Flow properties of homogeneously aerated,expanded emulsion phase of fine powders (quasi-solid emulsion phase viscosity)

The viscosity of quasi-solid emulsion phase (μ_e) of the “homogeneously aerated, expanded emulsion phase” (HAE emulsion phase) of fine powders within the gas velocity range of minimum fluidization (U_mf) and minimum bubbling (U_mb), was obtained at ambient and elevated temperatures by measuring the strain retardation time (τ) of the HAE emulsion phase in this study.The deformation coefficient (Y) was obtained by our previously developed experimental method [Powder Technol., 81 (1994) 177].We confirmed experimentally that the HAE emulsion phase behaves exactly as quasi-elastic body, by observing the emulsion phase volume expansion and contraction within the velocity range of U_mf and U_mb. It is to be noted that U_mb>U_mf. The volume element of the unit HAE emulsion phase could be expanded or contracted by the force balance between the excessive gas drag force (above the gravitational force) and the inter-particle force of the particles of the emulsion phase. This experimental evidence enabled us to decide using the visco-elastic rheological model of the Voigt–Kelvin model body (VK model body) in terms of mathematics to analyze our experimental data. The rheological parameters, i.e., the elastic deformation coefficient (Y) and quasi-solid viscosity (μ_e) of our experiments, were obtained by using the HAE emulsion phase.Using these experimental data together with the VK model body, we developed our experimental model equation including the measured strain retardation time (τ) to obtain the “quasi-solid viscosity” of the HAE emulsion phase (μ_e). The physical meaning of this viscosity of the HAE emulsion phase developed in this study is quite different from the “apparent quasi-liquid viscosity” defined in aggregative fluidized beds, under the condition of U_mf=U_mb.The interesting experimental data correlations of comprehensive rheological parameters (μ_e, Y, σ_f) of the HAE emulsion were obtained for fine powders at ambient and elevated temperatures.     

Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements

Computational fluid dynamics—discrete element method (CFD‐DEM) simulations were conducted and compared with magnetic resonance imaging (MRI) measurements (Boyce, Rice, and Ozel et al., Phys Rev Fluids. 2016;1(7):074201) of gas and particle motion in a three‐dimensional cylindrical bubbling fluidized bed. Experimental particles had a kidney‐bean‐like shape, while particles were simulated as being spherical; to account for non‐sphericity, “effective” diameters were introduced to calculate drag and void fraction, such that the void fraction at minimum fluidization (ε_mf) and the minimum fluidization velocity (U_mf) in the simulations matched experimental values. With the use of effective diameters, similar bubbling patterns were seen in experiments and simulations, and the simulation predictions matched measurements of average gas and particle velocity in bubbling and emulsion regions low in the bed. Simulations which did not employ effective diameters were found to produce vastly different bubbling patterns when different drag laws were used. Both MRI results and CFD‐DEM simulations agreed with classic analytical theory for gas flow and bubble motion in bubbling fluidized beds. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2555–2568, 2017     

Radial gas mixing in a fluidized bed using response surface methodology

Radial gas mixing in a fluidized bed was studied using response surface methodology (RSM), which enables effect examinations of parameters with a moderate number of experiments. All experiments were conducted in a 0.29-m ID fluidized-bed cold model. The gas dispersion process within the bed is described using the dispersed plug flow model. Pure carbon dioxide was used as the tracer gas, continuously injected into the center of the bed by a point source. The downstream radial tracer concentration profile was measured using a gas chromatograph.The radial gas dispersion coefficient, D_r, was well correlated with operating parameters and the particle and gas properties: (U−U_mf)/U_mf, H_s/d_b, φ_d, and Ar, with a determination coefficient R² of 0.966. Effect test indicates that the dimensionless characteristic velocity, (U−U_mf)/U_mf, has the most significant influence on D_r, while the static bed height to bed diameter ratio, H_s/d_b, is less remarkable. The interactions of (U−U_mf)/U_mf with the distributor open-area ratio, φ_d, and with the Archimedes number, Ar, both play important roles. An evolutive response surface model was proposed to describe the radial gas mixing in the bubbling/slugging fluidization regimes.     

