The solids flow in the CFB-riser quantified by single radioactive particle tracking

Single radioactive particle tracking was used to measure the overall solids residence time (and its distribution) in the riser of a CFB, operating at superficial air velocities (U) of 1 to 9 ms^− 1 and solids circulation fluxes (G) between 20 to 600 kg m^− 2s^− 1.The results demonstrate that the particle motion and mixing differ according to the operating mode of the riser, with a fairly constant velocity throughout the riser achieved in the dilute or dense riser flow, but with a significant amount of back-mixing for intermediate values of U and/or G. This back-mixing is due to the core-annulus mode of particle flow. Whereas experimental results and theoretical predictions are in fair agreement for the dilute and dense riser flow, the core-annulus regime needs to account for a U and G dependent slip factor (φ), in excess of the commonly proposed value φ = 2, especially at U-U_TR < 2 ms^− 1.Moreover, the previously published riser operation diagram is confirmed by the experiments, although a further analysis of the core-annulus regime is needed.     

Effects of riser height and total solids inventory on the gas-solids in an ultra-tall CFB riser

More and more CFB boilers with large capacity and ultra-tall furnaces are used for power generation. Understanding the fluid dynamics in the ultra-tall furnace is important. However, existing studies on fluid dynamics in the CFB furnace are limited to the risers with rather short height. An experimental study was conducted with a cold CFB test rig of 240 mm in I.D. and 38 m and 54 m in height respectively. The influences of total solid inventory I_v, and fluidizing gas velocity U_g on the axial voidage profile along the riser and solid circulation rate G_s were investigated. Experimental results showed that when U_g exceeded the transport velocity, an S-shaped voidage profile characterized by fast fluidization was established in the riser. In such circumstance, the voidage at top dilute section kept constant and G_s reached saturation carrying capacity (G_s = G_s^?) and inappreciably change with riser height and I_v. Moreover, G_s^? increased from 40 kg to 50 kg when the riser height increased from 38 m to 54 m. The results indicated that even for the 600 MWe supercritical CFB boiler with a 54 m tall furnace, only a modest increase of I_v and power of forced draft fans is needed to obtain high enough G_s to meet the requirements of heating surfaces arrangement in furnace and the circulation loop. The necessary conditions to form the S-shaped profile of voidage in the riser were also discussed.     

Hydrodynamic modeling of a circulating fluidized bed

Hydrodynamics plays a crucial role in defining the performance of circulating fluidized beds (CFB). The numerical simulation of CFBs is very important in the prediction of its flow behavior. From this point of view, in the present study a dynamic two dimensional model is developed considering the hydrodynamic behavior of CFB. In the modeling, the CFB riser is analyzed in two regions: The bottom zone in turbulent fluidization regime is modeled in detail as two-phase flow which is subdivided into a solid-free bubble phase and a solid-laden emulsion phase. In the upper zone core-annulus solids flow structure is established. Simulation model takes into account the axial and radial distribution of voidage, velocity and pressure drop for gas and solid phase, and solids volume fraction and particle size distribution for solid phase. The model results are compared with and validated against atmospheric cold bed CFB units' experimental data given in the literature for axial and radial distribution of void fraction, solids volume fraction and particle velocity, total pressure drop along the bed height and radial solids flux. Ranges of experimental data used in comparisons are as follows: bed diameter from 0.05-0.418 m, bed height from 5-18 m, mean particle diameter from 67-520 μm, particle density from 1398 to 2620 kg/m³, mass fluxes from 21.3 to 300 kg/m²s and gas superficial velocities from 2.52-9.1 m/s.As a result of sensitivity analysis, the variation in mean particle diameter and superficial velocity, does affect the pressure especially in the core region and it does not affect considerably the pressure in the annulus region. Radial pressure profile is getting flatter in the core region as the mean particle diameter increases. Similar results can be obtained for lower superficial velocities. It has also been found that the contribution to the total pressure drop by gas and solids friction components is negligibly small when compared to the acceleration and solids hydrodynamic head components. At the bottom of the riser, in the core region the acceleration component of the pressure drop in total pressure drop changes from 0.65% to 0.28% from the riser center to the core-annulus interface, respectively; within the annulus region the acceleration component in total pressure drop changes from 0.22% to 0.11% radially from the core-annulus interface to the riser wall. On the other hand, the acceleration component weakens as it moves upwards in the riser decreasing to 1% in both regions at the top of the riser which is an important indicator of the fact that hydrodynamic head of solids is the most important factor in the total pressure drop.     

