Maximaler Wärmeübergang in Apparaten mit dispersen Zweiphasensystemen

Maximum heat transfer in apparatus containing dispersed two phase systems . The structure of dispersed systems such as fluidized beds, bubble columns, and liquid/liquid spray columns in process apparatus can be either homogeneous or heterogeneous. When calculating heat transfer coefficients between such systems and vertical heat transfer areas it is necessary to know the structure of the bed. In homogeneous systems (for instance fixed beds) a relationship between the heat transfer and a Reynolds number was found. This Reynolds number embodies the volumetric flux density and a suitable hydraulic diameter. In gas fluidized beds with a heterogeneous structure the heat transfer depends on a Péclet number. The characteristic time of this number can be obtained by deviding the particle diameter by the mean rising velocity of gas bubbles. Maximum heat transfer coefficients for homogeneous and heterogeneous and heterogeneous systems can be described in a general way by plotting a Nusselt number versus the product Ar_p · Pr_c of the Archimedes number and the Prandtl number. Maximum coefficients are calculable without knowledge of the volumetric flux density. For low values of the product Ar_p · Pr_c there is a significant difference between homogeneous and heterogeneous beds.     

Heat Transfer from Immersed Vertical Cylinders in Gas‐Liquid and Gas‐Liquid‐Solid Fluidized Beds

The heat transfer coefficient, h, was measured using a cylindrical heater vertically immersed in liquid‐solid and gas‐liquid‐solid fluidized beds. The gas used was air and the liquids used were water and 0.7 and 1.5 wt‐% carboxymethylcellulose (CMC) aqueous solutions. The fluidized particles were sieved glass beads with 0.25, 0.5, 1.1, 2.6, and 5.2 mm average diameters. We tried to obtain unified dimensionless correlations for the cylinder surface‐to‐liquid heat transfer coefficients in the liquid‐solid and gas‐liquid‐solid fluidized beds. In the first approach, the heat transfer coefficients were successfully correlated in a unified formula in terms of a modified j_H‐factor and the modified liquid Reynolds number considering the effect of spatial expansion for the fluidized bed within an error of 36.1 %. In the second approach, the heat transfer coefficients were also correlated in a unified formula in terms of the dimensionless quantities, Nu/Pr^1/3, and the specific power group including energy dissipation rate per unit mass of liquid, E^1/3D^4/3/ν_l, within a smaller error of 24.7 %. It is also confirmed that a good analogy exists between the surface‐to‐liquid heat transfer and mass transfer on the immersed cylinder in the liquid‐solid and gas‐liquid‐solid fluidization systems.     

Wall-to-bed heat transfer in liquid—solid and gas—liquid—solid fluidized beds part I: Liquid—solid fluidized beds

Experimental work was conducted to investigate the effect of particle size and particle density upon the wall-to-bed heat transfer characteristics in liquid—solid fluidized beds with a 95.6 mm column diameter over a wide range of operating conditions. The radial temperature profile was found to be parabolic, indicating the presence of a considerable bed resistance. The effective radial thermal conductivity and the apparent wall film coefficient were obtained on the basis of a series thermal resistance model. The modified Peclet number of the radial thermal conductivity decreases upon the onset of fluidization, has a minimum at a bed porosity of 0.6 to 0.7 and increases with further increase of bed porosity. The modified Peclet number decreases considerably with decreasing particle size or increasing particle density. The apparent wall heat transfer coefficient can be represented well by a Colburn j-factor correlation over a wide range of data as follows: j′_H = 0.137 Re′^?0.271 A close analogy is found to exist between the modified j-factor for wall heat transfer coefficient and that for wall mass transfer coefficient, in liquid—solid fluidized beds.     

