Parametric studies of wall heat transfer in a fluidized bed circulating through a packed bed

In the analysis presented, the circulating fluidized bed is treated as equivalent to a gas-solid suspension flow. The heat transfer is modelled in terms of the effective increase in thermal conductivity of the gas. The results show that the increase in thermal conductivity of the continuum due to the molecular conductivity of the circulating particles has a much lower contribution than particle eddy conductivity. High mass ratio and low size of the circulating solids are beneficial. The results are a lower bound to the heat transfer increase possible. Additional contribution due to gas convection at high velocities can be simply modelled, by increasing the particle eddy conductivity suitably.

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Parameter-Studien von Wärmeübertragung in einer Wirbelschicht die durch ein Festbett zirkuliert

Zusammenfassung In der vorliegenden Untersuchung wird die zirkulierende Wirbelschicht wie eine Gas-Festkörper-Suspensions-strömung behandelt. Die Wärmeübertragung wird in Abhängigkeit vom effektiven Anstieg der thermischen Leitfähigkeit des Gases dargestellt. Die Ergebnisse zeigen, daß der Anstieg der thermischen Leitfähigkeit des Kontinuums in Folge von molekularer Leitung der zirkulierenden Partikel weniger bedeutend ist als die Wirbelleitfähigkeit. Große Massenverhältnisse und kleine Größen der zirkulierenden Festkörper sind vorteilhaft. Die Ergebnisse zeigen die mögliche Verbesserung der Wärmeübertragungswerte. Diese können in Folge von Gaskonvektion bei hohen Geschwindigkeiten durch geeignetes Ansteigen der Wirbelleitfähigkeit verbessert werden.

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Nomenclature B non-dimensional conductivity - C _p specific heat - d _p bed particle diameter - f solid volume fraction - Fo Fourier number - h heat transfer coefficient - k _B bulk conductivity - k _e equivalent conductivity - M mass ratio of the circulating bed - Nu Nusselt number - q heat flux - t _i initial temperature - t _o wall temperature - x distance from the wall Greek symbols _B bulk voidage of the circulating bed - _g density of gas - _s solid density - time     

Bed-to-surface heat transfer in a circulating fluidized bed

 The heat transfer characteristics between a circulating fluidized bed and a surface immersed inside it are investigated. This paper presents a statistical model describing the mechanism of heat transfer and the relationship between the heat transfer coefficient and the main parameters of the bed. The proposed model yields a satisfactory representation of heat transfer process in the circulating fluidized bed (CFB), it is consistent with experimental results and other researchers results. Received on 13 December 1999 / Published online: 29 November 2001     

Kinetic model of heat transfer processes in a fluidized bed

In the present paper equations are obtained for determining the temperature field in a fluidized layer. The heat and mass transfer processes in a fluidized bed depend significantly on the motion of the solid particles which form the bed. In any small volume of a fluidized bed with nonuniform thermal conditions there are particles with different average temperatures. Therefore it is natural to resort to the statistical representation of such a system, developed previously in [1, 2], for the study of the heat transfer processes. The expression obtained here for the heat conductivity coefficient of the bed is in good qualitative agreement with the experimental data.The author wishes to thank V. G. Levich for his interest and valuable discussions.     

Wall-to-bed heat transfer in supercritical water fluidized bed using CFD-DEM

Supercritical water fluidized bed(SCWFB)reactors are designed to gasify biomass or coal with high efficiency.In this paper,the wall-to-bed heat transfer charact...     

