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Knowledge of the division of gas flow between the bubble and dense phases is important for modelling and operation of bubbling fluidized beds. The two-phase theory of fluidization, which suggested that the bubble flow rate being equal to the excess gas flow above the incipient fluidization, has been proved to be an overestimation in most cases. While the two-phase theory has been modified by introducing a correction factor (Y), most previous studies were conducted for Geldart Group A powders. In the present work, the contribution to predict the parameter Y for Geldart Group B and D particles has been formulated based on almost all the available experimental data. The experimental results demonstrated that the Y value increases with decreasing particle size or density and increasing excess gas velocity. A new correlation has been developed to estimate the Y value for Geldart Group B and D particles Y = 1.72 Ar − 0.133 U g − U mf 0.024 with an overall standard deviation of 19%. It only requires the knowledge of Archimedes number and excess gas velocity. This correlation is in reasonable agreement with almost all the available data in literature and the present work.

In the present article, evaporation of a liquid drop spreading on hot surface, based on the lattice Boltzmann method, is simulated. Liquid and gas phases are considered to be incompressible. The divergence-free condition of the velocity field is no longer satisfied since the phase change occurs at the interface. In order to take into account the vaporization effects, the convective Cahn–Hilliard equation is extended. The phase change process is modeled by employing a proper source term at the interface. The D2Q9 structure is used in the present simulation. Effects of different non-dimensional parameters including the Bond number, liquid Archimedes number, gas Stefan number, density ratio, and the Prandtl number on behavior of liquid drop are investigated. Computational results showed that increasing the Bond number, liquid Archimedes number and density ratio accelerates the evaporation rate. The Leidenfrost regime is observed in high Stefan numbers, while in low Stefan numbers, the drop is attached to the heated wall. Furthermore, decreasing the equilibrium contact angle leads to the lagging of the Leidenfrost regime.

Prediction of horizontal pressure drop in dilute phase pneumatic conveying or slurry transport is among the fundamental issues of designing these systems. In this work a thorough literature survey demonstrates that there is no consensus on an integrative solution for conveying pressure drop, therefore a large data base of conveying systems' operating points at dilute phase is established and analyzed. It includes measurements taken at our 52 mm bore laboratory pneumatic conveying line, as well as thousands of data points collected from the literature. Two modelling approaches are attempted – the first is frictional representation based on dimensional analysis, which presents linear dependency between the pressure drop and the superficial fluid velocity normalized by the minimum pressure velocity of the transport curve. It had also been found that the pressure drop increase rate has a strong dependency on the Archimedes number. The second approach is an energy balance between the power of the drag force applied to the particles and the additional power required to drive the fluid due to particle presence. Unlike the common expressions, a modification to the drag coefficient is suggested, which takes into account pipe turbulence and particle acceleration. The two presented models do not require pilot plant calibration, and an applicability of one of them to slurry transport is demonstrated. Some future research routes are offered.

This paper presents a numerical simulation of a liquid droplet evaporation during penetration in a porous medium based on lattice Boltzmann method. The binary-fluid model of Lee, which is applicable to high density ratio, is combined with a passive scalar LB thermal model to simulate two-phase flow. A proper source term is incorporated at the phase interface, and the classical convective Cahn–Hilliard equation in the presence of phase change is employed in the multiphase LB framework of Lee. Effects of different non-dimensional parameters including the Archimedes number, the Bond number, the Stefan number, the Prandtl number, the porosity, contact angle and density ratio on the penetration of liquid inside the porous media and the droplet evaporation are investigated and temperature profiles, flow fields, mass source contours are analyzed. Increasing the Bond number, the Archimedes number and density ratio will decrease the penetration rate, and accelerates the evaporation. Also, increasing the Stefan number and porosity accelerate the evaporation, while increasing the Prandtl number leads reduction in evaporation rate.

The aim of present analysis is to investigate the effects of heat source/sink, chemical and material composition on steady MHD mixed convection axisymmetric flow of an incompressible Maxwell fluid between two infinite stretching disks in the presence of viscous dissipation and Joule heating. The lower disk is subjected to an exothermic surface reaction, while an upper disk is maintained at uniform temperature and concentration. Also an exothermal surface reaction modeled by Arrhenius kinetics supplied heat to the Maxwell fluid. Similarity transformations are used for simplifying equations governing the flow, thermal fields, material and chemical composition fields. The analytic solution of dimensionless governing ordinary differential equations is successfully obtained using homotopy analysis method (HAM). Here, convergence of the derived series solution is ensured. We mainly focus on the effects of Hartmann number, Archimedes number, Eckert number, Prandtl number, heat generation or absorption parameter, activation energy parameter, chemical reaction parameter on dimensionless velocity, pressure, temperature and concentration distribution. The results with several values of the problem parameters are expressed graphically. To understand the behavior of flow between stretching isothermal and exothermal disks, the values of skin friction coefficient, Nusselt number and Sherwood number are tabulated for both lower and upper disks. Further, the critical value of Frank-Kamenetskii are presented through graphs and tables and discussed for different values of parameters involved in problem.

