Solid Volume Fraction Profiles Research Articles

Atmospheric Bubbling Fluidized Bed Risers: Effect of Cone Angle on Fluid Dynamics and Heat Transfer

Abstract In this paper, a comparative study of fluid flow behavior and thermal characteristics of sand particles has been carried out numerically and experimentally in bubbling fluidized beds for five-cone angles of the riser wall having 0 deg, 5 deg, 10 deg, 15 deg, and 20 deg. An Eulerian model with a k–ε turbulence model is used to explore the numerical analysis, and the findings are compared to those of the experiments. For the study, the inlet air velocity is fixed at 1.5 m/s with sand particles filled up to 30 cm to maintain bubbling conditions in the risers. The results indicate that increasing the cone angle up to 10 deg while maintaining the amount of bed materials constant leads to a reduction in pressure drop. The expansion of particles along the riser is observed to decrease with the increase in the cone angle up to 10 deg. The radial solid volume fraction profile transforms to a U shape from the W-type profile as the cone angle increases up to 10 deg. Correspondingly, the solid velocity is found to have an inverted U-type and W-shaped profile for the risers. The granular temperature is also found to increase with a decrease in the solid percentage at any location. The average bed temperature, interphase, and bed-to-wall heat transfer coefficient at a location of 10 cm axial height also increase with the cone angle increase up to 10 deg. As a result, the conical riser, when designed with a greater cone angle up to 10 deg, exhibits more efficiency in terms of heat transfer characteristics. The 3D simulation results are in strong concurrence with the experimental results in all investigations.

Sensitivity analysis of a dense discrete phase model for 3D simulations of a tapered fluidized bed

This study aims to conduct a sensitivity analysis of closure models and modeling parameters for the Dense Discrete Phase Modeling (DDPM) approach in order to investigate the hydrodynamics of a 3D lab-scale Tapered Fluidized Bed (TFB). The closure models and model parameters under investigation include the gas-solid drag force, viscous models, particle-particle interaction models, restitution coefficient, specularity coefficient, and rebound coefficient. The primary objective of this sensitivity analysis is to optimize the numerical model's performance. The numerical results, in terms of axial and lateral Solid Volume Fraction (SVF) profiles obtained from the sensitivity analysis, indicate that the drag force and restitution coefficient significantly influence the hydrodynamics of the TFB. Properly selecting these parameters could result in the improved performance of the numerical model. However, the sensitivity of turbulence models, particle-particle interaction models, specularity coefficient, and rebound coefficient has a lesser impact on the hydrodynamics results. This work concludes with the recommendation of a set of closure models and modeling parameters that offer the most accurate prediction of the hydrodynamics of the TFB.

Experimental characterization and CFD simulation of gas maldistribution in turbulent fluidization of Group A particles

The study presented hereby investigates experimentally and with CFD simulations the gas distribution effect on the hydrodynamic of a Geldart Group A turbulent fluidized bed. Experiments were carried out on a cold flow fluidized bed column with an even and uneven gas distribution. Local solid volume fraction profiles were measured using optical probes at different bed heights and along two radial directions. Optical probe measurements allow catching a clear hydrodynamic difference between both even and uneven gas distributions. These results were then used to assess CFD simulations with the code Barracuda™ (MP-PIC approach). It is noteworthy that the choice of drag correlation and boundary conditions strongly influences the agreement between the experimental and CFD results. Once the correct parameters are chosen, CFD simulations captured the effect of gas distribution changes.

CFD simulations of shear induced migration in pressure-driven flow with non-Brownian suspensions

Solid-liquid suspension systems exist widely in various industrial processes. Shear induced migration (SIM) is one of the important phenomena for suspension transport. With the development of model and computational effort, Computational Fluid Dynamic (CFD) methods have been adopted to predict the SIM process. The commonly used method for SIM simulation is the Morris and Boulay model, which has been commonly adopted in 2-dimensional flow. In this paper, the 3-dimensional CFD simulation of shear induced migration for non-Brownian suspensions was established. The discrepancy was found between the simulation and experimental results, indicating that modification of model parameters is required. The modified model parameters were obtained based on the comparison of simulation and experiment results. On this basis, solid volume fraction (ϕ) profiles of suspensions in concentric pipes and concentric square channels were explored and predicted. The influence of the inlet volume fraction (ϕ0), the ratio of half gap width to particle radius (H/a), and the ratio of outer wall radius to inner wall radius (R2/R1) were studied. For concentric pipes, asymmetric distributions between inner and outer wall of the solid volume fraction were observed. For concentric square channels, regional increase of ϕ was observed around the outer corner of the channel.

