Heat transfer in a pulsed bubbling fluidized bed

Surface-to-bed heat transfer and pressure measurements were carried out in a 0.17 m ID pulsed bubbling fluidized bed with glass bead and silica sand particles having mean diameters ranging from 37 μm to 700 μm to investigate the effects of flow pulsation on heat transfer and bed hydrodynamics. A solenoid valve was used to supply pulsed air to the bed at 1 to 10 Hz. The bed surface was found to oscillate with the frequency of pulsation, the oscillation's amplitude decreasing with frequency. The standard deviation of the bed pressure drop in the pulsed bed was found to be larger than that in the conventional bed due to the acceleration force imposed by pulsation. For both Geldart B and A particles, high frequency pulsation (7, 10 Hz) enhances the heat transfer compared to continuous flow, the enhancement diminishing with superficial gas velocity and particle size. For Geldart B particles, the effect of pulsation on heat transfer ceases around U_o/U_mf = 3.5, whereas 24% improvement in heat transfer coefficient was obtained for 60 μm glass bead particles (Group A) at superficial gas velocities as high as U_o/U_mf = 27. Furthermore, in the fixed bed (U_o/U_mf < 1) for Geldart B particles, 1 Hz pulsation was found to be very effective resulting in two- to three-fold increase in heat transfer coefficient compared to continuous flow at the same superficial gas velocity. The flow pulsation loses its effect on heat transfer with increasing static bed height, i.e., when H_bed/D > 0.85.     

Effect of annular fins on heat transfer of a horizontal immersed tube in bubbling fluidized beds

Experiments were conducted in a bubbling air-fluidized bed to investigate the effect of annular fins of constant thickness on heat transfer. Steady state time averaged local heat transfer coefficient measurements were made by the local thermal simulation technique in a cold bubbling fluidized bed (90 mm ID, 260 mm tall) with horizontally immersed tube initially with no fin and then with three fixed annular fins of constant thickness. Silica sand of mean particle diameter 307 μm and 200 μm were used as the bed materials. The superficial velocity of air was from minimum fluidization conditions, u_mf, to approximately 3 × u_mf. The results indicate that, although the heat transfer coefficient falls with the use of fins, the total heat transfer rises as a result of the greater surface area. Increasing the particle diameter reduces the heat transfer coefficient not only for unfinned horizontal tube but also for annular finned horizontal tube at the same conditions of fluidized bed. Based on the experimental data, correlations are proposed for predicting heat transfer coefficient from fluidized bed to horizontally immersed tubes with and without fins.     

Transient thermal behaviour of a cylindrical wood particle during devolatilization in a bubbling fluidized bed

This work proposes a transient heat transfer model to predict the thermal behaviour of wood in a heated bed of sand fluidized with nitrogen. The 2-D model in cylindrical coordinates considers wood anisotropy, variable fuel properties, fuel particle shrinkage, and heat generation due to drying and devolatilization. The influence of initial fuel moisture content, thermal diffusivity, particle geometry, shrinkage, external heat transfer coefficient, chemical reaction kinetics and heats of reaction on temperature rise is presented. The cylindrical wood particles chosen for the study have length (l) = 20 mm, diameter (d) = 4 mm and l = 50 mm and d = 10 mm, both having an aspect ratio (l/d) of 5. The bed temperature is 1123 K. The model prediction is validated using measurements obtained from literature. The temperature rise in the wood particle is found to be sensitive to changes in the moisture content and thermal diffusivity and heat of reaction (in larger particles) while it is less sensitive to the external heat transfer coefficient and chemical kinetics. Also shrinkage is found to have a compensating effect and it does not have any significant influence on the temperature rise. Beyond an aspect ratio of three, the wood particle behaves as a 1-D cylinder.     

Inter-particle heat transfer in a riser of gas-solid turbulent flows

Effects of the particle-particle heat transfer in a gas-solid turbulent flow in a riser were evaluated. An Eulerian/Lagrangian four-way interaction formulation including the particle collisions in conjunction with the k − τ and the k_θ − τ_θ model equations were used in the numerical simulation. Inter-particles and particle-wall interactions were accounted for with an inelastic collision model, where the restitution coefficient was evaluated for each collision. The special case when the flow initially contains two groups of hot and cold particles was treated in details. Particular attention was given to the nature of heat transfer to particles due to inter-particle interactions. The results showed that the effect of particle-particle heat transfer was more significant for smaller sizes, lower flow Reynolds numbers, and for higher loading ratios. Solid thermal properties, however, did not have a noticeable effect on the inter-particle heat transfer. The simulation results indicates that although the heat transferred to each group of hot and cold particles was significant, the mean values of gas and particle temperatures and suspension heat transfer was insensitive to the inter-particle heat transfer.     