Fluidization with hot compressed water in micro-reactors

In this paper the concept of micro-fluidized beds is introduced. A cylindrical quartz reactor with an internal diameter of only 1 mm is used for process conditions up to and 244 bar. In this way, fast, safe, and inherently cheap experimentation is provided. The process that prompted the present work on miniaturization is gasification of biomass and waste streams in hot compressed water (SCWG). Therefore, water is used as fluidizing agent. Properties of the micro-fluid bed such as the minimum fluidization velocity (U_mf), the minimum bubbling velocity (U_mb), bed expansion, and identification of the fluidization regime are investigated by visual inspection. It is shown that the micro-fluid bed requires a minimum of twelve particles per reactor diameter in order to mimic homogeneous fluidization at large scale. It is not possible to create bubbling fluidization in the cylindrical micro-fluid beds used. Instead, slugging fluidization is observed for aggregative conditions. Conical shaped micro-reactors are proposed for improved simulation of the bubbling regime. Measured values of U_mf and U_mb are compared with predictions of dedicated 2D and 3D discrete particle models (DPM) and (semi)-empirical relations. The agreement between the measurements and the model predictions is good and the model supports the concept and development of micro-fluid beds.     

Fluidization of Group B particles with a rotating distributor

A novel rotating distributor fluidized bed is presented. The distributor is a rotating perforated plate, with 1% open-area ratio. This work evaluates the performance of this new design, considering pressure drop, Δp, and quality of fluidization. Bed fluidization was easily achieved with the proposed device, improving the solid mixing and the quality of fluidization.In order to examine the effect of the rotational speed of the distributor plate on the hydrodynamic behavior of the bed, minimum fluidization velocity, U_mf, and pressure fluctuations were analyzed. Experiments were conducted in the bubbling free regime in a 0.19 m i.d. fluidized bed, operating with Group B particles according to Geldart's classification. The pressure drop across the bed and the standard deviation of pressure fluctuations, σ_p, were used to find the minimum fluidization velocity, U_mf. A decrease in U_mf is observed when the rotational speed increases and a rise in the measured pressure drop was also found. Frequency analysis of pressure fluctuations shows that fluidization can be controlled by the adjustable rotational speed, at several excess gas velocities.Measurements with several initial static bed heights were taken, in order to analyze the influence of the initial bed mass inventory, over the effect of the distributor rotation on the bed hydrodynamics.     

Numerical simulation of pulsed fluidized bed with immersed tubes using DEM-LES coupling method

The present work is a 2-D numerical simulation of pulsed fluidized bed with immersed tubes using DEM-LES coupling method. The pulsed inflow of gas phase is modeled as U₀(1+sin(2πft)), in which four pulsating frequencies of f=5, 10, 15 and 20 of velocity inflow are used. The discrete element method (DEM) simulation for particle motion coupled with the large eddy simulation (LES) for gas phase is used. The fluidized bed with five immersed tubes of staggered arrangement and six immersed tubes of in-line arrangement is simulated, respectively. It is found that the pressure drop, the mean drag force and the mean pressure gradient force experienced by particles are forced oscillated. The different effects of pulsed fluidization on the circumferential distribution of particle-tube collision on the outer surface of tubes at different pulse frequencies and modes of arrangement of immersed tubes are numerically analyzed. Finally, it is found that the pulsed motion of fluid with high frequency leads to suppression of particle fluctuating motion.     

Numerical analysis of particle mixing in a rotating fluidized bed

This paper describes the numerical analysis of particle mixing in a rotating fluidized bed (RFB). A two-dimensional discrete element method (DEM) and computational fluid dynamics (CFD) coupling model were proposed to analyze the radial particle mixing in the RFB. Spherical polyethylene particles (Geldart group B particles) were used as model particles under the assumptions that they were cohesionless and mono-disperse with their diameter of 0.5 mm.The validity of the proposed model was confirmed by the comparison between the calculated degree of particle mixing and the experimental one, which was obtained by measuring the lightness of the recorded image taken by a high-speed video camera. Effects of the operating parameters (gas velocity, centrifugal acceleration, particle bed height, and vessel radius) on the radial particle mixing rate were numerically analyzed. The radial particle mixing rate was found to be strongly affected by the bubble characteristics, especially by the bubble size. The mathematical model for the rate coefficient of particle mixing as functions of operating parameters was empirically proposed. The radial particle mixing rate in a RFB could be well correlated by the three dimensionless numbers: dimensionless acceleration (Ac), bubble Froude number (Fr_b), and dimensionless radius on the surface of particle bed (β_s).     

