On the importance of modeling size and velocity polydispersion of alumina droplets with robust and accurate numerical schemes for the prediction of solid rocket motors instabilities

The proposed contribution aims at presenting a robust method of high accuracy to model and simulate the dynamics of moderately inertial polydisperse spray of droplets in industrial configuration. The choice of an Eulerian framework to model the spray is motivated by the efficiency of the related numerical methods to solve two-way coupled effects and their abilities for high performance computing. Aiming at solving moderately high inertia droplets and realistic sprays, the proposed modeling takes into account both local size and velocity dispersions and therefore enables trajectories of droplets of comparable size to cross. In order to provide second order accuracy in every conditions, drag, heat exchange and evaporation are computed simultaneously by a dedicated procedure. Inspired from previous works, this methods is extended to take into account velocity polydispersion, assumed under the form of a anisotropic Gaussian distribution. Thanks to an operator splitting, this method is coupled with an efficient scheme for droplets and gas transport in the physical space already presented by the authors. The efficiency of the method proposed at predicting instabilities is assessed in the field of solid rocket propulsion.