Wall-to-bed heat transfer coefficient in gas—liquid—solid fluidized beds

Wall to bed heat transfer has been studied in three-phase fluidized beds with a cocurrent up-flow of water and air. Six sizes of glass beads, two sizes of activated carbon beads and one size of alumina beads, varying in average diameter from 0.61 to 6.9 mm and in density from 1330 to 3550 kg/m³, were fluidized in a 95.6 mm diameter brass column heated by a steam jacket. Complementary heat transfer experiments have been performed also for a gas–liquid cocurrent column and liquid–solid fluidized beds. The wall-to-bed coefficient for heat transfer in the gas–liquid–solid fluidized bed is evaluated on the basis of the axial dispersion model concept. The ratio of the wall-to-bed heat transfer coefficient in the gas–liquid–solid fluidized bed to that in the liquid–solid fluidized bed operated at the same liquid flow rate is correlated in terms of the ratio of the velocity of gas to that of liquid and the properties of solid particles. A correlation equation for estimating the wall-to-bed heat transfer coefficient in the liquid–solid fluidized bed is also developed.     

HEAT TRANSFER CHARACTERISTICS OF THREE PHASE FLUIDIZED BEDS

Heat transfer characteristics of two (liquid-gas, liquid-solid) and three (liquid-gas-solid) phase fluidized beds have been studied in a 15.2 cm-ID column fitted with an axially mounted cylindrical healer. Effects of gas velocity (0-12 cm/s). liquid velocity (0-16cm/s), particle size (1.7-8.0 mm) and liquid viscosity (0.001-0.039 Pa s) on heat transfer coefficient were determined. The heat transfer coefficient increased with fluid velocities and particle size and it decreased with liquid viscosity in two and three phase fluidized beds. The bed porosity at which the maximum heat transfer occurred decreased with particle size but increased with liquid viscosity. The coefficient were correlated in terms of experimental variables. Modified Nusselt number from the present and previous studies has been correlated with modified Prandtl and Reynolds numbers.     

A CORRELLATION FOR CYLINDER-TO-BED HEAT TRANSFER IN AERATED VIBRATED BEDS OF SMALL PARTICLES

ABSTRACT

Beds of alumina particles (d_p= 27 μm and 100 μm) were vibrated in the vertical direction at frequencies frdm 0–25 Hz and half-amplitudes from 0–4 mm. Air flow rate through a single-hole or multiple-holes bottom plate varied from 0 to 2 times the minimum fluidizing velocity. The contact heat transfer coefficients at resonance are much higher than those in packed beds and in vibrated fluidized beds (up to 1.2 times). The high heat transfer rates are due to enhanced particle mobility which reaches a maximum at the resonant point. A simple semi-empirical correlation is developed for contact heat transfer which is based on particle mobility. Heat transfer coefficients are correlated with frequency using amplitude, bed height and particle size as adjustable parameters. The correlation is found explain the observed trends in the data reasonably well over the range of parameters studied.     

A generalized correlation for heat transfer between a gas—solid fluidized bed of small particles and an immersed staggered array of horizontal tubes

A generalized correlation for heat transfer coefficient between a horizontal staggered tube bundle and a gas—solid fluidized bed is proposed. The correlation is based on the experimental data for heat transfer coefficient between electrically heated horizontal tube bundles (12.7 and 28.6 mm diam.) and square fluidized beds (30.5 × 30.5 cm) of alumina ($\text{d}$_p = 259 μm) and silica sand ($\text{d}$_p = 167 and 504 μm). The tubes in the bundle are located at the vertices of equilateral triangles with pitch varying between 1.75 and 9 times the tube diameter. The proposed correlation is examined on the basis of existing data in the literature. The predicted values of heat transfer coefficient from the proposed correlation are, in general, in good agreement with experimental data in the literature.     

气固流化床传热特征区域的定量分析

基于作者在近期提出的一个新的综合考虑传导、对流和辐射热量传递模式的鼓泡流化床传热机理模型,对传热特征区域进行了定量的分析,提出了一个基于表征颗粒流化特性的Archemides数和传导与辐射相对重要性的Planck数的新的传热区域图。根据主导传热机理的变化,定义出9个特征区域,可供流化床设备的优化设计和正常操作参考。     

Heat transfer mechanisms in gas fluidized beds. Part 3: Heat transfer in circulating fluidized beds

Part 1 of this contribution reported on the effects of system properties on heat transfer between heating or cooling surfaces and bubbling fluidized beds. This investigation produced four correlations which define the respective maximum heat transfer. Part 2 of this study suggests that the heat transfer between exchanger surfaces and bubbling fluidized beds depends on superficial gas velocity, expressed as dimensionless excess gas velocity. The present paper shows that heat transfer coefficients in circulating fluidized beds can be predicted by evaluation of a state diagram, which combines three dimensionless groups: Nusselt number, Archimedes number and a dimensionless pressure gradient. A comparison of coal combustion experiments with own cold model measurements indicates that the radiative component of heat transfer coefficients is only evident at very low dimensionless pressure gradients.     

