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 is investigated with Direct Numerical Simulation based on multi-step chemistry and using a simplified one-step chemistry formulation. The dependency on pressure p of the cut-off length scale λc , that separates stable from unstable wavelengths of the initial perturbation, is computed for a number of different conditions. An increase of pressure causes a significant decrease of the cut-off length, as observed already in previous simulations and experiments. However, this decrease cannot be ascribed only to the decreased flame thickness due to elevated pressures, but the cut-off is 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, in accordance with previous experiments, 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 is linked to the increase of the Zeldovich number with pressure, caused by higher inner layer temperatures at higher pressures, which is a result of increased importance of chain termination reactions. The same behavior is observed also in a one-step chemistry approach if the Zeldovich number, appearing explicitly in the one-step model equations, is varied with pressure according to the results from multi-step chemistry. The analysis is extended to the non-linear phase of the instability, when typical strong cusps are observed on the flame surface, simulating a two-dimensional slot burner for different pressures; it is confirmed that the same pressure effects are observed also in more complex settings and in the non-linear regime