Lewis Number Effects on Flame Speed Statistics in Spherical Turbulent Premixed Flames

Abstract

AbstractThe 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.