EVALUATION OF OVERALL HEAT TRANSFER RATES BETWEEN BUBBLING FLUIDIZED BEDS AND IMMERSED SURFACES

A mechanistic model to evaluate heat transfer rates between the dense phase of gas fluidized beds and immersed surfaces has been recently presented by the authors. This model, denoted Generalized Heterogeneous Model (GHM), is formulated in terms of effective thermal properties for particles and interstitial gas. It has been conceived with the purpose of achieving a generalized formulation accounting simultaneously for conductive, gas convective and radiant effects.

The model was previously tested as regards its capability to predict radiative heat transfer rates in beds at high temperature and gas convective contribution in beds of large particles and high operating pressures.

It is the principal object of this contribution to evaluate the performance of the GHM for a wide range of particle sizes, covering from The purely conductive regime to the gas convection dominant regime.

Also, the main assumptions incorporated in the model are revised and some modifications are introduced, mainly on the basis of the results obtained by Mazza et al. (1997b).     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

MULTIPHASE HYDRODYNAMICS AND SOLID-LIQUID MASS TRANSPORT IN AN EXTERNAL-LOOP AIRLIFT REACTOR—A COMPARATIVE STUDY

The solid-solid mass transfer performance of an external-loop airlift reactor was measured by dissolution of benzoic acid coated on nylon-6 particles, and the hydrodynamics of the gas-liquid-solid multiphase system in the airlift reactor were investigated. The solid-liquid system was designed to simulate the micro-carrier culture of animal cells, and some typical suspensions of immobilized enzyme particles.

The solid-liquid mass transfer coefficient remained constant below a superficial air velocity of 0.04 ms^-1 for the particles examined, but increased rapidly with further increase in gas velocity. Solids loading (0.3-3.5% w/w) did not affect the mass transfer coefficient in turbulent flow.

The mass transfer coefficient was correlated with energy dissipation rate in the airlift reactor. The mass transfer coefficient in stirred vessels, bubble columns, fluidized beds, and airlift reactors was compared.

Over an energy dissipation Reynolds number of 4-400, the solid-liquid mass transfer coefficient in the airlift device was comparable to that obtainable in fluidized beds. The performance of the airlift was distinctly superior to that of bubble columns and stirred tanks.     

Drying Sawdust in a Pulsed Fluidized Bed

The objective of this work was the experimental and theoretical study of sawdust drying, in batch and continuous experiences, using a pulsed fluidized bed dryer.

In the batch experiences, a 2³ factorial design was used to determine the kinetics of drying, the critical moisture content, and the effective coefficients of both diffusivity and heat transfer, all of them as a function of the velocity and temperature of the air, the speed of turning of the slotted plate that generates the air pulses in the dryer, using sawdust with 65% moisture in each run.

In the continuous operation, a 2³ factorial design was used to study the effect of the solid flow and the velocity and temperature of the air on both the product moisture and the distribution of residence times. In order to determine these last ones, digital image processing was used, utilizing sawdust colored by a solution of methylene blue as tracer.

The statistically significant factors were the velocity and the temperature of the heating air, for both the continuous and batch operations. Although the speed of turn of the slotted plate was not significant, it was observed that the air pulses increased the movement of particles, facilitating its fluidization, especially at the beginning of drying.

The heat transfer coefficients were adjusted according to the equation Nu = 0.0014 Re_p^1.52, whose standard deviation of fit is 0.145.

The period of decreasing rate was adjusted to several diffusivity models, giving the best fit the simplified variable diffusivity model (SVDM). The curve of distribution of residence times was adjusted using the model of tanks in series, with values between 2.6 and 5 tanks.     

ATMOSPHERIC CONTACT DRYING OF GRANULAR BEDS WETTED WITH A BINARY MIXTURE

When regarding the atmospheric contact drying of granular beds wetted with a liquid mixture, both the drying rate and the selectivity of the process, i.e. the change of moisture composition, are of interest. The batch drying of a free flowing ceramic substance, wetted with a 2-propanol-water mixture, is investigated in a rotary dryer with heated wall and air flow.

