Comparison of decoupling methods for analyzing pressure fluctuations in gas‐fluidized beds

Two methods of decoupling pressure fluctuations in fluidized beds by using the incoherent part (IOP) of absolute pressure (AP) and differential pressure (DP) fluctuations are evaluated in this study. Analysis is conducted first to demonstrate their similarities, differences, and drawbacks. Then, amplitudes, power spectral densities, mean frequencies, coherence functions, and filtering indices of the IOP of AP and DP fluctuations are calculated and compared based on experimental data from a two‐dimensional fluidized column of FCC particles. Derived bubble sizes are also compared with the sizes of bubbles viewed in the two‐dimensional bed. The results demonstrate the similarity of these two methods in filtering out global compression wave components from absolute pressure fluctuations, especially those generated from oscillations of fluidized particles and gas flow rate fluctuations. However, both methods are imperfect. Neither can filter out all the compression wave components and retain all the useful bubble‐related wave components. Their amplitudes can be used to characterize global bubble property and quality of gas–solids contacting in bed, but they do not give accurate measurement of bubble sizes. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

气固流化床外取热器内流动和换热特性分析

外取热器是维持催化裂化反应-再生系统热平衡和保持装置平稳运行的关键设备之一。外取热器的优化设计和合理调控，要求深入理解外取热器内的流动特性、换热特性及两者之间关系。在一套大型冷模热态实验装置上，分别考察了表观气速、颗粒质量流率对换热管附近的局部固含率和气泡频率、床层与换热管间传热系数的影响。结果表明：增加表观气速可以降低局部固含率、增加局部气泡频率、强化床层与换热管间换热；随着颗粒质量流率增加，局部固含率和局部气泡频率均增加；在较低表观气速下，增加颗粒质量流率不利于换热，而在较高表观气速下，传热系数随颗粒质量流率逐渐增加。不同流型下，气固流动特性对换热特性的影响不同。在鼓泡床流型下，过高的局部固含率不利于颗粒在换热表面的更新，增加换热管附近的局部气泡频率可以明显强化换热；而在湍流床流型下，换热管附近的局部固含率和气泡频率的增加，均使传热系数逐渐增大。建立了针对不同流型的换热经验关联式，预测值与实验值的平均相对偏差分别为6.9%和1.3%。     

Extension of the kinetic theory of granular flow to include dense quasi-static stresses

Fluidized bed technology has diverse industrial applications ranging from the gasification of coal in the power industry to chemical reactions for the plastic industry. Due to their complex chaotic non-linear behaviour understanding the hydrodynamic behaviour in fluidized beds is often limited to pressure drop measurements and a mass balance of the system. Computational fluid dynamics has the capability to model multiphase flows and can assist in understanding gas-solid fluidized beds by modeling their hydrodynamics. The multiphase Eulerian-Eulerian gas-solid model, extended and validated here improves on the kinetic theory of granular flow by including a closure term for the quasi-static stress associated with the long term particle contact at high solid concentrations. Similar quasi-static models have been widely applied to slow granular flow such as chute flow, flow down an incline plane and geophysical flow. However combining the kinetic theory of granular flow and the quasi-static stress model for the application of fluidized beds is limited. The objective of the present paper is to compare two quasi-static stress models to the experimental fluidized bed data of Bouillard et al. [4]. A quasi-static granular flow model (QSGF) initially developed by Gray and Stiles [18] is compared to the commonly used Srivastava and Sundaresan [37]. Both models show good agreement with the experimental bubble diameter and averaged porosity profiles. However only the QSGF model shows a distinct asymmetry in the bubble shape which was documented by Bouillard et al. [4].     

