Numerical simulation of granular mixing in a rotary drum using a generalized interpolation material point method

Abstract

Numerical simulations using a generalized interpolation material point method (GIMP) and material point method were introduced into the studying of granular mixing in a rotary drum. A Drucker–Prager model that has an equal size with a Mohr–Coulomb criterion was adopted to predict the failure behavior of granular matter. Experiments and discrete element method simulations were conducted to validate the models, and GIMP was finally used due to its accuracy and the ability for eliminating the crossing boundary noise. Velocity field of bed surface and standard deviation were used to measure the mixing performance. In particular, the influence of mesh size, elastic modulus, cohesion, and filling level were investigated. The results of simulations show that the utilization of GIMP significantly reduces the computing cost of simulation. The analysis of mixing performance shows that mixing performance decreases with the increase of elastic moduli, cohesion of granular matter, and filling levels.

Nonconforming Dirichlet boundary conditions in implicit material point method by means of penalty augmentation

“…For the implicit calculation scheme a time step of 5 Â 10 À4 is used. Figure 14 presents the results of the simulation at time step t ¼ 0 s and t ¼ 3:5 s in comparison to [79]. It can be observed that the obtained results show less mixing of the two materials.…”

“…To show the performance of the moving boundaries including the releasing contact algorithm, the example of the rotating drum proposed by Zuo et al [79] is chosen. They compared the experimental data to the simulations obtained using the discrete element method as well as MPM and GIMP.…”

“…The rotating speed of the drum is x ¼ 10 rpm, while the gravitational acceleration is set as 9:81 m=s 2 . The material model chosen for this example is the Mohr-Coulomb model, whereas Zuo et al [79] used a Drucker-Prager yield surface with an equivalent set of parameters. The material parameters are set to be: E ¼ 2700 Pa, m ¼ 0:2, and q ¼ 920 kg=m 3 , for the Young's modulus, Poisson's ratio, and density of the material, respectively.…”

“…This is due to the fact that in the present simulation a contact model between the material points which allows relative sliding and separation between elements is not considered, while [79] considers friction contact condition between the granular material and drum particles. Nevertheless, the simulation results are in good agreement with the results by [79]. Furthermore, focusing on the boundary imposition two main achievements can be observed.…”

“…Furthermore, focusing on the boundary imposition two main achievements can be observed. First, the imposition of the nonconforming curved moving boundary can be imposed accurately without modeling the rotating drum as done by [79]. This may significantly reduce the computational cost.…”