A new correlation for predicting solids concentration in the fully developed zone of circulating fluidized bed risers

The present work focuses on developing a new comprehensive correlation for better prediction of the solids concentration in the fully developed region of co-current upward gas-solid flow in circulating fluidized bed (CFB) risers. Systematic experiments were carried out in two risers (15.1 m and 10.5 m high with the same 0.1 m i.d.) with FCC and sand particles. The results obtained from about 200 sets of operating conditions show that the average solids concentration in the fully developed region is more than just a function of the corresponding terminal solids concentration, as most previous correlations are based on. Operating conditions, particle properties and riser diameters also have significant effects on the solids concentrations in the fully developed region of CFB risers. Based on our experimental data and those reported in the open literature from CFB risers up to 0.4 m in diameter and 27 m in height with superficial gas velocities and solids circulation rates up to 11.5 m/s and 685 kg/m²·s, a new empirical correlation for predicting the average solids concentrations in the fully developed region of CFB risers is proposed. The correlation works well for a wide range of operating conditions, particle properties and riser diameters.     

Estimating radial voidage profiles for all fluidization regimes in circulating fluidized bed risers

In terms of variation characteristics of radial voidage profiles, we had identified that all fluidization regimes from minimum fluidization to pneumatic transport prevailing in circulating fluidized bed (CFB) risers can be grossly divided into two distinctive variational regions, the dense phase continuous bubbling flow region and the dilute phase continuous clustering flow region, at a cross-sectionally averaged voidage of 0.75 [Powder Technol. 101 (1999) 91]. Succeeding that work, this article is devoted to further estimating the radial voidage profiles in two such distinctive variational regions by concerning the case of circular circulating fluidized bed risers. A new correlation was proposed for the dense phase continuous bubbling flow region, while the equation of Zhang et al. [Chem. Eng. Sci. 46 (1991) 3045] was considered applicable to the dilute phase continuous clustering flow region. Further improving the equation of Zhang et al. according to the result obtained in our last report ensured the continuity between the two correlations. In addition, the article also highlighted the formation mechanics of the two distinctive variational regions for radial voidage profiles in terms of the different gas/particle hydrodynamic behaviors in bubbling and clustering flows.     

Radial profiles of solids loading and flux in a gas–solid circulating fluidized bed

An electrical-impedance tomography (EIT) system has been developed to non-invasively measure radial voidage profiles in the riser of a pilot-scale circulating fluidized bed (CFB), yielding quantitative information that is validated by comparison to a gamma-densitometry tomography (GDT) system. EIT and GDT were applied to the CFB riser (14-cm inner diameter, 5.77-m height) containing fluid catalytic cracking particles in air. For all cases, the average and near-wall voidages from EIT and GDT agreed to within 0.03 and 0.07, respectively. This good agreement suggests that, where feasible, EIT can be used in place of GDT, which is advantageous since EIT systems are often safer, less expensive, and faster than GDT systems. The results also compared well to two correlations for radial voidage profile from the literature. Finally, a procedure for determining radial solids flux profiles from radial voidage profiles using an additional correlation [M.J. Rhodes, X.S. Wang, H. Cheng, T. Hirama, B.M. Gibbs, Similar profiles of solids flux in circulating fluidized-bed risers, Chemical Engineering Science 47 (1992) 1635–1643] was investigated. It was found that the accuracy of this correlation strongly depends on the voidage and/or solids flux measurement at the riser center.     

上行气固两相流充分发展段颗粒浓度关联及预测

在高度分别为15.1m和10.5m的两套实验装置上,对快速流态化到稀相气力输送流型下提升管内的轴向压力梯度进行了系统测试,以研究提升管充分发展段内不同颗粒的浓度变化及其与操作参数的关系。实验在其中175组操作条件下展现出明显的充分发展段(>2.8m)。结果表明,表观气速在3~8m?s-1之间变化时,对充分发展段颗粒浓度随终端颗粒浓度的变化关系影响显著,但当表观气速>8m?s?1或<3m?s?1时,其对充分发展段颗粒浓度随终端颗粒浓度线性增加的关系影响极弱;在此基础上提出的预测关联式更明确地反映了操作条件等因素对充分发展段颗粒浓度的定量影响关系,其计算结果与本实验和相关文献的实验数据吻合良好。     

