Bed-to-wall heat transfer modelling in the top region of a CFB riser column with abrupt riser exit geometries

The paper presents a mechanistic model to predict bed-to-wall heat transfer coefficient in the top region of a circulating fluidized bed (CFB) riser column by considering the riser exit geometry effects on bed hydrodynamics. With abrupt riser exit geometry, some solids will reflect back in to the riser column, thereby increasing the solids concentration in the top region of the riser column of a CFB. This in turn results in higher bed-to-wall heat transfer coefficients in the top region. At present, not much information exists in the literature to predict bed-to-wall heat transfer coefficient in the top region of a riser column with riser exit geometry effects. In the present work, a mechanistic model is proposed to estimate bed-to-wall heat transfer coefficient with riser exit geometry configurations. The length of influence of gas–solid flow structure from the riser exit due to various riser exit geometries is also presented. The solids reflux ratio is an important parameter, which influences the heat transfer rate in the top region. For the same operating conditions the bed-to-wall heat transfer coefficient increases with the abrupt riser exit geometry configuration compared to a smooth riser exit in the top region. The proposed model predictions are compared with the published experimental data for right angle exit configuration and a reasonable agreement is observed.     

Numerical modeling of axial bed-to-wall heat transfer in a circulating fluidized bed combustor

The water-wall surfaces located above the secondary air inlet within the circulating fluidized bed (CFB) combustor are exposed to the axial bed-to-wall heat transfer process. In the current work, the axial bed-to-wall heat transfer coefficients are estimated for three different axial voidage profiles (covering three widely occurring average particle concentrations) in order to investigate the effect of voidage, time, initial and fixed temperature of the bed and annulus, and gas gap between wall and solid particles; on the axial heat transfer process. A 2D thermal energy balance model is developed to estimate the axial heat transfer values for the gas–solid suspension along the height of the riser column with horizontally changing mass distribution. The gas–solid mass distribution is fixed with time thus providing a spectrum of changes in axial bed-to-wall heat transfer profile with time. The current work provides an opportunity to understand the axial heat transfer relationship with particle concentration and instantaneous behaviour. The results from the work show that: (i) first few seconds of the suspension temperature near the wall has maximum energy thus providing a small time frame to transfer more heat to the surface (CFB wall); (ii) both axial and horizontal particle concentrations (influenced by the operating conditions) affect the axial heat transfer locally; (iii) initial temperature of the bed between average and maximum values provide end limits for the axial heat transfer; (iv) annulus region has higher thermal energy than the core due to increased particle presence; and (v) a particle-free zone near the wall (gas gap) having a maximum thickness of 1 mm, tends to reduce up to 25% of axial heat transfer value. The model trends have close agreement with experimental trends from published literature; but the model values differ when correlating with real values due to inconsistencies in riser diameter and nature of variation in parameters.     

A study on the effects of operational parameters on bed-to-wall heat transfer

In this study the effects of operational parameters on bed-to-wall heat transfer in CFBs are investigated such as solids volume fraction, particle diameter, suspension density, solid circulation rate. Based on a previously developed 2D CFB model, a modified cluster renewal model is used in this investigation. The model uses the particle-based approach (PBA) and integrates the hydrodynamics and combustion aspects. The study is also validated with experimental data. As a result of this study, it is observed that the bed-to-wall heat transfer coefficients are strongly dependent on particle diameter and solids concentration at the riser wall. The smaller particles result in higher heat transfer coefficients than larger particles for the same solids volume fraction values. The heat transfer coefficient increases with suspension density. However, at a constant suspension density, the superficial velocity does not have a significant influence on the heat transfer coefficient. PBA is satisfactorily adapted to cluster renewal model so that to define the bed-to-wall heat transfer mechanisms for the upper zone.     

