Heat transfer of gas flow through a packed bed

This paper reports an experimental study of both the transient and steady-state heat transfer behaviour of a gas flowing through a packed bed under the constant wall temperature conditions. Effective thermal conductivities and convective heat transfer coefficient are derived based on the steady-state measurements and the two-dimensional axial dispersion plug flow (2DADPF) model. The results reveal a large temperature drop at the wall region and the temperature drop depends on the axial distance from the inlet. The 2DADPF model predicts the axial temperature distribution fairly well, but the prediction is poor for the radial temperature distribution. Length-dependent behaviour of the effective heat transfer parameters and non-uniform flow behaviour are proposed to be responsible. A comparison with previously published correlations and data in the literature shows that the relationships proposed by Bunnell et al. and Demirel et al. agree well with the measured effective radial thermal conductivity, whereas the wall-fluid heat transfer coefficient is better represented by the Li-Finlayson correlation.     

Identification of Flow Regimes in a Concurrent Gas Liquid Upflow through Packed Beds

The flow regimes bubble flow, pulse flow, and spray flow were identified by visual observation in a packed column. Three gas‐liquid systems (air/water, air/56 % glycerol, and air/monoethanolamine) and four column packings (Raschig rings, Intalox saddles, and two sizes of spheres) were investigated to cover wide ranges of physical properties of gas liquid systems and characteristics of column packings affecting the flow regime transition. Criteria for the flow regime transition were developed in terms of system and operating variables.     

Heat transfer and flow pattern in vertical liquid-solids flow

Wall-to-bed heat transfer in hydraulic transport of spherical glass particles of diameter 1.20, 1.94 and 2.98 mm and in single-phase flow regime was studied. Experiments were performed by transporting the spherical glass particles with water in a 25.4 mm I.D. copper tube equipped with a steam jacket.In the runs without particles, the tube Reynolds number varied between 2280 and 21,300, while in hydraulic transport runs, the tube Reynolds number varied between 3300 and 20,150. The loading ratio (G_p/G_f) was between 0.07 and 0.328, and the fluid superficial velocity was between 0.29·U_t and 2.86·U_t, where U_t represents the single particle terminal velocity. For these ratios, the voidage ranged from 0.715 to 0.895.The data for the heat transfer factor (j_H) in single-phase flow are correlated using a general form j_H=f(Re). The data for wall-to-bed heat transfer in the hydraulic transport of particles show that an analogy between heat and momentum transfer exists. The data were correlated by treating the flowing fluid-particle suspension as a pseudofluid, by introducing a modified suspension-wall friction coefficient (f_w) and a modified Reynolds number (Re_m).     

Phenylacetylene hydrogenation in a three-phase catalytic packed-bed reactor: experiments and model

A mathematical model was developed for the cocurrent operation of a three-phase catalytic packed-bed reactor under both trickling- and pulsing-flow regimes. The local fluctuations of liquid-solid mass transfer, liquid flow rate, and liquid holdup in unsteady pulsing-flow were simulated as periodic square-wave functions. The transport properties employed in the model were obtained using published correlations, while expressions for the intrinsic reaction kinetics were taken from our previous work. The model results were found to be in good agreement with experimental data obtained from a laboratory-scale reactor, and verified the advantage of pulsing-flow operation over trickling-flow.     

Evaluation of pseudohomogeneous models for heat transfer in packed beds with gas flow and gas-liquid cocurrent downflow and upflow

Several pseudohomogeneous models are used by researchers in the study of heat transfer in packed beds. In this work, five of the most used pseudohomogeneous models (to one, two and three parameters) are analyzed, for gas and gas-liquid flow configurations. The models were evaluated concerning the following aspects: (a) the fitting between calculated and measured temperatures, (b) the values of thermal parameters, (c) their confidence intervals, (d) the quality of the estimation of the thermal parameters by analysis of their Box biases, and (e) the nonlinear dependence of the calculated temperatures on the thermal parameters (using the curvature measures of Bates and Watts). It was observed, particularly in gas-liquid flow, that the fittings between calculated and measured temperature profiles are better for models in which a wall heat transfer coefficient is incorporated to consider the convective resistance at the bed wall. It was also noted that the values of the thermal parameters fitted from the pseudohomogeneous models may be very different at identical operational conditions. The effective axial thermal conductivity may be neglected in the modeling because its estimation does not affect the residual functions. Besides, the estimation of k_a is tricky because it depends on the initial guess and also because the parameter is extremely sensitive to changes in the operational conditions. The confidence intervals for the parameters depend on the model and are also affected by the experimental conditions. The estimation of the parameters was adequate for the k_r-h_W and k_r-k_a models and the curvatures measures were satisfactory only for models in which h_W was not incorporated.     

