Solids Concentration Profiles Research Articles

A simple EMMS drag model for the simulation of bubbling fluidized beds using mesoscience-based structural model

State-of-the-art EMMS drag model for bubbling fluidization needs an empirical correlation for bubble diameter. In this short communication, an EMMS drag model is developed to predict the effective drag coefficient without the use of an empirical correlation for bubble diameter. The model is then coupled with mesoscience-based structural model to simulate the hydrodynamics of three bubbling fluidized beds, it is shown that the bed hydrodynamics can be predicted reasonably well, in terms of axial and radial solid concentration profiles. Present study establishes an effective and simple model for simulating bubbling fluidization using mesoscience-based structural model.

Validation of mesoscience-based structural model for simulating gas–solid flows in circulating-turbulent fluidized beds

The circulating-turbulent fluidized bed (CTFB) is an important fluidization regime that can maintain a high solid concentration and high reaction intensity as in turbulent fluidized bed, and suppress solids back-mixing as in circulating fluidized bed. Computational fluid dynamics (CFD) studies on it are however very sparse. In this study, extensive three-dimensional CFD simulations of CTFB are carried out using the mesoscience-based structural model (Liu et al., 2023), where the gas-rich dilute phase and the particle-rich dense phase are defined as the two interpenetrating continua, instead of treating the gas and particles as the two interpenetrating continua as in classical two-fluid models. It is shown that the model is able to faithfully predict the hydrodynamics of CTFB, in terms of axial and radial solid concentration profiles and radial solid velocity profiles. This study not only provides a systematical CFD study on the hydrodynamics of gas–solid flow in CTFB but also offers validations of the mesoscience-based structural model via simulating the hydrodynamics of new fluidization regime (CTFB).

Coarse-graining dense discrete phase model for modeling particle dynamics in a 3D tapered fluidized bed coater: Analysis of different drag models

Fluidized bed coating (FBC) is widely employed in the food industry to microencapsulate food powder ingredients, primarily using a top-spray design in a tapered fluidized bed (TFB). A comprehensive understanding of particle dynamics is crucial for successfully designing FBC processes. This study focuses on developing and analyzing the coarse-graining dense discrete phase model (CG-DDPM) to investigate particle fluid dynamics in tapered fluidized bed coater (TFBC). Following the successful development of the CG-DDPM, we conducted a sensitivity analysis of drag force models due to the unique operating conditions involved. Five drag models were investigated, including four classic homogeneous drag models (Gidaspow, Wen-Yu, Syamlal-O'Brien, and Huilin-Gidaspow) and one advanced energy-minimization-multiscale bubbling (EMMS-B) heterogeneous model. While all drag models exhibited reasonable qualitative behavior, the EMMS-B model demonstrated superior quantitative performance, particularly at a gas velocity (Ug) of 1.75 m/s. However, at Ug = 1 m/s, none of the drag models perfectly resolved the axial and lateral solids concentration profiles. This study's findings contribute to identifying the best-performing drag model and highlight the need for more appropriate drag models to represent particle fluid dynamics in TFBC accurately. Moreover, employing the EMMS-B model in the top-spray design of TFBC can enhance the microencapsulation of food powder ingredients due to its superior particle dynamics predictions compared to homogeneous drag models.

Hydrogen direct reduction ironmaking process for zero CO2 emission: A study on the effect of particle properties changes during the multiple non-catalytic gas-solid reactions

Direct hydrogen reduction (H-DR) is one of the most attractive technologies for decarbonization in the iron and steelmaking industries. Improvements in process efficiency depend on a multi-scale evaluation since the industrial performance is significantly affected by transient non-catalytic gas–solid reactions at the pellet scale. This study investigated the effect of temperature-dependent morphological changes in industrially produced pellets during isothermal reduction temperatures from 600 to 900 °C. A 2D axisymmetric pellet grain model using the finite element method and considering the three reduction reactions and the mass and heat transfer phenomena was developed to evaluate the evolution of the solid transformations along the pellet radius during the reduction time. Based on the experimental results, structural properties of the pellets, such as grain size, tortuosity, and transient porosity, were incorporated into the proposed pellet model. The simulation results under different conditions show good agreement with experimental data when changes in the pellet tortuosity are considered, particularly at higher temperatures. Furthermore, predictions of solid and gas concentration and temperature profiles over the pellet radius during the reduction process evidenced the transient behavior of the process. The findings represent an important contribution to the degree of knowledge on the H-DR process application by providing information on the effect of structural parameters of the pellets for the current status of mathematical models of the process.