This work presents a volume-filtered formulation for describing chemically reacting flows in the presence of solid catalytic particles. The equations are discretized in a Eulerian–Lagrangian framework and applied to flows of isothermal, heterogeneously reacting chemical species in fully developed three-dimensional risers. The aim of this study is to identify and quantify the influence of particle clusters on heterogenous reactions. The Archimedes number, Ar, is varied from 500 to 12,500, and the Damkohler number, Da, from 0.1 to 10. To assess the multiphase dynamic effects on the chemistry, conversion times from the three-dimensional simulations are compared to a zero-dimensional model that solves for the temporal evolution of the species mass fraction and ignores all spatial variations. The conversion process associated with the three-dimensional simulations is shown to be significantly longer compared to the zero-dimensional solution, with an increasing effect for larger values of Da. The discrepancies can be fully attributed to the presence of clusters, which are accounted for in the zero-order equations by an additional term that contains the covariance between species mass fraction and particle volume fraction fluctuations, which needs to be modeled. To this purpose, contributions to the fluctuating chemical source term are evaluated from the three-dimensional data and discussed, and a presumed-shape probability distribution function (PDF) approach is investigated. This PDF approach models the fluctuating chemical source term by a product of a beta distribution for the species mass fraction and a lognormal distribution for the particle concentration, and yields a mean species solution that agrees very well with the three-dimensional results for the range of Ar and Da considered in this study.

Hydrodynamic similarity in the liquid–solid circulating fluidized bed systems under different operating conditions was investigated. The experimental data obtained from this work and in the literature show that when the scaling parameter, Gs/(ρpjl), is modified as (ja/jl), ratio of auxiliary liquid velocity to total liquid velocity, a detailed hydrodynamic similitude of the liquid–solid circulating fluidized risers under different operating conditions can be achieved. Furthermore, the experimental results from different liquid–solid flow systems show that as long as (ja/jl)0.3 remains constant, the solid concentrations in the zone of CFB risers increase linearly. Archimedes number, Ar, Galileo number and Froude number, FrD were used to use the modified scaling parameter, (ja/jl), without power. Experimental results show that as long as Ar− 0.07(ja/jl), Ga− 0.07(ja/jl) and FrD− 0.07(ja/jl) is maintained, the similarity of the liquid–solid circulating fluidized bed riser is obtained using the new similarity parameter without using power. The empirical similarity parameter, (ja/jl), appears to have incorporated the effects of operating parameters (Gs and jl).

The axial dispersion coefficient of liquid in downflow slurry bubble column is estimated experimentally by the residence time distribution (RTD) technique. Its variation with superficial gas and slurry velocities, separator pressure, and slurry concentration is analyzed. The axial dispersion coefficient is correlated in terms of dispersion number with the velocity ratio of slurry to gas, Archimedes number, and Reynolds number by dimensional analysis. The mixing time is represented by the isotropic turbulence theory. We found that the axial dispersion coefficient in this present gas-liquid-solid three-phase downflow bubble column is an order of magnitude higher than that in upflow three-phase system. The dispersion coefficient of bubble motion (Db) and the velocity characteristic factor (k) are analyzed based on velocity distribution theory. The present study may be useful for further understanding and developing of specific multiphase reactor in industrial applications.

The rotary chamber technique is capable of observing small levitated bubbles in liquid for various research purposes. The present paper focuses on diffusion of a small spherical bubble into undersaturated water. The decaying bubble size is recorded in time by image processing. The results are plotted as Sherwood versus Reynolds number where the Schmidt number is of order 300. Similarity is found for each of four gases in water. The boundary layer prediction Sh is confirmed in general. A physically accountable model provides a good representation of results.

Experimental data available in the literature for bed voidage and bed expansion index of biofilm-coated particles in a fluidized bed was extracted, sorted and used to study the validation of the proposed bed expansion index equations in the literature. Drag coefficients of biofilm-coated particles for all the aforementioned data were calculated using a new proposed equation [1] that describes drag forces as a function of Archimedes numbers. Archimedes number was proposed to be superior to Reynolds number for bed expansion definition. New equations based on Archimedes number and physical properties of biofilm-coated particles were proposed to calculate the bed expansion index of fluidized biofilm-coated particles as well as bed voidage in fluidized bed bioreactors. The new equations predicted the existing experimental bed expansion index and voidage with less standard average error than all other literature equations that related bed expansion to Reynolds number.

Thus far, studies on the effects of the polydisperse size distribution on the minimum particle entrainment velocity (UPU) in horizontal pneumatic transport are limited to binary mixtures of sandlike particles. Herein we experimentally investigate UPU of ternary mixtures involving large (i.e., 400 and 170 μm) and fine particles (40 μm), where the roles of the fine particles in the entrainment of the large particles are elucidated. The presence of the 40 μm particles below ≈20% (w/w) enhances the entrainment of the 400 and 170 μm particles attributed to the high interstitial velocity of the conveying air because the fine particles occupy the interstitial spaces of the larger particles. Similar to monodisperse particles, a master curve of the particle Reynolds number versus Archimedes number is obtained for the ternary mixtures. From the master curve, a new empirical correlation for polydisperse UPU is derived using the Sauter mean diameter, where improved UPU predictions are demonstrated.