Convective heat and mass transfer coefficient measurements and correlations for particle beds using temperature and humidity step changes with air flow through a test bed

In this paper, transient responses of a porous urea particle bed subject to a step change in the inlet temperature or humidity for a forced convective air flow through the particle bed are investigated to determine the convective heat and mass transfer coefficients inversely by comparing the measured time constant with the predicted characteristic time constant, which is a function of the convection coefficients and Reynolds number. The experimental results show, that although both the time constants for temperature and humidity step changes are dependent on Reynolds number, the temperature response time constant (35-1300 s) is much larger than the humidity response time constant (4-25 s) for the Reynolds number range of 300-5. The surface adsorption of water vapor is very rapid but the absorption inside the porous urea particle is slowed by a very low internal effective diffusion coefficient within the particles whereas the very low Biot number for heat transfer in the particles implies a complete thermal interaction with the air flow throughout each particle and a much larger time constant. Empirical correlations of the Chilton-Colburn j-factor and Nusselt number versus Reynolds number are compared with the correlations of other researchers. These new correlations, which include an uncertainty analysis, imply much lower convective coefficients than those reported previously in the literature.     

Heat transfer of gas-solid two-phase mixtures flowing through a packed bed

This paper reports an experimental study on both transient and steady-state heat transfer behavior of a gas-solid two-phase mixture flowing through a packed bed under constant wall temperature conditions. A logarithmic mean temperature difference (LMTD) method is used to process the temperature data to obtain the overall heat transfer coefficient. The influences of particle loading and gas flow Reynolds number are investigated. The results show that the introduction of suspended particles greatly enhances heat transfer between the flowing gas-solid two-phase mixture and the packed bed, and the enhancement increases approximately linearly with increasing particle loading. The heat transfer coefficient data are processed to give the Nusselt number, which is found to correlate well to the Reynolds number, the Archimedes number and the suspended particle loading ratio. A comparison of the data of this work with the published data reveals large discrepancy. Possible reasons for the discrepancy are discussed.     

Characteristics of liquid and tracer dispersion in trickle-bed reactors: Effect on CFD modeling and experimental analyses

The characteristics of mechanical dispersion of tracer and liquid are analyzed using CFD modeling and experimental results from the literature. The most significant differences are underlined and their impact is discussed further. When compared to uniform liquid distribution, the more complicated flow conditions in liquid source measurements are considered to have a significant effect on result analysis and should be paid more attention to. Modeling of mechanical dispersion of liquid using CFD is discussed. Finally, liquid source dispersion cases are simulated and the results are compared to the experimental liquid as well as tracer dispersion results.     

Hydrodynamic and transport properties of packed beds in small tube-to-sphere diameter ratio: pore scale simulation using an Eulerian and a Lagrangian approach

In fixed bed catalytic reactors radial heterogeneities of the granular structure are present owing to topologic constraints imposed by the reactor wall. In order to analyse the influence of this structure on the fluid flow and the radial mass transfer properties, the study of sphere packings in cylindrical container and flow simulations at the pore scale are carried out. A collocated finite volume is used to solve the 3D Navier-Stokes equations. The Reynolds number ranges from 7 to 200 allowing to use the direct numerical simulation method in stationary flow regime combined to the no-slip condition at the interface solid/fluid. Therefore no correlation are used in this study. Furthermore, representative fixed beds, composed of several hundreds of spheres, are used for a diameter ratio of 5.96 and 7.8. Radial profile of the longitudinal velocity and the probability density function of the velocity components agree with the experimental data found in the literature. At low Reynolds number, the computation of current lines reveals the presence, at the reactor wall, of a layer whose width is around one-fourth of the sphere diameter. In this layer, the fluid flow is longitudinal and tangential. Particle tracking reveals also the existence of a second layer all along the spheres in contact with the reactor wall. Mass transfer in these two regions is controlled by the diffusive mechanism at low Reynolds number. The flow structure at high Reynolds number contains lots of eddies distributed homogeneously in the fixed beds. These structures are not recirculating zones (particle traps). On contrary, they accelerate the radial mass transfer so that the layers found at low Reynolds number tend to disappear at high Reynolds.     