Isolation of relaxation times under open-circuit conditions: Toward prognosis of nascent short circuits in Li-ion batteries

Li-ion battery mishaps are primarily attributed to short circuits, which missed early detection. In this study, a method is introduced to address this issue by analyzing the voltage relaxation, after initiating a rest period. The voltage equilibration arising from solid-concentration profile relaxation is expressed by a double-exponential model, whose time constants, τ1& τ2, capture the initial, rapid exponential contour and the long-term relaxation, respectively. By tracking τ2, which is very sensitive to small leakage currents, it is possible to detect a short early on and estimate the short resistance. This method, validated with experiments on commercial batteries induced with short circuits of varying extents, has >90% prediction accuracy and enables clear differentiation between different short severities, while factoring in the influence of temperature, state of charge (SOC), state of health (SOH), and idle currents. The method is applicable across different battery chemistries and form factors, offering precise and robust nascent-stage short detection-estimation for on-device implementation.

Dimensioning Air Reactor and Fuel Reactor of a Pressurized Chemical Looping Combustor to Be Coupled to a Gas Turbine: Part 1, the Air Reactor

This paper provides a simple methodology for the design of the air reactor of a chemical looping combustor to optimize its characteristics when it is employed connected to a turbo expander to produce power. The design process, given a certain objective (e.g., electric power) defines the reactor specifics, namely height and diameter, taking into account the following aspects: solids inventory of the air reactor; gas velocity; air reactor transport disengaging height (TDH); solids concentration profile along the reactor height, dense bed height; freeboard height; pressure drop depending on air reactor injectors design and configuration. The total air reactor height was about 9.5 m, while the diameter was about 1.8 m. The total inventory was about 10,880 kg; while the circulation rate in the air reactor was about 110 kg/s. The operating pressure and temperature were, respectively, 12 bar and 1200 °C. The average velocity of the gases inside the reactor was about 4 m/s. The fluidization regime resulted to be comprised between turbulent and fast fluidization. Further work must be directed into the estimate of the pressure drop of the reactor, which will affect the plant efficiency in a considerable way.

Numerical prediction of slurry flows through 90° bend pipelines

Transporting fly ash slurry via long pipelines concerns power plants and other industries. Assessment of two-phase flow in pneumatic conveying is still a major concern in many industrial and technological applications. Due to the large number of geometrical and dynamical variables and their interaction, the slurry flow pattern in pneumatic conveying through pipeline is very complex.The solid concentration and velocity profile of fly ash have been examined in this study using numerical modelling to determine how they affect the pressure drop in a 900 bend pipe. Ansys Fluent software is employed to simulate the k - ε turbulence model. The pressure drop increases with increasing velocity and solid concentration.The present study aims to improve our knowledge of two-phase flow and slurry piping system design.

Predicting pressure-drop for pseudo-homogeneous slurry flows using the mixture model at high solids concentrations

The main contribution of this paper is applying computational fluid dynamics (CFD) using the two-phase mixture model with algebraic slip, and turbulent dispersion to the slurry flow experiment of Kaushal et al. (2012). The results obtained were compared to the experimental results and numerical results reported by the same authors who used the mixture model as well as a more advanced Eulerian granular flow model. The authors reported that the mixture model predicted the pressure drops with very high errors, especially for the highest solids loading simulated with errors as high as 400% compared to their experimental data. They conclude that the mixture model cannot be used to predict the pressure drop of the slurry flow investigated at higher concentrations (30-50% solid fraction). In contrast to this, the pressure-drop predictions of the two-phase mixture model with algebraic slip and turbulent dispersion used in this study were in good agreement with the measured values. This calls the conclusion of Kaushal et al. (2012). to question, because they did not present any justification for 3-4 times higher pressure drop observed in their study using the mixture model in combination with the fact that no anomalies in particle concentration profiles were observed by them for the mixture model. A comparison between the two mixture models reveals that although they differ in some details, the basic structure of the models is the same. We conclude that the mixture model with algebraic slip, turbulent dispersion, and a suspension viscosity model can be used for pressure drop predictions for the slurry flow investigated even for high solids fraction. We also demonstrate that the laterally averaged solids concentration profiles are not predicted very accurately by the mixture model as well as the more complex granular model. The concentration profiles predicted by the mixture model is easily understood in contrast to the profiles predicted by the granular flow model. From an engineering viewpoint, preference should be given to a simpler model, as was used in this study which can predict pressure drop with similar accuracy compared to a more complex approach with a larger number of uncertainty parameters. Further research is necessary to correctly predict the solids concentration profile for slurry flow in pipelines.