Experiments on the local heat transfer characteristics of a circulating fluidized bed

The role of particle diameter in the heat transfer of a gas–solid suspension to the walls of a circulating fluidized bed was studied for particles of uniform size. This work reports and analyzes new experimental results for the local bed to wall heat transfer coefficient, not including the radiation component, in a long active heat transfer surface length laboratory bed, which extend previous findings and clear up some divergences. The research included determining the effects of extension and location of the heat transfer surface, circulating solids mass flux and average suspension density. An experimental set-up was built, with a 72.5 mm internal diameter riser, 6.0 m high, composed of six double pipe heat exchangers, 0.93 m high, located one above the other. Five narrow sized diameter quartz sand particles − 179, 230, 385, 460 and 545 μm − were tested. Temperature was kept approximately constant at 423 K and the superficial gas velocity at 10.5 m/s. The major influence of suspension density on the wall heat transfer was confirmed, and contrary to other authors, a significant effect of particle size was found, which becomes more relevant for smaller particles and increasing suspension density. It was observed that the extension of the heat transfer surface area did not influence the heat transfer coefficient for lengths greater than 0.93 m.The heat transfer surface location did not show any effect, except for the exchanger at the botton of the riser. A simple correlation was proposed to calculate the heat transfer coefficient as a function of particle diameter and suspension density.     

Parametric studies and effect of scale-up on wall-to-bed heat transfer characteristics of circulating fluidized bed risers

In the present work a comparative study of steady state wall-to-bed heat transfer was conducted along the risers of height 2.85 m of three different circulating fluidized beds (CFBs) with bed cross sections of 0.15 m × 0.15 m, 0.20 m × 0.20 m, and 0.25 m × 0.25 m, respectively. Experiments were conducted on each CFB unit for five superficial air velocities (U = 2.5 m/s, 2.75 m/s, 3 m/s, 3.3 m/s, and 4 m/s) and two different weights of sand inventory per unit area of the distributor plate (P = 1750 N/m² and P = 3050 N/m²) with average sand particle size of 460 μm. Bed temperature distributions across the three risers were measured and compared at different heights (1.04 m, 1.64 m, and 2.24 m above the distributor plate). Axial distribution of heat transfer coefficient along the height of riser was evaluated and compared for the three bed cross sections. Effect of superficial velocity of air, sand inventory, and bed cross section on bed temperature and heat transfer coefficient was investigated. An empirical correlation was developed for the bed Nusselt number as a function of various non-dimensional parameters based on the parametric study. The correlation was compared with available literatures.     

Characteristics of heat transfer between particles and fluid in aggregative fluidized bed

Measurements are made on the heat-transfer coefficients between particles and fluid in the aggregative fluidized bed. In order to evaluate the heat-transfer coefficients, a proposed model takes into account of the variation of the particles-temperature and the fluid-temperature distributions throughout the bed is developped on the basis of an experimental investigation of the fluidizing behavior. The heat-transfer coefficients obtained by conforming the outlet-air temperature profile to be predicted with the one measured are found to be varied significantly depending on the static bed height, as well as particle diameter and fluid velocity.     

Local heat transfer coefficients around a horizontal heated tube immersed in a gas fluidized bed

The heat transfer characteristics around a single horizontal heated tube immersed in air fluidized bed was investigated, to clarify the mechanism of heat transfer in a fluidized bed heat exchanger. The local heat transfer coefficient around the tube was measured at various fluidization velocities and five different solid particles. The experimental values of the local heat transfer coefficient at the minimum fluidization velocity condition were correlated with the particle size in two empirical equations. The predicted results were in good agreement with the experiment data.     

Melting heat transfer along a horizontal heated tube immersed in a fluidized liquid ice bed

An experimental study was performed to determine the melting heat transfer characteristics along a horizontal heated circular tube immersed in a solid-air-liquid three-phase fluidized liquid ice bed. A mixture of fine ice particles and ethylene glycol acqueous solution was adopted as the liquid ice for the test. Measurements were carried out for a range of parameters such as airflow rate, heated tube diameter, and initial concentration of acqueous binary solution. It was found that the heat transfer coefficient for the fluidized liquid ice bed might be more than 20 times as large as that for the fixed liquid ice bed.     

