Multi-scale analysis of flow structures in fluidized beds with immersed tubes

Multi-scale analysis and non-linear analysis were combined to investigate the hydrodynamics of fluidized beds with and without horizontal tubes. Pressure fluctuations were measured and analyzed employing discrete wavelet analysis, recurrence plot analysis, and recurrence quantification analysis. A systematic procedure was followed to determine wavelet parameters. At low gas velocities, the energy of macro-structures reduces with the addition of the first tube and then increases with the addition of a second tube. However, there is no notable difference at high gas velocities. Determinism is high for the bed without tubes, which can be attributed to the periodic behavior of bubbles. Determinism decreases with the addition of tubes because the breakage of bubbles results in less periodic behavior. The three methods of analysis used in this study captured the effects of immersed tubes on the hydrodynamics of fluidized beds. Recurrence quantitative analysis was found to be a powerful and easy-to-use method that can capture the nonlinear characteristics of fluidized beds much more quickly than conventional methods of nonlinear analysis. This method can thus be effectively used for the online monitoring of hydrodynamic changes in fluidized beds.     

Influence of vertical internals on a bubbling fluidized bed characterized by X-ray tomography

An ultra-fast X-ray tomographic scanner is applied to study the hydrodynamics in a bubbling fluidized bed with and without vertical internals (e.g., heat exchanger tubes). The objective of this study is to understand the influence of vertical internals on hydrodynamic properties such as bubble volume, size and velocity and to provide measurement data for the design and scale-up of catalytic bubbling fluidized bed reactors with vertical internals. With these new measurements, correlations of bubble properties can be developed to reliably scale-up bubbling fluidized beds with vertical internals. For the investigated reactor with Geldart A/B particles, no relation between bubble size and velocity was observed for individual bubbles, i.e.; smaller bubbles tend to rise with higher velocities. A significant reduction in bubble size and sharpening of the bubble size distribution was generally obtained for a bed with vertical internals.     

Bubbling behavior of cohesive particles in a two-dimensional fluidized bed with immersed tubes

Fluidization hydrodynamics are greatly influenced by inter-particle cohesive forces. This paper studies the fluidization of large cohesive particles in a two-dimensional fluidized bed with immersed tubes using “polymer coating” to introduce cohesive force, to gain better understanding of bubbling behavior when particles become cohesive and its effect on chemical processes. The results show that the cohesive force promotes bubble splitting in the tube bank region, thereby causing an increase in the number and a decline in the aspect ratio of the bubbles. As the cohesive force increases within a low level, the bubble number increases and the bubble diameter decreases, while the aspect ratio exhibits different trends at different fluidization gas velocities. The difference in the evolution of bubble size under various cohesive forces mainly takes place in the region without tubes. When the cohesive force is large enough to generate stable agglomerates on the side walls of the bed, the bubble number and the bed expansion sharply decrease. The tubes serve as a framework that promotes the agglomeration, thus accelerating defluidization. Finally, the bubble profile around tubes was studied and found to greatly depend both on the cohesive forces and the location of tubes.     

Determination of hydrodynamic behavior of gas–solid fluidized beds using statistical analysis of acoustic emissions

In the processes involving the movement of solid particles, acoustic emissions are caused by particle friction, collision and fluid turbulence. Particle behavior can therefore be monitored and characterized by assessing the acoustic emission signals. Herein, extensive measurements were carried out by microphone at different superficial gas velocities with different particle sizes. Acoustic emission signals were processed using statistical analysis from which the minimum fluidization velocity was determined from the variation of standard deviation, skewness and kurtosis of acoustic emission signals against superficial gas velocity. Initial minimum fluidization velocity, corresponding to onset of fluidization of finer particles in the solids mixture, at which isolated bubbles occur, was also detected by this method. It was shown that the acoustic emission measurement is highly feasible as a practical method for monitoring the hydrodynamics of gas–solid fluidized beds.     

