A general solution of the drag force in packed beds of multi-sized particles under creeping fluid flow conditions

Drag correlations for fluid-particles interactions of multi-sized particle systems are important in many industries. Currently such correlations are modelled at particle-scale (Method A) or cell-scale (Method B). However, they are often inconsistent in predicting either the overall fluid-drag force in a packed bed or the individual drag forces for different sized particles in the bed. In this work, a new model is proposed to build up a linkage between the two approaches (Methods A and B) for estimation of the drag forces in packed beds of multi-sized particles under creeping fluid flow conditions. The new model is based on using both the particle-scale parameter, the effective individual porosity, as well as the cell-scale parameter, the effective average diameter. A set of closed equations have been formulated to link these parameters, which can be solved by numerical iterations. The model is shown to be able to satisfactorily predict the overall and individual drag forces. In addition, the predicted effective individual porosity is comparable to the local porosity defined in terms of Voronoi or radical cells, and the effective average diameter reduces to those well-defined ones (such as the harmonic mean and volume-width mean diameters) at different conditions. Then, the model is used to study the effects of overall porosity and particle size distribution on the mean local porosity around a component particle and the effective average diameter. And based on the data predicted by the model, empirical equations are developed to predict the effective average diameter and mean local porosity. Finally, a bridge is established to connect those two approaches for drag force calculation in the literature