Numerical Study of Forced Convective Heat Transfer in Structured Packed Beds of Dimple-Particles

ABSTRACT

In this paper, the flow and heat transfer performances inside small pores of structured packed beds of dimple particles are numerically investigated for the first time and some interesting transport phenomena are obtained. Three-dimensional Navier–Stokes equations and SST k-ω turbulence model are adopted for the simulations. The effect of dimple depth is studied in detail, and the flow and heat transfer performances in the packed beds with dimple particles and smooth particles are also compared with each other. It is found that, with the same inlet velocity, the pressure drop and heat transfer in the packed bed with dimple particles would be lower than those in the packed bed with smooth particles, while the overall heat transfer efficiency of packed bed with dimple particles is higher. Furthermore, for the packed bed of dimple particles, the effect of dimple depth is remarkable. With the same inlet velocity, both the pressure drop and heat transfer rate of the packed bed decrease as dimple depth increases, while the overall heat transfer rate is similar for the packed bed with different dimple depths.     

贴体坐标系下喷动床内气固两相流体动力特性的数值模拟

采用稠密固相动力-摩擦应力模型,建立喷动床内气固两相双流体模型．应用贴体坐标系使得计算网格与喷动床的倒锥体边界相一致．通过数值模拟获得喷动床内喷射区、环隙区和喷泉区内颗粒速度及浓度分布．计算结果表明,喷泉区具有强烈的气固两相质量和动量交换．当倒锥体倾斜角度达到60°,在射流入口处形成一瓶颈．研究表明颗粒间滑动-滚动摩擦应力对环隙区颗粒流动具有明显的影响．     

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.     

Semi-empirical correlations for gas turbine emissions, ignition, and flame stabilization

For operating conditions where the fuel evaporation rate is fast compared to the fuel vapor/air mixing rate, a characteristic time model has been formulated to predict gaseous emissions and efficiency in terms of combustor inlet conditions and geometry. The model, which involves kinetic and fluid mechanic times, has been used to design low NO_x burners, and study of several different conventional engine combustors suggests that the correlation may be universal. A related model, which includes a fuel droplet evaporation time, is being validated with data from laboratory combustors for spark ignition and lean flame stabilization. The preliminary application of this latter model to engine situations is described.     

Spouted and spout-fluid bed combustors 1: Devolatilization and combustion of coal volatiles

The devolatilization and volatile combustion of a single coal particle in spouted and spout-fluid beds have been studied. The results showed that the flame extinction time increases with the particle diameter, and decreases with the bed temperature. When the bed temperature and the air flow rate were fixed, the operation modes (spouted or spout-fluid bed) showed less effect on the mean flame extinction time. A mathematical model of the spouted bed mode for preignition and postignition periods has also been developed assuming the devolatilization rate to be controlled by heat transfer and multireaction pyrolysis kinetics based on volatile products. Ignition, heat transfer back from the volatile flame to the particle surface, variation in flame temperature, and the hydrodynamics of SB are taken into account. The model predictions, with some adjusting parameters, were in good agreement with experimental results.     

Recent Chinese heat-transfer research on bubbling and circulating fluidized beds

Recent research work conducted in China on heat transfer to immersed surfaces in bubbling and circulating fluidized beds, including coal combustors and boilers, is reviewed. Studies include measurements of heat-transfer coefficients (local and total) from horizontal and vertical tubes in bubbling fluidized beds and their variations with operating and system parameters. Special designs developed for heat-transfer probes and theoretical models for the computation of heat-transfer coefficients are discussed. Recent work is presented on circulating fluidized beds with emphasis on hydrodynamics and heat transfer. Proposed correlations and novel designs of thin-film heat-transfer and capacitance probes are included.     

Equilibrium modeling of gasification: Gibbs free energy minimization approach and its application to spouted bed and spout-fluid bed gasifiers

Spouted beds have been found in many applications, one of which is gasification. In this paper, the gasification processes of conventional and modified spouted bed gasifiers were considered. The conventional spouted bed is a central jet spouted bed, while the modified spouted beds are circular split spouted bed and spout-fluid bed. The Gibbs free energy minimization method was used to predict the composition of the producer gas. The major six components, CO, CO₂, CH₄, H₂O, H₂ and N₂, were determined in the mixture of the producer gas. The results showed that the carbon conversion in the gasification process plays an important role in the model. A modified model was developed by considering the carbon conversion in the constraint equations and in the energy balance calculation. The results from the modified model showed improvements. The higher heating values (HHV) were also calculated and compared with the ones from experiments. The agreements of the calculated and experimental values of HHV, especially in the case of the circular split spouted bed and the spout-fluid bed were observed.     