Behaviour of gas-fluidized beds of fine powders part I. Homogeneous expansion

The minimum bubbling velocity has been correlated from the results of experiments on 48 gas/solid systems and is a function of the density and viscosity of the fluidizing gas, the mean sieve size of the powder and the fraction of fines less than 45 μm. An improved equation is presented to predict U_mb/U_mf; this parameter also correlates well with the maximum non-bubbling bed expansion ratio H_mb/H_mf which is used to calculate the maximum dense phase voidage ?_mb. An equation based on the Carman-Kozeny theory can be used to predict bed voidages between incipient fluidization and bubbling. An accurate value of particle density is essential in these equations and a simple comparative method has been used to determine particle densities of fine porous powders.     

Modified gas‐perturbed liquid model (GPLM) for minimum fluidization velocity in a two‐phase inverse fluidized bed reactor with Newtonian and non‐Newtonian systems

In the present investigation minimum fluidization velocity, U_mf, in a two‐phase inverse fluidized bed reactor is determined using low‐density polyethylene and polypropylene particles of different diameters (4,6 and 8 mm) by measuring pressure drop. In a glycerol system U_mf decreased gradually with increase in viscosity up to a value of 6.11 mPa s (60%) and on further increase there was a slight increase in U_mf. In the case of the glycerol system the U_mf was found to be higher when compared to water. In the non‐Newtonian system (carboxymethylcellulose), U_mf decreased with increase in concentration in the range of the present study. The U_mf was found to be lower when compared to water as liquid phase. The modified gas‐perturbed liquid model was used to predict the minimum fluidization liquid velocity (U_lmf) for Newtonian and non‐Newtonian systems. Copyright © 2006 Society of Chemical Industry     

Effect of elevated temperature and silica sand particle size on minimum fluidization velocity in an atmospheric bubbling fluidized bed

The impact of temperature and particle size on minimum fluidizing velocity was studied and analyzed in a small pilot scale of bubbling fluidized bed reactor. This study was devoted to providing some data about fluidization to the literature under high temperature conditions. The experiments were carried out to evaluate the minimum fluidizing velocity over a vast range of temperature levels from 20 °C to 850 °C using silica sand with a particle size of 300–425 μm, 425–500 μm, 500–600 μm, and 600–710 μm. Furthermore, the variation in the minimum fluidized voidage was determined experimentally at the same conditions. The experimental data revealed that the U_mf directly varied with particle size and inversely with temperature, while ε_mf increases slightly with temperature based on the measurements of height at incipient fluidization. However, for all particle sizes used in this test, temperatures above 700 °C has a marginal effect on U_mf. The results were compared with many empirical equations, and it was found that the experimental result is still in an acceptable range of empirical equations used. In which, our findings are not well predicted by the widely accepted correlations reported in the literature. Therefore, a new predicted equation has been developed that also accounts for the affecting of mean particle size in addition to other parameters. A good mean relative deviation of 5.473% between the experimental data and the predicted values was estimated from the correlation of the effective dimensionless group. Furthermore, the experimental work revealed that the minimum fluidizing velocity was not affected by the height of the bed even at high temperature.     

The flow of solid particles in an aerated inclined channel

The dynamic behavior of the flow of solid particles in an inclined open channel with air flow introduced through a porous base plate was examined. The solid particle velocity distributions were measured in detail using an optical probe.Five types of flow patterns were found depending on the air velocity and the slope of the channel. They were: sliding flow, immature sliding flow, splashing flow, bubbling flow, and gliding flow. The first two could be observed when the air velocity was less than the minimum fluidization velocity, U_mf, for the particles. The last two were observed when it became higher than U_mf. Splashing flow occurred when the slope of the channel was steep.     