The theoretical analysis is based on physical models for heat and mass transfer, moisture migration and particle transport, which are presented in examples.

The experimental and theoretical results show that higher selectivities can be achieved by reducing the particle size because of the lower liquid-phase mass-transfer resistance. An increase of the rotational speed leads to a higher drying rate with slightly decreased selectivity if the particles are sufficiently small, since contact heat transfer is enhanced.     

PHASE HOLDUPS AND LIQUID-LIQUID EXTRACTION IN THREE PHASE FLUIDIZED BEDS

Effects of the continuous phase velocity (0.01-0.08 m/s(, the dispersed phase velocity (0.0-0.04 m/s) and particle size (1.0-3.0 mm) on the individual phase holdups and the mass transfer coefficient have been determined in two (liquid-liquid) and three (liquid-liquid-solid) phase fluidized beds.

In the beds, the dispersed phase holdup increased with dispersed phase velocity but it decreased with continuous phase velocity. Whereas the continuous phase holdup decreased with dispersed phase velocity but it increased with continuous phase velocity. The bed porosity increased with both the dispersed and continuous phase velocities in the beds of 1.7 and 3.0 mm particles. In addition, the continuous phase holdup decreased with the presence of solid particles in the bed, however, the dispersed phase holdup was not affected by the presence of the particles.

The overall mass transfer coefficients in the continuous and dispersed phases increased with increasing fluid velocities but it decreased with the bed height.

The continuous phase holdup and mass transfer coefficient data have been correlated with the operating variables and the dimensionless groups.     

TRANSITION OF FLOW REGIME IN FLUIDIZED BEDS WITH SLANTING BLADE BAFFLES

A flow model is proposed to investigate the transition of flow regime from bubbling to turbulent fluidization postulating that the flow in the emulsion phase follows the Richardson-Zaki equation.

Void fraction of the whole bed ε_f and the mean velocity of bubbles U_b were measured in fluidized beds of 0.3 and 0.5 m ID, in which slanting blade baffles were positioned. Mo-catalyst, silica gel, sand and glass beads with size between 135-443 μm were fluidized by air.

Void fraction of the emulsion phase ε _e was calculated on the basis of the above model. Correlating ε _e with superficial gas velocity U_ƒ, we found that ε _e was very close to ε _mƒ in the bubbling regime and that e, increased with increasing U_ƒ in the turbulent regime.

Calculated values of the volume fraction of bubble phase δ were correlated with U_ƒ, from which apparent transition point from bubbling to turbulent regime was estimated. Combining information obtained, transition of flow regime in the above type of fluidized beds is discussed     

HEAT TRANSFER IN SPOUTED BEDS

Experiments were carried out in order to analyse the wall-to-bed and fluid-to-particle heat transfer coefficients in spouted Beds. wall-to-bed heat transfer coefficients were determined in cylindrical-conical and conical spouted beds for various gas flow rates, particle sizes and bed heights for spouted beds with and without draft tubes.

A new definition for wall-to-bed transfer coefficient was proposed baaed on experimental observations.

The heat tranefer area was also studied to ensure that a physically significant fluid-to-particle heat transfer coefficient was achieved.     

UNSTEADY, TWO-DIMENSIONAL HEAT AND MASS TRANSFER IN A PACKED BED OF FINE PARTICLES WITH AN ENDOTHERMIC PROCESS

The basic differential equations controlling the temperature and concentration field in a single packed bed of fine particles were derived and solved for the general case in which unsteady, two-dimensional heat and mass transfer lakes place with an endothermic process.

The time-change of particle- and fluid-temperature and concentration of water vapor (humidity) were calculated by a numerical method which assumed that the rate of the endothermic process can be expressed by a first-order rate equation and that the fluid flowing through the bed is of the piston flow type.

