Granular flows, solids pressur

Fixed Beds of Granular Solids Pressure-drop prediction is complicated by the variety of granular materials and of their packing arrangement. For flow of a single incompressible fluid through an... 

The first term on the right-hand side represents momentum exchange between solid phases I and s and Kis is the solid-solid exchange coefficient. The last term represent additional shear stresses, which appear in granular flows (due to particle translation and collisions). Expressions for solids pressure, solids viscosity (shear and bulk) and solid-solid exchange coefficients are derived from the kinetic theory of granular flows. 

Several different expressions have been derived for solids pressure, solids shear viscosity and solids bulk viscosity, employing different approximations and assumptions while applying the kinetic theory of granular flows. Some of the commonly used equations are described below (see Gidaspow, 1994 and a review given by Peirano, 1998) Solids 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. 

Porous Media Packed beds of granular solids are one type of the general class referred to as porous media, which include geological formations such as petroleum reservoirs and aquifers, manufactured materials such as sintered metals and porous catalysts, burning coal or char particles, and textile fabrics, to name a few. Pressure drop for incompressible flow across a porous medium has the same quahtative behavior as that given by Leva s correlation in the preceding. At low Reynolds numbers, viscous forces dominate and pressure drop is proportional to fluid viscosity and superficial velocity, and at high Reynolds numbers, pressure drop is proportional to fluid density and to the square of superficial velocity. 

The structure of the solid determines the mechanism for which internal liquid flow may occur. These mechanisms can include (1) diffusion in continuous, homogeneous solids, (2) capillary flow in granular and porous sohds, (3) flow caused by shrinkage and pressure gradients, (4) flow caused by gravity, and (5) flow caused by a vaporization-condensation sequence. 

Permeability Bulk sohd permeability is important in the iron and steel industiy where gas-solid reactions occur in the sinter plant and blast furnace. It also strongly influences compac tion processes where entrapped gas can impede compaction, and solids-handling equipment where restricted gas flow can impede product flowabihty. The permeabihty of a granular bed is inferred from measured pressure drop under controlled gas-flow conditions. 

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