Multi-scale modeling of gas–liquid–solid three-phase fluidized beds using the EMMS method

A multi-scale model for the gas–liquid–solid three-phase fluidized beds is developed on the basis of the principles of the EMMS model. For this purpose, the flowing structure in the gas–liquid–solid system is divided into five phases and considered under different spatial scales: a solid–liquid phase describing the micro-scale interaction between solid particles and liquid, a gas phase, a bubble wake phase and two inter-phases that, respectively, describe the meso-scale interaction of the dispersed bubbles and bubble wakes with the surrounding liquid–solid pseudo-homogeneous suspension. In order to obtain the steady state of such a system with eight unknowns, in addition to seven mass and momentum conservation conditions and an inequality constraint for the mean bubble diameter, the stability condition Nst → min is used.The model is solved and checked with the experimental data available in several references which cover a broad range of operating conditions from the conventional expanded fluidized bed to the circulating fluidized bed, indicating that the model is capable of describing the global hydrodynamics of the complex flow in the three-phase system with acceptable accuracy.