Effect of riser exit geometry on bed hydrodynamics and heat transfer in a circulating fluidized bed riser column

This paper reports the variation of suspension density along the riser column and the effect of riser exit geometry on bed hydrodynamics and heat transfer in the upper region of a circulating fluidized bed (CFB) riser column. The experiments are conducted in a CFB riser column which is 102 mm × 102 mm in bed cross‐section (square), 5.25 m height, with a return leg of the same dimension. The unit is made up of interchangeable plexiglass columns. The superficial primary air velocity is varied between 4.2 and 6.4 m/s. The suspension density profile along the riser height is influenced by the exit geometry. With a 90° riser exit geometry, the suspension density profile in the upper region of the CFB riser column increases towards the riser exit. This particular trend has been observed for about 2 m length in the top region of the riser. The change in suspension density profile in the top region influences the variation of heat transfer coefficient. With a 90° riser exit geometry, the suspension density increases towards the riser exit, which in turn increases the heat transfer coefficient. The effect of riser exit geometry on hydrodynamics and heat transfer is significant for about 2 m length in the upper region of the riser column. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of dilute and dense phase operating conditions on bed-to-wall heat transfer mechanism in a circulating fluidized bed combustor

In the present paper investigations are conducted on bed-to-wall heat transfer to water-wall surfaces in the upper region of the riser column of a circulating fluidized bed (CFB) combustor under dilute and dense phase conditions. The bed-to-wall heat transfer depends on the contributions of particle convection, gas convection and radiation heat transfer components. The percentage contribution of each of these components depends on the operating conditions i.e., dilute and dense phase bed conditions and bed temperature. The variation in contribution with operating conditions is estimated using the cluster renewal mechanistic model. The present results contribute some fundamental information on the contributions of particle convection, gas convection and radiation contributions in bed-to-wall heat transfer under dilute and dense phase conditions with bed temperature. This leads to better understanding of heat transfer mechanism to water-wall surfaces in the upper region of the riser column under varying load conditions i.e., when the combustor is operated under dilute and dense phase situations. The results will further contribute to understanding of heat transfer mechanism and will aid in the efficient design of heat transfer surfaces in the CFB unit.     

Experimental investigations on heat transfer from suspension to impact separators in the riser column of a circulating fluidized bed combustor

In the present work experiments are conducted to investigate the effect of operating parameters on heat transfer from bed to U-beam impact separators located in the top region of the riser column. The effect of suspension density and bed temperature on heat transfer from bed to the impact separators (test sections) are investigated. The experimental unit consists of a circulating fluidized bed riser column, which is 0.23 m×0.23 m in bed cross-section, 6.3 m in height with a return leg and back pass. The U-beam impact separators are located in the top region of the riser column. Furnace oil # 2 is burnt in the unit and the experimental investigations are conducted. Water is circulated through the U-beam impact separators. The presence of the impact separators in the top region of riser column helps in solids separation and also to absorb certain fraction of heat liberated in the furnace. The bed to U-beam impact separator heat transfer coefficient increases with suspension density due to increased particle concentration, which results in higher cluster and particle heat transfer. The heat transfer coefficient increases with bed temperature due to increased convection and radiation.     

Effect of pressure on thermal aspects in the riser column of a pressurized circulating fluidized bed

In the present paper the effect of pressure on bed‐to‐wall heat transfer in the riser column of a pressurized circulating fluidized bed (PCFB) unit is estimated through a modified mechanistic model. Gas–solid flow structure and average cross‐sectional solids concentration play a dominant role in better understanding of bed‐to‐wall heat transfer mechanism in the riser column of a PCFB. The effect of pressure on average solids concentration fraction ‘c’ in the riser column is analysed from the experimental investigations. The basic cluster renewal model of an atmospheric circulating fluidized bed has been modified to consider the effect of pressure on different model parameters such as cluster properties, gas layer thickness, cluster, particle, gas phase, radiation and bed‐to‐wall heat transfer coefficients, respectively. The cluster thermal conductivity increases with system pressure as well as with bed temperature due to higher cluster thermal properties. The increased operating pressure enhances the particle and dispersed phase heat transfer components. The bed‐to‐wall heat transfer coefficient increases with operating pressure, because of increased particle concentration. The predicted results from the model are compared with the experimentally measured values as well as with the published literature, and a good agreement has been observed. The bed‐to‐wall heat transfer coefficient variation along the riser height is also reported for different operating pressures. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical modeling of bed-to-wall heat transfer in a circulating fluidized bed combustor based on cluster energy balance

