Collision modelling for the interface-resolved simulation of spherical particles in viscous fluids

Abstract

AbstractThe paper presents a model for particle–particle and particle–wall collisions during interface-resolving numerical simulations of particle-laden flows. The accurate modelling of collisions in this framework is challenging due to methodological problems generated by interface approach and contact as well as due to the greatly different time scales involved. To cope with this situation, multiscale modelling approaches are introduced avoiding excessive local grid refinement during surface approach and time step reduction during the surface contact. A new adaptive model for the normal forces in the phase of ‘dry contact’ is proposed, stretching the collision process in time to match the time step of the fluid solver. This yields a physically sound and robust collision model with modified stiffness and damping determined by an optimization scheme. Furthermore, the model is supplemented with a new approach for modelling the tangential force during oblique collisions which is based on two material parameters: a critical impact angle separating rolling from sliding and the friction coefficient for the sliding motion. The resulting new model is termed the adaptive collision model (ACM). All proposed sub-models only contain physical parameters, and virtually no numerical parameters requiring adjustment or tuning. The new model is implemented in the framework of an immersed boundary method but is applicable with any spatial and temporal discretization. Detailed validation against experimental data was performed so that a general and versatile model for arbitrary collisions of spherical particles in viscous fluids is now available.