Three-dimensional numerical modelling of interactions between a gas–liquid jet and a fluidized bed

This paper presents the development of a novel mathematical model that describes spray injection and spreading into a fluidized bed of solid particles. The model also includes the gas–liquid flow through the nozzle followed by the gas-assisted atomization. An Eulerian approach that is independent of the nature of the continuous phase is adopted for all phases, which are gas (or bubbles), liquid (or droplets), and solid particles that may be covered with a liquid layer. Variation in sizes of bubbles and droplets is represented by the particle number density approach that takes into account both break-up and coalescence. The atomization is considered as a catastrophic phase inversion triggered by a critical local volume fraction. New relationships were obtained for liquid spreading due to wet particle collisions and for heat conduction between a solid particle and a surrounding liquid layer. The model is applied to simulate liquid injection into the fluidized bed for conditions that were previously experimentally studied and published. The comparison reveals a reasonable agreement in prediction of the cumulative liquid distribution for two experimental cases. In addition, we evaluated a jet penetration distance with the model to compare it with the one measured in another set of experiments. This comparison also yields a good qualitative agreement. Finally, we evaluated the influence of the fluidization velocity on liquid distribution in the bed.     

Horizontal gas and gas/solid jet penetration in a gas–solid fluidized bed

In this paper, the real time, dynamic phenomena of the three-dimensional horizontal gas and gas/solid mixture jetting in a 0.3 m (12 in) bubbling gas–solid fluidized bed are reported. The instantaneous properties of the shape of the jets and volumetric solids holdup are qualified and quantified using the three-dimensional electrical capacitance volume tomography (ECVT) recently developed in the authors’ group. It is found that the horizontal gas jet is almost symmetric along the horizontal axis during its penetration. As the jet width expands, the total volume of the gas jet increases. A mechanistic model is also developed to account for the experimental results obtained in this study. Comparison of jet penetration length and width between the model prediction and ECVT experiment shows that both the maximum penetration length and the maximum width of the horizontal gas jet increase with the superficial gas velocity. When the horizontal gas jet coalesces with a bubble rising from the bottom distributor, it loses its symmetric shape and can easily penetrate into the bed. For the horizontal gas/solid mixture jet penetration in the bed, the tail of the jet at the nozzle shrinks and the jet loses its jet shape immediately when the jet reaches its maximum penetration length, which are different from the characteristics exhibited by the gas jet. The solids holdup in the core region of the gas/solid mixture jet is higher than that in the gas jet. The penetration length of the horizontal gas/solid mixture jet is also larger than that of the gas jet.     

Euler multiphase-CFD simulation on a bubble-driven gas–liquid–solid fluidized bed

An integrated flow model was developed to simulate the fluidization hydrodynamics in a new bubble-driven gas–liquid–solid fluidized bed using the computational fluid dynamic (CFD) method. The results showed that axial solids holdup is affected by grid size, bubble diameter, and the interphase drag models used in the simulation. Good agreements with experimental data could be obtained by adopting the following parameters: 5 mm grid, 1.2 mm bubble diameter, the Tomiyama gas–liquid model, the Schiller–Naumann liquid–solid model, and the Gidaspow gas–solid model. At full fluidization state, an internal circulation of particles flowing upward near the wall and downward in the centre is observed, which is in the opposite direction compared with the traditional core-annular flow structure in a gas–solid fluidized bed. The simulated results are very sensitive to bubble diameters. Using smaller bubble diameters would lead to excessive liquid bed expansions and more solid accumulated at the bottom due to a bigger gas–liquid drag force, while bigger bubble diameters would result in a higher solid bed height caused by a smaller gas–solid drag force. Considering the actual bubble distribution, population balance model (PBM) is employed to characterize the coalescence and break up of bubbles. The calculated bubble diameters grow up from 2–4 mm at the bottom to 5–10 mm at the upper section of the bed, which are comparable to those observed in experiments. The simulation results could provide valuable information for the design and optimization of this new type of fluidized system.     