Effect of drag models on hydrodynamic behaviors of slurry flows in horizontal pipes

The Eulerian–Eulerian method is efficient when dealing with liquid–solid slurry flows containing a large number of particles, but its reliability relies on an accurate description of liquid–particle interaction for which numerous interphase drag models have been proposed. However, the performance of these models has not been systematically evaluated when applied to slurry flows. In this study, slurries in horizontal pipes under various flow conditions are simulated using the Eulerian–Eulerian method. Six commonly used drag models, such as the Schiller–Naumann, Wen–Yu, Gibilaro, Gidaspow, Syamlal–O'Brien, and Huilin–Gidaspow models, are assessed based on their predictions of streamwise velocity, secondary flow, solid concentration, and liquid turbulent kinetic energy. Under normal operations, all models provide similar streamwise velocities and secondary flow patterns. However, the Schiller–Naumann model presents an intensified secondary flow and a flattened solid concentration profile. All models perform poorly for the solid concentration distribution, which may be corrected by considering the overall mean solid concentration. Additionally, the Wen–Yu model, which has previously been thought applicable only for dilute systems, behaves very closely to the Gidaspow model, which is usually recommended for dense fluidized beds.

Numerical investigation for the suitable choice of bubble diameter correlation for EMMS/bubbling drag model

Mesoscale bubbles exist inherently in bubbling fluidized beds and hence should be considered in the constitutive modeling of the drag force. The energy minimization multiscale bubbling (EMMS/bubbling) drag model takes the effects of mesoscale structures ( i.e ., bubbles) into the modeling of drag coefficient and thus improves the coarse-grid simulation of bubbling and turbulent fluidized beds. However, its dependence on the bubble diameter correlation has not been thoroughly investigated. The hydrodynamic disparity between homogeneous and heterogeneous fluidization is accounted for by the heterogeneity index, H d , which can be affected by choice of bubble diameter correlation. How this choice of bubble diameter correlation influences the model prediction calls for further fundamental research. This article incorporated seven different bubble diameter correlations into EMMS/bubbling drag model and studied their effects on H d . The performance of these correlations has been compared with the correlation used previously by EMMS/bubbling drag model. We found that some of the correlations predicted lower H d by order of a magnitude than the correlation used by the original EMMS/bubbling drag. Based on such analysis, we proposed a modification in the EMMS drag model for bubbling and turbulent fluidized beds. A computational fluid dynamics (CFD) simulation using two-fluid model with the modified EMMS/bubbling drag model was performed for two bubbling and one turbulent fluidized beds. Voidage distribution, time averaged solid concentration and axial solid concentration profiles were studied and compared with the previous version of the EMMS/bubbling drag model and experimental data. We found that the right choice of bubble diameter correlations can significantly improve the results for CFD simulations.

Floating particles mixing characteristics in an eccentric stirred tank coupled with dislocated fractal impellers

Abstract The mixing characteristics of floating particle dispersion process in an eccentric stirred tank with dislocated fractal impellers were investigated using computational fluid dynamics (CFD) and experimental analyses. Solid concentration distribution, axial solid concentration profile, cloud height, solid integrated velocity, power consumption and just drawdown speed were investigated. Results showed that dislocated fractal impeller can enhance solid integrated velocity and fluid turbulent fluctuation intensity compared with dislocated pitched blade impeller, and eccentric agitation coupled with dislocated fractal impeller could destroy the typical circulation loops and symmetric flow field and improve the axial circulation efficiency of floating particles on the basis of dislocated fractal impeller. Eccentric agitation coupled with dislocated fractal impeller could further enhance the floating particle dispersion homogeneity (MI) and decrease the just drawdown speed (N jd) on the basis of dislocated fractal impeller and dislocated pitched blade impeller at the specific power consumption. Meanwhile, eccentric ratio of 0.3 or 0.4 was optimal for the floating particle mixing process in this work.