In gas-solid riser flows, meso-scale structures affect the overall performance significantly. The two-fluid model (TFM) with structure-dependent EMMS (energy-minimization multi-scale) drag coefficient has proved to allow grid-independent solutions of the effect of meso-scale structures, and succeeded in predicting riser flows with the Geldart A particles (Lu et al., 2009, Chem. Eng. Sci., 64: 3427-3447). In this paper, to investigate the effects of particle properties on these meso-scale structures, for all particle types, two-fluid modeling with and without consideration of meso-scale structures were performed and compared. Generally, the modeling with EMMS drag coefficient shows better results than without considering meso-scale structures, but their discrepancy decays with the Archimedes number. (C) 2011 Elsevier Ltd. All rights reserved.

Experiments were conducted to investigate the hydrodynamic behaviour of lithium titanate (Li(2)TiO(3)) in gas-solid fluidized bed. The objective of the study was to study the fluidization properties of Li(2)TiO(3) particles. These studies will be useful to find the applicability of fluidization to increase the effective thermal conductivity and wall to bed heat transfer coefficient of Li(2)TiO(3) particulate bed in test blanket module of fusion reactor. Li(2)TiO(3) was synthesized by solid state reaction process and different particle sizes were classified. Experiments were conducted in a cylindrical column of 90 mm diameter and 650 mm height in perspex material with metallic distributor plate. Dry compressed air was used as fluidizing medium. From the experiments it was observed that Li(2)TiO(3) is fluidizable, but severe slugging and bubbling were observed in the fluidized bed. Minimum fluidization and bubbling velocity of Li(2)TiO(3) particles were determined and compared to that of white sand of similar particle size and density. The experimental details and observations are discussed in this paper. (C) 2011 Elsevier B.V. All rights reserved.

A method is described to estimate solid mass flow rate based on measurement of pressure drop in horizontal section of circulating fluid bed (CFB). A theoretical model was derived based on momentum balance equation and used to predict the solids flow rate. Several approaches for formulating such models are compared and contrasted. A correlation was developed that predicts the solids flow rate as a function of pressure drop measured in the horizontal section of piping leading from the top of the riser to the cyclone, often referred to as the cross-over. Model validation data was taken from literature data and from steady state, cold flow, CFB tests results of five granular materials with various sizes and densities in which the riser was operated in core-annular and dilute flow regimes. Experimental data were taken from a 0.20 m ID cross-over piping and compared to literature data generated in a 0.10 m ID cross-over pipe. The solids mass flow rate data were taken from statistically designed experiments over a wide range of Froude number U g 2 g D , 25 – 2 00 , load ratio G s ρ g U g , 0. 2 – 23 , Euler number 2 Δ P Horiz ρ g U g 2 ,2 – 5 0 , density ratio ρ p − ρ g ρ g , 6 0 – 2 000 , Reynolds number ρ g U g d p μ g , 6 0 – 16 00 , and Archimedes number ρ s − ρ g ρ g d p 3 μ g 2 , 29 – 95 00 . Several correlations were developed and tested to predict the solids mass flux based on measuring pressure drop in the horizontal section of CFB. It was found that load ratio G s ρ g U g is a linear function of the Euler number 2 Δ P Horiz ρ g U g 2 and that each of these expressions all worked quite well (R2 > 95%) for the data within the range of conditions from which the coefficients were estimated.

Fluidized bed combustors are commonly operating with complex bed materials of feeding solid wastes, sorbent, bottom ash, sinter and particle split. In the present study, the effects of gas velocities to the fluidized (draft tube) and the moving (annulus section) beds and the weight percent of additive (alumina) on the solid circulation rate (Gs), gas bypassing flow rates (QDA, QAD, Qor) and pressure drop across the orifices (∆Por) of binary bed materials have been determined in a square internally circulating fluidized bed (0.28 m width × 2.6 m height) with an orifice-type square draft tube (0.1 m width × × × × × 0.9 m height). The gas bypassing flow rate through an orifice (Qor), Gs and ∆Por increase with increasing weight percent of the additive. The solid circulation rate has been correlated with ∆ ∆ ∆ ∆ ∆Por and the opening area ratio based on the orifice theory. Also, ∆Por, QDA, QAD and Qor have been correlated with gas velocities to the fluidized and the moving beds and Archimedes number.

This work reports experimental results on the heat transfer between a fluidised bed of fine particles and a submerged surface. Experiments have been carried out using different bed materials (polymers, ballotini, corundum, carborundum and quartz sand) with Archimedes number between 2 and 50. Dry air at ambient pressure and temperature has been used as fluidising gas. Three different exchange surfaces, namely a sphere and two cylinders with different base diameter and same height, have been used. Experimental results show that the heat transfer coefficient increases with particle Archimedes number and is almost independent from particle thermal conductivity for K p / K g > 30. Finally, the comparison of heat transfer coefficient for the different surfaces shows that the effect of the surface geometry may account for a 30% variation in the heat transfer coefficient, with higher differences occurring for coarser particles.

This paper presents a semi empirical single particle model for the description of heat transfer coefficient between a submerged surface and a fluidized bed. The model is applied to several experimental data and gives a satisfactory description of the effect of pressure, temperature and bed material properties on the heat transfer coefficient either in bubbling or slugging fluidized beds. The model considers the averaged surface void fraction as the only regression parameter for the description of experimental data. Surface void fraction results to be a function of Archimedes number and minimum fluidization bed voidage and its value is consistent with the numerical and experimental data reported in literature.

