## DNS of Compressible Reacting Turbulent Shear Layer

##### Abstract

Direct numerical simulations (DNS) of temporally evolving shear layers have been performed to investigate the mechanisms associated with the entrainment process and to study the dynamics and the kinematics of turbulent/non-turbulent interface (TNTI). In order to study the effects of compressibility, heat release, and interaction of the flame with the TNTI on turbulence several cases with different convective Mach numbers, heat release levels, and stoichiometric mixture fractions are chosen for the simulations. The chosen values for convective Mach number cover a wide range of compressibility levels from subsonic and nearly incompressible to supersonic and highly compressible flows. Moreover, several heat release levels are opted for the reacting cases with the highest level of heat release corresponding to hydrogen combustion in air. Infinitely fast chemistry approximation is used to model a one-step irreversible global reaction that involves fuel, oxidizer, and product.
Since entrainment is intimately related to the TNTI, the characteristics of this interface are studied and their effects on the entrainment examined. As the compressibility level increases, the average size of the structures that form the local shape of the TNTI increases, however, as the heat release level increases, the average size of the structures that form this interface decreases. The geometrical shape of the TNTI looking from the turbulent region is examined. It is observed that in non-reacting cases this interface is dominated by the concave shaped surfaces. As the level of compressibility increases, the probability of finding highly curved concave shaped surfaces on the TNTI decreases, while the probability of finding flatter concave and convex shaped surfaces increases. In reacting flows with high heat release level, the TNTI is dominated by the convex shaped surfaces. As the heat release level increases the probability of finding highly curved convex shaped surfaces on the TNTI increases, whereas the probability of finding flatter concave and convex shaped surfaces decreases.
In order to gain a better understanding of features of the transport mechanisms across the TNTI, the budgets of enstrophy transport equation are studied. In a low compressible non-reacting flow, in addition to vortex stretching and viscous dissipation terms, which are dominant inside the fully turbulent region, the viscous diffusion term also becomes important in contributing to the total change of enstrophy inside the interface layer. However, in compressible or reacting cases there are additional terms contributing to the total change of enstrophy. In reacting and non-reacting flows, a viscous superlayer (VSL) is observed to be present at the outer edge of the interface layer. It is shown that compressibility seems to have little effect on the thickness of VSL, however, as the level of heat release increases the thickness of this layer decreases.
Examining the intense vorticity structures (IVSs) in the non-reacting cases, reveals that some of the important parameters that can affect the entrainment process, such as the thickness of VSL and the distance from the TNTI at which the average values of some of the generation terms in the enstrophy transport equation reaches a maximum, is approximately equal to the average radius of the IVSs. In the configuration studied here, it is observed that as the IVSs interact with the TNTI, the pressure gradient vectors become misaligned with the density gradient vectors, which are aligned with the direction normal to the TNTI, and generate a baroclinic torque. It is also shown that compressibility has a small effect on the structural features (size, orientation, and strength) of the IVSs in the shear layer.
Entrainment is studied via two mechanisms; nibbling, considered as the vorticity diffusion across the TNTI, and engulfment, the drawing of the pockets of the outside irrotational fluid into the turbulent region. As the levels of compressibility or heat release increases, the total entrained mass flow rate into the shear layer decreases. It is observed that nibbling is a viscous dominated mechanism in non-reacting cases, whereas it is mostly carried out by inviscid terms in reacting flows with high heat release level. It is shown that the contribution of the engulfment to entrainment is small for the non-reacting flows, while mass flow rate due to engulfment can constitute up to forty percent of total entrainment in reacting cases. This increase is primarily related to a decrease of entrained mass flow rate due to nibbling, while the entrained mass flow rate due to engulfment does not change significantly in reacting cases. In a low compressible reacting case, the decrease of entrained mass flow rate due to nibbling is shown to be mostly due to a reduction of the local entrainment velocity, while the surface area of the TNTI does not change significantly. In a high compressible case, both local entrainment velocity and surface area of the TNTI decrease resulting in a reduction of entrained mass flow rate due to nibbling.