Direct lagrangian simulations of a mixing layer by the transport-element method

Results are presented of Direct Lagrangian Simulations (DLS) of an unsteady, two-dimensional planar mixing layer by means of the “transport-element method.” The simulated results are used to understand the mixing behavior in a non-reacting flow, and to assess the limiting rate of the reactant conversion in a layer under the influence of a non-heat releasing reaction of the type A + B → Products. Both unforced and harmonically forced layers are considered. It is shown that harmonic perturbation results in a significant enhancement of mixing at initial stages of the flow development. However, it does not have a substantial influence at later stages. In all the cases considered the statistical results generated by DLS are shown to compare well with experimental data. Therefore, based on the DLS results the extent of validity of some of the turbulence closures of reacting flows is assessed. With this assessment it is demonstrated that the limiting rate of reactant conversion can be accurately predicted by the use of a Beta density model for the probability distribution of an appropriately defined Shvab-Zeldovich variable. Also, it is shown that the gradient diffusion model works reasonably well in accounting for the effects of turbulent convective fluxes.