Heat transfer to a bayonet heat exchanger immersed in a gas-fluidized bed

Bayonet tubes are frequently used for heat removal in fluidized bed coal combustors and gasifiers. They consist of two coaxial tubes, through which the cooling fluid flows; first through the inner tube, and then back through the annulus, or vice versa. Such a flow arrangement creates obvious difficulties in defining a characteristic temperature difference to which the heat transfer rate can be related, and on the basis of which the heat transfer coefficient between the bed and the tube can be evaluated. A bayonet tube-fluidized bed system is mathematically modelled here, and an analytical scheme is presented for the calculation of the bed-tube heat transfer coefficient. A characteristic temperature difference (CTD) is defined which reduces to the familiar logarithmic mean temperature difference (LMTD) for a particular case. A set of curves is presented relating the CTD with the LMTD.     

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.     

Heat recovery from hot solid particles in a shallow fluidized bed

A heat exchanger with a shallow gas–solid fluidized bed was experimentally studied in order to analyze energy recovery from solid particles leaving a combustion process. The experiments were carried out with and without vertical baffles in a fluidized bed with immersed horizontal tubes filled with water, in a counter flow arrangement. Two particle diameters (254 and 385 μm), two solid flow rates (50 and 80 kg/h) and two gas flow rates (46 and 50 kg/h) were tested. The bed temperature along the equipment length, the mass flow rate and the inlet and outlet temperatures of solid particles, air and water were measured in order to obtain the bed-tube heat transfer coefficient and the heat exchanger effectiveness. An increment of about 55% in the heat transfer coefficient and higher values of the heat exchanger effectiveness, in experiments with the presence of baffles, was verified. The experimental results also showed that the suspension-wall heat transfer coefficient increased considerably with the solid flow rate and also when the particle diameter decreased.     

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     

Experimental Investigation of Two-Phase Flow Instabilities in Low-Mass-Flux Water Wall Tubes of Supercritical Circular Fluidized Bed Boilers

For the purpose of disclosing the hydrodynamic flow characteristics, under the low mass velocity conditions of the 600-MW supercritical circular fluidized beds boilers, experimental studies on instability of two-phase flow in parallel vertical internally ribbed tubes were conducted. Two kinds of oscillations, pressure-drop oscillation and density-wave oscillation, have been observed. In the range of test parameters the effects of pressure, mass flux, inlet subcooling, compressible volume, exit throttle, and asymmetric heat flux to the two-phase instability were explored and analyzed. Indications from experiment data are: To increase system pressure, mass flux and inlet subcooling will intensify the stability of water wall tubes. To increase exit throttle will intensify the instability of water wall tubes. The bounding pressure and bounding mass flux of density-wave oscillations and the bounding pressure of pressure-drop oscillation have been obtained. Based on the results of testing and using a homogeneous model, the threshold relational expressions of instability were obtained. The results may be used for the design and safe operation of parallel vertical rifled water wall tubes of supercritical circular fluidized beds boilers.     

Finite element analysis of the flow and heat transfer of solid particles in moving beds

A numerical analysis for the flow and heat transfer of solid particles in moving beds of heat exchangers is presented. The solid particles pass through a bundle of heat source tubes as the result of the gravitational force. Heat energy is transferred through direct contact of particles with the heat source tubes. A viscous-plastic fluid model and a convective heat transfer model are employed in the analysis. The flow field dominantly determines the total heat transfer in the heat exchanger. As the velocities of solid particles around the heat source tubes increase, the heat transfer from the tubes also increases. Examples are presented to show the performance of the numerical model. The effect of flow on heat transfer has also been studied. © 1998 John Wiley & Sons, Ltd.     

