Particulate flow model

The particulate removal efficiency of a TSS is difficult to calculate with a single theoretical relationship. The technology licensors have utilized pilot plants and cold flow modeling to improve their removal efficiencies to meet stricter environmental regulations. While there is no theoretical relationship that exactly matches removal efficiencies, the following efficiency relationship from Rosin, Rammler, and Intehnann [2] is often used to understand cyclone fundamentals ... 

Calculation of the Particulate Solids Conveying a Screw Feeder The performance of a feed screw of 1.0-in flight diameter, 0.325-in screw root diameter and 1.2-in lead was experimentally executed for LDPE pellets with a bulk density of 0.45 g/cm3 by measuring the mass flow rate in the rotational speed range of 10-215 rpm. The results are shown in the table below. Construct a particulates drag-flow model that calculates with results that are in close agreement with the experimental results. 

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. 

The two-fluid granular flow model is formulated applying the classical Eulerian continuum concept for the continuous phase, while the governing equations of the particle phase are developed in accordance with the principles of kinetic theory. In this theory it is postulated that the particulate system can be represented considering a collection of identical, smooth, rigid spheres, adapting a Boltzmann type of equation. This microscopic balance describes the rate of change of the distribution function with respect to position and time. 

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... 

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. 

Laminar flow is assumed and the modeling of (S)f, (S)s, and xd are pursued similar to the hydrodynamics of the particulate flow. Since the solid particles are not spherical, the dendritic arms and other geometric parameters should be included in the models. Ahuja et al. [159] develop a drag coefficient for equiaxed dendrites. 

Since the permeating fluids are liquids, the question of the flow regime does not apply, but the pore numbers require a viscous flux model. If usual assumptions on the pore geometry are done, Hagen-Poiseuille (for cylindrically shaped pores) or Car-man-Kozeny (for ceramic particulate media) models should be applied. 

Sommerfeld, M. Theoretical and Experimental Modeling of Particulate Flow Overview and Fundamentals. Lecture Series 2000-2006. Belgium Von Karman Institute for Fluid Dynamics 2000. 

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