An extension of the hard-sphere particle–particle collision model to study agglomeration

When performing Eulerian–Lagrangian simulations of particle–fluid flows collisions between the particles need to be accounted for. One of the methods used for this is the hard-sphere model. This model, however, does not take into account cohesive forces between the particles, and for this reason it is not able to simulate many aspects of real flows, such as the formation of agglomerates. There have been some attempts in literature to treat cohesive forces in simulations of particulate flows but none of these methods were actually implemented directly into the hard-sphere model but rather have been solved separately as a part of the numerical scheme. In this paper we show how the standard hard-sphere model may be extended to include these important interactions in an efficient and proper way. The extended model is presented in detail and some numerical results are shown.     

Numerical simulation of turbulent gas–particle flow in a 90° bend: Eulerian–Eulerian approach

A numerical investigation into the physical characteristics of dilute gas–particle flows over a square-sectioned 90° bend is reported. The modified Eulerian two-fluid model is employed to predict the gas–particle flows. The computational results using both the methods are compared with the LDV results of Kliafas and Holt, wherein particles with corresponding diameter of 50 μm are simulated with a flow Reynolds number of 3.47 × 10⁵. RNG-based κ–? model is used as the turbulent closure, wherein additional transport equations are solved to account for the combined gas–particle interactions and turbulence kinetic energy of the particle phase turbulence. Moreover, using the current turbulence modelling formulation, a better understanding of the particle and the combined gas–particle turbulent interaction has been shown. The Eulerian–Eulerian model used in the current study was found to yield good agreement with the measured values.     

Numerical simulation and experimental study of gas cyclone–liquid jet separator for fine particle separation

To address the shortcomings of existing particulate matter trapping technology, especially the low separation efficiency of fine particles, herein, a novel gas cyclone–liquid jet separator was developed to research fine particle trapping. First, numerical simulation methods were used to investigate the flow field characteristics and dust removal efficiency of the separator under different working conditions,and to determined suitable experimental conditions for subsequent dust removal experiment...     

Numerical simulation of fine particle liquid–solid flow in porous media based on LBM-IBM-DEM

Fine particle liquid–solid flow in porous media is involved in many industrial processes such as oil exploitation, geothermal reinjection, and filtration systems. It is of great significance to master the behaviours of the fine particle liquid–solid flow in porous media. At present, there are few studies on the influences of the migration of fine particles on the flow field in porous media, and the effects of the porosity of porous media and inlet fluid velocity on the migration behaviours of fine particles in porous media. In this paper, a liquid–solid flow model was established based on the lattice Boltzmann method (LBM)-immersed boundary method (IBM)-distinct element method (DEM) and verified by the classical Drag Kiss Tumble (DKT) phenomena and flow around a cylinder successfully. In this model, the interaction between solid particles is analyzed using the distinct element method, and the interaction between fine particles and flow field is handled by IBM. Then, the migration and blockage of fine particles in porous media was studied using this model. It is found that, in addition to the blockage, a large amount of blocked-surface sliding-separation occur in fine particles. At the same time, the decrease in porosity increases the damage degree of fine particles on the permeability. The porosity exerts great influence on the penetration rate and dispersion behaviour of fine particles. The inlet fluid velocity mainly affects the residence time of fine particles and the average velocity of motion in the direction perpendicular to the main flow direction.     

DEM simulations of spherical particle–particle collisions

The randomness, diversity, and complexity of the high-speed particle crushing process bring great difficulties to the theoretical analysis of powder engineering. In this paper, the discrete element method is used to simulate the collision of spherical particles, which provides a reference for studying the process and mechanism of crushing between particles under impact load. The Hertz–Mindlin with bonded contact model is used as the particle–particle contact model. The central collisions of particles with different diameter ratios under different high-speed motions and the eccentric collisions with different eccentricities are discussed. The results show that the bond damage increases with the increase of relative velocity in both centre impact and eccentric impact. In centre collisions, particles of smaller objects are more fragmented than particles of larger objects. For smaller target particles, the larger the diameter ratio is, the more particle elements are detached from the target particles, and the greater the bond breakage rate. For larger target particles, the larger the diameter ratio is, the less the particle element falls off and the smaller the bond breakage rate. This provides guidance for the collision and crushing of particles with different particle size ratios and different eccentricities during high-speed motion in engineering applications in the future.     

