The late-time dynamics of premixed flames driven by the Rayleigh–Taylor (RT) instability reveal a self-similar state in which the flame accelerates and widens at constant rates. This behavior is of particular interest for understanding the deflagration phase of Type Ia supernovae and its possible transition to detonation. In this work, RT-unstable flames are analyzed within the Boussinesq approximation to establish a theoretical link between their self-similar evolution and the large-scale dynamics of the flow. This analysis provides bounds and estimates for the admissible values of the self-similar constants and suggests that the flow progressively loses memory of its initial conditions. It further indicates that the properties of this self-similar evolution are not strongly influenced by the details of the reaction model within the assumptions considered. The results also clarify how turbulent flame-speed relations emerge in RT-unstable configurations and provide guidance for calibrating the turbulent flame-speed models used in simulations of Type Ia supernovae. Direct numerical simulations and large-eddy simulations are performed to assess these predictions.Novelty and significance statementThis study introduces a theoretical framework to investigate the self-similar properties of Rayleigh–Taylor unstable premixed flames in the Boussinesq limit. By extending concepts from classical turbulence theory, we show that the admissible acceleration and widening rates of RT-unstable flames are primarily governed by the large-scale properties of the flow rather than by small-scale combustion processes. Large-domain calculations offer detailed characterization of turbulent RT flames and support this interpretation. Together, the analysis and simulations clarify how flame propagation develops in RT-unstable configurations. They also establish a physical basis for interpreting turbulent flame-speed formulations used in simulations of Type Ia supernova explosions.
Experiments with confined spherical laminar flames expanding in lean (the equivalence ratio ϕ = 0.45) H2/O2/N2/He mixtures under room conditions are performed using high-speed Schlieren technique. Measured dependencies of (i) flame radius on time and (ii) flame speed on flame stretch rate are analyzed using four state-of-the-art methods. The following results are worth emphasizing. First, at large ratios of mole fractions XHe and XN2 of He and N2, respectively, e.g., XHe/XN2=1.81, no visible cellularity was observed within the investigated flame radius range. Second, experimental data obtained at XHe/XN2=0.51 or 0.45 indicate that both (i) cells on flame surface and (ii) an increase in the flame speed due to flame instability appear at sufficiently large flame radii, more than 7 ms after the end of the spark discharge. This experimental finding is consistent with the standpoint that high stretch rates can suppress diffusional-thermal and Darrieus-Landau instabilities. Third, the performed measurements demonstrate that changing He:N2 ratio in lean H2/O2/N2/He mixtures offers the opportunity to explore onset of cellular instability by separating it from ignition stage. Fourth, the experiments also show that although the truncation of the data obtained at large flame radii offers the opportunity to explore apparently stable flames in the case of a negative Markstein number Mab, such a method results in fitting-dependent and scattered values of laminar flame speeds and, especially, Mab.