Effect of air flowrate on particle velocity profile in a circulating fluidized bed

The research was conducted in a cold flow circulating fluidized bed (CFB). The diameter and height of riser are 5 and 200 cm, respectively. The objective is to study effect of gas velocity on hydrodynamic of glass beads having mean diameter of 547 micron and density of 2,400 kg/m³. The measurement of particle velocity profile was achieved by using a high-speed camera and an image processing software. A probe of 0.5 cm in diameter was inserted into the riser at the height of 110 cm from gas distributor and was set at 3 positions along the radius of the riser; 0, 0.6, and 1.8 cm from center. Transport velocity (U _tr ), core-annulus velocity (V _CA ) and minimum pneumatic velocity (V _mp ) were employed in determining solid flow pattern in the riser. It was observed that the flow regimes changed from fast fluidization to core-annulus and to homogeneous dilute bed when the gas velocities increased from 7, 8 and 9 m/s, respectively. The results from high-speed camera showed that glass beads velocity existed a maximum value at the center of the riser and gradually decreased toward the wall for all three gas velocities. It was also found that most of solid traveled upward in the core of the riser, however, solid traveled downward was identified at the wall layer.     

Solids mixing in a down-flow circulating fluidized bed of 0.418-m in diameter

The axial and lateral solids mixing in a down-flow circulating fluidized bed of 0.418-m diameter was investigated by a pneumatic injection phosphor tracer technique (PIPTT). The axial and lateral solids dispersion were determined by measuring the solids RTD at same axial but different lateral positions using point sources for tracer injection. A two-dimensional dispersion model described the measured RTD curves satisfactorily. The results were compared to those obtained in the small scale downers and the scale-up effect was investigated. The axial solids Peclet number Pe_a is around 110 and invariable with changing U_g, G_s and ?_s, while the lateral solids Peclet number Pe_r is linearly increasing with ?_s. And Pe_r is found to decrease with the square root of inner diameter (ID) in comparison with the results obtained in small ID downers. Correlation of Pe_r, Pe_r = (15 + 70.7 ?_s)D^− 0.5, is proposed.     

The solids flow in the riser of a Circulating Fluidised Bed (CFB) viewed by Positron Emission Particle Tracking (PEPT)

Circulating Fluidised Beds (CFB) are attracting increasing interest for both gas-solid and gas-catalytic reactions, although the operating modes in these two cases are completely different. In modelling CFBs as reactors, the solids residence time is an important parameter. Previous studies mostly assess operations at moderate values of the solids circulation rates (≤ 100 kg/m² s), whereas gas-catalytic reactions and e.g. biomass pyrolysis require completely different operating conditions. In the current work, Positron Emission Particle Tracking (PEPT) is used to study the movement and population density of particles in the CFB-riser.The PEPT results can be used to obtain: (i) the vertical particle movement and population density in a cross sectional area of the riser; (ii) the transport gas velocity (U_tr) required in order to operate in a fully established circulation mode; (iii) the overall particle movement mode (core flow versus core/annulus flow); and (iv) the particle slip velocity (U_s).Only in a core flow mode can the particle slip velocity be estimated from the difference between the superficial gas velocity (U) and the particle terminal velocity (U_t). The slip velocity is lower than U − U_t outside the core flow mode. To operate in core flow, the superficial gas velocity should exceed U_tr by approximately 1 m/s and the solids circulation rate should exceed 200 kg/m² s.     

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.     

Flow structure and thickness of annular downflow layer in a circulating fluidized bed riser

Flow structures were determined in a circulating fluidized bed (CFB) riser (0.203 m i.d.×5.9 m high) of FCC particles (d_p=70 μm, ρ_s=1700 kg/m³). A momentum probe was used to measure radial momentum flux profiles at several levels and to distinguish between upward and downward flow regions. Time-mean dynamic pressure (ΔP_m) decreases towards the wall in the range U_g=5-8 m/s, G_s=10-340 kg/m² s. The thickness of the annular downflow layer based on ΔP_m=0 reaches a maximum with increasing height. The annular downflow layer disappears locally with increasing solids mass flux (G_s) at a constant gas velocity, with achievement of the dense suspension upflow (DSU) regime. A new correlation is developed to predict the time-mean thickness of solids down-flowing layer based on solids mass flux and momentum flux. It successfully accounts for the variation of the annular layer thickness with height and G_s, and covers a wide G_s range right up to near the onset of the DSU regime.     

