Evolution of flame-conditioned velocity statistics in turbulent premixed jet flames at low and high Karlovitz numbers

Abstract

Turbulence in low Karlovitz number premixed flames is strongly affected by small-scale combustion heat release. At low Karlovitz number conditions, flame-normal thermal expansion leads to increased anisotropy of the velocity field, and pressure-dilatation becomes the most significant source of turbulent kinetic energy (TKE). These effects are balanced in TKE budgets by the phenomenon of “negative production,” which leads to changes to the Reynolds stress tensor that are independent of the mean strain-rate tensor. The resulting statistical misalignment contributes to the failure of Boussinesq-type turbulence models in low Karlovitz number turbulent premixed combustion. Attempts have been made to develop turbulence models for premixed combustion, but these models depend on theoretical frameworks that are valid only in the zero- and infinite-Karlovitz number limits. In this work, a new statistical framework is introduced that could provide a foundation for turbulence models in flames of arbitrary Karlovitz number. In this framework, velocity statistics conditioned on a reaction progress variable are capable of distinguishing between actual turbulent fluctuations and fluctuations due to the motion of the flame. This capability is evaluated using data from Direct Numerical Simulations (DNS) of spatially-evolving turbulent premixed jet flames at low and high Karlovitz numbers. The evolution equation of the conditional mean velocity is derived, and budgets of the cross-stream, that is, essentially flame-normal, conditional mean velocity are compared in the two Karlovitz number regimes. At low Karlovitz number, the pressure gradient source is found to be balanced by the terms associated with the progress variable source term, indicating a dominance of flame effects on the turbulence dynamics. Conversely, at high Karlovitz number, physical-space transport terms are found to become leading-order, indicating a reduced effect of the flame on the turbulence dynamics.