Budgets of flame-conditioned second-order turbulence statistics in low and high Karlovitz number turbulent premixed jet flames

Small-scale heat release in low Karlovitz number turbulent premixed combustion significantly affects large-scale turbulence dynamics through nonlinear interactions occurring within the flame structure. These interactions result in flame-local changes to the alignment of the Reynolds stress and scalar fluxes with the mean gradients that lead to failure of commonly-used Boussinesq and gradient diffusion-type turbulence models. In this work, flame-conditioned second-order turbulence statistics, that is, velocity correlations and cross-correlations conditioned on a reaction progress variable, are computed following the concept of Conditional Moment Closure (CMC). By conditioning on a local flame coordinate, this statistical basis removes effects of flame motion that are responsible for the observed statistical misalignment at low Karlovitz number. The turbulent kinetic energy (TKE) is evaluated using data from Direct Numerical Simulation (DNS) of spatially-evolving turbulent premixed jet flames at low and high Karlovitz numbers. The evolution equations are derived, and budgets of these equations are computed in the two Karlovitz number cases. In analysis of these budgets, more precise mechanisms of interaction between combustion heat release and turbulence are suggested, and implications for modeling efforts are discussed.