A MAXIMUM ENTROPY PRINCIPLE MODEL FOR THE INITIALIZATION OF EULERIAN–LAGRANGIAN SPRAY SIMULATIONS

Abstract

NOx emission regulations have become more and more restrictive for internal combustion engine-powered vehicles, especially for road transport applications. To minimize emissions and comply with regulations, selective catalytic reduction (SCR) systems are the most efficient deNOx technology thanks to the injection of a urea-water solution (UWS). State-of-the-art computational fluid dynamics (CFD) techniques employ Eulerian-Lagrangian frameworks to deal with the two phases of such problems. Still, the associated low velocities of UWS applications make it difficult to use standard breakup models (Kelvin-Helmholtz, Rayleigh-Taylor, Taylor analogy breakup) to generate initial drop size distributions. Hence, these specific studies end up needing experimentally characterized drop size distributions to initialize the CFD simulations or using expensive Eulerian-Eulerian simulations to obtain the outcomes of the primary breakup of the liquid jet. The maximum entropy principle (MEP) allows generating a droplet size-velocity probability distribution function (PDF) from initial injection conditions and injector characteristics while satisfying conservation equations. The most probable PDF curve is determined by the distribution that maximizes the entropy of the problem. A critical Weber number has been proposed to select which droplets will break up subsequently after the initial droplet break up. The model has been validated against experimental results obtained by high-resolution laser backlight imaging. Comparable results have been found and realistic tendencies were achieved, decreasing the expected droplet size with increasing injection pressures. The proposed model could help with introducing alternative breakup models for low-velocity applications without the need for prior droplet size knowledge.