Thermal energy storages which store energy as heat, can compensate energy imbalance between heat generation and consumption. Several types of ice storage systems are applied to heating, ventilating, and air conditioning systems. In this paper, experiments on ice-on-coil and dynamic type are reported to examine thermal characteristics of tanks according to dimensionless response of outlet temperature. Efficiencies of the tank are discussed with respect to dimensionless response, response in a system and volumetric consideration of the tank. For the ice-on-coil type, the Archimedes number at inlet and the inlet enthalpy flow rate are the dominant parameters. Large Archimedes number and intermediate enthalpy flow rate result in lower outlet temperatures. For the dynamic type, as the mechanism of heat transfer is slightly different from the ice-on-coil type, higher velocity of inlet water maintains a lower outlet temperature. From the experimental results, simulation models for both types were developed. Simulations were conducted to estimate the volumetric efficiency under various conditions, considering actual applications. Eight factors were selected as design conditions. The relations among these factors and their potential effects on the thermal characteristics and the volumetric efficiency were derived by system simulations. The significance of the factors on the system was quantified and different effects on ice-on-coil and dynamic ice storage systems were found. Estimation tables to determine volumetric efficiency from the significant factors are presented. Copyright © 2007 John Wiley & Sons, Ltd.

The present investigation addresses the determination of minimum fluidization velocities at elevated temperatures for Geldart’s group-B powders. New experiments have been carried out to obtain bed porosity and air velocity at incipient fluidization over a wide range of temperatures between 298 K and 973 K using particles of ilmenite, sand, limestone, and quartz magnetite of varying sizes. A relatively simple linear empirical correlation between Reynolds number and Archimedes number has been developed to predict minimum fluidization velocity at high temperatures. The predicted values are in good agreement with the new experimental results and existing data in open literature within an error of ±15%. A best fit correlation (±4% error) for the bed porosity at incipient fluidization as a function of Reynolds number and Archimedes number has also been obtained.

This paper reports an experimental study on both transient and steady-state heat transfer behavior of a gas–solid two-phase mixture flowing through a packed bed under constant wall temperature conditions. A logarithmic mean temperature difference (LMTD) method is used to process the temperature data to obtain the overall heat transfer coefficient. The influences of particle loading and gas flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances heat transfer between the flowing gas–solid two-phase mixture and the packed bed, and the enhancement increases approximately linearly with increasing particle loading. The heat transfer coefficient data are processed to give the Nusselt number, which is found to correlate well to the Reynolds number, the Archimedes number and the suspended particle loading ratio. A comparison of the data of this work with the published data reveals large discrepancy. Possible reasons for the discrepancy are discussed.

An experimental study has been carried out on both the transient and steady state heat transfer of a gas–solid two-phase mixture flowing through a cylindrical packed bed reactor under the constant wall heat flux conditions. A logarithmic mean temperature difference (LMTD) method is used to process the steady state data to obtain the overall heat transfer coefficient. The effects of solids loading, particle size and flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances the heat transfer and the enhancement increases approximately linearly with solids loading and the effect of particle size is relatively weak under the conditions of this work. A correlation is proposed based on the experimental data, which relates well the Nusselt number to the Reynolds number, the Archimedes number and the suspended solids loading. Given other conditions, the Nusselt number at the constant wall heat flux conditions is much higher than that under the constant wall temperature conditions. It is shown that the Reynolds number and particle loading have a greater influence on the Nusselt number under the constant heat flux conditions than that under the constant wall temperature conditions investigated by the authors in a previous study.

Of the various transition velocities that delineate flow regimes in multiphase pneumatic and hydraulic conveying, the critical deposition velocity is important because it separates depositing and non-depositing flows. However, no distinction has been made between the dependence of the critical deposition velocity on physical parameters and flow conditions at low solid volume fractions and in the limit of zero volume fraction, which are distinct mathematically. Here, the two cases are analysed separately, and a general functional form in terms of the particle Reynolds number and Archimedes number is proposed that is valid up to volume fractions of several per cent. An ultrasonic method for determining the critical value of the particle Reynolds number is presented, and results for four particle types at several nominal volume fractions (0.5, 1 and 3% by volume) are combined with a number of data from the literature. The resulting expressions are found to compare well with several similar correlations for the critical deposition velocity and other transition velocities, and, unlike a recent best-fit approach for the pick-up velocity, incorporate an explicit dependence on volume fraction, to which the critical deposition velocity is most sensitive at very low volume fractions. Lastly, it is found that the functional forms for the critical deposition velocity in the literature are unable to reproduce the available data at higher volume fractions, and a number of suggestions are made for resolving this issue.

The onset of bubbling in a fluidised bed is defined in this study as the situation where the bubble rise velocity equals the maximum propagation velocity of voidage change. In this way the bed porosity at the onset of bubbling is correlated with the physical properties of the solid particles and of the fluidising fluid with the bubble size as critical parameter. Application of minimum fluidisation results in a scientific sustained description of the boundary between class A and class B fluid–solid systems. For ambient air, this A/B boundary is compared with the earlier introduced Ar = 88.5 criterion and with the criteria proposed by Geldart and Molerus presuming a bubble size 5 times that of the representative particle. Data from literature related to the minimum bubbling superficial velocity are assessed to calculate the bubble size for real gas–solid systems. It appears that the bubble size for these literature data is about 1 to 5 times larger than the particle diameter except for a specific case.