The onset velocity of a liquid–solid circulating fluidized bed

The critical transition velocity, U_cr, previously defined by Liang et al. [W.-G. Liang, S.-L. Zhang, J.-X. Zhu, Y. Jin, Z.-Q. Yu and Z.-W. Wang, Flow characteristics of the liquid–solid circulating fluidized bed, Powder Technol., 90 (1997) 95–102.] to demarcate the liquid–solid conventional and circulating fluidization regimes, was found to vary with the total solids inventory and the solids feeding system. In this work, an onset velocity for circulating fluidization regime, U_cf, is proposed to give the lowest U_cr value and to provide a convenient demarcation velocity that is independent of system geometry. This liquid velocity is obtained by measuring the time required to empty all particles in a batch operated fluidized bed under different liquid velocities. This method can be used for a wide range of particles and involves less influence of the operating conditions such as the solids inventory and the solids feeding system. Compared to the critical transition velocity, this newly defined onset velocity is a more intrinsic parameter, only dependent on the liquid and particle properties. Based on the experimental results obtained in this work and other published results, the influence of particle properties and equipment setup on the onset velocity is also discussed.     

Dynamic characteristics of the volatile cloudy zone in a gas–solid fluidized bed with hydrocarbon liquid spray

In a gas–solid fluidized bed with continuous hydrocarbon liquid spray, a volatile “cloudy zone” could be formed, defined as a dynamically steady liquid-affected zone, including droplets, wet particles, and the gas which passes through the zone. A new flow pattern with the dynamic coexistence of cloudy zone and non-cloudy zone (gas–solid zone), is accordingly established. The temperature, particle concentration, and particle velocity fields are measured in real-time via infrared thermography and particle imaging velocimetry, respectively. Results show that the area and range of central position of the cloudy zone illustrate a heavier fluctuant trend with the increasing velocity of liquid spray, and the main frequency of area fluctuation is close to that of the bubble rising. Moreover, the particle concentration and particle velocity in the cloudy zone are lower than those in the non-cloudy zone, breaking the conventional symmetrical distributions of hydrodynamic parameters of particles in a gas–solid fluidized bed.     

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.     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

Development and verification of coarse-grain CFD-DEM for nonspherical particles in a gas–solid fluidized bed

Computational fluid dynamics coupled with discrete element method (CFD-DEM) has been widely used to understand the complicated fundamentals inside gas–solid fluidized beds. To realize large-scale simulations, CFD-DEM integrated with coarse-grain model (CG CFD-DEM) provides a feasible solution, and has led to a recent upsurge of interest. However, when dealing with large-scale simulations involving irregular-shaped particles such as biomass particles featuring elongated shapes, current CG models cannot function as normal because they are all developed for spherical particles. To address this issue, a CG CFD-DEM for nonspherical particles is proposed in this study, and the morphology of particles is characterized by the super-ellipsoid model. The effectiveness and accuracy of CG CFD-DEM for nonspherical particles are comprehensively evaluated by comparing the hydrodynamic behaviors with the results predicted by traditional CFD-DEM in a gas–solid fluidized bed. It is demonstrated that the proposed model can accurately model gas–solid flow containing nonspherical particles, merely the particle dynamics are somewhat lost due to the scaleup of particle size. Finally, the calculation efficiency of CG CFD-DEM is assessed, and the results show that CG CFD-DEM can largely reduce computational costs mainly by improving the calculation efficiency of DEM. In general, the proposed CG CFD-DEM for nonspherical particles strikes a good balance between efficiency and accuracy, and has shown its prospect as a high-efficiency alternative to traditional CFD-DEM for engineering applications involving nonspherical particles.     

Hydrodynamics of an inverse liquid–solid circulating conventional fluidized bed

An inverse liquid–solid circulating conventional fluidized bed (I-CCFB) is realized by injecting particles from the top of a conventional liquid–solid fluidized bed (0.076 m ID and 5.4 m height) that is operated in a newly developed circulating conventional fluidization regime located between the conventional and circulating fluidization regimes. The I-CCFB can achieve a higher solids holdup compared to both conventional and circulating liquid–solid fluidized beds. A new parameter, the bed intensification factor, is defined to quantify the increased solids holdup observed with external solids circulation. The Richardson–Zaki equation is shown to be applicable to the I-CCFB regime and can be used to correlate the slip velocity and solids holdup, both of which increase with the solids circulation rate. A new flow regime map is presented, including the I-CCFB and a variety of other liquid–solid fluidized beds.     

Minimum superficial fluid velocity in a gas–solid swirled fluidized bed

A swirl flow is achieved in a bed of solids by passing air through multiple fluid inlets, which are tangentially located at the base of a flat-based circular column. The minimum superficial velocities needed to achieve swirling of the bed are measured experimentally under varied conditions. An empirical correlation for the minimum swirl velocity has been proposed. The results indicate that a stable swirling regime operation of the bed is possible. There exists an upper limit of static bed depth beyond which stable swirling of entire bed is not possible. The minimum swirl velocities are found to be 1.2–1.3 times the minimum fluidization velocities predicted for conventional fluidized beds.     