Systematic mesh development for 3D CFD simulation of fixed beds: Single sphere study

To develop and validate meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds, a single particle is often used as a test case. We present results for drag coefficient (C_D) and heat transfer Nusselt number (Nu) for flow past a sphere, focusing on high flow rates typical of industrial steam reformers (400 < Re < 20,000). Over this range, good predictions of C_D were obtained using large eddy simulation (LES) to capture vortex shedding and wake dynamics, with a mesh refined downstream from the sphere. The small time-steps and high cell count required make this too expensive for fixed beds. Nu can be accurately calculated using a Reynolds-averaged Navier-Stokes (RANS) method with shear-stress transport (SST) k-ω closure provided the mesh at the particle surface is fine enough and covers most of the boundary layer. Single sphere simulations of heat transfer are more useful for fixed bed mesh development than drag coefficient calculations.     

Bed-to-wall heat transfer characteristics in a circulating fluidized bed

The bed-to-wall heat transfer coefficients were measured in a circulating fluidized bed of FCC particles (d_p = 65 μm). The effects of gas velocity (1.0–4.0 m/s), solid circulation rate (10–50 kg/m²s) and particle suspension density (15–100 kg/m³) on the bed-to-wall heat transfer coefficient have been determined in a circulating fluidized bed (0.1 m-ID x 5.3 rn-high). The heat transfer coefficient strongly depends on particle suspension density, solid circulation rate, and gas velocity. The axial variation of heat transfer coefficients is a strong function of the axial solid holdup profile in the riser. The obtained heat transfer coefficient in terms of Nusselt number has been correlated with the pertinent dimensionless groups     

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

     

Experimental study and simulation of vibrated fluidized bed drying

The paper addresses numerical simulation for the case of convective drying of seeds (fine-grained materials) in a vibrated fluidized bed, analyzing agreement between the numerical results and the results of corresponding experimental investigation. In the simulation model of unsteady simultaneous one-dimensional heat and mass transfer between gas phase and dried material during drying process it is assumed that the gas-solid interface is at thermodynamic equilibrium, while the drying rate (evaporated moisture flux) of the specific product is calculated by applying the concept of a “drying coefficient”. Mixing of the particles in the case of vibrated fluidized bed is taken into account by means of the diffusion term in the differential equations, using an effective particle diffusion coefficient. Model validation was done on the basis of the experimental data obtained with narrow fraction of poppy seeds characterized by mean equivalent particle diameter (d_S,d = 0.75 mm), re-wetted with required (calculated) amount of water up to the initial moisture content (X₀ = 0.54) for all experiments. Comparison of the drying kinetics, both experimental and numerical, has shown that higher gas (drying agent) temperatures, as well as velocities (flow-rates), induce faster drying. This effect is more pronounced for deeper beds, because of the larger amount of wet material to be dried using the same drying agent capacity. Bed temperature differences along the bed height, being significant inside the packed bed, are almost negligible in the vibrated fluidized bed, for the same drying conditions, due to mixing of particles. Residence time is shorter in the case of a vibrated fluidized bed drying compared to a packed bed drying.     

Effects of Chaotic Temperature Fluctuations on the Heat Transfer Coefficient in Liquid‐Liquid‐Solid Fluidized Beds

The effect of chaotic temperature fluctuations on the immersed heater‐to‐bed heat transfer coefficient (h) are investigated in a liquid‐liquid‐solid fluidized bed (0.152 m ID × 2.5 m in height). The time series of temperature fluctuations are measured and analyzed by means of the multidimensional phase space portraits and Kolmogorov entropy (K), in order to characterize the chaotic behavior of heat transfer coefficient fluctuations in the bed. The overall heat transfer coefficient is inversely proportional to the Kolmogorov entropy of temperature fluctuations, as well as the fluctuation range of heat transfer coefficient (Δh_i). The Kolmogorov entropy and fluctuation range of the heat transfer coefficient (Δh_i) increase with increasing dispersed phase velocity, but decrease with increasing particle size. However, they attain their minima with variation of the continuous phase velocity as well as the bed porosity, at which point the flow regime of particles in the beds changes. The overall heat transfer coefficient is directly correlated with the Kolmogorov entropy, as well as the fluctuation range of heat transfer coefficient.     

