Solids Mass Flux Research Articles

A computational particle fluid-dynamics simulation of hydrodynamics in a three-dimensional full-loop circulating fluidized bed: Effects of particle-size distribution

A computational particle fluid-dynamics model coupled with an energy-minimization multi-scale (EMMS) drag model was applied to investigate the influence of particle-size distribution on the hydrodynamics of a three-dimensional full-loop circulating fluidized bed. Different particle systems, including one monodisperse and two polydisperse cases, were investigated. The numerical model was validated by comparing its results with the experimental axial voidage distribution and solid mass flux. The EMMS drag model had a high accuracy in the computational particle fluid-dynamics simulation of the three-dimensional full-loop circulating fluidized bed. The total number of parcels in the system (Np) influenced the axial voidage distribution in the riser, especially at the lower part of the riser. Additional numerical simulation results showed that axial segregation by size was predicted in the two polydisperse cases and the segregation size increased with an increase in the number of size classes. The axial voidage distribution at the lower portion of the riser was significantly influenced by particle-size distribution. However, radial segregation could only be correctly predicted in the upper region of the riser in the polydisperse case of three solid species.

Mechanism analysis of the solids holdup variations in downer reactors based on volumetric flux

Solids volumetric flux (Vs), which is expected to replace the solids mass flux (Gs) as the key factor influencing solids holdup in circulating fluidized beds, was proposed to investigate the solids holdup variation and predict the extreme operation conditions in the downers. In this work, by using more than 400 sets of experimental data from different literature in Response Surface Methodology (RSM) analysis, it is found that the overestimation of particle density effect on the solids holdup can be avoided by converting the Gs into Vs. Further studies indicated that the difference of solids holdup (Δεs) resulted from the different types of particles increased with the increase in Vs as well as the decrease in superficial gas velocity (Ug). Based on the normalized fitting results, the effects of different factors on the solids holdup were characterized. It is concluded that the effect extent was in the order of Vs > Ug >> particle size (dp) > particle density (ρp), which provided a guidance to control the solids holdup to satisfy the requirements in the downer by adjustment of various parameters, that is, Vs and Ug can adjust solids holdup roughly whereas dp and ρp can adjust solids holdup finely. Meanwhile, it is found that the upper limit of solids volumetric flux (Vs,max) can be increased by the increase of Ug, dp and/or ρp. In addition, it is considered that using Vs to replace Gs to define high-density operation in the downer could be more suitable in this study.

LDV measurements of particle velocity distribution in an annular stripper

Abstract Particle descent velocities in an annular stripper were measured by a laser Doppler velocimetry (LDV) system. In the radial direction, particle descent velocity was relatively constant in the mid-region of the stripper and increased towards the walls on both sides, exhibiting an anti-U-shaped distribution. Particle descent velocity in the radial mid-region increased with the increase of superficial gas velocity, and the maximum in the outer wall region increased significantly with the increase of solid mass flux. Superficial stripping gas velocity had stronger effect on particle velocity distributions near the stripper gas distributor, and such effect weakened with the increase of the distance from the distributor. Local particle velocity and its radial profiles could be adjusted by changing the superficial stripping gas velocity. Empirical formulas were established to describe the relationships between the local particle velocity and cross-sectional averaged velocity based on the effects of operating conditions and measuring positions. The result showed that the predicted data was in good agreement with the experimental value.

Computational fluid dynamics simulation of system hydrodynamics in a riser of stage circulating fluidized bed reactor

AbstractThe riser of conventional and stage circulating fluidized bed reactors were simulated using computational fluid dynamics. The objective was to examine the design parameter effects using a 23 statistical experimental design method. The results showed that number of reactor stages had the highest effect on the standard deviation of the solid volume fraction (SVF), the average SVF, and standard deviation of gas temperature in a horizontal direction. In addition, the reactor wall temperature had the highest effect on the average holding time of catalysts. Increasing the number of reactor stages could reduce the back‐mixing and increase the system turbulence. The average vertical and horizontal solid particle velocities in the reactor stage region were higher than in the other regions. At the reactor stage region, peaks in the gas temperature were observed. The advantages of a stage reactor were confirmed to be applied in all the operating condition cases, independent of the solid particle mass flux.

