Particulate flows

Numerical Simulations of the Fluid and Particulate Flows in the Cyclone... 

Law. S. E., Thompson, S. A., and Balachandran, W., Electroclamping forces for controlling bulk particulate flow charge relaxation effects, J. Electrostatics, 37 79-94 (1996)... 

Nonetheless, mathematical analyses of milling operations, particularly for ball mills, roller mills, and fluid energy mills, have been moderately successful. There continues to be a pronounced need for more complete understanding of micromeritic characteristics, the intrinsic nature of the milling operation itself, the influence of fines on the milling operation, and phenomena including flaw structure of solids, particle fracture, particulate flow, and interactions at both macroscopic and microscopic scales. 

Boundary element methods can be used for particulate flows where direct1 formulations can be used. The surface tractions on the solids are integrated to compute the hydrodynamic force and torque on those particles, which for suspended particles must be zero. 

Yuan, Z. and Michaelides, E. E. (1992). Turbulence Modulation in Particulate Flows - a Theoretical Approach. Int. J. Multiphase Flow, 18,779. 

In polymer processing practice, we need to ensure that the particulate gravitational mass flow rate of the hopper exceeds, over the complete operating range, the extruder open discharge rate (i.e., the rate without any die restriction). That is, hoppers must not be the production-rate limiting factor. Second, and more importantly, it is necessary for stable extrusion operations and extruded product quality that the flow be steady and free of instabilities of the particulate flow emerging from the hoppers. Finally, as we will see in Chapter 9, we need to know the pressure under the hopper in order to determine the pressure profile in a SSE. 

In Sections 4.4 and 4.5, we dealt briefly with particulate flow instabilities in hoppers and the nonhomogeneous stress distributions created under uniaxial loading of a particulate assembly. In this section, we will expand on the discrete nature of such assemblies, and refer the reader to the computational and experimental tools that have been developed, and are rapidly advancing, to study such phenomena. 

Relatively simple optical experimental techniques to study noncohesive particulate flow have also been developed, such as the polarized light probe system by Allersma (42,43). With this technique, the principal stress distribution and displacement of photoelastic granular material flowing in two-dimensional hoppers, with and without obstructions (distribution bars), can be obtained, as shown in Fig. 4.18. 

Johnson, P C., Frictional-collisional equations of motion for particulate flows with applications to chutes and shear cells, Ph.D. dissertation, Princeton University, 1987. 

Yamane, K., Nakagawa, M., Altobelli, S., Tanaka, T., and Tsuji, Y. (1998), Steady particulate flows in a horizontal rotating cylinder, Phys. Fluids, 10,1419-1427. 

Particulate flow A y y solid particles in gas solid particles in liquid gas fluidized beds liquid fluidized beds... 

Type, size, composition and amount of particulate Flow rate, agitation, filtration... 

Ishii, M. and Zuber, N. (1979), Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE J., 15, 843-855. 

Fig. 6. Brittle fault seal analysis strategy. The strategy aims to quantify the sealing capacity of brittle faults by first predicting the deformation mechanism. Particulate flow faults are treated as non-sealing. Cataclastic faults have variable sealing properties according to fault throw and matrix properties. The chart in the lower left of this figure is reproduced at a larger scale in Fig. 8.

Experimental data Field data A Cataclastic faults Slip planes O Particulate flow... 

Enskog s dense gas theory for rigid spheres is also used as basis developing granular flow models. The modifications suggested extending the dense gas kinetic theory to particulate flows are discussed in chap 4. 

Fig. 3.1. Multiphase flow regimes. A Slug flow. B Bubbly flow. C Droplet Flow. D Annular flow. E Packed and porous fixed bed. F Particulate flow. G Stratified free surface flow.

Another possible conceptualization of the ensemble average imagines that the process is affected by small random forces through the motion. Particulate flows can then be described by distributions of positions, velocities and sizes adopting the basic principles of kinetic theory [85, 247, 248, 169, 249]. This alternative ensemble averaging approach is examined in relation to granular flows in chap 4. 

Johnson PC, Jackson R (1987) Erictional-coUisional constitutive relations for granular materials, with application to plane shearing. J Fluid Mech 176 67-93 Johnson PC, Nott P, Jackson R (1990) Frictional-colhsional equations of motion for particulate flows and their application to chutes. J Fluid Mech 210 501-535 Jung J, Gidaspow D, Gamwo IK (2006) Bubble Computation, Granular Temperatures, and Reynolds Stresses. Chem Eng Comm 193 946-975... 

These correlations are often used simulating particulate flows in chemical reactors. 

Ishii M, Zuber N (1978) Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulative Flows. AlChE J 25(5) 843-854... 

Tiwari P, Antal SP, Burgoyne A, Belfort G, Podowski MZ (2004) Multifield computational fluid dynamics model of particulate flow in curved circular tubes. Theoret Comput Fluid Dynamics 18 205-220... 

Johnson PC, Nott P, Jackson R (1990) Prictional-coUisional equations of motion for particulate flows and their application to chutes. J Fluid Mech 210 ... 

Chapter 4 contains a summary of the basic theory of granular flow. These concepts have been adopted describing particulate flows in fluidized bed reactors. The theory was primarily used for dense bed reactors, but modified closures of this type have been employed for more dilute flows as well. Compared to the continuum theory presented in the third chapter, the granular theory is considered more complex. The main purpose of introducing this theory, in the context of reactor modeling, is to improve the description of the particle (e.g., catalyst) transport and distribution in the reactor system. 

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