Heat release effects on the Reynolds stress budgets in turbulent premixed jet flames at low and high Karlovitz numbers

In turbulent premixed flames at low Karlovitz number, combustion heat release can have a significant impact on turbulence. Thermal expansion in flame induces dilatation, and the corresponding pressure–dilatation correlation acts as a primary source of turbulent kinetic energy (TKE). As a consequence, the flame-normal component of the normal Reynolds stresses significantly increases. Additionally, for sheared flames, typical of jet flames, the shear component of the Reynolds stresses exhibits counter-Boussinesq behavior. For flames at low Karlovitz number, where these effects dominate, no models have successfully predicted all Reynolds stress components. To develop more complete turbulence models, heat release effects on the evolution of all Reynolds stress components need to be analyzed. In this work, Reynolds stress budgets are evaluated from Direct Numerical Simulation (DNS) databases of spatially-evolving turbulent premixed planar jet flames at low and high Karlovitz numbers. In the Reynolds stress budgets, the velocity–pressure gradient correlation term is important at both Karlovitz numbers but serves fundamentally different roles in each case. In the budgets for the normal components, the velocity–pressure gradient correlation term is decomposed into a redistribution term and an isotropic term, where the redistribution term acts to redistribute energy between the Reynolds stress components and the isotropic term is the pressure–dilatation source term of turbulent kinetic energy. At high Karlovitz number, the isotropic term is negligible, and the redistribution term acts to isotropize the turbulence as in non-reacting flows. Conversely, at low Karlovitz number, the isotropic term acts as a large source, and the redistribution term preferentially injects energy into the flame-normal component at the expense of other components which acts to make the turbulence less isotropic. In the budget for the shear component, the shear production term dominates the velocity–pressure gradient correlation term at high Karlovitz number, but the opposite is observed at low Karlovitz number. The dominance of the velocity–pressure gradient correlation term at low Karlovitz number is primarily induced by the flame-generated mean pressure gradient and ultimately leads to the counter-Boussinesq behavior of the shear component. The overall analysis indicates that any turbulence model that relies on small-scale isotropy and/or rapid isotropization will fail to capture the heat release effects on turbulence at low Karlovitz number.