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## Kinetic Theory Based CFD Models for Polydisperse Multiphase Flow

Kinetic theory is a useful theoretical framework for developing CFD models for disperse multiphase flows. For example, Lagrangian particle tracking methods such as KIVA can be formulated in terms of a kinetic equation written in an Eulerian framework. For most applications, direct solution of the kinetic equation is intractable due to the high dimensionality of the phase space. A key challenge is thus to reduce the dimensionality of the problem without losing the underlying physics.

Lagrangian methods and Eulerian multi-fluid models are two widely used CFD tools for accomplishing this task. In theory, starting from the same kinetic equation, Lagrangian and Eulerian CFD models should yield identical results for multiphase statistics (e.g. phase volume fractions, phase velocities, etc.) but this is often not the case. More often than not, the reason for the discrepancy can be found in the closures invoked in deriving the Eulerian CFD model.

Recently, we have developed a more general closure approximation based on reconstructing the distribution function in the kinetic equation from its moments using a quadrature-based methodology. In principle, this Eulerian CFD approach can treat polydisperse multiphase flows as accurately as the corresponding Lagrangian approach. Using examples from liquid sprays, gas-particle flow, and bubbly flow, we discuss the underlying fundamentals of quadrature-based moment methods for simulating polydisperse multiphase flows.