Semi-empirical prediction of bubble diameter in gas fluidized beds

Theoretical expressions for bubble diameter in both small and large particle fluidized beds are derived by the application of two phase theory and gas flow continuity. Comparison with experimental data suggests that the numerical and analytical solution of these expressions, combined with empirical bubble frequency relations, can provide an accurate prediction of bubble size and its parametric trends.Several commonly employed empirical correlations of bubble diameter are shown to be derivable from a common theory, with differences among the correlations ascribed to variations in flow regime and bubble frequency.     

Bubble wake solids content in three-phase fluidized beds

It is shown that existing equations for predicting the holdups of wakes behind bubbles in three-phase fluidized beds are not entirely satisfactory. A new model is then developed whereby the wake is treated as the sphere-completing volume of a spherical cap bubble, due allowance being made for hydrodynamic interactions between bubbles. The generalized wake equations of Bhatia & Epstein (1974) are applied to compute the ratio of solids holdup in the wakes to that in the remaining liquid of the bed. Using experimental data from the literature, a rational equation is then generated for predicting this ratio from measured variables, and a mechanism for wake solids entrainment is proposed which is consistent with this equation.     

Mass transfer between bubbles and the dense phase in gas fluidized beds

Mass transfer between a bubble and the dense phase in gas fluidized beds of Group A and Group B particles was proposed based on previous experimental results and literature data.The mass transfer coefficient between bubbles and the dense phase was determined by k_(be) = 0.21d_b.A theoretical analysis of the mass transfer coefficient between a bubble and the dense phase using diffusion equations showed that the mass transfer coefficient between a bubble and the dense phase is k_(be) ∝ε_(mf)(Du_b/d_b)~(1/2) in both three- and two-dimensional fluidized beds.An effective diffusion coefficient in gas fluidized beds was introduced and correlated with bubble size as De = 13.3d_b~(2.7)7 for Group A and Group B particles.The mass transfer coefficient k_(be) can then be expressed as k_(be) = 0.492ε_(mf)(u_bd_b~(1.7))~(1/2) for bubbles in a three-dimensional bed and k_(be) = 0.576ε_(mf)(u_bd_b~(1.7))~(1/2) for bubbles in a two-dimensional bed.     

Propagation characteristics of pressure disturbances originated by gas jets in fluidized beds

An experimental investigation has been carried out on velocities and amplitudes of pressure disturbances in fluidized beds made of 100–200 μm glass ballotini. Disturbances were originated by gas jetting in a 0.35 m i.d. fluidized bed. A fluidization tube 0.10 m i.d. has also been used. Different types of disturbances have been induced in the bed contained in this tube: injection of a freely rising bubble and of a captive bubble; injection of a bubble chain; and compression of the bed free surface. The dynamic wave character of the disturbances has been shown. Velocities and amplitudes of waves moving through the beds have been measured. In particular, wave velocities have been compared with theoretical results obtained by the application of “pseudo-homogeneous” and “separated phase flow” models.     

Segregation characteristics of irregular binaries in gas solid fluidized beds——An ANN-approach

Binary mixtures of irregular materials of different particle sizes and/or particle densities are fluidized in a 15-cm diameter column with a perforated plate distributor. An attempt has been made in this work to determine the segregation characteristics of jetsam particles for both the homogeneous and heterogeneous binary mixtures in terms of segregation distance by correlating it to the various system parameters, viz. initial static bed height, height of a layer of particles above the bottom grid, superficial gas velocity and average particle size and/or particle densities of the mixture through the dimensional analysis. Correlation on the basis of Artificial Neural Network approach has also been developed with the above system parameters thereby authenticating the development of correlation by the former approach. The calculated values of the segregation distance obtained for both the homogeneous and heterogeneous binary mixtures from both the types of fluidized beds (i. e. under the static bed condition and the fluidized bed condition) have also been compared with each other.     

Time-series analysis of pressure fluctuations in gas–solid fluidized beds – A review

This work reviews methods for time-series analysis for characterization of the dynamics of gas–solid fluidized beds from in-bed pressure measurements for different fluidization regimes. The paper covers analysis in time domain, frequency domain, and in state space. It is a follow-up and an update of a similar review paper written a decade ago. We use the same pressure time-series as used by Johnsson et al. (2000). The paper updates the previous review and includes additional methods for time-series analysis, which have been proposed to investigate dynamics of gas–solid fluidized beds. Results and underlying assumptions of the methods are discussed.     

Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe

The bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe was experimentally investigated. The bubble characteristics were measured using a dual optical probe, while the liquid-phase turbulence was measured using hot-film anemometry. Measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. At low void fraction flow, the radial void fraction distribution showed a wall peak which changed to a core peak profile as the void fraction was increased. The liquid average velocity and the turbulence intensities were less uniform in the core region of the pipe as the void fraction profile changed from a wall to a core peak. In general, there is an increase in the turbulence intensities when the bubbles are introduced into the flow. However, a turbulence suppression was observed close to the wall at high liquid superficial velocities for low void fractions up to about 1.6%. The net radial interfacial force on the bubbles was estimated from the momentum equations using the measured profiles. The radial migration of the bubbles in the core region of the pipe, which determines the shape of the void profile, was related to the balance between the turbulent dispersion and the lift forces. The ratio between these forces was characterized by a dimensionless group that includes the area averaged Eötvös number, slip ratio, and the ratio between the apparent added kinetic energy to the actual kinetic energy of the liquid. A non-dimensional map based on this dimensionless group and the force ratio is proposed to distinguish the conditions under which a wall or core peak void profile occurs in bubbly flows.     

