A three-dimensional model for suspension-to-membrane-wall heat transfer in circulating fluidized beds

A three-dimensional model is proposed for both furnace-side and wall-side heat transfer in circulating fluidized beds with membrane walls. Following previous publications (Int. J. Heat Mass Transfer (2003a, b)), a core-annulus flow structure is employed in the model, with consideration of the membrane wall influence on bed hydrodynamics. The model couples radiation, conduction and convection on the furnace side to conduction and convection on the wall side. Radiation in the wall layer is simulated by the moment method. A finite-element method is employed to solve the set of non-linear, partial differential equations. The solution is demonstrated for a typical example. The model gives predictions of suspension-to-wall heat transfer which show satisfactory agreement with published experimental data.     

流化床浸没换热管传热研究进展

论述了前人对流化床与浸没换热管间传热规律的理解和认识,介绍了常用的传热模型及其实用条件,总结了近年来在实验研究等方面所取得的进展。     

Eulerian–Eulerian simulation of heat transfer between a gas–solid fluidized bed and an immersed tube-bank with horizontal tubes

A two dimensional Eulerian–Eulerian simulation of tube-to-bed heat transfer is carried out for a cold gas fluidized bed with immersed horizontal tubes. The horizontal tubes are modelled as obstacles with square cross section in the numerical model. Simulations are performed for two gas velocities exceeding the minimum fluidisation velocity by 0.2 and 0.6 m/s and two operating pressures of 0.1 and 1.6 MPa. Local instantaneous and time averaged heat transfer coefficients are monitored at four different positions around the tube and compared against experimental data reported in literature. The effect of constitutive equations for the solid phase thermal conductivity on heat transfer is investigated and a fundamental approach to modelling the solid phase thermal conductivity is implemented in the present work. Significant improvements in the agreement between the predicted and measured local instantaneous heat transfer coefficients are observed in the present study as compared to the previous works in which the local instantaneous heat transfer coefficients were overpredicted. The local time averaged heat transfer coefficients are within 20% of the measured values at the atmospheric pressure. In contrast, underprediction of the time averaged heat transfer coefficient is observed at the higher pressure.     

Effect of annular fins on heat transfer of a horizontal immersed tube in bubbling fluidized beds

Experiments were conducted in a bubbling air-fluidized bed to investigate the effect of annular fins of constant thickness on heat transfer. Steady state time averaged local heat transfer coefficient measurements were made by the local thermal simulation technique in a cold bubbling fluidized bed (90 mm ID, 260 mm tall) with horizontally immersed tube initially with no fin and then with three fixed annular fins of constant thickness. Silica sand of mean particle diameter 307 μm and 200 μm were used as the bed materials. The superficial velocity of air was from minimum fluidization conditions, u_mf, to approximately 3 × u_mf. The results indicate that, although the heat transfer coefficient falls with the use of fins, the total heat transfer rises as a result of the greater surface area. Increasing the particle diameter reduces the heat transfer coefficient not only for unfinned horizontal tube but also for annular finned horizontal tube at the same conditions of fluidized bed. Based on the experimental data, correlations are proposed for predicting heat transfer coefficient from fluidized bed to horizontally immersed tubes with and without fins.     

Heat transfer between very shallow fluidized beds and an immersed horizontal tube

A new correlation is proposed for the heat transfer coefficient between an immersed horizontal tube and very shallow fluidized beds (static bed heights of 10-40 mm). The correlation is based upon experimental data obtained in this work for a horizontal tube with an outside diameter of 13.1 mm, immersed in beds of spherical alumina particles with mean particle sizes of 335-1261 microns. The maximum bed pressure drop was 92.5 mm water. The effects of tube elevation, static bed height and distributor design were investigated. Nine different distributors were used, with maximum pressure drops ranging from 3 to 800 mm water and open areas from 2.2 to 36%. A comparison between the proposed correlation and data reported in the literature showed an agreement of approximately ±10%.     

