Modelling the particle stress at the dilute-intermediate-dense flow regimes: A review

Abstract

Gas-solid f low systems are found in many industrial applications such as catalytic reactions, pneumatic conveying, granulation, crystallisation, mineral classification, etc. The operational hydrodynamics can vary depending on the operation method from fast dilute flow, which is dominated by collisional particle-particle contacts, to dense slow flow, which is dominated by sustained frictional contacts. For many years, the former has been successfully modelled using the classic kinetic theory for granular flow, while the latter has been modelled based on soil mechanics principles. At the intermediate- dense regime, three different modelling approaches are identified: (1) the kinetic-frictional model using an ad hoc patching together of the stress from the two limiting regimes at a specific solid fraction (Johnson and Jackson, 1978; Ocone et al., 1993; Syamlal et al., 1993); (2) the switching from one regime to another using different solid stress formulations (Laux, 1998; Makkawi and Ocone, 2005); and (3) the new emerging fluid mechanic approach which allows for a smooth transition from one regime to another using a unified model (Tardos et al., 2003, Savage, 1998). In this study, a one-dimensional fully developed gas-solid f low model for horizontal f low will be used to review the various treatments of solid stresses, and the sensitivity of the f low predictions to the frictional stress will be assessed.