Three-dimensional Fluidized Bed Research Articles

Parameters of surface standing waves in fluidized bed apparat with different diameter

Regarding medium- and low-temperature processes of heterogeneous heterophase interaction in the units for cleaning from pollutants and trapping CO2, the analogy of the behavior of standing surface waves of an ideal liquid with oscillations of the surface of a fluidized bed is considered. Waves on the surface of a fluidized bed are formed when gas bubbles leave it and are one of the elements of the mechanism of self-sustained fluctuations of the entire mass of the bed. The frequency modes of the surface waves correspond to the main modes in the spectra of pressure fluctuations in the bed and depend on its geometry. The fluctuations of a bubble three-dimensional fluidized bed in apparatuses of different sizes are numerically simulated in a high-performance parallel computing mode using the Ansys Fluent program. Comparison of analytical calculations for fluid oscillations in a vessel with the results of numerical simulation of a fluidized bed and experimental data on the frequency of the emergence of bubbles and modes of surface waves is carried out.

Unified gas-kinetic wave-particle method for three-dimensional simulation of gas-particle fluidized bed

The gas–solid particle two-phase flow in a fluidized bed shows complex physics. The multi-scale algorithm composed of the coupled gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic wave-particle method (UGKWP) for the solid particle phase is developed for three-dimensional fluidized bed study. For the solid-particle phase, different from the widely-used Eulerian and Lagrangian approaches, the UGKWP unifies the wave (dense particle region) and discrete particle (dilute particle region) formulation seamlessly according to a continuous variation of particle cell’s Knudsen number (Kn). The GKS-UGKWP for the coupled gas-particle evolution system can automatically become an Eulerian–Eulerian (EE) method in the high particle collision regime and Eulerian–Lagrangian (EL) formulation in the collisionless particle regime. In the transition regime, the UGKWP can achieve a smooth transition between the Eulerian and Lagrangian limiting formulation. More importantly, the weights of mass distributions from analytical wave and discrete particle are related to the local Kn by (1−exp(−1/Kn)) for wave and exp(−1/Kn) for discrete particle. The UGKWP provides an optimal modeling in capturing the particle phase in difference regimes with the full consideration of physical accuracy and numerical efficiency. In the numerical simulation, the UGKWP does not need any prior division of dilute/dense regions, which makes it suitable for the fluidized bed problem, where the dilute/transition/dense regions instantaneously coexist and are dynamically interconvertible. In this paper, based on the GKS-UGKWP formulation two lab-scale fluidization cases, i.e., one turbulent fluidized bed and one circulating fluidized bed, are simulated in 3D and the simulation results are compared with the experimental measurements. The typical heterogeneous flow features of the fluidized bed are well captured and the statistics are in good agreement with experiment data.

Numerical Simulation of the Operating Conditions for the Reduction of Iron Ore Powder in a Fluidized Bed Based on the CPFD Method

In this work, the computational particle fluid dynamics (CPFD) method is used to simulate the high-pressure visual fluidized bed experimental equipment independently designed and developed by the experimentation of the fluidized reduction process of iron ore powder. A numerical model for reducing iron ore fines in a three-dimensional fluidized bed is established, and the model is verified by combining numerical simulation and experimental testing. Moreover, the influences of different reducing factors on the reduction effect in the process of the fluidized reduction of iron ore fines are simulated in detail. Via the CPFD simulation of the fluidized reduction of iron ore fines, the optimal reduction pressure is found to be 0.2 MPa, and the optimal reducing gas is found to be H2. Moreover, the optimal gas velocity is 0.6 m/s, and the optimal reduction temperature is 923 K. This conclusion is consistent with the experimental measurements, so the simulation results can be used to verify the reliability of the optimal operating conditions.

Numerical analysis of CO2 capture process with potassium-based sorbent in a three-dimensional fluidized bed

CO2 capture process with potassium-based sorbents in fluidized beds is an emerging technology in industries, yet the in-furnace solid transportation and thermal characteristics are still lacking. In this work, the CO2 process capture with K2CO3 adsorbents in a three-dimensional fluidized bed is numerically explored using a recently developed reactive multiphase particle-in-cell model under the Eulerian-Lagrangian framework. After model validation, the spatial distribution of K2CO3 particles and the effect of key operating parameters on the flow and thermal behaviours in the fluidized bed are investigated. The results indicate that elevating the particle size distribution enhances CO2 capture and increases the absorbent temperature due to the extended residence time of K2CO3 particles and the resulting enhanced exothermic carbonation reactions. Enlarging the inlet gas velocity increases the gas concentration in the reactor outlet because a part of CO2 without enough time to react with K2CO3 particles is entrained out of the reactor by bubbles with the increase of gas velocity, indicating the optimal inlet gas velocity (0.71 m/s) for CO2 capture using K2CO3 adsorbents in this fluidized bed. The particle temperature rises with enlarging inlet gas velocity due to enhanced exothermic carbonation reactions. The results obtained can help to understand the regularity of CO2 capture process based on K2CO3 absorbents in fluidized beds.

