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.     

Dimension measurements of hydrodynamic attractors in circulating fluidized beds

Experimental measurements of the correlation dimension, Kolmogorov entropy, and Lyapunov exponent of circulating fluidized bed (CFB) chaotic attractors were obtained by recording differential pressure and γ-ray porosity time series along the height of a cold experimental CFB operating with 75 μm diameter fluid catalytic cracking (FCC) catalyst. The attractor dimension did not vary with respect to the type of measurement taken. Both differential pressure and localized γ-ray densitometry measurements showed the existence of a low order hydrodynamic attractor, whose dimension varied between 1.5 and 2.0 over the range of gas velocities and solids fluxes studied. Differential pressure measurements indicated that the attractor dimension decreased slightly in the lower section of the CFB and at higher solids fluxes. Localized radial γ-ray bed porosity measurements indicate that the attractor dimension did not significantly vary across the bed cross-section but did show a tendency to be slightly lower near the riser wall.     

EFFECTS OF SECONDARY AIR INJECTION ON GAS-SOLID FLOW BEHAVIOR IN CIRCULATING FLUIDIZED BEDS

Effects of secondary air injection on the hydrodynamics such as solid holdup and gas-solid flow behavior were investigated in a circulating fluidized bed. The gas velocity in the riser, the ratio of secondary air velocity to that of primary air, and the solid circulating rate were chosen as operating variables. Fluid cracking catalyst(FCC) with a density of 1840 kg/m³ and a mean diameter of 74 um was employed as the solid phase. The secondary air was fed to the riser radially or tangentially at the wall of the column. Pressure drop fluctuations in the riser were measured and analyzed by adopting the stochastic method to characterize the effects of secondary air injection on the gas-solid flow behavior in the bed.

It has been found that the injection of secondary air into the riser can increase the solid holdup in the riser considerably, and that the tangential injection of secondary air is more effective for the increasing the solid holdup than the radial injection. However, the gas-solid flow behavior has been found to become less persistent with the injection of secondary air; the resultant flow behavior is more complex when the air is injected tangentially than radially. The solid holdups in the primary as well as secondary zones of the riser have been well correlated in terms of not only operating variables but also fractal dimension of the pressure fluctuations.     

EFFECTS OF SECONDARY AIR INJECTION ON GAS-SOLID FLOW BEHAVIOR IN CIRCULATING FLUIDIZED BEDS

Effects of secondary air injection on the hydrodynamics such as solid holdup and gas-solid flow behavior were investigated in a circulating fluidized bed. The gas velocity in the riser, the ratio of secondary air velocity to that of primary air, and the solid circulating rate were chosen as operating variables. Fluid cracking catalyst(FCC) with a density of 1840 kg/m³ and a mean diameter of 74 um was employed as the solid phase. The secondary air was fed to the riser radially or tangentially at the wall of the column. Pressure drop fluctuations in the riser were measured and analyzed by adopting the stochastic method to characterize the effects of secondary air injection on the gas-solid flow behavior in the bed.

It has been found that the injection of secondary air into the riser can increase the solid holdup in the riser considerably, and that the tangential injection of secondary air is more effective for the increasing the solid holdup than the radial injection. However, the gas-solid flow behavior has been found to become less persistent with the injection of secondary air; the resultant flow behavior is more complex when the air is injected tangentially than radially. The solid holdups in the primary as well as secondary zones of the riser have been well correlated in terms of not only operating variables but also fractal dimension of the pressure fluctuations.     

Hydrodynamics and Flow Development in a 15.1 m Circulating Fluidized Bed Riser

Hydrodynamics and flow development are studied in a long riser circulating fluidized bed reactor (15.1 m). Optic fiber probes were used for the measurement of local solids distribution. Pressure drops were also measured with pressure transducers along the riser. The flow development in the riser center is almost instant with solids holdup remaining constant and low, and particle velocity remaining high along the riser. The particle flow is firstly developed from center, and then towards the wall. The riser height is an important factor for the design of circulating fluidized bed reactors. Increasing the solid circulating rate significantly slows down the flow development process, while increases in the superficial gas velocity accelerate it.     