The bed-to-wall heat transfer in a circulating fluidized bed (CFB) combustor depends on the heat transfer contributions from particle clusters, dispersed/gas phase and radiation from both of them. From the available CFB literature, most of the theoretical investigations on cluster and bed-to-wall heat transfer are based on mechanistic models except a few based on mathematical and numerical approaches. In the current work a numerical model proposed to predict the bed-to-wall heat transfer based on thermal energy balance between the cluster/dispersed phase and the riser wall. The effect of cluster properties and the thermal boundary conditions on the cluster heat transfer coefficient are analyzed and discussed. The fully implicit finite volume method is used to solve the governing equations by generating a 2D temperature plot for the cluster and the dispersed phase control volumes. From this 2D temperature profile, space and time averaged heat transfer coefficients (for cluster, dispersed phase and radiation components) are estimated for different operating conditions. The results from the proposed numerical simulation are in general agreement with published experimental data for similar operating conditions. The results and the analysis from the current work give more information on the thermal behavior of the cluster and dispersed phases, which improves the understanding of particle and gas phase heat transfers under different operating conditions in CFB units.     

3D modelling of radiative heat transfer in circulating fluidized bed combustors: influence of the particulate composition

A three-dimensional model is developed to predict the bed-to-wall radiative heat transfer coefficient in the upper dilute zone of circulating fluidized bed (CFB) combustors. The radiative transfer equation is solved by the discrete ordinates method and Mie scattering theory is applied to calculate the absorption and scattering efficiency factors of particles existing in CFB combustors. Empirical correlations calculate both spacial variation of solid volume fraction and temperature distribution at the wall. The model considers the influences of the particle properties (including particle size distribution, particle optical constants and solid composition) on the radiative heat transfer coefficient. Simulation results show that the particle properties have significant influences on the bed-to-wall radiative heat transfer coefficient in CFB combustors. A very good agreement of predicted results is shown with experimental data.     

Fundamental heat transfer mechanism between bed‐to‐membrane water‐walls in circulating fluidized bed combustors

In the present work, the fundamental mechanism between bed‐to‐membrane water‐walls in the riser column of a circulating fluidized bed (CFB) combustor is presented. The bed‐to‐membrane water‐wall heat transfer depends on the contributions of particle heat transfer, dispersed phase heat transfer and radiation heat transfer. The fundamental mechanism of particle heat transfer and the effect of fraction of wall exposed to clusters and gas gap thickness between cluster and wall on particle heat transfer coefficient and bed‐to‐wall heat transfer coefficient are investigated. The influence of operating parameters like cross‐sectional average volumetric solids concentration and bed temperature on particle and bed‐to‐wall heat transfer are also reported. The present work contributes some fundamental information on particle heat transfer mechanism, which is responsible for increasing the bed‐to‐wall heat transfer coefficient (apart from dispersed phase convection and radiation heat transfer). The details on particle heat transfer mechanism will enable to understand the basic heat transfer phenomena between bed‐to‐membrane water‐walls in circulating fluidized bed combustors in a detailed way, which in turn will aid for better design of CFB combustor units. The particle heat transfer mechanism is significantly influenced by the fraction of wall exposed to clusters and gas gap thickness between clusters and wall. Copyright © 2003 John Wiley & Sons, Ltd.     