Three-dimensional dynamic characterization of square-nosed slugging phenomena in a fluidized bed

Slugging represents one of the major regimes in fluidization, which occurs in small diameter beds with large bed height-to-diameter ratio or in large diameter beds with internals that resemble multiple small diameter fluidized beds. Slug types include round-nosed slug, wall slug and square-nosed slug. Studies of the slugs have been mainly focused on round-nosed or wall slugs known as half slug, typically occurring in Geldart group A particle fluidization. The square-nosed slug typically occurring for Geldart group D particles appears to be regarded as simple in its structure. The Electrical Capacitance Volume Tomography (ECVT) imaging of the square-nosed slugging phenomena conducted in this study reveals otherwise. That is the structure of the square-nosed slug is, in fact, complex, particularly with respect to its dynamic variation in fluidization. More broadly, this study examines experimentally the hydrodynamic characteristics of the square-nosed fluidization regime. Specifically, simultaneous measurements from multiple ECVT sensors provide non-invasive, continuous, 3-dimensional imaging of the entire flow region of the slugging bed and hence enabling the dynamic characterization of the evolution of the slugs. The analysis of the 3D images reconstructed for real-time gas–solid volume fraction profile of the slugging fluidized bed indicates that there are three different zones, namely, the bottom fluidization zone, the gas slug zone, and the solid slug zone, co-existing in the bed. The three zones present different hydrodynamic characteristics during the slug evolution. It is found that varying the gas velocity of the slugging bed mainly varies the maximum length of the gas slug zone, while it only has a minor effect on the lengths of the bottom fluidization zone and solid slug zone. It also has an insignificant effect on the solid volume fraction of the three zones.

Effect of software implementation on the result of computational fluid dynamics simulation of circulating fluidized bed risers

AbstractWhile in scientific literature much focus is directed toward model validation, comparison, and even parametric investigations on individual model parameters, the possible effects of the used computational fluid dynamics (CFD) software on the results are largely neglected. In this article, CFD modeling of circulating fluidized beds (CFB) are performed with Ansys Fluent and OpenFOAM to investigate the effect of software implementation on the simulation results. Transient Eulerian–Eulerian simulations are performed of two different laboratory‐scale CFB cold models in turbulent and circulating fluidized bed conditions. The same mesh and as identical models and settings as possible are utilized on both software. The obtained time‐average profiles of pressure, velocity, and solids volume fraction are compared between the software and with available measurements. A difference in the granular energy equation was identified between the software, and a modification was made to achieve the same formulation. The effect of boundary conditions was also investigated. It was found that depending on the case, the software could have a notable effect on the results. These differences are found especially in particle distribution, visible in the vertical pressure and solids volume fraction profiles as well as in external circulation mass flow rates.

A coupled hydrodynamic‐biokinetic simulation of three‐phase flow in an oxidation ditch using CFD

AbstractCoupling the hydrodynamic and biokinetic models, was done on a lab‐scale oxidation ditch as the bioreactor of the activated sludge process and validated against the available experimental data. The simulation was carried out in three‐phase, three‐dimensional conditions with k‐є and Eulerian–Eulerian methods. A simplified activated sludge model No.1 (ASM1) has been added to transport terms to account for the biokinetic model. Rotatory speed for surface aerator was initially increased and its corresponding effects on solid volume fraction, dissolved oxygen, and velocity profile and values were observed. A 150 rpm increase in the rotational velocity resulted in 36% higher average liquid phase velocity for the one‐aerator arrangement, which was 3% more than that of the two‐aerator oxidation ditch. The 150% increase in the solid volume fraction led to a 10% reduction in the maximum liquid phase velocity. The effect of aerators number has been considered explicitly on baffle performance and liquid phase velocity profile. Finally, a new design for the aerator has been offered that provides an ordered flow field and optimal conditions for the performance of the baffle and oxidation process.

