UBC Theses and Dissertations
Mathematical modelling of gas and gas-liquid jets injected into a fluidized bed Pougatch, Konstantin
This thesis presents the development of novel mathematical models of jet injection into fluidized beds. Two types of injections are considered: the first is gas-assisted liquid atomization including flow through a variable cross-section nozzle, followed by spray dispersion and interaction with fluidized bed particles (jet-bed interaction), and the second is a high speed injection of a gas jet with a purpose to break down solid particles (particle attrition). Both models are based on a multi-fluid Eulerian-Eulerian treatment and include the system of the ensemble-averaged Navier-Stokes equations together with the particle number density equation for each phase written independently of the local nature of the continuous phase. The models rely on a number of sub-models that form constitutive equations. Some of the sub-models, such as ones used for atomization, moisture and heat transport in a bed due to particle collisions, heat conduction through the particle core, multiphase wall functions, and breakage frequency, are developed during the course of this project. The jet-bed interaction model includes break-up and coalescence of bubbles and droplets due to interfacial (mean and turbulent) shear and collisions in order to account for spatial variations of the average diameters. Atomization is considered as a catastrophic phase inversion triggered by a critical local volume fraction. The jet-bed interaction model is applied to gas-liquid flow through a nozzle, spray dispersion in open air, and spray injection into the bed. Modelling results are compared with experimental data for pressure variation along the nozzle wall, radial profiles of the liquid flow rate and average droplet diameter, and cumulative liquid distribution in a fluidized bed. It is demonstrated that there is an overall satisfactory agreement. The particle attrition model connects the solid phase properties and the granular temperature with the breakage rate. Modelling results allow calculation of the grinding efficiency – a quantitative measure of the attrition performance. For validation purposes, the model is applied to a number of cases that have been previously investigated experimentally with a good agreement. Both models are also applied to cases of practical interest, and a detailed flow analysis is conducted.
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