Discrete particle simulation of gas–solid flow in a blast furnace

Gas–solid flow plays a dominant role in the multiphase flow in an ironmaking blast furnace (BF), and has been modelled by different approaches. In the continuum-based approach, the prediction of the solid flow pattern remains difficult due to the existence of the stagnant zone in the BF lower central part. This difficulty has recently been shown to be overcome by discrete particle simulation (DPS). In this work, the DPS is extended to couple with computational fluid dynamics (CFD) to investigate the gas–solid flow within a BF. The results demonstrate that the DPS–CFD approach can generate the stagnant zone without global assumptions or arbitrary treatments. It confirms that increasing gas flow rate can increase the size of the stagnant zone, and in particular changes the solid flow pattern in the furnace shaft. More importantly, microscopic information about BF gas–solid flow, such as flow and force structures that are extremely difficult to obtain in continuum-approach or experiments, can be analyzed to develop better understanding of the effect of gas phase, and the underlying gas–solid flow mechanisms.     

Development and test of CFD–DEM model for complex geometry: A coupling algorithm for Fluent and DEM

CFD–Discrete Element Method (DEM) model is an effective approach for studying dense gas–solid flow in fluidized beds. In this study, a CFD–DEM model for complex geometries is developed, where DEM code is coupled with ANSYS/Fluent software through its User Defined Function. The Fluent Eulerian multiphase model is employed to couple with DEM, whose secondary phase acts as a ghost phase but just an image copy of DEM field. The proposed procedure preserves phase conservation and ensures the Fluent phase-coupled SIMPLE solver work stable. The model is used to simulate four typical fluidization cases, respectively, a single pulsed jet fluidized bed, fluidized bed with an immersed tube, fluidization regime transition from bubbling to fast, and a simplified two-dimensional circulating fluidized bed loop. The simulation results are satisfactory. The present approach provides an easily implemented and reliable method for CFD–DEM model on complex geometries.     

Discrete particle simulation of solids motion in a gas–solid fluidized bed

The solids motion in a gas–solid fluidized bed was investigated via discrete particle simulation. The motion of individual particles in a uniform particle system and a binary particle system was monitored by the solution of the Newton's second law of motion. The force acting on each particle consists of the contact force between particles and the force exerted by the surrounding fluid. The contact force is modeled by using the analogy of spring, dash-pot and friction slider. The flow field of gas was predicted by the Navier–Stokes equation. The solids distribution is non-uniform in the bed, which is very diluted near the center but high near the wall. It was also found that there is a single solids circulation cell in the fluidized bed with ascending at the center and descending near the wall. This finding agrees with the experimental results obtained by Moslemian. The effects of the operating conditions, such as superficial gas velocity, particle size, and column size on the solids movement, were investigated. In the fluidized bed containing uniform particles better solids mixing was found in the larger bed containing smaller size particles and operated at higher superficial gas velocity. In the system containing binary particles, it was shown that under suitable conditions the particles in a fluidized bed could be made mixable or non-mixable depending on the ratios of particle sizes and densities. Better mixing of binary particles was found in the system containing particles with less different densities and closer sizes. These results were found to follow the mixing and segregation criteria obtained experimentally by Tanaka et al.     

A simulation model and parametric study of MED–TVC process

The present work summarizes the MED–TVC (multi effect desalination with thermal vapor compression) technique associated with the state of the art of modern desalination. In addition, a computer simulation model for all types of evaporation processes is presented. This program provides engineers with cost-effective tools for designing, developing and optimizing thermal desalination plants. It is the objective of this article to develop a mathematical model which would predict the influence of all factors on heat transfer coefficients, temperature and pressure, total capacity and performance ratio of the system under design and operating conditions. The transient nature of temperature during the seasons is modeled by ordinary differential equations based on mass and energy balance. Heat exchangers and thermo-compressor are designed based on the results of mass and energy balance. The validated model is further used to test the effect of variations in certain parameters in the process in order to investigate their influence on the total capacity of the plant. By means of parametric study, the computer simulation tool developed will help designers to achieve the best setting for the desalination process to minimize energy consumption. The comparison between the simulation results and experimental data well proves the program validity.     

Experimental characterization of liquid film behavior during droplets–polyethylene particle collision

Nowadays, the droplet–particle collision characteristics in the gas-phase ethylene polymerization process are still unclear. The high-speed photography and a quasi-circle imaging approach are employed to study the collision interaction characteristics between liquid droplets and polyethylene particles. The liquid film evolution is studied through variations of the film thickness on the particle north pole, the dynamic contact angle, center angle and film thickness at the maximum extension. Results have found that for n-hexane the threshold temperature of the recoil happening increases with increasing initial Weber number, but for 1-hexene it is stable. Over 70°C evaporation and splash occurs immediately. Under low Weber numbers, the water droplet stays for damping oscillations, the reference stable height of which is linearly related to temperatures. Moreover, three regimes of film thickness variation with time are identified and mathematically described, while Regime 3 characteristics are found strongly dependent on the liquid species, Weber number, and particle temperature.     

