Modeling and simulation of bubbling fluidized beds containing particle mixtures

A comprehensive model is presented for mathematically describing the isothermal, non-reactive, fluid dynamics of a mixture of particles in a gas. A multifluid approach was followed in which macroscopic transport equations were derived by taking suitable ensemble averages of the local gas and particle dynamic equations. A standard phasic ensemble average was selected for the gas phase, whereas the particle equations were derived using a kinetic theory approach in which collisional transfer is included. Separate transport equations were constructed for each of the particle classes, allowing for the description of the independent acceleration of the particles in each class and the equilibration processes whereby momentum and energy are exchanged between each class, leading to a wider range of applicability than common mixture equations have. Closure of the particle equations was exercised by providing separate velocity distributions for each of the particle classes, here specified as Gaussian: this is a valid approach for small gradients in the mean variables, and for nearly elastic particles. In the region of very high solids volume fractions, the relations obtained for the stress tensor were augmented by a model describing frictional transfer. The model was applied to three different test cases: (1) prediction of the shear and normal stresses in a homogeneous shear flow, (2) simulation of the particle pressure along the wall of a bubbling bed, and (3) a comparison between simulations of monodisperse and binary mixtures in a homogeneously aerated bed. Where possible to compare, correspondence between simulations and available experimental data is reasonable.