Characterization of gas-solid fluidization: A comparative study of acoustic and pressure signals

The hydrodynamics of fluidized beds strongly influence their operation, but are complicated and chaotic. There are many measurement techniques, but none fully characterizes gas-solid fluidized beds. Acoustic signals from fluidized beds cover a wide frequency spectrum and can be correlated to bed characteristics. Experiments were conducted to study the acoustic signals from ultrasonic transducers mounted on the outer wall of a two-dimensional fluidization column. The acoustic signals were related to bubble behavior in 550 μm glass beads. Simultaneous acoustic and pressure measurements allowed direct comparison of these signals for single bubbles, pairs and chains of bubbles. The envelope of acoustic signals, generated by particle collisions and particle-wall impacts, provided information on the behavior of bubbles. Significant peaks appeared as the top portions of the bubble wakes approached the acoustic sensor. Pressure waves propagated considerably in the horizontal direction, whereas acoustic signals propagated little in the lateral direction, but transmitted forward in the wall in the direction of bubble motion, maintaining the wave profile invariant during transmission. The strong lateral localization of acoustic signals is promising for determining the lateral bubble position in the bed. Acoustic signals provide a potential means of determining such bubble properties as velocity, frequency and volume, with some advantages relative to pressure signals.     

采用切圆射流及旋流布风板改进鼓泡床行为

用侧面切圆射流和旋流布风板造成了鼓泡流化床内气固流动的新流型。本文将改进鼓泡床与普通鼓泡床进行比较,在同样的空气量下,气泡尺寸减小,床面波动降低,加强了固体颗粒的横向混合,延长了颗粒床内停留时间。还研究了侧面切圆射流占总风量的份额、射流速度、喷入位置及角度对流化质量的影响。     

Pulsed fluidization—a DEM study of a fascinating phenomenon

An investigation of pulsed fluidization by discrete element method simulation is presented. The particles used were 0.5 mm in diameter and 2650 kg/m³ in density. The pulsed gas flow consisted of a fluctuating component superimposed on a constant component. The effect of gas pulsation was assessed through examination of bed pressure drop and bubble patterns for a wide range of conditions. The influence on fluidized bed behaviour of frequency and amplitude of pulsation, superficial gas velocity of the base flow, and the nature (type) of pulsation was studied. Transition from chaos to ordered behaviour and formation of regular bubble patterns were reproduced. It was found that regular bubble patterns arise from periodical formation of horizontally aligned voids near the distributor plate.     

Effect of cohesive powders on pressure fluctuation characteristics of a binary gas-solid fluidized bed

The effect of cohesive particles on the pressure fluctuations was experimentally investigated in a binary gas-solid fluidized bed. The pressure fluctuation signals were measured by differential pressure sensors under conditions of various weight percentages of cohesive particles. The cohesive particles increased the fixed bed pressure drop per unit height and decreased the minimum fluidization velocity. The Wen & Yu equation well predicts the minimum fluidization velocity of the binary system. The addition of cohesive particles slightly decreased the bubble size in bubbling flow regime when the cohesive particles and the coarse particles mixed well, while the bubble size greatly decreased when the cohesive particles agglomerated on the bed surface. The time series of pressure fluctuations was analyzed by using the methods of time domain, frequency domain and wavelet transformation. The normalized standard deviation of pressure fluctuations decreased with increasing weight percentages of cohesive particles. A wide bandwidth frequency of 0 to 1Hz got narrower with a single peak around 0.6Hz with an increase in proportion of the cohesive particles. The meso-energy and micro-energy of pressure fluctuations were decreasing with increasing cohesive particles proportions, which indicated that adding cohesive particles could reduce the energy dissipation of bubble and particle fluctuations.     

鼓泡流化床离散模拟中的一个局部空隙率模型

气固流化床离散颗粒模拟中通常采用面积加权平均法计算局部空隙率,不能较好地反映流化床中显著的非均匀结构特性.为了考虑非均匀结构对局部空隙率的影响,文中提出一个适用鼓泡流化床的局部空隙率模型.将流场划分为稀区(气泡区)和密区(乳相区);非均匀结构对密区局部空隙率的影响通过引入局部空隙率下限和非均匀影响系数描述;将提升管流动...     

