A modified direct method for void fraction calculation in CFD–DEM simulations

•A modified direct method has been proposed for accurate void fraction calculation.•PMM inherits the simplicity and computational advantage of the direct method.•There is a minimum particle grid number required to reach the stable simulation.•PMM shows even higher computational efficiency than that of analytical approach.•PMM exhibits potential to handle arbitrarily complex domain and particle geometries.

The void fraction of computational cells in numerical simulations of particulate flows using computational fluid dynamics–discrete element method (CFD–DEM) is often directly (or crudely) calculated assuming that the entire body of a particle lies in the cell at which the particle centroid resides. This direct method is most inexpensive but inaccurate and may lead to simulation instabilities. In this study, a modified version of the direct method has been proposed. In this method, referred to as the particle meshing method (PMM), the particle is meshed and the solid volume in a fluid cell is calculated by adding up the particle mesh volume with the basic working principle being the same as that of the direct method. As a result, the PMM inherits the simplicity and hence the computational advantage from the direct method, whilst allowing for duplicating the particle shape and accurate accounting of particle volume in each fluid cell. The numerical simulation characteristics of PMM including numerical stability, minimum particle grid number, prediction accuracy, and computational efficiency have been examined. The results showed that for a specific cell-to-particle size ratio, there was a minimum particle grid number required to reach the stable simulation. A formula of estimating the minimum particle grid number was derived and discussed. Typically, a particle grid number of about 5 times the minimum number was suggested to achieve the best computational efficiency, which was comparable or even higher than that of simulations using the analytical approach. PMM also exhibited the potential to be applied for complex computational domain geometries and irregular shaped particles.

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