Local hydrodynamics and heat transfer in fluidized beds of different diameter

Heat transfer coefficients were measured in fluidization columns of 0.29 m and 1.56 m ID at fixed distance above the distributor, using an identical vertical heater, the same alumina particles and geometrically scaled bubble-cap distributors. The magnitude of the maximum heat transfer coefficients was found to be unaffected by the column diameter, but occurred at higher superficial velocities in the larger column. When the local flow structure near the heater corresponded to the turbulent flow regime of fluidization, the local heat transfer coefficients were independent of radial position in both columns.     

Numerical investigation of gas-solid heat transfer in rotating fluidized beds in a static geometry

Gas-solid heat transfer in rotating fluidized beds in a static geometry is theoretically and numerically investigated. Computational fluid dynamics (CFD) simulations of the particle bed temperature response to a step change in the fluidization gas temperature are presented to illustrate the gas-solid heat transfer characteristics. A comparison with conventional fluidized beds is made. Rotating fluidized beds in a static geometry can operate at centrifugal forces multiple times gravity, allowing increased gas-solid slip velocities and resulting gas-solid heat transfer coefficients. The high ratio of the cylindrically shaped particle bed “width” to “height” allows a further increase of the specific fluidization gas flow rates. The higher specific fluidization gas flow rates and increased gas-solid slip velocities drastically increase the rate of gas-solid heat transfer in rotating fluidized beds in a static geometry. Furthermore, both the centrifugal force and the counteracting radial gas-solid drag force being influenced by the fluidization gas flow rate in a similar way, rotating fluidized beds in a static geometry offer extreme flexibility with respect to the fluidization gas flow rate and the related cooling or heating. Finally, the uniformity of the particle bed temperature is improved by the tangential fluidization and resulting rotational motion of the particle bed.     

Comparison of heat transfer models in DEM-CFD simulations of fluidized beds with an immersed probe

The basic mechanisms governing the process of surface-to-bed heat transfer in fluidized beds and their relative importance have not been fully characterized yet, mainly owing to the lack of reliable data at the particle scale. Numerical simulations based on the discrete element method may prove successful in predicting the evolution of the fluid and particles' temperature fields. In the present work, microscopic models of the fluid-particle, particle-particle, fluid-surface and particle-surface heat transfer have been implemented in a DEM-CFD hydrodynamic code. Details are discussed on the methodology adopted to include immersed objects in the computational domain. Thus, three approaches to represent particle-particle heat transfer are analysed and compared against experimental values, taken from the literature, of the heat transfer coefficient between a hot fluidized bed and a spherical probe. Unfortunately, some parameters appearing in the formulations are difficult to determine, so reasonable estimates are calculated and used in the simulations. Under conditions similar to the experiments, simulation predictions of the heat transfer coefficient range from 43 to 340 W/(m² K) depending on the model used, while the experimental values are located around 160 W/(m² K). The variability of these numerical results confirms their sensitivity to the particle-particle mechanism considered. Finally, it is shown that using the model that produces results in agreement with experiments the heat flows due to the particle convective and the fluid convective transfer are of comparable importance.     

Evaluation of heat transfer coefficient in gas-solid fluidized beds using cluster-based approach

The concept of temperature penetration depth is used to investigate the heat transfer behavior near the wall of fluidized beds, according to the cluster-based approach. The process of heat transfer through clusters which exist adjacent to the wall was viewed in context of partial and total heat penetration. In the case of partial heat penetration, the heat flux applied to the wall side of the clusters has not reached its bed-side, while in the case of total heat penetration the heat flux has completely crossed the cluster, and the temperature of its bed-side would differ from the bed temperature. Based on the heat balance equation inside the cluster, two different expressions were derived for heat transfer coefficient for each penetration period. The predictions of the proposed model are in close agreement with experimental values and to some extent better than existing models.     