Steady state pool boiling heat flux data has been obtained for acetone-isopropanol-water and acetone-MEK(methyl ethyl ketone)-water ternary mixtures. The data shows that to obtain a given heat flux, the wall superheat required is greater for mixtures than for the pure components constituting the mixture. The measured heat transfer coefficients were compared with predictions from literature correlations for multicomponent mixtures. In all the cases, overestimation or underestimation of the data was observed. Therefore, a new correlation has been proposed for the heat flux in terms of Archimedes number, Prandtl number, surface–liquid interaction parameter, modified Jakob number, dimensionless surface roughness group, properties-profile parameter and an effective temperature driving force. In general, the effective temperature driving force in binary mixtures is less than that encountered in pure components and is obtained by incorporating the binary diffusivity of the mixture. In multicomponent systems, the multicomponent diffusion coefficients have to be incorporated into the expression for the effective temperature driving force. The heat flux correlation predicts the present experimental data as well as literature data, satisfactorily. The heat flux was found to be a function of the difference between the equilibrium vapour and liquid concentration, (y − x) of the light component(s) and the minimum heat flux occurs at the maximum of (y − x) of the light component(s).

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 R 2 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.

This paper presents an experimental study of gas mixing processes and heat transfer augmentation by a forced jet in a large cylindrical enclosure with an isothermal bottom heating/cooling surface. Cold/hot air was injected at several positions with varying pipe diameters and injection orientations, and was removed from the top of the enclosure. Under natural convection, the mean Nusselt number was correlated by the enclosure Rayleigh number RaD1/3, and under strong forced convection, by the jet Reynolds number Rej2/3. A combining rule for mixed convection was found for both the stabilizing (cooled surface) and destabilizing (heated surface) density gradients. Using the ratio of forced and free convection Nusselt numbers, this correlation could be further reduced to predict forced-jet augmentation as a function of the Archimedes number, with a correction factor to account for jet orientation and enclosure aspect ratio.

The attachment of fluid jets to walls when blown closed to these walls is known by the name of the Coanda effect and is widely used in practice, e.g., for the ventilation and air-conditioning of rooms. When a jet of air cooler than the ambient air is blown horizontally along the ceiling, the jet adheres to the ceiling over a given distance even though it is heavier than the ambient air. The aim of this paper is to provide a satisfactory explanation for the phenomenon, on the basis of a theoretical analysis of the equilibrium of a layer of fluid that is denser than the ambient fluid, when it is driven by a translation movement in relation to the ambient fluid and is located under a flat wall in a gravity field. The analysis makes it possible to formulate the separation distance of the jet depending on its properties at the blowing slot. That distance is then compared with the available experimental results. The resultant formula, connecting the ratio between the separation distance and the height of the blowing slot and the Archimedes number of the jet, is as follows: x S th a = 3.6 Ar 0 0.64 . The agreement between the results of the theory proposed here and the available experimental results in the literature bears out the validity of the theory.

The type transition in onset condition of turbulent fluidization in gas fluidized beds was investigated to obtain the relation representing more precise roles of physical properties of gas and solid particles. The type transition in onset condition of turbulent fluidization occurs at Archimedes number of 20.87 by type transition of bubble breakup. The maximum stable bubble diameter (d bmax ) is greater than the equilibrium bubble diameter (d beq ) in the region, Ar d bmax in the region, Ar>20.87. Therefore, the onset of turbulent fluidization is determined in the region, Ar20.87, by d bmax as the limit of bubble growth. The uc decreases in the region, Ar 20.87 as temperature increases.

Behavior of particle mixtures was investigated in a liquid-fluidized bed experimentally. In the experiment, two kinds of particles of different diameters, and of the same or different materials, were charged in a fluidization column and fluidized by water. Based on the observation of fluidization, a flow pattern map was proposed using the Archimedes number ratio and the terminal velocity ratio, which classifies the two patterns, that is, separation and homogeneous mix. Measured mean void fractions of particle mixtures agreed well with the values calculated from those for each particle independently. © 2001 Scripta Technica, Heat Trans Asian Res, 30(3): 175–184, 2001

The natural stratification of turbulent flows in an axisymmetric, cylindrical, chilled-water storage tank has been investigated numerically. The calculations involve the injection of cold water through a slot in the base of an insulated tank, within which the fluid is initially at rest and at constant temperature. Calculations are presented for inlet Reynolds numbers ranging from 500–3000, and Archimedes numbers ranging from 0.5-5.0. Results obtained by employing both κ—e and full Reynolds stress turbulence closure models are presented and contrasted, and indicate that to ensure stratified flow the Archimedes number should be greater than two, independent of the inlet Reynolds number. In addition, considerable differences were found in terms of the thickness of the evolving thermocline between the predictions of the κ—e and Reynolds stress models.

A two-dimensional turbulence k–e model is used to predict distribution of air velocity, temperature and turbulence kinetic energy in an air-conditioned room using ceiling air supply. Mixing characteristics of the airflow are analyzed under different air supply velocities and temperatures. A modified Archimedes number is correlated with the parameters characterizing heat transfer, ventilation system, and turbulence kinetic energy of room air flow. Significant correlations have been shown. It is found that the linear ceiling air supply air-conditioning system with a high level return air provides excellent air mixing across a wide range of Archimedes numbers. The results are useful for air-conditioning design and thermal comfort study.

