This article is dedicated to Moshe Matalon on the occasion of his 70th birthday, for his numerous contributions to the field of combustion and, in particular, to the rich and varied topic of premixed flame stability. Here, we follow in his footsteps and propose a subfilter modelling framework for thermo-diffusively unstable premixed flames, such as lean hydrogen–air flames. Performing an optimal estimator analysis for the unfiltered and filtered heat release rate of the lean premixed hydrogen–air flames, the latter is found to require at least two scalars for an appropriate representation while for large filter sizes, the heat release appears to require only one scalar for parametrisation. As a result, we develop a modelling strategy based on the construction of thermochemical tables for each unclosed term as a function of two variables as well as the filter size. The framework is based on the filtered tabulated chemistry approach, where, in lieu of a one-dimensional unstretched flame, we adopt a data-driven paradigm and filter fully resolved two-dimensional simulations of variable size. Models originating from small- and medium-sized simulations are tested a-priori on a large-size simulation, thus highlighting the role of the lateral domain in the dataset used for tabulation. The concept of a minimum domain size is thus discussed, leading to a dataset exhibiting the minimal properties for sufficiently accurate thermochemical tables. The strategy is shown to be more accurate than a classical one-dimensional filtered tabulated chemistry approach and shows promise in future LES modelling of laboratory and industrial scale hydrogen flames.

这篇文章是在 Moshe Matalon 70 岁生日之际献给他的，因为他在燃烧领域做出了许多贡献，尤其是对预混火焰稳定性这个丰富多样的话题。在这里，我们跟随他的脚步，为热扩散不稳定的预混火焰（例如贫氢-空气火焰）提出了一个子过滤器建模框架。对贫预混氢-空气火焰的未过滤和过滤热释放率进行最佳估计分析，发现后者至少需要两个标量才能适当表示，而对于大尺寸过滤器，热释放似乎只需要一个用于参数化的标量。其结果，我们开发了一种建模策略，基于为每个未封闭项构建的热化学表作为两个变量和过滤器尺寸的函数。该框架基于过滤的列表化学方法，其中，代替一维未拉伸火焰，我们采用数据驱动范式并过滤完全解析的可变尺寸二维模拟。源自中小型模拟的模型在大型模拟上进行了先验测试，从而突出了横向域在用于制表的数据集中的作用。因此讨论了最小域大小的概念，导致数据集表现出足够准确的热化学表的最小属性。