Bed Of Solid Particles Research Articles

Hyperbolic high-fidelity simulations of cratering on a particle bed induced by a turbulent supersonic plume

A recently proposed hyperbolic granular model (Balakrishnan and Bellan, 2024) has been used to investigate the problem of supersonic-jet induced cratering on a solid-particle bed. This model relies upon the concept of added mass and a fluid-mediated particle pressure to render the system of equations hyperbolic. The jet is modeled using Large Eddy Simulation (LES) and the solid phase is modeled in an Eulerian framework using a Kinetic-Theory-based model modified for dense particle collections. The formulation also incorporates pseudo-turbulent kinetic energy (PTKE) which has been shown to modify a flow field laden with particles. The results explore the influence of the jet-to-ambient fluid density ratio, of the ambient fluid density, and of PTKE. A detailed analysis of the local and time-wise evolution of the added mass is presented through quantification of convection, added mass source and velocity-difference contributions. A quantitative assessment of the PTKE equation shows that while production is mostly effective at the crater base and walls, the dissipation and source term, both of which are also effective in the ejecta, nearly balance each other. The influence of the PTKE is mostly observed in the dilute particle regions (soil/gas interface and ejecta), with no effect on the macroscopic length scales of the flow. Both the jet-to-ambient fluid density ratio and the ambient fluid density affect the macroscopic crater features through entertainment into the jet that is determined by the former, and through the density of the fluid entrained, determined by the latter. This complex interaction governs the evolution of the crater diameter, visible top-view depth, and lower depth of the compacted region.

A Volume-Averaged Hyperbolic System of Governing Equations for Granular Turbulent Flow Modeling With Phase Change

Abstract A formulation is developed using volume-averaging and the concept of added mass to derive a hyperbolic system of governing equations for modeling turbulent, dense granular flows. The large eddy simulations (LES) framework is employed for the fluid phase, whereas the solid phase equations are based on enlarged Kinetic Theory concepts. To obtain the LES equations, the volume-averaged equations are filtered and the filtered terms not directly computable from the LES solution are generically modeled. Additionally, the pseudo-turbulent kinetic energy (PTKE) is included in the formulation and it is shown how its contribution is distinct from turbulence and leads to different terms that must be modeled in the conservation equations. Volume-averaging of the continuity, momentum and energy equations result in many integrals that are used to rigorously define the meaning of terms that have only been included heuristically in existing formulations. Simulations with this model are conducted in a configuration representing the interaction of a turbulent supersonic jet with a bed of solid particles. The results are analyzed to demonstrate hyperbolicity. Comparisons of results from a model including PTKE and one excluding it show that the inclusion of PTKE has no role in bestowing hyperbolicity to the model, and furthermore does not affect the macroscopic aspects of the crater. Comparisons between results obtained with a hyperbolic model and a model that is hyperbolic everywhere except in regions of particle/fluid interaction show that the macroscopic crater aspects are different, affecting the crater shape and topography.

Introducing an efficient capped fluidized bed and quantifying its flow and heat transfer performance

Fluid-solid particle beds have a very wide range of industrial applications but there are few publications relating to a general method to quantify solid particle bed performance for a comparative efficiency study. The conventional approach of characterizing bed efficiency involves bubble sizes, bubble frequency, byproduct quantity for bed reactors, and pressure drop for minimum fluidization. However, different solid particle beds have different states with varying flow rates, which makes the comparative study more difficult to achieve. In this work, a common approach to measure solid particle bed efficiency in terms of heat transfer is presented. The two cases considered here are 1) When work is done by the particles such as in a catalytic reactor, and 2) When work is done on the particles such as in cooling/drying of particles. In addition to the packed bed and fluidized bed, a solid particle bed called a capped fluidized bed is introduced. The Eulerian–Lagrangian method, also known as CFD-DEM simulation, is adopted for this analysis. Numerical simulations show potentially significant advantages of capped beds over packed and fluidized beds under certain fluidization states. Capped fluidized bed pressure drop is comparatively lower than that for a packed bed and similar to a fluidized bed, which allows it to operate at a wider range of flow states. Current fluidized bed performance is limited by the entrainment and possible loss of particles at high flow rates. However, the capped fluidized bed restricts the particles from leaving the bed and thus permits higher flow rate operation. Further experimental research is required to more completely characterize this type of solid particle bed.

