this paper proposes an empirical formula that yields the value of (cid:1993) with errors less than 1% in most cases (less than 2% in all the cases) tested in this study.
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