Complete liquid-solid momentum coupling for unresolved CFD-DEM simulations

Liquid-solid systems are frequently encountered in industrial processes and it is broadly recognised that numerical simulations are a useful tool for gaining insight in these processes. In this study, the unresolved CFD-DEM approach is extended with a complete momentum coupling for liquid-solid flows. Established correlations are used for the drag and lift forces, while new implementations are introduced for the unsteady interaction forces. A virtual mass force model based on the work of Felderhof (Felderhof 1991) is introduced, which accounts for the local particle volume fraction and the liquid-solid density ratio. The Basset history force, which is usually neglected due to computational difficulties related to its implementation, is evaluated according to the approach proposed by Parmar et al. A liquid fluidised bed is used as a demonstration case for the extended model. In this work, it is shown that with appropriate stabilisation measures, the Basset history force is approximated accurately (within 5%), while computational efficiency is maintained ( < 30% increase in computational time). Furthermore, the relevance of the complete momentum coupling is demonstrated by analysis of the solids mixing in the liquid fluidised bed. It is shown that when accounting for the complete interaction force, solids mixing is up to 20% slower compared to simulations with the drag-only approach.