Alexander V. Potapov

Liquid–solid flows using smoothed particle hydrodynamics and the discrete element method

Abstract This study presents a computational method combining smoothed particle hydrodynamics (SPH) and the discrete element method (DEM) to model flows containing a viscous fluid and macroscopic solid particles. The two-dimensional numerical simulations are validated by comparing the wake size, drag coefficient and local heat transfer for flow past a circular cylinder at Reynolds numbers near 100. The central focus of the work, however, is in computing flows of liquid–solid mixtures, such as the classic shear-cell experiments of Bagnold. Hence, the simulations were performed for neutrally buoyant particles contained between two plates for different solid fractions, fluid viscosities and shear rates. The tangential force resulting from the presence of particles shows an increasing dependence on the shear rate as observed in the Bagnold experiments. The normal force shows large variations with time, whose source is presently unclear but independent of the direct collisions between particles and the walls.

Computer simulation of impact-induced particle breakage

Abstract The breakage induced in single circular particles that impact on solid plates has been studied using a two-dimensional simulation of solid fracture. The simulation allows the computer ‘experimenter’ to vary independently material properties such as Youngs modulus, Poissons ratio and work of fracture, flexibility that is unavailable in direct experimentation. Where comparison is possible, the simulation appears to mimic experimental results accurately. This study shows that the size distributions are, as would be expected, most strongly dependent on the collisional energy. Of secondary importance is the ratio of the impact velocity to the sound speed within the solid material. Finally, the size distributions show little effect of Poissons ratio.

Computer simulation of hopper flow

This paper describes two‐dimensional computer simulations of granular flow in plane hoppers. The simulations can reproduce an experimentally observed asymmetric unsteadiness for monodispersed particle sizes, but also could eliminate it by adding a small amount of polydispersity. This appears to be a result of the strong packings that may be formed by monodispersed particles and is thus a noncontinuum effect. The internal stress state was also sampled, which among other things, allows an evaluation of common assumptions made in granular material models. These showed that the internal friction coefficient is far from a constant, which is in contradiction to common models based on plasticity theory which assume that the material is always at the point of imminent yield. Furthermore, it is demonstrated that rapid granular flow theory, another common modeling technique, is inapplicable to this problem even near the exit where the flow is moving its fastest.

Computer simulation of shear-induced particle attrition

This paper describes a computer simulation study of brittle particle attrition in a shear cell in two dimensions. The results obtained indicate that the rate of attrition is directly related to the total amount of work performed on the system, including the initial work required to accelerate and expand the bed. These results seems to be in general agreement with the results of similar experiments performed in three dimensions for some materials. The results indicate that experimental errors may arise from the inertia of the movable plate of the shear cell.

A fast model for the simulation of non-round particles

Abstract This paper describes a new, computationally efficient model for the discrete element simulation of a certain class of non-round particles. The boundaries of the particles in this model are constructed from the circular segments of different radii in such a way that connections between these segments are continuous. As such, the model does not permit the simulation of arbitrarily shaped particles, but it does allow a wide enough variety of shapes to assess the effects of non-round shapes (in particular, particle interlocking) in an efficient manner. A direct test of the models performance demonstrates that the model is much more efficient than other models for non-round particles currently available and is less than two times slower than models for the same number of round particles.

A TWO-DIMENSIONAL DYNAMIC SIMULATION OF SOLID FRACTURE PART I: DESCRIPTION OF THE MODEL

This paper describes a two-dimensional computer simulation of solid fracture that allows the body and the fragments to be followed well beyond the point of simple crack formation. The model is based on discrete particle computer simulations used for studying granular flows. Here, macroscopic polygonal solid are constructed by “gluing” together small elements. Depending on the stress conditions the glued bonds between the elements can respond elastically, undergo plastic failure or break, allowing cracks to propagate across the macroscopic particle along the boundaries between their microscopic constituents. In essence, this process creates a simulated material upon which breakage occurs. Several element shapes have been studied.

Parametric dependence of particle breakage mechanisms

Abstract It has been observed that the pattern of particle impact breakage in two-dimensional systems is a result of two mechanisms. “Mechanism I” accounts for the breakage induced by the stresses that appear in unbroken particles. “Mechanism II” breakage is due to the buckling of the Mechanism I fragments. The purpose of this paper is to try and understand the parameters that govern the magnitude of the breakage induced by the various mechanisms—in particular, to understand the specific effects of impact velocity on the size distribution. To that end, a dimensionless parameter that governs the magnitude of the breakage induced by Mechanism I in both two and three dimensions is developed. The two-dimensional analysis demonstrates a velocity dependence for the Mechanism I breakage that accounts for the observed velocity effect on the generated size distributions. However, the three-dimensional analysis demonstrates no such velocity effect. Both findings are supported by simulation results.

The two mechanisms of particle impact breakage and the velocity effect

This paper describes a two-dimensional computer simulation study of the impact induced breakage of brittle solid particles. The work started as an attempt to understand the effect of impact velocity on the induced breakage and in particular to explain why there is a shift in the slope of the size distribution at large impact velocities. The results indicate that the observed breakage pattern is the result of two breakage mechanisms. When an unbroken particle experiences an impact, tensile stresses are generated along any line projecting radially outward from the contact point. This will generate cracks along those lines which we refer to as Mechanism I breakage and will be the dominant mode of breakage while the particles center of mass is still approaching the plate. However, before breakage is complete, cracks will form perpendicular to the Mechanism I cracks. This we refer to as Mechanism II breakage. As no tensile stresses in directions perpendicular to Mechanism I cracks would appear in an unbroken particle, the stresses that lead to Mechanism II breakage must only appear as a result of Mechanism I breakage. The simulations show that the Mechanism II breakage appears to be a result of the buckling of the fragments remaining after the Mechanism I breakage. Finally, the velocity effect appears to be a result of the tradeoff between these two modes of breakage. For high velocity impacts the Mechanism I stresses are large and thus Mechanism I breakage is dominant. At smaller velocities Mechanism II plays a larger role in the overall breakage.

A Two-Dimensional Dynamic Simulation Of Solid Fracture Part Ii: Examples

This paper uses the model described in Ref. 1 to simulate fracture in many simple systems with the goal of evaluating the advantages and deficiencies of the model. The examples include compressive failure of a rectangular sample, four-point shear failure of a beam and the impact of particles with a plate and binary impacts of particles. Where possible, the simulated results seem to be in good agreement with typical experimental results. Finally, a simulation of ball-milling, which involves the flow and fracture of many particles is shown to demonstrate the overall utility of the model.