Dense Gas-solid Fluidized Bed Research Articles

Multi-scale simulation of particle density effects on hydrodynamics in dense gas-solid fluidized beds

Gas-solid fluidization has gained prominence in chemical engineering, particularly for processes involving high-density particles. However, a notable dearth of research on the fundamental fluidization of high-density particles exists, distinct from the well-studied low-density particles. This knowledge gap presents significant challenges in designing and operating fluidized beds for such processes. In this study, we employ the CPFD scheme to comprehensively investigate how particle density affects hydrodynamics. Simulation results consistently align with experiments for pressure drop and minimum fluidization velocity, underscoring the model reliability. Importantly, typical empirical correlations for predicting minimum fluidization velocity display substantial inaccuracies, particularly for high-density particles. Additionally, we identify marked disparities in fundamental fluidization behavior between high and low-density particles, with increasing density leading to deteriorating fluidization performance, characterized by larger bubbles, defluidized regions, gas streaming, and reduced bed expansion ratios. Investigating high-density particle gas-solid fluidization systems promises valuable theoretical insights, bridging the gap between theory and practice.

Comparative CFD modeling of a bubbling bed using a Eulerian–Eulerian two-fluid model (TFM) and a Eulerian-Lagrangian dense discrete phase model (DDPM)

Eulerian–Eulerian and Eulerian-Lagrangian numerical approaches are both widely used to investigate hydrodynamic behavior in dense gas-solid fluidized bed reactors, yet there has been a lack of comparative investigations involving the two. Therefore, the present work compares the numerical performance of a two-fluid model (TFM) and a dense discrete phase model (DDPM) in describing the hydrodynamic behavior of a pilot-scale bubbling bed reactor. The effects of several different parameters – drag force, grid size, fluid time-step, time-averaging interval, particle-wall specularity coefficient, particle-particle restitution coefficient, particle-wall reflection coefficient, and numbers of parcels (the latter two parameters only for the DDPM) – are investigated and compared for the two approaches using two-dimensional (2D) simulations. The numerical results for both models indicate that sub-grid drag correction based on the energy minimization and multiscale (EMMS) theory is the most essential modeling parameter to account for the multiscale structures (i.e., bubbles and void spaces) and to resolve the axial and radial solid distributions. Both the TFM and DDPM, coupled with the EMMS/bubbling drag, predict similar hydrodynamics behavior; however, the better accuracy in terms of axial and radial solids concentration profiles is achieved from the TFM approach. Further, our grid size analysis results indicate that the DDPM generates a better grid-independent solution than the TFM. This important advantage of the DDPM over TFM makes it a suitable candidate for large-scale industrial applications by employing it on much coarser grids. Meanwhile, the results from the time-step, time-averaging interval, specularity coefficient, restitution coefficient, reflection coefficient, and numbers of parcels represent a minor effect on the overall hydrodynamics behavior of the pilot-scale bubbling bed reactor.

Study of particle residence time in a pressurized fluidized bed with in-bed heat exchanger tubes

