Vikrant Verma, Tingwen Li, Jean-François Dietiker, William A. Rogers, Sub-grid drag model for immersed vertical cylinders in fluidized beds, Powder Technology, Volume 316, 1 July 2017, Pages 225-232, ISSN 0032-5910, https://doi.org/10.1016/j.powtec.2016.12.044.
Abstract: Immersed vertical cylinders are often used as heat exchanger in gas-solid fluidized beds. Computational Fluid Dynamics (CFD) simulations are computationally expensive for large scale systems with bundles of cylinders. Therefore sub-grid models are required to facilitate simulations on a coarse grid, where internal cylinders are treated as a porous medium. The influence of cylinders on the gas-solid flow tends to enhance segregation and affect the gas-solid drag. A correction to gas-solid drag must be modeled using a suitable sub-grid constitutive relationship. In the past, Sarkar et al.  have developed a sub-grid drag model for horizontal cylinder arrays based on 2D simulations. However, the effect of a vertical cylinder arrangement was not considered due to computational complexities. In this study, highly resolved 3D simulations with vertical cylinders were performed in small periodic domains. These simulations were filtered to construct a sub-grid drag model which can then be implemented in coarse-grid simulations. Gas-solid drag was filtered for different solids fractions and a significant reduction in drag was identified when compared with simulation without cylinders and simulation with horizontal cylinders. Slip velocities significantly increase when vertical cylinders are present. Vertical suspension drag due to vertical cylinders is insignificant however substantial horizontal suspension drag is observed which is consistent to the finding by Sarkar et al.  for horizontal cylinders.
Keywords: Two-fluid model; Filtered model; Fluidized bed; Cylinders; Drag force