Analogy between pressure drop and heat transfer in liquid–solid circulating fluidized beds

An analogy was found between the frictional pressure drop and the heat transfer in liquid–solid circulating fluidized beds. This investigation is based on the predicting correlations for the particle holdup, the heat transfer coefficient, and the pressure drop, which were all developed by the authors. When the heat transfer coefficients were expressed in terms of the modified j‐factor, then a close mutual relationship was observed between the modified j‐factor and the friction factor of the pressure drop due to liquid and particle flow. A correlation to express this mutual relationship was derived, which consists of the density ratio of particle to liquid and the non‐dimensional riser diameter. The heat transfer coefficient predicted from the derived correlation agreed well with the experimental data by the authors, and with existing data. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20246     

Particle holdup in a liquid–solid circulating fluidized bed

An experiment was conducted to acquire a set of systematic data of particle holdup in risers of a liquid–solid circulating fluidized bed. In the experiment, two kinds of riser were provided, their inner diameter being 24 mm and 36 mm, respectively. Tested particles were of glass and ceramics, having a diameter range from 2.10 to 4.95 mm. Water at ambient conditions was used as the fluidizing liquid. Particle holdup was measured using a shut‐off method. Based on the experimental data, a correlation for predicting the particle holdup was derived, which could reproduce almost all experimental data with an accuracy of ±15%. The effect of the wall was not recognized within the experimental range, i.e., the diameter ratio of particle to riser is less than 0.2. The independent parameters affecting the flow characteristics of liquid–solid circulating fluidized beds were identified. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(3): 184–196, 2008; Published online in Wiley InterScience ( www. interscience.wiley.com ). DOI 10.1002/htj.20194     

Heat transfer characteristics of liquid–solid circulating fluidized beds

An experiment was conducted to obtain heat transfer data in liquid–solid circulating fluidized beds. In the experiment, two kinds of risers were provided, their inner diameter being 24 mm and 12 mm, respectively. Tested particles were of glass and ceramics, having a diameter range from 2.10 to 4.95 mm. Water at ambient conditions was used as the fluidizing liquid. The experimental data showed a trend where the heat transfer coefficient increases gradually with increasing liquid velocity approaching that for a liquid single‐phase flow (“heat transfer enhanced region”), and finally coincides with that for a liquid single‐phase flow (“liquid single‐phase heat transfer region”). The heat transfer coefficient in the heat transfer enhanced region was found to be a function of the slip velocity between liquid and particles. Based on the experimental data, a correlation was proposed for predicting the heat transfer coefficient in the entire region from the heat transfer enhanced region to the liquid single‐phase heat transfer region, which could reproduce the experimental data with an accuracy of ±15%. The proposed correlation agreed well with existing data. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(3): 127–137, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20200     

Analysis of particle motion and heat transfer in circulating fluidized beds

In this study, the forces affecting the motion of particle clusters near the wall of a CFB were theoretically analysed. The motion trajectory and the contact time of clusters were determined from the proposed model for two cases, steel ball having density of 6980 kg m^?3 and sand having density of 2500 kg m^?3. Computational results showed that the construction and operational parameters such as the bed equivalent diameter, the gas velocity and the bed temperature have great influence on the contact time of clusters. Based on analysis of the contact time of clusters, a theoretical model was developed for predicting the particle–gas convection heat transfer coefficient. The results were compared with experiments and were a quite agreement with the measured data in the open literature which suggests that the theoretical analysis conducted in this work can very well describe the convection heat transfer in a CFB. Copyright © 2004 John Wiley & Sons, Ltd.     

Heat transfer on tube bundles embedded vertically in liquid‐fluidized beds

Bed voidage was measured in liquid‐fluidized beds having tube bundles embedded vertically in beds, and the heat transfer coefficient was measured on the outer surface of the tube. There were six kinds of test channels used, and a total of nine types of particles of glass and ceramics were tested. The measured bed voidage agreed well with those developed for in‐column fluidization, when the hydraulic equivalent diameter was used. Measured heat transfer coefficients on the vertically embedded tube bundles were higher than those on the vertically embedded single tubes, the calculated values for the in‐column fluidization, and the calculated values for the horizontally embedded tube bundles. Correlations for predicting the heat transfer coefficient were derived for the vertically embedded tube bundles and single tubes. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20267     

Heat transfer in liquid‐fluidized beds affected by column wall

Heat transfer from a column wall to liquid‐fluidized beds was investigated experimentally. The diameter ratio of particle to column was changed from 0.089 up to 0.332, using 11 sizes of particles and two sizes of columns. It was found from the experiment that the critical diameter ratio of particle to column is 0.2; below this value a good fluidizing condition is maintained for any flow rate and the heat transfer coefficient changes smoothly from the minimum fluidization to the liquid single‐phase flow. Based on the experimental data, a correlation was derived to predict heat transfer coefficients for the case affected by a column wall. © 2000 Scripta Technica, Heat Trans Asian Res, 29(7): 598–608, 2000     