Bubble characterization in the gas-solid fluidized bed using an intrusive acoustic emission sensor array

Bubble behaviors in fluidized beds were investigated by a self-designed double-core screened waveguide. Experiments presented that, the bubble dome and vortex would generate AE signals with different shapes when passing through the waveguide, which could be further used to precisely detect the bubble sizes and velocities both in pseudo-two-dimensional and three-dimensional fluidized beds. Compared with results from pressure fluctuations, bubble sizes measured by AE methods in three-dimensional fluidized beds were more consistent with empirical formulas results and displayed similar robustness. Furthermore, the measured bubble distributions demonstrated that bubbles tended to rise along an annular zone in the cross-section of the fluidized bed, and the annular zone shrank with the increasing height due to the net inward movement of bubbles. Under high gas velocities, the annular zone would shrink until reaching the centerline, while under low gas velocities, a steady annular zone existed at a certain radial position.

Numerical investigation of agglomeration phenomenon in fluidized beds by a combined CFD-DEM/PBM technique

PurposeThe purpose of this paper is to fundamentally develop a mathematical model for predicting the particle size distribution (PSD) in fluidized beds because their hydrodynamics depend on the PSD and its evolution during operation. To predict the gradual PSD change in a fluidized bed by using the population balance method (PBM), the kinetic parameter for agglomerate formation should be known and this parameter, in this work, is determined by the results of computational fluid dynamic–discrete element method (CFD-DEM) simulation.Design/methodology/approachMomentum and energy conservation equations and soft-sphere DEM are used to simulate the agglomeration phenomenon at high temperature in a two-dimensional air-polyethylene fluidized bed in bubbling regime. The Navier–Stokes equations for motion of gas are solved by the SIMPLE algorithm. Newton’s second law of motion is applied to describe the motion of individual particles. Collision between particles is detected by the no-binary search algorithm.FindingsA correlation is proposed for estimating the kinetic parameter for agglomerate formation based on collision frequency, collision efficiency and inlet gas temperature. Based on the corrected kinetic parameter, the PBM is able to predict the PSD evolution in the fluidized bed in a fairly good agreement with the results of the CFD-DEM.Research limitations/implicationsThe results of the agglomeration process cannot be compared quantitatively with experimental results. Because three-dimensional fluidized bed mostly contains millions of particles and simulating them takes a long computing time in DEM. As far as temperature is a dominant parameter in the agglomeration process, effects of inlet gas temperature are examined on the kinetic parameter. On the other hand, wider and deeper insights in which the effect of other parameters, such as velocity and so on will be studied, is one of the goals in the authors’ next works to compensate for the shortcomings in this work.Originality/valueThis study helps to understand the effect of the inlet gas temperature during the agglomeration process on the kinetic parameter and provides fundamental information in dealing with kinetic parameter to attain PSD in fluidized bed by the PBM.

Experimental study of bubble dynamics and flow transition recognition in a fluidized bed with wet particles

This paper studies the bubble dynamics and flow transition behavior in wet particle systems. Non-coherent algorithm was used to quantitatively calculate the bubble diameters in a three-dimensional fluidized bed system loaded with wet particles, obtaining the bubble dynamics under the action of liquid. The results indicate that the incoherent analysis can detect the formation of even tiny bubbles in the fluidized bed. The kurtosis and skewness of the pressure fluctuation signal was used to obtain the critical transition conditions of the flow pattern from turbulent to laminar. Through the decay index of the incoherent spectrum, the operating conditions of the Levy-Kolmogorov flow pattern to the Kolmogorov flow region were determined. From the comparison of the liquid bridge and the drag forces, the competitive mechanism of different forces acting on the particles that conformed the bed was analyzed, reflecting the change of the apparent minimum fluidization velocity of wet particles.

