Modeling of Axisymmetric Two-phase Dilute Flows

This paper deals with the numerical treatment of Eulerian approach for dilute two-phase compressible flows (gas-particles mixtures) in axisymmetric configurations. For dilute flows, two classes of models depending on the dispersed phase volumetric fraction can be found. The volume occupied by the particles may be considered, that yields a model in which the gas phase and the dispersed phase equations are coupled through the void fraction and the source terms (Delhaye model). The void fraction effects can be neglected, that means the gas phase is a carrier phase for the particles (Ishii model). The mathematical nature of the two models is demonstrated from analysis of characteristic directions. For the Delhaye's model, a centered scheme is used to solve the system of partial differential equations, while an upwind TVD scheme is used for the Ishii's one. Then, it is shown that the problem of symmetry boundary conditions does not depend on the physical approach, as long as the flow remains dilute. However, a classical treatment for symmetry boundary conditions at the geometrical axis leads to large errors. A particular treatment for this boundary is presented: a new class of particles, described by a supplementary system of equations, is required.