A hydrodynamic model of a circulating fluidised bed with low‐density particles

In this study, a two‐dimensional mathematical model was developed considering the hydrodynamic behaviour of a circulating fluidised bed biomass gasifier (CFBBG), which is also applicable for other low‐density particles. In the modelling, the CFB riser was divided into two regions: a dense region at the bottom and a dilute region at the top of the riser. Kunii and Levenspiel's [Kunii and Levenspiel, Powder Technol. 61, 193‐206 (1990)] model was adopted to express the vertical solids distribution with some other assumptions. Radial distributions of bed voidage were taken into account in the upper zone by using Zhang et al.'s [Zhang et al., Chem. Eng. Sci. 46(12), 3045‐3052 (1991)] correlation. For model validation purposes, a cold model CFB was employed, in which sawdust was transported with air as the fluidising agent. The column is 10 m in height and 280 mm in diameter, and is equipped with pressure transducers to measure axial pressure profile and with a reflective optical fibre probe to measure local solids holdup. A satisfactory agreement between the model predictions and experimental data was found. © 2011 Canadian Society for Chemical Engineering     

A two-dimensional model for gas mixing in the upper dilute zone of a circulating fluidized bed

Based on measurements in a circulating fluidized test unit with a riser of 0.4 m i.d., a two-dimensional two-phase model for gas mixing has been developed. Radial gas dispersion and gas backmixing caused by dense clusters falling countercurrently to the main flow of a lean gas/solid suspension are considered. The model has successfully been compared with experimental data over a wide range of operating conditions. The model accounts for the main mixing phenomena and may be applied to calculations of chemical reactions in CFB risers.     

Effects of riser height and total solids inventory on the gas-solids in an ultra-tall CFB riser

More and more CFB boilers with large capacity and ultra-tall furnaces are used for power generation. Understanding the fluid dynamics in the ultra-tall furnace is important. However, existing studies on fluid dynamics in the CFB furnace are limited to the risers with rather short height. An experimental study was conducted with a cold CFB test rig of 240 mm in I.D. and 38 m and 54 m in height respectively. The influences of total solid inventory I_v, and fluidizing gas velocity U_g on the axial voidage profile along the riser and solid circulation rate G_s were investigated. Experimental results showed that when U_g exceeded the transport velocity, an S-shaped voidage profile characterized by fast fluidization was established in the riser. In such circumstance, the voidage at top dilute section kept constant and G_s reached saturation carrying capacity (G_s = G_s^?) and inappreciably change with riser height and I_v. Moreover, G_s^? increased from 40 kg to 50 kg when the riser height increased from 38 m to 54 m. The results indicated that even for the 600 MWe supercritical CFB boiler with a 54 m tall furnace, only a modest increase of I_v and power of forced draft fans is needed to obtain high enough G_s to meet the requirements of heating surfaces arrangement in furnace and the circulation loop. The necessary conditions to form the S-shaped profile of voidage in the riser were also discussed.     

NUMERICAL SIMULATION OF THE GAS-PARTICLE FLOW IN RISERS I: THE MACRO FLOW BEHAVIOR

The steady gas-particle flow in risers under variant operating conditions was predicted based on a k-ε-k_p-ε_p-Θ two-fluid model, which describes the dense turbulent gas-particle flow by the Eulerian method, considering the turbulence of both gas and particles as well as the particles' collisional effects. Much information on the macro flow behavior in risers, such as the profiles of local particle axial velocity, solids volume fraction, and solids mass flux in different operating regimes was obtained, and the predicted results show satisfactory agreement with experimental data. Further analysis of the predictions gives the comprehension of flow characteristics on the macro scale.     

Experimental study on solids concentration distribution in a two-dimensional circulating fluidized bed

The axial and lateral solids holdup profiles in a 2-D circulating fluidized bed (CFB) were measured with an optical fibre probe under a wide range of operating conditions. The CFB is 7.6 m in height and has a 19×114 mm² narrow cross-section riser. The results showed that the operating conditions influence the flow structure significantly and control the flow in the same manner as that in cylindrical risers. The solids had lower concentrations at the riser centre than the near wall region. Compared with data from cylindrical columns, the axial and lateral profiles of solids holdup in 2-D riser had a similar pattern in shape, but were more uniform. The geometry of the riser was found to be an important factor that affects the solids distribution due to differences in terms of the perimeter per unit cross-sectional area and the wall-to-centre distance. To some extent, the two-dimensional and three-dimensional risers are more comparable under fast fluidization conditions. Generally, the solids distributions along the axial and the lateral directions in 2-D riser were dissimilar to those in cylindrical risers, while the main differences have been discussed in the current study.     

