Solid–fluid force modeling: insights from comparing a reduced order model for a pair of particles with resolved CFD-DEM

Solid–fluid force models are essential to efficiently model multiple industrial apparatuses such as fluidized beds, spouted beds, and slurry transport. They are generally built using strong hypotheses (e.g. fully developed flow and no relative motion between particles) that affect their accuracy. We study the effect of these hypotheses on particle dynamics using the sedimentation of a pair of particles. We develop new induced drag, lift and torque models for pairs of particles based on an artificial neural network (ANN) regression. The fluid force model covers a range of Reynolds numbers of 0.1 to 100 and particle centroid distance of up to 9 particle diameters. The ANN model uses 3475 computational fluid dynamics (CFD) simulation results as the training data set. Using this fluid force model, we develop a reduced-order model (ROM), which includes the virtual mass force, the Meshchersky force, the history force, the lubrication force, and the Magnus force. Using the results of a resolved computational fluid dynamics coupled with a discrete element method (CFD-DEM) model as a reference, we analyze the discrepancies between the ROM and CFD-DEM results for a series of sedimentation cases that cover particle Archimedes number from 20 to 2930 and particle to fluid density ratio of 1.5 to 1000. The errors primarily stem from particle history interactions that are not accounted for by the fully developed flow hypothesis. The importance of this effect on the dynamic of two particles is isolated and it is shown that it is more pronounced in cases with a lower particle-to-fluid density ratio (such as solid–liquid cases). This work underscores the need for more research on these effects to increase the precision of solid–fluid force models for small particle-to-fluid density ratios (1.5).

Uncontrolled Keywords

pair-wise particle interaction; reduced order modeling; immersed boundary; Navier–Stokes incompressible flow; computational fluid dynamics with the discrete element method (CFD-DEM)