Heat transfer in a swirling fluidized bed with geldart type-D particles

A relatively new variant in fluidized bed technology, designated as the swirling fluidized bed (SFB), was investigated for its heat transfer characteristics when operating with Geldart type D particles. Unlike conventional fluidized beds, the SFB imparts secondary swirling motion to the bed to enhance lateral mixing. Despite its excellent hydrodynamics, its heat transfer characteristics have not been reported in the published literature. Hence, two different sizes of spherical PVC particles (2.61 mm and 3.65 mm) with the presence of a center body in the bed have been studied at different velocities of the fluidizing gas. The wall-to-bed heat transfer coefficients were measured by affixing a thin constantan foil heater on the bed wall. Thermocouples located at different heights on the foil show a decrease in the wall heat transfer coefficient with bed height. It was seen that only a discrete particle model which accounts for the conduction between the particle and the heat transfer surface and the gas-convective augmentation can adequately represent the mechanism of heat transfer in the swirling fluidized bed.     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

Wall-to-bed heat transfer in liquid—solid and gas—liquid—solid fluidized beds part II: Gas—liquid—solid fluidized beds

Wall-to-bed heat transfer in gas—liquid—solid fluidized beds with a cocurrent upflow was analyzed on the basis of a series thermal resistance model. The effective radial thermal conductivity and the apparent wall heat transfer coefficient were determined over a wide range of experimental conditions. The behavior of the effective thermal conductivity strongly depends on the flow mode for the three-phase fluidized bed, directly indicating the trend of the radial liquid mixing. The modified Peclet number for the radial thermal diffusivity takes on a minimum with respect to the liquid velocity in a manner similar to that in a liquid—solid fluidized bed, but the value of the modified Peclet number decreases significantly with gas velocity. The apparent wall heat transfer coefficient can be correlated well with a Colburn type equation which at zero gas velocity reduces to the same equation as that proposed for liquid—solid fluidization, as follows: j′_H = 0.137 Re′_l.g^?0.271     

Heat transfer to submerged surfaces in coarse-grained pressurized fluidized beds and fixed beds

This contribution reports on the theory underlying a uniform representation of heat transfer to submerged surfaces in fixed bed reactors and of gas convective part of heat transfer in fluidized beds with coarse-grained bulk solids and/or at elevated pressure. Based on an analysis of the pressure drop behaviour of fixed bed percolation at different gas pressures and with different bulk solids, a new dimensionless pressure drop parameter was developed. Fixed bed heat transfer data are very well correlated by this new dimensionless number. As soon as fluid throughput is in excess of minimum fluidization velocity, the pressure drop parameter transforms into the well-known Archimedes number. These two dimensionless numbers are connected by the condition of equilibrium for pressure drop and mass of practices in a fluidized bed. This equilibrium is fulfilled as soon as fluidization commences. Up to now, the Archimedes number has been generally accepted as the significant parameter, determining the gas convective part of heat transfer in fluidized beds; however, without any physical interpretation of this parameter. Introduction of the pressure drop number, which is consistent with the Archimedes number, reduces the heat transfer behaviour to pressure drop characteristics. The usefulness of this concept is proven by the comparison of experimental results and prediction.     

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

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

On the heat transfer mechanism in three phase fluidized beds

A two resistance model is proposed for the heat transfer between a coaxially mounted heater and a three phase fluidized bed. Effects of gas and liquid velocity and particle size on individual heat transfer resistances in the heater and in the fluidized bulk zones have been determined. The optimum bed porosity at which the maximum heat transfer coefficient occurred coincided with the bed porosity at which the boundary layer thickness around the heater attained a minimum value. The fluidized bed resistance attained its minimum value when the maximum heat transfer coefficient is achieved in two and three phase fluidized beds. The heat transfer in the zone adjacent to the healer is found to be the rate controlling step since the contribution of fluidized bed resistance was found to be less than 10% of the heater zone resistance in two and three phase fluidized beds. The heat transfer resistances in liquid and three-phase fluidized beds have been represented by a modified Stanton and Peclet numbers based on the heat transfer resistances in the heater zone and in the fluidized bulk zone in series.     

