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Abstract: This study is a sequel to the paper of Savage and Oger ( this issue) that reviewed experimental studies of airslides. These devices make use of fluidization to facilitate the transport of granular materials over long distances. The present paper describes a detailed and comprehensive consideration of the various contributions to the governing multiphase flow equations and proceeds to carry out numerical simulations of airslide flows and compare the results with laboratory experiments. It was carried out in part using the open source multiphase flow CFD program MFIX. Revisions and additions to the governing equations used in the distribution version of MFIX were made. The results of previously published molecular dynamics simulations were used to formulate a revised radial distribution function. The forms of the quasi-static stress contributions were designed to permit the development of higher concentration flows typical of experimentally observed airslide flows. Finally, additional terms were included in the particle fluctuation energy equation to account for (i) the viscous dissipation of the fluctuating particles due to the interstitial air, and (ii) the energy source term arising from the transfer of energy from the fluid to the particles. These expressions have been incorporated in the computational scheme and simulations of fluidized granular flows in a rectangular channel having frictional side walls were carried out. Some initial exploratory calculations were performed to examine the effects of various parameters on the mass flow rates and the velocity profiles. Different wall conditions were studied by varying the particle and wall restitution coefficients. The effects of varying the minimum fluidization velocity and the solid fraction thresholds were also examined. The simulation scheme was then applied to model two of the better documented fluidized chute flow experiments; those of Botterill and Bessant (1976), and the McGill University fluidized solids flow channel experiments of Liot (1979) and Chan (1979). Results of these computations and comparisons with observed experimental airslide behavior are discussed. Good agreement is found between the simulations and the experimental airslide flow characteristics. [Copyright &y& Elsevier]

Abstract: Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, are widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas–solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas–solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve the 2D numerical simulations of pseudo-2D gas–solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data. [Copyright &y& Elsevier]

Abstract: A DNS (Direct Numerical Simulation) model for solid, liquid, and gas three-phase flow, mainly targeting to simulate the nucleation processes in wet granulation, is presented in this paper. A liquid–gas two-phase flow is solved by using the CIP (Constrained Interpolation Profile) method, which is one of the CFD multi-phase solvers, and a solid particle flow is solved by DEM (Discrete Element Method) separately. The interaction between fluid (liquid and gas) and solid phases is taken into account by coupling CFD and DEM. A new model is developed to account for the capillary force exerted on particles, i.e. the surface tension force which pulls a particle along with the solid–liquid–gas contact line, and the accuracy of the model is examined. Although the main focus in this study is to develop a CFD–DEM coupling and the capillary force models for wet granulation, some simulation results are also presented to see the droplet behaviour often encountered in a wet granulation process, i.e. the droplet penetration into a static particle bed as well as the droplet impingement onto a dynamic particle bed. The simulation results are compared with the experimental results in the literature and it shows a good agreement in terms of tendency. [Copyright &y& Elsevier]

Abstract: This paper describes the model development of dynamic sweating in falling film melt crystallization (FFMC) using fractal porous media theory. The crystal layer has the characteristics of a fractal porous medium. An overall mass balance is applied to determine the structural and characteristic parameters of the crystal layer. Two ideal hypothetical models are adopted to describe the dynamic change of flow rate in sweating under sweating conditions. The characteristic factor φ is introduced to modify the model to describe the real process. The model is validated by experiment, and the simulated result agrees well with the experimental result. The model is then exploited to understand sweating behavior and the structure and permeability variations of the crystal layer in FFMC. More significantly, the sweating model is also an important part of the model system of the overall FFMC process. [Copyright &y& Elsevier]

Abstract: Many novel reactor concepts based on the integration of membranes in fluidized beds have been proposed. For the detailed numerical investigation of such systems, a method is required describing the motion of the particles while accounting for (i) the gas motion and (ii) the encounters between particles and confining walls/membranes. In this paper a novel hybrid computational method is presented, combining the Discrete Particle Model (DPM) and the Immersed Boundary Method (IBM). The first part focuses on the implementation and validation of these models. The IBM component of the model has been verified by comparing the computed drag coefficients for Simple Cubic (SC) arrays of cylinders with data of Sangani and Acrivos (1982) at creeping flow conditions. For higher Reynolds numbers the code has been compared to Ferziger and Peric (2002) for a single off-center cylinder, after which simulations with addition and extraction of gas through the membrane surface have been conducted. In the second part of this work we will focus on actual fluidized bed membrane systems, and will report results of simulations for several membrane geometries as well as permeation ratios. [Copyright &y& Elsevier]

