The effects of heat release on the energy exchange in reacting turbulent shear flow

Abstract

The energy exchange between the kinetic and internal energies in non-premixed reacting compressible homogeneous turbulent shear flow is studied via data generated by direct numerical simulations (DNS). The chemical reaction is modelled by a one- step exothermic irreversible reaction with Arrhenius-type reaction rate. The results show that the heat release has a damping effect on the turbulent kinetic energy for the cases with variable transport properties. The growth rate of the turbulent kinetic energy is primarily in uenced by the reaction through temperature-induced changes in the solenoidal dissipation and modifications in the explicit dilatational terms (pressure–dilatation and dilatational dissipation). The production term in the scaled kinetic energy equation, which is proportional to the Reynolds shear stress anisotropy, is less affected by the heat release. However, the dilatational part of the production term increases during the time when the reaction is important. Additionally, the pressure–dilatation correlation, unlike the non-reacting case, transfers energy in the reacting cases, on the average, from the internal to the kinetic energy. Consequently, the dilatational part of the kinetic energy is enhanced by the reaction. On the contrary, the solenoidal part of the kinetic energy decreases in the reacting cases mainly due to an enhanced viscous dissipation. Similarly to the non-reacting case, it is found that the direct coupling between the solenoidal and dilatational parts of the kinetic energy is small. The structure of the flow with regard to the normal Reynolds stresses is affected by the heat of reaction. Compared to the non-reacting case, the kinetic energy in the direction of the mean velocity decreases during the time when the reaction is important, while it increases in the direction of the shear. This increase is due to the amplification of the dilatational kinetic energy in the x2-direction by the reaction. Moreover, the dilatational effects occur primarily in the direction of the shear. These effects are amplified if the heat release is increased or the reaction occurs at later times. The non-reacting models tested for the explicit dilatational terms are not supported by the DNS data for the reacting cases, although it appears that some of the assumptions employed in these models hold also in the presence of heat of reaction.