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.

Residence time distribution of particles in circulating fluidized bed risers

Solids Residence Time Distribution (RTD) in Circulating Fluidized Bed (CFB) risers has received increasing attention due to its vital role in determining the operating condition, particle property, and reactor geometry in industrial CFB applications. In recent years, various solids RTD experimental techniques and theoretical models have been utilized and proposed to study CFB risers. Some controversial issues, however, also arose in the open publications. By means of exploring the advantages and disadvantages of each available RTD experimental technique and model when they are applied to particles in CFB risers, this study discussed the primary causes leading to the huge discrepancy in magnitude of solids dispersion coefficient and Peclet number, which can achieve 4 orders or span from 1 to 100. On the basis of the massive experiment data collected from the literature, the variations of average residence time, Peclet number and dispersion coefficient of solids with superficial gas velocity, solids mass flux and solids concentration were presented. By applying the transition of flow regime in CFB mode, we provided a helpful way to explain some existing contradictions in the reported effects of operating conditions on solids RTD. The possible reasons were also summarized to clarify why some researchers measured a double- or multi-peak solids RTD curve and the others could not in a similar situation.

Coarse grid simulation of the hydrodynamics of binary gas‐solid flow in CFB risers

AbstractCFD simulation has become an effective way to study the mixing and segregation characteristics of gas‐solid flow in CFB risers, which is important for the proper operation and design of such reactors. In this study, the numerical solution of a recently developed EMMS drag model for binary gas‐solid flow which considers the effect of particle clustering structures on the interphase drag forces was first improved, it was then coupled with a multifluid model to perform extensive 3D simulations of the mixing and segregation pattern of binary gas‐solid flow in CFB risers. It was shown that the experimental data of axial solid concentration profiles and radial solid mass flux distributions can be captured reasonably by the combined EMMS‐multifluid model, indicating that the model is able to reproduce the hydrodynamics of complex gas‐solid flow with particle size distribution.

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.

Heat transfer and gas-solid behaviors in pneumatic transport reactor used of carbon capture system

A pneumatic transport reactor can be used for continuous carbon capture processes using a dry sorbent because it can handle large quantities of flue gas. To design efficient reactors, it is necessary to understand the internal characteristics of a reactor with a complicated gas-solid flow. Computational fluid dynamics using an Eulerian-Eulerian approach was adopted to simulate gas-solid two-phase flow to better understand the gas-solid behaviors and heat transfer characteristics in a pneumatic transport reactor. Numerical simulations were used to analyze the pressure difference, solid mass flux, and heat transfer coefficient. The results showed that the gas-solid behavior was unstable and that localized particle flow affects the heat transfer characteristics. The degree of particle mixing near the solid return inlet was lower than that at greater heights within the reactor; in the inlet region, the heat transfer coefficient is not uniform in accordance with the non-uniformity of solid particle behavior.

Experiments on particle cluster behaviors in a fast fluidized bed

A three-dimensional (3D) fast fluidized bed with the riser of 3.0 m in height and 0.1 m in inner diameter was established to experimentally study the cluster behaviors of Geldart B particles. Five kinds of quartz sand particles (dp = 0.100, 0.139, 0.177, 0.250 and 0.375 mm and ρp = 2480 kg·m− 3) were respectively investigated, with the total mass of the bed material kept as 10 kg. The superficial gas velocity in the riser ranges from 2.486 to 5.594 m·s− 1 and the solid mass flux alters from 30 to 70 kg·(m− 2·s)− 1. Cluster characteristics and evolutionary processes in the different positions of the riser were captured by the cluster visualization systems and analyzed by the self-developed binary image processing. The results found four typical cluster structures in the riser, i.e., the macro stripe-shaped cluster, saddle-shaped cluster, U-shaped cluster and the micro cluster. The increasing superficial gas velocity and particle sizes result in the increasing average cluster size and the decreasing cluster time fraction, while the solid mass flux in the riser have the reverse influences on the cluster size and time fraction. Additionally, clusters in the upper region of the riser often have the larger size and time fraction than that in the lower region. All these effects of operating conditions on clusters become less obvious when particle size is less than 0.100 mm.