Dynamics of a draft tube gas—liquid—solid fluidized bed bioreactor for phenol degradation

The transient response of a draft tube gas—liquid—solid fluidized bed biofilm reactor (DTFB) to a step increase in influent phenol concentration was experimentally investigated. A mathematical model, which considers the external mass transfer resistance, the simultaneous diffusion, reaction, and adsorption of phenol and oxygen inside the bioparticles, the dynamics of biofilm growth, and the time delay of microbial growth during the transient period, is proposed. The biofilm properties such as thickness and density are allowed to vary in the model with biofilm growth to simulate the real biofilm system. Simulation results predicted from the proposed model show reasonable agreement with the experimental data.     

Flow regimes in a gas–liquid–solid three-phase moving bed

The gas–liquid–solid three-phase moving beds could supply a potential solution for multiphase reactions with catalyst easily deactivated, and the flow regimes in it were studied by optical method and pressure drop measurement. Results showed that taking the trickle flow as the initial flow regime, the flow channels were more obvious as the particle velocity increased. When the initial flow regimes were pulse flow and bubble flow respectively, the pulse-to-trickle and bubble-to-pulse flow transitions mainly occurred at moderate-to-high particle velocities (0.01–0.04 m s⁻¹ under conditions used in this work). Moreover, the flow regime map in the three-phase moving bed was constructed and shown that the region of trickle flow increased and the region of bubble flow decreased. Finally, the application of three-phase moving beds was discussed, and it could be suitable for those reactions, which had to operate in the pulse flow, bubble flow, and transition zone.     

Numerical simulation of local and global mixing/segregation characteristics in a gas–solid fluidized bed

Researches on solids mixing and segregation are of great significance for the operation and design of fluidized bed reactors. In this paper, the local and global mixing and segregation characteristics of binary mixtures were investigated in a gas–solid fluidized bed by computational fluid dynamics-discrete element method (CFD-DEM) coupled approach. A methodology based on solids mixing entropy was developed to quantitatively calculate the mixing degree and time of the bed. The mixing curves of global mixing entropy were acquired, and the distribution maps of local mixing entropy and mixing time were also obtained. By comparing different operating conditions, the effects of superficial gas velocity, particle density ratio and size ratio on mixing/segregation behavior were discussed. Results showed that for the partial mixing state, the fluidized bed can be divided into three parts along the bed height: complete segregation area, transition area and stable mixing area. These areas showed different mixing/segregation processes. Increasing gas velocity promoted the local and global mixing of binary mixtures. The increase in particle density ratio and size ratio enlarged the complete segregation area, reduced the mixing degree and increased the mixing time in the stable mixing area.     

Study on the flow characteristics of the pulsating intermittent liquid–solid fluidized bed with step liquid velocity by CFD approach

A new type of liquid–solid fluidized bed (LSFB), the pulsating intermittent LSFB (PI-LSFB), which uses pulsating liquid flow, was analyzed through numerical and experimental study. A good agreement between numerical simulation results and laboratory experimental measurement data was achieved. The mass transfer efficiency between the liquid and solids phases was enhanced since the relative velocity was significantly improved. The flow characteristics of the PI-LSFB were analyzed through the Eulerian–Eulerian approach, incorporating the kinetic theory of granular flow. The solids holdup in the middle part of the PI-LSFB increases first and then decreases as the step liquid velocity increases. The relative velocity increases first and then decreases as the pulsation period or the liquid velocity increases. The PI-LSFB performs similar flow regimes under step and sinusoidal liquid velocities. The proposed PI-LSFB may provide a reference in biological wastewater treatment applications.     

Hydrodynamics of gas–solid flow in the circulating fluidized bed reactor for dry flue gas desulfurization

Process design and scale-up require a fundamental understanding of the hydrodynamics of gas–solid flow in the circulating fluidized bed flue gas desulfurization (CFB-FGD) reactor although the CFB system has been widely used in flue gas desulfurization and flue gas cleaning processes. The hydrodynamics in the CFB-FGD reactor model was investigated by pressure measurements and specially designed sampling probe based on three dimensionless groups for practicable similarity of industrial CFB-FGD process. The results show that the pressure drop in the venturi section is predominant as high as 60% of the total pressure drop and the total pressure drop significantly increases with the increasing external solid circulating rates at the same superficial gas velocity. Moreover, the measurements of radial solid mass fluxes show that the flow pattern in the CFB-FGD reactor is a typical core–annulus flow and this flow structure prevails until the top of the reactor. Reflux ratios are used to quantitatively evaluate the internal solid reflux in the reactor and the values in the low section of the reactor are much higher than those in the upper section.     

