Modeling of flame-generated turbulence based on direct numerical simulation databases

Turbulent premixed flames propagating in homogeneous isotropic turbulent flows were simulated directly with a single-step irreversible reaction. Two cases were calculated, case H, with a high-density ratio of flame pu/pb=7.53, and case L, low-density ratio of flame pu/pb=2.50, while u′/uL was nearly equal to unity. We obtained databases of fully developed stationary turbulent flames. These databases were investigated by analyzing the transport equation for turbulent kinetic energy to study flame-generated turbulence and its models. We found that turbulent fluctuations of all components, especially the streamwise component, were amplified in the flame brush and that flame-generated turbulence increased for a larger density ratio of the flame. Analysis based on the Favre-averaged transport equation for turbulent kinetic energy showed that pressure-related terms produced kinetic energy in the flame brush, the mean pressure gradient term was most important in case H and the pressure work term was most important in case L. On the other hand, the diffusion and dissipation term and velocity gradient term decreased kinetic energy. Next, modeling of the important terms in the balance equations were discussed. The mean pressure gradient term, pressure dilatation term, and additional dissipation components were modeled and compared with the direct numerical simulation (DNS) results. The mean pressure gradient term was modeled with assumption on the density, and the model was in good agreement with DNS. The other two terms were also modeled by scaling and these models mimicked DNS well.