Influence of the lift force closures on the numerical simulation of bubble plumes in a rectangular bubble column

Numerical Eulerian-Eulerian simulations of the unsteady gas-liquid flow in a centrally aerated two-dimensional bubble column were carried out in order to understand the effect of different formulations of the lift force coefficient (C_L) on the computational results. Three different values of the superficial gas velocity (U_G=2.4, 12.0 and 21.3 mm s⁻¹) that ensure the existence of different flow regimes were experimentally and computationally studied. The validation of the simulated results was based on visual observations and measurements of the global gas hold-up (ε_G) and the plume oscillation period (POP). The results presented reveal that, at U_G=12.0 and 21.3 mm s⁻¹, using C_L<0 results in under- and over-estimation of the ε_G and POP, respectively. On the other hand, taking C_L>0 does not affect the POP while it leads to increasingly higher ε_G values, which are different from those experimentally reported. At U_G=2.4 mm s⁻¹, the effect of the lift force is not so evident, although it slightly improves the prediction of experimental values. Particularly interesting is the case of C_L>0.4 at U_G=21.3 mm s⁻¹, producing a non-symmetric bubble plume oscillation. Since using Tomiyama's lift coefficient correlation does not improve the results, including the lift force into the simulation of bubble plumes is not recommended.     

Experimental study of high-density gas-solids flow in a new coupled circulating fluidized bed

Experiments were carried out in a specially designed high-density coupled circulating fluidized bed system. Fluidized catalytic cracking (FCC) particles (ρ_p=1300 kg/m³, d_p=69 μm) were used. When the solids circulation flux is 400 kg/m²·s, the apparent solids holdup exceeds 20% near the top of the riser A, and the volumetric solids fraction (apparent solids holdup) is larger than 5.2% in the fully developed region of the downer. Hence, a high particle suspension density covers the entire coupled CFB system. Under the high-density conditions, the primary air rate had a small influence on the solids circulation flux, while the secondary air rate had an important effect on it. The results indicate a particle acceleration region and a fully developed region were identified along the downer from the pressure gradient profiles. In the fully developed region of the downer, the volumetric solids fraction increases with increasing solids circulation flux or decreasing superficial gas velocity U₁.     

Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

气固循环流化床提升管环核区颗粒质量传递系数的估计

Based on analysis of energy dissipation in the core region of gas-solid fluidized bed risers,a simplified model for determination of core-annulus solids mass transfer coefficient was developed according to turbulent diffu- sion mechanism of particles.The simulation results are consistent with published experimental data.Core-annulus solids mass transfer coefficient decreases with increasing particle size,particle density and solids circulation rate, but generally increases with increasing superficial gas velocity and riser diameter.In the upper dilute region of gas-solid fiuidized bed risers,core-annulus solids mass transfer coefficient was found to change little with the axial coordinate in the bed.     

Flow behavior and regime transition in a high-density circulating fluidized bed riser

Flow behavior and flow regime transitions were determined in a circulating fluidized bed riser (0.203 m i.d. × 5.9 m high) of FCC particles (, ). A momentum probe was used to measure radial profiles of solids momentum flux at several heights and to distinguish between local net upward and downward flow. In the experimental range covered (; ), the fast fluidization flow regime was observed to coexist with dense suspension upflow (DSU). At a constant gas velocity, net downflow of solids near the wall disappeared towards the bottom of the riser with increasing solids mass flux, with dense suspension upflow achieved where there was no refluxing of solids near the riser wall on a time-average basis. The transition to DSU conditions could be distinguished by means of variations of net solids flow direction at the wall, annulus thickness approaching zero and flattening of the solids holdup versus G_s trend. A new flow regime map is proposed distinguishing the fast fluidization, DSU and dilute pneumatic transport flow regimes.     

Granular temperature in a liquid fluidized bed as revealed by diffusing wave spectroscopy

We report granular temperature and solid fraction fields for a thin rectangular bed (20×200 mm cross-section and 500 mm high) of glass particles (mean diameter of 165 μm and density of 2500 kg/m³) fluidized by water for superficial velocities ranging from 0.05U_t, which is approximately double the minimum fluidization velocity, to 0.49U_t, where U_t is the particle terminal velocity estimated by fitting the Richardson-Zaki correlation to the bed expansion data. At superficial velocities below 0.336U_t, the solid fraction and granular temperature are uniform throughout the bed. At higher superficial velocities, the solid fraction tends to decrease with height above the distributor, whilst the granular temperature first increases to a maximum before decaying towards the top of the bed. Correlation of the mean granular temperature with the mean solid fraction and the local granular temperature with the local solid fraction both suggest that the granular temperature in the liquid fluidized bed can be described solely in terms of the solid fraction. The granular temperature increases monotonically with solid fraction to a maximum at φ≈0.18 where it then decreases monotonically as φ approaches the close-packed limit.     