A new approach to the identification of transitions in fluidized beds

Earlier work with silica sand has indicated that in a system where a bed of particles is aerated at increasing superficial velocities, the von Neumann ratio, T, based on the bed pressure drop, may be useful in identifying both minimum fluidizing velocity, U_mf, and minimum bubbling velocity, U_mb. Plots of T^− 1 against superficial velocity exhibited significant change at velocities consistent with those where bed height first changed (onset of fluidization), the packed bed pressure drop underwent a transition from a monotonic linear function of superficial velocity to a steady value (onset of fluidization) and standard deviation of bed pressure drop rapidly increased (onset of bubbling). However, the suggestion that T might be a valid indicator of U_mf was supported by data for a single material only. In this paper additional data is presented that supports the suggestion that T might be useful in measuring U_mf, and also provides additional evidence for the potential utility of T in determining U_mb. In principle, this would allow a single campaign of pressure measurements to be used to identify both U_mf and U_mb.     

On the onset of incipient fluidization

The onset of incipient fluidization is investigated theoretically and simulated by a computational fluid dynamics (CFD) procedure. The onset of incipient instability in a particle bed is preceded by stable gas diffusion in the interstices and is caused by a critical momentum force that may overcome the inertia of the particles. The critical momentum force is provided by the critical superficial gas velocity U_c in the form of critical mass flux of diffusion. It is found that the first movement of particles may be predicted by a critical transient Rayleigh number determined by a critical superficial velocity equals to the minimum fluidization velocity, U_mf. The onset of incipient fluidization was found to occur at a critical transient Rayleigh number of 3.1, which is close to the lowest theoretical value for buoyancy convection in a porous medium bounded by free surfaces. Consequently the onset times of incipient fluidization may be predicted accurately. The finding has been found to be supported by the present CFD study, past experiments and simulations in the literature.     

The rise of a buoyant sphere in a gas-fluidized bed

The rise velocity, V, of a single sphere, released in the bottom of a bed of sand fluidized by air, was measured: the sphere had a diameter of 9.0 or 13.2 mm; its density ranged from 900 to . These experiments with a single sphere used: (i) a bubbling bed, diameter 141 mm, with 1.05<U/U_mf<2.00, (ii) a slugging bed, diameter 24 mm, with 1.70<U/U_mf<3.20. Here U is the fluidizing velocity; U=U_mf at incipient fluidization. It was found that, for each sphere in a given bed, V=V_mf+C(U-U_mf): the constant C was up to 10 times larger for bubbling beds than slugging beds.The rise velocity at incipient fluidization, V_mf, is governed, for both types of bed, by the apparent viscosity of the incipiently fluidized bed. Therefore, Stokes's law was used to predict V_mf, but using an important modification: since each buoyant sphere appears to carry on its top a defluidized ‘hood’ of particles, Stokes's law was applied to the composite ‘particle’ consisting of the sphere plus its hood. Analysis of the measured V_mf then gave the volume of the hood, in agreement with direct measurements of it above a fixed cylinder in a two-dimensional bed. In addition, the analysis gave the apparent viscosity of the incipiently fluidized bed to be 0.66 Pa s, in excellent agreement with the estimate of Grace (Can. J. Chem. Eng. 48 (1970) 30) for similar sand.     

Particle motion in L-valve as observed by positron emission particle tracking

L-valves are widely used in circulating fluidized beds (CFB) to control the solid circulation rate. Positron emission particle tracking (PEPT) is used to view and study the real-time particle motion in the L-valve. The paper presents experimental results of the solid motion and solid flux in the L-valve, G_s, as a function of the superficial injection air velocity, U. Results are compared with earlier work. The size of the L-valve is 4.5 cm I.D. Two different experimental configurations (L-valve discharge in a CFB riser and free discharge) were used. The L-valve flow regime is stable until approximately 6 U / U_mf, with proportionality between solid flux and U / U_mf. At a higher U / U_mf, unsteady fluctuations in the solid flow gradually increase due to cavity formation around the L-valve elbow. Increasing the air flow even further, a maximum flow is reached, corresponding to the maximum discharge rate through the cyclone or hopper apex. PEPT has also confirmed the existence of a dune flow. For the first time, it gives quantitative data of the velocity profile of the dune flow which is governed by two important factors. The first factor is the distance of solids from the base of the L-valve, with solid velocity increasing away from the base. The second factor is the location of solids with respect to the dune, i.e. solid velocity is minimum at the base of the dunes and maximum at the top of the dunes. The average voidage in the L-valve is approximately constant and independent of U.     

