Computational study of heat transfer in a bubbling fluidized bed with a horizontal tube

A combined approach of discrete particle simulation and computational fluid dynamics is used to study the heat transfer in a fluidized bed with a horizontal tube. The approach is first validated through the good agreement between the predicted distribution and magnitude of local heat transfer coefficient with those measured. Then, the effects of inlet fluid superficial velocity, tube temperature and main particle properties such as particle thermal conductivity and Young's modulus are investigated and explained mechanistically. The relative importance of various heat transfer mechanisms is analyzed. The convection is found to be an important heat transfer mode for all the studied conditions. A large convective heat flux corresponds to a large local porosity around the tube, and a large conductive heat flux corresponds to a large number of particle contacts with the tube. The heat transfer is enhanced by the increase of particle thermal conductivity while it is little affected by Young's modulus. Radiative heat transfer becomes increasingly important as the tube temperature is increased. The results are useful for temperature control and structural design of fluidized beds. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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.     

Computational fluid dynamics simulations of pressure drop and heat transfer in fixed bed reactor with spherical particles

Fixed bed reactors are among the most important equipment in chemical industries as these are used in chemical processes. An accurate insight into the fluid flow in these reactors is necessary for their modeling. The pressure drop and heat transfer coefficient have been studied for the fixed bed reactor with tube to particle diameter ratio (N) of 4.6 and comprising 130 spherical particles using computational fluid dynamics (CFD). The simulations were carried out in a wide range of Reynolds number: 3.85≤Re≤611.79. The RNG k-ɛ turbulence model was used in the turbulent regime. The CFD results were compared with empirical correlations in the literature. The predicted pressure drop values in laminar flow were overestimated compared with the Ergun’s [27] correlation and underestimated in the turbulent regime due to the wall friction and the flow channeling in the bed, respectively. It was observed that the CFD results of the pressure drop are in good agreement with the correlations of Zhavoronkov et al. [28] and Reichelt [29] because the wall effects have been taken into account in these correlations. Values of the predicted dimensionless heat transfer coefficient showed better agreement with the Dixon and Labua’s [32] correlation. This is explained by the fact that this correlation is a function of the particle size and shape in the bed.     

Computational fluid dynamics simulations of heat transfer between the dense‐phase of a high‐temperature fluidized bed and an immersed surface

The transient process of heat transfer between a high‐temperature emulsion packet and the wall of an immersed surface is simulated using computational fluid dynamics (CFD). From these simulations, the total heat transfer coefficient and its radiant contribution due to the emulsion (dense) phase are evaluated. The results are compared with experimental data (Ozkaynak et al., “An experimental investigation of radiant heat transfer in high temperature fluidized beds,” in Fluidization IV, 1983:371–378) and with predicted values from the generalized heterogeneous model (GHM), (Mazza et al., “Evaluation of overall heat transfer rates between bubbling fluidized beds and immersed surfaces,” Chem Eng Commun., 1997;162:125–149). The CFD simulations are in good agreement with both, experimental data and theoretical GHM predictions and provide a reliable way to quantify the studied heat transfer process. Also, the GHM is validated as a practical tool to this end. © 2011 American Institute of Chemical Engineers AIChE J, 58: 412–426, 2012     

竖直管气固鼓泡流化床传热机理的CPFD模拟

针对细颗粒气固鼓泡流化床中床料与竖直传热管壁面间的传热行为,在前期实验的基础上,采用计算颗粒流体力学(CPFD)方法从颗粒在传热壁面更新的角度,深入分析了传热特性与壁面气固流动行为之间的关联性。结果表明,模拟得到的传热管壁面颗粒更新通量和基于颗粒团更新模型的颗粒团平均停留时间均能很好解释实验测得的传热系数变化规律,这证实颗粒团更新是影响传热过程的控制性因素。模拟还发现随加热管从床层中心向边壁的移动,加热管周向方向上颗粒更新通量和传热系数的不均匀性都呈增大趋势。随着表观气速的增大,气泡行为导致床层颗粒内循环流率增大,这是导致颗粒团在加热管壁面上的更新频率增大以及床层与壁面间传热系数增大的根源。     

Computational fluid dynamics of a circulating fluidized bed under various fluidization conditions

A computational fluid dynamics (CFD) model was developed to simulate the hydrodynamics of gas-solid flow in a circulating fluidized bed (CFB) riser at various fluidization conditions using the Eulerian-Granular multiphase model. The model was evaluated comprehensively by comparing its predictions with experimental results reported for a CFB riser operating at various solid mass fluxes and superficial gas velocities. The model was capable of predicting the main features of the complex gas-solids flow, including the cluster formation of the solid phase along the walls, for different operating conditions. The model also predicted the coexistence of up-flow in the lower regions and downward flow in the upper regions at the wall of the riser for high gas velocity and solid mass flux, as reported in the literature. The predicted solid volume fraction and axial particle velocity were in good agreement with the experimental data within the high density fast fluidization regime. However, the model showed some discrepancy in predicting the gas-solid flow behavior in the riser operating in dense suspension up-flow and low density fast fluidization regimes.     