Assessing the conveyance of fluidized natural gas hydrate in a horizontal tubing

This study evaluates the transportability of clayey-silt natural gas hydrate (NGH) solid particles during solid fluidization in horizontal tubing, a crucial step in recovering marine NGH. Non-uniform solid particle distribution in horizontal flows can cause unstable operations and financial losses. Thus, assessing transportability is necessary to avoid these issues and harness the potential of NGH as an alternative energy source. This study introduces a model based on each phase's two-layer approach and momentum balance equation, considers potential hydrates (re)formation, and overcomes previous models’ limitations. Moreover, it assumes that the critical settling velocity marks the moment when the lower bed of solid particles stagnates, thereby leading to the disappearance of frictional pressure in the lower bed. The proposed model is evaluated and compared with existing models using a laboratory dataset and the South China Sea offshore field dataset and found to provide the highest prediction accuracy and precision. Moreover, it reveals that the tubing diameter, solid particle diameter, and solid particle concentration are the major influential parameters affecting the solid particle conveyance. Consequently, the proposed model is suitable for evaluating the transportability of those solid particles in horizontal tubing, making it ideal for assessing their transportability in pipelines.

Hydrodynamics of a reactor for thermocatalytic oxidation of sewage sludge

One of the promising methods for the disposal of municipal sewage sludge is its thermocatalytic oxidation in fluidized bed reactors. An important factor determining the stability of the operation of fluidized bed reactors is the uniform introduction of the air flow, which, on the one hand, fluidizes a bed of catalyst solid particles and solid sewage sludge, and, on the other hand, the oxygen of the air flow serves as an oxidizing agent in chemical reactions occurring in the reactor. A pilot plant for thermocatalytic oxidation, created according to the technology of the Boreskov Institute of Catalysis, is operated at JSC Omskvodokanal (Omsk, Russia). The plant's capacity is 50 thousand tons per year of mechanically dehydrated sludge with a water content of 70–80 wt%. The cross-sectional area of the sludge combustion zone is 3.8 m2. The heat flow from the incoming sludge (physical heat and heat of combustion) is 6527000 kcal/h. The air flow was introduced into the fluidized bed reactor with a sparger of 6 perforated pipes arranged horizontally and in parallel. The purpose of this work is to investigate the influence of inlet conditions on fluidized bed hydrodynamics. The results obtained showed that despite the uneven distribution of air flow through the holes of the sparger tubes, each pair of adjacent sparger tubes mutually compensate each other in terms of air flow per unit area of the cross section of the reactor. It is also shown that during the operation of the reactor, air cavities are formed under the sparger pipes, which are practically free of solid particles. The position of such air cavities and their approximate volume are stationary in time for a developed fluidized bed, and the volume of the cavities is approximately proportional to the dimensions of the respective sparger tubes. These air cavities periodically eject bubbles into the overlying portions of the fluidized bed. The dimensions of the bubbles are comparable to the transverse dimensions of the pipes.

Determination of void fraction for upward steam-water flow in a packed bed

This paper presents the results of a void fraction study for a steam-water flow in a channel that contains a close-packed bed of solid spherical particles. Investigations of a two-phase flow motion through random layers of solid particles are crucial for the energy industry to design future nuclear reactors with spherical coated fuel particles and analyze post-emergency cooling of material fragments in the core of light water reactors. An experimental setup and a new measurement method combining a flow cutoff method and the use of additional water are described. Experiments were carried out with a packed bed of particles with diameters of 2 and 4 mm at a pressure of 0.12–0.9 MPa and a mass velocity of 28–300kgm−2s−1. Some measurements were made in a particle-free pipe 39 mm in diameter. The findings have established that the void fraction in packed beds is higher than in a particle-free pipe, is insensitive to the particle size, and, in the considered range of values, increases with a rise in the flow rate or a decline in pressure. The analysis of the known correlations for heated and unheated channels of different geometries and packed beds is conducted. The obtained experimental data is generalized using the drift-flux model and adapted slip ratio models. The paper proposes a modified version of the one-parameter equation for the void fraction in a packed bed with constraints imposed on the difference in the vapor and water filtration velocities.

Correlation for predicting minimum fluidization velocity with different size distributions and bed inventories at elevated temperature in gas-solid fluidized bed

This study presents extensive experimental details of the effects of the solid particle size distribution (PSD), bed inventory, and bed temperature on the minimum fluidization velocity (Umf). Silica sand with three average solid particle diameters and five PSDs was used. The results showed that the Umf values of the wide PSDs were lower than those of the narrow cut particles with the same average particle diameter. The standard deviation (SD) and skewness of the PSD also influenced Umf variation. Furthermore, the Umf decreased with increasing bed inventory and bed temperature. The influencing parameters were recast into a dimensionless group and included in a new correlation for predicting Umf. The proposed correlation estimated an average absolute deviation of 14.6% between the experimental data and predicted values. Furthermore, the new correlation was evaluated with a dataset from the literature and gave an average absolute deviation of 15.6%.

