Drag reduction and cluster formation in a circulating fluidised bed

In this paper we give an extensive summary of the results obtained during the past years with the Eulerian–Lagrangian modelling approach developed by the authors. Further on, we continue the investigation of a model approach accounting for two different classes of clusters: dilute and dense. It is based on the assumption that there co-exist two antagonistic drag effects on an individual particle depending on the interparticle distance within a cluster. A cluster is a group of particles held together as a result of hydrodynamic effects. A first type, diluted clusters, feature a low concentration of solids (less than 3%–5% solids volume fraction), and form a group of particles that fall faster than the settling velocity of individual particles. The reduction of the dynamic pressure within the wake of the lead particles in the flow direction results in the suction of the rear particles in the cluster, and leads to a decrease in the drag coefficient on the total cluster area. Secondly, within a well-defined higher concentration range of dense clusters (more than 10% solids volume fraction), hindered settling characterises the suspension. The restriction of the flow spaces between the particles in the plane perpendicular to the flow direction results in steeper velocity gradients of the gas phase, thus resulting in greater shearing stresses and an increase in the drag coefficient on the total cluster area. A numerical Eulerian–Lagrangian approach is used to investigate these effects of clusters on the gas–solid flow rate in a circulating fluidised bed. The results are compared to experimental results of a pilot riser in order to propose the general form of a combined drag law spanning from very diluted to dense suspensions of particles. Even though the numerical results show a good agreement in this study, the appropriate form of the general drag law should be calibrated with results from experiments and direct numerical simulations for a large range of Reynolds particle numbers.

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