Numerical analysis of interphase heat and mass transfer of cluster in a circulating fluidized bed

Interphase heat and mass transfer characteristics of a naphthalene particle cluster in a circulating fluidized riser are numerically analyzed using a three-dimensional CFD model. Heat and mass transfer characteristics of gas over an in-line array of three naphthalene particles and an isolated naphthalene particle are analyzed. Distributions of gas concentration, temperature and velocity are obtained. The heat and mass transfer rates of gas-to-cluster increase with the increase of the cluster porosity and Reynolds number. Present simulations indicate that the small cluster gives higher heat and mass transfer coefficients than those of the large cluster. The heat and mass transfer rates of individual particles in the cluster are lower than that of an isolated particle and particles in an in-line array under a given cluster porosity.     

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     

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.     

Insights in distributed secondary gas injection in a bubbling fluidized bed via discrete particle simulations

Experiments have shown that distributed secondary gas injection via a fractal injector in fluidized beds can significantly reduce the bubble size, and may also decrease the bubble fraction. In order to gain insight into the distribution of the gas between the phases and the mechanisms behind these effects simulations of small bubbling fluidized beds with one or two secondary gas injection points were carried out using a discrete particle model. Although the systems are very small, so that wall effects cannot be excluded, the model predicts that the bubble size and bubble fraction both decrease with secondary gas injection, while the gas flow through the dense phase increases. The secondary gas tends to stay in the dense phase, which limits the amount of gas available to form bubbles and is the main contributor to the decrease in the bubble size and fraction. The gas-solid contact improves as a result.     

Hydrodynamics and interphase heat transfer in a swirled spouted bed

A new modification of a spouting technique, a swirled spouted bed (SSB), is developed and proposed to increase the efficiency of heat treatment of polyfractional and fine particles and to reduce their entrainment. It is shown that under the developed spouting conditions the SSB pressure drop is 20-30% and incipient spouting velocity is 40-50% lower whereas an interphase heat transfer rate is 15-25% higher as compared to a classical spouted bed (CSB). An empirical correlation is proposed to determine the SSB pressure drop under developed conditions.     

Computation of the mass transfer coefficient of FCC particles in a thin bubbling fluidized bed using two- and three-dimensional CFD simulations

In this study, the standard kinetic theory based model with a modified drag correlation was successfully used to compute the mass transfer coefficients and the Sherwood numbers of FCC particles in a thin bubbling fluidized bed column using the additive diffusional and chemical reaction resistances concept. Also, the effects of the computational domain (two- or three-dimensional) and the reaction rate constant (low and high) are discussed.The computations show that the Sherwood numbers are in agreement with the measurement ranges for small particles in the fluidized bed system. The mass transfer coefficients and the Sherwood numbers are high near the inlet section, and decrease to a constant value with increasing height in the column. The two-dimensional computational domain simulations provide enough information to explain the phenomena inside a symmetrical system, but three-dimensional computational domain simulations are still needed for asymmetrical systems. Finally, the mass transfer coefficients and the Sherwood numbers increased with the larger reaction rate constant.     

Full‐physics simulations of spray‐particle interaction in a bubbling fluidized bed

Numerical simulations of a gas‐particle‐droplet system were performed using an Euler‐Lagrange approach. Models accounting for (1) the interaction between droplets and particles, (2) evaporation from the droplet spray, as well as (3) evaporation of liquid from the surface of non‐porous particles were considered. The implemented models were verified for a packed bed, as well as other standard flow configurations. The developed models were then applied for the simulation of flow, as well as heat and mass transfer in a fluidized bed with droplet injection. The relative importance of droplet evaporation vs. evaporation from the particle surface was quantified. It was proved that spray evaporation competes with droplet deposition and evaporation from the particle surface. Moreover, we show that adopting a suitable surface coverage model is vital when attempting to make accurate predictions of the particle's liquid content. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2569–2587, 2017     

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.     

柱形流化床传热特性的数值模拟

对Shedid等搭建的圆柱体流化床采用欧拉?欧拉法进行三维数值模拟,考察了颗粒球形度、表观进气速度和床料初始堆积高度对流化床内垂直加热壁面与流动床料之间对流传热特性的影响,采用有效导热系数分别计算气相和固相的对流传热系数。结果表明,随表观进气速度增大,流化床内颗粒物料湍流运动加剧,加热壁面平均温度和流体平均温度下降,壁面流体间传热平均温度差减小,壁面流体间对流传热系数增大;随初始床料高度增加,流化床内颗粒与加热壁面的接触面积增大,导致固相平均对流传热系数增大。     