Numerical Simulation of Liquid–Solid Countercurrent Fluidization inside an Extraction Column Based on Particle Trajectory Model

The liquid–solid countercurrent fluidization process in an extraction column was numerically simulated based on the particle trajectory model of Eulerian–Lagrangian method. The simulation approach was validated by previous experiments. A power function correlation was proposed for dimensionless slip velocity U_slip/U_t and hold-up fraction ϕ, and the operational zone in the countercurrent fluidization was determined. Simultaneous countercurrent fluidization of particles with different diameters was also simulated. The comparison shows that the simulation results are consistent with the calculation values from the multi-particle free sedimentation model based on non-interference assumption, verifying the reliability of the approach in present work.     

Mass transfer to large particles in fluidised beds of smaller particles

A theory is proposed for predicting the transfer of a gas through a fluidised bed of small particles to a large particle. It is proposed that non steady-state mass transfer of the gas occurs by two mechanisms: (i) mass transfer of gas in clusters or packets of the smaller particles approaching the large particle; and (ii) gas convection. The theory developed enables prediction of the Sherwood number (N_sh, the dimensionless mass transfer coefficient) for a large particle, diameter d: N_sh=2ε_mf+$\text{4}\text{g3}\text{mfd}\text{(U}\text{mf}\text{ε}\text{mf}\text{+}\text{uinb}$)/π D_A${}^1{}^2$ where U_mf is the minimum fluidising velocity, εmf is the bed voidage at U_mf-0u_b is the mean bubble rise velocity and D_A is the gas diffusivity. This equation is shown to be in excellent agreement with Sherwood numbers determined from combustion experiments in which single large particles of petroleum coke were burned in air fluidised beds over a wide range of operating conditions. It is also shown that predictions using this expression are in close agreement with those from an empirical expression previously proposed by the autho     

Étude hydrodynamique des lits fluidisés sous vide et sous haute température

After having analyzed the few literature results concerning fluidized beds hydrodynamics under reduced pressure, new theoretical elements are proposed which provide an estimation of the beginning and finishing fluidization velocities. Numerous experimental results(U_mfapp, U_mb, U_mp, ?_mf, ?_mb, ?_mp), obtained at 20 and 500°C, are then presented for several sub-atmospheric pressures. Finally, f& the first time, at leastto our knowledge, by high frequency recording pressure drops through the bed, the influence of pressure decreases on the hydrodynamics is accurately analyzed.     

Determination of minimum fluidization velocity by pressure fluctuation measurement

Using the standard deviation of pressure fluctuations to find the minimum fluidization velocity, U_mf, avoids the need to de-fluidize the bed so U_mf, can be found for operational bubbling fluidized beds without disrupting the process provided only that the superficial velocity may be altered and that the bed remains in the bubbling fluidized state. This investigation has concentrated on two distinct aspects of the pressure fluctuation method for U_mf determination: (1) the minimum number of pressure measurements required to obtain reliable estimates of standard deviation has been identified as about 10000 and (2) pressure fluctuation measurements in the plenum below the gas distributor are suitable for U_mf determination so the problems of pressure probe clogging and erosion by bed particles may be avoided.     

The effects of particle and gas properties on the fluidization of Geldart A particles

We report on 3D computer simulations based on the soft-sphere discrete particle model (DPM) of Geldart A particles in a 3D gas-fluidized bed. The effects of particle and gas properties on the fluidization behavior of Geldart A particles are studied, with focus on the predictions of U_mf and U_mb, which are compared with the classical empirical correlations due to Abrahamsen and Geldart [1980. Powder Technology 26, 35-46]. It is found that the predicted minimum fluidization velocities are consistent with the correlation given by Abrahamsen and Geldart for all cases that we studied. The overshoot of the pressure drop near the minimum fluidization point is shown to be influenced by both particle-wall friction and the interparticle van der Waals forces. A qualitative agreement between the correlation and the simulation data for U_mb has been found for different particle-wall friction coefficients, interparticle van der Waals forces, particle densities, particle sizes, and gas densities. For fine particles with a diameter , a deviation has been found between the U_mb from simulation and the correlation. This may be due to the fact that the interparticle van der Waals forces are not incorporated in the simulations, where it is expected that they play an important role in this size range. The simulation results obtained for different gas viscosities, however, display a different trend when compared with the correlation. We found that with an increasing gas shear viscosity the U_mb experiences a minimum point near , while in the correlation the minimum bubbling velocity decreases monotonously for increasing μ_g.