Granular Flow Closure Limitations

There are many aspects of rapid granular flows that have barely been studied and require further considerations to provide appropriate closures for reactor flows. 

The theoretical studies of rapid granular flows are generally based on the assumption that the energy dissipation in a binary particle collision is determined by a constant coefficient of restitution e, the ratio of the relative approach to recoil velocities normal to the point of impact on the particle. However, measurements show that the coefficient of restitution is a strong function of the relative impact velocity [10]. Physically, the energy dissipation relates to the plastic deformation of the particle s surface. Thus, a realistic microscopic model should include the deformation history of the particle s surface. However, such a model might become computationally demanding and thus not feasible. 

Moreover, most theoretical studies performed so far are based on the assumption that the granular material is composed of uniformly sized disk or spheres. However, real materials may have a wide distribution of particle sizes affecting the properties of the flow. 

In addition, granular materials in industrial units operations will generally be highly angular. Yet all of the analyzes and most of the computer simulations have been performed for perfect spheres or disks. 

Sphericity has been assumed in most studies for many reasons. In theoretical work and computer simulations it is easy to detect a collision of spherical particles, as particles are in contact whenever their centers are a distance of two radii apart. For non-spherical particles, the contact mechanisms become much more complicated, as the orientation of the particle, which changes as the particle rotates, must be taken into account. For this reason the assump -tion of spherical particles are normally considered a fair approximation for catalyst pellets. 

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