Anthropogenic climate change is amongst the greatest of challenges to human civilization. A key area that will play a large role in mitigating its effects are clean fossil fuel applications. Clean coal combustion can be achieved with an oxygen-fired pressurized fluidized bed combustor incorporating carbon capture and storage. In relation to pressurized fluidization processes, understanding the influence of pressure on fluidized bed hydrodynamics and, in turn, their effect on parameters including fuel residence time is essential. For the combustor under consideration here, a fraction of the heat exchanger boiler tubes are submerged in the fluidized bed such that the effect of the horizontal tube bundle on the fuel residence time is of great importance. The main focus of the present work was to evaluate the impact of gas velocity, pressure, presence or absence of a horizontal tube bundle and fuel feed rate on the average fuel residence time in a dense gas-solid fluidized bed. Experiments were conducted under cold flow conditions in a pressurized fluidized bed with an inner diameter of 0.15 m. The fluidization material was large glass beads (1.0 mm in diameter) while fuel particles were simulated with smaller glass beads (64 and 83 μm in Sauter mean diameter) that were susceptible to entrainment. Operating pressures and superficial gas velocities were maintained between 101.3 and 1200 kPa and 1.5 and 3.2 Umf, respectively. To simulate continuous fuel injection, experiments were conducted with the fuel surrogate particles being continuously fed to the fluidized bed of large particles over a desired period of time. Downstream, entrained particles were captured to determine the average entrainment rate and average mass of fuel particles inside the fluidized bed at steady state, which yielded the average fuel residence time. The combination of elevated pressure with the tube bundle present was found to have the most influential impact when compared to base conditions of atmospheric pressure and with no tube bundle present. It was found to enhance gas bubble break up and reduce the average gas bubble size substantially. In turn, this increased the average residence time of 83 μm particles by nearly three-fold in comparison to the case of atmospheric pressure with no tube bundle present. The effect of gas velocity on particle residence time was not found to be statistically significant under the range tested. Similarly, the effect of increasing fuel feed rate by 50% had no statistically significant impact.

Borescopic particle image velocimetry in bubbling gas–solid fluidized beds

In this work, the borescopic particle image velocimetry (BPIV) technique was applied to a bubbling gas–solid fluidized bed, and the results were compared with published positron emission particle tracking (PEPT) measurement data. Before performing the experiments, the sensitivity of the BPIV results to the illumination power, light reflectivity of the particles, and location of the borescope was also investigated. The BPIV and PEPT results were in fair agreement; however, some discrepancies were observed. The difference between the two sets of results were mainly caused by the intrusiveness of BPIV, the fact that the local solids volume fraction was not accounted for in the BPIV analysis, and the intrinsic differences of these two methods. Therefore, measurement of the local solids volume fraction with the borescope is highly recommended for further development of the BPIV method, which will also enable measurement of the local solids mass fluxes inside dense gas–solid fluidized beds.

Hydrodynamics of dense gas-solid fluidized beds with immersed vertical membranes using an endoscopic-laser PIV/DIA technique

The hydrodynamic behavior of a bubbling gas-solid fluidized bed with vertically immersed membrane tubes has been studied using an endoscopic-laser PIV/DIA technique. The solids mass flux and hold-up profiles were determined together with the bubble phase properties (equivalent bubble diameter and bubble rise velocity) for different operating conditions and different membrane bundle configurations. The obtained results revealed that the lateral solids motion can be significantly hampered due to the presence of the membrane tubes resulting in a very high solids hold-up near the walls and much diluted regions in the middle of the bed. The obtained results from the experiments with a different number of membranes, membranes with a different outer diameter, and positioned with the bottom of the bundle at different axial positions in the bed, give guidelines to optimize the membrane configurations to achieve the highest lateral gas dispersion and optimal bubble breakage. These experimental results have also demonstrated the very important effect of tube spacers on the hydrodynamics. Moreover, the analysis of the bubble phase properties confirmed the enormous decrease in equivalent bubble diameter (up to a factor 3.5) for fluidized beds with immersed vertical membranes with spacers in comparison with a fluidized bed without internals, showing the great potential for improvement of the bubble-to-emulsion phase mass transfer rate.This work has been selected by the Editors as a Featured Cover Article for this issue.