Heat transfer in fluidized beds: design methods

Large-scale fluidized beds for commercial processes commonly require heat transfer surfaces. Design then demands that heat transfer coefficients be specified. Empirical correlations are unable to cover the wide range of variables and conditions encountered. Mechanistic models are more reliable, but must be chosen carefully. For bubbling beds, the packet model approach gives reasonable predictions for the convective component of transfer, but further work is required to provide reliable estimates of two required time constants, dependent on the hydrodynamics. For industrial-scale circulating beds, a mechanistic model that incorporates the key factors influencing heat transfer, assumes fully developed transfer, and utilizes results from large-scale units is recommended.     

Prediction of heat transfer to liquid-solid fluidized beds

Heat transfer coefficients to a liquid-solid fluidized bed in a cylindrical tube have been measured using water as liquid phase and three types of cylindrical steel particles, as well as glass, nickel, copper and lead spheres of different sizes as solid phase. The independent varaibles included heat flux, liquid velocity and particle physical properties. The experimental results as well as a data bank containing a large number of measured heat transfer coefficients for solid-liquid fluidization over a wide range of operational parameters have been compared with the predictions of most published correlations. A model for the prediction of heat transfer coefficients is proposed which predicts the present experimental data and the data of other investigators with good accuracy.     

Radiative heat transfer in circulating fluidized bed furnaces

Three methods of estimating the effective emissivity of a gas-particle suspension are compared and the radiative heat transfer coefficient of an isothermal suspension is defined. Heat flux measurements obtained from circulating fluidized bed combustors are examined. Radiation from a particle suspension with core temperature dominates the radiative heat transfer in the upper part of the furnace, where the particle density is low and no substantial particle boundary layers are formed. Over the lower parts of the heat transfer surfaces, where significant thermal and particle boundary layers are present, the radiative heat flux is dominated by emission from the relatively low temperature particle layer in the vicinity of the heat receiving surface.     

Experimental investigation of particle contact time at the wall of gas fluidized beds

The contact time of particles at the walls of gas fluidized beds has been studied using a radioactive particle tracking technique to monitor the position of a radioactive tracer. The solids used were sand or FCC particles fluidized by air at room temperature and atmospheric pressure at various superficial velocities, covering both bubbling and turbulent regimes of fluidization. Based on the analysis of tracer positions, the motion of individual particles near the walls of the fluidized bed was studied. The contact time, contact distance and contact frequency of the particles at the wall were evaluated from these experimental data. It was found that in a bed of sand particles, the mean wall contact time of the fluidized bed of sand particles decreases by increasing the gas velocity in the bubbling and increases in the turbulent fluidization. In other words, the particle-wall contact time is minimum at the onset of turbulent fluidization in the bed of sand particles. However, the mean wall contact time is almost constant in both regimes of fluidization in the bed of FCC particles. All the existing models in the literature predict a decreasing contact time when the gas velocity in the bed is increased. It was also shown that the contact distance increases monotonously by increasing the gas velocity in the bed of sand particles, while it is almost constant for the bed of FCC particles. Contact frequency has a trend similar to that of the contact time for both sand and FCC particles.     

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.     

Effect of agglomerate properties on agglomerate stability in fluidized beds

Fluidized bed agglomeration is used to stabilize particulate mixtures and reduce dust emissions. This technology is applied to a variety of production processes for the pharmaceutical, chemical, fertilizer and food industries. In most of these applications, agglomerate stability is an essential criterion. Agglomerates and granules that do not conform to size and shape specifications may create problems in downstream processes, such as tableting, thus compromising process efficiency and product quality. When an agglomerate is formed in a fluidized bed, it can grow by incorporating other bed particles, split into smaller fragments, or be eroded by fluidized bed solids. The objective of the present study is to determine the critical agglomerate liquid content at which the rates of agglomerate growth and shrinkage are balanced when artificial agglomerates made from glass beads and water are introduced into a fluidized bed. This study examined the effects of agglomerate size, agglomerate density, liquid viscosity, binder concentration, and fluidizing gas velocity on the critical initial liquid content. This study found that small agglomerates and low density agglomerates displayed higher critical initial moisture contents. When the viscosity was increased by using sugar solutions, agglomerates were very stable and had very low critical initial moisture contents. The study also found that as the superficial gas velocity increased, the agglomerates started to fragment, rather than erode.     

