The Analysis of Particle Number Densities in Dilute Gas-Particle Flows: The Eulerian and Lagrangian Methods

The predictions of the conditional quadrature methods of moments, conventional Lagrangian, and fully Lagrangian (FLA) approaches to the calculation of particle number densities in hyperbolic and Lamb vortex flows are compared. All these methods predict similar distributions of particle number densities at low Stokes numbers. For single-fold particle trajectory crossings (PTC) at high Stokes numbers in the hyperbolic flow, the two-point quadrature approximation is shown to be in good agreement with both Lagrangian approaches, while the three-point approximation of the VDF leads to worse prediction than the two-point approximation. Thus, the number of nodes in the approximation has to be chosen based on the characteristics of the flow. The predictions of the FLA are shown to agree with those of the conventional Lagrangian approach when sufficiently large numbers of particles are used in calculations. The FLA is shown to be the most CPU efficient method among those considered in our analysis.