The influences of characteristic Lewis number $$ \hbox{Le} $$ Le on the statistics of density-weighted displacement speed and consumption speed in spherically expanding turbulent premixed flames have been analysed using three-dimensional direct numerical simulations data for $$ \hbox{Le} = 0.8 $$ Le = 0.8 , 1.0 and 1.2 under statistically similar flow conditions. It has been found that the extents of flame wrinkling and burning increase with decreasing $$ \hbox{Le} $$ Le , which is reflected in increasing trends of mean and most probable values of both density-weighted displacement and consumption speed. Moreover, in all cases the marginal probability density functions of density-weighted displacement speed show finite probabilities of obtaining negative values, whereas consumption speed remains deterministically positive. The strain rate and curvature dependences of scalar gradient and temperature have been found to be strongly dependent on $$ \hbox{Le} $$ Le , and these statistics, along with the interrelation between strain rate and curvature, influence the local strain rate and curvature responses of consumption speed and both reaction and normal diffusion components of density-weighted displacement speed. Density-weighted displacement speed and curvature have been found to be negatively correlated, whereas positive correlations are obtained between density-weighted displacement speed and tangential strain rate for all flames considered here. The positive correlation between temperature and curvature arising from differential diffusion of heat and mass in the $$ \hbox{Le} = 0.8 $$ Le = 0.8 case induces a positive correlation between consumption speed and curvature, whereas these correlations are negative in the $$ \hbox{Le} = 1.2 $$ Le = 1.2 flame. The statistical behaviour of density-weighted displacement speed has been utilised to demonstrate that Damköhler’s first hypothesis does not strictly hold for spherically expanding turbulent premixed flames.

中文翻译：

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刘易斯数对球形湍流预混火焰中火焰速度统计的影响

用$$\hbox的三维直接数值模拟数据分析了特征Lewis数$$\hbox{Le}$$Le对球形膨胀湍流预混火焰密度加权位移速度和消耗速度统计的影响{Le} = 0.8 $$ Le = 0.8、1.0 和 1.2 在统计上相似的流动条件下。已经发现，随着$$ \hbox{Le} $$ Le 的减小，火焰起皱和燃烧的程度增加，这反映在密度加权位移和消耗速度的均值和最可能值的增加趋势上。此外，在所有情况下，密度加权位移速度的边际概率密度函数显示获得负值的有限概率，而消耗速度仍然确定性为正。已发现标量梯度和温度的应变率和曲率依赖性强烈依赖于 $$ \hbox{Le} $$ Le ，这些统计数据以及应变率和曲率之间的相互关系影响局部应变率和消耗速度的曲率响应以及密度加权位移速度的反应和法向扩散分量。已发现密度加权位移速度和曲率呈负相关，而此处考虑的所有火焰的密度加权位移速度和切向应变率之间获得正相关。$$ \hbox{Le} = 0.8 $$ Le = 0 中由热量和质量的微分扩散引起的温度和曲率之间的正相关。8 case 导致消费速度和曲率之间存在正相关，而这些相关性在 $$ \hbox{Le} = 1.2 $$ Le = 1.2 火焰中为负。密度加权位移速度的统计行为已被用来证明 Damköhler 的第一个假设并不严格适用于球形膨胀的湍流预混火焰。