Extension of the kinetic theory of granular flow to include dense quasi-static stresses

Fluidized bed technology has diverse industrial applications ranging from the gasification of coal in the power industry to chemical reactions for the plastic industry. Due to their complex chaotic non-linear behaviour understanding the hydrodynamic behaviour in fluidized beds is often limited to pressure drop measurements and a mass balance of the system. Computational fluid dynamics has the capability to model multiphase flows and can assist in understanding gas–solid fluidized beds by modeling their hydrodynamics. The multiphase Eulerian–Eulerian gas–solid model, extended and validated here improves on the kinetic theory of granular flow by including a closure term for the quasi-static stress associated with the long term particle contact at high solid concentrations. Similar quasi-static models have been widely applied to slow granular flow such as chute flow, flow down an incline plane and geophysical flow. However combining the kinetic theory of granular flow and the quasi-static stress model for the application of fluidized beds is limited. The objective of the present paper is to compare two quasi-static stress models to the experimental fluidized bed data of Bouillard et al. [4]. A quasi-static granular flow model (QSGF) initially developed by Gray and Stiles [18] is compared to the commonly used Srivastava and Sundaresan [37]. Both models show good agreement with the experimental bubble diameter and averaged porosity profiles. However only the QSGF model shows a distinct asymmetry in the bubble shape which was documented by Bouillard et al. [4].

Graphical AbstractThis article presents an extended multiphase Eulerian–Eulerian, gas–solid model which improves on the kinetic theory of granular flow by including a closure term for the quasi-static stress. Simulations of a bubble's growth and its travel through a two-dimensional fluidized bed are compared to results from a quasi-static stress model and experimental measurements. Results show the model agrees well with the experimental bubble diameter and averaged voidage profiles.Average axial porosity profiles at x = 0.10 m from the bed centerline.Figure optionsDownload as PowerPoint slide