ANALYSIS OF SIMULTANEOUS RADIATIVE AND CONDUCTIVE HEAT TRANSFER IN FLUIDIZED BEDS

In the bubbling regime of operation for fluidized beds, the major mechanism for heat transfer is transient conduction to periodic packets of densely packed particles at the heat transfer surface. The well known Mickley and Fairbanks model, with various subsequently proposed modifications, adequately describes this transient conduction mechanism. However, no adequate theory exists for heat transfer in high-temperature fluidized beds where radiative contribution becomes significant.

Analysis of the radiative contribution is complicated by the nonlinear interaction of radiation with conduction/convection. This paper describes a differential formulation of the combined radiative/ conductive heat transfer process. The discrete flux method used by Churchill et al. for radiative transport in heterogeneous media is applied here to the problem of transient heat transfer to packets in fluidized beds. Packets are modeled as radiatively participating media with absorption, scattering, and emission of radiation. Simultaneous solution of the governing differential equations for temperature and forward and backward radiation fluxes permits calculation of instantaneous heat flux at the heat-transfer surface. Radiative transfer during bubble contact is added as a time-weighted contribution.

Using experimental data on radiative cross sections (from packed media experiments) and experimental data on packet residence times (from fluidized bed experiments), the combined conductive/radiative heat transfer to packets was obtained for examples of fluidized beds at different fluidizing velocities and wall temperatures. The analytical results indicate that the relative importance of radiation is affected by particle size, average packet residence time, and the radiative attenuation cross sections. For operating conditions representative of fluidized bed combustion, the model estimates a 10 to 20 percent contribution by radiation to the total heat transfer. Comparison to limited experimental data from the literature shows reasonable agreement.     

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

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

Particle-to-particle heat transfer in fluidized bed drying

Particle-to-emulsion and interparticle heat transfer rates were estimated in the range 1.5 ? u/u_mf ?3.5, 0.69 ? d_p ? 2.15 mm by drying wet refractory particles in fluidized beds of similar dry particles of the same sizes. Overall particle-to-emulsion heat transfer coefficients decrease roughly as the inverse of the particle diameter. Particle-to-particle heat transfer coefficients vary with the power-2 of the particle diameter and decrease as the fluidization velocity increases.     

Contribution à l'étude du transfert de chaleur à la paroi dans les récteurs à lit fluidisé gaz-liquide-solide à faible vitesse de liquide

A study has been made of the wall to bed heat transfer in three-phase fluidized beds with cocurrent upflow of the gas and the liquid, the liquid being the continuous phase. The experiments were done using five different liquids (tetra-chloroethene, cyclohexane, kerosene, gas oil, water), three different kinds of particles (glass beads, porous alumina spheres and cylinders) at liquid velocities below 30 mm/s and gas velocities from 10 to 150 mm/s. The phenomena observed with a foaming liquid are described. Different literature correlations proved to be non-applicable at the velocities used in this work; moreover, they are not able to take into account the influence of the nature of the liquid. Therefore, a new correlation which fits well our results is proposed. The areas requiring further investigation before a safe prediction of the wall heat transfer coefficient in three phase fluidized beds can be possible are detailed.     

Mass transfer in liquid-fluidized and spouted beds of ion exchange resin at low Reynolds number

Rates of mass transfer from the liquid phase to small ion exchange resin particles (0.78 mm in mean diameter) in fluidized and spouted beds were studied experimentally. Dilute aqueous solution of sodium hydroxide was fed into the beds of strong cation exchange resin and the exit concentration of the solution was determined by conductivity measurement. In spouted beds, the initial conversion and K_l increased with bed height, but decreased with fluid flowrate. The model, applying material balance of the reactant and axisymmetric flow of fluid in the annulus of a spouted bed, predictions of the initial conversion in spouted beds are satisfactory. In fluidized beds, the obtained mass transfer coefficients were correlated and compared with other works.