Heat transfer in a particle curtain falling through a horizontally-flowing gas stream

A study of heat transfer between horizontally-flowing air and a free-falling particle curtain was reported. A steady and uniformly distributed stream of cold particles was fed through a rectangular slit and allowed to fall to form a curtain across the entire width of a horizontal duct of cross-section of 0.15 × 0.60 m. Warm air, at velocities in the range of 0.9 m/s to 1.2 m/s and with a uniform velocity profile, flowed horizontally through the duct. A range of curtain thickness (4 cm to 10 cm) and mass flow rate (0.031 kg/s to 0.040 kg/s) were used to investigate the heat transfer characteristic of the free-falling particle curtain in a uniform cross-flowing gas. Particle temperatures within the curtain and air temperatures outside the curtain were measured as a function of vertical position in the duct. A simple model based on single particle behaviour was developed. The predicted solid temperatures agreed well with the experimental results. However, the predictions for the gas temperatures were less satisfactory.     

Experimental and Theoretical Investigation of Concentration and Temperature Profiles in a Narrow Packed Bed Adsorber

Significant radial profiles of concentration and temperature may exist in packed bed adsorbers, leading to a different breakthrough behavior at the wall than in the core of the bed. Respective data have been gained by near‐infrared tomography for zeolite and water in relatively narrow tubes, and are compared with the predictions of a two‐dimensional model. Though the agreement is satisfactory in total, some deviations from the experimental results have been observed. Model reductions can not be recommended due to complex interactions between thermal effects, channelling, and non‐linear equilibrium in the dynamic process.     

The heat transfer coefficient between a particle and a bed (packed or fluidised) of much larger particles

The heat transfer coefficient has been measured for a heated phosphor-bronze sphere (diam. 2.0, 3.0 or 5.56 mm) added to a bed of larger particles, through which air at room temperature was passed. The bronze heat transfer sphere was attached to a very thin, flexible thermocouple and was heated in a flame to before being immersed in the bed. The cooling of the bronze sphere enabled the heat transfer coefficient, h, to be measured for a variety of U/U_mf, as well as diameters of both the particles in the bed and the heat transfer sphere. It was found that before the onset of fluidisation, h rose with U, but h reached a constant value for U?U_mf. These measurements indicate that in this situation (of a relatively small particle in a bed of larger particles) all the heat transfer is between the hot bronze sphere and the gas flowing over it. Consequently, a Nusselt number, based on the thermal conductivity of the gas, is easy to define and for U?U_mf (i.e. a packed bed), Nu is given by

     

Simulation of Turbulent Flow in a Packed Bed

Numerous models for simulating the flow and transport in packed beds have been proposed in the literature with few reported applications. In this paper, several turbulence models for porous media are applied to the gas flow through a randomly packed bed and are examined by means of a parametric study against some published experimental data. These models predict widely different turbulent eddy viscosity. The analysis also indicates that deficiencies exist in the formulation of some model equations and selection of a suitable turbulence model is important. With this realization, residence time distribution and velocity distribution are then simulated by considering a radial profile of porosity and turbulence induced dispersion, and the results are in good agreement with the available experimental data.     

Heat transfer study in a pilot-plant scale bubble column

The effects of superficial gas velocity on heat transfer coefficient and its time-averaged radial profiles along the bed height have been investigated in a pilot-plant scale bubble column of 0.44 m diameter using air-water system. Notable differences were observed in heat transfer coefficients along the bed axial locations particularly between the sparger (Z/D = 0.28) and the fully developed flow (Z/D = 4.8) regions. In the fully developed flow region larger heat transfer coefficient values were obtained compared to those in the sparger region. About 14-22% increase in heat transfer coefficients measured in the fully developed flow region has been observed compared to those measured in the distributor region when the superficial gas velocity increases from 0.05 to 0.45 m/s. The heat transfer coefficients in the column center for all the conditions studied are about 9-13% larger than those near the wall region. It has been noted that in the fully developed flow region, the axial variation of the heat transfer coefficients was not significant.     