Measurement of radiative heat transfer coefficient in a high temperature circulating fluidized beds

Experimental measurements of the radiative heat flux were made, and radiative heat transfer coefficients were determined for a circulating fluidized bed of sand particles of mean diameters of 137 and 264 microns. The bed used in this study measured 0.05 m in diameter. The heat transfer test section was 0.9 m long and located in the middle of CFB riser. Operating temperature was varied from 200–600 °C, and the gas velocity in the CFB riser varied from 6 m/s to 11 m/s. The suspension densities covered a range from 3 to 35 kg/m³. Time-averaged radiative heat flux was directly measured with a radiometer. Radiative heat flux and suspension emissivity showed strong dependence on the suspension density. Particle size effect on suspension emissivity was observed. Experimentally determined suspension emissivities, which ranged from 0.3 to 0.85, were in good agreement with the predicted suspension emissivity based on independent scattering theory. The radiative heat transfer coefficients were determined from the measured radiative heat fluxes and were found to be well predicted by the Stefan-Boltzmann law. It was also found that for a dilute system, the prediction of suspension emissivity by Hottel and Sarofim, in conjunction with independent scattering theory of Brewster and Tien, showed good agreement with experimentally determined suspension emissivity.     

Size segregation in gas-solid fluidized beds with continuous size distributions

Discrete-particle simulations of a gas-solid fluidized bed are used to investigate the species segregation (de-mixing) behavior of systems with continuous particle size distributions. Both Gaussian and lognormal distributions are investigated over a range of distribution widths, restitution and friction coefficients, and gas velocities. The results indicate that: (i) the average particle diameter decreases as the height within the bed increases, (ii) the level of segregation increases with an increase in the width of the particle size distribution, and (iii) segregation is attenuated as bubbling becomes more vigorous. Furthermore, the shape of the local size distribution (i.e., Gaussian or lognormal) is found to mimic that of the overall size distribution in most regions of the fluidized bed.     

Particle scale study of heat transfer in packed and bubbling fluidized beds

The approach of combined discrete particle simulation (DPS) and computational fluid dynamics (CFD), which has been increasingly applied to the modeling of particle‐fluid flow, is extended to study particle‐particle and particle‐fluid heat transfer in packed and bubbling fluidized beds at an individual particle scale. The development of this model is described first, involving three heat transfer mechanisms: fluid‐particle convection, particle‐particle conduction and particle radiation. The model is then validated by comparing the predicted results with those measured in the literature in terms of bed effective thermal conductivity and individual particle heat transfer characteristics. The contribution of each of the three heat transfer mechanisms is quantified and analyzed. The results confirm that under certain conditions, individual particle heat transfer coefficient (HTC) can be constant in a fluidized bed, independent of gas superficial velocities. However, the relationship between HTC and gas superficial velocity varies with flow conditions and material properties such as thermal conductivities. The effectiveness and possible limitation of the hot sphere approach recently used in the experimental studies of heat transfer in fluidized beds are discussed. The results show that the proposed model offers an effective method to elucidate the mechanisms governing the heat transfer in packed and bubbling fluidized beds at a particle scale. The need for further development in this area is also discussed. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Three-dimensional numerical study of heat and mass transfer in fluidized beds with spray nozzle

The numerical computations of temperature and concentration distributions inside a fluidized bed with spray injection in three-dimensions are presented. A continuum model, based on rigorous mass and energy balance equations developed from Nagaiah et al., is used for the three-dimensional simulations. The three-dimensional model equation for nozzle spray is reformulated in comparison to Heinrich. For solving the non-linear partial differential equations with boundary conditions a finite element method is used for space discretization and an implicit Euler method is used for time discretization.The time-dependent behavior of the air humidity, air temperature, degree of wetting, liquid film temperature and particle temperature is presented using two different sets of experimental data. The presented numerical results are validated with the experimental results. Finally, the parallel numerical results are presented using the domain decomposition methods.