On the internal solids circulation rates in freely-bubbling gas-solid fluidized beds

The solids mass flux distribution and internal solids circulation rates in freely-bubbling gas-solid fluidized beds has been studied in detail in a pseudo-2D column. A non-invasive Particle Image Velocimetry (PIV) combined with Digital Image Analysis (DIA) technique has been further extended to investigate and quantify the gas and solids phase properties simultaneously for different particle types and sizes (all Geldart B type) at different fluidization velocities. It is found that the solids fluxes increase strongly, practically linearly, as a function of the vertical position and depend on the excess gas velocity but not on the particle size, while the most often used phenomenological two-phase fluidized bed models assume the vertical solids fluxes to be constant. To further investigate this important discrepancy, the underlying assumptions of the phenomenological models have been validated, especially concerning the average solids fraction inside the bubbles, the laterally and time-averaged axial bubble fraction profile (or visual bubble flow rate) and the wake parameter (the amount of solids carried along a bubble relative to the bubble volume). To this end, the PIV/DIA technique was further extended and a new method for the determination of the wake parameter is proposed. From the experimental results, it was concluded that i) the average solids fraction inside the bubbles is about 2.5–3% for glass beads and alumina particles and is practically independent of the excess gas velocity and particle size; ii) the measured laterally and time-averaged bubble fractions are considerably lower compared to often used correlations from literature, which would lead to a significant over-prediction of the visual bubble flow rate and iii) the wake parameter depends strongly on the bubble size and with the developed correlation the axial solids mass fluxes as a function of the vertical position can be well described. Finally, the influence of these findings was evaluated by performing a sensitivity analysis with an existing phenomenological model for fluidized beds with the new values and closures considering the case of the heterogeneously catalyzed steam methane reforming. With the developed findings and correlations the predictions with the two-phase phenomenological models can be further improved, especially concerning the hydrodynamics of the solids phase.

Effect of solid mass flux on anisotropic gas–solid flow in risers determined with an LES-SOM model

Within the framework of the two-fluid approach, gas was treated with a large-eddy simulation and a sub-grid-scale (SGS) turbulent kinetic energy model while particles were treated with a second-order-moment method to describe the anisotropy of the fluctuating velocity. A modified Simonin model was derived for the gas–solid interphase fluctuating energy transfer. The anisotropic gas–solid flow in a circulating fluidized bed was investigated. Predictions were in good agreement with experimental data. The distributions of the second-order moment of particles and SGS-turbulent kinetic energy of gas were simulated at different solid mass fluxes. The effects of the solid mass flux on the particle second-order moment, particle anisotropic behavior, gas SGS-turbulent kinetic energy and gas SGS energy dissipation were analyzed for the circulating fluidized bed.