Abstract: The paper presents the first mathematical model that can simulate the oscillatory behaviour during methane oxidation over Pd catalysts. The main experimental results are reproduced, including the anti-phase oscillations of the concentrations of the reaction products, CO2 and H2O. In line with the experimental results, it is demonstrated that the oscillations are related to periodic oxidation and reduction of the Pd catalyst. The complicated waveform of the oscillations and the anti-phase oscillations of two reactant products originate due to the periodic accumulation and removal of bulk carbon. The simulation results show that the anti-phase oscillations of CO2 and H2O concentrations can occur only in the case of a high rate of carbon diffusion and a large depth of penetration of carbon into the Pd catalyst. [Copyright &y& Elsevier]

Abstract: This paper was concerned with the model development and experimental validation of the detailed crystal layer growth and multi-ions impurity distribution process in the falling film melt crystallization (FFMC) model. The phosphoric acid (PA) was separated and purified by FFMC to obtain a hyperpure phosphoric acid (HPA), which was a vital electronic chemical in IT industry. To establish a valid model, which offered an easy and convenient path of the simulation, dynamic heat and mass balance, approaches were adopted to describe the variation of crystal layer growth rate along the crystallizer. An impurity balance approach was adopted to describe the change of distribution coefficient for multi-ion impurity. A criterion was proposed to determine the formation of branched-porous (B–P) structure. The model was validated by experimental results with various equipments and operational conditions and a good agreement was obtained. The effective distribution coefficient K eff for multi-ion impurities were less than 0.2 (Na+), 0.25 (Fe3+) and 0.35 (Ca2+) with proper operation conditions. The resulting model was directly exploited to understand crystal layer growth and impurity distribution behaviors in FFMC from laboratory to industrial scale. More significantly, the model proposed a method for the separation effect evaluation and the key operational conditions (feed rate and cooling rate) determination which could readily develop optimal crystal layer growth route during industrial crystallization. In addition, the model was a vital base to describe the subsequent purification step of FFMC: sweating process. [Copyright &y& Elsevier]

Abstract: A precise mechanistic model is fundamental in simulation, control and optimization of ethylene pyrolysis process. In the Kumar kinetics model proposed by Kumar and Kunzru, there are ten changeable selectivity coefficients and minor-changeable kinetics parameters in the primary reaction equation. They are mainly determined by oil properties, especially the oil composition. This paper proposes a new method of compromising adjustment solution based on target decomposition strategy and Error Correction Chaos Optimization (ECCO) algorithm to mainly acquire rational primary coefficients, and kinetics parameters when necessary. The core idea is to realize atoms balances of the carbon and hydrogen in the primary reaction, as well as minimum yield errors of products based on ECCO algorithm. It exceeds existing methods mentioned by other literatures in its preferable compromise between overall elemental balances and minimal yield errors. It also takes minor tuning of kinetics parameters into consideration. Moreover, this method has been proven effective and applicable to many naphthas with different properties. These data are from a real ethylene plant. The results are helpful in the design of optimal operational conditions and ultimately in controlling of ethylene cracking furnaces which will be discussed briefly. [Copyright &y& Elsevier]

Abstract: MP-PIC (multi-phase particle in cell) method combined with the EMMS (energy minimization multi-scale) drag force model was implemented with the open source program MFIX to simulate the gas–solid flows in CFB (circulating fluidized bed) risers. Calculated solid flux by the EMMS drag agrees well with the experimental value; while the traditional homogeneous drag over-predicts this value. EMMS drag force model can also predict the macro- and meso-scale structures. Quantitative comparison of the results by the EMMS drag force model and the experimental measurements show high accuracy of the model. The effects of the number of particles per parcel and wall conditions on the simulation results have also been investigated in the paper. This work proved that MP-PIC combined with the EMMS drag model can successfully simulate the fluidized flows in CFB risers and it serves as a candidate to realize real-time simulation of industrial processes in the future. [Copyright &y& Elsevier]