Effect of the double vacancy on heat transfer performance of solid particle bed in particle waste heat recovery

In industrial processes, a huge number of high temperature solid particles are produced, and thus, the waste heat resource is abundant. In order to improve the efficiency of waste heat recovery heat exchanger, based on the primary recovery method, a heat transfer model of two-dimensional steady-state particle bed with double vacancy was established. The effects of double vacancy and the variation of vacancy gap on heat transfer of particle bed were studied. The results showed that the double vacancy hinders heat transfer, causing heat currents to flow around the vacancy. In the area close to the vacancy, the particle temperature fluctuates violently and the isotherm changes greatly. At the vacancy area, the heat conduction in X direction increases, in Y direction decreases, and the radiative heat transfer increases. As the number of the gap between double vacancies increases from 0 to 4, the interaction between double vacancies on the temperature field gradually decreases. Compared with the condition without vacancy particle bed, the total heat transfer decreases, and the minimum heat transfer is 33.24 W, the apparent thermal resistance is increased,and the maximum gap is 11.63 °C/W.

New hydraulic insights into rapid sand filter bed backwashing using the Carman–Kozeny model

Fluid flow through a bed of solid particles is an important process that occurs in full-scale water treatment operations. The Carman–Kozeny model remains highly popular for estimating the resistance across the bed. It is common practice to use particle shape factors in fixed bed state to match the predicted drag coefficient with experimentally obtained drag coefficients. In fluidised state, however, where the same particles are considered, this particle shape factor is usually simply omitted from the model without providing appropriate reasoning. In this research, it is shown that a shape factor is not a constant particle property but is dependent on the fluid properties as well. This dynamic shape factor for irregularly shaped grains increases from approximately 0.6 to 1.0 in fluidised state.We found that unstable packed beds in moderate up-flow conditions are pseudo-fixed and in a setting state. This results in a decreasing bed voidage and simultaneously in a decreasing drag coefficient, which seems quite contradictory. This can be explained by the collapse of local channels in the bed, leading to a more uniform flow distribution through the bed and improving the available surface for flow-through. Our experimental measurements show that the drag coefficient decreases considerably in the laminar and transition regions. This is most likely caused by particle orientation, realignment and rearrangement in particles’ packing position.A thorough hydraulic analysis shows that up-flow filtration in rapid sand filters under backwash conditions causes the particle bed to collapse almost imperceptibly. In addition, an improved expression of the drag coefficient demonstrated that the Carman–Kozeny model constant, however often assumed to be constant, is in fact not constant for increasing flow rates. Furthermore, we propose a new pseudo-3D image analysis for particles with an irregular shape. In this way, we can explain the successful method using optimisation of the extended terminal sub-fluidisation wash (ETSW) filter backwashing procedure, in which turbidity and peaks in the number of particles are reduced with a positive effect on water quality.

Determination of void fraction in a bed of solid particles by the method of flow cutoff

The paper presents a new method for determining the void fraction of two-phase flow with a condensable vapor phase. This method relies on the known technique of blocking the flow and allows measuring void fraction in the pore space of solid particle packings. The paper presents the results of experiments with packed beds of steel balls with diameters of 2 mm and 4 mm, 250 mm high. A comparison with some techniques for calculation of void fraction for empty vertical pipes is made.

Numerical Simulation on Coiled Tubing Erosion During Hydraulic Fracturing

Hydraulic fracturing operation through coiled tubing is a safe, economical, and efficient well stimulation technique. During the operation, the wall of coiled tubing spooled on the reel is abraded and eroded by high-concentration proppants. Because of the high-concentration solid phase, a discrete phase model is not appropriate for erosion prediction during a hydraulic fracture operation. In this paper, the monolayer energy dissipation erosion model is used to predict the erosion of coiled tubing. The simulation results show that the sand particles accumulate at the tubing extrados to form a sliding bed and slide along the tubing wall. Therefore, the erosion of the tubing wall spooled on the reel is mainly due to the friction abrasion caused by the sliding bed of solid particles and is related to the centrifugal force of particles. Erosion rate, which is highest at the coiled tubing extrados, has a cubic relationship to the flow rate of the fracturing fluid, has a linear relationship with the sand volume fraction, and is inversely related to the reel radius. The more viscous the fluid, the more uniform the particles distribute, so the erosion rate is reduced with the increase in fluid viscosity.