Heat Transfer to Immersed and Boundary Surfaces in Fluidized Beds

An experimental study of heat transfer into gas‐fluidized beds has been carried out with heat transfer into discriminated areas of the boundary walls, and into single and multiple elements immersed in the bed. The experiments have been carried out with glass ballotini ranging in size from 100 μm to 1 mm in diameter, on Diakon (Perspex) particles of 325 μm, and on nickel particles of 275 μm and 325 μm covering a range of Archimedes numbers from 100 to 10⁵. Beds of different diameter with distributors of several different types have been examined. The entire experimental results have been compared with literature data on heat transfer to immersed elements. It is shown that the onset of slugging in the fluidized bed has a large effect on heat transfer. Once the effect of slugging has been introduced, it is shown that the results of this investigation and others in the literature within the range of Archimedes numbers from 100 to 10⁹ may be correlated.     

Radiative heat transfer in circulating fluidized bed furnaces

Three methods of estimating the effective emissivity of a gas-particle suspension are compared and the radiative heat transfer coefficient of an isothermal suspension is defined. Heat flux measurements obtained from circulating fluidized bed combustors are examined. Radiation from a particle suspension with core temperature dominates the radiative heat transfer in the upper part of the furnace, where the particle density is low and no substantial particle boundary layers are formed. Over the lower parts of the heat transfer surfaces, where significant thermal and particle boundary layers are present, the radiative heat flux is dominated by emission from the relatively low temperature particle layer in the vicinity of the heat receiving surface.     

The generalized Lévêque equation and its practical use for the prediction of heat and mass transfer rates from pressure drop

Based on the generalized Lévêque equation (GLE) a new type of analogy between pressure drop and heat transfer has been discovered, that may be used in the cross corrugated channels of chevron type plate heat exchangers, in packed beds, in tube bundles, in crossed rod matrices or in many other spacewise periodic arrangements.Experimental data on heat transfer in tube bundles in crossflow, both inline, and staggered arrangements, had been recently tested in greater detail. Using an empirical correlation for pressure drop in these arrangements from the literature that has been successfully tested against a large number of experimental pressure drop data, heat transfer data collected earlier could be very well represented from the pressure drop correlation and the GLE. The data for staggered bundles have been shown to be in better agreement with this new method, than with the existing empirical heat and mass transfer correlations. Somewhat larger deviations for inline tube bundles had been found at lower Reynolds numbers. Here a simple and physically reasonable correction function of Re is presented, which leads to a better agreement for the inline bundles, too.Additionally, it can be shown for a number of literature data on tube bundles and on crossed rod matrices that the agreement with the GLE prediction is even better if original pressure drop data from the same sources are available in place of a pressure drop correlation.The method results in reasonable heat or mass transfer predictions from frictional pressure drop, which may be widely used in chemical engineering applications.     

Effect of Thermal Asymmetry on Heat Transfer in a Laminar Annular Flow

The effect of thermal asymmetry on heat transfer in a hydrodynamically developed annular flow has been investigated numerically. The surfaces confining the fluid space are kept at constant but different temperatures. Depending on the fluid inlet temperature, the thermal asymmetry can lead to a discontinuity of the Nusselt number on one surface. With the thermally developed flow the exact expressions for the Nusselt numbers have been obtained.     

A fractal approach for interpretation of local instantaneous temperature signals around a horizontal heat transfer tube in a bubbling fluidized bed

Temperature signals measured around a horizontal heat transfer tube in a bubbling fluidized bed have been analyzed using Hurst's rescaled range (R/S) analysis. This analysis estimates and identifies long-term persistence or correlation in measured time series. The Hurst exponent H, which is evaluated from R/S analysis, also provides the local fractal dimension of the time series. A new approach to analyze an air fluidized particle system is proposed based on the evaluation of the Hurst exponent. Two Hurst exponents can be evaluated from a single time series, one from the discrete time fractional noise (where the linearity of the signal is subtracted and short-term fluctuations are emphasized) and the other from the signal itself (without subtracting the linearity of the signal). The authors argue that the Hurst exponent obtained from discrete time fractional noise characterizes the particle motion, whereas the Hurst exponent obtained from the signal itself characterizes the bubble motion. Moreover, a comparison between these two Hurst components identifies the zones where an alternating type of contact between the tube surface and the bubble-emulsion phase occur. The results were interpreted in conjunction with the mutual information function. The mutual information function provides the relationship between the data points separated in time and uses only the statistical relationship between the data points. The mutual information functions and the Hurst exponents exhibited similar trends around the heat transfer tube.