Local heat transfer coefficients on the circumference of a tube in a gas fluidized bed

A heated horizontal heat transfer tube was installed 14.8 cm above the distributor plate in a square fluid bed measuring 30.5 × 30.5 cm. Four different Geldart B sized particle beds were used (sand of two different distributions, an abrasive and glass beads) and the bed was fluidized with cold air. The tube was instrumented with surface thermocouples around half of the tube circumference and with differential pressure ports that can be used to infer bubble presence. Numerical execution of the transient conduction equation for the tube allowed the local time-varying heat transfer coefficient to be extracted. Data confirm the presence of the stagnant zone on top of the tube associated with low superficial velocities. Auto-correlation of thermocouple data revealed bubble frequencies and the cross-correlation of thermal and pressure events confirmed the relationship between the bubbles and the heat transfer events. In keeping with the notion of a “Packet renewal” heat transfer model, the average heat transfer coefficient was found to vary in sympathy with the root-mean square amplitude of the transient heat transfer coefficient.     

Numerical prediction of heat transfer between a bubbling fluidized bed and an immersed tube bundle

In this paper a numerical analysis of the heat transfer between a bubbling fluidized bed of mono-dispersed glass beads of Geldart type B and an immersed heated tube bundle is investigated. The numerical procedure is based on a solution of the mass, momentum and energy equations of both phases with an Eulerian approach. Different physical models for the thermal transport coefficient of the solid phase were used. The results are compared with new experimental data. The numerical and the experimental results show a strong correlation between fluid dynamics and heat transfer similar to the packet theory of Mickley and Fairbanks (1955). B Defined in equation (15) – - c _p Specific heat J/kg/K - d _s Particle diameter m - d _Tube Diameter of the heat transfer tube m - g, Gravitational constant m/s² - g ₀ Radial distribution function – - h Specific enthalpy J/kg - k Solids fluctuating energy diffusion coefficient Pa s - Nu Nusselt number – - p Pressure N/m² - p _s Solid pressure N/m² - Heat flux W - Heat flux W - Re Reynolds number – - T Temperature K - T(t) Measured foil temperature K - t Time s - tr Trace of a tensor (sum of main-diagonal elements) m/s - v Velocity, v-direction m/s - Velocity vector m/s - x x-coordinate m - y y-coordinate m - Volumetric interphase heat transfer coefficient W/m³/K - Bed-to-wall heat transfer coefficient W/m²/K - _gs Fluid-particle heat transfer coefficient W/m²/K - _T Heat transfer coefficient at tube surface W/m²/K - Interphase drag coefficient kg/m³/s - Thickness of CuNi foil m - Dissipation of fluctuating energy Pa/s - Volume fraction – - Angle ° - Thermal conductivity W/m/K - _cyl Defined in equation (13) – - Fluctuating energy exchange Pa/s - Volumetric heat generation rate W/m³ - Density kg/m³ - Granular temperature m²/s² - Viscous stress tensor N/m² - Defined in equation (14) – - Bulk Bulk properties - g Gas phase - gas Gas - i i = g, s (gas or solid) - m Mixture - pen Penetration theory - pm Particle material - s Solid phase - T Tube - Tube Tube - t total - W Wall - * Parameter multiplied by the volume fraction of its phase     

Heat transfer characteristics in a horizontal swirling fluidized bed

An innovative horizontal swirling fluidized bed (HSFB) with a rectangular baffle in the center of an air distributor and three layers of horizontal secondary air nozzles located at each corner of fluidized bed was developed. Experiments on heat transfer characteristics were conducted in a cold HSFB test model. Heat transfer coefficients between immersed tubes and bed materials in the HSBF were measured with the help of a fast response heat transfer probe. The influences of fluidization velocity, particle size of bed materials, measurement height, probe orientation, and secondary air injection, etc. on heat transfer coefficients were intensively investigated. Test results indicated that heat transfer coefficients increase with fluidization velocity, and reach their maximum values at 1.5-3 times of the minimum fluidization velocity. Heat transfer coefficients are variated along the circumference of the probe, and heat transfer coefficients on the leeward side of the probe are larger than that on the windward side of the probe. Heat transfer coefficients decrease with increasing of measurement height; heat transfer coefficients of the longitudinal probe are larger than that of the transverse probe. The proper secondary air injection and particle size of bed materials can generate a preferred hydrodynamics in the dense zone and enhance heat transfer in a HSFB.     