Temperature fluctuations and heat transfer in a circulating fluidized bed

Characteristics of temperature fluctuations and heat transfer coefficient have been investigated in the riser of a circulating fluidized bed (0.102 m ID and 4.0 m in height). Effects of gas velocity and solid circulation rate on the temperature fluctuations, suspension density and heat transfer coefficient between the immersed heater and the bed have been considered in the riser. To analyze the characteristics of temperature fluctuations at the wall of the riser, the phase space portrait and Kolmogorov entropy of the fluctuations have been obtained, and the relation between the temperature fluctuations and the heat transfer coefficient has been examined. It has been found that the heat transfer system becomes more complicated and irregular with decreasing gas velocity and increasing solid circulation rate or suspension density in the riser. The heat transfer coefficient and Kolmogorov entropy of the temperature fluctuations have decreased with increasing the superficial gas velocity, while they have increased with increasing the solid circulation rate or suspension density in the bed. The heat transfer coefficient has been well correlated in terms of the Kolmogorov entropy, suspension density as well as operating variables in the riser. This paper is dedicated to Professor Dong Sup Doh on the occasion of his retirement from Korea University.     

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.     

Computational fluid dynamics of high density circulating fluidized bed riser: Study of modeling parameters

CFD modeling of air and fluid catalytic cracking (FCC) particles in the riser of a high density circulating fluidized bed (HDCFB) has been performed. The implementation of correct inlet conditions was found to be critical for the successful simulation of the hydrodynamics. The simulated profiles of gas and solid velocity and volume fraction were overall in good agreement with experimental data reported in the literature. However, due to the difficulties in accurate modeling of the solid segregation toward the wall, the solid volume fraction was under predicted near the walls. The effect of modeling parameters including different drag models, wall restitution coefficient values, and solid slip conditions have been evaluated. While the wall restitution coefficient did not exhibit a significant effect on the riser hydrodynamics, the appropriate slip condition aided in predicting the solid segregation toward the wall.     

Oxidative coupling of methane in a bubbling fluidized bed reactor

The oxidative coupling of methane to higher hydrocarbons (C₂₊) was studied in a bubbling fluidized bed reactor between 700°C and 820°C, and with partial pressures of methane from 40 to 70 kPa and of oxygen from 2 to 20 kPa; the total pressure was ca 100 kPa. CaO, Na₂CO₃/CaO and PbO/γ-Al₂O₃ were used as catalytic materials. C₂₊ selectivity depends markedly on temperature and oxygen partial pressure. The optimum temperature for maximizing C₂₊ selectivity varies between 720 and 800°C depending on the catalyst. Maximum C₂₊ selectivities were achieved at low oxygen and high methane partial pressures and amounted to 46% for CaO (T = 780°C; P_CH4 = 70 kPa; P_O2 = 5 kPa), 53% for Na₂CO₃/CaO (T = 760°C; P_CH4 = 60 kPa; P_O2 = 6 kPa) and 70% for PbO/γ-Al₂O₃ (T = 720°C; P_CH4 = 60 kPa; P_O2 = 5 kPa). Maximum yields were obtained at low methane-to-oxygen ratios; they amounted to 4.5% for CaO (T = 800°C; P_CH4 = 70 kPa; P_O2 = 12 kPa), 8.8% for Na₂CO₃/CaO (T = 820°C; P_CH4 = 60 kPa; P_O2 = 20 kPa) and 11.3% for PbO/γ-Al₂O₃ (T 2= 800°C; P_CH4 = 60 kPa; P_O2 = 20 kPa).     

Circulation of an object immersed in a bubbling fluidized bed

The motion of a large object in a bubbling fluidized bed was experimentally studied using digital image analysis (DIA). The experiments were performed in a 2-D bubbling fluidized bed with glass spheres as bed material. The object motion was measured using non-intrusive tracking techniques, while independent measurements of the dense phase velocity (using Particle Image Velocimetry (PIV)) and bubble velocity (using DIA) were carried out. The effect of the dimensionless gas velocity on the object motion was also analyzed.This work characterizes the circulation patterns of an object with a density similar to that of the bed, but much larger in size. Object size and density remained constant throughout the experiments. A comparison between the motion of sinking objects and the motion of the dense phase provided evidence of the feeble effect of buoyant forces on the motion of sinking objects. In contrast, the motion of rising objects is linked to the motion of bubbles. It was found that objects may be raised to the surface of the bed either by the action of a single bubble (one-jump) or by several passing bubbles (multiple-jumps). Based on these results, the circulation time of objects throughout the bed is a function of two parameters: the maximum depth attained by an object and the number of jumps during its rising path. This relationship is presented along and the multiple-jumps phenomenon is studied in detail. Finally, an estimate of the circulation time of an object based on semi-empirical expressions is presented for different dimensionless gas velocities. The probability density function of the circulation time shows two different modes as the object was less prone to be raised at moderate depths. The estimate of the circulation time was found to be in good agreement with our experimental data.