Computational Approaches for Studying the Granular Dynamics of Continuous Blending Processes, 1 – DEM Based Methods

Abstract

Computational methods using mechanistic modeling with a specific application in the area of continuous blending are presented. These methods complement experimental designs and aim to reduce the amount of time, effort, and material required to characterize a device or a process. The discrete element method is applied to the specific case of continuous mixing using two approaches. The first approach models an entire blender and studies the impact of changing impeller speed on residence time distribution (RTD), number of blade passes experienced by the powder, and mean centered variance of the particle residence time. The mean centered variance and the number of blade passes exhibit a maximum with increasing impeller speed, indicating optimal mixing behavior at an intermediate speed range. The second DEM approach utilizes a periodic slice of the full blender in order to explore in detail the effect of speed, fill level, and cohesion on mixing performance. The results show that the transverse mixing rates were generally higher than the corresponding axial mixing rates. Transverse diffusion was highest for large impeller speeds at larger fills, and axial diffusion was highest for large impeller speeds at smaller fills. Variations in particle–particle cohesion within the investigated range do not affect diffusion values significantly. The axial diffusion coefficient can be reasonably predicted from the residence time distribution using the 1D advection‐diffusion model. magnified image

Analyzing the Mixing Dynamics of an Industrial Batch Bin Blender via Discrete Element Modeling Method

“…Higher overlap signifies more deformation; hence, there is a possibility that the model will not stay within the elastic range (and the Hertzian contact force model is valid within the elastic range only). It has been seen in the previous studies that the shear modulus and Poisson's ratio can have similar values for different systems [13,14]. However, the interaction parameters are more sensitive towards the flow pattern of the solid particles.…”

“…This will make the model extremely computationally intensive. Scaling up the particle size will allow the same processing volume to be filled by a lesser number of particles, which will increase the simulation speed [13]. The total number of particles to be simulated and the scaled-up particle radius have been decided in a manner such that the fill level and the mass of the batch match with the experimental setup.…”

“…Here, µs pp , µs pw , µr pp and µr pw are the coefficient of static friction (particle-particle), the coefficient of static friction (particle-wall), the coefficient of rolling friction (particle-particle) and the coefficient of rolling friction (particle-wall), respectively. The coefficient of restitution has been kept at a low value of 0.1 as powder particles undergo inelastic collisions [13]. The particle shear modulus and Poisson's ratio are 2 MPa and 0.33, respectively.…”

“…The position of the particles is updated from Euler's equations of rotational motion as shown in Equation (3) [13]. Here, x, y and z are the spatial coordinates of the particle position; I is the moment of inertia; Ω is the angular velocity vector; and τ is the torque.…”

“…Here, F C is the normal or tangential contact force; δ is the normal or tangential overlap; k is the stiffness coefficient factor;δ is the rate of normal or tangential deformation; and γ is the damping coefficient. The detailed expressions of these parameters have been given by Dubey et al [13]. The stiffness coefficient controls the particle stiffness and is a function of the particle size and other material properties (i.e., Poisson's ratio and Young's modulus).…”