Effect of specularity coefficient on hydrodynamic behaviors of slurry flows in horizontal pipes

The Eulerian–Eulerian two-fluid model (TFM) in combination with the kinetic theory of granular flow (KTGF) and the Johnson and Jackson boundary condition is widely used to simulate multiphase flows in engineering. However, this model requires the calibration of several parameters. One of these parameters is the specularity coefficient, which characterizes the particle–wall collisions. Thus far, research on this parameter has been lacking in the field of slurry flow simulations. In this study, the integration of TFM with KTGF and the Johnson and Jackson boundary condition is used to simulate the transportation of sand–water slurry in horizontal pipes. The effects of different specularity coefficient values on the predicted solids wall shear stress, velocity, and concentration are analyzed. It is found that the solids wall shear stress increases with the specularity coefficient and is more sensitive to the smaller specularity coefficient. As the specularity coefficient increases, the profiles of the solids velocity and concentration are rotated clockwise, shifting the maximum velocity point to a higher vertical location and producing a plumper solids concentration profile. These qualitative conclusions may be used as a reference for the specularity coefficient tuning process in the field of slurry transport simulations.

Numerical simulation to access the bend effect for the flow of fly ash slurry

The secondary forces formed on the bend, which are responsible for the excessive pressure drop, were investigated using CFD modeling. Different flow parameters which are very important in the design of slurry pipeline such as pressure drop and concentration solid profiles for the flow of 25 µm fly ash were analysed in a 50 mm pipe diameter at different flow velocities ranging from 1 to 2.5 m/s. In this research work, Ansys Fluent software’s was chosen for numerical simulations to investigate the intricate fluid flow pattern of fly ash slurries at increased solids. To explore the flow patterns of solid-liquid flow, pressure drop and solid concentration profiles were forecast and analysed in relation to real flow parameters to investigate the flow patterns of solid-liquid flow. This technology can also be used to provide route flexibility in slurry pipelines.

Understanding the isotopic composition of sedimentary sulfide: A multiple sulfur isotope diagenetic model for Aarhus Bay

Measurement of the multiple sulfur isotopes (³²S/³³S/³⁴S) enables the calibration of microbial biosignatures and provides a unique diagnosis of S-based metabolic processes: sulfate reduction, disproportionation, and sulfide oxidation. All three metabolisms carry distinct geochemical consequences for S cycling in modern systems, and are particularly powerful for paleoenvironmental interpretations if their respective contributions can be separated. To hone those interpretations and to further develop a quantitative context for understanding early diagenetic sulfur cycling, we constructed a multiple S isotope reactive transport model for the sediments of a geochemically well-characterized system (Aarhus Bay, Denmark). The model reconciles pore water and solid phase concentration profiles of the major species associated with Fe/S/C cycling, and uses multiple S isotope systematics to predict the isotope profiles of the major S species, including pore water sulfate, free sulfide and solid phase pyrite. We note that very large fractionations associated with sulfate reduction (³⁴ε_sr = 70‰) are required to reproduce the observed pore water profiles, and we reconcile these fractionations with low temperature theoretical predictions for isotope equilibrium fractionation. The minor sulfur isotope values (noted as Δ³³S) of sulfate increase at shallow depths within the Aarhus Bay core, and decrease when sulfate drops below 10 mM. Values (Δ³³S) for sulfide decrease nearly monotonically towards seawater sulfate values near the zone of sulfate depletion. Pyrite Δ³³S values are nearly uniform downcore (0.170 ± 0.010‰) despite a ∼10‰ enrichment in surface versus deep pyrite δ³⁴S values. Sulfate reduction is the most important process controlling S isotope pore water distributions, with modest contributions from oxidative S cycling. Further, microbial sulfate reduction demonstrates large fractionations typically not expected for shallow, organic rich (TOC ∼ 4%) continental margin systems.

CFD modelling of coal gasification in a fluidized bed with the effects of calcination under different operating conditions

This paper investigates the thermochemical and physical conversion processes of coal gasification numerically with particular interest on calcination in a bubbling fluidized bed furnace. A comprehensive Eulerian-Eulerian three-dimensional model is developed for studying the gasification process. Three calcination cases are carried out under different operating conditions while one inert case is conducted to evaluate the effect of calcination. The presented numerical results aim at determining the mechanism of coal gasification in an air-steam environment with different flowrates. Evidence of particle segregation is found in the bed of coal and limestone due to density reduction and diameter shrinkage. Char conversion is investigated for different air-coal and steam-coal ratios, also the effect of bed temperature, fluid flowrate and fuel feeding rate on the carbon conversion is studied comprehensively. The highest char conversion rate is observed in the airflow rate of 17.0 kg/h where the bed temperature is found to be maximum. A noticeable impact of calcination is found in the gaseous emission while increasing CO2 concentration. Time averaged solid and gas temperature and species concentration profiles indicate the steady-state condition of numerical simulation.

