LES of a high-Reynolds number, chemically reacting mixing layer

In this work we perform large eddy simulations of high-Reynolds number, chemically reacting, spatially developing mixing layers with the goal of reproducing the experimental results obtained by Slessor at al. The chemical mechanism is the reaction of hydrogen and fluorine to produce HF. This is an exothermic, kinetically-fast reaction (Da » 1) in which the heat release (and the consequent temperature rise) is a direct measure of the product formation. The upper stream has a velocity of U_1 = 100 m/s and it is composed of a mixture of H_2 and inert gases, while the bottom stream has a lower velocity, U_2 = 40 m/s, and carries F_2 diluted in inert gases. Both streams have the same density. The mixing layer develops from a splitter plate and is characterized by a fairly large Reynolds number (Re_(δT) = 2·10^5 ). Although we do not explicitly model the boundary layers developing on the splitter plate, we impose laminar boundary-layer profiles at the inflow consistent with those reported in Slessor et al. The three-dimensional simulations show an excellent agreement with the experiments for the mean velocity, although some discrepancies are found in the temperature/product formation profiles. LES results tend to overestimate the molecular mixing in the flow: In the very high Damköhler regime this results In an overprediction of product formation and temperature rise. We study these issues by conducting some two-dimensional simulations using the Filtered Mass Density Function methodology which alleviates this problem. We compute the probability density functions of the mixture fraction as a function of the transverse coordinate and we confirm that the most probable mixture fraction in the layer is the one predicted by the asymmetric entrainment ratio model. In particular, about ~30% more mass is entrained into the layer from the high-speed stream as compared to the lower stream