Characterization of various structures in gas-solid fluidized beds by recurrence quantification analysis

Gas-solid fluidized beds are widely considered as nonlinear and chaotic dynamic systems. Pressure fluc- tuations were measured in a fluidized bed of 0.15 m in diameter and were analyzed using multiple approaches： discrete Fourier transform （DFT）, discrete wavelet transform （DWT）, and nonlinear recur- rence quantification analysis （RQA）. Three different methods proposed that the complex dynamics of a fluidized bed system can be presented as macro, meso and micro structures. It was found from DFT and DWT that a minimum in wide band energy with an increase in the velocity corresponds to the transition between macro structures and finer structures of the fluidization system. Corresponding transition veloc- ity occurs at gas velocities of 0.3, 0.5 and 0.6 m]s for sands with mean diameters of 150, 280 and 490/~m, respectively. DFT, DWT, and RQA could determine frequency range of0-3.125 Hz for macro, 3. ! 25-50 Hz for meso, and 50-200 Hz for micro structures. The RQA showed that the micro structures have the least periodicity and consequently their determinism and laminarity are the lowest. The results show that a combination of DFT, DWT, and RQA can be used as an effective approach to characterize multi-scale flow behavior in gas-solid fluidized beds.     

Characterization of gas–solid fluidized bed hydrodynamics by vibration signature analysis

Vibration measurement, as a non-intrusive technique, was used to characterize the hydrodynamics of fluidized beds. A series of experiments were performed in a lab-scale fluidized bed using two accelerometers for measuring the vibration of the bed and a pressure probe for measuring pressure fluctuations. The output signals were analyzed by statistical methods. The results show that the vibration technique can predict transition velocities at high velocities and indicate that analyzing the vibration signals can be an effective non-intrusive technique to characterize the hydrodynamics of fluidized beds. It was shown that transition from bubbling to turbulent velocity can be determined from the variation of standard deviation and kurtosis of vibration signals against superficial gas velocity of the bed. However, this point could be determined only from standard deviation of pressure fluctuations, and not from skewness or kurtosis of pressure fluctuations.     

Bubble chains in large diameter gas fluidized beds

Using statistically based measuring methods for the determination of local bubble size distributions and local average bubble shapes in gas fluidized beds, bubble characteristics have been measured in a fluidized bed column of 1 m diameter where quartz sand (minimum fluidizing velocity 0.0135 m/sec) was fluidized with air at velocities ranging from 0.05 to 0.30 m/sec. The results present experimental evidence that bubbles within large diameter fluidized beds do not rise completely randomly distributed in space but rather in the form of bubble chains which is in agreement with industrial operating experience in large scale fluid bed systems. Since the formation of bubble chains considerably reduces the residence time of the bubble gas this finding is of significance for the performance of fluidized bed reactors. The influence of the operating parameters on the extent of the bubble chain formation has been investigated and possible consequences of these results are discussed.     

Hydrodynamics of a bubble-induced inverse fluidized bed reactor with a nanobubble tray

This paper reports on the hydrodynamics of a bubble-induced inverse fluidized bed reactor, using a nanobubble tray gas distributor, where solid particles are fluidized only by an upward gas flow. Increasing the gas velocity, the fixed layer of particles initially packed at the top of the liquid starts to move downwards, due to the rise of bubbles in this system, and then gradually expands downwards until fully suspended. The axial local pressure drops and standard deviation were examined to delineate the flow regime comprehensively under different superficial gas velocities. Four flow regimes (fixed bed regime, initial fluidization regime, expanded regime, and post-homogeneous regime) were observed and three transitional gas velocities (the initial fluidization velocity, minimum fluidization velocity, and homogeneous fluidization velocity) were identified to demarcate the flow regime. Three correlations were developed for the three transitional velocities. As the fine bubbles generated from the nanobubble tray gas distributor are well distributed in the entire column, the bed expansion process of the particles is relatively steady.     

