(24c) CFD Simulations of Gas Fluidized Beds Using a Revised Formulation of the Multi-Dimensional “Particle Bed Model”
Fluidization is nowadays employed in a wide range of industrial processes, finding useful applications in industries as different as those of power generation, chemicals, petrochemicals, and pharmaceuticals to mention just a few. Even so, the design of industrial scale fluidized bed plants still poses a major challenge to process engineers. Since the performance of these plants is strongly affected by the fluid dynamics attained within the fluidized beds, a reliable design requires the ability not only of predicting the highly complex hydrodynamic behaviour of such systems, but also of understanding how changes in geometry or scale would affect this behaviour. In this regard, Computational Fluid Dynamics (CFD) proves a valuable research means. Over the years CFD has been widely employed by the industry for supporting engineering design, particularly with respect to single-phase systems. Recently, however, the considerable progress made in the field of multi-phase fluid dynamics, has turned CFD into a fundamental component of research also for multi-phase systems, including fluidization. The main goal is simulating and investigating directly commercial size units so as to envisage their fluid dynamic behaviour and relate it to geometrical and process variables. CFD models catering for fluid-particle systems can be divided in two main groups: the Lagrangian-Eulerian models, and the Eulerian-Eulerian models. The first approach considers the fluid as a continuum whilst dealing with the solid phase at a particle level solving for each particle the Newtonian equations of motion for translation and rotation. The second approach, on the other hand, models both phases as interpenetrating continua trying to translate the dispersed nature of the solid phase into the equation of motion describing its flow field. Between the two, the latter has proved until now more successful since it provides satisfactory results with far less computational effort. As regards the Eulerian-Eulerian approach, the ?Granular Kinetic Model? advanced by Gidaspow (1994) is often considered state-of-the-art. Resorting to the kinetic theory in order to translate the distinctive features of the solid phase into a continuum, this model accounts for the solid stress by developing suitable constitutive expressions for the particulate viscosity and the solid pressure. However, including the solid stress tensor in the equations of change has proved not essential for a correct prediction of the fluidization dynamics; many mathematical models developed without taking into account this contribution have yielded equally satisfactory results. The main idea behind this approach is that direct collisions between particles are not a necessary condition for the particles to exchange momentum, the latter being exchangeable by means of purely fluid dynamics mechanisms. In this last category, the multi-dimensional formulation of the ?Particle Bed Model? recently proposed by Chen et al. (1999) stands out for its valuable feature of presenting a good trade-off between accuracy and complexity. In the present work, fluid-bed simulations of Geldart Group A and B powders have been performed using a revised formulation of the Eulerian-Eulerian multi-dimensional ?Particle Bed Model? proposed by Chen et al. (1999). The main differences between the original formulation and the revised one concern both equations of change and closure relationships. The buoyancy has been modified by employing the relation based on the density of the fluid alone. The drag force employs a new corrective function accounting for the nature of the dense suspension. The elastic force has been modified by regarding it as proportional to the drag force, thus ceasing to be a vector constant in direction and parallel to the gravitational field. The equations of change themselves have been partly revised. The pressure gradient is no longer shared by the fluid and solid phases in proportion to their volume fractions, but has been accounted for only in the fluid phase. Conversely, the elastic force has been included, albeit with opposite signs, in the linear momentum equations pertaining to both phases, so that the principle of action and reaction, whereto the force is subjected, is fulfilled. The numerical simulations have been carried out employing the program CFX-4.4, a commercially available Computational Fluid Dynamics code developed by CFX Ltd. (formerly AEA Technology). During the numerical integration of the differential equations of change, a numerical correction proposed by Lettieri et al. (2003) has been implemented in order to perform a tight control of the fluidized bed voidage at maximum packing. In the present study, both homogeneous and bubbling regimes of fluidization have been examined by simulating the behaviour of Geldart Group A and B powders. In particular, as for the Geldart Group A powder, both stable fluidization and transition from particulate to aggregative fluidization have been analyzed. The results have been thereafter compared with experimental data and numerical results obtained by means of alternative Eulerian-Eulerian models, namely the ?Granular Kinetic Model? of Gidaspow (1994) and the multi-dimensional ?Particle Bed Model? of Chen et al. (1999).
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