Marginal stability of thermodiffusively unstable circular expanding flames

The linear stability analysis of premixed stretched flame configurations, such as circular and spherical flames, as well as flames in a stagnation point flow, has been of interest in literature theoretically, experimentally, and numerically, to understand the consequences of the onset of instabilities in their interaction with turbulence and in the performance of combustion devices. Existing linear stability theories have been developed for flames characterized by a Lewis higher than a critical value, which are stable to thermodiffusive effects, and they are able to predict the critical radius at which the flame becomes unstable due to hydrodynamic effects. For mixtures characterized by a Lewis number lower than a critical value, no linear stability theories have been proposed other than for constant densities flows, and no attempts to recreate marginal stability curves numerically for such mixtures can be found in literature. This work presents an investigation into the marginal stability of thermodiffusively unstable circular expanding flames through Direct Numerical Simulations (DNS). The analysis initially employs a one-step deficient reactant model to verify the methodology, which is then extended to detailed chemistry simulations for lean 𝐻2 -air mixtures. Key findings include the identification of critical Peclet numbers and corresponding perturbation wavenumbers for the onset of instability. Marginal stability curves are then constructed, indicating that the stability characteristics depend not solely on the flame’s thermophysical characteristics, but also on its initial stretched configuration.