Scalar Transport Near the Turbulent/Non-Turbulent Interface in Reacting Compressible Mixing Layers

Abstract

Direct numerical simulations of temporally evolving compressible reacting mixing layers with Schmidt number equal to one are performed to examine the transport of a conserved scalar across the turbulent/non-turbulent interface (TNTI). The budgets of the scalar-gradient transport equation are used to study the effects of compressibility and heat release on the mixing. The simulations include a wide range of convective Mach number (\(M_c\)) from a subsonic and nearly incompressible case (\(M_c = 0.2\)) to a supersonic mixing layer at \(M_c = 1.8\). Furthermore, the highest level of heat release for the reacting simulations is opted to correspond to hydrogen combustion in air. The results suggest that the primary influence of the compressibility and heat release on the mixing of a conserved scalar is felt in a thin interface layer close to the TNTI whose thickness scales with the scalar-Taylor length scale. This interface layer is a juxtaposition of two dynamically different sub-regions referred to as laminar superlayer (LSL) and turbulent sublayer (TSL), whose thicknesses are of order of Kolmogorov and scalar-Taylor length scales, respectively. The transport of scalar is predominately governed by the molecular diffusion inside the LSL, whereas the inertial turbulent production dominates the transport within the TSL. It is shown that as the level of compressibility or heat release increases the rate of scalar mixing decreases. Compressibility affects the scalar mixing via a weakened turbulent production mechanism in the turbulent sublayer part of the interface layer, while the molecular diffusion process remains dynamically unaffected. On the other hand, in reacting cases the molecular diffusion inside the laminar superlayer and the turbulent production across the adjacent turbulent sublayer are subdued, which result in a decreased mixing rate.