Phenomenological study of saltating motion of individual particles in horizontal particle–gas systems

A comprehensive use of particle–fluid conveying systems for a wide range of industries requires a deep understanding in all interactions of the particular conveying process. One of the most common particle motions occurring in conveying systems is the saltating motion of particles. Although the literature abounds with theoretical, empirical and numerical studies that investigate the saltation phenomenon, there remain many questions and misunderstandings. Some of the recently solved issues are: which non-dimensional groups are introducing the particle saltating motion, how the saltation length might be predicted, how the pipe diameter and the coefficient of restitution influence the saltation velocity and length.The present work investigates the motion of individual saltating particles and presents a wide range of experimental measurements of the conveying length for a variety of particulate solids, sizes and shapes. The total conveying length was divided into three lengths: the first flight, the rebound and the rolling/sliding and each one of them is theoretically and empirically analyzed and compared. This phenomenological study presents the theoretical evidence to previously empirical findings. The theoretical analysis is further used to define the border conditions between various mechanisms. The results show that for coarse particles the rebound and rolling/sliding motions might be presented by a simple relationship between the Reynolds and Archimedes numbers. Additionally we find that the preferred saltation mode of fine powders depends on the conveying system length and diameter. For example for large pipe diameters and short length the first flight mode is the dominant; however, for small pipe diameters and long systems length the rebound mode is the dominant.     

Influence of slug flow on flow fields in a gas–liquid cylindrical cyclone separator:A simulation study

A simulation method for slug flow based on the VOF multiphase flow model was implemented in ANSYS? Fluent via a user-defined function(UDF) and applied to the dissipation of liquid slugs in the inlet pipe of a gas–liquid cylindrical cyclone(GLCC) separator while varying the expanding diameter ratio and angle of inclination. The dissipation of liquid slug in inlet pipe is analyzed under different expanding diameter ratios and inclination angles.In the inlet pipe, it is found that increasing expanding diameter ratio and inclination angle can reduce the liquid slug stability and enhancing the effect of gravity, which is beneficial to slug flow dissipation. In the cylinder, increasing the expanding diameter ratio can significantly reduce the liquid carrying depth of the gas phase but result in a slightly increase of the gas content in the liquid phase space. Moreover, increasing the inclination angle results in a decrease in the carrying depth of liquid in the vapor phase, but enhances gas–liquid mixing and increases the gas-carrying depth in the liquid phase. Taking into consideration the dual effects of slug dissipation in the inlet pipe and carrying capacity of gas/liquid spaces in the cylinder, the optimal expanding diameter ratio and inclination angle values can be determined.     

Clarification of suspensions: a study of particle deposition in granular media: Part II—A theory of clarification

The observations in Part I [1] on particle deposition have been incorporated into theoretical equations to describe pressure drop and concentration over the complete clarification run—i.e. from the initial transient to the final steady state. The equations differ from those of previous workers in having no arbitrary constants or empirical correlations—all parameters have a precise physical significance and the pressure drop is derived directly from the Kozeny equation. Experiments were performed on a model bed, a packed bed and a sintered disc filter. In all three cases, deviation from the theoretical curves was about 5 per cent maximum in those runs in which parameter values were measured directly, and about 15 per cent maximum when these parameters were estimated completely independently of the run.     

Extraction of cadmium by TODGA–dodecane and TBP–dodecane: A comparative study by MD simulation

Molecular dynamics (MD) simulation of [Cd(II)] along with nitrate ions and water in dodecane was carried out for different nitric acid concentrations. The extraction process using N,N,N’,N’-tetraoctyldiglycolamide (TODGA) and tributyl phosphate (TBP), in biphasic systems, is also simulated at three nitric acid concentrations. In the TBP-based system, the formation of a third phase was observed at 3 M nitric acid concentration. Cd(II) ions form reverse micelles-like clusters with TODGA as an extractant in dodecane. The mass percentage of TODGA in these clusters decreases with increase in the acid concentration while increasing the size of the aggregates at the same time.     