The purpose of the present work is to investigate the potential for buoyancy induced stratification and /or turbulent mixing as a function of the Archimedes number. Both axisymmetric cylindrical and rectangular storage tanks are considered

The expansion of gas-fluidised beds has been examined in the range of Archimedes number from 100 to 105 using five grades of glass ballotini and two grades of lead shot of narrow size distribution, and Diakon particles of wide size distribution. A porous plastic distributor plate was used in beds of diameters 89 and 290 mm. Power law and exponential correlations of the expansion were examined. All of the experimental data were correlated within experimental error by the equation ρbρmf = exp[−0.0052U∗(UUmf−1)] . The dimensionless group U∗, not apparently considered elsewhere, is defined as Ut(ρμg)13 where Ut is the particle terminal velocity.

The onset of the aggregative mode of liquid-solid fluidization was explored. The experimental findings were interpreted by means of the dynamic (elastic) wave velocity and the voidage propagation (continuity) wave velocity. For widely different systems, the mapping of regimes has been presented in terms of the Archimedes number, the Froude number and the fluid-solid density ratio. The proposed diagram also depicts the typical Geldart's Group A particles fluidized with air.

The single particle flow behavior of food (carrot, parsnip and potato cubes) and Nylon spheres was investigated in simulated holding tubes at different temperatures under pressurized (110C) and nonpressurized (80 and 100C) flow conditions using different carrier fluids (water and 2, 3 and 4% starch suspensions). It was found that the particle to fluid velocity ratio (u p /u) was a function of carrier fluid effective viscosity, temperature and flow rate, and particle relative size, density and shape. The maximum value of u p /u ranged from 0.4-1.9 which increased almost linearly with temperature showing no specific deviations in the flow behavior of particles as conditions changed from the nonpressurized (

On the basis of a new theoretical model recently proposed by the authors for heat transfer between walls and fluidized beds, a quantitative analysis on heat transfer regimes is presented in this paper. From the dimensionless, differential equations describing the heat transfer modes; i.e., conduction, convection, and radiation is mainly determined by the characteristic numbers: Archimedes number, Ar; and Planck number, N * . It is found that the convection in laminar regime and conduction in turbulent regime are still non-negligible components. A heat transfer diagram in a Archimedes number versus Planck number is proposed. Nine domains are defined according to the variation of the dominant heat transfer mechanism.

The incipient or start-up fluid velocity of water and starch suspensions (2 and 4%) containing discrete food particles (carrot, parsnip, and potato cubes) as well as nylon spheres was investigated in the following range of conditions: temperatures of 80, 100 and 110 °C; particle sizes for spheres of 19.1, 12.7, 9.53 and 6.35 mm diameter and for cubes of 12.7, 10 and 7.6 mm; tube diameters of 29.5, 41.3 and 54.6 mm; a tube length of 1.2 m; and a tube inclination of upward 1.19 °. The incipient velocity was found to be a function of the fluid effective viscosity, the particle-to-fluid density simplex (a), the particle-to-tube diameter ratio ( d e D ) and the sphericity of the particle (Ψ). The following regression equation (R2 = 0.94) described the dimensionless correlation: GRe0 = 0.0056Ar0.615 ( d e D ) −0.07 Ψ−8.5, where GRe0 is the generalized incipient Reynolds number and Ar is the Archimedes number, both with tube diameter D as the characteristic dimension. Viscosity of the carrier fluid showed a much stronger influence, resulting in dampening of the density effect on incipient velocity.

The monotonic instability of a horizontal layer of a viscous liquid with soluble-gas bubbles is demonstrated. The critical values of the modified Archimedes number are calculated and the corresponding critical motions of the liquid are considered.

A spouted bed was used to study the effect of temperature on hydrodynamic performance, as measured by parameters such as pressure, minimum spouting velocity, and spout-annulus residence time distribution. Three bed temperature regimes were investigated: ambient, preheat (∼200°C. using a small hydrogen pilot flame), and combustion (∼800°C, using a premixed toluene flame). A stable operating regime for the system under combustion conditions was characterized on a plot of gas velocity vs. equivalence ratio. Pressure and temperature profiles in the bed were developed. The effect of temperature on the minimum spouted velocity was evaluated in terms of the minimum spouting Reynolds number, Rems, and the Archimedes number. The effect of particle shape on spout-annulus flow disribution appeared to be greater than the effect of temperature.

The dynamics of a Taylor bubble rising in stagnant liquids is numerically investigated using a front tracking coupled with finite difference method. Parametric studies on the dynamics of the rising Taylor bubble including the final shape, the Reynolds number $({\text{Re}}_{T})$, the Weber number $({\text{We}}_{T})$, the Froude number (Fr), the thin liquid film thickness $(w/D)$, and the wake length $({l}_{w}/D)$ are carried out. The effects of density ratio $(\ensuremath{\eta})$, viscosity ratio $(\ensuremath{\lambda})$, E\"otv\"os number (Eo), and Archimedes number (Ar) are examined. The simulations demonstrate that the density ratio and the viscosity ratio under consideration have minimal effect on the dynamics of the Taylor bubble. E\"otv\"os number and Archimedes number influence the elongation of the tail and the wake structures, where higher Eo and Ar result in longer wake. To explain the sudden extension of the tail, a Weber number $({\text{We}}_{l})$ based on local curvature and velocity is evaluated and a critical ${\text{We}}_{l}$ is detected around unity. The onset of flow separation at the wake occurs in between $\text{Ar}=2\ifmmode\times\else\texttimes\fi{}{10}^{3}$ and $\text{Ar}=1\ifmmode\times\else\texttimes\fi{}{10}^{4}$, which corresponds to ${\text{Re}}_{T}$ between 13.39 and 32.55. Archimedes number also drastically affects the final shape of Taylor bubble, the terminal velocity, the thickness of thin liquid film, as well as the wall shear stress. It is found that $w/D=0.32\text{ }{\text{Ar}}^{\ensuremath{-}0.1}$.