The experiments were conducted for the drying of silica-gel and the two-stage dehydration reaction of natural gypsum to demonstrate the applicability of the present theoretical analysis.

It has been found that the calculated results show satisfactory agreement with the measured data within the range of the experimental conditions employed.     

A MONTE-CARLO APPROACH TO THE INTERPRETATION OF BUBBLE PROBE SIGNALS IN FREELY BUBBLING FLUID BEDS†

The interpretation of the signals generated by a double probe may be done by the three characteristic times method:

t₁ the time duration of the pulses;

t₂ the time shift between the signals of the two probes;

t₃ the time interval between two pulses on one channel.

Each of these times is largely dispersed and the corresponding histograms may be constructed.

The present work is a trial to go over from the time histograms to physical properties of the bubbles combining a Monte-Carlo simulation and a flexible simplex optimisation procedure.

As a result, the percentage of oblique bubbles cutting just one level, the bubble size distribution, the average velocity-size relation, and the individual dispersion around it may be defined.

The procedure is finally applied to experimental results obtained with a light probe in a fluid bed of glass beads.     

CHARACTERIZATION OF FLUIDIZED BED REACTORS WITH GAS TRACER MEASUREMENTS

In a steady state bench scale fluidized bed the decomposition reaction of NaHCO₃ was carried out. The residence times distributions, DRT, of carbon dioxide (the gaseous product) and non adsorbing argon (the reference tracer) were mass spectroscopically measured as a function of the bed temperature. By means of single-, two- and three-phase dispersion models as well as by a cell model, the DRT's were evaluated on line by a computer.

The steady state transverse and longitudinal concentration profiles of these tracers upstream from the plane source were also measured and evaluated by a dispersion model as well as by a counter current back mixing model. Comparison of the steady state and nonsteady state dispersion coefficient measurements indicate that the longitudinal gas mixing is only partially due to backmixing. The experimentally determined wake fractions agree well with those published in the literature. Since the adsorption rate of CO₂ on the pore surface area of the particles in the dense phase is high no interphase transfer from the interstitial gas of the dense phase into the bubble phase takes place.

The desorption of CO₂ and its return into the interstitial gas and than into the gas phase occurs only slowly and with an initial time lag. The on-line DRT can be used as a diagnostical technique for investigation of the reactor during its operation, if operation disturbances or breakdowns occur.     

STEAM CONDENSATION IN A VERTICAL CORRUGATED DUCT

An experimental investigation was made on the condensation of water steam in a vertical corrugated duct. The data have been correlated as follows

Co=5.11Re^-0.431 150 ≤ Re ≤ 350 Co = 0.034311Re^-0.425350 ≤Re ≤l000

The vertical corrugated duct is constructed of two corrugated plates with corrugation inclination angles of β = 0 and β = 45° respectively (relative to the overall flow direction).

The condensation heat transfer coefficient in the corrugated duct is more than two times higher than that of bulk condensation on a vertical plate. A physical model was proposed to explain the heat transfer enhancement. Attention was also paid to the effect of exit steam velocity on the heat transfer during partial condensation. It was demonstrated that the heat transfer in the corrugated duct was strongly affected even at a low exit velocity, which was different from the case of bulk condensation on a vertical plate. Experimental apparatuses and the method for examining their reliability are described in detail.     

Particle Adhesion in Model Systems: 16. Barium Sulfate Particles on Glass and Protein Surfaces

The adhesion phenomena of monodispersed barium sulfate (BaSO₄) particles on gelatin-coated glass beads were evaluated using the packed column technique and compared with the same system in the absence of the protein.