Sequence of monolithic converters DOC–CDPF–NSRC for lean exhaust gas detoxification: A simulation study

With increasingly strict automotive emission regulations the exhaust gas aftertreatment becomes more complex and expensive. Mathematical modelling and simulations play an important role in design of the aftertreatment systems consisting of multiple catalytic devices, reducing the time and cost demands of the system design. In this paper a combined exhaust gas aftertreatment system for diesel engines is studied. It consists of a diesel oxidation catalyst (DOC) for CO and hydrocarbons oxidation, a catalyzed diesel particulate filter (CDPF) for soot filtration, and an NO_x storage and reduction catalyst (NSRC, also called lean NO_x trap, LNT) for NO_x abatement. Effective mathematical models of the individual converters are presented and used first to demonstrate the functionalities of the system, and then to conduct a parametric simulation study. The aim of this study is to map the influence of the individual components on the performance of the entire system in standard test driving cycle. The sizes of the DOC, CDPF, and NSRC converters are varied while the overall volume of the combined system is kept constant. The resulting maps of pressure drop, CO, HC, particulate matter, and NO_x conversions show non-linear dependences on the sizes of individual converters. Co-operative and competitive effects occurring in the combined system are discussed. Suitable reactors sizes are found that enable high conversions of all controlled exhaust gas components.     

Lateral migration of cylindrical particle in a constricted microchannel—A numerical study

Inertial migration of a single cylindrical particle in a constricted microchannel is addressed in this work. A computational model (two-dimensional) has been constructed with the assistance of the immersed boundary finite volume method. The feedback forcing strategy is utilized for the simulation of lateral migration. The parameters like equilibrium position, migration time, and shortest equilibrium distance are computed to analyze the inertial migration characteristics of the particle. Also, a comprehensive parametric study has been performed on the migration behaviour of particles inside the constricted channel by addressing the effects of Reynolds number, diameter, initial release position, and constriction clearance. The parametric study shows that the equilibrium position changes with variations in the initial release position and particle diameter. On the other hand, it stays unaffected by changes in Reynolds number and constriction clearance. The parameters like the shortest equilibrium distance and migration time increase with a rise in Reynolds number and particle diameter. On the other hand, it reduces with the reduction in constriction clearance. Inspired by the parametric study results, in the following stage, a prediction model is created with an artificial neural network algorithm. This is used for an effective forecast of equilibrium position, migration time, and shortest equilibrium distance. Further, the computational model is utilized to check for the existence of a critical Reynolds number for the particle movement in a constricted microchannel. It is observed that the critical Reynolds number remains unchanged with a change in particle diameter. However, it increases linearly with an increase in constriction clearance.     

Numerical simulation of flow behavior of agglomerates in gas–cohesive particles fluidized beds using agglomerates-based approach

Flow behavior of gas and agglomerates is numerically investigated in fluidized beds using a transient two-fluid model. It is assumed that the particles move as agglomerates rather than single particles in the gas–cohesive particles fluidized beds. The present model is coupled a modified kinetic theory model proposed by Arastoopour (2001) with an agglomerate-based approach (ABA). The interaction between gas and agglomerates is considered. The agglomerates properties are estimated from the ABA. Predictions are compared with experimental data measured by Jiradilok (2005) in a bubbling fluidized bed and Li and Tong (2004) in a circulating fluidized bed. The distributions of velocity, concentration and diameter of agglomerates, and pressure drop are numerically obtained. The influences of the contact bonding energy on the distributions of velocity and concentration of agglomerates are analyzed.     

Photocurrent contribution from inter-segmental mixing in donor–acceptor-type polymer solar cells: A multiscale simulation study

Polymer solar cells possess a promising perspective for generating renewable energy at affordable costs, provided their performance and durability can be improved considerably. To this end, several experimental and theoretical techniques have been devised recently, establishing a direct link between local morphology, local opto-electronic properties and device performance. However, their reliability is still unclear to this day. Here, we demonstrate by using a recently developed particle-based multiscale solar cell approach and comparing its results with the ones of a field-based solar cell algorithm that inter-mixing of the electron-donor(D)- and -acceptor(A)-type of segments in a lamellar-like poly(9,9’-dioctylfluorene-co-bis-N,N'-(4-butylphenyl)-bis-N,N'-phenyl-1,4-phenylene-diamine)-poly(9,9'-dioctylfluorene-co-benzothiadiazole) (PFB-F8BT) blend causes that the major part of the charge generation and charge transport takes place inside the nanophases of the nanostructured polymer solar cells in agreement with recent experimental measurements and not, as commonly believed, at the visible domain boundaries of the DA interface. Moreover, we show that the contribution of the exciton dissociation efficiency to the internal quantum efficiency, due to inter-monomeric mixing, is significant and cannot be neglected in simulation studies at the nanoscale. Finally, we demonstrate that keto-defects on the fluorene moiety of the F8BT phase, induced by photo-oxidation, causes a simultaneous increase of the intra-chain contribution and decrease of the inter-chain contribution to the electronic current density, whereas in the reduced form the difference between both contributions is significantly smaller. This antagonistic effect leads to keto-induced electron trapping, resulting in a deteriorated electronic transport efficiency in devices with a photo-oxidized F8BT phase.