International audience; The velocity, shape, and trajectory of the rising bubble in polyacrylamide (PAM) and carboxymethylcellulose (CMC) aqueous solutions were experimentally investigated using a set of homemade velocimeters and a video camera. The effects of gas the flowrate and solution concentration on the bubble terminal velocity were examined respectively. Results show that the terminal velocity of the bubble increases with the increase in the gas flowrate and the decrease in the solution concentration. The shape of the bubble is gradually flattened horizontally to an ellipsoid with the increase in the Reynolds number (Re), Eoumltvoumls number (Eo), and Morton number (Mo). With the increase in the Re and Eo, the rising bubble in PAM aqueous solutions begin to oscillate, but there is no oscillation phenomena for CMC aqueous solutions. By dimensional analysis, the drag coefficient of a single bubble in non-Newtonian fluids in a moderate Reynolds number was correlated as a function of Re, Eo, and Archimedes number (Ar) based on the equivalent bubble diameter. The predicted results by the present correlation agree well with the experimental data.

Part 1 of this contribution reported on the effects of system properties on heat transfer between heating or cooling surfaces and bubbling fluidized beds. This investigation produced four correlations which define the respective maximum heat transfer. Part 2 of this study suggests that the heat transfer between exchanger surfaces and bubbling fluidized beds depends on superficial gas velocity, expressed as dimensionless excess gas velocity. The present paper shows that heat transfer coefficients in circulating fluidized beds can be predicted by evaluation of a state diagram, which combines three dimensionless groups: Nusselt number, Archimedes number and a dimensionless pressure gradient. A comparison of coal combustion experiments with own cold model measurements indicates that the radiative component of heat transfer coefficients is only evident at very low dimensionless pressure gradients.

The difference of static mixers as internals on expansion and dispersion characteristics of a liquid fluidized bed was studied experimentally. The column diameter was varied between 39 and 300 mm. Fluidized bed reactors equipped with internals exhibit a high hydrodynamic stability accompanied by an increase in the operating range in terms of flow rate by a factor of 4-5 compared to the classical fluidized bed. The axial dispersion of the liquid depends on the Archimedes number, the hydraulic diameter of the static mixer and expansion. The dispersion increases with decreasing Archimedes number and increasing hydraylic diameter of the bed. Dispersion was in general reduced with bed expansion.

The settling velocity of solids has been determined experimentally in a fluidizing column. The bed expansion characteristics of monodispersed (single component) systems have been noted using water as the fluid. The experimentally determined bed voidages have been plotted against particle Reynolds number, Re p on a log-log graph paper. The settling velocity, u t , has been obtained by extrapolating the resulting straight line to ϵ =1.0. Close-cut size fractions of coal, graphite, sand, limestone, chalcopyrite and magnetite have been used as different solids. Water has been used as the fluidizing fluid throughout the experiment. The experimental values of Re t have been empirically correlated with the relevant system properties, e.g., particle diameter, its shape, density of liquid and solid, liquid viscosity—all of these being represented by Archimedes number and shape factor, φ s . The correlation proposed is: Re t =0.103(Ar 0.804 ( φ s ) 0.745 The standard deviation of the proposed correlation has been calculated to be ±15.2%. The ranges of Ar and φ s are: 53≤ Ar ≤3761; 0.5000≤ φ s ≤0.9740 The present correlation has been compared with existing equations for monodispersed systems whereby a fair agreement is obtained. This is also found to be reasonably accurate for polydispersed systems when the calculated u t values, based on average bed properties, are compared with those calculated theoretically after being multiplied with the Pettyjohn-Christiansen sphericity correction factor.

The results of an experimental study of melting of a free solid in a cylinder heated by external forced convection have been presented. The ranges for the average wall Stefan number and Archimedes number have been varied between 0.026 to 0.053 and 8.76×106 to 3.34×108 respectively. Multiple runs have been made for most of these cases using different values of Reynolds number and free stream temperature to obtain the desired average wall Stefan number. Though the melt rate is almost identical to that for the isothermally heated capsule in about half the tests, it is strongly affected by the dynamics of the melting process in other cases, where two different melt patterns are observed.