Numerical Simulation of the Solid Particle Sedimentation and Bed Formation Behaviors Using a Hybrid Method

In the safety analysis of sodium-cooled fast reactors, numerical simulations of various thermal-hydraulic phenomena with multicomponent and multiphase flows in core disruptive accidents (CDAs) are regarded as particularly difficult. In the material relocation phase of CDAs, core debris settle down on a core support structure and/or an in-vessel retention device and form a debris bed. The bed’s shape is crucial for the subsequent relocation of the molten core and heat removal capability as well as re-criticality. In this study, a hybrid numerical simulation method, coupling the multi-fluid model of the three-dimensional fast reactor safety analysis code SIMMER-IV with the discrete element method (DEM), was applied to analyze the sedimentation and bed formation behaviors of core debris. Three-dimensional simulations were performed and compared with results obtained in a series of particle sedimentation experiments. The present simulation predicts the sedimentation behavior of mixed particles with different properties as well as homogeneous particles. The simulation results on bed shapes and particle distribution in the bed agree well with experimental measurements. They demonstrate the practicality of the present hybrid method to solid particle sedimentation and bed formation behaviors of mixed as well as homogeneous particles.

Assessment of mass transfer intensification potential for a CO2 capture process using three-phase fluidized bed

In order to assess the post-combustion CO2 capture intensification potential, a detailed mathematical model was developed for a three-phase fluidized bed. As solvents, various aqueous solutions were used e.g. NaOH and MEA with and without glycerol addition. An innovative mass transfer equipment is presented, a three-phase gas-solid-liquid fluidized bed absorber, in which the bed of low-density inert solid particles is fluidized by the counter current flow of gas as a continuous phase and liquid as a dispersed phase. Experimental data from a pilot plant was used to validate the developed model. The hydrodynamic parameters determined were the followings: fluidized bed expansion ratio, liquid holdup and bed pressure. The most important efficiency parameter, the effective mass transfer area, was assessed. The results show that by using a three-phase fluidization column, the mass transfer parameters exhibit significant increases (8–10 times) in comparison to conventional packed beds. In addition, introducing glycerol to NaOH and MEA solutions was investigated as a potential method to further improve the overall CO2 absorption performance. As the results show, the glycerol addition intensifies the CO2 absorption process by about 10 %.

Toz Gıda Proseslerinde Akışkan Yatak Uygulamaları

Akışkan yatak sistemi, ağır sanayiden, eczacılık, kimya ve gıda sanayisine kadar geniş kullanım alanı bulmaktadır. Bu sistemde küçük katı parçacıklar hava ile temas ettirilir ve hareketleri sağlanarak yatak içerisinde askıda tutulmaları sağlanır. Yatak içerisinde akışkanlaşmanın başladığı andaki hız olarak tanımlanan minimum akışkanlaşma hızı, akışkan yatak sistemlerin en önemli tasarım ve işletme parametresidir. Toz gıdalarda akışkan yatak, kurutma, aglomerasyon, granülasyon ve kaplama proseslerinde yaygın olarak kullanılmaktadır. Akışkan yatak teknolojisinde birçok olay eş zamanlı olarak gerçekleştiğinden sistem üzerine etki eden çok sayıda değişken mevcuttur. Bu derlemede, akışkan yatak, toz gıda proseslerinde akışkan yatak uygulamaları ve akışkan yatak sisteminin kullanılması sırasında dikkat edilmesi gereken parametreler hakkında bilgi sunulmaktadır.

Heat transfer characteristics from high temperature gas in packed bed of solid particles

Heat transfer characteristics from high temperature gas in packed bed of solid particles

An analytical model of subcritical and critical vapor-liquid flow through a granular bed

This paper presents a computational and experimental justification of a theoretical model for the two-phase vapor-liquid flow through a fixed bed of solid particles. The theoretical description is based on the equations of gas dynamics of the granular bed and the homogeneous model of a single-component two-phase flow, given the difference between the velocities of liquid and vapor phases. Relationships between the phase slip ratio and polytropic coefficient of isenthalpic expansion of vapor-liquid flow were obtained using the multi-parameter nonlinear regression. We used the experimental data on the vapor-liquid flow with an inlet pressure, P1, of 0.6-1.2 MPa and an inlet flow quality, x1, of 0.016-0.178 through a H=50-355 mm bed consisting of steel spheres, 2 and 4 mm in diameter, d. An expression for the critical pressure ratio in the granular bed is proposed. The developed model makes it possible to predict the values of mass velocity of the mixture over the entire range of experimental data with an average error of 3%. Based on the model equations, we obtained expressions for dimensionless mass velocity depending on the pressure ratio that can be applied to two-phase flows through both granular beds and other porous media.