An analytical-empirical model to predict heat transfer coefficients in circulating fluidized bed combustors

An analytical-empirical model was developed to predict local heat transfer coefficients in circulating fluidized bed (CFB) combustors. The fluid is considered to be composed of a dispersed phase and cluster of particles. Both convection and thermal radiation are taken into account. The estimation of the parameters in the model is discussed and suggestions as well as a sensitivity analysis are given. The model is applied to predict heat transfer coefficients on membrane walls of a CFB boiler for which an experimental investigation had been carried out previously. The predictions were in good agreement with experimental results.

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Ein analytisch-empirisches Modell zur Bestimmung der Wärmeübergangskoeffizienten in zirkulierenden Wirbelschichtöfen

Zusammenfassung Ein analytisch-empirisches Modell zur Ermittlung der lokalen Wärmeübergangskoeffizienten in zirkulierenden Wirbelschichtöfen wird vorgestellt, wobei das Fluid aus einer dispersen Phase und einem Cluster von Partikeln zusammengesetzt sein soll. Sowohl Konvektion als auch Wärmestrahlung finden Berücksichtigung. Die das Modell beschreibenden Parameter werden abgeschätzt und eingehend diskutiert. Das Modell dient zur Ermittlung von Wärmeübertragungskoeffizienten an der Membranwand eines CFB-Verdampfers, für den eine experimentelle Untersuchung vorliegt. Die Übereinstimmung zwischen Theorie und Experiment ist gut.

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Nomenclature B backscatter fraction - C _pc specific heat of cluster, J/kg K - C _pg specific heat of gas, J/kg K - C _pp specific heat of particle, J/kg K - d _p particle diameter, m - e _c emissivity of the cluster - e _w emissivity of the wall surface - e _dis effective emissivity of the dispersed phase - e _p emissivity of the particle - f time fraction the wall surface is covered by the clusters - h _c total convective heat transfer coefficient, W/m²K - h _cc heat transfer coefficient due to cluster convection, W/m²K - h _cclj heat transfer coefficient due to cluster convection fromjth subsection inlth wall section, W/m²K - h _cd heat transfer coefficient due to dispersed phase convection, W/m²K - h _r total radiative heat transfer coefficient, W/m²K - h _rc heat transfer coefficient due to cluster radiation, W/m²K - h _rd heat transfer coefficient due to dispersed phase radiation, W/m²K - h _ov overall heat transfer coefficient, W/m²K - g acceleration due to gravity, m/s² - i arbitrary wall section - j arbitrary subsection - k _i number of subsections in wall sectioni - K constant in Eq. (17) - K _c effective thermal conductivity of the cluster, W/mK - K _gg effective thermal conductivity of gas, W/mK - K _gf thermal conductivity of the gas film calculated at (T _b +T _w )/2, W/mK - K _p thermal conductivity of the particles, W/mK - L _lj residence length of the cluster of thejth subsection inlth section at the wall, m - m _i mass flow rate to theith section from the core, kg/m²s - t _lj residence time of the cluster fromjth subsection inlth section, s - T _b bulk bed temperature, K - T _c cluster temperature, K - T _w wall temperature, K - U _c cluster velocity, m/s - U _g superficial gas velocity, m/s - U _t terminal settling velocity, m/s - Y volume fraction of solid in the dispersed phase Greek letters _g thickness of the gas film between the cluster and the wall surface, m - _rough r.m.s. value of surface roughness, m - _c cluster voidage - _sus average cross-sectional voidage - _dis voidage of the dispersed phase - _w voidage near the wall - dynamic viscosity, kg/ms - _c density of the cluster, kg/m³ - _dis density of the dispersed phase, kg/m³ - _g density of gas, kg/m³ - _p density of particle, kg/m³ - _sus suspension density, kg/m³ - Stefan-Boltzmann's constant, 5.67×10^–8, W/m²K⁴     

