Recent advances in well-posed Eulerian models for polydisperse multiphase flows.

The current state-of-the-art for computational modeling of polydisperse multiphase flows is reviewed and future research directions are discussed. Physics-based computational models at three distinct levels of abstraction: the microscale, mesoscale and macroscale; are discussed and compared. Special emphasis is placed on the relationship between the models at different scales and on how information from the finer scales is used to provide closures at the coarser scales. For disperse multiphase flows, it is argued that the passage from a direct-numerical simulation at the microscale to the kinetic description at the mesoscale is the crucial step for ensuring the validity of the macroscale model. In particular, the passage from the microscale to the mesoscale requires physics-based closures, while the passage from the mesoscale to the macroscale requires mathematical closures. The choices made in the physical and mathematical closures of the spatial fluxes and coupling terms will determine whether the Eulerian model is well-posed. In addition, the use of quadrature-based moment methods for polydisperse particles is presented as an efficient macroscale closure when dealing with a distribution of particle sizes. Examples of monodisperse and polydisperse multiphase flows are provided for cases where the fluid phase is compressible (high speed) and incompressible (low speed). [Display omitted] • Kinetic-based modeling of polydisperse multiphase flows is reviewed. • A multiscale modeling framework consisting of micro-, meso- and macroscale models is proposed. • The links between the micro- and mesoscale and the meso- and macroscale models are described using gas–particle flow. • The importance of verifying that the model is well-posed as each scale is emphasized. • The multiscale modeling approach is shown to reproduce the correct physics over a wide range of parameters. [ABSTRACT FROM AUTHOR]