Modeling and evaluation of designs for solid hydrogen storage beds

Mathematical models have been developed to predict the performance of metal-hydride beds used for hydrogen storage. The relative importance of heat transfer, mass transfer, chemical kinetics and equilibrium have been evaluated by comparison of the models with experimental data supplied by Brookhaven National Laboratory for a cylindrical bed containing iron-titanium (FeTi) alloy. Of these factors, only mass transfer was found to be negligible. An equilibrium model without empirical parameters produces bed pressure and temperatures that show good agreement with experimental data; however, events such as maximum pressure and centerline temperatures are predicted at times that differ from those observed. This model is used to evaluate two proposed designs for solid hydrogen storage beds in which (1) FeTi alloy is contained in tubes that are externally cooled, and (2) FeTi alloy is contained in a bed that is penetrated by cooling tubes. The model predicts that heat transfer surface area is utilised most effectively with the second cooling configuration.     

Mechanisms of heat transfer between a surface and a gas-fluidized bed for combustor application

There is currently considerable interest in the development of fluidized-bed boilers for efficient and environmentally clean combustion of coal. Fluidized beds have the advantages of high heat transfer rates and intimate mixing of additives such as limestone or dolomite for sulfur dioxide absorption produced as a result of combustion of coal containing sulfur. However, design for optimum heat transfer remains uncertain and essentially empirical. The mechanisms of heat transfer are complicated because of the many variables in a commercial combustion operation such as particle size distribution, particle shape, particle and gas thermal properties, reactor geometry and boiler tube design.An understanding of the mechanisms of bed to tube heat transfer is essential to sound design and interpretation of empirically derived correlations. Here we will review and criticize the major mechanisms of heat transfer that have been proposed. These mechanisms are proposed and developed from two schools of thought: (a) The principal resistance to heat transfer is a fluid film, and the moving fluidized particles scour the film to reduce the resistance to heat transfer; (b) Heat is absorbed by the fluidized particles and the rate of heat transfer depends on the rate of heat absorption.Radiant heat transfer is also discussed in this review in detail. Heat transfer by radiation is an important consideration in combustors but has received limited attention. The results of theoretical calculations are given which have been recently reported on the basis of the alternate-slab model of Gabor.The review will predominantly deal with the mechanistic models of heat transfer and various correlations developed over years will not be covered as this topic is dealt with in another review article by Saxena, Grewal, Gabor, Zabrodsky and Galershtein.     

Heat recirculating reactors: Fundamental research and applications

Worldwide emphasis on fuel efficiency, low emissions, and use of low-quality fuels such as biogas continues to drive the development of combustors that operate over a wider range of fuel/air ratios and with higher burning velocities than their conventional counterparts. Enhancement of reaction rates is required to increase burning velocities and widen fuel/air operating ranges over values achievable in conventional combustors, and extensive research over the last few decades has shown that transferring heat in a reactor from hot combustion products to incoming reactants can accomplish this enhancement without external energy addition. These reactors, called heat recirculating reactors, use various geometries and flow strategies to optimize the heat transfer. In this paper, research on heat recirculating reactors is reviewed with an emphasis on the most important designs and applications. The basic characteristics of a heat recirculating reactor are encompassed in a simple configuration: a flame stabilized in a tube with high thermal conductivity. More complex designs that have evolved to further optimize heat transfer and recirculation are then described, including porous reactors with or without flame stabilization and channel reactors consisting of parallel tubes or slots. Advanced designs introduce additional means of heat transfer, such as transverse heat transfer from hot products through channel walls to incoming reactants, thereby leading to the counter-flow channel reactor. The flexibility of heat recirculating reactors to operate on a variety of fuels and over wide operating ranges has led to many applications including fuel reformers, radiant heaters and thermal oxidizers, and important work on these applications is reviewed. Finally, future research directions are discussed.     