This research investigates experimentally mixed convection and heat transfer augmentation by forced jets in a large enclosure, at conditions simulating those of actual passive containment cooling systems and scales approaching those of actual containment buildings or compartments. The experiment was designed to measure the key parameters governing the heat transfer augmentation by forced jets and investigate the effects of geometric factors, including the jet diameter, jet injection orientation, interior structures, and enclosure aspect ratio. The tests cover a variety of injection modes leading to flow configurations of interest that contribute to reveal the nature of mixing and stratification phenomena in the containment under accident conditions of interest. By nondimensionalizing the governing equations, the heat transfer of mixed convection can be predicted to be controlled by jet Archimedes number and geometric factors. Using a combining rule for mixed convection and appropriate forced and natural convection models, the correlations of heat transfer augmentation by forced jets are developed and then tested by experimental data. The effects of jet diameter, injection orientation, interior structures, and enclosure aspect ratio on heat transfer augmentation are illustrated with analysis of experimental results.Copyright © 2004 by ASME

The influence of a thermal heterogeneity boundary conditions on the air change efficiency (ACE) of a mechanical ventilation system in a test room was experimentally evaluated by means of the “step-down” tracer gas technique in 24 different experimental conditions. The experiments were performed under isothermal condition, varying the air supply temperature with respect to the walls and varying the surface temperature of a wall with respect to the other walls and the supply air, simulating both heating and cooling situations. Changing the position of the outlet grid two different configurations of the ventilation system were tested. The nominal supply air velocity varied between 0.04 and 0.11 m/s, corresponding to a range from 1 to 3 ach, and the temperature differences varied from 0 to 5°C. Results are reported in terms of air change efficiency indexes, both local and global. The global air change efficiency (ACE), values are presented as a function of the Archimedes number (Ar), whose values were in the range 0 to 181. The reported results suggest that the Ar number may be used to organize the ACE values when in the presence of thermal heterogeneity, both in the external envelope and in the supplied air. The obtained results show that there is a logarithmic relation between Ar and ACE. In particular, for both ventilation strategies tested, the increase of the absolute value of Ar leads to an increase of ACE when the supply air is warmer than the walls, and to a decrease of ACE when the supply air is colder than the walls. Under isothermal conditions the Reynolds number (Re) fairly correlates the experimental results.

Hot wire anemometry used inside air fluidized beds of glass (175 mu m), FCC (75 mu m) and silica (85 mu m) powders (Archimedes numbers of 510, 29 and 16, respectively) allowed the measurement of the time-resolved local heat transfer coefficient. Time averages of this coefficient reproduce the same behaviour found by other authors with different experimental techniques. A stochastic model for the heat transfer rate has been developed on the basic hypothesis that heat transfer fluctuations are due to the continuous renewal of packets of solid particles along the wire. The most relevant simplifying hypothesis is that the contact time between the wire and the packet is much shorter than the characteristic heating time of the packets. With this model, probability density distributions of the heat transfer coefficient are evaluated. Comparison between experimental and theoretical results is fairly good in all experimental conditions relative to fully developed aggregative fluidization. The model is less reliable in conditions of incipient and homogeneous fluidization, where the simplifying hypotheses may not apply. Calculated values of packet to particle size ratios, lambda/d(p), are around 8 for glass, between 14 and 36 for FCC and between 17 and 32 for silica. The increasing number of particles inside a packet seems, therefore, to be correlated, on one hand, to the decreasing Archimedes number, and on the other, to an apparently reduced particle mobility of powders belonging to the Group A of the Geldart [D. Geldart, Types of gas fluidization, Powder Technol., 7 (1973) 285-292] classification. (C) 1999 Elsevier Science S.A. All rights reserved.

The wall-to-suspension heat transfer in circulating fluidized beds depends on the fluid mechanics immediately near the wall and on the thermal properties of the gas used. Experimental investigations of circulating fluidized beds of low dimensionless pressure gradients with different solid particles like bronze, glass and polystyrene at ambient temperatures show no influence of the conductivity and the heat capacity of the solids on the heat transfer coefficient. Consequently the heat transfer coefficient in form of the dimensionless Nusselt number can be described in dependence of dimensionless numbers which characterize the gas-solid flow near the wall. These numbers are the Archimedes number and the pressure-drop number. The last number relates the cross-sectional average solids concentration to the solids concentration at minimum fluidization condition. With the aid of the model of the segregated vertical gas-solid flow the flow pattern in the wall region can be calculated and consequently the wall heat transfer which depends only on heat conduction in the gas and on the convective heat transfer by the gas. With elevated suspension temperatures radiation contributes additionally to the heat transfer. When the solids concentration is low the effect of the radiation on the heat transfer is high. Increasing solids concentration results in a decrease of the radiation. With high solids concentration the wall will be shielded by the cold solids clusters moving down the wall from the radiation of the hot particles in the core region. A simple correlation is presented for calculating the heat transfer in circulating fluidized beds.

Maximum heat transfer in apparatus containing dispersed two phase systems. The structure of dispersed systems such as fluidized beds, bubble columns, and liquid/liquid spray columns in process apparatus can be either homogeneous or heterogeneous. When calculating heat transfer coefficients between such systems and vertical heat transfer areas it is necessary to know the structure of the bed. In homogeneous systems (for instance fixed beds) a relationship between the heat transfer and a Reynolds number was found. This Reynolds number embodies the volumetric flux density and a suitable hydraulic diameter. In gas fluidized beds with a heterogeneous structure the heat transfer depends on a Peclet number. The characteristic time of this number can be obtained by deviding the particle diameter by the mean rising velocity of gas bubbles. Maximum heat transfer coefficients for homogeneous and heterogeneous and heterogeneous systems can be described in a general way by plotting a Nusselt number versus the product Arp · Prc of the Archimedes number and the Prandtl number. Maximum coefficients are calculable without knowledge of the volumetric flux density. For low values of the product Arp · Prc there is a significant difference between homogeneous and heterogeneous beds.