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.     

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.     

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.     

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.     

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.     

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.     

循环流化床锅炉炉膛的传热计算

结合以往对循环流化床(CFB)锅炉炉膛传热系数的研究成果,建立了CFB锅炉炉膛传热系数的计算模型,并对辐射传热系数和对流传热系数的计算分别进行了相应的分析.对某CFB锅炉在100%负荷条件下的炉膛传热系数进行了计算,并对影响该传热系数的主要因素进行了分析,包括受热面结构尺寸、床层温度Tb、工质温度Tf、工质侧传热系数af以及壁面黑度εw等.结果表明:该模型能够合理地反映出以上因素对CFB锅炉炉膛传热系数的影响.     

Modelling heat transfer in a circulating fluidized bed

A model for the bed-to-wall heat transfer under low temperature condition in a circulating fluidized bed (CFB) was developed based upon a simplified cluster renewal concept. The age of clusters in contact with the wall at different locations along the height of the CFB was estimated as the weighted average age considering their formation and disintegration. One set of experimental data on heat transfer in a 4.5-metre high, 0.15-metre diameter CFB under low temperature condition (67–77°C) was chosen for comparison with prediction of local heat transfer coefficient. The experimental observation and prediction have shown a qualitative agreement.     

循环流化床中的气固两相传热模型

循环流化床中存在着分散固体颗粒的连续上升气相和相对紧密的颗粒团两部分,颗粒团聚物对气固两相传热有着重要的影响。采用拟Boltzmann动力学方法描述循环流化床中颗粒团的动力学行为,建立了循环流化床中气固两相间传热过程的理论模型,对气体表观流速、固体颗粒循环率等对气固传热系数沿床高分布规律的影响进行了分析和讨论。模型计算结果与参考文献中的实验数据进行了比较,两者符合较好。     

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.     

Modeling the radiation of anisotropically scattering media by coupling Mie theory with finite volume method

A new mathematical model and code for radiative heat transfer of particulate media with anisotropic scattering for 2-D rectangular enclosure is developed. The model is based on the coupling of (i) finite volume method for the solution of radiative transfer equation with (ii) Mie equations for the evaluation of scattering phase function. It has not been done before to the authors’ best knowledge. The predictions were compared against the only found results, published 15 years ago. For those results the S-N discrete ordinates method for the solution of radiative transfer equation and the Legendre polynomials expansions for the evaluation of scattering phase function were used. The agreement between the results is very good. The advantages of new model and code are in their straight forward application to any given particles parameters without the need for previously designed analytical expression for scattering phase function. In addition, that analytical expression, with generated expansion coefficients, is restricted and can be used only for that particular case of particle parameters. The new model was applied to the solid particles of several various coals and of an ash and the series of 2-D predictions are performed. The effects of particle size parameter and of scattering albedo on radiative heat flux and on incident radiation were analyzed. It was found that the model developed is reliable and very accurate and thus suitable for extension towards: (i) 3-D geometries, (ii) mixtures of non-gray gases with particles as well as for (iii) incorporation in computational fluid dynamics codes.     

循环流化床传热系数的计算模型

本文在循环流化床流动模型的基础上建立了传热模型，流动模型根据实际运行情况考虑了颗粒的宽筛分，并把床层在轴向上分为密相床和稀相床两部分。在密相床内，传热按照鼓泡床传热微型进行计算；在稀相床内，传热模型建立在颗粒团更新的假设基础上，根据假设，床层由颗粒浓度很低的上升稀相和相对颗粒浓度较大的颗粒团两部分组成，两部分交替地与床壁面接触，床层和受热面间局部换热系数和颗粒浓度及两部分接触壁面的份额有关。模化结     

循环流化床锅炉物料浓度分布的影响因素分析

循环流化床(CFB)锅炉炉膛物料浓度分布直接影响炉膛内的传热特性和锅炉负荷。基于CFB锅炉炉膛内气固两相流动特性,建立了密相区以上区域的物料浓度数学计算模型。以1台1 060 t/h CFB锅炉为研究对象,数值计算分析不同煤种、给煤粒度分布、流化风速、分离器效率及床压降对炉膛物料浓度分布的影响,计算分析结果表明,CFB锅炉运行中,针对不同煤质,可以通过优化给煤粒度分布和床压降来调节炉膛上部的物料浓度分布,低挥发分煤种的给煤粒度分布中细颗粒的比例要大一些。分离器性能越好,床质量越好,在相同的流化风速和床压降下,炉膛出口处物料浓度随d50、d99的减小而增大。     

Transient thermal analysis of semitransparent composite layer with an opaque boundary

Transient coupled radiative and conductive heat transfer in a two-layer, absorbing, emitting, and isotropically scattering non-gray slab is investigated by the ray tracing method in combination with Hottel's zonal method. One outer boundary is opaque, and another is semitransparent. The radiative energy transfer process in a semitransparent composite is divided into two sub-processes, one of which considers scattering, the other does not. The radiative transfer coefficients of the composite are deduced under specular and diffuse reflection and combined specular and diffuse reflection, respectively. The radiative heat source term is calculated by the radiative transfer coefficients. Temperature and heat flux are obtained by using the full implicit control-volume method in combination with the spectral band model. The method presented here needs only to disperse the space position, instead of the solid angle. A comparison with previous results shows that the results are more accurate.     