Mass loss and apparent kinetics of a thermally thick wood particle devolatilizing in a bubbling fluidized bed combustor

This work presents the results of experiments conducted to determine the mass loss characteristics of a cylindrical wood particle undergoing devolatilization under oxidation conditions in a bubbling fluidized bed combustor. Cylindrical wood particles having five different sizes ranging from 10 to 30 mm and aspect ratio (l/d = 1) have been used for the study. Experiments were conducted in a lab scale bubbling fluidized bed combustor having silica sand as the inert bed material and air as the fluidizing medium. Total devolatilization time and mass of wood/char at different stages of devolatilization have been measured. Studies have been carried out at three different bed temperatures (T_bed = 750, 850 and 950 °C), two inert bed material sizes (mean size d_p = 375 and 550 μm) and two fluidizing velocities (u = 5u_mf and u = 10u_mf). Devolatilization time is most influenced by the initial wood size and bed temperature. Most of the mass is lost during the first half of the devolatilization process. There was no clear influence of the fluidization velocity and bed particle size on the various parameters studied. The apparent kinetics estimated from the measured mass history show that the activation energy varied narrowly between 15 and 27 kJ/mol and the pre-exponential factor from 0.11 and 0.45 s⁻¹ for the wood sizes considered.     

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.     

Numerical and experimental analyses of anti‐fouling and heat transfer in the heat exchanger with circulating fluidized bed

Fluidized bed type heat exchangers are known to increase the heat transfer and prevent the fouling. For proper design of circulating fluidized bed heat exchanger it is important to know the effect of design and operating parameters on the bed to the wall heat transfer coefficient. The numerical analysis by using CFX 11.0 commercial code was done for proper design of the heat exchanger. The present experimental studies were also conducted to investigate the effects of circulating solid particles on the characteristics of fluid flow, heat transfer, and cleaning effect in the fluidized bed vertical shell and tube type heat exchanger with counterflow, at which a variety of solid particles such as glass (3 mmØ), aluminum (2–3 mmØ), steel (2–2.5 mmØ), copper (2.5 mmØ), and sand (2–4 mmØ) were used in the fluidized bed with a smooth tube. Seven different solid particles have the same volume, and the effects of various parameters such as water flow rates, particle diameter, materials, and geometry were investigated. The present experimental and numerical results showed that the flow velocity range for collision of particles to the tube wall was higher with heavier density solid particles, and the increase in heat transfer was in the order of sand, copper, steel, aluminum, and glass. This behaviour might be attributed to the parameters such as surface roughness or particle heat capacity. Fouling examination using 25,500 ppm of ferric oxide (Fe₂O₃) revealed that the tube inside wall is cleaned by a mild and continuous scouring action of fluidized solid particles. The fluidized solid particles not only keep the surface clean, but they also breakup the boundary layer improving the heat transfer coefficient even at low‐fluid velocities.     

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.     

Fluidized bed pyrolysis of HDPE: A study of the influence of operating variables and the main fluidynamic parameters on the composition and production of gases

In the present work, a preliminary study of the pyrolysis process of high density polyethylene (HDPE) in a fluidized bed is investigated in order to determine the influence between the fluidynamic properties of the bed reactor and the amount and composition of the gases produced. As is known, fluidized bed technology is a very interesting option to apply in the pyrolysis field due to i) the lack of moving parts in the hot region that facilitates the maintenance of equipment, ii) the high surface area to volume ratio available in the bed, and iii) the high heat transfer coefficient reached which governs the reaction products. But, heat and mass transfer coefficients are strongly affected by the fluidynamic properties of the bed.During the pyrolysis of HDPE, a fluidynamic characterization of the bed particles that consist of char-coated sand of HDPE has been carried out. Parameters such as the minimum fluidizing velocity (u_mf), terminal velocity (u_t), bed height (h_f), bed voidage (ε_f), fraction of the bed occupied by bubbles (δ), bubble diameter (d_b), bubble velocity (u_b), the mass transfer coefficients between the bubble and the cloud (K_bc) and between the cloud and the emulsion (K_ce) were determined. Subsequently, the influence of major operating variables and the fluidynamic parameters on the composition and the gas yield of the pyrolysis of HDPE were studied.     

