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Partic. vol. 40 pp. 23-33 (October 2018)
doi: 10.1016/j.partic.2017.11.010

Direct calculation of voidage in the fine-grid CFD–DEM simulation of fluidized beds with large particles

Lihua Wang, Jie Ouyang*, Chuntao Jiang

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    • A judgment criterion of particle–cell overlap was proposed. • Eight cases of the overlap volume of particle and cell were ascribed to a unified formula. • Radial voidage profiles and vertical particle velocities agreed well with experimental data. • The S-shaped axial voidage profiles were investigated.


Voidage is important in determining the hydrodynamic behavior of a fluidized bed and estimating the drag force. Exact calculation methods are limited, especially in terms of determining the intersection of a particle and cell. This paper presents a method of directly calculating voidage. First, a judgment criterion of particle–cell overlap, which relies on the relationship of the distance from the particle to a cell face, edge, or vertex, is proposed. Eight cases of the overlap volume of a particle and cell are then ascribed to a unified formula in the framework of the cuboid cell. This formula relies on the volume of two kinds of segments named the hemispherical segment and quarter-spherical segment. The presented method is validated by calculating the voidage of simple cubic packing. Moreover, a three-dimensional fluidized bed with large particles is simulated and the results of numerical simulation are compared against experimental and simulation results reported in the literature. All numerical results are in good agreement with corresponding experimental data, and demonstrate the accuracy and reliability of the presented method in the three-dimensional simulation of fluidized beds.

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Voidage; Direct calculation; Computational fluid dynamics–discrete element method; Fluidized beds