Computational fluid dynamics simulation of methanol to olefins in stage circulating fluidized bed riser: Effect of reactor stage parameters on product yields

The risers of a conventional fluidized bed reactor and a stage fluidized bed reactor for the convention of methanol to olefins (MTO) were simulated using computational fluid dynamics. The reaction rates of the MTO reaction were validated to successfully match with the literature experiment. Then, the reactor stage parameters were examined by using the 2k design of the experiment method, including the number of reactor stages, the thickness of the reactor stage, and the wall temperature of the reactor stage. The stage circulating fluidized bed riser decreased the yield of ethene but increased the yield of propene and light olefins. From the obtained solid volume fraction profile, the stage circulating fluidized bed riser could reduce the back-mixing and increase the system turbulence, which promotes the light olefins of the MTO reaction yield. The wall temperature of the reactor stage did not significantly affect the chemical reaction in the circulating fluidized bed riser.

Shear‐induced migration and axial development of particles in channel flows of non‐Brownian suspensions

AbstractWe present an experimental study on the shear‐induced migration and axial development of particles in the channel flows of non‐Brownian suspensions. The suspending fluid is Newtonian. We investigate fracturing flows with a Hele‐Shaw type scaling through building a unique channel setup and an advanced optical system. The local particle concentration profiles are measured via the refractive‐index matching technique for a wide range of bulk volume fraction, that is, . Simultaneously, the particle image velocimetry is performed to determine the velocity profile of the particle phase. We compare our experimental results with the available two‐phase continuum frameworks and show discrepancies and similarities in the fully developed and axial development of the solid volume fraction profiles. We discuss directions in which the continuum frameworks require improvements.

Modeling and analysis of flow regimes in hydraulic conveying of coarse particles

Different flow regimes may take place during hydraulic conveying but are not fully understood. This paper presents a numerical study of the horizontal hydraulic conveying of coarse particles by means of the combined approach of computational fluid dynamics (CFD) for the liquid phase and discrete element method (DEM) for particles. The validity of the model is first verified by comparing the measured and predicted radial profiles of solid volume fraction under different operational conditions. On this basis, the model is used to predict the flow regime transition and the corresponding pressure characteristics as the conveying speed increases keeping a constant feed solid volume fraction. It is observed that the flow regimes transit from the stationary-bed flow, through the moving-bed flow, and finally, to the heterogeneous-suspension flow, which is consistent with the experimental observation in the literature. The numerical results are analyzed in detail in terms of flow and force structures. A new phase diagram in terms of the forces acting on particles is proposed to identify flow regimes and their transition. Based on the simulation data, correlations are formulated to predict the pressure drop of the horizontal hydraulic conveying considered.

Development of computational fluid dynamics model for two initial CO2 concentration in circulating fluidized bed reactor

Nowadays, the global warming is considered as a world problem because it influences the environment by increasing the average temperature of earth surface. One of the greenhouse gases that release from human activities and fossil fuels combustion in industry is CO2. Several technologies are applied to reduce the CO2 emission to atmosphere. In this study, the aim is to capture the CO2 by solid sorbent adsorption with potassium carbonate supported on gamma alumina using full loop circulating fluidized bed reactor in commercial computational fluid dynamics program, ANSYS FLUENT. This study focuses on the effect of initial CO2 concentrations from cement industry and power plant on CO2 removal efficiency. Besides, the solid volume fraction profile is also considered. The simulation results showed the hydrodynamics in circulating fluidized bed reactor that the solid sorbent was high at the reactor wall and low at the reactor center. In addition, the independent input variables were investigated which were percentage of K2CO3 loading on sorbent and gas velocity. The increasing of K2CO3 loading on sorbent and the decreasing of gas velocity increased the CO2 capture efficiency.

Computational Fluid Dynamics Studies of Gas-Solid Flows in a Horizontal Pipe, Subjected to an Adiabatic Wall, Using a Variable Gas Properties Eulerian Model

Abstract In the present paper, a variable gas properties Eulerian model is employed to model the gas-solid heat transfer in a three-dimensional horizontal pipe, subjected to an adiabatic wall. The numerical model has been validated with the benchmark experimental data and other theoretical results available in the literature, and found satisfactory agreements. Moreover, the numerical heat transfer results considering the variable gas properties (i. e. density, dynamic viscosity, thermal conductivity, and specific heat) and constant gas properties are compared. It is noticed that the variable gas properties significantly affect the heat transfer, when compared to the constant gas properties. Therefore, the consideration of constant gas properties for the prediction of heat transfer may not be suitable in gas-solid flows, subjected to an adiabatic wall. Moreover, the temperature profiles, solid volume fraction profiles, and gas-solid Nusselt number are discussed. Finally, the pressure drop prediction with respect to the solid loading ratio is studied, and found that the pressure drop slightly decreases with increasing the solid loading ratio.

