Turbulent transport in spatially developing reacting shear layers

Abstract

Direct numerical simulation (DNS) of turbulent reacting shear layers with significant heat release and local Reynolds numbers up to 1000 based on the Favre-averaged vorticity thickness was performed. The combustion is simulated by a single-step, second-order reaction with an Arrhenius reaction rate. The transport equations are solved using a low Mach number approximation in which the effects of heat release are accounted for through variable density. Two-dimensional simulations illustrate how growth rate decreases with increasing heat release and how the shear layer is sensitive to reaction rate. A three-dimensional simulation is used to generate data to study in detail how the flame alters the turbulence using budgets of turbulent kinetic energy. The three-dimensional results reveal that turbulent transport and pressure transport have a unique role in the overall energy balance in that they tend to increase kinetic energy near the edges of the layer while decreasing it at the center. Opposite behavior is found for pressure dilatation. Dissiplation and convection everywhere act as sinks for turbulence. The DNS results are compared with the standard k-∈ model for production and turbulent transport. The Boussinnesq approximation with a typical eddy viscosity constant yields the proper profile for production but, in general, overpredicts the peak value. The evaluation also reveals that the dilatation dissipation is small compared with the solenoidal dissipation. The standard gradient-diffusion model for turbulent transport/molecular diffusion is satisfactory when the molecular diffusion is small. The similarity between pressuren transport and turbulent transport suggests that pressure transport could also be modeled using a gradient-diffusion expression.