Effects of Lewis and Karlovitz numbers on transport equations for turbulent kinetic energy and enstrophy

A three-dimensional Direct numerical simulation (DNS) with complex chemistry was employed to examine the statistical behavior of turbulent kinetic energy (TKE) and enstrophy transport equations in hydrogen (Lewis number ( Le ) ≈ 0.4) and dodecane ( Le ≈ 4.2) flames. The Karlovitz ( Ka ) numbers ranged from 4 to 150, involving both the thin and broken reaction zones. Budget analyses of TKE and enstrophy transport equations are performed, and scaling terms in the literature are re-examined. Similar to thin reaction zone flames, viscous dissipation term appears to be the most important term in the TKE balance, while viscous dissipation and vortex-stretching terms are the dominant terms in the enstrophy transport equation at high Ka number. The velocity-pressure gradient and the mean velocity dilatation in the TKE transport equation and the dilatation term in enstrophy budget are found to be affected by the Le . Modified scaling estimations for those terms affected by Le are proposed in this work to account for the Le effects spanning different combustion regimes. This work confirmed that Kolmogorov’s first hypothesis is not valid for low Ka number flames investigated in this study, where the vortex stretching and viscous dissipation terms cannot be scaled with local dissipation and viscosity. At sufficiently high Ka number flames, the vorticity can be scaled with the Kolmogorov time scale, and the mean enstrophy value approaches homogeneous, isotropic, non-reacting turbulence flow, but lower Le fuels require much higher Ka number to achieve that.