Direct calculation of voidage in the fine-grid CFD–DEM simulation of fluidized beds with large particles

Voidage is important in determining the hydrodynamic behavior of a fluidized bed and estimating the drag force. Exact calculation methods are limited, especially in terms of determining the intersection of a particle and cell. This paper presents a method of directly calculating voidage. First, a judgment criterion of particle–cell overlap, which relies on the relationship of the distance from the particle to a cell face, edge, or vertex, is proposed. Eight cases of the overlap volume of a particle and cell are then ascribed to a unified formula in the framework of the cuboid cell. This formula relies on the volume of two kinds of segments named the hemispherical segment and quarter-spherical segment. The presented method is validated by calculating the voidage of simple cubic packing. Moreover, a three-dimensional fluidized bed with large particles is simulated and the results of numerical simulation are compared against experimental and simulation results reported in the literature. All numerical results are in good agreement with corresponding experimental data, and demonstrate the accuracy and reliability of the presented method in the three-dimensional simulation of fluidized beds.

Three-dimensional fluidized beds with rough spheres: Validation of a Two Fluid Model by Magnetic Particle Tracking and discrete particle simulations

Two fluid model simulations based on our recently introduced kinetic theory of granular flow (KTGF) for rough spheres and rough walls, are validated for the first time for full three-dimensional (3D) bubbling fluidized beds. The validation is performed by comparing with experimental data from Magnetic Particle Tracking and more detailed Discrete Particle Model simulations. The effect of adding a third dimension is investigated by comparing pseudo-2D and full 3D bubbling fluidized beds containing inelastic rough particles. Spatial distributions of key hydrodynamic data as well as energy balances in the fluidized bed are compared. In the pseudo-2D bed, on comparison with the KTGF derived by Jenkins and Zhang, we find that the present KTGF improves the prediction of bed hydrodynamics. In the full 3D bed, particles are more homogeneously distributed in comparison with the pseudo-2D bed due to a decrease of the frictional effect from the front and back walls. The new model results are in good agreement with experimental data and discrete particle simulations for the time-averaged bed hydrodynamics.

Effect of particle stress tensor in simulations of dense gas–particle flows in fluidized beds

A two-fluid model based on the kinetic theory of granular flow for the rapid-flow regime and the Coulomb friction law for the quasi-static regime is applied to predict the hydrodynamics of dense gas–particle flow in a three-dimensional fluidized bed. Two different models for the particle stress tensor that use different constitutive equations in the elastic-inertial regime are examined to assess their ability to predict bed dynamics. To understand how particle stress models affect structural features of the flow, a quantitative analysis is performed on some important aspects of the mechanics of bubbling beds that have received relatively little attention in the literature. Accordingly, different flow regimes are identified in the context of fluidized beds through the dimensionless inertial number, and the main characteristics of each regime are discussed. In addition, how the particle stress tensor manifests itself in the bubble characteristics, natural frequency of the bed, and particle Reynolds stress are investigated, all of which help to better understand the complex dynamics of the fluidized bed. The numerical results are validated against published experimental data and demonstrate the significant role of the stress tensor in the elastic-inertial regime.

Controlling the Quality of Two-Way Euler/Lagrange Numerical Modeling of Bubbling and Spouted Fluidized Beds Dynamics

We numerically simulate three-dimensional fluidized beds of monodisperse spheres using a two-way Euler/Lagrange method. Particles trajectories are tracked in a Lagrangian way, and particles collisions are computed by a soft sphere model. The fluid conservation equations are written in a classical Eulerian fashion and are locally averaged on cells 1 order of magnitude larger than particles. We detail the equations of the model and their numerical implementation. We study the influence of numerical parameters and simulation domain size on computed results in a biperiodic fluidized bed. We then validate the model against theoretical results for a bubbling fluidized bed and against experimental data for a single- and multi-nozzle spouted bed. Finally, we investigate the influence of the Coulomb friction coefficient magnitude on a single-nozzle spouted bed dynamics in order to emphasize the importance of tangential friction in such processes.

Monitoring Electrostatics and Hydrodynamics in Gas–Solid Bubbling Fluidized Beds Using Novel Electrostatic Probes

The ability of recently developed novel electrostatic probes to monitor particle charge density and hydrodynamics in freely bubbling two- and three-dimensional fluidized beds of glass beads and polyethylene particles is demonstrated. Particle charge density and bubble properties in the beds were altered by abruptly changing superficial gas velocity or by impulsively adding antistatic agent to the bed. The probes were then utilized to quantitatively monitor the particle charge density and bubble rise velocity. The current signals from the probes responded quickly and significantly to abrupt changes in the superficial gas velocity. By analyzing time-series signals from the probes, the particle charge density and the bubble rise velocity deduced from the probes were found to be of similar order of magnitudes and changed consistently with those obtained from Faraday cup and video measurements. Charge densities from the Faraday cup decreased when an antistatic agent was added, as registered by the probe.