Scaling-up down flow reactors. CPFD simulations and model validation

Abstract The present study reports a scaled-up down flow reactor study using 2.54-cm and 5.08-cm internal diameter units both utilizing Computational Particle Fluid Dynamics (CPFD) modeling and experimental data. The solid particles used are Fluid Catalytic Cracking (FCC) catalyst particles with a 84.42 μm mean diameter and a 1722 kg/m 3 particle density. The gas velocity and solid mass flux are varied from 1.1 to 2.0 m/s and from 7 to 50 kg/m 2 s, respectively. Experimental data is obtained using a CREC-GS-Optiprobe** sensors to be able to account for individual particle clusters. Data analysis involves the setting of the data baseline in compliance with solid mass balances. On the other hand, a CPFD method is applied to simulate the complex CFB downer fluid dynamics. With the CPFD method, cluster behaviour is extensively studied for a wide set of operating conditions. Cluster sizes are obtained experimentally for each of the operating conditions considered. CPFD simulations are compared with experimental results. Good agreement is observed in all cases, except in the near-wall region. It is also proven in the present study that, near-wall discrepancies between experimental findings and hybrid CPFD modeling predictions are significantly reduced in the 5.08-cm ID downer unit. Thus, it is anticipated that this hybrid CPFD model provides a fully trustable computational method for the scaling-up of industrial down flow reactor units with diameters larger than 5.08-cm ID.

Modifying the inter‐phase drag via solid volume fraction gradient for CFD simulation of fast fluidized beds

The conventional drag model in two‐fluid simulation, which assumes uniform particle distribution in a computational grid, overestimates the drag force, thus failed in capturing the subgrid‐scale strands and resolvable‐scale clusters. This work proposed a new modification to the conventional drag model through considering the heterogeneous distribution of solid volume fraction (SVF), especially, in the inter‐phase boundary (i.e., cluster boundary). The resulting drag model is a function of particle Reynolds number, SVF and the gradient of SVF. This straightforward modification is consistent with the elaborately filtered‐approach‐based modification method in nature. A CFD simulation for a two‐dimensional riser was conducted to validate the new drag model. The outlet solid mass flux, axial and radial time‐averaged voidages from the new drag model agreed well with the experimental measurements, and these results were far better than those from the conventional homogeneous drag models. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2588–2598, 2017

Solids flux measurements via alternate techniques in a gas-fluidized bed

A transportable fluidization column, operating under identical conditions at three different locations, was employed to compare three experimental solids flux measurement techniques for hydrodynamic characterization of gas-fluidized beds. This paper compares measurements of solids mass and momentum flux obtained by radioactive particle tracking at the Ecole Polytechnique, positron emission particle tracking at University of Birmingham, and borescopic high speed particle image velocimetry at PSRI, carried out with FCC particles of mean diameter 107μm. These techniques provided broadly similar time-average solids flux profiles, but there were significant quantitative differences. Analysis of the results, focusing on the fundamentals of each measurement technique, provides valuable insights into the reasons for the discrepancies. The results also add to a unique hydrodynamic database for validation of CFD and other models.

Gravity separation of ultra-fine iron ore in the REFLUXTM Classifier

The REFLUX™ Classifier is a recently developed water-based gravity separation technology that is already being used worldwide to beneficiate particles above 0.100 mm in size. This paper reports tests performed on an ultra-fine iron ore with nominal top size of 0.106 mm, but with 59 wt-% being below 0.038 mm in size. The REFLUX™ Classifier consists of a set of parallel inclined channels positioned above a vertical fluidised section. The Boycott effect generates a powerful throughput advantage and using narrow channels gives a high shear rate which generates a hydrodynamic lift force that helps to selectively re-suspend and elutriate the lower-density particles. The iron ore feed had a head grade of 35 wt-% FeT. At a low feed solids mass flux of 1.5 t m−2 h−1, the REFLUX™ Classifier produced high-grade products at a high recovery. Overall a grade of 66.1 wt-% FeT with Fe recovery of 80 wt-% could be achieved in a single-stage separation. Within the 0.020–0.038 mm size fraction, grades of 68.8 wt-% FeT were achieved with iron recoveries of 94.7 wt-%. Excellent recoveries of up to 57.0 wt-% were achieved even for the −0.020 mm size fraction.