Heat and mass transfer studies in a batch fluidized bed dryer using Geldart group D particles

The drying behavior at low temperatures has been studied with four different uniformly sized particles and three different binary mixtures at different dilutions ranging from 10 to 40 % with an interval of 10 % varying parameters such as air velocity, initial moisture content, initial bed height and temperature. Falling rate period one and two were observed and correlations were developed to predict the drying rate in falling rate periods one and two. Correlations were also developed to predict the average moisture content by considering the effect of various parameters for uniformly sized particles and binary mixture of solids. The heat and mass transfer coefficients have been found for different conditions and compared. Comparison of experimental and predicted average moisture contents for uniformly sized particles and for various binary mixtures has been made and the predicted average moisture content has been found to be in good agreement with experimental average moisture content.     

Effect of acoustic field on heat transfer in a sound assisted fluidized bed of fine powders

The fluidized beds are widely used in a variety of industries where heat transfer properties of the fluidized system become important for successful operation. Fluidized are preferred in heat recovery processes because of their unique ability of rapid heat transfer and uniform temperature. Fine powders handling and processing technologies have received widespread attention due to increased use of fine powders in the manufacture of drugs, cosmetics, plastics, catalysts, energetics and other advanced materials. A better understanding of fluidization behavior of fine powders is of great importance in applications involving heat transfer, mass transfer, mixing, transporting and modifying surface properties etc. The difficulty in putting the fine powders in suspension with the fluidizing gas is related to the cohesive structure and to the physical forces between the primary particles. The sound waves agitate bubbling and this results in improving solids mixing in the fluidized bed. The improved solids mixing results in uniform and smooth fluidization, which leads to better heat transfer rates in the fluidized bed.     

Experimental and numerical investigation of dynamic heat transfer parameters in packed bed

Dynamic experiments in a nonadiabatic packed bed were carried out to evaluate the response to disturbances in wall temperature and inlet airflow rate and temperature. A two-dimensional, pseudo-homogeneous, axially dispersed plug-flow model was numerically solved and used to interpret the results. The model parameters were fitted in distinct stages: effective radial thermal conductivity (K _r) and wall heat transfer coefficient (h _w) were estimated from steady-state data and the characteristic packed bed time constant (τ) from transient data. A new correlation for the K _r in packed beds of cylindrical particles was proposed. It was experimentally proved that temperature measurements using radially inserted thermocouples and a ring-shaped sensor were not distorted by heat conduction across the thermocouple or by the thermal inertia effect of the temperature sensors.     

Charge transfer and bipolar charging of particles in a bubbling fluidized bed

Particle-particle and particle-wall collisions in gas-solid fluidized beds lead to charge accumulation on particles.This work evaluated the effect of fluidization time on charge transfer and bipolar charging(charge separation)and their influence on hydrodynamic structures in a fluidized bed.Experiments were performed with glass beads and polyethylene particles in a glass column.The pressure fluctuations and net electrostatic charge of particles were measured during fluidization.Wavelet and short-time Fourier transforms were used to analyze pressure fluctuations.The results revealed that bipolar charging is the dominant tribocharging mechanism in a bed of glass beads.Bipolar charging in a bed of particles with a narrow size distribution does not affect either hydrodynamic structures or the transition velocity to the turbulent regime.A large difference between the work functions of the wall and particle in the bed of polyethylene particles leads to high charge transfer.Formation of a stagnant particle layer on the wall eventually causes the energy of macro-structures to increase to its maximum.At longer fluidization times,the macro-structural energy decreases and bubbles shrink until the electrostatic charge reaches the equilibrium level.These results well describe the effect of fluidization time on hydrodynamic structures.     

Heat and mass transfer through a horizontal grid grating in a fluidized bed

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 81–88, September–October, 1990.