Soret- Dufour Effect on Mixed Convection Past a Vertical Plate in Non-Darcy Porous Medium Saturated With Buongiorno Nanofluid in the Presence of Thermal Dispersion

ABSTRACTNumerical analysis was investigated for steady two-dimensional double diffusive mixed convection boundary layer flow over a semi-infinite vertical plate embedded non-Darcy porous medium filled with nanofluid, in presence of thermal dispersion and under convective boundary conditions. The Buongiorno nanofluid model is used, while the porous medium is described by the Darcy-Forchheimer extension. The governing partial differential equations are transformed into four coupled nonlinear ordinary differential equations using an appropriate similarity transformations and the resulting system of equations is then solved numerically by the finite-difference method. Numerical results are presented to illustrate how the physical parameters affect the flow field, temperature, concentration and solid volume fraction profiles. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of pertinent parameters.

CFD Modeling of the Feed Distribution System of a Gas-Solid Reactor

Granular flow simulation using CFD has received a lot of attention in recent years. In such cases, CFD is either, coupled with Discrete Element Method (DEM) techniques for appropriate incorporation of inter-particle collisions, or the Eulerian CFD approach is used in which granular particles are treated as they were fluid. In the present study, a CFD analysis was performed for granular flow in an industrial screw feeder to study the choking phenomena. Eulerian multiphase flow model, also known as two-fluid model in the case of two phases, was used along with the solids closures based on Kinetic Theory of Granular Flow (KTGF). The rotating effect of the half pitch screw was incorporated by using the immersed boundary method (IMB). Variation of mass flow through change in revolution per minute (RPM) and moisture content was studied in this work. A jump condition in the axial profiles of both the solid phase volume fraction and pressure was observed near the inlet. It was found that the jump condition in solid phase volume fraction and pressure profiles reduces by increase in the RPM of the screw.

Gas-solid flow in a ring-baffled CFB riser: Numerical and experimental analysis

Circulating fluidized beds (CFBs) are used in a variety of industrial applications in which the homogeneous distribution of the solid phase is desirable. The core-annulus concentration profile is a characteristic of the flow profile in these devices and it leads to solids concentration near the wall. The use of airfoil-shaped ring-type baffles is an alternative to improve the solids distribution in the cross section of CFB risers. In this study, the solids velocity and volume fraction profiles were obtained by PDA measurements and used to validate a computational fluid dynamics (CFD) model. Improvements in the solids distribution are evaluated using a statistical coefficient of variation. The results demonstrate that the ring baffles increase the solids velocity near the wall and redirect the particles to the riser center. The more homogeneous distribution of the particles in the radial direction, shown by both the experimental and numerical solids volume fraction coefficients of variation, improves the gas-solids contact and consequently could increase the yield and selectivity of products of the chemical reactions. In addition, it was found that the insertion of the ring baffles caused a pressure drop reduction in the riser flow. This study enables the investigation of the solids distribution in CFB risers in large scale.

CFD simulation of a spouted bed: Comparison between the Discrete Element Method (DEM) and the Two Fluid Model (TFM)

A spouted bed was simulated through two Computational Fluid Dynamic models: CFD-TFM and CFD-DEM. The two models were compared and validated with data from literature, showing good agreement between experimental and simulated results. Both models were able to predict the dynamics of the bed from the static situation to stable spouting conditions, even though some discrepancies in the solid volume fraction or velocity profiles were observed. Overall, CFD-DEM reproduced better the experimental measurements, and, since the computational effort was proved to be similar in both cases due to the low number of particles in the bed, it was preferred to describe the present spouted bed. In larger systems, however, CFD-DEM might not be so convenient, requiring the evaluation of the degree of accuracy and the computational costs prior to the application of this or alternative models.

