Numerical aspects of Eulerian gas-particles flow formulations

Abstract

An Eulerian two-fluid numerical solver with kinetic-frictional theory for granular flows has been implemented and validated on the open-source code platform OpenFOAM®. Several aspects of the numerical treatment are discussed: maximum packing and phase disappearing limits, phase accumulation, cell-face fields interpolation and reconstruction practices, drag coupling approaches and different levels of conservativeness of the momentum equations. These last two topics are studied in depth. On the drag coupling analysis, it is observed that the partially implicit method (PIM) exhibits a convergence performance similar to the partial elimination algorithm (PEA) for a Geldart B particulate fluidized bed problem. But, for strongly coupled conditions (e.g. smaller particles) the use of the PEA becomes essential to meet a prescribed convergence criteria. Secondly, the conservativeness of the advective term of the momentum equations is analyzed by comparing three formulations of the advective term (the conservative form, the nonconservative form and the phase-intensive form). The impact of each formulation on the velocity field prediction is quantified for a shallow water problem and then extended to two-dimensional gas-liquid and gas-particle systems. The results show that the adoption of a conservative formulation is crucial to obtain accurate solutions in transient problems. However, for time-averaged analysis, which is often used for the study of fluidized bed systems, the nonconservative phase-intensive form is still a useful tool.