Abstract: In this paper, an enhanced virtual reference feedback tuning (EVRFT) design method with specific application to adaptive PID controller design is developed. The proposed EVRFT design is an extension of conventional VRFT design and adaptive VRFT (AVRFT) design previously developed in the literature. The EVRFT design makes use of a second-order reference model instead of the first-order reference model used by both VRFT and AVRFT designs. In addition, unlike the AVRFT design, the parameter of reference model in EVRFT design is updated at each sampling instant to further enhance the performance of resulting adaptive PID controller. Simulation results demonstrate that the adaptive PID controller using the proposed EVRFT design gives better response than those obtained by the VRFT and AVRFT designs. [Copyright &y& Elsevier]

Abstract: Various algorithms have been presented in the literature for contact detection between three-dimensional bi-convex objects, such as pharmaceutical tablets. Most are approximations to true bi-convex shapes, e.g., glued spheres, sphere-intersections, sphero-cylinders, and super-ellipsoids, and others, such as the discrete function representation, are computationally expensive. In this paper, algorithms are presented for determining if two, true bi-convex tablets, or a bi-convex tablet and an infinite plane, are in contact. A bi-convex tablet has two spherical caps and a cylindrical band. In all, ten contact scenarios are examined involving all components of the tablets, i.e., caps, band, and edges. In addition to checking for contact, relations for determining the contact location, overlap, and unit normal vector for the contact are presented for use in discrete element method computer simulations. These algorithms have been validated for single and multiple tablet scenarios: (a) comparing translational and angular velocities of a single bi-convex tablet impacting a flat plane, (b) comparing the fill fractions of bi-convex tablets in a container, and (c) comparing the dynamic angle of repose of bi-convex tablets in a rotating drum. [Copyright &y& Elsevier]

Abstract: This work presents a novel use of the Discrete Element Method (DEM) combined with inter-particle mass transfer in order to simulate polymer swelling and dissolution. Each particle can absorb water and swell, pushing on its neighbours and causing an overall expansion. Once the disentanglement threshold is reached, the polymer dissolves and the particle reduces in size. This paper applies DEM to simulate the radial swelling and dissolution of cylindrical tablets. The method was validated against exact numerical solution of the same system to assess the accuracy of the DEM simulations for different DEM particle sizes. Parametric studies were done to assess the impact of physical parameters – namely the concentration-dependent diffusion coefficient of water through the polymer, the dissolution rate constant of the polymer and the disentanglement threshold of the polymer – on the radial expansion of the tablet. It was found that different settings of the concentration-dependent water diffusion coefficient function could produce similar radial expansion curves but with different internal concentration profiles. Increasing the dissolution rate constant or decreasing the disentanglement threshold of the polymer caused a reduction in the maximum radius of tablet. Lastly, ATR-FTIR spectroscopic imaging was used to obtain chemical images of a pure hydroxy-propyl methylcellulose (HPMC) tablet swelling and dissolving. The model was optimised to match both the HPMC tablet radius and the concentration profiles over time. [Copyright &y& Elsevier]

Abstract: In this paper, a numerical model for the flow of foams in flotation cells in up to three dimensions is described. By using finite elements to solve Laplace''s equation for a potential scalar, the flow pattern and velocity of the foam can be obtained. This has allowed, for the first time, the carrying out of numerical investigations of foam flow patterns regardless of the symmetry of the system. The numerical model has been implemented in Fluidity, a general purpose finite element method code that allows simulations to be carried out on anisotropic unstructured meshes. Such a model is of particular interest since other phenomena occurring in flotation depend on the foam velocity. Convergence tests that verify the numerical model are presented, and simulation results that showcase important features of the present implementation are discussed. [Copyright &y& Elsevier]

Abstract: The present paper describes an Euler–Lagrange model utilizing a drag closure derived from direct numerical simulations (front-tracking model) for (i) single isolated bubbles and (ii) bubbles rising in bubble swarms, expressed as a function of the local gas fraction. The model is applied to the prediction of an air/water system in a bubble column and for which experimental data is available. The effect of variation in size of the mapping window for the interphase coupling between the Eulerian and Lagrangian framework is investigated for both closure relations. It is found that the drag closure as a function of the local gas fraction is an improvement over the use of the drag closure for isolated single bubbles for the prediction of bubbly flow. [Copyright &y& Elsevier]