Radial nonuniformity index (RNI) in fluidized beds and other multiphase flow systems

The radial nonuniformity index (RNI) is a new non‐dimensional index recently devised to quantify the extent of radial variations of flow parameters in fluidized beds and other multiphase flow systems. The index, defined as the ratio of the standard deviation of the given flow parameter in the radial direction to the maximum practically possible standard deviation of that particular parameter, is shown to be an excellent measure of the radial flow structure. This index allows the use of a single value to summarize the radial variation of a given flow parameter. The higher the value of the RNI the less uniform is the flow, and vice versa. Using this technique, radial distributions of local solids concentration and particle velocities from different circulating fluidized bed systems (gas‐solid and liquid‐solid, upflow and downflow) were examined. It has been found that the RNI can be confidently related to the flow conditions in the circulating fluidized beds, and more insight understanding has been achieved.     

Investigation on gas–solid flow regimes in a novel multistage fluidized bed

Gas–solid flow regime in a novel multistage circulating fluidized bed is investigated in this study. Pressure fluctuations are first sampled from gas–solid flow systems and then are analyzed through frequency and time–frequency domain methods including power spectrum and Hilbert–Huang transform. According to the flow characteristics obtained from pressure fluctuations, it is found that the gas–solid motions in the multistage circulating fluidized bed exhibit two dominant motion peaks in low and high frequencies. Moreover, gas-cluster motions become intensive for the multistage circulating fluidized bed in comparison with the fast bed. Unlike the traditional methods, the fuzzy C-means clustering method is introduced to objectively identify flow regime in the multistage circulating fluidized bed on the basis of the flow characteristics extracted from bubbling, turbulent, fast, and multistage fluidized beds. The identification accuracy of fuzzy C-means clustering method is first verified. The identification results show that the flow regime in the multistage circulating fluidized bed is in the scope of fast flow regime under examined conditions. Moreover, the results indicate that the consistency of flow regime between two enlarged sections exists. In addition, the transition onset of fast flow regime in the multistage circulating fluidized bed is higher than that in the fast bed.     

Detection of singularities in the pressure fluctuations of circulating fluidized beds based on wavelet modulus maximum method

Pressure fluctuations are often selected to analyze the dynamic changes in the gas-solid fluidized bed. In this study, the wavelet modulus maximum method is applied to analyze the pressure fluctuations in a circulating fluidized bed. Continuous wavelet transform is put on the pressure signals, then, maxima lines are extracted and the Lipschitz exponent, α, of every maximum line is calculated using the non-linear least-squares method. The mean of the negative α is adopted to describe the hydrodynamic characteristics in the circulating fluidized bed. The value of the mean of the negative α increases with the superficial gas velocity and turns stable when the flow regime is fast fluidization. This method has been tested effective under various operation conditions.     

An analysis of pressure drop fluctuation in a circulating fluidized bed

The characteristics of pressure drop fluctuation in a 5.0 cm I.D.×250cm high circulating fluidized bed with fine polymer particles of PE and PVC were investigated. The measurements of time series of the pressure drop were carried out along the three different axial locations. To determine the effects of coarse particles and relative humidity of air on the flow behavior of polymer powders-air suspension in the riser, we employed deterministic chaos analysis of the Hurst exponent, correlation dimension and phase space trajectories as well as classical methods such as standard deviation, probability density function of pressure drop fluctuation. From a statistical and chaos analysis of pressure fluctuations, the upper dilute region was found to be much more homogenous flow compared to that in the bottom dense region at the same operating conditions. It was also found that the addition of coarse particles and higher humidity of air reduced the pressure fluctuations, thus enhancing flow stability in the riser. The analysis of pressure fluctuations by statistical and chaos theory gave qualitative and the quantitative information of flow behavior in the circulating fluidized bed.     

Phase holdup and liquid dispersion in gas-liquid-solid circulating fluidized beds

Axial and radial profiles of gas and solids holdups have been studied in agas-liquid-solid circulating fluidized bed at 140mm i.d..Experimental results indicate that the axialand radial profiles of gas and solids holdups are more uniform than those in a conventionalfluidized bed.Axial and radial liquid dispersion coefficients in the gas-liquid-solid circulating fluidizedbed are investigated for the first time.It is found that axial and radial liquid dispersioncoefficients increases with increaes in gas velocity and solids holdup.The liquid velocity has littleinfluence on the axial liquid dispersion coefficient,but would adversely affect the redial liquiddispersion coefficient.It can be concluded that the gas-liquid-solid circulating fluidized bed hasadvantages such as better interphase contact and lower liquid dispersion along the axial directionover the expanded bed.     

