Data-driven modeling of resolved and filtered thermo-diffusively unstable hydrogen–air flames

Hydrogen premixed flames, under technically relevant conditions, are affected by intrinsic instabilities due to hydrodynamic and thermodiffusive effects, which are not taken into account by traditional turbulent combustion models. In this work, a data-driven approach is proposed for lean, premixed, unstable, self-wrinkling, hydrogen flames, based on a tabulated lower-dimensional manifold representation, wherein two scalars are defined based on species mass fractions. The model leverages a fully-resolved, two-dimensional, multi-step chemistry DNS dataset for the development of the tables. Both a flame-resolved and a filtered formulation are presented, and the additional terms that appear in the latter are closed following the filtered tabulated chemistry formalism. Two sets of tables are generated, using as a data source a small-scale and a medium-scale DNS, respectively. The a-priori analysis demonstrated the capability of the model to reproduce the flame structure with limited errors for both formulations. The flame-resolved formulation is validated a-posteriori for both table sets, showing that the flame correctly transitions to a fully-developed, corrugated state, although with a systematic small underestimation of the consumption speed. Given the agreement between the results obtained with the two sets of tables, the filtered a-posteriori analysis is conducted only for the table originating from the small-scale DNS, considering three different filter sizes. A set of one-dimensional flames is first simulated to assess the grid requirements for the non-trivial filtered simulations. Then, both the small-scale and large-scale domains are simulated. For both, it is observed that the characteristic flame structures are fairly reproduced using the small filter size, whereas the medium and large filter sizes produce a significant underestimation of consumption speed, as they fail to generate sufficient flame area through self-wrinkling. Overall, this approach represents a starting point for the development of turbulent combustion models including multi-step chemistry and the intrinsic instabilities effects.