Systematic mesh development for 3D CFD simulation of fixed beds: Contact points study

In the development of meshes for computational fluid dynamics (CFD) simulations of transport in fixed beds of spheres, particle–particle and wall–particle contact points often present difficulties. We give results for drag coefficient (C_D) and heat flow (Q) for flow past sphere–sphere and wall–sphere contact points, focusing on higher flow rates typical of industrial steam reformers (500 < Re < 10,000). Global methods, in which all particles in a bed are either shrunk or enlarged uniformly, change bed voidage giving erroneous results for C_D. Local methods, in which bridges are inserted or spherical caps are removed only at the points of contact, give much better results for C_D. The bridges approach is preferable for heat transfer, as fluid gaps reduce heat transfer too much, and particle overlaps increase it. A set of graphs is presented to allow estimation of the error introduced by the various methods of dealing with contact points.     

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.     

Prediction of single particle settling velocities through liquid fluidized beds

Single particle settling velocities through water fluidized beds of mono-sized glass spheres (d_p = 0.645, 1.20, 1.94, 2.98 and 5 mm in diameter) were studied experimentally using a column, 40 mm in diameter. The settling spherical particles (D_p = 10 and 19.5 mm) had different densities (1237 to 8320 kg/m³), while the settling particles (D_p = 5 and 2.98 mm) were glass spheres. The pseudo-fluid model, which considers a liquid fluidized bed as a homogenous pseudo-fluid, predicts single particle settling velocities quite well if the ratio D_p/d_p is larger than about 10. With decreasing ratio D_p/d_p, the overall friction between the settling particle and the fluidized media increases. A method for predicting single particle settling velocities through a liquid fluidized bed is proposed and discussed. Following the approach of Van der Wielen et al. [L.A.M. Van der Wielen, M.H.H Van Dam, K.C.A.M. Van Luyben, On the relative motion of a particle in a swarm of different particles, Chem. Eng. Sci. 51 (2006) 995-1008], the overall friction is decomposed into a particle-fluid and a particle-particle component. The effective buoyancy force is calculated using the transition function proposed by Ruzicka [M.C. Ruzicka, On buoyancy in dispersion, Chem. Eng. Sci. 61 (2006) 2437-2446]. A simple model for predicting the collision force is proposed, as well as a correlation for the collision coefficient. The mean absolute deviation between the experimental and calculated slip velocities was 5.08%.     

Computational modelling of the impact of particle size to the heat transfer coefficient between biomass particles and a fluidised bed

The fluid-particle interaction and the impact of different heat transfer conditions on pyrolysis of biomass inside a 150 g/h fluidised bed reactor are modelled. Two different size biomass particles (350 μm and 550 μm in diameter) are injected into the fluidised bed. The different biomass particle sizes result in different heat transfer conditions. This is due to the fact that the 350 μm diameter particle is smaller than the sand particles of the reactor (440 μm), while the 550 μm one is larger. The bed-to-particle heat transfer for both cases is calculated according to the literature. Conductive heat transfer is assumed for the larger biomass particle (550 μm) inside the bed, while biomass-sand contacts for the smaller biomass particle (350 μm) were considered unimportant. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Biomass reaction kinetics is modelled according to the literature using a two-stage, semi-global model which takes into account secondary reactions. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase. FLUENT 6.2 has been used as the modelling framework of the simulations with the whole pyrolysis model incorporated in the form of User Defined Function (UDF).     

Mass transfer around freely moving active particles in the dense phase of a gas fluidized bed of inert particles

The mass transfer coefficient around freely moving active particles under bubbling/slugging fluidized bed conditions was measured in a lab-scale reactor. The technique used for the measurements consisted in the oxidation reaction of carbon monoxide at over one or few Pt catalyst spheres immersed in an inert bed of sand. It was shown that this technique is simple and accurate, and allows to overcome most of the difficulties and uncertainties associated with other available techniques. The experimental campaign was carried out by varying the fluidization velocity (0.15-0.90 m/s), the active particle size (1.0-10.0 mm) and the inert particle size (0.1-1.4 mm). Results were analyzed in terms of the particle Sherwood number. Experimental data showed that Sh is not influenced by the fluidization velocity and by a change of regime from bubbling to slugging, whereas it increases with a square root dependence with the minimum fluidization velocity and with the active particle size. These results strongly suggest that the active particles only reside in the dense phase and never enter the bubble/slug phase. Data were excellently fitted by a Frössling-type correlation:

Sh=2.0·ε_mf+K·(Re_mf/ε_mf)^1/2·Sc^1/3