CFD–DEM study of effect of bed thickness for bubbling fluidized beds

The effect of bed thickness in rectangular fluidized beds is investigated through the CFD–DEM simulations of small-scale systems. Numerical results are compared for bubbling fluidized beds of various bed thicknesses with respect to particle packing, bed expansion, bubble behavior, solids velocities, and particle kinetic energy. Good two-dimensional (2D) flow behavior is observed in the bed having a thickness of up to 20 particle diameters. However, a strong three-dimensional (3D) flow behavior is observed in beds with a thickness of 40 particle diameters, indicating the transition from 2D flow to 3D flow within the range of 20–40 particle diameters. Comparison of velocity profiles near the walls and at the center of the bed shows significant impact of the front and back walls on the flow hydrodynamics of pseudo-2D fluidized beds. Hence, for quantitative comparison with experiments in pseudo-2D columns, the effect of walls has to be accounted for in numerical simulations.     

Vibration time series analysis of bubbling and turbulent fluidization

A non-intrusive vibration monitoring technique was used to study the hydrodynamics of a gas–solid fluidized bed. Experiments were carried out in a 15 cm diameter fluidized bed using 226, 470 and 700 μm sand particles at various gas velocities, covering both bubbling and turbulent regimes. Auto correlation function, mutual information function, Hurst exponent analysis and power spectral density function were used to analyze the fluidized bed hydrodynamics near the transition point from bubbling to turbulent fluidization regimes. The first pass of the autocorrelation function from one half and the time delay at which it becomes zero, and also the first minimum of the mutual information, occur at a higher time delay in comparison to stochastic systems, and the values of time delays were maximum at the bubbling to turbulent transition gas velocity. The maximum value of Hurst exponent of macro structure occurred at the onset of regime transition from bubbling to turbulent. Further increase in gas velocity after that regime transition velocity causes a decrease in the Hurst exponent of macro structure because of breakage of large bubbles to small ones. The results showed these methods are capable of detecting the regime transition from bubbling to turbulent fluidization conditions using vibration signals.     

Propagation characteristics of pressure disturbances originated by gas jets in fluidized beds

An experimental investigation has been carried out on velocities and amplitudes of pressure disturbances in fluidized beds made of 100–200 μm glass ballotini. Disturbances were originated by gas jetting in a 0.35 m i.d. fluidized bed. A fluidization tube 0.10 m i.d. has also been used. Different types of disturbances have been induced in the bed contained in this tube: injection of a freely rising bubble and of a captive bubble; injection of a bubble chain; and compression of the bed free surface. The dynamic wave character of the disturbances has been shown. Velocities and amplitudes of waves moving through the beds have been measured. In particular, wave velocities have been compared with theoretical results obtained by the application of “pseudo-homogeneous” and “separated phase flow” models.     

The local structure of gas fluidized beds —II. The spatial distribution of bubbles

The spatial distribution of bubbles in gas fluidized beds has been investigated with the measuring system described in Part I of this paper in beds of 0.10, 0.20, 0.45 and 1.0 m dia. The results indicate that in gas fluidized beds a characteristic flow profile of the bubble phase exists such that near the distributor a zone of increased bubble development exists in an annulus near the wall. This zone moves towards the vessel centre-line with increasing height above the distributor. The merging of the annular zone in the vessel centre-line marks the beginning of the transition of the fluidized bed to the state of slugging. The spatial flow profile of the bubble phase is shown to be responsible for the existence of characteristic solids circulation patterns in gas fluidized beds.     