Particle velocities and their residence time distribution in the riser of a CFB

The riser of a Circulating Fluidised Bed (CFB) is the key-component where gas-solid or gas-catalytic reactions occur. Both types of reactions require different conditions of operating velocities (U), solids circulation fluxes (G), overall hydrodynamics and residence times of solids and gas. The solids hydrodynamics and their residence time distribution in the riser are the focal points of this paper. The riser of a CFB can operate in different hydrodynamic regimes, each with a pronounced impact on the solids motion. These regimes are firstly reviewed to define their distinct characteristics as a function of the combined parameters, U and G.Experiments were carried out, using Positron Emission Particle Tracking of single radio-actively labelled tracer particles. Results on the particle velocity are assessed for operation in the different regimes. Design equations are proposed.The particle velocities and overall solids mixing are closely linked. The solid mixing has been previously studied by mostly tracer response techniques, and different approaches have been proposed. None of the previous approaches unambiguously fits the mixing patterns throughout the different operating regimes of the riser. The measured average particle velocity and the velocity distribution offer an alternative approach to determine the solids residence time distribution (RTD) for a given riser geometry. Findings are transformed into design equations.The overall approach is finally illustrated for a riser of known geometry and operating within the different hydrodynamic regimes.     

Dependence of particle fluctuation velocity on gas flow, and particle diameter in gas fluidized beds for monodispersed spheres in the Geldart B and A fluidization regimes

In this paper we present new experimental data on the steady-state, mean squared, fluctuation velocity, or granular temperature, of Geldart B polymer, glass, nickel, and stainless steel monodispersed spheres averaged over the wall of a gas fluidized bed, as a function of gas flow and sphere diameter. The granular temperature is obtained by Acoustic Shot Noise technology—namely power spectral analysis of the steady state vibrational energy of the wall excited by random sphere impact, and calibrated by hammer excitation over the wall. The new data extends to polymer and metallic spheres the experimental discovery of a 1996 paper of Cody et al. that the fluctuation velocity of Geldart B glass spheres when scaled to the gas superficial velocity, U_s, is inversely proportional to sphere diameter, directly proportional to a fundamental length scale, D_o^B, and is a universal function of U = (U_s / U_mf). We also demonstrate that the new data is consistent with the diameter dependence of the fluctuation velocity that can be derived from both the 1997 paper of Menon and Durian, who measured random sphere motion near the wall through the spectroscopy of scattered laser light, and the 1992 paper of Rahman and Campbell, who measured the average granular pressure of random sphere impact on a porous steel membrane. While the inverse scaling of the fluctuation velocity with sphere diameter, and the existence of a fundamental length scale for gas fluidization, D_o^B, had not been a feature of any published fundamental model, or computer simulation, of the steady state granular temperature of spheres in gas fluidized beds, we show that it is a feature of two recent dense kinetic fluidization models published in 1999, by Buyevich and Kapbasov, and Koch and Sangani. Both theories implicitly define a fundamental length scale for the fluctuation velocity, D^? = (μ_f² / ρ_p²g)^1 / 3, where ρ_p is the sphere density, μ_f is the gas viscosity, and g is the laboratory gravitational field. The new data for polymer, glass, nickel and stainless steel spheres presented in this paper, defines D_o^B = (56 ± 2)D^?. We use the Anderson-Jackson stability model to show that the length scale D_o^B, also defines a stability length scale, such that for D < D_o^B(D > D_o^B), the uniform dense phase of the fluidized bed is stable (unstable), against one dimensional, first order fluctuations in sphere concentration. The length scale, D_o^B is thus the theoretical equivalent to the empirical scaling length introduced by Geldart, D_B/A, to distinguish spheres (D > D_B/A) that bubble at fluidization, from spheres (D < D_B/A) that fluidize before bubbling. Finally, we present new experimental data, on the remarkable changes in the granular temperature, bed expansion, and bed collapse time, between Geldart B and Geldart A monodispersed glass spheres, and compare that data to granular temperature, and bed expansion, for Geldart A rough, non-spherical, log-normal dispersed diameter catalytic particles.     

