Two-size moment Eulerian multi-fluid method describing the statistical trajectory crossing: modeling and numerical scheme

High fidelity modeling and simulation of turbulent dispersed two-phase flows is still a major challenge for many applications. Eulerian approaches are well suited for high performance computations of such flows. Recently, hybrid Eulerian methods that combine the multi-fluid approach-where the size is discretized-and the moment method were developed. On the one hand, in order to capture efficiently the size-polydispersion, two size moments were used on each interval of the size discretization (Two Size Moment method). On the other hand, the Anisotropic Gaussian (AG) velocity closure has been introduced as a relevant model to describe velocity dispersion occurring when the particles from the disperse phase have a significant inertia compared to the time scales of the flow, leading to particle trajectory crossings. The purpose of this contribution is to develop a model able to describe size and velocity dispersion, coupling the two-size moment Eulerian multi-fluid method and the anisotropic velocity closure. Adapted numerical schemes based on a relaxation method are provided. This new model (AG-TSM) is then evaluated on various test cases relevant to rocket propulsion and two-phase combustion.