Abstract Neglecting the effect of thermal diffusion (Soret effect), we consider different formulations of multicomponent diffusion as proposed by Arias-Zugasti et al. (2016), for mixtures of dilute gases with large numbers of components. In particular, we detail the practical implementation of Model 1 + M (loc.cit.) using the lowest order approximation. This is a simple and easy to implement approach, where the 1 + M main species can be chosen locally (see the example provided as supplementary material). These new formulations of multicomponent diffusion are compared to the formulation of Dixon-Lewis, used for instance in the Chemkin package, and also to the widely used mixture-averaged simplification. Steady flamelets are first considered for very different fuels (hydrogen, methane or dodecane) in order to show some differences and limitations of the different formulations, and in order to compare computational costs when different numbers of species are involved. An unsteady auto-igniting counterflow diffusion flamelet of methane in a coflow of hot products is also considered. In this way, unsteady 1D calculations can be performed, still including all the challenges of multicomponent diffusion transport as would appear for instance in Direct Numerical Simulations (DNS) of turbulent flames. The different comparisons in terms of precision and cost show that Model 1 + M truncated to the lowest order can be more efficient than the mixture-averaged approach, while reproducing the results of Dixon-Lewis multicomponent diffusion. The efficiency of the proposed approach is mainly due to the evaluation of fewer binary diffusion coefficients, therefore reducing significantly the number of time-consuming operations. Finally, we show that the definition of 1 + M main species can also be used to simplify the time-consuming evaluation of the mixture viscosity, leading to an important further reduction of CPU time that makes the lowest order Model 1 + M always more efficient than the mixture-averaged formulation.

中文翻译：

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以比混合物平均近似值更低的成本获得准确的多组分 Fick 扩散：在稳定和非稳定逆流小火焰中的验证

摘要 忽略热扩散的影响（Soret 效应），我们考虑了 Arias-Zugasti 等人提出的多组分扩散的不同公式。(2016)，用于具有大量组分的稀释气体的混合物。特别是，我们详细介绍了使用最低阶近似值的 Model 1 + M (loc.cit.) 的实际实现。这是一种简单且易于实施的方法，可以在本地选择 1 + M 种主要物种（参见作为补充材料提供的示例）。这些多组分扩散的新公式与 Dixon-Lewis 公式进行了比较，例如在 Chemkin 包中使用的公式，以及广泛使用的混合平均简化。稳定小火焰首先被考虑用于非常不同的燃料（氢、甲烷或十二烷）以显示不同配方的一些差异和局限性，并在涉及不同数量的物种时比较计算成本。还考虑了热产品合流中甲烷的不稳定自燃逆流扩散火焰。通过这种方式，可以执行非定常一维计算，仍然包括多组分扩散传输的所有挑战，例如在湍流火焰的直接数值模拟 (DNS) 中出现的挑战。精度和成本方面的不同比较表明，模型 1 + M 截断到最低阶可以比混合平均方法更有效，同时再现 Dixon-Lewis 多分量扩散的结果。所提出方法的效率主要是由于对较少的二元扩散系数的评估，因此显着减少了耗时操作的数量。最后，我们表明 1 + M 主要物种的定义也可用于简化混合物粘度的耗时评估，从而进一步减少 CPU 时间，使最低阶模型 1 + M 始终更高效比混合平均公式。