A study of heat transfer in a circulating fluidized bed

An experimental investigation was carried out to study the effects of operating parameters on the local bed-to-wall heat transfer coefficient in a 4.5 m tall, 0.150 m diameter circulating fluidized bed with a bed temperature in the range of 65°C to 80°C, riser flow rate varying from 1400 litres/min to 2000 litres/min, bed inventory in the range of 15 kg to 25 kg of sand, and average sand sizes of 200 μm, 400 μm and 500 μm. A heat flux probe was attached to the riser wall at five different vertical locations for measuring the heat flux from the bed to the wall surface. From the present work, the heat transfer coefficient in the dilute phase was found to be in the range of 62 to 83 W/m²K, 51 to 74 W/m²K, and 50 to 59 W/m² K for sand sizes of 200 μm, 400 μm and 500 μm, respectively. Relevant mathematical correlations were developed to predict local heat transfer coefficient based on the results of the practical work.     

Simulation study of the effect of the restitution coefficient on interphase heat transfer processes and flow characteristics in a fluidized bed

This article discusses a simulation study performed to investigate the effect of particle collision on inter-particle and gas–solid heat transfer processes, and other related bed flow characteristics. The effect of particle elasticity is presented using different values of the particle–particle coefficient of restitution. The simulation study was carried out using a two-dimensional model of a fluidized bed reactor incorporated to ANSYS Fluent 16.2 software. Two different materials, steel beads and sand particles, were used as the bed material fluidized by air. The simulation results are compared to those from previous studies on fluidized bed reactors containing a single bed material. The coefficient of restitution affected the bed hydrodynamics. Specifically, an increasing coefficient of restitution resulted in an increasing bed pressure drop and decreasing void fraction, granular temperature, particle velocity, and collision frequency. Conversely, increasing the particle coefficient of restitution resulted in decreasing the particle–particle heat exchange coefficient and the gas–particle heat transfer coefficient. The gas–particle heat transfer coefficient for sand particles was higher than that for steel beads. The effect of the coefficient of restitution on the flow characteristics from a binary mixture bed was quite similar to those of single material beds found in previous studies. This study demonstrated that the restitution coefficient clearly affected both the particle–particle and gas–particle heat transfer processes.     

Effect of pressure and temperature on cluster and particle heat transfer in a pressurized circulating fluidized bed

The present work reports the influence of pressure and bed temperature on particle‐to‐wall heat transfer in a pressurized circulating fluidized bed (PCFB). The particle convection heat transfer plays a dominant role in determining the bed‐to‐wall heat transfer coefficient. So far, no information is reported on the effect of pressure and bed temperature on particle‐to‐wall heat transfer in a PCFB in the published literature. The present investigation reports some information in this direction. The effect of system pressure and bed temperature are investigated to study their influence on cluster and particle heat transfer. The particle convection heat transfer coefficient increases with system pressure and bed temperature due to higher cluster thermal conductivity. The increase in particle concentration (suspension density) results in greater cluster solid fraction and also the particle concentration near the wall is enhanced. This results in higher cluster and particle convection heat transfer between the bed and the wall. Higher particle convection heat transfer coefficient results in enhanced heat transfer between the bed and the wall. The results will also help to understand the bed‐to‐wall heat transfer mechanism in a better way in a PCFB. Copyright © 2001 John Wiley & Sons, Ltd.     

Heat transfer in a crater bed

The aim of this work is to study heat transfer in a laboratory scale crater bed, which was set up from a cylindrical acrylic/quartz tube, using sand as the bed particle. The bed employs a downward gas jet from a nozzle which causes the particles to ascend fountain-like into the freebroad, leaving a crater on the bed surface. After reaching a certain height, these particles will descend again to the bed surface and move into the crater, where the cycle or circulation pattern starts again. The study had been separated into three parts. Firstly, the void fraction of the bed fountain zone was studied by direct measurement of the ascending sand weight within the specific volume. Secondly, the convection heat transfer coefficients between the fountain zone and the external surface of the gas inlet tube were determined by measuring the quantity of heat loss from an electrical heater that was wrapped on the outside surface at desired positions of the gas inlet tube. Thirdly, the radiation heat transfer coefficients were evaluated by heat balance of LPG combustion in the crater bed. From experimental results, the void fraction of the fountain zone could be approximated as a dilute bed (>0.98). For convective heat transfer coefficients, the value found experimentally varied from 80–260 W/m² K depending on the experimental conditions, showing an increase when the gas velocity increases, and a decrease along the height of the gas inlet tube. Radiation heat transfer coefficients, the values of which are (within the experimental temperature range), the same order as the convective mode, increase when the bed temperature is increased and when the bed particle diameter is decreased. Empirical correlations for both bed voidage and heat transfer coefficients are proposed. The combined model, gas and particle convection and the published data on radiation heat transfer, showed good prediction when compared with experimental data.     