Annular wall layer thickness in circulating fluidized bed risers

The thickness of downward-flowing annular wall layers in circulating fluidized bed risers has been determined in the literature based on measured radial profiles of both local particle velocity and solids flux. The thickness of the wall layer is shown to be larger based on solids flux profiles than when based on particle velocity profiles, because fluctuations in local instantaneous particle velocity are correlated with fluctuations in local solids concentration. A new correlation is developed to predict the time-average thickness of the downflowing particle streamer layer based on solids flux measurements as a function of the cross-sectional average voidage. It successfully accounts for the variation of the wall layer thickness with axial location and solids circulation rate.     

A critical review of the complex pressure fluctuation phenomenon in gas-solids fluidized beds

The complex pressure fluctuation phenomenon in gas-solid fluidized beds is systematically examined in this paper based on a comprehensive review of the literature data. The local pressure fluctuations are composed of multiple sources, including local bubble induced fluctuations, global bed oscillations and propagating pressure waves originating in other locations (e.g. bed surface, distributor and windbox). The interaction and coupling among bubble motion, under-damped oscillations of fluidized particles and bed surface, propagating compressible pressure waves and flow pulsation in gas-solid fluidized beds creates the complexity of local pressure fluctuations, and is likely responsible for the formation of complex but unique flow patterns. A few attempts have been reported in the literature on examining the interaction between bed oscillations, plenum chamber air pulsation and propagating pressure waves in fluidized beds, showing some promises on predicting the local pressure fluctuations. Future work should be focused on predicting local and global pressure fluctuations and the formation of unique surface flow patterns by coupling different contributing mechanisms.     

低密度循环流化床局部颗粒速度的轴径向分布的研究

在高8m,内径186mm的循环流化床中,利用光纤激光多普勒测速仪测量了FCC颗粒的局部速度沿轴径向的分布。实验结果表明:局部颗粒速度沿径向分布是不均匀的,床中心区域分布比较平坦,近壁环形区域分布较陡,颗粒沿轴向运动有较长的加速段。由实验数据回归得到预测低密度循环流化床局部颗粒速度的经验关联式。     

Circulating fluidized bed hydrodynamics with air staging: an experimental study

The influence of secondary air injection (SA) on the hydrodynamics of circulating fluidized beds was studied in a 0.23-m ID riser. The secondary to primary air ratio, the vertical position, and the mode of injection (radial, tangential, and 45° entrance) are considered to be the key parameters of SA injection. It was found that the amount and location of SA have direct influence on the solids holdup and the segregation patterns in the riser. The SA divided the riser into two different flow zones: a dense turbulent zone below and a relatively dilute bed above the injection port. The mean solids velocity is found to be upwards with a greater magnitude in the center region. It is downwards with a smaller magnitude along the walls, suggesting core-annular flow structures for both above and below the SA injection region.     

Experimental study of the effect of internals on optimizing gas-solid flow in a circulating fluidized bed

The solids concentration in a circulating fluidized bed of flue gas desulfurization (CFB-FGD) is low, and the gas-solid mixing needs to be strengthened to improve the reaction efficiency. The addition of internals in a square CFB-FGD is studied here. Different sizes of wedge-shaped internals were set in the middle of the riser on opposite sides of the bed, at same height or at different heights. By comparing the concentration distributions, we found that positioning the internals at different heights is more effective in increasing the density of the center region. By observing the radial distribution of the fractal dimension, we found that a strong degree of turbulence can improve the gas-solid mixing. A larger upper/smaller lower arrangement of the internals with a moderate apparent gas velocity provided the best flow field, with increased concentration gradients and improved gas-solid mixing.     

