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 λ_c, 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 ℓ_T or the diffusive flame thickness ℓ_D. For the conditions analyzed, the cut-off can be well approximated by the power-law ${\lambda }_c\propto p^{-0.8},$ while the thermal and diffusive flame thicknesses, in accordance with previous experiments, are proportional and scale as ${\ell }_T\propto {\ell }_D\propto p^{-0.3}$. Therefore, the non-dimensional cut-off scales as ${\lambda }_c/{\ell }_T\propto {\lambda }_c/{\ell }_D\propto p^{-0.5}$. 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.

通过基于多步化学的直接数值模拟和简化的一步化学公式，研究了压力对贫甲烷-空气预混火焰的水动力稳定性极限的影响。上压依赖性p截止长度尺度的λ _Ç，从初始扰动的不稳定波长中隔离稳定，被计算为许多不同的条件。如先前的模拟和实验中所观察到的，压力的增加导致截止长度的显着减小。然而，这减少不能归因仅向火焰厚度由于升高的压力下降，但即使通过归一化或者热火焰厚度ℓ截止被显著降低_Ť或扩散火焰厚度ℓ _d。对于所分析的条件，可以通过幂律很好地近似截止值${\lambda }_C\propto p^{-0.8}，$ 而根据先前的实验，火焰的热扩散厚度与扩散火焰的厚度成比例，且比例为 ${\ell }_{Ť}\propto {\ell }_d\propto p^{-0.3}$。因此，无量纲截止尺度为${\lambda }_C/{\ell }_{Ť}\propto {\lambda }_C/{\ell }_d\propto p^{-0.5}$。这种行为与Zeldovich数随压力的增加有关，这是由于在较高压力下较高的内层温度引起的，这是链终止反应重要性增加的结果。如果在一步模型方程式中明确出现的Zeldovich数根据多步化学的结果随压力而变化，则在一步化学方法中也观察到相同的行为。当在火焰表面观察到典型的强尖点时，将分析扩展到不稳定性的非线性阶段，模拟不同压力下的二维狭缝燃烧器。可以肯定的是，在更复杂的环境和非线性条件下也观察到相同的压力效应。