Lagrangian model simulations of molecular mixing, including finite rate chemical reactions, in a temporally developing shear layer

A local integral model for approximate simulations of the molecular mixing and chemical reaction processes in turbulent reacting flows is presented. The model is based on recent experimental results, which show that essentially all of the molecular mixing in turbulent flows occurs in thin strained laminar diffusion layers, and that the internal structure within these layers is essentially self-similar. This motivates a local integral treatment of the mixing and reaction processes in these layers that removes the resolution requirements imposed on full simulations by the steep gradients within the molecular diffusion and chemical reaction scales of the flow. The resulting integral model is applied to predict the mixing and reaction progress in a temporally developing shear layer over a range of Reynolds and Damköhler numbers, and to make comparisons with results obtained from full finite difference simulations. The resulting reactant and product concentration fields, as well as the temperature and reaction rate fields obtained from the model, are in good agreement with the full simulations. The results indicate that the model is able to accurately follow even highly sensitive nonlinear measures of the mixing and reaction progress such as the local extinction phenomenon characteristic of large Zel'dovich number Arrhenius kinetics.