Hydrodynamics and heat transfer around a horizontal tube immersed in a Geldart b bubbling fluidized bed

In dense gas–solid fluidized beds the heat transfer to immersed objects is strongly coupled to the hydrodynamic behavior. The objective of this study is to experimentally and numerically assess the heat transfer coefficient around a horizontal tube in a Geldart B bubbling fluidized bed and derive a numerical-correlative approach for predicting the angular dependent heat transfer coefficient. The considered system consists of corundum as the solid bed material and air as the fluidization gas, entering the cylindrical geometry through a Tuyere nozzle distributor. Experimental data are obtained from a pilot scale test-rig with different tubular heat transfer probes and evaluated in a comprehensive uncertainty analysis. The resulting magnitude and angle dependent variations of the heat transfer coefficient at different superficial gas velocities are compared to three dimensional numerical simulations. The applied CFD model of the fluidized bed treats both gas and powder as Eulerian phases. The size distribution of the particles is described by two granular phases with corresponding mean diameters and a sphericity factor to account for their non-spherical shape. The fluid–solid interactions in this Multi Fluid Model are considered by incorporating the Kinetic Theory of Granular Flow and a sphericity-adapted drag model. The hydrodynamics at the tube surface, e.g. solid volume fraction, gas and particle velocities, are used for a novel numerical-correlative calculation of the angle dependent heat transfer coefficient between the bed material and the immersed tube. Special focus is set on depicting the particle contact time at the tube surface appropriately. The numerical results show the correct tendency of an increasing heat transfer coefficient with rising gas velocity and are partially in good agreement with the experimental observations.

Analysis of interaction between bubbles and particles in a dense gas-vibro fluidized bed

Gas-solid fluidized beds are widely used for their excellent characteristics of heat and mass transfer. An active pulsating air flow is introduced into a dense gas-solid fluidized bed, forming a dense gas-vibro fluidized bed (DGVFB), to modify the fluidization quality. Interaction between the bubbles and particles in the DGVFB was investigated based on the results of numerical simulations and experiments. Micro-bubbles in the DGVFB were regarded as springs, and therefore, the interaction between the bubbles and particles was considered to be equivalent to a linear vibration system with n degrees of freedom. A dynamic model for the vibration system was developed, and modal analysis was conducted. Results of this theoretical analysis showed that the dominant frequency of pressure fluctuations in the DGVFB was equal to the frequency of active pulsating air flow. The dynamic model described the interaction between the bubbles and particles effectively in the DGVFB at low gas pulsating frequency, and shallow fluidized beds.

Modification of kinetic theory of granular flow for frictional spheres, Part I: Two-fluid model derivation and numerical implementation

We derive a kinetic theory of granular flow (KTGF) for frictional spheres in dense systems, including rotation, sliding and sticking collisions. We use the Chapman–Enskog solution procedure of successive approximations, where the single-particle velocity distribution is assumed to be nearly Maxwellian both translationally and rotationally, as assumed by McCoy et al. (1966). An expression for the first-order particle velocity distribution function is derived, which includes the effects of particle rotation and friction. Using a simple moment method, balance equations for mass, momentum and energy are derived with closure equations for viscosities, and thermal conductivities and collisional energy dissipation rates of angular and translational kinetic energy. Because the internal angular momentum changes are coupled to the flow field, the stress tensor contains anti-symmetric components which are associated with a rotational viscosity. In the resulting closure equations, the rheological properties of the particles are explicitly described in terms of the friction coefficient. The model has been incorporated into our in-house two-fluid model (TFM) code for the modeling of dense gas–solid fluidized beds. For verification, a comparison of the present model in the limit of zero friction with the original (frictionless) KTGF model is carried out. Simulation results of both models agree well. In the next part, simulation results obtained with the new model will be compared with experimental data and discrete particle model (DPM) simulations.

Eulerian–Eulerian simulation of irregular particles in dense gas–solid fluidized beds