Origin of pressure fluctuations in an internal-loop airlift reactor and its application in flow regime detection

The origin of pressure fluctuations in an internal-loop airlift reactor (ILALR) and its application in the flow transition detection are investigated. It is found that pressure fluctuations can be characterized as global pressure fluctuations and local pressure fluctuations by frequency domain analysis and wavelet analysis. The global pressure fluctuations generated by gas compression in the gas plenum and flow fluctuations in the gas-supply system have almost a linear attenuation in the downcomer and almost no attenuation in the riser, especially in heterogeneous flow regime. However, it is found that the pressure wave from bubble eruption at bed surface has little impact on the wall pressure fluctuations. The global pressure fluctuations may be explained by Sasic's model. The local bubble-induced pressure fluctuations generated by bubble passage, coalescence and breakage can be determined by bubble passage frequency bandwidth and lower coherence. After extracting the local bubble-induced pressure fluctuations from the origin wall pressure fluctuations, it is shown that the Hurst exponent of the local pressure fluctuations increases faster in the homogeneous flow regime than in the heterogeneous flow regime, which can be employed to indicate the flow regime transition.     

Hydrodynamics of Geldart group A particles in gas-solid fluidized beds

Geldart group A particles were fluidized in a 10 cm i.d.×1.8 m high Plexiglas-made bed with ambient air to determine the hydrodynamic properties in a gas-solid fluidized bed. The effects of static bed heights, position of pressure measuring points, differential and absolute pressure fluctuations on the hydrodynamic behavior of a Geldart group A particles in a gas-solid fluidized bed were investigated. The particles used in this study were 80 micrometer FCC powders and 60 micrometer glass beads. The variance of pressure fluctuations was used to find the minimum bubbling velocity. The obtained minimum bubbling velocity was compared with the other methods available in the literature. This method was found to be much easier and had better data reproducibility than the classical visual method or sedimentation method. The variance of pressure fluctuations increased due to the increase of superficial gas velocity and static bed height. The obtained minimum bubbling velocity and pressure fluctuations were found to depend on the measuring position along the axial direction. The effect of measuring position was discussed. Cross-correlation of two pressure signals was used to find the delay time, then the bubble rising velocity.     

Hydrodynamics of gas-solid flow around immersed tubes in bubbling fluidized beds

A numerical study was conducted based on the gas-solid two-fluid model using the body-fitted coordinate system to analyze the behavior of particles and bubbles flow in bubbling fluidized beds without and with immersed tubes. The kinetic theory of granular flow was implemented in the model. The images of simulated instantaneous particle concentration and velocity gave the process of the formation, coalescence and eruption of bubbles. The effects of the tube pitch and superficial gas velocity on the fluidization in a bubbling fluidized bed were investigated. Calculated bubble frequencies without and with immersed tubes were in agreement with previous experimental and simulation findings. The wavelet multi-resolution analysis was used to analyze the simulated data of instantaneous particle concentration. From the random-like particle concentration fluctuations, the fluctuating components due to particle flow and bubble motion can be extracted based on the wavelet multi-resolution analysis over a time-frequency plane.     

电容层析成像在气固流化床测量中的应用

气固流化床广泛应用于化工、炼油、冶金、电力等工业生产领域。由于流化床中气固两相流动的复杂性,流化床测量方法的研究成为了一个重要的研究领域。电容层析成像（ECT）是20世纪80年代以来发展起来的一种非介入式多相流测量技术,已经在多相流测量领域发挥了重要作用。总结了国内外近年来应用ECT技术进行气固流化床测量的进展,特别是对气固流化床内固体相浓度、流化床流型识别、固体相速度等方面工作进行了总结,并简单介绍了ECT在流化床干燥中的应用,讨论了ECT和其他测量方法结合使用情况。最后对ECT在流化床测量中的局限性和发展方向进行了讨论。     

Experimental validation of CFD models for fluidized beds: Influence of particle stress models, gas phase compressibility and air inflow models

