A critical comparison of frictional stress models applied to the simulation of bubbling fluidized beds

The behaviour of a gas-solid flow in a bubbling fluidized bed operated near the minimum fluidization condition is strongly influenced by the frictional stresses between the particles, these being highly concentrated and their motion dominated by enduring contact among them and with the walls. The effect of the introduction of frictional stresses in a Eulerian-Eulerian two fluid model based on the kinetic theory of the granular flow is evaluated. The models of Johnson and Jackson [1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. Journal of Fluid Mechanics 176, 67-93], Syamlal et al. [1993. Mfix documentation: volume I, theory guide. Technical Report DOE/METC-9411004, NTIS/DE9400087, National Technical Information Service, Springfield, VA], and Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] are compared with the kinetic theory of the granular flow and with experimental data both in a bubbling fluidized bed with a central jet and in a bubbling fluidized bed with a porous distributor. The predicted evolution of the bubble diameter along the height of the fluidized beds is examined, the shapes of the bubbles predicted by the models are compared and the evolution in time of the bubbles is shown. In the case of the bed with a central jet, the bubble detachment time is also calculated. The results show that the introduction of a frictional stress model improves the prediction of the bubbles diameter in a bubbling fluidized bed with a central jet and positively affects the bubbles diameter distribution in a uniformly fed bubbling fluidized bed. The high sensitivity of the model to the value of the particulate phase fraction at which frictional stresses start to be accounted for is pointed out through a sensitivity analysis performed on the Srivastava and Sundaresan [2003. Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129, 72-85] model.