Bubble behavior in a three-phase fluidized bed

Bubble size measurements by off-axis holography are reported for the first time in three-phase fluidized beds. The solid material was glass cylinders, with the liquid in one case having matching refractive index. Two different columns, 76 and 152 mm dia, were employed. An interpolative correlation was developed for the solid volume fraction of the bed as a function of liquid flux. A generalized dimensionless model was developed to predict the equilibrium bubble size in both fixed and fluidized beds.     

Bubble dynamics in a two-dimensional gas-solid fluidized bed

Related referential studies on gas-solid two-phase flows were briefly reviewed. Bubble ascending in a two-dimensional （2D） gas-solid fluidized bed was studied both experimentally and numerically. A modified continuum model expressed in the conservation form was used in numerical simulation. Solid-phase pressure was modeled via local sound speed; gas-phase turbulence was described by the K-ε two-equation model. The modified implicit multiphase formulation （IMF） scheme was used to solve the model equations in 2D Cartesian/cylindrical coordinates. The bubble ascending velocity and particle motion in the 2D fluidized bed were measured using the photochromic dye activation （PDA） technique, which was based on UV light activation of particles impregnated with the dye. Effects of bed height and superficial gas velocity on bubble formation and ascent were investigated numerically. The numerically obtained bubble ascending velocities were compared with experimental measurements. Gas bubble in jetting gas-solids fluidized bed was also simulated numerically.     

The local structure of gas fluidized beds —I. A statistically based measuring system

A system is described for measuring the parameters characterizing the local state of fluidization in beds of arbitrary sizes. This system is based on a miniaturized capacitance probe shaped so as not to disturb the local state of fluidization. Based on a statistical analysis of the signal, the mean bubble pulse duration, the number of bubbles striking the probe per unit time and the local mean bubble rise velocity are measured. The latter is measured by using the cross-correlation technique. From these parameters, further characteristics of the local state of fluidization are derived, in particular the local mean pierced length of bubbles, the local bubble volume fraction and the local bubble gas flow.     

Gas and particle motion in jets in fluidized beds

Entrainment of solid particles by gas jets discharged downwards through slotted nozzles into bubble-free beds of fluidized particles is considered. The gas flow in the jet is calculated for irrotational flow, using a correlation established previously for slot opening as a function of operating variables. The momentum boundary layer thickness and shear stress at the horizontal interface between jet and particles are then calculated by integral boundary layer analysis. The calculated shear stress distributions are consistent with measurements of the momentum of bed particles caused to saltate by the jet, and explain the dependence of particle movement on the various operating variables. The results provide a direct confirmation of a hypothesis due to Owen on the mechanism of saltation.     

Flow regimes and flow transitions in liquid fluidized beds

Using two-dimensional liquid fluidized beds of glass particles in water, we have been able to identify at least four discrete fiow regimes. The points of transition between these regimes are sharp and non-hysteretic. The regimes include (in the order of increasing gm/gm_mf), wavy fiow, wavy fiow with transverse structure, fine-scale turbulent flow, and bubbling states. Characterization of each of these regimes is given in terms of the rime and length scales of the motion, as measured by light transmission, optical scanning, and digital time-series analysis. Features of the mechanics of these states are discussed. Observation of the bubbling state for particles of moderate density (ρ_s = 3990 kg/m³) in liquid beds is new, and is shown to be related fo anomalous expansion data reported by earlier investigators.     

Continuous segregation of binary heterogeneous solids in fluidized beds

Continuous segregation of a binary mixture of heterogeneous (different density) solids is carried out in a gas–solid fluidized bed. We investigate how gas velocity, solids feed rate, flotsam feed composition, bottom discharge pipe diameter, and minimum fluidization velocity ratio of the flotsam to jetsam particles influence the solids holdup, separation factor, and product quality (flotsam purity at the top outlet). The results are interpreted in terms of solids holdup information. The results indicate that the separation factor decreases when the gas velocity, bottom discharge pipe diameter, flotsam feed composition, or the minimum fluidization velocity ratio increase, while the separation factor increases as the solids feed rate increases. The product quality decreases when the gas velocity, solids feed rate, or minimum fluidization velocity ratio increase, while the product quality increases as the bottom discharge pipe diameter or flotsam feed composition increase. Correlations for predicting the separation factor and product quality are proposed using a logistic model for individual flotsam feed compositions, which satisfactorily compares with the present experimental data.     

A model for expansion ratio in liquid-solid fluidized beds

Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.