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     

Numerical investigation of gas-to-particle cluster convective heat transfer in circulating fluidized beds

Convective heat transfer between gas and cluster in a circulating fluidized bed (CFB) riser is numerically studied using a three-dimensional computational fluid dynamic (CFD) model. Distributions of gas velocity and temperature as well as the gas-cluster heat flux and convective heat transfer coefficient are obtained. Variations of heat flux of each particle in the cluster are predicted. The heat flux of the individual particle inside the cluster is smaller than that of an isolated particle. The convective heat transfer coefficients increase with the increase of cluster porosity and Reynolds number. The convective heat transfer coefficients of the downward moving cluster are larger than that of upward moving cluster. Numerical results of an isolated particle are in agreement with data from previously published correlations.     

Experimental study of pressurized gas-fluidized bed heat transfer

This paper reports on an experimental study of the influence of operating pressure, in the range 150-1100 kPa, on wall-to-bed heat transfer coefficient in a bubbling fluidized bed. Both Geldart Group A and B solids were studied and the fluidizing gases were air and superheated steam. Fluidizing velocities were in the range 1-33 U_mf and wall temperatures in the range 125-275°C. Wall-to-bed heat transfer coefficients were found to increase steadily with increasing fluidizing gas velocity and not to pass through a maximum. Increase in operating pressure was found generally to result in an increase in wall-to-bed heat transfer coefficient, although the effect is probably non-linear. In the bubbling regime, the wall-to-bed heat transfer coefficient was found to change with vertical position in the bed. Wall-to-bed heat transfer coefficients decreased when the bed entered the slugging regime.     

Local instantaneous temperature and time‐averaged heat transfer coefficient in the bottom zone of a circulating fluidized bed

Local instantaneous temperature signal and time‐averaged heat transfer coefficient were measured using a miniature heat transfer probe. The experiments were carried out in the bottom zone of a 5.8m high, 0.3m×0.5m rectangular cross‐section circulating fluidized bed. The results show that the heat transfer coefficient was higher near the walls, and became lower near the central region, and that the heat transfer coefficient decreases with increment of the air velocity due to the associated reduction of solids holdup in the bottom zone. In addition, the power spectrum density functions of the local instantaneous temperature signal can be characterized by the 1/f‐like distribution. Copyright © 2004 John Wiley & Sons, Ltd.     

The impact of bed temperature on heat transfer characteristic between fluidized bed and vertical rifled tubes

In the present work, the heat transfer study focuses on assessment of the impact of bed temperature on the local heat transfer characteristic between a fluidized bed and vertical rifled tubes (38mm-O.D.) in a commercial circulating fluidized bed (CFB) boiler. Heat transfer behavior in a 1296t/h supercritical CFB furnace has been analyzed for Geldart B particle with Sauter mean diameter of 0.219 and 0.246mm. The heat transfer experiments were conducted for the active heat transfer surface in the form of membrane tube with a longitudinal fin at the tube crest under the normal operating conditions of CFB boiler. A heat transfer analysis of CFB boiler with detailed consideration of the bed-to-wall heat transfer coefficient and the contribution of heat transfer mechanisms inside furnace chamber were investigated using mechanistic heat transfer model based on cluster renewal approach. The predicted values of heat transfer coefficient are compared with empirical correlation for CFB units in large-scale.     

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