Non-intrusive determination of bubble size in a gas–solid fluidized bed: An evaluation

Bubble sizes measured in a column of diameter 290 mm with FCC particles utilizing both an intrusive optical probe and non-intrusive pressure analysis are compared. The pressure signals were decoupled by differential pressure analysis and incoherence analysis. It is shown that pressure fluctuations induced by jetting/bubble formation can be effectively filtered out by differential pressure and incoherence analysis. The differential pressure signals measured across a vertical interval less than half the maximum bubble size unreasonably damps the power spectral density intensity, leading to underestimation of bubble size and overestimation of mean frequency. In the present work, the incoherence analysis tends to estimate greater bubble size than differential pressure analysis. Bubble chord lengths are overestimated by optical probe signals because small bubbles are not detected. Bubble sizes calculated by the equation of Horio and Nonaka (1987) agree reasonably well with that estimated by incoherence analysis at relatively high superficial gas velocities.     

Modelling and numerical simulation of liquid–solid circulating fluidized bed system for protein purification

A novel liquid–solid circulating fluidized bed (LSCFB) was modelled for protein recovery from the feed broth. A typical LSCFB system consists of downer and riser, integrating two different operations simultaneously. A general purpose, extensible, and dynamic model was written based on the tanks-in-series framework. The model allowed adjusting the degree of backmixing in each phase for both columns. The model was validated with previously published data on extraction of bovine serum albumin (BSA) as model protein. Detailed dynamic analysis was performed on the protein recovery operation. The interaction between the riser and downer were captured. Parametric studies on protein recovery in LSCFB system were carried out using the validated model to better understand the system behaviour. Simulation results have shown that both production rate and overall recovery increased with solids circulation rate, superficial liquid velocity in the downer and riser, and feed solution concentration. The model was flexible and could use various forms of ion exchange kinetics and could simulate different hydrodynamic behaviours. It was useful to gain insight into protein recovery processes. The general nature of the model made it useful to study other protein recovery operations for plant and animal proteins. It could also be useful for further multi-objective optimization studies to optimize the LSCFB system.     

On-line detection of bed fluidity in gas–solid fluidized beds with liquid injection by passive acoustic and vibrometric methods

Passive acoustic and vibrometric methods were investigated for the detection and monitoring of changes in bed fluidity in a large scale gas–solid fluidized bed after liquid injection. Water was injected into a 9 tonne air-fluidized bed of silica sand using an industrial nozzle and pre-mixer assembly. Acoustic signals were recorded using non-intrusive and externally mounted microphones. Vibration data was recorded using an accelerometer mounted to a rod inserted into the bed. The signals were analyzed offline using Fourier and wavelet analysis techniques. The average frequency of the acoustic and vibration measurements decreased as the bed solids dried while the standard deviation of the coefficients in the 10–20 kHz band characterized from wavelet analysis increased during drying. Samples from the bed were taken and evaluated for flowability by measuring the median avalanche time with a Revolution Powder analyzer. Linear and power law regressions of the wavelet and Fourier analyzed vibration measurements provided a reliable correlation of the flowability of the bed solids and thus could be successfully used as a passive and real-time monitoring method of bed fluidity.     

Experimental studies and empirical models for the prediction of bed expansion in gas–solid tapered fluidized beds

Studies in the expansion behaviour of tapered fluidized bed systems are important for specifying the height of the bed. Data have been obtained on the expanded heights of tapered fluidized beds and bed expansion ratios for spherical and non-spherical particles have been calculated. Based on dimensional analysis, models have been developed as a function of geometry of tapered bed, static bed height, particle diameter, density of solid and gas and superficial velocity of the fluidizing medium. The data used to derive the models cover a wide range of operating conditions, with varying fluidization velocities. Effects of static bed height, particle diameter, density, tapered angle and superficial gas velocity over minimum fluidization velocity on bed expansion ratios have been investigated experimentally. A comparison has been made between the calculated values of bed expansion ratios using proposed models and the experimental data. It has been seen that calculated values by models agree well with the experimental values. Models have also been compared with literature data of conventional bed and found its applicability at higher gas velocities with good accuracy.