Plasma Heating and Temperature Difference Between Gas Pellets in Packed Bed With Dielectric Barrier Discharge Under Natural Convection Condition

A particular phenomenon was found in packed beds with dielectric barrier discharge (DBD): The temperature of the gaseous phase is significantly higher than that of the pellet phase. This is completely different from the conventional packed bed where the phases have essentially the same temperature. A simplified model was developed to estimate this phenomenon in the packed bed with DBD under natural convection. The power consumption mechanism was investigated. The mechanisms for the electrical energy of inlet plasma transformed into heat energy in the two phases, gaseous and pellets of the packed bed reactor, are different. The energy transformation in the gaseous phase includes electron absorption as well as ion absorption. The energy absorbed by electrons, including ohmic heating and stochastic heating, maintains plasma condition. The energy absorbed by ions transfers to other heavy particles with frequent collisions in plasma sheath and, finally, raises the macro temperature of the gas. The energy consumption in pellet phase is dielectric polarization loss and depends on packed bed geometry and DBD. These mechanisms of energy consumption are introduced into the packed bed heat transfer model to develop the simplified model. Some experiments are performed and the results agree well with the numerical simulation of this model.     

Pressure Drops and Dryout Heat Fluxes of Packed Beds with Cylindrical Particles

Abstract

Motivated by reducing the uncertainties in coolability analysis of a debris bed formed in severe accident of nuclear reactors, the pressure drops of single-/two-phase flow and dryout heat fluxes of the packed beds with non-spherical particles are investigated in the present study. Both adiabatic single-/two-phase flow tests and boiling tests are performed on a particulate porous bed packed with cylindrical particles separately, the pressure drops and dryout heat fluxes under different conditions are measured to identify and validate the debris coolability analysis models. The results show that for a particulate bed packed with non-spherical particles such as cylinders, the effective particle diameter can be represented by the equivalent diameter of the particles, which is the product of Sauter mean diameter and the shape factor. Given this diameter, the measured pressure drops and the dryout heat fluxes are comparable with the predictions of Reed model. Comparing with the cooling scheme of top-flooding case, the bottom injection improves the dryout heat flux significantly.     

A study on heat transfer in a conical fluidized-bed reactor with an immersed cylindrical heater

In this paper, numerical and experimental analyses of the heat transfer between an immersed heater and a cone bed of sand particles were carried out. A three-dimensional (3D) model using the Eulerian–Eulerian model coupled with the kinetic theory for granular flow was used to simulate heat transfer and the related bed flow characteristics. The effects of different inlet gas velocities, represented by the fluidizing number (the ratio between inlet gas velocity to minimum fluidizing velocity), and different particle-wall boundary conditions on heat transfer and hydrodynamics were investigated. Both the experiments and numerical simulation results showed that the heat transfer coefficient and the bed expansion ratio increased with increasing the inlet gas velocity. For the particle-wall boundary condition, applying the no-slip condition showed the best agreement in the heat transfer coefficient and the bed expansion ratio to the experimental results.     

Heat transfer characteristics of the metal hydride vessel based on the plate-fin type heat exchanger

Heat transfer characteristics of the metal hydride vessel based on the plate-fin type heat exchanger were investigated. Metal hydride beds were filled with AB₂ type hydrogen-storage alloy’s particles, Ti_0.42Zr_0.58Cr_0.78Fe_0.57Ni_0.2Mn_0.39Cu_0.03, with a storage capacity of 0.92 wt.%. Heat transfer model in the metal hydride bed based on the heat transfer mechanism for packed bed proposed by Kunii and co-workers is presented. The time-dependent hydrogen absorption/desorption rate and pressure in the metal hydride vessel calculated by the model were compared with the experimental results. During the hydriding, calculated hydrogen absorption rates agreed with measured ones. Calculated thermal equilibrium hydrogen pressures were slightly lower than the measured hydrogen pressures at the inlet of metal hydride vessel. Taking account of the pressure gradient between the inlet of metal hydride vessel and the metal hydride bed, it is considered that this discrepancy is reasonable. During the dehydriding, there were big differences between the calculated hydrogen desorption rates and measured ones. As calculated hydrogen desorption rates were lower than measured ones, there were big differences between the calculated thermal equilibrium hydrogen pressures and the measured hydrogen pressures at the inlet of metal hydride vessel. It is considered that those differences are due to the differences of the heat transfer characteristics such as thermal conductivity of metal hydride particles and porosity between the assumed and actual ones. It is important to obtain the heat transfer characteristics such as thermal conductivity of metal hydride particles and porosity both during the hydriding and dehydriding to design a metal hydride vessel.