As an important and essential physical property, particle shape affects fluidization characteristics of dense gas–solid fluidized beds greatly. However, numerical studies of irregular particles in gas–solid fluidization, especially using Eulerian–Eulerian model, are relatively scarce, primarily due to the lack of an appropriate inter-phase drag model. To this end, a simple and effective drag model was proposed in this work to address the critical role of particle shape in determining the inter-phase drag force. This drag model features the usage of Ganser correlation and Ergun correlation, respectively, in dilute and dense solid concentration conditions. Moreover, particle sphericity is introduced as a concise shape descriptor, and can be calibrated by experimentally measured minimum fluidization velocity and the corresponding voidage. To verify the established numerical model, experimental study was also conducted in a lab-scale three-dimensional rectangular bed filled with irregular Geldart group B particles. Other two kinds of irregular bed materials from open literature were investigated as well to provide further validation. The predicted results using the proposed drag model are overall in relatively better quantitative agreement with the experimental data or available empirical correlations, in terms of both macro-scale and micro-scale behavior. In contrast, the numerical model with the drag force assuming perfectly spherical particles completely fails to reproduce the experimental hydrodynamics of the gas–solid fluidized bed. In addition, sensitivity analysis of the proposed drag model demonstrated its weak sensitivity to the minimum fluidization characteristics of particles. The sufficient comparison and analysis indicated that the proposed drag model together with the estimation method of particle sphericity is quite reasonable and convenient for Eulerian–Eulerian simulation of irregular particles behavior in lab-scale dense gas–solid fluidized beds.

Experimental investigation of cluster properties in dense gas–solid fluidized beds of different diameters

The local solid flow structure of a bubbling fluidized bed of sand particles was investigated in three different columns to characterize the properties of clusters. The experiments were performed using a reflective optical fiber probe. The variations in size, velocity, and void fraction of the clusters due to changes in the superficial gas velocity, particle size, and radial positions were studied. The results indicate that the velocity of the clusters remained unchanged while their size increased as the column diameter increased. In addition, the radial profile of the clusters’ velocity did not depend on the radial position. The results indicate that larger particles form larger clusters, which move slower.

Fluidization Characteristics of the Dense Gas-Solid Fluidized Bed Separator Based on the Mixed-Medium Solids of Magnetite and Paigeite Powder

Fluidization characteristics of the mixed magnetite and paigeite powder were studied by the combination approach of numerical simulation and experimental verification to optimize the design of the medium solids used in the dense gas-solid fluidized bed separator (DGSFBS). The experimental results showed that the favorable fluidization performance could be achieved with the weight proportion of paigeite powder in the mixture 25% ≤ α ≤ 35%, while the relative deviation in the bed density should be Δρ ≤ 0.025 g/cm3. The corresponding simulation results were obtained by selecting suitable mathematical models and parameters. It also indicated that the fluidized bed with mixed solids could provide a good fluidization performance and stable density distribution. The laboratory-scale DGSFBS was used to conduct the separation experiments on raw coal with size range of 13–6 mm and ash content of 33.43%. With the parameter α = 30%, the experiment resulted in the coal ash content being reduced from 33.43% to 11.63% with a probable error, E P of 0.07 and a recovery efficiency of 98.59%. Utilization of either magnetite or paigeite powder alone was not effective; however, fluidization performance and separation efficiency of DGSFBS improved with the utilization of mixed solids.

Gas jet penetration lengths from upward and downward nozzles in dense gas–solid fluidized beds

Abstract The penetration lengths of a jet issuing from upward and downward injection nozzles were measured in a dense fluidized bed of Geldart A to Geldart B particles, operated at superficial velocity well beyond the minimum bubbling velocity. Nozzle orientation, injection velocity and injected gas density were found to be the parameters having the most influence on the jet penetration lengths. Three distinct jet penetration lengths were determined for the upward nozzle: Lmin, Lmax and Lb, in accordance with Knowlton and Hirsan's (1980) definition [1], while for the downward nozzle, only Lmin and Lmax were observed. The jet penetration lengths were correlated with respect to dimensionless groups in a systematic approach in an effort to identify the most important terms. For each nozzle orientation, the analysis yielded unique correlation format which could be applied to each characteristic jet length by changing the correlation parameters. Fundamental distinctions between the upward and downward nozzles were uncovered. The mechanism responsible for the jet momentum dissipation was found to be gravitational forces acting on the jet volume for the upward nozzle and drag forces exerted on the entrained particles for the downward nozzle. Five new correlations were derived for the prediction of the characteristic jet lengths for upward and downward nozzles. The correlations retained for the upward nozzle were also found to be in good agreement with data from a high pressure fluidized bed.

