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.