Dimitri Gidaspow

Hydrodynamics of binary fluidization in a riser: CFD simulation using two granular temperatures

A new computational fluid-dynamic (CFD) model with a separate granular temperature (2/3 random particle kinetic energy per unit of mass) equation for each phase or particle size was developed using constitutive equations derived earlier by Huilin, Gidaspow and Manger. In agreement with the experiment and model of Mathiesen, Solberg and Hjertager the new model computes the observed core-annular flow regime. It predicts the trends of the observed radial and axial particle diameter distributions. For elastic particles the computed particle velocity distributions are parabolic. They are close to the laminar type approximate analytical solution for flow in a pipe, where the mean velocity equals the inlet flux divided by the particle density and volume fraction. The computed turbulent intensity is lower for large particles than for small particles, as measured. This is in agreement with an approximate analytical solution for the granular temperature in the developed flow region of a riser for elastic particles. Computations show that for sufficiently inelastic particles the granular temperature in the center can be lower than near the wall resembling the measured particle fluctuating velocity distribution.

Hydrodynamic simulation of gas-solid flow in a riser using kinetic theory of granular flow

Abstract The dynamic behavior of gas–solids flow in a 6-m high riser was predicted using a transient two-dimensional (2D) hydrodynamic model based on the kinetic theory of granular flows. Instantaneous and local gas-particle velocity, void fraction and turbulent parameters were obtained. Predicted time-averaged particle concentrations and velocities reflect the classical core-annular flow structure in agreement with experimental measurements, in particular, with those reported by Miller and Gidaspow [AIChE J. 38 (1992) 1801]. Predicted instantaneous solids concentration frequencies compared well with the experimental data for various regions of the riser. Computed total granular temperature distributions in the riser qualitatively agree with experimental data. High thermal conductivities of fluidized powders (about 50 times that of the fluidizing gas) were estimated from the kinetic theory without adjusted parameters. Effects of initial conditions, inlet geometry, riser diameter and riser vertical inclination were assessed. Unexpected strong distortions of solids concentrations and vertical fluxes were predicted for small inclination angles of the order of 2°. Analysis of experimental data should, therefore, be carefully conducted to ensure that riser inclination is not too important over the length of the riser in order to eliminate potential artifacts due to this geometric parameter.

Characteristics and Stability Analyses of Transient One-Dimensional Two-Phase Flow Equations and Their Finite Difference Approximations

AbstractEquation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. The main purpose of this paper is to study the mathematical nature of these equations, not their physics, although it is realized that these two problems are not entirely independent. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to ensure well-posedness. In the absence of lower order source or sink terms, that can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths.Analytical and numerical examples show that the ill posedness of IVPs for the two-phase flow partial differential equatio...

Size segregation of binary mixture of solids in bubbling fluidized beds

The fluidization behavior of binary mixture differing in size in the gas bubbling fluidized bed is experimentally and theoretically studied. The segregation phenomena are analyzed, and the relevancy of the pressure drop profile of binary mixture to the definition of its minimum fluidization velocity is discussed. The distributions of mass fraction of particles along the bed height are measured, and the profiles of the mean particle diameters of binary mixture are determined. A multi-fluid gas–solid flow model is presented where equations are derived from the kinetic theory of granular flows. Separate transport equations are constructed for each of the particle class, allowing for the interaction between size classes, as well as the momentum and energy are exchanged between the respective classes and the carrier gas. The segregations of the mean diameter are predicted. The numerical results are analyzed and compared with experimental data. D 2003 Elsevier B.V. All rights reserved.

Hydrodynamic modelling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow

Abstract A multi-fluid Eularian CFD model with closure relationships according to the kinetic theory of granular flow has been applied to study the motions of particles in the gas bubbling fluidized bed with the binary mixtures. The mutual interactions between the gas and particles and the collisions among particles were taken into account. Simulated results shown that the hydrodynamics of gas bubbling fluidized bed related with the distribution of particle sizes and the amount of energy dissipated in particle–particle interaction. In order to obtain realistic bed dynamics from fundamental hydrodynamic models, it is important to correctly take the effect of particle size distribution and energy dissipation due to non-ideal particle–particle interactions into account.

