Modeling granular material segregation using a combined finite element method and advection–diffusion–segregation equation model

Abstract

A two-dimensional, transient, multi-scale modeling approach is presented for predicting the magnitude and rate of percolation segregation for binary mixtures of granular material in a rotating drum and conical hopper. The model utilizes finite element method simulations to determine the bulk-level granular velocity field, which is then combined with particle-level diffusion and segregation correlations using the advection-diffusion-segregation equation. The utility of this modelling approach is demonstrated by predicting segregation patterns in a rotating drum and during the discharge of conical hoppers with different geometries. The model exhibits good quantitative accuracy in predicting DEM and experimental segregation data reported in the literature for cohesionless granular materials. Moreover, since the numerical approach does not directly model individual particles, it is expected to scale well to systems of industrial scale.

Coupling rheology and segregation in granular flows

“…More complex models that do use a continuum approach to calculate the bulk flow in a circular drum (e.g. Liu, Gonzalez & Wassgren 2018, 2019), do so with rate-independent elasto-plastic constitutive laws which are prone to ill posedness (Schaeffer 1987). This paper goes considerably further, by using the partially regularized -rheology and the recent segregation model of Trewhela et al.…”

An experimental scaling law for particle-size segregation in dense granular flows

“…1998; Fan et al. 2012), silos (Bates 1997; Schulze 2008; Liu, Gonzalez & Wassgren 2019; Isner et al. 2020) and rotating tumblers (Gray & Hutter 1997; Hill et al.…”

Determining of the influence of reactor parameters on the uniformity of mixing substrate components

“…However, these methods have not become widely used since the accuracy of numerical calculations is significantly limited due to the pre-uncertain initial conditions and the non-physical nature of boundary conditions [25]. The results reported in works [22][23][24][25] are typical of the operation of drum mixers without blades and when mixing materials that have a defined granulometric composition of the mixture components. The use of the reported models to describe the process of agitating organic compost would lead to significant deviations from the given results.…”

“…Both the low reliability of control devices and the complexities of mathematical calculations reduce the effectiveness of known techniques to determine the kinematic parameters of the movement of the particle of the material in a rotating drum. Therefore, the analytical and experimental studies' results, reported in works [15][16][17][18][19][20][21][22][23][24][25][26][27], are approaching the actual modes of movement of the studied environment only in terms of external features and qualitative characteristics. In addition, they mainly relate to dry loose materials.…”

“…There are no such studies in the multicomponent substrates with humidity up to 80 %. In addition, according to quantitative indicators, the data from works [15][16][17][18][19][20][21][22][23][24][25][26][27] differ significantly.…”