EVALUATION OF CONDUCTIVE HEAT TRANSFER MECHANISMS BETWEEN AN IMMERSED SURFACE AND THE ADJACENT LAYER OF PARTICLES IN BUBBLING FLUIDIZED BEDS

The evaluation of the heat transfer coefficient h_wp between a heat exchanging surface immersed in a gas fluidized bed and the adjacent layer of dense phase particles is analyzed in this contribution. Gas convective and radiant effects are not included in the present analysis.

The inclusion of h_wp, or an equivalent formation, in mechanistic models describing heat transfer has been necessary because the sudden voidage variation close to the immersed wall restrains significantly the heat transfer rate. However, there is not at present a widely accepted expression to evaluate h_wp.

A precise formulation for h_wp accounting for transient conduction inside spherical particles, the Smoluchowski effect, the concentration of particles in the adjacent layer (N_p) and an effective separation gap (l₀) is developed here.

Although N_p can be estimated, in principle, from experimental evidence in packed beds, and it is reasonably expected that l₀ = 0, the analysis of experimental heat transfer rates in moving beds, packed beds, and bubbling fluidized beds indicate that values of h_wp are, in general, smaller than expected from these assumptions. Appropriate values of l₀ and N_p are then stimated by fitting the experimental data.

The probable effect of surface asperities is also discussed by analyzing a simplified geometrical model. It is concluded that the parameter l₀ can be also effective to account for particle roughness, independently of thermal properties.     

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.     

AN INTEGRAL MODEL FOR DRYING OF HYGROSCOPIC AND NONHYGROSCOPIC MATERIALS WITH DIELECTRIC HEATING

Heat and mass transport phenomena in drying assisted by microwave or radio-frequency dielectric heating are analyzed. When drying at temperatures near boiling point or with high temperature gradients, the effect of the gas phase pressure gradient on moisture transfer within the solid can be important. The governing heat and mass transfer equations, including consideration of internal heat generation and the effect of the gas phase pressure gradient, are derived and solved in a one-dimensional system using an integral method. The integral model has been used to simulate dielectrically-enhanced convective drying of beds of polymer pellets, glass beads and alumina spheres with flow over the bed surface. Model predictions of drying rates and temperatures agree well with experimental data for these cases.

The model provides a relatively fast and efficient way to simulate drying behavior with dielectric heating, and may be useful in design and optimization of dielectrically-enhanced convective drying processes.     

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.     

HEAT TRANSFER IN TRICKLE-BED REACTORS

The mechanism of radial heat transfer in two-phase flow through packed beds is examined. A model with 2 parameters: an effective radial thermal conductivity in the bed, k_e, and a heat transfer coefficient, h_w, at the wall, give a satisfactory interpretation of the radial temperature profile.

k_e was expressed in terms of a stagnant contribution, due to the heat conduction through the solid and the fluid in the void space, and a radial mixing contribution of the gas and liquid phases, due to the radial component of the velocity of both fluids. The radial mixing contribution of the liquid ( k_e)_L was compared with radial mass dispersion data, and a satisfactory agreement was obtained.

Moreover, ( k_e)was much higher than the gas mixing and the stagnant contributions.

Correlations for hw and k_e)_L have been proposed in accordance with the hydrodynamic regimes of the two-phase flow.     

A phenomenological model for heat transfer in freeboard of fluidized beds

A phenomenological model was developed to predict heat transfer to tubes located in the freeboard region of gas fluidized beds. The model is concerned with the conductive/convective mechanism of heat transfer. For high temperature applications, an additional contribution by thermal radiation would need to be incorporated. The model considers that the tube surface experiences alternating contact with a dense emulsion phase and a lean void phase. Contributions by dense and lean phases are represented by transient conduction and convection mechanisms, respectively. Particletube contact information was obtained experimentally for a wide range of operating conditions at room temperature and pressure. Predictions of the model were compared with measured heat transfer coefficients. Over a 20-fold range in magnitudes of heat transfer coefficients, the model successfully predicted the measured values with an average deviation of 44 percent.     

