Estimating hydrogen/air flame acceleration induced by 3D flame instabilities from 2D simulations

The estimation of flame acceleration induced by thermo-diffusive and hydrodynamic instabilities is a key step toward developing accurate models for lean hydrogen combustion. One way to estimate this acceleration is to perform Direct Numerical Simulations (DNS) of laminar unstable flames. However, previous studies have shown that the 3D nature of instabilities significantly enhances the flame propagation speed compared to the 2D predictions. Systematically performing 3D simulations of laminar unstable flames remains out of reach due to prohibitive computational costs. In this work, a series of 2D and 3D DNS under various conditions are performed to establish a link between 2D and 3D flame wrinkling and stretch factors. Linear correlations are proposed that accurately estimate the 3D quantities from their 2D counterparts, leading in particular to an improved prediction of the 3D flame consumption speed. The robustness of these correlations is assessed using simulations performed with another chemical mechanism, and using published data obtained with another CFD solver. The prediction of the wrinkling factor is found to be highly robust, while the stretch factor exhibits slightly larger deviations. Overall, the resulting 3D flame consumption speed predictions are very satisfactory. These findings pave the way for improved subgrid-scale models of flame instabilities in RANS and LES frameworks.