Novel phenomenological discrete bubble model of freely bubbling dense gas–solid fluidized beds: Application to two‐dimensional beds

AbstractA phenomenological discrete bubble model has been developed for freely bubbling dense gas–solid fluidized beds and validated for a pseudo‐two‐dimensional fluidized bed. In this model, bubbles are treated as distinct elements and their trajectories are tracked by integrating Newton's equation of motion. The effect of bubble–bubble interactions was taken into account via a modification of the bubble velocity. The emulsion phase velocity was obtained as a superposition of the motion induced by individual bubbles, taking into account bubble–bubble interaction. This novel model predicts the bubble size evolution and the pattern of emulsion phase circulation satisfactorily. Moreover, the effects of the superficial gas velocity, bubble–bubble interactions, initial bubble diameter, and the bed aspect ratio have been carefully investigated. The simulation results indicate that bubble–bubble interactions have profound influence on both the bubble and emulsion phase characteristics. Furthermore, this novel model may become a valuable tool in the design and optimization of fluidized‐bed reactors. © 2012 American Institute of Chemical Engineers AIChE J, 2012

CFD modeling of particle–particle heat transfer in dense gas-solid fluidized beds of binary mixture

This paper presents a computational investigation of heat transfer, especially the direct particle–particle heat transfer between different particle classes in a dense gas–solid fluidized bed of binary particles using a computational fluid dynamics (CFD) method. A particle–particle heat transfer model between different particle classes is proposed in a gas–solid fluidized bed. By incorporating it into the multi-fluid model, a Eulerian–Eulerian CFD model is established. The heat transfer in a fluidized bed containing binary particles is thus investigated. The results indicated that particle–particle heat exchange coefficient between different particle classes increases with increasing large particle size and superficial gas velocity. However, it first increases and then decreases with increasing the large particle content in the fluidized bed. Gas–particle heat transfer is still the dominant heat transfer mode in the fluidized bed of binary particles. The ratios of particle–particle heat transfer to gas–particle heat transfer range from 1.27% to 3.09% for various operating conditions.

Direct numerical simulation of complex multi-fluid flows using a combined front tracking and immersed boundary method

In this paper a simulation model is presented for the Direct Numerical Simulation (DNS) of complex multi-fluid flows in which simultaneously (moving) deformable (drops or bubbles) and non-deformable (moving) elements (particles) are present, possibly with the additional presence of free surfaces. Our model combines a Front Tracking (FT) model developed by van Sint Annaland et al. (2008. Numerical simulation of dense gas–solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47–70.) and an Immersed Boundary (IB) model developed by van der Hoef et al. (2008. Numerical simulation of dense gas–solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47–70.) The FT part circumvents the explicit computation of the interface curvature. The IB part incorporates both particle–fluid and particle–particle interaction via a direct forcing method and a hard sphere Discrete Particle (DP) approach. In our model a fixed (Eulerian) grid is utilised to solve the Navier–Stokes equations for the entire computational domain. The no-slip condition at the surface of the moving particles is enforced via a momentum source term that only acts in the vicinity of the particle surface. For the enforcement of the no-slip condition Lagrangian force points are used, which are distributed evenly over the surface of the particle. Dissipative particle–particle and/or particle–wall collisions are accounted via a hard sphere DP approach using a three-parameter particle–particle interaction model accounting for normal and tangential restitution and tangential friction. The capabilities of the hybrid FT-IB model are demonstrated with a number of examples in which complex topological changes in the interface are encountered.