Computational fluid dynamics simulations of heat transfer between the dense‐phase of a high‐temperature fluidized bed and an immersed surface

The transient process of heat transfer between a high‐temperature emulsion packet and the wall of an immersed surface is simulated using computational fluid dynamics (CFD). From these simulations, the total heat transfer coefficient and its radiant contribution due to the emulsion (dense) phase are evaluated. The results are compared with experimental data (Ozkaynak et al., “An experimental investigation of radiant heat transfer in high temperature fluidized beds,” in Fluidization IV, 1983:371–378) and with predicted values from the generalized heterogeneous model (GHM), (Mazza et al., “Evaluation of overall heat transfer rates between bubbling fluidized beds and immersed surfaces,” Chem Eng Commun., 1997;162:125–149). The CFD simulations are in good agreement with both, experimental data and theoretical GHM predictions and provide a reliable way to quantify the studied heat transfer process. Also, the GHM is validated as a practical tool to this end. © 2011 American Institute of Chemical Engineers AIChE J, 58: 412–426, 2012     

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.     

MODEL SELECTI0N IN AIR DRYING OF FOODS

The purpose of this investigation is to compare various drying models with respect to (a) the accuracy in calculating the material moisture content and temperature versus time and (b) the computation time required.

Mechanistic as well as phenomenological heat and mass transfer models are considered. The mechanistic models are formulated by considering different combinations of mechanisms between (1) moisture diffusion in the solid towards its external surface (2) vaporization and convective transfer of the vapor into the air stream (3) convective heat transfer from the air to the solid's surface (4) conductive heat transfer within the solid mass. The phenomenological model incorporates the drying constant while the mechanistic models incorporate the mass diffusivity, the mass transfer coefficient in the air boundary layer, the thermal conductivity, and the heat transfer coefficient in the air boundary layer.

The proposed methodology is applied to experimental data of four vegetables, namely, potato, onion, carrot, and green pepper. The experiments involve three thickness levels, five temperatures, three water activities, and three air velocities. The results obtained concern (a) the standard deviations between experimental and calculated values of material moisture content andtemperature, which, in combination with the computation time, are the necessary information for model selection for a special application, and (b) the model parameter estimates which are necessary to use the selected model.     

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.     

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.     

Sublimation Kinetics during Freeze-Drying of Pharmaceutical Protein Formulation

The influence of total gas pressure and shelf temperature on sublimation kinetics of BSA-based formulation in glass vial as geometrical configuration was determined with a pilot freeze-dryer in standard operating freeze-drying conditions.

The sublimation rate curves showed three different periods with a plateau corresponding to a stationary regime. These kinetics data were mainly dependent on the shelf temperature and slightly influenced by the total gas pressure. Thus, the sublimation process in our conditions was mainly governed by overall heat transfer rate from the plate and from the surroundings to the sublimation front.

Moreover, it proved that the water vapor mass transfer mechanism through the dried layer occurs by molecular diffusion in Knudsen regime.

Finally, these experimental sublimation kinetics data were found in a quite fair agreement with the set up results. They confirm the validation of previous modeling of mean product temperature profiles during the freeze-drying by using the finite element code FEMLAB in real vial geometry (2-D).     

CARBON COMBUSTION RATES AND TEMPERATURES IN SHALLOW FLUIDIZED BEDS

The mechanism of combustion of carbon in shallow fluidized beds at temperatures 750-1000°C is studied by measuring burning rates and temperatures of spherical carbon particles ranging from 2 mm to 12 mm diameter directly in an experimental fluidized bed. Among variables investigated were inert particle size, superficial fluidizing velocity, temperature, the influence of neighbouring active particles and oxygen concentration in the fluidizing gas.

Under the experimental conditions explored, combustion was mainly kinetically controlled, so that with carbon particles larger than about 4 mm, burning rates are significantly higher than those predicted by combustion models which assume combustion to be controlled by the rate at which oxygen diffuses through a stagnant particulate phase surrounding the burning particle. The higher burning rate seems to arise because the greater mobility of particles in the bed causes the restriction to oxygen flow to the carbon surface offered by the particulate phase to be reduced and has important consequences for combustor design.

