Numerical study of unstable hydrogen/air flames: Shape and propagation speed

Extensive numerical simulations with detailed chemistry and transport are performed to identify the range of dominance (in terms of equivalence ratio and domain size) of the hydrodynamic instability, the shape of the structures that evolve at long times, and their propagation speed. The calculations were performed in two-dimensional domains of lateral extent 3-100 flame thicknesses. Hydrogen/air mixtures ranging from rich (φ=2) to lean conditions (φ=0.5) were considered, expecting that thermo-diffusive effects will start becoming important only at the lean end. The initial growth of a perturbed planar flame front is found to agree qualitatively, and to a large extent even quantitatively, with the asymptotic theoretical predictions. Beyond linearity it is shown that the dynamics depend strongly on the equivalence ratio (or on the effective Lewis number of the mixture) and the domain lateral size. For stoichiometric and rich mixtures, the flame shape is generally characterized by a single-cusp structure that propagates at a constant speed. The propagation speed increases with increasing lateral domain size and asymptotes to a value nearly 24% larger than the laminar flame speed. For the lean mixtures, the flame does not assume a well-defined structure even after a long time. It is regularly contaminated by small cells that result from thermo-diffusive effects and cause a significant increase in the propagation speed (nearly 60% above the laminar flame speed) that varies continuously in time. Except for the lean cases, the simulation results compare well with the asymptotic hydrodynamic theory both in the flame shape and propagation speed.