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

Abstract

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.