Development of an endoscopic-laser PIV/DIA technique for high-temperature gas–solid fluidized beds

To enable the investigation of the hydrodynamics of gas–solid fluidized bed reactors at high-temperatures and reactive conditions, a new non-invasive experimental technique has been developed, based on the extension of Particle Image Velocimetry (PIV) coupled with Digital Image Analysis (DIA) using dedicated high-temperature endoscopes for image recording and laser illumination. The new endoscopic-laser PIV/DIA technique (ePIV/DIA) allows to determine simultaneously information from the emulsion and bubble phase with high spatial and temporal resolution in a pseudo-2D columns.The ePIV/DIA technique with single-source laser illumination has first been thoroughly validated at cold-flow conditions by comparison with a standard PIV/DIA technique with LED-illumination, showing very good agreement of the results in terms of particle velocity and solids mass flux profiles. The technique has subsequently been applied to fluidized beds in the bubbling fluidization regime at elevated temperatures to demonstrate its unique possibilities to measure detailed bed hydrodynamics at elevated temperatures.

Experimental and simulated solids mixing and bubbling behavior in a scaled two-section two-zone fluidized bed reactor

Digital Image Analysis techniques, a phenomenological Counter-Current Back-Mixing model (CCBM) and Two-Fluid Model (TFM) simulations were employed to evaluate the effect of scale on the Two-Section Two-Zone Fluidized Bed Reactors (TS-TZFBR) fluid dynamics, i.e. bubble characteristics, axial mixing of solids and defluidization phenomena. The reactor scaling did not affect the quality of the TFM bubble size predictions. A bubble size correlation previously proposed by the authors for TS-TZFBR units was able to predict the experimental axial bubble size evolution at the different reactor scales and gas velocities (ugas/umf=1.5–3.0) with a relative error under 17%. The TFM simulated axial solid mass fluxes were same order as these obtained by Particle Image Velocimetry for every reactor size. However, the classical CCBM model was unable to predict the effect of scale on the solids axial mixing in a TS-TZFBR. The inclination angle of the defluidized bed regions found within the TS-TZFBR tapered zone, β, increased by (ugas/umf)0.25 when duplicating the reactor size. Nevertheless, it did not exceed the prescribed upper limit of β=80° for any of the conditions tested.

Experimental evaluation and modeling of liquid jet penetration to estimate droplet size in a three-phase riser reactor

In this work, the effects of injecting an evaporating liquid jet into solid–gas flow are experimentally investigated. A new model (SHED model) and a supplementary model (spray model) have also been proposed to investigate some flow-field characteristics in three-phase fluidized bed with the mean relative error 4.3% between model and measured results. Some experiments were conducted to study the influences of flow-field parameters such as liquid volumetric flow rate, injection velocity, jet angle and gas superficial velocity as well as solid mass flux on the jet penetration depth (JPD). In addition, independent variables were experimentally employed to propose two empirical correlations for JPD by using multiple regression method and spray cone angle (SCA) by using dimensional analysis technique. The mean relative errors between the JPD and SCA correlations versus experimental data were 7.5% and 3.9%, respectively. In addition, in order to identify the variable effect, a parametric study was carried out. Applying the proposed model can avoid direct use of expensive devices to measure JPD and to predict droplet size.

Application of parallel distributed Lagrange multiplier technique to simulate coupled Fluid-Granular flows in pipes with varying Cross-Sectional area

Fluid-granular flows are common phenomena in nature and industry. Here, an efficient computational technique based on the distributed Lagrange multiplier method is utilized to simulate complex fluid-granular flows. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. The particle–particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEM method (Cundall and Strack, 1979) with some modifications using the volume of an overlapping region as an input to the contact forces. A parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library.Application of this method to simulate fluid-granular flows in pipes with a step decrease in cross-sectional area is discussed. Correlations between pressure losses and solid mass fluxes in a pipe for different particle concentrations, pipe diameters and particle sizes are studied. Results of the simulations agree well with available experimental data for the mass flow ratio vs pressure drop during conveying.