Fluidization and bubbling behavior of potash particles in a deep fluidized bed

Most existing models for predicting bubble size and bubble frequency have been developed for freely bubbling fluidized beds. Accurate prediction of bubbling behavior in deep fluidized beds, however, has been a challenge due to the higher degree of bubble coalescence and break up, high probability of the slugging regime, partial fluidization, and chaotic behavior in the bubbling regime. In this work, the bubbling and fluidization behavior of potash particles was investigated in a deep fluidized bed employing a twin-plane electrical capacitance tomography (ECT) system. Solid volume fraction, average bubble velocity, average bubble diameter, and bubble frequency in both bubbling and slugging regimes were measured at two different bed height ratios (H/D = 3.5 and H/D = 3.78). This work is the first to illustrate a sequential view of bubbles at different superficial gas velocities in a fluidized bed. The results show that both the bubble diameter and rising velocity increased with increasing the superficial gas velocity for the two bed heights, with larger values observed in the deeper bed compared to the shallower one. Predicted values for bubble diameter, bubble rise velocity and bubble frequency from different models are compared with the experimental data obtained from the ECT system in this work. Good agreement has been achieved between the values predicted by the previous models and the experimental data for the bubble diameter and bubble rise velocity with an average absolute deviation of 16% and 15% for the bed height of 49 cm and 13% and 8% for the bed height of 53 cm, respectively.     

A novel dual-material probe for in situ measurement of particle charge densities in gas–solid fluidized beds

Particle charge density is vitally important for monitoring electrostatic charges and understanding particle charging behavior in fluidized beds. In this paper, a dual-material probe was tested in a gas–solid fluidized bed for measuring the charge density of fluidized particles. The experiments were conducted in a two-dimensional fluidized bed with both single bubble injection and freely bubbling, at various particle charge densities and superficial gas velocities. Uniformly sized glass beads were used to eliminate complicating factors at this early stage of probe development. Peak currents, extracted from dynamic signals, were decoupled to determine charge densities of bed particles, which were found to be qualitatively and quantitatively consistent with charge densities directly measured by Faraday cup from the freely bubbling fluidized bed. The current signals were also decoupled to estimate bubble rise velocities, which were found to be in reasonable agreement with those obtained directly by analyzing video images.     

Dual characters of interaction between particles and fluid

The unique characteristics of gas-solids two-phase flow and fluidization in terms of the flow structures and the apparent behavior of particles and fluid-particle interactions are closely linked to physical properties of the particles, operating conditions and bed configurations. Fluidized beds behave quite differently when solid properties, gas velocities or vessel geometries are varied. An understanding of hydrodynamic changes and how they, in turn, influence the transfer and reaction characteristics of chemical and thermal operations by variations in gas-solid contact, residence time, solid circulation and mixing and gas distribution is very important for the proper design and scale-up of fluidized bed reactors. In this paper, rather than attempting a comprehensive survey, we concentrate on examining some important positive and negative impacts of particle sizes, bubbles, clusters and column walls on the physical and chemical aspects of chemical reactor performance from the engineering application point of view with the aim of forming an adequate concept for guiding the design of multiphase fluidized bed chemical reactors.One unique phenomenon associated with particle size is that fluidized bed behavior does not always vary monotonically with changing the average particle size. Different behaviors of particles with difference sizes can be well understood by analyzing the relationship between particle size and various forces. For both fine and coarse particles, too narrow a distribution is generally not favorable for smooth fluidization. A too wide size distribution, on the other hand, may lead to particle segregation and high particle elutriation. Good fluidization performance can be established with a proper size distribution in which inter-particle cohesive forces are reduced by the lubricating effect of fine particles on coarse particles for Type A, B and D particles or by the spacing effect of coarse particles or aggregates for Type C powders.Much emphasis has been paid to the negative impacts of bubbles, such as gas bypassing through bubbles, poor bubble-to-dense phase heat & mass transfer, bubble-induced large pressure fluctuations, process instabilities, catalyst attrition and equipment erosion, and high entrainment of particles induced by erupting bubbles at the bed surface. However, it should be noted that bubble motion and gas circulation through bubbles, together with the motion of particles in bubble wakes and clouds, contribute to good gas and solids mixing. The formation of clusters can be attributed to the movement of trailing particles into the low-pressure wake region of leading particles or clusters. On one hand, the existence of down-flowing clusters induces strong solid back-mixing and non-uniform radial distributions of particle velocities and holdups, which is undesirable for chemical reactions. On the other hand, the formation of clusters creates high solids holdups in the riser by inducing internal solids circulations, which are usually beneficial for increasing concentrations of solid catalysts or solid reactants.Wall effects have widely been blamed for complicating the scale-up and design of fluidized-bed reactors. The decrease in wall friction with increasing the column diameter can significantly change the flow patterns and other important characteristics even under identical operating conditions with the same gas and particles. However, internals, which can be considered as a special wall, have been used to improve the fluidized bed reactor performance.Generally, desirable and undesirable dual characteristics of interaction between particles and fluid are one of the important natures of multiphase flow. It is shown that there exists a critical balance between those positive and negative impacts. Good fluidization quality can always be achieved with a proper choice of right combinations of particle size and size distribution, bubble size and wall design to alleviate the negative impacts.     