Measured carbon particle temperatures were influenced considerably by bed operating conditions ranging from 15 to 215°C higher than bed temperature.

Measured burning rates of carbon particles were found to be reduced significantly when other active particles were present in the bed. This sensitivity of burning rate to changes in active particle concentration in the bed was shown to be increasingly important once the concentration of carbon in the bed exceeded about 1%

Increasing the bed inert particle size, superficial fluidizing velocity, oxygen concentration in the fluidizing gas and bed temperature resulted in higher burning rates. The implication of these findings on combustor design are discussed.     

HEAT AND MASS TRANSFER DURING SAPWOOD DRYING ABOVE THE FIBRE SATURATION POINT

Pine sapwood was dried in an air convection kiln at temperatures between 60-80 °C. Temperature and weight measurements were used to calculate the position of the evaporation front beneath the surface. It was assumed that the drying during a first regime is controlled by the heat transfer to the evaporation front until irreducible saturation occurs. Comparisons were made with CT-scanned density pictures of the dry shell formation during initial stages of drying of boards.

The results indicate a receding evaporation front behaviour for sapwood above approximately 40-50% MC when the moisture flux is heat transfer controlled. After that we finally reach a period where bound water diffusion is assumed to control the drying rate.

The heat transfer from the circulating air to the evaporation front controls the migration flux. In many industrial kilns the heating coils therefore have too small heat transfer rates for batches of thin boards and boards with high sapwood content.     

DRYING OF GRANULAR PARTICLES IN A MULTISTAGE INCLINED FLUIDIZED BED WITH MECHANICAL VIBRATION

A mathematical model for the drying rate of granular particles in a multistage inclined fluidized bed(IFB) is presented from the standpoint of simultaneous heat and mass transfer, with taking the effect of mechanical vibration added vertically into consideration.

Steady-state distributions for the temperatures and concentrations of the particles and the heating gas, and for the moisture content of the particles are numerically calculated based on the present model. The calculated results show fairly good agreement with the experimental data, which were obtained from the drying experiments of brick particles in a three-stage IFB using comparatively low temperature air(40-60°C) as the heating gas.

It has been found within the range of the experimental conditions employed that, the mechanical vibration added vertically enhances the over-all drying rate of the particles and its effect can be considered equivalent to an increase in the air velocity.     

TWO-PHASE FLOW HEAT TRANSFER IN A HORIZONTAL STEAM WATER SYSTEM

There are various correlations available for predicting heat transfer coefficients during forced convective two-phase flow. The present work was undertaken to gather heat transfer rate data for the steam-water system and to evaluate (and if necessary, to modify) the available correlations in light of those data.

A boiling water loop, capable of being operated at pressures up to 1300 kPa, was used. The test section was in the form of a U-tube with two straight horizontal sections connected by a 180^° return bend. Using this loop, accurate pressure drop and heat transfer data were gathered over a wide range of mass and heat fluxes.

The data obtained were used to arrive at an improved correlation for the two-phase convective heat transfer coefficient h_pfor steam-water systems at relatively low pressures (800 kPa). The proposed correlation shows h_pis a much stronger function of Lockhart-Martinelli parameter than is indicated by most of the other correlations. Among the existing correlations evaluated, the correlation proposed by Davis and David [ 1964] and the one proposed by Dengler and Addoms (1956) fit our data best.     

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     

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.     

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.     

THE EFFECT OF TEMPERATURE ON FLUIDIZED BED BEHAVIOUR

Most published correlations for the minimum fluidizing gas velocity have been derived from tests under ambient conditions and increasing discrepancy is found in their application over wider ranges of operating conditions. Up to 1000°C the Ergun equation is reliable but it requires a knowledge of the particle shape factor and bed voidage for its application. Bed voidage is found to vary with temperature for laminar gas flow conditions.

Paralleling changes in gas flow conditions with operating temperature are changes in bed-to-surface heat transfer coefficients. There is a distinct transition from the interphase gas convective to the particle convective component of heat transfer being the dominant mechanism as the operating temperature increases and Re_mf reduces through 12,5 at Ar ∼ 26000. This is thought to be a consequence of change in bed bubbling behavior.