FLUIDIZATION OF A BED OF SOLID PARTICLES IN A TWO DIMENSIONAL VERTICAL BOX

Simulation of fluidization of a bed of solid particles in a two-dimensional box is performed using molecular dynamics methods by assuming that superposition of buoyant, gravitational, viscous, collision force will make the particle to move in two dimensions. Two different fluid type is used in this simulation, i.e., gas and liquid fluid. By increasing the fluid velocity from small to high, then minimum fluidization condition reached. As a result, fluidization of alumina particle with liquid fluid has a minimum fluidization velocity lower than gas fluid.

A positivity-preserving central-upwind scheme for isentropic two-phase flows through deviated pipes

Directional drilling in oil and gas extraction can encounter difficulties such as accumulation of solids in deviated pipes. Motivated by such phenomenon, we consider a model for isentropic two-phase flows through deviated pipes. The system of partial differential equations is aimed at simulating the dynamics between a particle bed and a gas phase. The pipe can be either horizontal or vertically deviated where the effects of gravity are incorporated. Furthermore, the acceleration or deceleration due to friction between phases is investigated and spectral properties of the hyperbolic system of balance laws are described. The existence and characterization of steady states under appropriate conditions is analyzed. A new type of steady states arises when a balance between gas and solid phases results in a non-uniform solid particle bed and vanishing solid velocity. This state corresponds to an accumulation of sedimented solids. A central-upwind scheme that preserves the positivity of the gas and solid densities and volume fractions is presented. Including an application of the model to an analysis of accumulation of solids, a variety of numerical tests is presented to show the merits of the scheme.

Catalytic oxidation of crotonaldehyde to crotonic acid in a gas-liquid-solid mini-fluidized bed

Oxidation of crotonaldehyde to crotonic acid is an important chemical reaction process because crotonic acid, its derivative and copolymer are ubiquitous in the productions of chemical, cosmetic, and medicines. However, the reactor safety and process efficiency are still not satisfactory. In order to solve such problems, a novel reactor of gas-liquid-solid mini-fluidized bed with bed inner diameter of 3 mm was developed to carry out the selective catalytic oxidation reaction. The effects of operation conditions and solid particle properties on the conversion rate of reactant crotonaldehyde and the selectivity of product crotonic acid were investigated. The causes of these effects are explained from the standpoint of residence time and gas-liquid mass transfer flux. Moreover, the comparison of reactor performance between the three-phase mini-fluidized bed and the batch stirred tank reactor as a traditional one was made to evaluate the performance of such a reactor. Experimental results show that the average reaction or conversion rate of the mini-fluidized bed is about 30 times much higher than that of batch stirred tank reactor to evaluate the improved performance. But the selectivity is less affected by the operation conditions and solid particle bed properties. The size reduction of three-phase mini-fluidized bed decreases the mass transfer distance of molecular diffusion, and the solid particles and mini-bubbles not only provide the higher specific interface area but also cause hydrodynamics changes that is to intensify the interface disturbance, which effectively accelerate the mass transfer.

Early Time Evolution of Circumferential Perturbation of Initial Particle Volume Fraction in Explosive Cylindrical Multiphase Dispersion

When an annular bed of solid particles that surrounds a cylindrical high-energy explosive core gets radially dispersed after detonation, the expanding front of particles undergoes instabilities. One of the possible causes of the instabilities is an inhomogeneous initial distribution of particles. This study explores this possibility by introducing two-dimensional perturbations to the initial distribution of particles within the annular bed and quantifying the growth of these perturbations over time using two-dimensional simulations. The initial perturbations are in the form of superposition of up to three sinusoidal azimuthal modal variations in the initial particle volume fraction (PVF, ratio of particle to cell volume). These are observed to impact the particle distribution at later times through a channeling instability whose effects are: (i) to decrease the velocity in regions of larger particle volume (PV) and (ii) to facilitate circumferential particle migration into the slow moving high PV sectors. These departures from axisymmetry are quantified by introducing two metrics. The effect of varying the number of azimuthal modes contained in the initial PVF perturbation, along with their amplitudes, wavelengths, and relative phases is investigated. The proposed metrics do not vary substantially with the relative phases; however, there is a strong variation in the metrics due to changes in the wavenumber. Unimodal perturbations were found to amplify both metrics the most.