Synthesis and characterization of the LDH hydrotalcite-pyroaurite solid-solution series

A layered double hydroxide (LDH) hydrotalcite-pyroaurite solid-solution series Mg₃(Al_xFe_1 − x)(CO₃)_0.5(OH)₈ with 1 − x = 0.0, 0.1……1.0 was prepared by co-precipitation at 23 ± 2 °C and pH = 11.40 ± 0.03. The compositions of the solids and the reaction solutions were determined using ICP-OES (Mg, Al, Fe, and Na) and TGA techniques (CO₃²⁻, OH⁻, and H₂O). Powder X-ray diffraction was employed for phase identification and determination of the unit cell parameters a_o and c_o from peak profile analysis. The parameter a_o = b_o was found to be a linear function of the composition. This dependency confirms Vegard's law and indicates the presence of a continuous solid-solution series in the hydrotalcite-pyroaurite system. TGA data show that the temperatures at which interlayer H₂O molecules and CO₃²⁻ anions are lost, and at which dehydroxylation of the layers occurs, all decrease with increasing mole fraction of iron within the hydroxide layers.Features of the Raman spectra also depend on the iron content. The absence of Raman bands for Fe-rich members (x_Fe > 0.5) is attributed to possible fluorescence phenomena.Based on chemical analysis of both the solids and the reaction solutions after synthesis, preliminary Gibbs free energies of formation have been estimated. Values of ΔG°_f(hydrotalcite) = − 3773.3 ± 51.4 kJ/mol and ΔG°_f(pyroaurite) = − 3294.5 ± 95.8 kJ/mol were found at 296.15 K. The formal uncertainties of these formations constants are very high. Derivation of more precise values would require carefully designed solubility experiments and improved analytical techniques.     

Experimental and numerical simulation studies of the fluidization characteristics of a separating gas-solid fluidized bed

Gas-solid fluidized bed separation expands the choices of highly efficient dry coal beneficiation methods. The hydrodynamics of 0.3-0.15 mm large Geldart B magnetite powder were studied using a combination of experimental and numerical methods to optimize the design of the solid medium used in the fluidized bed. The results show that the Syamlal-O'Brien drag model is suitable for simulating the bed and it is verified that simulated and experimental results are consistent with each other. If the static bed height is no more than 300 mm then the bed height has minimal effect on the fluidization characteristics. As the superficial gas velocity increases the bed activity is improved. However, at the same time the uniformity and stability of the bed drop. Therefore, the gas velocity should be adjusted to no more than 2.0U_mf. The density of the Geldart B bed is uniform and stable, which indicates a relatively high fluidization quality. Furthermore, compounded medium solids consisting of < 0.3 mm magnetite powder with a 0.3-0.15 mm particle content of 65.25% and < 1 mm fine coal were used in a pilot gas-solid fluidized bed of 5-10 ton/h capacity. The pilot bed was used to separate 50-6 mm coal. This test resulted in the coal ash content being reduced from 23.74% to 11.79% with a probable error, E, of 0.07 g/cm³ and a recovery efficiency of 98.26%. This indicates that the bed has good separating performance. Nevertheless, to increase the applicability of the separating bed a further study emphasizing a decrease in the lower size limit of the magnetite powder should be performed.     

The nature of the flow just above the perforated plate distributor of a gas-fluidised bed, as imaged using magnetic resonance

Flow patterns within a 3D bed of oil-containing seeds fluidised by nitrogen have been observed for the first time using magnetic resonance imaging (MRI). Attention was focused on the lower region of the bed, just above the multi-orifice distributor: the orifices were 1.0 or 1.5 mm in diameter with square or triangular layouts, of pitch 7-10 mm. Two sizes of seeds were used: 1.2 and 0.50 mm. Each MRI image was a time-average over and measured the local concentration of seeds. Values of U/U_mf were in the range 0.0-3.6, where U is the superficial gas velocity and U=U_mf at incipient fluidisation. The images revealed:

(1)

There was a substantial ‘jet’ above each orifice in the distributor, remarkably these ‘jets’ were found even when U?U_mf. The length of a ‘jet’ increased with U/U_mf. Because of the time-averaged nature of the measurements, a ‘jet’ could be: (a) a permanent void, (b) a stream of bubbles, or (c) a ‘jet’ followed by bubbles.

(2)

When U/U_mf<1.0, the particles surrounding each ‘jet’ were in motion. This was apparent, particularly as U/U_mf approached 1.0, even though the bed was not fully fluidised at all points.

(3)

When U/U_mf>1.0, the upper parts of the ‘jets’ merged with each other forming a central dilute core. For the first time, a time-averaged velocity map over a horizontal plane was obtained; it demonstrated that the central core was rising upwards and that the surrounding material was descending.

(4)

Between each pair of ‘jets’, there was a small region of motionless particles sitting on the upper surface of the distributor, forming a fixed dead zone. A criterion for the maximum pitch of the orifices, to minimise the volume of this dead zone between pairs of ‘jets’, has been derived.

Simple correlations between dimensionless groups summarise the measurements well, giving the length and half angle of a ‘jet’ in terms of the gas velocity and other variables. These correlations are consistent with published results and include a dependence on the pitch of the orifices, which was found to be important.     

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.