This work compares numerical simulations of fluid dynamics in fluidized beds using different closure models and air feed system models. The numerical results are compared to experiments by means of power spectral density distributions of fluctuating pressure signals and bubble statistics obtained from capacitance probe measurements. Two different particle rheology models are tested in combination with two different values of the maximum particle volume fraction. The first particle model predicts the particle pressure by an exponential power law and assumes a constant particle viscosity (CPV), and the second model predicts the stresses using the kinetic theory of granular flow (KTGF). Furthermore, two model approaches for the air inflow are evaluated. The first inflow model includes the coupling between the air-feed system and the fluidized bed in the simulation, and the second model assumes a constant mass flow of gas into the fluidized bed. Finally, the influence of the compressibility of the gas phase on the numerical predictions is investigated. The numerical simulations are made using the CFX-4.4 commercial flow solver.The simulations show that the KTGF model gives a more evenly distributed bubble flow profile over the bed cross-section, while the CPV model gives a more parabolic bubble flow profile, with a higher bubble flow in the central part of the bed. This work shows that the KTGF model results are in significantly better agreement with the experiments. It is furthermore shown that the modelling of the air-feed system is crucial to for predicting the overall bed dynamic behaviour.     

Forced bed mass oscillations in gas–solid fluidized beds

A second-order mechanical vibration model is proposed to explain the oscillation phenomena and pressure fluctuations in gas–solid fluidized beds. Experiments were conducted in a 0.1-m ID gas–solid fluidized bed driven by periodic gas pulses with the frequency varying from 0.2 to 10 Hz. Experimental results indicate that the proposed mechanical vibration model, which considers the pressure fluctuation as the results of the response of the fluidized bed to the external excitation forces related to the bubble behavior in the bed, can reasonably explain the pressure fluctuations of the gas–solid fluidized bed. The behavior of pressure fluctuations is correlated with characteristics of both the bed system and excitation forces.     

Study of pressure fluctuations in an internal loop airlift bioreactor

The origin and coupling of pressure fluctuations in an internal loop airlift bioreactor are investigated. The pressure fluctuations in the reactor are divided into two categories: global pressure fluctuations and local pressure fluctuations. It is found that the coupling between global pressure fluctuations and local pressure fluctuations mainly focuses in the frequency region between 10 and 30 Hz. Local pressure fluctuations in the reactor are strongly affected by pressure waves originating from the air‐supply system, while pressure fluctuations caused by the bubble eruption at the liquid surface have less influence on local pressure fluctuations. Based on the coherence analysis, the pressure signal at a certain position in the reactor is decomposed into three different parts: coherent part, joint incoherent part and exclusive incoherent part. The energy ratios of these different parts are helpful to study the interaction among pressure fluctuations from different sources. Three flow regimes were identified from the evolution of the energy ratio of the joint incoherent part. © 2011 Canadian Society for Chemical Engineering     

Oscillations in gas-fluidized beds: Ultra-fast magnetic resonance imaging and pressure sensor measurements

Ultra-fast Magnetic Resonance Imaging (MRI) and pressure sensor measurements have been applied to study: (i) pressure fluctuations, (ii) the eruption of bubbles at the top of a bed and (iii) the formation of bubbles in a gas-fluidized bed. Ultra-fast MRI has been applied for the first time to study the formation and eruption of bubbles; the technique is non-intrusive and provides measurements with good temporal and spatial resolutions. The MRI measurements revealed that bubbles are formed periodically, rather than randomly at a distributor, which in this case was a perforated plate. The frequency at which bubbles erupted from the top of the bed matched the frequency of the pressure fluctuations measured just above the distributor, where the measured pressure is predicted very well for the case of slug flow by Kehoe and Davidson's [P.W.K. Kehoe, J.F. Davidson, Pressure fluctuations in slugging fluidized beds, AIChE Symp. Ser. 128 (69) (1973) 34-40] correlation, originally developed for locations high up a bed. Both findings lead to the conclusion that the passage and eruption of bubbles at the top of a bed are the dominant cause of the pressure fluctuations, which are subsequently propagated downwards through the bed. Two new correlations are proposed for predicting the frequency of pressure fluctuations in a bubbling bed; both correlations agree well with experimental measurements. A modification of Baeyens and Geldart's [J. Baeyens, D. Geldart, An investigation into slugging fluidized beds, Chem. Eng. Sci. 29 (1974) 255-265] correlation predicts the frequency of pressure fluctuations when slugs are formed, but are not fully developed. The frequency of bubble formation, as measured by MRI, is equal to or higher than both the frequency of bubble eruption at the top of the bed and the frequency of pressure fluctuations, depending on the depth of the bed. The frequency of bubble formation is significantly lower than predicted by Davidson and Schüler's [J.F. Davidson, B.O.G. Schüler, Bubble formation at an orifice in an inviscid liquid, Trans. Inst. Chem. Eng. 38 (1960) 335-342] equation, originally developed for gas-liquid systems.     