CFD–PBM coupled simulation of silicon CVD growth in a fluidized bed reactor: Effect of silane pyrolysis kinetic models

The coupled numerical code of Eulerian–Granular model and population balance model was applied to simulate silane-derived silicon chemical vapor deposition growth in a three-dimensional fluidized bed reactor. Two silane homogenous kinetic models were used to obtain the gaseous concentration of silicon cluster for further calculation on cluster scavenging rate, and two heterogeneous kinetic models implemented to evaluate the rate of silane surface deposition. The applicability of silane pyrolysis kinetic models on gaseous species and silicon growth were analyzed in detail after the verification of fundamental flow behavior. The results showed that the growth rate agreed well with Hsu’s experimental data under the combination kinetic models of Hogness’s homogenous and Furusawa’s heterogeneous ones, in which a complete silane decomposition was almost achieved, but the impractical growth result was obtained as inlet silane mole fraction higher than 0.5. Moreover, the interphase mass transfer of silane surface deposition and cluster scavenging was also focused, which showed that silane surface deposition tended to occur at the solid dense bottom region with higher mass transfer rate and cluster scavenging happened in almost the whole solid phase.

Numerical Investigation on the Effect of Pressure on Fluidization in a 3D Fluidized Bed

We apply a two-fluid model to investigate hydrodynamic differences in a three-dimensional fluidized bed operating at pressures of 1, 2, 4, 8, 16, 20, and 32 bar. The simulation results are compared with experimental results from the literature and show very good agreement. A detailed investigation is carried out on pressure fluctuations, porosity distribution, and bubble and solids flow characteristics. At high pressure, the porosity distribution is homogeneous and fluidization is smooth. The bubble size depends upon the location in the 3D bed, showing different trends at different pressures. The average bubble size is reduced with an increase in pressure, caused by a difference in coalescence and splitting of bubbles. An initial increase in pressure from 1 to 2 bar shows an increase in bubble rise velocity, but a further increase in pressure causes bubbles to rise more slowly. High up-flow of solids is observed in the center at high pressures, with pronounced differences in solids circulation vortices.

Verification and validation of a coarse grain model of the DEM in a bubbling fluidized bed

Dense granular flows are encountered in various engineering fields. The discrete element method (DEM) is used extensively for the numerical simulation of these flow types. Improvements in computer specifications have made it possible to apply the DEM in various systems. Although the DEM is well-established, it has a fatal problem. The problem is that the number of calculated particles is substantially restricted when the simulation needs to be finished within practical time using a single personal computer. On the other hand, many industries require application of the DEM to large scale systems on a single personal computer. We therefore developed the DEM coarse grain model in our previous studies. In the coarse grain model, a group of original particles is simulated using a large-sized particle termed a coarse grain particle, where the total energy is modeled to agree between the coarse grain and original particles. The coarse grain model therefore makes it feasible to perform large scale DEM simulations by using a smaller number of particles than the actual number. The coarse grain model thus far has been verified in two-dimensional fluidized beds. In this study, adequacy of the coarse grain model is verified and validated in a three-dimensional fluidized bed, where scaling ratio is low and high respectively. Consequently, the coarse grain model is shown to simulate the macroscopic behavior of solid particles in three-dimensional dense gas–solid flows.

Numerical analysis of the dynamics of two- and three-dimensional fluidized bed reactors using an Euler–Lagrange approach

Biomass thermochemical conversion, often done in fluidized beds, recently gained a lot of attention due to its potential to efficiently produce renewable liquid fuels. Optimization of reactor design and operating conditions, however, requires a fundamental understanding of bed dynamics. In this work, a numerical framework based on an Euler–Lagrange approach is developed and used to perform and analyze large-scale simulations of two- and three-dimensional periodic fluidized beds. Collisions are handled using a soft-sphere model. An efficient parallel implementation allows one to explicitly track over 30million particles, which is representative of the number of particles found in lab-scale reactor, therefore demonstrating the capability of Lagrangian approaches to simulate realistic systems at that scale. An on-the-fly bubble identification and tracking algorithm is used to characterize bubble dynamics for inlet velocities up to 9 times the minimum fluidization velocity. Statistics for gas volume fraction, gas and particle velocities, bed expansion, and bubble size and velocity, is compared across the two- and three-dimensional configurations, and comparison with literature data generally shows good agreement. The wide distribution of gas residence times observed in the simulations is linked to the different gas hold-up characteristics of the gas–solid system.

