Critical comparison of hydrodynamic models for gas–solid fluidized beds—Part II: freely bubbling gas–solid fluidized beds

Abstract

Correct prediction of spontaneous bubble formation in freely bubbling gas–solid fluidized beds using Eulerian models, strongly depends on the description of the internal momentum transfer in the particulate phase. In this part, the comparison of the simple classical model, describing the solid phase pressure only as a function of a solid porosity by an empirical correlation and assuming the solid phase viscosity constant, which is referred to as the constant viscosity model (CVM), with the more fundamental model based on the kinetic theory of granular flow (KTGF), in which the solid phase properties are described in much more detail in terms of instantaneous binary particle–particle interactions, has been extended for freely bubbling fluidized beds. The performance of the KTGF and the CVM in predicting the hydrodynamics of freely bubbling fluidized beds has been compared with experimental data and correlations taken from the literature. In freely bubbling fluidized beds at relatively low gas velocities, bubble formation is initiated by inelastic particle–particle interactions. When accounting for the dissipation of granular energy by particle collisions, the KTGF predicts much larger bubbles with a much sharper interface in comparison to the CVM. The average bubble size distribution predicted by the KTGF showed better agreement with correlations as well as experimental data from the literature. Although both models showed an increase in the predicted average bubble size with increasing superficial gas velocities, the discrepancy in the predicted bubble size becomes smaller, indicating the growing importance of the gas particle interactions in the bubble formation process at higher gas velocities. The rise velocity predicted by the KTGF and the CVM is approximately the same and in good agreement with correlations available in the literature. Since the KTGF predicts somewhat larger bubbles, also the predicted visible bubble flow is higher in comparison to the CVM. In very dense regions in the fluidized bed the KTGF based on instantaneous binary collisions needs to be extended for additional frictional stresses in addition to the kinetic and collisional transport mechanisms. The extra frictional stresses were implemented via a relatively simple semi-empirical closure model and proved to have a significant influence on the predicted bubble size, rise velocity and visible bubble flow rate, where the model predictions strongly depend on the empirical constants. To further enhance the performance of the KTGF to describe the hydrodynamics of freely bubbling beds a more fundamental description of the frictional stresses on the particle level should be incorporated.