Numerical investigation of gas-solid heat transfer in rotating fluidized beds in a static geometry

Gas-solid heat transfer in rotating fluidized beds in a static geometry is theoretically and numerically investigated. Computational fluid dynamics (CFD) simulations of the particle bed temperature response to a step change in the fluidization gas temperature are presented to illustrate the gas-solid heat transfer characteristics. A comparison with conventional fluidized beds is made. Rotating fluidized beds in a static geometry can operate at centrifugal forces multiple times gravity, allowing increased gas-solid slip velocities and resulting gas-solid heat transfer coefficients. The high ratio of the cylindrically shaped particle bed “width” to “height” allows a further increase of the specific fluidization gas flow rates. The higher specific fluidization gas flow rates and increased gas-solid slip velocities drastically increase the rate of gas-solid heat transfer in rotating fluidized beds in a static geometry. Furthermore, both the centrifugal force and the counteracting radial gas-solid drag force being influenced by the fluidization gas flow rate in a similar way, rotating fluidized beds in a static geometry offer extreme flexibility with respect to the fluidization gas flow rate and the related cooling or heating. Finally, the uniformity of the particle bed temperature is improved by the tangential fluidization and resulting rotational motion of the particle bed.     

近似熵的性质及其在气固流化床复杂性研究中的应用

介绍了一种新的度量序列复杂性的统计方法——近似熵(ApEn),并将其应用于气固流化床流型识别中。通过分析和研究不同操作条件下气固流化床压力脉动时间序列,证明了近似熵与气泡行为有着良好的对应关系,能够较好反映床内复杂性的变化,可以作为有效辨识气固流化床起始鼓泡态、充分鼓泡态和湍动流化态等流型的特征参数。实验数据的计算和分析也表明了近似熵随数据长度的变化小,只需要较短的时间序列就能得到较为稳定的ApEn值;受数据中的瞬态噪声影响小,抗干扰能力强。是一种适合数据变化快、干扰大的工业现场测量的复杂性参数。     

摇摆流化床的气固流动特性

采用二维床及D类玻璃珠颗粒,在表观气速U_g=0.267~0.978 m/s、摇摆幅值Θ=5°~15°、摇摆周期T=8~20 s的实验条件下,对摇摆流化床内气固流动过程及气体通过流化床的时均总压降进行了研究,并通过与常规直立床和倾斜床进行对比,分析了床体摇摆对气固流动的影响。结果表明,在平均角速度ω_ave>2(°)/s的条件下,当初始装料量和表观气速相同时,气体通过摇摆流化床的时均总压降低于直立床,高于相同最大倾角时的倾斜床;惯性力所产生的压降在0.15 kPa以下,其对床层压降的影响较小,床体倾斜导致气体向边壁区域聚集是影响摇摆流化床内气固流动特性的主要因素,由此导致床内存在固定床和下行移动床状态的非流化区域,使得处于流化区域的颗粒量减少,同时还降低了流化床层在竖直方向的静压。非流化区域的存在还会造成流化区域的气速高于直立床表观气速,两者表观气速之比为1.04~1.49。