(273a) Stress Distribution in the Avalanching Flow of Cohesive Granular Materials in a Rotating Vessel
- Conference: AIChE Annual Meeting
- Year: 2006
- Proceeding: 2006 Annual Meeting
- Group: Particle Technology Forum
- Time: Tuesday, November 14, 2006 - 3:15pm-3:36pm
The storage and transport of dry cohesive granular materials is extremely important within the process industries. Problems in processing itself and the ultimate product quality are encountered due to the erratic discharge, segregation and internal stress distributions. Rotating drums are extensively used in the chemical and process industries as kilns, mixers, reactors and dryers, which often displays the avalanching flow of granular material. We used soft particle dynamics based DEM to include cohesive and frictional forces to characterize the behavior of cohesive granular systems. Our model system consisted of 20,000 rough and inelastic particles of 2 mm diameter in a cylindrical vessel with a 9 cm diameter, 1 cm length, and frictionless sidewalls. In the cohesive model, the cohesive force between particles is simulated using a square-well potential; a constant-intensity normal force is applied whenever particles are in contact. The numerical model gives a satisfactory reproduction of experimental cohesive granular flow profiles as we observe the direct dependency of avalanche size with cohesion. The aim of this micro-structural approach is to find macro-level state variables that are based on micro-variables such as contact forces, grain displacements and local geometric characteristics.
In an avalanching flow in a rotating drum, two distinct regions namely: quasi-static region, and cascading dynamic layer are observed. The output from the simulation is a time-referenced set of variables at the particle level (components of position vector, displacement vectors, linear and angular velocity vector), which enables us to estimate the density and velocity field within the granular bed. Moreover, a detailed study of stress field arising from two modes of momentum-transfer mechanisms: the streaming or kinetic mode, by which momentum is carried by particles as they move through the bulk material; and the collisional mode, by which momentum is transferred from one location to the another in the material by inter-particle collisions, has been achieved. To properly estimate the stress field and voidage (density), a spatial grid based local averaging procedure is used. A particular consideration involved in the choice of grid size is that it must be small enough to allow the investigation of activity within the cascading layer. We chose an optimized square cell with sides of length equal to 5 particle diameters which is an appropriate size for the analysis of the cascading and quasi-static layers and it contains enough particles for stress and voidage calculations to be meaningful.
As expected, the simulations show that the collisional mode dominates the momentum transport throughout the granular bed. The quasi-static region clearly shows lower values of voidage than the avalanching dynamic regions. We investigated the distribution of normal and shear stresses as a function of voidage by estimating the temporal evolution of the stress field for grids located in both the static and cascading layers. For a cohesive system, normal stresses in the quasi-static region are two orders of magnitude larger than normal stresses in the cascading region. Shear stresses of the quasi-static layer are also higher than stresses in the cascading region. Our simulations show that higher stress is associated with low voidage irrespectively of the degree of cohesion. Increase of the rotational speed of the vessel causes more fluctuations in the stress field, however the magnitudes of the normal stresses remain unaltered. Speed makes shear stress rise significantly in the cascading layer. In all types of flows, the coherent group of particles forming one avalanche is being tracked to estimate the corresponding avalanche kinematics, the macroscopic deformation rate and the stress tensor. The non-Newtonian behavior of the granular bed is quantified in terms of the first normal stress difference (N1). N1 remains negative in the grids of the cascading and quasi-static regions but it decreases with the increase in voidage of the bed.