Direct numerical simulations (DNS) are conducted of two-dimensional (2D) exothermic reacting mixing layers laden with either solid particles or evaporating liquid droplets. An irreversible reaction of the form Fuel+r Oxidizer -> (1+r) Products with exothermic Arrhenius kinetics is considered. The temporally developing mixing layers are formed by the merging of parallel flowing oxidizer and fuel streams, each uniformly laden with non-reacting particles or droplets. The gaseous phase is governed by the compressible form of the Navier-Stokes equations together with transport equations for the fuel, oxidizer, product and evaporated vapor species concentrations. Particles and droplets are assumed smaller than the Kolmogorov scale and are tracked individually in the Lagrangian reference frame. Complete ``two-way'' couplings of mass, momentum and energy between phases are included in the formulation. The simulation parameters are chosen to study the effects of the mass loading ratio, particle Stokes number, vaporization, flow forcing and reaction Zeldovich number on the flame evolutions.

Quasi- one-dimensional simulations reveal that the asymptotic state of the laminar flames is independent of the particle or droplet loading. For forced 2D simulations, both particles and droplets are preferentially concentrated into the high strain braid regions of the mixing layer. Cold solid particles entrained into the mixing zone cool the flame in the braid regions due to their finite thermal inertia. This results in flame suppression and, under certain conditions, local flame extinction in the braids. The potential for flame extinction is substantially enhanced by evaporating droplets through the latent heat, and also by the addition of non-reacting evaporated vapor which locally dilutes the reactant concentrations. In contrast, combustion proceeds robustly within vortex cores which have relatively dilute droplet distributions due to preferential concentration; particularly at moderate Stokes numbers. The extent of flame suppression and local extinction are increased with increasing reaction activation energy, dispersed phase mass loading, and also by decreasing particle or droplet Stokes number.

The figures at the right depict contours from a liquid droplet laden mixing layer simulation at a mass loading ratio of 0.5. The flow variables presented are the fuel species mass fraction, product species mass fraction, evaporated vapor mass fraction, temperature, and the droplet number density. The upper stream is initially comprised of pure oxidizer with a mean velocity to the right in the figures. In contrast, the lower stream is composed of pure fuel species and moves to the left in the pictures creating the observed fluid shearing region. The convective Mach number of the mixing layer is 0.35. The simulation was conducted with a grid resolution of 512 x 576 grid points and 288,000 individual droplets were tracked.

GOVERNING EQUATIONS