Granular flow collisional pressure

One can see as granular densities and pressures grow very quickly near the plane of jet interaction. Thus, solids deceleration is carried out in granular shock waves. The rapid decrease in axial components of particle velocities confirms a wavy nature of the granular flow. Radial particle velocity distributions on the jet periphery demonstrate the gas influence on the particle removal from the milling zone. This influence is observed for particles, which are smaller than 10 pm. The intensity of particle chaotic motion (relative particle-particle velocities) drops quickly with decrease in the particle diameters below 15 pm. This drop is caused by particle deceleration in a viscous gas (if collisions are elastic) and additionally by chaotic particle-particle collisions (if collisions are inelastic). This collisional intensity decrease causes a maximum of the relative particle-particle chaotic velocity at some distance from the plane of symmetry that is more explicit for inelastic collisions. Partial particle nonelasticity defines considerable drop in the chaotic velocity. The formation of a maximum of the collisional capacity at some distance from the plane of symmetry means that the maximal probability of particle fragmentation has to be also there. 

In the literature numerous two-fluid models of different complexity have been proposed to predict the fluidized bed reactor cold flow and reactive flow behaviors. Four decades ago emphasis was placed on the modeling of the velocity fluctuation co-variance terms in the dispersed particle fluid phase momentum equations. The early one-dimensional models were normally closed by an elasticity modulus parameterization for the particle phase collisional pressure and a constant viscosity parameter for the corresponding shear stresses. Later, with the improved computer memory and speed capacities, multi-dimensional flow models and more advanced model closures were developed based on the kinetic theory of granular flow (KTGF). Moreover, the... 

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