Direct numerical simulations (DNS) of turbulent premixed methane/air flames are carried out to investigate the effects of equivalence ratio on the turbulent flame speed in lean mixtures. Turbulent flames are simulated as statistically stationary following a Lagrangian framework using an inflow–outflow configuration. The inflow velocity is dynamically adjusted at run-time to stabilize the flame brush location within the computational domain. Linear forcing is applied inside the unburned mixtures to maintain the turbulent intensities at desired levels. For the same turbulence properties, several equivalence ratios near the lean limit are selected and it is shown that the normalized turbulent flame speed is a function of the equivalence ratio. Velocity and length scales of the imposed turbulence are then selected in such a way that the Karlovitz and Damköhler numbers remain constant for flames of different equivalence ratios. Simulations are run for more than 80 eddy turnover times and the turbulent flame speed is derived by averaging the inflow velocity. The results show that equivalence ratio does not have an explicit effect on the normalized turbulent flame speed above the lean limit. Analysis of flame surface area shows that surface wrinkling generated by eddies of different scales is not affected by variation in equivalence ratios when the Karlovitz and Damköhler numbers are fixed. Furthermore, flame surface generated by large-scale eddies is independent of the Karlovitz and Damköhler numbers. Examining the flame surface statistics, it is shown that the flame surface normal is preferentially parallel to the most compressive strain rate direction for all equivalence ratios.

对湍流的甲烷/空气预混合火焰进行了直接数值模拟（DNS），以研究当量比对稀薄混合气中湍流火焰速度的影响。在拉格朗日框架下，使用流入-流出配置，将湍流火焰模拟为统计上固定的。在运行时动态调整流入速度，以稳定火焰刷在计算域内的位置。在未燃烧的混合物内部施加线性强迫，以将湍流强度保持在所需水平。对于相同的湍流特性，选择了接近稀薄极限的几个当量比，这表明归一化的湍流火焰速度是当量比的函数。然后，选择湍流的速度和长度尺度，以使Karlovitz和Damköhler数对于不同当量比的火焰保持恒定。模拟进行了80多个涡流转换时间，并且通过平均流入速度得出湍流火焰速度。结果表明，当量比对稀薄极限以上的标准化湍流火焰速度没有明显影响。火焰表面积的分析表明，当卡洛维兹数和达姆霍勒数固定时，由不同尺度的涡流产生的表面皱纹不受当量比变化的影响。此外，由大型涡流产生的火焰表面与Karlovitz和Damköhler数无关。检查火焰表面统计数据，