Theoretical performance analysis of the multi‐stage gas–solid fluidized bed air preheater

The multi‐stage fluidized bed can be used to preheat the combustion air by recovering the waste heat from the exhaust gas from industrial furnaces. The dilute‐phase fluidized bed may be formed to exclude the excessive pressure drop across the multi‐stage fluidized bed. But, in this case, the solid particles do not reach to the thermal equilibrium due to relatively short residence time in each layer of fluidized bed. In this study, a theoretical analysis on the dilute phase multistage fluidized bed heat exchanger was performed. A parameter related to the degree of thermal equilibrium between gas and solid particles at the dilute‐phase fluidized beds was derived. Using this parameter, a relatively simple expression was obtained for the thermal efficiencies of the multi‐stage fluidized bed heat exchanger and air preheater. Copyright © 2001 John Wiley & Sons, Ltd.     

Eulerian simulations of bubble behaviour in a two‐dimensional gas–solid bubbling fluidized bed

In the present study, the CFD model is based on a two‐fluid model extended with the kinetic theory of granular flow. The simulation results of bubble diameter and bubble rise velocity are compared to the Darton equation and the Davidson model in a free bubbling fluidized bed. The predicted values are in reasonable agreement with the values from the Darton bubble size equation and the Davidson model for isolated bubbles. It is shown that the break‐up and direct wall interaction effects influence the dynamic bubble behavior in the free bubbling fluidized beds. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical study of different gas–solid flow regimes effects on hydrodynamics and heat transfer performance of a fluidized bed reactor

In this study, a two‐?uid Eulerian–Eulerian model has been carried out applying the kinetic theory of granular flow (KTGF) to study the hydrodynamics and heat transfer behavior of a fluidized bed reactor simultaneously. The effects of different gas–solid flow regimes on the operating conditions and heat transfer rate between the hot air and two types of low and high‐density inert particles are investigated in a fluidized bed dryer. Different gas–solid flow regimes for wood and glass particles of groups A, B, and D of Geldart's classification are simulated to introduce the most optimal flow regime in terms of heat transfer rate and operating costs. The compromise between the heating rate, the height required for the reactor, and the ratio of the final mass to the initial mass of solid particles, which specifies the need for a cyclone separator showed that the bubbling regime of Geldart B powder for low‐density particles and the turbulent regime of Geldart D powder or bubbling regime of Geldart B powder for high‐density particles are the optimal operating conditions and flow regimes. Furthermore, it was concluded that the convective heat transfer is the dominant mechanism, which increases with increasing the air velocity and decreasing the particle diameter in each group.     

Characteristics of particle mixtures in a liquid‐fluidized bed

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     

CFD simulation of jet behaviour and voidage profile in a gas–solid fluidized bed

Based on an Eulerian–Eulerian approach, a computational fluid dynamic (CFD) model for gas–solid system has been developed to investigate the hydrodynamics in fluidized beds. With this model, jet penetration height, jet frequency, time‐averaged axial gas velocity profile, and time‐averaged voidage profile have been simulated in a two‐dimensional bed. The computational results indicate that the jet penetration height increases with increasing the jet gas velocity. The jet frequency decreases with increasing the jet gas velocity and decreasing particle diameter. The time‐averaged axial gas velocity profile becomes ‘lower’ and ‘wider’ and the time‐averaged voidage decreases with increasing distance from the jet nozzle. These conclusions appear in good agreement with the experimental and simulated data in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow characteristics of circulating gas–solid fluidized bed heat exchanger with multiple vertical pipes

Flow characteristics of a circulating gas–solid fluidized-bed heat exchanger with multiple vertical pipes were studied. The glass beads were circulated inside the vertical pipes of the heat exchanger with fluidizing air. The pressure drop and the circulation rate of solid particles were measured. In addition, one-dimensional velocity distribution of solid particles and the pressure distribution inside the vertical pipe were analysed. The prediction on the pressure drop with the circulation of solid particles was proved to be reasonably accurate by comparing with the measured results. © 1998 John Wiley & Sons, Ltd.     

Investigations of pressure fluctuation history records of gas–solid fluidized beds

A transducer pressure probe is devised to measure the pressure‐history curves up to a maximum frequency of 200 Hz. It is installed on the wall of a 153 mm² fluidized bed and is employed to establish the solids mixing and movement pattern of an air fluidized bed comprising of glass beads of 2093 μm average diameter. The pressure variations recorded with a speed of about 11 Hz for a period of 92 s are employed to compute several statistical functions and analysed to infer the quality of fluidization. For the range of fluidization number 1.05–1.48, it is inferred that in this bubbling regime, the solids near the bed wall region descend down while the air bubbles drift to the central region and rise up in the fluidized bed. This bulk macroscopic hydrodynamic picture of solids movement is in conformity with the conclusions of other co‐workers. Copyright © 2000 John Wiley & Sons, Ltd.     