Local heat transfer coefficients on the circumference of a tube in a gas fluidized bed

A heated horizontal heat transfer tube was installed 14.8 cm above the distributor plate in a square fluid bed measuring 30.5 × 30.5 cm. Four different Geldart B sized particle beds were used (sand of two different distributions, an abrasive and glass beads) and the bed was fluidized with cold air. The tube was instrumented with surface thermocouples around half of the tube circumference and with differential pressure ports that can be used to infer bubble presence. Numerical execution of the transient conduction equation for the tube allowed the local time-varying heat transfer coefficient to be extracted. Data confirm the presence of the stagnant zone on top of the tube associated with low superficial velocities. Auto-correlation of thermocouple data revealed bubble frequencies and the cross-correlation of thermal and pressure events confirmed the relationship between the bubbles and the heat transfer events. In keeping with the notion of a “Packet renewal” heat transfer model, the average heat transfer coefficient was found to vary in sympathy with the root-mean square amplitude of the transient heat transfer coefficient.     

Using S-statistic for investigating the effect of temperature on hydrodynamics of gas–solid fluidization

The influence of temperature on fluidization was investigated by a statistical chaotic attractor comparison test known as S-statistic. After calibration of the variables used in this method, the S-test was applied to the radioactive particle tracking (RPT) data obtained from a lab-scale fluidized bed. Experiments were performed with sand as fluidized particles and in temperatures from ambient up to 600 °C with superficial gas velocities of 0.29, 0.38 and 0.52 m/s. Considering the behavior of bubbles and comparing with frequency domain analysis, it was concluded that S-statistic is a reliable method for characterization of fluidization process behavior at different temperatures.     

Bubble characteristics in a bubbling fluidized bed with a rotating distributor

In this paper, the effect of a novel rotating distributor for fluidized beds on the bubble size is studied. The distributor is a perforated plate that rotates around the vertical axis of the column.The formation of the bubbles on the rotating distributor is theoretically analyzed. The pierced length of the bubbles ascending in the bed were measured using optical probes. The probability distribution of bubble diameter was inferred from these experimental measurements using the maximum entropy method. The radial profile of the bubble diameter is presented for the static and rotating configurations at different gas velocities. The frequency of bubble passage and the distribution of bubbles in the cross section of the bed are also reported. Results were finally shown for different heights above the distributor.A radial decrease in the bubble size when the distributor rotates is found. The bubble growth with the bed height is also lower in the rotating case.     

A novel dual-material probe for in situ measurement of particle charge densities in gas-solid fluidized beds

Particle charge density is vitally important for monitoring electrostatic charges and understanding particle charging behavior in fluidized beds.In this paper,a dual-material probe was tested in a gas-solid fluidized bed for measuring the charge density of fluidized particles.The experiments were conducted in a two-dimensional fluidized bed with both single bubble injection and freely bubbling,at various particle charge densities and superficial gas velocities.Uniformly sized glass beads were used to eliminate complicating factors at this early stage of probe development.Peak currents,extracted from dynamic signals,were decoupled to determine charge densities of bed particles,which were found to be qualitatively and quantitatively consistent with charge densities directly measured by Faraday cup from the freely bubbling fluidized bed.The current signals were also decoupled to estimate bubble rise velocities,which were found to be in reasonable agreement with those obtained directly by analyzing video images.