Interface-resolved simulations of particle suspensions in Newtonian, shear thinning and shear thickening carrier fluids

We present a numerical study of non-colloidal spherical and rigid particles suspended in Newtonian, shear thinning and shear thickening fluids employing an immersed boundary method. We consider a linear Couette configuration to explore a wide range of solid volume fractions ($0.1\leqslant \unicode[STIX]{x1D6F7}\leqslant 0.4$) and particle Reynolds numbers ($0.1\leqslant Re_{p}\leqslant 10$). We report the distribution of solid and fluid phase velocity and solid volume fraction and show that close to the boundaries inertial effects result in a significant slip velocity between the solid and fluid phase. The local solid volume fraction profiles indicate particle layering close to the walls, which increases with the nominal $\unicode[STIX]{x1D6F7}$. This feature is associated with the confinement effects. We calculate the probability density function of local strain rates and compare the latter’s mean value with the values estimated from the homogenisation theory of Chateau et al. (J. Rheol., vol. 52, 2008, pp. 489–506), indicating a reasonable agreement in the Stokesian regime. Both the mean value and standard deviation of the local strain rates increase primarily with the solid volume fraction and secondarily with the $Re_{p}$. The wide spectrum of the local shear rate and its dependency on $\unicode[STIX]{x1D6F7}$ and $Re_{p}$ point to the deficiencies of the mean value of the local shear rates in estimating the rheology of these non-colloidal complex suspensions. Finally, we show that in the presence of inertia, the effective viscosity of these non-colloidal suspensions deviates from that of Stokesian suspensions. We discuss how inertia affects the microstructure and provide a scaling argument to give a closure for the suspension shear stress for both Newtonian and power-law suspending fluids. The stress closure is valid for moderate particle Reynolds numbers, $O(Re_{p})\sim 10$.

Comparison of two-fluid and discrete particle modeling of gas-particle flows in micro fluidized beds

The formation of a more porous zone in the near wall region has been commonly suggested to be one of the main mechanisms of the delayed onset of fluidization in micro fluidized beds (MFBs). If such geometrical effect still plays a major role once the bed is fluidized, it will challenge the applications of Two-Fluid Model (TFM) to simulate micro fluidized beds. In this work this issue is assessed by taking the simulation results of the Computational Fluid Dynamics coupled with the Discrete Element Method (CFD-DEM) as the benchmark data. Both the delayed onset of fluidization and the advanced onset of turbulent fluidization predicted by CFD-DEM simulations are successfully captured by the TFM simulations. The radial profiles of solids volume fraction and solids axial velocity predicted by TFM and CFD-DEM simulations are also in well agreement. Such results demonstrate that TFM can be appropriately used to model micro fluidized beds systems. Parameter analyses show that TFM simulation results are closely related to the input parameter setting. The minimum bubbling velocity predicted by TFM simulations closely depends on the chosen value of frictional packing limit. And the specularity coefficient has a significant impact on the predicted solids flow behavior.

Visualization of flow structures inside a conical spouted bed by electrical capacitance volume tomography

Electrical capacitance volume tomography (ECVT) was conducted to measure instantaneous gas–solid flow structures in a conical spouted bed. The sensor has 24 electrodes/channels and was used to make three-dimensional measurements of the solid volume fraction. Flow structures in the conical spouted bed were analyzed using quantitative ECVT images. Three-dimensional images of gas–solid flow structures and time-averaged vertical and radial solid volume fraction profiles are presented. Different fluidization regimes in spouted beds were characterized by analyzing pressure fluctuation signals and ECVT images. ECVT was shown to be robust and powerful for the three-dimensional visualization and quantitative measurement of a gas–solid fluidization system.

The influence of pressure and temperature on gas-solid hydrodynamics for Geldart B particles in a high-density CFB riser

The effects of operating pressure and temperature on the flow behavior in the riser of a high-density circulating fluidized bed have been numerically studied using the two-fluid model coupled with the EMMS-based drag model. When the operating pressure is below 0.4MPa, the flow regime in the riser experiences the fluid dominated (FD) zone, the transition zone from FD to the particle-fluid compromising (PFC), and the PFC zone with the increase of solids circulating flux. Under the same solids circulating flux, the solids axial velocity increases while the solids volume fraction decreases with the increase of operating pressure. In terms of axial profiles of solids volume fraction and axial velocity, there exists a critical operating pressure, above which the axial profile changes little with further increase of operating pressure, while it is hard to find a critical pressure in terms of radial profiles. When the gas density is kept the same, the increase of gas viscosity caused by higher temperature has only minor effect on the axial profiles of solids volume fraction, but it makes the solids axial velocity increase in the core zone and decrease slightly near the wall.