Modeling granular material blending in a rotating drum using a finite element method and advection‐diffusion equation multiscale model

Abstract

A multiscale model is presented for predicting the magnitude and rate of powder blending in a rotating drum blender. The model combines particle diffusion coefficient correlations from the literature with advective flow field information from blender finite element method simulations. The multiscale model predictions for overall mixing and local concentration variance closely match results from discrete element method (DEM) simulations for a rotating drum, but take only hours to compute as opposed to taking days of computation time for the DEM simulations. Parametric studies were performed using the multiscale model to investigate the influence of various parameters on mixing behavior. The multiscale model is expected to be more amenable to predicting mixing in complex geometries and scale more efficiently to industrial-scale blenders than DEM simulations or analytical solutions. V C 2018 American Institute of Chemical Engineers AIChE J, 00: 000-000, 2018

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

“…This work extends the model developed by Liu et al [42,43] to include segregation. FEM simulations with a Mohr-Coulomb elasto-plastic material model are used to provide a prediction of the advective flow field.…”

“…For example, a uniaxial compression test can be used to calibrate the bulk density, Young's modulus, and Poisson's ratio, while a shear cell test can be used to calibrate the material's internal friction angle and wall friction angle. Refer to Liu et al [42], and references therein, for a detailed description of these experimental techniques. As a side note, the effort required to obtain model parameters should not be underestimated.…”

“…Gravity is increased gradually to fill the drum and allow material to settle before the drum rotates. Further details on the model set up can be found in previously published work [42]. Figure 2 shows the geometries of the simulated conical hoppers, which correspond to the hoppers used by Ketterhagen et al [44] in their experimental work.…”

“…Since a quasi-2D rotating drum flow [22] and axisymmetric conical hopper flows [44] are studied in this work, a two-dimensional segregation model is developed as an extension of the two-dimensional blending model in [42]. The following sub-sections present the main aspects of the segregation model.…”

Modeling a flow pattern of the granular fill in the cross section of a rotating chamber

“…The Euler's multiphase model of the method for computational fluid dynamics was applied in [19] in order to determine flow patterns of the chamber's fill depending on a change in the rotation velocity and the degree of filling. In [20], authors examined the use of a finite element method's large-scale model and its advantages in comparison with the DEM method, in order to determine the flow of granular fill in a slow-rotating chamber.…”