Data-driven subfilter modelling of thermo-diffusively unstable hydrogen–air premixed flames

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.