Macroscopic modelling of fluid dynamics in large-scale circulating fluidized beds

Macroscopic (semi-empirical) models for fluid dynamics of circulating fluidized bed (CFB) units are presented, with emphasize on applications for conditions relevant to industrial units such as fluidized-bed combustors. In order to make a structured analysis of the models, the CFB unit is divided into 6 fluid dynamical zones, which have been shown to exhibit different fluid-dynamical behaviour (bottom bed, freeboard, exit zone, exit duct, cyclone and downcomer and particle seal). The paper summarizes the main basis and assumptions for each model together with major advantages and drawbacks. In addition, a practical example on how a selected set of these local models can be linked to an overall model of the fluid dynamics of the entire CFB loop is presented. It is shown that it is possible to reach good agreement between the overall model and experimental data from industrial units.     

Heat transfer on tube bundles embedded horizontally in a liquid‐fluidized bed

Heat transfer on tube bundles embedded horizontally in a liquid‐fluidized bed was investigated experimentally. In the experiment, a total of 5 kinds of tube bundles in an equilateral triangular staggered arrangement, including a single tube, was used. Tested particles were of glass and ceramics, and their diameter range was from 2.1 to 6.0 mm. It was found that the distribution of local heat transfer coefficients around a tube depends not on the kind of particles, but on the tube pitch only, when a good fluidizing condition is maintained. Based on the experimental data, a new method was proposed to predict average heat transfer coefficient, which can be applicable for tube bundles having a tube pitch to diameter ratio of 1.2 to infinity (single tube). © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(2): 85–98, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20048     

Flow boiling heat transfer in circulating fluidized bed

In order to enhance heat transfer and mitigate contamination in the boiling processes, a new type of vapor-liquid-solid (3-phase) circulating fluidized bed boiling system has been designed, combining a circulating fluidized bed with boiling heat transfer. Experimental results show an enhancement of the boiling curve. Flow visualization studies concerning flow hydrodynamics within the riser column are also conducted whose results are presented and discussed.     

Flow boiling heat transfer in circulating fluidized bed

In order to enhance heat transfer and mitigate contamination in the boiling processes, a new type of vapor-liquid-solid (3-phase) circulating fluidized bed boiling system has been designed, combining a circulating fluidized bed with boiling heat transfer. Experimental results show an enhancement of the boiling curve. Flow visualization studies concerning flow hydrodynamics within the riser column are also conducted whose results are presented and discussed.     

Study on gas holdup in a fluidized flotation column from bed pressure drop

This paper investigated the overall gas holdup characteristics in a cocurrent three-phase fluidized flotation column with liquid as the continuous phase. The air, water, and glass beads with a diameter of 3 mm were, respectively, used as the gas, liquid, and solid phases in the flotation column. The gas holdup studies were carried out in a plexiglass column with 0.05 m in internal diameter and 2.2 m in height. Bed pressure drop measurements were used to calculate the fractional gas holdup. During the measurements, the superficial gas and liquid velocities, respectively, varied from 0.42 to 2.55 cm/s and from 6.47 to 10.82 cm/s. Detailed experimental investigations were carried out to study the effects of static liquid height, initial static bed height, gas velocity, liquid velocity, and frother concentration on gas holdup in a cocurrent three-phase fluidized flotation column. It was found that the gas holdup increased with the flow rate of air and decreased with an increase in the water flow rate. Certain effect of the static bed height on gas holdup was observed when the gas velocity varied. But the increase in the static liquid height resulted in the decrease in gas holdup when the gas velocity varied.     

A study on thermal conductivity of a quasi‐ordered liquid layer on a solid substrate

In the present paper, a study on thermal conductivity of a quasi‐ordered liquid layer on a solid surface was performed by molecular dynamic simulation. Results showed that the motion of the molecules and their radial distribution function in the quasi‐ordered liquid layer were similar to those of solid molecules. By using the Green–Kubo formula, the thermal conductivity of the layer was calculated. It was found that it increased with the increase of the parameters of ordering. The size effect and the influence of the boundary condition were also discussed. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(7): 429–434, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20171     

The heat transfer heterogeneities of bends in flow boiling of hairpin tubes

A series of visual experiments were conducted for liquid– vapor two‐phase flow in hairpin tubes, and it was observed that most of the nucleation sites were located at the outer tube wall of the bend. From the simulation, it was concluded that the uneven velocity distribution in the bend induced the heat transfer heterogeneity. Furthermore, the nucleation of both the inner and outer tube wall of the bend and the wall temperature distribution were discussed to understand the physical phenomena. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20269