High-velocity fluidization of solid particles in a liquid-solid circulating fluidized bed system

Particulate and aggregative fluidizations in a liquid-solid circulating fluidized bed system are characterized by chaotic time series analysis of local voidage and heat transfer fluctuations in terms of the correlation dimension and Kolmogorov entropy. Both correlation dimension and Komogorov entropy of the voidate fluctuation are found to decrease with decreasing bed voidage in both fluidization regimes, suggesting the suppression of chaotic motion of individual particles due to high solid concentration. The correlation dimension of the heat transfer fluctation in the aggregative fluidization regime is higher than that in the particulate fluidization regime. This reflects the complex convective motion of liquid and solid phases induced by the formation of the liquid streaks and aggregates of particles.     

液固两相外循环流化床压力波动信号的统计及频谱分析

压力波动信号是表征流化床内流体运动特性的重要信息. 为了更好地了解液固外循环流化床内流体流动特征,在液固外循环流化床中,对床体壁面压力波动信号进行了时域、频域及自相关性分析. 结果表明,沿床体稳定流化段上的压力波动特征相似,流体流动和颗粒运动所引发的压力波动能量频带分别集中在0~10和30~40 Hz之间,压力波动的概率密度近似呈正态分布,液固两相外循环流化床中的压力波动信号介于周期信号和随机信号之间.     

Investigation of the Dynamics of a High‐Flux CFB Riser Using Chaos Analysis of Pressure Fluctuations

The dynamics of a high‐flux circulating fluidized bed riser (10 m high with i.d. of 76.2 mm) were studied using a chaos analysis technique with differential pressure signals sampled at 400 Hz. Spent FCC particles (d_p = 67 μm) were used as the solid phase. The solids flux ranged between 50–400 kg/m² s while the gas velocity was varied between 4.0–10.0 m/s. Using the measured signals, the complexity and predictability of the gas‐solids flow were characterized using correlation dimension and Kolmogorov entropy. The axial profiles of the dimension and entropy revealed a more complex and less predictable gas‐solids flow in the transition section of the riser. Both dimension and entropy decreased with increasing solids holdup and solids flux. Moreover, the correlation dimension increased exponentially with decreasing average absolute deviation (AAD), at a power of 0.3. On the other hand, the entropy was observed to decrease exponentially with increasing average cycle time (ACT) of the pressure fluctuations at a characteristic power ranging between 0.95 and 1.10. Also, a comparison was made between low‐ and high‐flux conditions based on the dynamic properties of the riser.     

Hydrodynamics of gas fluidized beds with mixture of group D and B particles

The dynamics of a gas‐solid fluidized bed containing Geldart Group D particles mixed with a small proportion of Geldart Group B particles are investigated using pressure fluctuations data. Time series analysis, using a variety of nonlinear dynamics tools, shows that the slugging present with Group D particles can be suppressed by the addition of a small proportion of Group B particles. The power spectra and the auto‐correlation function are used for a preliminary evaluation of dominant slug frequencies. It is shown that the bed fluidized with the mixture of Group D and B particles behaves in a less periodic manner and is dominated by more random bubble motion. On the other hand, the correlation integral is used to analyze the chaotic behaviour of the flow, through evaluation of the fractal structure of the reconstructed attractors. It is shown that the bed fluidized with Group D particles is characterized by a combination of steady slug motion and irregular particles motion. The behaviour of the fluidized bed of Group D/B particles mixture is characterized by a single correlation dimension for a wide range of fluidization velocities.     

Radial Particle Profiles in a Liquid‐Solid CFB with Varying Viscosity

Flow structure was characterized in a 76 mm diameter by 2.0 m high liquid‐solid circulating fluidized bed (LSCFB) with different viscous liquids ranging from 1.0 mPa·s to 4.8 mPa·s. Measurements of mean and local solids holdup were carried out in the axial and the radial direction, respectively. The results showed that a uniform axial and a nonuniform radial distribution of the time‐averaged solids holdup appeared in the LSCFB. The viscosity of the liquid phase reduces the nonuniform distribution of solid particles in the radial direction. By examining the instantaneous data signals, flow behavior in a viscous system was found to be more uniform and less vigorous. To further understand the hydrodynamics in a LSCFB, Hurst's rescaled range (R/S) analysis was also adopted to analyze its stochastic characteristics and the local flow properties.