Detailed knowledge of solids circulation, bubble motion, and frequencies of porosity oscillations is needed for a better understanding of tube erosion in fluidized bed combustors. A predictive two-phase flow model was derived starting with the Boltzmann equation for velocity distribution of particles. The model is a generalization of the Navier-Stokes equations of the type proposed by R. Jackson, except that the solids viscosities and stresses are computed by simultaneously solving a fluctuating energy equation for the particulate phase. The model predictions agree with time-averaged and instantaneous porosities measured in two-dimensional fluidized beds. Observed flow patterns and bubbles were also predicted.

No abstract

The hydrodynamics of gas-solid flow, usually referred to as circulating fluidizedbed flow, wasstudied in a 7.5-em clear acrylic riser with 75-pm FCC catalystparticles.Data were obtained for three central sections as a function of gas and solids flow rates. Fluxes were measured by means of an extraction probe. Particle concentrations were measured with an X-ray densitometer. In agreement with previous investigators, these data showed the flow to be in the core-annular regime, with a dilute rising core and a dense descending annular region. However, unlike the previous studies conducted worldwide, the data obtained in this investigation allowed us to determine the viscosity of the suspension. The viscosity was a linear function of the volume fraction of solids. It extrapolates to the high bubbling-bed viscosities.

No abstract

[1] A multiparticle thermofluid dynamic model was developed to assess the effect of a range of particle size on the transient two-dimensional behavior of collapsing columns and associated pyroclastic flows. The model accounts for full mechanical and thermal nonequilibrium conditions between a continuous gas phase and N solid particulate phases, each characterized by specific physical parameters and properties. The dynamics of the process were simulated by adopting a large eddy simulation approach able to resolve the large-scale features of the flow and by parametrizing the subgrid gas turbulence. Viscous and interphase effects were expressed in terms of Newtonian stress tensors and gasparticle and particle-particle coefficients, respectively. Numerical simulations were carried out by using different grain-size distributions of the mixture at the vent, constitutive equations, and numerical resolutions. Dispersal dynamics describe the formation of the vertical jet, the column collapse and the building of the pyroclastic fountain, the generation of radially spreading pyroclastic flows, and the development of thermal convective instabilities from the fountain and the flow. The results highlight the importance of the multiparticle formulation of the model and describe several mechanical and thermal nonequilibrium effects. Finer particles tend to follow the hot ascending gas, mainly in the phoenix column and, secondarily, in the convective plume above the fountain. Coarser particles tend to segregate mainly along the ground both in the proximal area close to the crater rim because of the recycling of material from the fountain and in the distal area, because of the loss of radial momentum. As a result, pyroclastic flows were described as formed by a dilute fine-rich suspension current overlying a dense underflow rich in coarse particles from the proximal region of the flow. Nonequilibrium effects between particles of different sizes appear to be controlled by particle-particle collisions in the basal layer of the flow, whereas particle dispersal in the suspension current and ascending plumes is determined by the gas-particle drag. Simulations performed with a different grain-size distribution at the vent indicate that a fine-grained mixture produces a thicker and more mobile current, a larger runout distance, and a greater elutriated mass than the coarse-grained mixture.

The overall objective of this investigatfm is to develop experimentdly verified models for circulating fluidized bed (CFB) combustors. This report presents the author's derivation of analytical solutions useful in understanding the operation of a CFB. The report is in a form of a chapter that reviews the kinetic theov applications. DISCLAIMERThis report was prepared as an account of work sponsored by at1 agency of the (Jnitcd States Government. Ncither the United Statcs Government nor any itgency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refcrence herein to any specific cominercial product, process, or service by t r d e name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its cndorsetnent, recornmendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. APPLICATIONS OF KINETIC THEORY GRANULAR SHEAR FLOWThe simplest solution to the Nsvier-Stokes' equation for a fluid is that of shear or Couettc flow (Scldichting, 1966). It is assunied that the flow is steady, incompressible and fully developed. The latter condition insures that the velocity is nonzero in one direction, say in the x direction only. Then the continuity eqiiation with coIistant porosity shows that the gradient of velocity is zero, I-Icncc all accelerations vanish and the momentum balance for granular flow is simplywhere P is given by Equation (9-250). Furthermore, anadlogous to the fluid pressure one assumes the solids pressure in the x direction to be constant. The momentum balance then assumes the simple formIn the simple shear flow one assumes a no slip boundary condition at one w d l .The second wail is assumed to move with velocity U. With the fluid adhering to the wall the boundary conditions are The velocity profile is then us = Uy/h 2 (9 -' 275) (9 -275) ..llthotigh Equation (9-274) docs not permit a direct dctcrmination of viscosity as is done in the Poiseuille viscorrieter in which the pressure in Equation (9-273) varies with lcngth of flow, it turns out that thc granular tcnperature biLltlncc, Equation 8, ( 9 2 1 1 ) permits one to estimate the viscosity, as developed below, 19~1. D ISWith the same assumptions made for the simple shear flow discussed in the previous paragraph, the granular temperature Equation (9-21 1) with 110 production due to fluid turbulence or molecular fluid collisions is as follows.(9 -276)(9 -2 7 6~)In obtaining the dissipation by the wall in Equation ( 2 -h q it was assumed that the granular heat flux in Equation (9-211) is a constant and that the granular heat flow wits developed, as is done in the thermal forced convection problems.For an elastic...

Flow regimes of dense‐phase vertical pneumatic transport of solids, referred to in the literature as circulating fluidized beds, have been computed using a generalization of the Navier‐Stokes equations for two fluids. In the less dense regime corresponding to volume fractions of solids of about 1%, the flow consists of centrally upward moving solids and downward moving clusters. The computations agree with observations made by high‐speed motion pictures and with measurements of radial solids concentrations and velocities. In the dense regime, corresponding to volume fractions of about 10%, a core‐annulus type of regime is obtained, with solids descending down at the wall. The computed voidage distributions and velocity profiles agree with measurement done at the Institute of Gas Technology.

A review of the hydrodynamic models of fluidization is presented. Three hydrodynamic models have been programmed on supercomputers to predict the variation of void fractions, pressure, and gas and solid velocities as a function of position and time. The ability of the models to predict bubbles in fluidized beds, bed-to-wall heat transfer coefficients, and product distributions in gasifiers shows their great potential as new research and development tools. These supercomputer models should aid in improving the performance of chemical plants processing solids that are reported to have been performing below their design expectations for the last 20 years (Merrow, 1985).