Continuum modeling of multidisperse and polydisperse granular materials in transient and developing flows

Deng, Zhekai

doi:https://doi.org/10.21985/n2-1g1d-yc86

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Continuum modeling of multidisperse and polydisperse granular materials in transient and developing flows

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Segregation of polydisperse granular materials remains to be a challenging problem in many industrial processes. However, most studies have focused either on bidisperse (two different particle size species) materials, which are not representative of most real mixtures, or on polydisperse materials in an idealized simple geometry. Additionally, most studies have focused on steady granular flows (time-independent flow kinematics), even though many flows encountered in industrial applications are unsteady (time-dependent flow kinematics). To address these challenges, we study and extend the application of the modified continuum model for bidisperse segregation that captures the effects of segregation, diffusion, and advection to polydisperse (continuous distribution of particle size) segregating materials in three ways. First, we consider tridisperse (three different particle size species) size segregating flow in developing inclined chute flow, which is an important stepping stone between bidisperse segregation and polydisperse segregation. The continuum model is validated using DEM simulations over a wide range of flow conditions. The approach accurately models tridisperse chute flow as indicated by the close agreement between its predictions and results from DEM simulations over a wide range of flow conditions including different incline angles, particle size distributions, flow rates, and flowing layer thicknesses. Second, we consider polydisperse segregating flow in developing segregation and transient segregation. In both cases, several terms in the model that were zero in the previously examined case of fully-developed streamwise-periodic steady segregation in a chute are now non-zero, which makes application of the model substantially more challenging. Predictions of the model agree quantitatively with experimentally validated discrete element method simulations of both size polydisperse and density polydisperse mixtures having uniform, triangular, and log-normal distributions. Finally, the continuum model is then extended to unsteady flows (time dependent flow kinematics) in feed-rate-modulated heap flow and hopper discharge flow, which could be viewed as a simplified version of industrial 3D conical heap filling and discharge operation. The model accurately predicts the segregation patterns inside the hopper and the discharge segregation profiles for both initially well-mixed and segregated conditions resulted from center filling. The agreement between experiment and continuum model further corroborates our modeling approach.

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