The effect of pressure on the hydrodynamic stability limit of premixed flames

The effect of pressure on the hydrodynamic stability limits of lean methane-air premixed flames was studied by direct numerical simulation using both a detailed multi-step chemistry model and a simplified one-step formulation. The dependency on pressure p of the cut-off length scale λc, that separates stable from unstable wavelengths of the initial perturbation, was computed for different conditions. The cut-off length scale λc significantly decreased with increasing pressure. However, this decrease cannot be ascribed only to the decreased flame thickness due to elevated pressures, but the cut-off was reduced significantly even if normalized by either the thermal flame thickness ℓT or the diffusive flame thickness ℓD. For the conditions analyzed, the cut-off can be well approximated by the power-law λc ∞ p-0.8, while the thermal and diffusive flame thicknesses are proportional and scale as ℓT ∞ ℓD ∞ p-0.3. Therefore, the non-dimensional cut-off scales as λc/ℓT ∞ λc/ℓD ∞ p-0.5. This behavior was linked to the increase of the Zeldovich number with pressure, caused by higher inner layer temperatures at higher pressures, which was a result of increased importance of chain termination reactions. The same behavior was observed also in a one-step chemistry approach if the Zeldovich number, appearing explicitly in the one-step model equations, was varied with pressure according to the results from multi-step chemistry. The analysis was extended to the non-linear phase of the instability, when typical strong cusps were observed on the flame surface, simulating a two-dimensional slot burner for different pressures. The same pressure effects were observed also in more complex settings and in the non-linear regime.