Multilayer deposition was observed with the uncoated glass beads at pH 4, 5 and 6, while at pH 9, which is above the isoelectric point (pH ∼ 6) of BaSO₄ particles, monolayer deposition took place, even though the BaSO₄ particles and glass beads bore the same sign of charge. At pH = 10, no uptake was observed on the glass beads, but the addition of 10^-4 mol dm^-3 BaCl₂ induced multilayer deposition due to the adsorption of the Ba²⁺ cation on BaSO₄ particles, which causes a reversal of their charge to positive.

The formation of multilayers was found to occur over a much wider pH range on the gelatin coated glass beads.

BaSO₄ particles deposited in multilayers could not be removed from either glass beads or gelatin-coated glass beads by rinsing the loaded column with solutions of pH 11.5, but could be detached from monolayers on glass beads only.     

SUBLIMATION OF PURE SUBSTANCES IN GAS FLUIDIZED BEDS AT ATMOSHPERIC PRESSURE.

This paper deals with the sublimation of large bodies, or “objects”, made up from a pure substance in a bubbling gas fluidized bed of considerably smaller particles, or “fines”. The influence of such parameters as the gas velocity, the bed temperature, the size and the adsorption capacity of the fines has been investigated.

The results obtained clearly show that the rate of sublimation in fluidized beds is far higher than in air alone. It increases with increasing bed temperature, decreasing particle size, increasing powder mass capacity, and roughly varies as a parabolic function of time. It has also been observed that the temperature difference between the bed and the object surface, or “temperature depression”, depends on the fines characteristics as well as on bed temperature, but is independent of gas velocity when good solid mixing conditions are achieved.

Bed-to-object heat and mass transfer coefficients have been deduced from data points and attempts have been made to provide a reasonable theory to account for them. After a complete examination, the idea of interpreting transport phenomena based on a well-adapted “surface renewal model” has been proposed.     

EFFECTS OF GEOMETRY ON HYDRODYNAMICS IN EXTERNAL-LOOP AIRLIFT REACTORS

Experimental investigations were carried out in model external-loop airlift reactors. Two reactors of laboratory scale (riser liquid height ranged between 1.16-1.56 m, riser diameter 0.03 m, A_D/A_R ratio between 0.111-1,000, total liquid volume V_T = (1.189-2.446).10^-3m³) and pilot-plant scale (riser liquid height of 4.4 and 4.7 m, respectively, riser diameter 0.200 m, A_D/A_R ratio of 0.1225 and 0.040 m, total liquid volume, V_T = (0.144-0.170) m³) were used.

The influences of reactor geometry characterized by some parameter as: A_D/A_R ratio, liquid height in riser and downcomer and liquid height in gas separator, together with the amount of introduced air, on the basic hydrodynamic design parameters: gas holdup and liquid circulation velocity were analysed.

The influence of gas sparger design on gas holdup and liquid velocity was found to be negligible.

The experimental liquid circulation velocity was correlated using a simplified form of the energy balance in airlift reactors, valid for external-loop airlift reactors with almost complete phase separation at the top.

An original dimensionless correlation for gas holdup prediction involving superficial velocities of gas and liquid, cross sectional areas, dispersion height, riser diameter, as well as Froude number, was obtained.     

A STRUCTURAL PORE DEVELOPMENT MODEL FOR CALCINATION

A structural pore development model has been developed to describe microscopic pore evolution from the thermal decomposition reaction of a single calcium carbonate sphere, this model depicts a uniform distribution of equal sized pores growing from the surface of the sphere toward its center while CO₂ is evolved from the pore bottom. The chemical reaction at the interface, as well as heat transfer from the surroundings to the decomposing sphere and transport of CO₂ from the pore bottom to the bulk gas, are included in the model. The model shows good agreement with experimental data for CaCO₃, and limestone particles of size ranging from 10 μm to 1.1 cm in diameter at various background CO₂, pressures and temperatures

The simulation of the calcination reaction confirms the experimental observations indicating slower calcination rates at higher background CO₂ pressures, mainly due to internal unsteady-state buildup of CO₂ in the pore. The effect of the background₂ pressure is significantly more prominent in the smaller particles. The activation energy derived from the model is equal to 38.0 kcal/g-mol which is in the range of those reported by other investigators and is noticeably close to the heat of the calcination reaction.     