60米高循环流化床内物料浓度分布的冷态试验

利用电厂循环流化床锅炉现有的结构和设备, 搭建提升管高度60m、内径400mm的超高循环流化床冷态实验台, 重点研究了流化风速和颗粒密度对提升管内轴向和径向空隙率分布的影响。实验结果表明:空隙率分布形式与流化风速和物料密度密切相关, 对于一定的床料高度, 在底部密相区一直有床料堆积的情况下, 随着流化风速的增加, 提升管底部密相区空隙率增大, 上部稀相区的空隙率减小并且其在径向的分布变得更加不均匀;在一定的流化风速下, 密度较小的物料将更多的被带入上部稀相区, 上部稀相区的空隙率减小, 其在径向分布将变得更加不均匀。     

Voidage profiles in magnetically fluidized beds

Voidage profiles in a fluidized bed of iron particles (230 μm) were investigated under the influence of an external uniform axial magnetic field. Passing a direct current through five solenoids generated uniform magnetic field. The five solenoids were arranged elaborately to get larger uniform magnetic space than that generated by Helmholtz electromagnet coils. A sensitive optical measuring system, based on detection of light reflected by particles, was used to measure local voidage in both dense and dilute phases.

Local voidage was measured as a function of superficial fluidizing air velocity, magnetic field intensity and the position in the bed. At a given magnetic field intensity and at the same position in the bed, the voidage was constant for a low air velocity range (in a fixed bed). The local voidage changed irregularly with increasing air velocity for an intermediate air velocity range (in a magnetically stabilized fluidized bed, MSFB). The local voidage changed linearly with increasing air velocity for a slightly high air velocity range (in a magnetized bubbling fluidized bed, MBFB). A general correlation was developed to predict the local solids fraction at the arbitrary position in the bed: (1−)=(1−)_c+[(1−)_w−(1−)_c](r/R)^B where (1−), (1−)_c and (1−)_w represent the local solids fraction at arbitrary position in the bed, at the bed center and on the bed wall; and B, (1−)_c and (1−)_w are the function of air velocity, distance from the distributor and magnetic field intensity.     

Mean and fluctuating gas phase velocities inside a circulating fluidized bed

Gas phase velocities is an area in circulating fluidized beds (CFB) that has traditionally received little attention. The dynamics and motion of particles or clusters inside the bed has been the main focus of research. This is because particles dominate the fluid mechanics and heat transfer inside a CFB. However, gas phase motions also effect particle motion. Gas eddies or fluctuations can play an important role in transporting particles to and from the wall. They also help in providing a uniform temperature throughout the bed by promoting mixing. This paper deals with how particles effect the mean and fluctuating gas velocities throughout the cross-section of a riser.Gas velocities were measured inside a cold scale model CFB using a shielded hot wire anemometer. At the centerline, typical mean gas velocities were measured which were approximately twice the superficial gas velocity. These high velocities are likely caused by the negligible net gas upflow in the annulus region. The presence of many dense, downward flowing clusters in the annulus makes this a reasonable assumption.Previous work on gas phase turbulence in two phase flows has typically used either laser measurement techniques in very small diameter risers or in larger risers with very low particle concentration. The general results have shown that smaller particles, on the same order of magnitude as those typically used in CFB and FCC reactors, tend to damp out the gas phase fluctuations. This implies that gas phase motion behaves close to a laminar fashion. This present research measures gas phase fluctuations with typical particle concentrations inside a CFB (∼1-5%). The results indicate that at larger particle concentrations where clusters are formed, the gas phase fluctuations increase dramatically. This suggests that length scales based on cluster size, as opposed to particle size, should be used in estimating the increased levels of gas fluctuations caused by the solid phase. Hence, models which ignore the effect of clusters on the gas or which treat the gas phase as laminar like flow, yield a misleading picture of the flow dynamics inside a CFB riser.     

New closure models for CFD modeling of high-density circulating fluidized beds

Experimental results from a high-density circulating fluidized bed (CFB) riser have been used to develop new closure models for the drag coefficient and the gas-solid mixture viscosity. The models predict a rapid increase in both viscosity and drag associated with the high solids concentrations near the riser wall. These new models have been incorporated into the commercial Computational Fluid Dynamics software FLUENT and the predictions of FLUENT have been compared with experimental data from the literature. With the inclusion of the new closure models, FLUENT was able to predict the radial distribution of solids concentration and solids mass flux found experimentally in three different cold-flow CFB risers operated at solids mass fluxes between 148 kg/m²·s and 455 kg/m²·s and superficial gas velocities between 4.7 and 10 m/s. These conditions lead to average solid concentrations in excess of 10 vol%, which corresponds to high-density CFB operation.     