Drag model validation of slurry pipeline using CFD

A number of drag models have been suggested for the interaction of fluid particles in slurry flow over the previous centuries. It is necessary to examine the correctness and applicability of these models in the slurry transportation. Based on this concept, a comparative analysis of the different drag models is performed for the 0.0549 m diameter slurry pipeline. The research is carried out by using three drag models: Syamlal-obrien, Schiller-naumann and Gidaspow due to their accessibility in the Fluent commercial software. The simulation is performed at mean flow velocity range, Vm= 2–5 ms-1 and solid concentration range, Cvf = 10– 20% (by volume) using computational drag models. The simulated outcomes for solid particle size 440 μm having density 2470 kg/m3 are recorded using Eulerian two-phase model with selected drag models in the computational domain. It has been found that the Eulerian two-phase model with Syamlal O’brien drag model gives the accurate and meticulous results with the published data in the literature. Finally, the simulated outcomes of solid concentration contours, solid concentration profiles and pressure drop are predicted at distinct velocity and solid concentration range for chosen drag models.

Investigation of dense slurry suspensions with coaxial mixers: Influences of design variables through tomography and mathematical modelling

The coaxial mixers enhance the suspension of concentrated slurries in an agitated reactor. In this research work, the complex slurry suspension and dissemination behavior in a coaxial slurry mixing system (comprised of a close clearance anchor rotating with a low speed and an inner axial impeller rotating with a high speed) was analyzed employing ERT (electrical resistance tomography, a non-intrusive flow visualization technique), and computational fluid dynamics (CFD). The numerical models were validated by comparing the axial solid concentration profiles generated using the ERT data and the CFD simulation results. The influences of various important parameters such as the diameter of the inner axial impeller, the inner impeller type, and the inner impeller spacing on the hydrodynamic characteristics of the slurry suspensions in a coaxial mixing vessel were thoroughly analyzed. The radial and axial velocity profiles of solid particles were generated using the validated mathematical models. The assessment of energy loss due to the solid–solid collisions, the particle–fluid frictions, and the particle–vessel wall collisions was conducted. The evaluation of optimum inner impeller clearance and inner impeller diameter is essential to attain a high degree of solids suspension and dissemination in a coaxial slurry mixing system.

Using flow visualization and numerical methods to investigate the suspension of highly concentrated slurries with the coaxial mixers

The major purpose of this investigation was aimed at assessing the mixing capability of a coaxial system comprised of a central pitched blade impeller with a high rotating speed and a wall scrapping outer anchor with a low rotating speed in suspending highly concentrated slurries using flow visualization (electrical resistance tomography) and numerical (computational fluid dynamics) techniques. The 2D images acquired by tomography and simulation methodologies were utilized in creating solid concentration profiles. Different mixing indexes were employed to analyze the impacts of solids concentration gradients on the solids distribution. The effects of different factors namely solid concentration, average particle size, speed ratio, anchor speed, rotating mode, and solid specific gravity on the suspension and dispersion quality was analyzed. The results clearly revealed that the coaxial mixer provided better suspension quality at lower power utilization compared to that achieved by a single central impeller in dense suspension systems.

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.

Numerical investigation of zinc tailings slurry flow field in a horizontal pipeline

Thispaperreportsthefindingsofnumericalinvestigationofdenseparticulateslurryflowfieldinaslurrypipelinewith an objective of examining erosive wear. Parametric study with velocities 2 m/s, 2.75 m/s and 3.5 m/s, and volumetric concentration of 4% and 26% were carried out on a pipeline of nominal inside diameter 105 mm. The range of volumetric concentration was chosen to ascertain the flow field characteristics for low to high particle loading. All the simulations have been computationally performed using ANSYS-FLUENT. The dense particulate slurry is modelled using Eulerian-Eulerian approach while finite volume method (FVM) is employed as the numerical method. Mesh refinement study and validation with experimental results for pressure drop have been reported. Solids concentration and velocity profiles show dependence on flow velocity and inlet average concentration. The distribution of solids concentration and its dependence on the bulk flow velocity qualitatively indicates the regions of relatively higher erosion wear.