Maximum entropy estimation of the bubble size distribution in fluidized beds

This work presents a new methodology, based on the maximum entropy method, to obtain bubble characteristics in fluidized beds. The probability distributions (PDF) of bubble pierced length and velocity are obtained applying the maximum entropy principle to experimental measurements. In addition, the bubble diameter distribution has been inferred from experimental pierced length measurements. This method is applied to characterize bubbles in fluidized beds for the first time and the most general bubble geometry, a truncated spheroid, is considered. The distance between probes, s , which is the minimum pierced length that is possible to measure accurately using intrusive probes, has been introduced as a constraint in the derivation of the size distribution equation. The maximum entropy method is applied to experimental measurements of bubble characteristics carried out using optical and pressure probes in a three-dimensional fluidized bed of Geldart B particles. Results on bubble size obtained from pressure and optical probes are very similar, although optical probes provide more local information and can be used at any position in the bed. The maximum entropy principle has been found to be a simple method that offers many advantages over other methods applied before for size distribution modeling in fluidized beds.

CFD simulation of fluidization quality in the three-dimensional fluidized bed

Multiphase computational fluid dynamics (CFD) has become an alternative method to experimental investigation for predicting the fluid dynamics in gas–solid fluidized beds. The model of Brandani and Zhang, which contains additional terms in both the gas- and solid-phase momentum equations, is employed to explore homogeneous fluidization of Geldart type A particles and bubbling fluidization of Geldart type B particles in three-dimensional gas-fluidized beds. In this model, only a correlation for drag force is necessary to close the governing equations. Two kinds of solids, i.e., fine alumina powder ( d p = 60 μm and ρ p = 1500 kg/m 3) and sand ( d p = 610 μm and ρ p = 2500 kg/m 3), are numerically simulated in a rectangular duct of 0.2 m (long) × 0.2 m (wide) × 0.5 m (high) size. The results show good agreement with the classic theory of Geldart.

Numerical simulation of horizontal jet penetration in a three-dimensional fluidized bed

The introduction of reactant gas as a jet into a fluidized bed chemical reactor is often encountered in various industrial applications. Understanding the hydrodynamics of the gas and solid flow resulting from the gas jet can have considerable significance in improving the reactor design and process optimization. In this work, a three-dimensional numerical simulation of a single horizontal gas jet into a cylindrical gas–solid fluidized bed of laboratory scale is conducted. A scaled drag model is proposed and implemented into the simulation of a fluidized bed of FCC particles. The gas and particles flow in the fluidized bed is investigated by analyzing the transient simulation results. The jet penetration lengths of different jet velocities have been obtained and compared with published experimental data as well as with predictions of empirical correlations. The predictions by several empirical correlations are discussed. A good agreement between the numerical simulation and experimental results has been achieved.

Digital image analysis of hydrodynamics two-dimensional bubbling fluidized beds

A new method of digital image analysis has been developed to study the hydrodynamics of two-dimensional bubbling fluidized beds with a digital video camera. The method comprises simultaneous of the size and velocity of gas bubbles, and the axial and radial distribution of bubble voidage. It provides a better estimation of the visible bubble flow than from local probe methods. Also a good estimation of the throughflow can be gotten, which is of great importance for combustor applications. Parallel to the approach of Darton et al. (Transactions of the Institution Chemical Engineering 55 (1977) 274) for three-dimensional fluidized beds, an equation for the bubble diameter of two-dimensional beds is developed, D b=0.89[(U 0−U mf) (h+3.0 A 0/t)] 2/3 g 1/3, where h is the bed height above air distributor; t is the thickness of the two-dimensional bed. For Group B particle and a given gas velocity U 0, if the bed height is sufficient, bubble diameter D b could be able to reach a maximum value at a certain height. The height is defined as the maximum bubble height h ∗ , beyond which bubbles do not grow further and become unstable and break up. The height h ∗ is a particle-size dependency, and can be expressed as h ∗=A(1+3 exp(−U 0/U mf))D t, where A=0.45 and D t is the bed diameter. The bubble rising velocity U b can be described by U b=Φ gD b (Φ=0.80−1.0) within the height h ∗ . Also, the bubble velocity is kept constant beyond the height h ∗ . The bubble density δ b is not uniform over the bed cross-section. It increases with particle size, and increases quite slowly for high fluidization velocities. The gas throughflow decreases much slowly along with the bed height. Beyond the height h ∗ , the gas throughflow is almost kept constant. Also, the throughflow is a significant part of the total gas flow, especially for high fluidization velocity, and increases almost linearly with the fluidization velocity.