Electrostatic separation of powder mixtures based on the work functions of its constituents

Abstract The objective of this study was to investigate the feasibility of a dry electrostatic process to separate a powder mixture into its components based on their work functions. We studied the dry electrostatic beneficiation of high-sulfur, high-ash Illinois coals and relatively low carbon-containing oil shales, and separation of synthetic mixtures consisting of charcoal and silica to demonstrate the feasibility of such a separation. For nearly complete liberation of mineral inclusions from the organic matrix, both coal and shale need to be ground to a very fine particle size (below 5 μm). This is typically true for most of the mineral ores. The driving force in the electrostatic beneficiation of coal and shale is the observation that carbonaceous and non-carbonaceous matter can be imparted positive and negative surface charges, respectively, with a copper tribocharger. The polarity of surface charge is found to depend on the work function values of the particles and the tribocharger. Separation tests in a batch laboratory electrostatic separator showed that the efficacy of the electrostatic separation is strongly dependent on the hydrodynamic conditions such as gas velocity, electric field strength, and particle concentration in carrier gas. A dimensionless group called an ‘electrodiffusion number’ was identified which qualitatively described the separation process. Furthermore, the extent of separation was found to be limited by a strong cohesive force acting between the oppositely charged particles which resulted in the formation of agglomerates.

Hydrodynamics of sedimentation of multisized particles

Abstract A one-dimensional hydrodynamic model for the sedimentation of multisized particles was developed. The basic model was solved by the ICE numerical method, using a modified K-FIX computer code. The predicted settling rates agree with Selims et al. settling data of two heavy species and Fessas and Weilands experiments of heavy, buoyant two-species settling. The model also computes reasonable concentration profiles in the settler. To effectively simulate the sedimentation of multisized fine colloidal particles in non-aqueous media, the model was modified to be a diffusion-type matrix equation and solved by the method of characteristics. Surface charge effect of colloidal particles was included in the model The predicted concentration profiles for the settling of fine illite particles in toluene with asphaltene agree well with the recent experimental data reported by Shih et al.

The role of colloid chemistry in modeling deep bed liquid filtration

Abstract From mass balance on the suspension and filter and a charge balance on the filter, a set of hyperbolic partial differential equations is derived which describes how the suspension concentration, surface charges of the filter and particles, porosity of the filter, and the pressure drop vary with filter depth and time. These equations include a local deposition term which is evaluated by considering transport of the suspension particles to the filter particles by Brownian diffusion, interception, and sedimentation. The effect of the surface forces due to electrical double layer and van der Waals interactions was taken into account by treating the surface of the filter particles as possessing first order intermediate reaction kinetics, for which the rate constant is a function of the stability ratio of colloid chemistry. The governing equations were solved numerically, and the results compared with experimental data for unflocculated particles. The proposed filtration model is an advance over present models in that it contains no empirical factors which must be evaluated from filter runs and the effects of surfactants, pH, and ionic strength are accounted for.

Analysis of IGT pneumatic conveying data and fast fluidization using a thermohydrodynamic model

Abstract Pressure drop and choking were calculated for dense-phase vertical pneumatic conveying of solids using a model employing two continuity and two momentum equations. The relative equation of motion studied has been previously derived using the methods of non-equilibrium thermodynamics. The calculated pressure drops and choking velocities were found to be in a good agreement with IGT high-pressure lift-line experiments. To compare calculations with data, it was necessary to assume an effective particle size and an inlet void fraction which were not measured. Uncertainties in drag correlations for various flow regimes do not at present permit an equally good mathematical description of fast fluidization.

Validation of computed solids hydrodynamics and pressure oscillations in a bubbling atmospheric fluidized bed

Abstract The ensemble- and time-averaged solids velocity field and bed dynamics in the form of pressure oscillations taken in the atmospheric ‘thin’ (3.81 cm×40 cm) bubbling fluidized bed at the University of Illinois at Urbana—Champaign (UIUC) have been analyzed using Argonne National Laboratorys hydrodynamic model FLUFIX implemented on a Cray X-MP/18 supercomputer. The fluidized bed contained a simulated triangular pitch tube array consisting of five, round, 5.08-cm diameter cylinders. The bed material consisted of soda lime glass beads having a narrow size range averaging 460 μm in diameter. The fluidizing air was introduced at 39 cm s−1. Generally correct solids motion is predicted by the FLUFIX computer program. The uncertainties in the UIUC solids motion data varied greatly from location to location; hence, a sensitivity analysis was performed by varying the inlet fluidizing-gas velocity distribution. A convergence study was performed by varying (1) the size of the mesh used to approximate the obstacles and (2) the accuracy of the numerical solution. Essential grid independence is demonstrated for time-averaged axial solids velocities and porosities for the tubes modeled as 2×2 and 4×4 squares and a very tight convergence. Good agreement is obtained for the power spectra of the absolute pressure fluctuations using the fast Fourier transform technique. The computed and experimental major frequencies lie in the relatively narrow range of 2–3 Hz.