The Combined Radiative Integral Equations and Finite-Element Method for Radiation in Anisotropic Scattering Media

A combined procedure of the radiative integral equation and finite-element method (IEFEM) is proposed for handling radiative heat transfer in linearly anisotropic scattering media. The IEFEM can eliminate the angular discretization and easily handle irregular geometries. The present work provides a solution of radiative transfer in rectangular and irregular quadrilateral enclosures containing participating media. The influences of emissivities, albedos, and anisotropy on the boundary fluxes or incident intensity have been analyzed. Compared with the results in published references, the present IEFEM has no limitation to geometry and can predict the radiative heat transfer in linearly anisotropic scattering media accurately.     

Experimental Determination of the Radiative Properties of Particle Suspensions for High-Temperature Solar Receiver Applications

This study combines experimental measurements with a numerical method to determine the effective radiative properties of particle suspensions. A spectroscopic goniometry system is applied to measure the attenuation and angular radiation distribution of irradiated samples produced by uniformly suspending particles within a transparent epoxy resin. Samples of varying porosity and thickness are examined. A collision-based Monte Carlo model is formulated for a continuous participating medium representing the particle suspension. The volume-averaged radiative properties, namely, the extinction coefficient, the scattering albedo, and the scattering phase function, are determined for porosities between 0.72 and 0.95 by fitting to the experimental data. Extended correlations of the independent scattering theory show good match with the experimental determined extinction coefficient and capture the dependent scattering effect. The modified double Henyey–Greenstein scattering phase function yields the best agreement between experimental and numerical results, and is characterized by a strong forward scattering preference.     

Modeling of heat transfer coefficient in the furnace of CFB boilers by artificial neural network approach

The present work introduces a way of predicting the local heat transfer coefficient in the combustion chamber of the circulating fluidized bed boiler (CFB) by the artificial neural network (ANN) approach.Neural networks have been successfully applied to calculate the local overall heat transfer coefficient for membrane walls, Superheater I (SH I, Omega Superheater) and Superheater II (SH II, Wing-Walls) in the combustion chamber of the 260 MWe CFB boiler. The previously verified numerical model has been used to obtain the overall heat transfer coefficients, necessary for training and testing the ANN. It has been shown, that the neural networks give quick and accurate results as an answer to the input pattern. The local heat transfer coefficients evaluated using the developed ANN model have been in a good agreement with numerical and experimental results.     

Effect of operating parameters on bed-to-wall heat transfer in a high temperature circulating fluidized bed

An experimental investigation was made to study the effect of some operating parameters on the bed-to-wall heat transfer in a 5.25 m-tall circulating fluidized bed having a 102 mm-square cross-section with a bed temperature varying from 350 to 1173 K, a superficial velocity from 4 to 8 m/s, and a bed inventory from 15 to 40 kg of sand with a mean particle diameter of 309 μm. Two heat flux probes were used at two different locations in the furnace for measuring the heat transfer coefficient. The experimental results were compared with those of other investigators and also with the data predicted from a proposed theoretical model.     

Tomography based pore-level optimization of radiative transfer in porous media

A non-energy-partitioning Monte Carlo Ray Tracing (MCRT) model is employed to optimize radiative transfer in porous media. The pore level geometry is incrementally modified using 3D equivalents of image manipulation algorithms such as erosion, dilation, opening, and closing. Subsequently, direct, pore-level analysis of radiative transfer is carried out for each modification step to optimize the pore-level geometry for maximum absorptance. Results have been obtained for an opaque, diffusely or specularly reflecting solid phase within a non-participating void phase. Model media studied are: (i) reticulate porous ceramics (RPCs) and (ii) packed beds of CaCO₃ particles. The extinction coefficient and the forward scattering fraction have been determined for the media via a two-flux model of radiative transfer. Optimum porosities for maximizing absorptance at given medium thicknesses are then obtained from the analytical model. For the RPC, the forward scattering fraction varies between 0.38 and 0.57, and the extinction correlation coefficient varies between 9.56 and 7.03. For the packed CaCO₃ particle bed, the forward scattering fraction varies between 0.6 and 0.72, and the extinction coefficient varies between and 2.84 and 2.14.     

Local Heat and Mass Transfer for Gas—Solid Two Phase Flow in CFB

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