Particle Velocity in a Dense Gas-Solid Fluidized Bed

The upflowing and downflowing particle velocities are investigated by using a two-optical fiber probe system in the dense gas-solid fluidized bed with an inner diameter of 0.185 m and a height of 3.000 m. Two kinds of glass ballotinis, belonging to Geldart type B classification, are selected as solid material. Experiments are conducted under different operating gas velocities, static bed heights, and particle diameters. The results indicate that the upflowing particle velocity is a strong function of operating gas velocity and particle diameter, while the downflowing particle velocity depends mainly on the operating gas velocity. When the ratio of the operating gas velocity to the minimum fluidization velocity of the particles keeps the same constant, the effect of the particle diameter on the upflowing and downflowing particle velocities can be ignored. Both direction and size of the solid particle velocity are related to the bubble behaviors in the fluidized bed, and the upflowing particle velocity is lower than the bubble rise velocity. Furthermore, the across-sectional, non-uniform flow structure in the bed increases slightly with increasing static bed height at the high operating gas velocity.

Computational fluid dynamics for dense gas-solid fluidized beds: a multi-scale modeling strategy

Dense gas-particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic and is related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas-particle flows both (effective) fluid-particle and (dissipative) particle-particle interactions need to be accounted for because these phenomena to a large extent govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas-solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid-particle and particle-particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid-particle (lattice Boltzmann model) and particle-particle (discrete particle model) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig.1) involves the lattice Boltzmann model, the discrete particle model, the continuum model based on the kinetic theory of granular flow, and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.

Computational fluid dynamics for dense gas–solid fluidized beds: a multi-scale modeling strategy

Dense gas–particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic, which can be related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas–particle flows both (effective) fluid–particle and (dissipative) particle–particle interactions need to be accounted for because these phenomena, to a large extent, govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas–solid contact and as a direct consequence thereof strongly affect the performance of the process. Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid–particle and particle–particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid–particle (lattice Boltzmann model (LBM)) and particle–particle (discrete particle model (DPM)) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1) involves the LBM, the DPM, the continuum model based on the kinetic theory of granular flow, and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.

Effect of Pulsating Gas Injection on Granular Flow in Gas-Solid Fluidized Beds.

We performed two-dimensional DEM simulation to investigate the effcts of pulsating gas injection on the flows in dense gas-solid fluidized bed. Geldart D particles were assumed as the solid particles. The effects of the mean gas velocity, the frequncy and the amplitude of the gas injestion were examined. To evaluate the effects quantitatively, we analyzed the transport properties of the predicted granular flows, such as granular convection energy or fluctuating energy of particles. The present simulation showed that the pulsation promotes the granular convection for moderate pulsation frequencies and the predicted flow properties saturated for the variation of the pulsation frequencies in the high frequency region. We proposed an equation to estimate the relaxation time scale of the beds for the fluctuation of gas velocity based on Ergun's equation. The estimated relaxation time scale agreed well with the predicted saturation frequency of the bed.

Mesoscopic approach to correlate surface heat transfer coefficients with pressure fluctuations in dense gas-solid fluidized beds

A dimensionless frequency number, N f (ƒd p 2/α c) , is proposed to understand better and predict the bed-to-surface heat transfer coefficients in dense gas-solid fluidized beds. A total of 756 sets of pressure signals were acquired simultaneously with the measurement of local, time-averaged bed-to-surface heat transfer coefficients. The experimental matrix included 3 different locations for the pressure probes, 13 different powders, (with d sv in the range 20 μm–1789 μm), 3 powders at least, in each of Geldart A, B and D categories, two different distributor plates, and a wide range of fluidization velocities (up to 2.4 m/s). Fast Fourier Transforms were utilized to analyze and interpret the pressure signals. First principle models that retain picture of Mickley and Fairbank's [H.S. Mickley, L.R. Fairbanks, AIChEJ. 3 (1995) 374] packet theory were scaled into mesosopic correlations. The experimental data were compared with the mesoscopic correlations derived from first principles models.