ABSORPTION OF NO BY NaClO2 SOLUTION: PERFORMANCE CHARACTERISTICS

The absorption of lean NO (200 ∼ 1000 ppm) gases in aqueous NaClO₂ solution was investigated in both a mechanically stirred vessel and a packed tower. The chemical reaction rate between NO and NaClO₂ in alkaline solution was shown to be second-order with respect to NO concentration and first-order to NaClO₂ concentration. After including mass transfer considerations, the absorption rate equation established in this work (under the condition of NaClO₂ concentration less than 1.0 M and temperature at 30°C) is given as:

$

In addition, a robust design method was also used to study the performance of this de NO_x process by NaClO₂ solution in a packed tower. S/N analysis of the results indicated that the pH of liquor, NaClO₂ concentration and NaOH concentration were the major factors in affecting both NO oxidation and absorption efficiencies.     

DRYOUT OF WATER FILM ON A HEATED TUBE SURFACE CAUSED BY AN OBSTRUCTION IN A BOILING TWO-PHASE VERTICAL UPWARD FLOW

Due to the increasing consumption of energy and the green house effect caused by C0₂ nudear power stations have been playing more important role than ever in the electric power generation. And both the economy and the safety of the nuclear power station are strongly demanded. One of the restriction in the thermal design of the safe and economic nuclear reactor, especially in BWR is pointed out to be the heat removal from the fuel rods near the rods supporting spacer.

The purpose of the present paper is to investigate the mechanism of the water film breakdown which results in the burnout of heating tube near the spacer under various flow pattern.

The experimental results show that the film breakdown occurs near the leading edge, i.e., just below the spacer, as well as the inside of the down part of the gap between the heating tube and the spacer.     

RAINING OF PARTICLES FROM AN EMULSION-GAS INTERFACE IN A FLUIDIZED BED

This paper deals with the raining of particles from an interface between a dense fluidized phase and a gas phase with the fluidized phase uppermost. Such interfaces occur at the upper surfaces of gas bubbles and slugs in fluidized beds. Particle rain in these cases would enhance contact between gas and particles within the bubbles and slugs.

The rise velocities of single square-nosed slugs injected in incipiently fluidized beds of different diameters were measured. Relatively small columns of internal diameters of 0.0125, 0.019 and 0.0254 m were employed in the experiments; In such beds, square-nosed slugs are formed which span the entire cross-section of the beds and rise entirely due to raining of particles from their top surfaces. Since the upper surface of such slugs is flat, their motion can be analyzed using the one-dimensional hydrodynamic theory. Glass ballotini and sand of different sizes were used as bed particles. Comparison of theory and experiment has enabled the determination of the dimensionless gradient diffusivity characterizing the motion of particles induced by a gradient in the void fraction. The results confirm the scaling proposed by Batchelor (1988). The use of the calculated gradient diffusivity in the criterion for stability of a gas fluidized bed predicts the systems under consideration to be always unstable.     

RADIO FREQUENCY ENHANCED DRAUGHT TUBE SPOUTED BED DRYER

A study of the operation of a draught tube spouted bed in conjunction with dielectric heat addition was carried out. The addition of radio frequency allowed a greater amount of energy to be input into the particulate material in any given time, increasing the drying rate: however, the drying pattern was unaffected by the ratio of radio frequency to convective heat addition. The rate of moisture loss was proportional only to the total energy input. The synergy which often occurs with low levels of radio frequency addition does not occur with rf enhanced spouted beds.

The properties of spouted beds seem to be improved only for moisture contents at which packed bed drying can perform effectively.

Although the properties of spouted beds can be improved by radio frequency heat addition, their qualities although useful for specific operations, are unsuitable for more general use.