Voidage waves in hydraulic conveying through narrow pipes

The nature of voidage waves in hydraulic conveying systems has been investigated computationally in this study. Voidage waves consisting of alternating regions of high and low solid fractions were observed to form spontaneously in hydraulic conveying through vertical pipes. The wavelengths of these voidage waves were found to be inversely related to mean solid fraction but independent of liquid conveying velocities for elastic solid particles. The wave structure in terms of the thickness and shape of the solid fraction profile over each dense phase was dependent on the mean solid fraction used. Pressure distributions along the longitudinal direction of the conveying pipe exhibited an interesting ‘step’ profile due to unequal pressure drops across the dense and dilute regions. With inelastic solid particles, a lower tendency for voidage wave formation was observed and a phase diagram was constructed to show combinations of operating conditions under which voidage waves would form. Finally, the study of voidage waves in hydraulic conveying systems was extended to the case of hydraulic conveying through horizontal channels. In addition to the various system parameters, voidage wave formation in this case was also affected by gravitational settling of the solid particles.     

Analysis of Regime Transitions and Flow Instabilities in Vertical Conveying of Coarse Particles Using Different Solids Feeding Systems

The transition between dense and dilute flow in vertical conveying of Geldart D particles were investigated for risers of different diameters using a spouted bed as a solid feeding system. The transition and choking velocities were identified by combining analyses of pressure gradient versus air velocity diagrams, pressure fluctuation signals and voidage values. Experimental data were used to evaluate the effect of particle and riser diameters on the pressure gradient, mean mixture voidage, the regime transition and choking velocities. The transition velocity from dilute to dense phase could be identified, as well as the onset of the choking condition, which appeared as the air velocity was further reduced. Data obtained in the same experimental apparatus facility using a screw conveyor and a gravitational system as solid feeding devices have been used as a reference to be compared to those obtained using the spouted bed feeder.     

NUMERICAL SIMULATION OF THE GAS-PARTICLE FLOW IN RISERS I: THE MACRO FLOW BEHAVIOR

The steady gas-particle flow in risers under variant operating conditions was predicted based on a k-?-k_p-?_p-Θ two-fluid model, which describes the dense turbulent gas-particle flow by the Eulerian method, considering the turbulence of both gas and particles as well as the particles' collisional effects. Much information on the macro flow behavior in risers, such as the profiles of local particle axial velocity, solids volume fraction, and solids mass flux in different operating regimes was obtained, and the predicted results show satisfactory agreement with experimental data. Further analysis of the predictions gives the comprehension of flow characteristics on the macro scale.     

Predicting axial pressure profile of a CFB

The numerical simulation of CFBs is an important tool in the prediction of its flow behavior. Predicting the axial pressure profile is one of the major difficulties in modeling a CFB. A model using a Particle Based Approach (PBA) is developed to accurately predict the axial pressure profile in CFBs. The simulation model accounts for the axial and radial distribution of voidage and velocity of the gas and solid phases, and for the solids volume fraction and particle size distribution of the solid phase. The model results are compared with and validated against atmospheric cold CFB experimental literature data. Ranges of experimental data used in comparisons are as follows: bed diameter from 0.05 to 0.305 m, bed height between 5 and 15.45 m, mean particle diameter from 76 to 812 μm, particle density from 189 to 2600 kg/m³, solid circulation fluxes from 10.03 to 489 kg/m² s and gas superficial velocities from 2.71 to 10.68 m/s. The computational results agreed reasonably well with the experimental data. Moreover, both experimental data and model predictions show that the pressure drop profile is affected by the solid circulation flux and superficial velocity values in the riser. The pressure drop increases along the acceleration region as solid circulation flux increases and superficial velocity decreases.     

Chaotic characteristics of local voidage fluctuation in a circulating fluidized bed

Local voidage fluctuations have been measured by using an optical transmittance probe at various axial and radial positions in a circulating fluidized bed riser with a 0.1 m i. d. and 10 m height. The chaotic time series analysis of the local voidage fluctuations has been adopted to characterize the nonlinear dynamics of the circulating fluidized bed riser. The variations of the correlation dimension and the Kolmogorov entropy of the voidage fluctuation were found to depend on the local time-average voidage. The axial and radial distributions of the correlation dimension and the Kolmogorov entropy were strongly affected by the solids flow structures (e.g. core-annulus flow) in various operating conditions. The correlation dimension of local voidage fluctuations increases along the riser, except the position near the distributor. Both, the correlation dimension and the Kolmogorov entropy of local voidage fluctuations near the wall, were found to be smaller than those at the center of the riser, independent of the solids circulation rate and the axial position.