Abstract: With the study object of an 100kt/a SL-II ethylene cracking furnace, this paper used Computational Fluid Dynamics (CFD) method to carry out coupled simulation studies on the flow, combustion, radiative heat transfer and thermal cracking reaction processes in the cracking furnace. The standard k–ε two-equation model was applied to turbulence simulation. The finite-rate/eddy-dissipation model was used for modeling of non-premixed combustion of the bottom burners and premixed combustion of the sidewall burners. The Discrete Ordinates (DO) model was applied to the simulation of radiative heat transfer of furnace. The simulation results show the detailed information about velocity, temperature and concentration fields in the furnace and heat flux distribution on the reactor tubes skin. This work will provide a theoretical basis for the optimization of the geometrical structure and operational parameters of the cracking furnace. [Copyright &y& Elsevier]

Abstract: Bubbly flows exist extensively in industrial processes, so it is very meaningful to study hydrodynamic characteristics of them to improve efficiency of bubbly flow equipments. This paper introduces a numerical method of the Euler–Lagrange two-way model for the air–water bubbly flows in detail. The flow field is simulated by using direct numerical simulations (DNS) in Euler frame of reference, while the bubble dynamics are fully analyzed by integration of Newtonian equations of motion taking into account interphase interaction forces including drag force, lift force, wall lift force, pressure gradient force, virtual mass force, gravity force, buoyant force, and inertia force in Lagrange frame of reference. The coupling between phases is considered by regarding the interphase interaction forces as a momentum source term of the continuous phase. Bubbles distribution and turbulent statistics of the liquid phase are comprehensively analyzed. The results show that an overwhelming majority of bubbles cluster near the walls, and turbulent structures of the liquid phase are modified to some certain by addition of bubbles, namely, the mean streamwise velocity become increased at the core of the channel, the wall-normal and spanwise turbulent intensities and Reynolds stress are reduced. Redistribution of turbulent energy from the streamwise velocity components to wall-normal and spanwise velocity components is also suppressed due to the addition of bubbles. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This paper investigates inter-tablet coating variability, specifically, the variability of tablet residence times within the spray zone of a horizontal coating pan. Results from experiments, discrete element method (DEM) computer simulations, and an analytical model developed to describe the coating mass distribution are presented. The simulations indicate that the coefficient of variation of tablet residence times, and subsequently, of coating mass, decreases with time following a power law relation. The theoretical model demonstrates that the coefficient of variation of residence time for a randomly mixed tablet bed is inversely proportional to the square root of the number of coating “trials”. DEM simulations show that during each pan revolution, tablets in the spray zone remain in a quasi-segregated state from tablets located outside the spray zone for some time period termed Δt seg. Increasing the pan''s Froude number, the spray zone aspect ratio, and the tablet–tablet and tablet–pan friction coefficient all act to decrease Δt seg, leading to more uniform residence times and less inter-tablet coating variability for a given operating time. The relationship between Δt seg and tablet load is more complex due changes in bed dynamics. In addition to the variability studies, a model is developed that relates coating fraction, effective mass flow rate, Δt seg, and the desired coating mass to the allowable fraction of tablets with a coating mass lying outside of a specified range of coating masses. [Copyright &y& Elsevier]

Within the last 20 years, computer simulations of materials have evolved from an academic curiosity to a predictive tool for addressing structure–property–processing–performance relations that are critical to the design of new products and processes. Chemical engineers, with their problem-oriented thinking and their systems approach, have played a significant role in this development. The computational prediction of physical properties is particularly challenging for polymeric materials, because of the extremely broad spectra of length and time scales governing structure and molecular motion in these materials. This challenge can only be met through the development of hierarchical analysis and simulation strategies encompassing many interconnected levels, each level addressing phenomena over a specific window of time and length scales. In this paper we will briefly discuss the fundamental underpinnings and example applications of new methods and algorithms for the hierarchical modelling of polymers. Questions to be addressed include: How can one equilibrate atomistic models of long-chain polymer melts at all length scales and thereby predict thermodynamic and conformational properties reliably? How can one quantify the structure of entanglement networks present in these melts through topological analysis and relate it to rheological properties? Are there ways to predict the microphase-separated morphology and stress–strain behaviour of multicomponent block copolymer-based materials, such as pressure sensitive adhesives? Is it possible to anticipate changes in the barrier properties of glassy amorphous polymers used in packaging applications as a consequence of modifications in the chemical constitution of chains? [Copyright &y& Elsevier]

This paper presents a mathematical model based on a three-phase theory, which is used to describe the mass and heat transfer between the gas and solids phases in a batch fluidised bed dryer. In the model, it is assumed that the dilute phase (i.e., bubble) is plug flow while the interstitial gas and the solid particles are considered as being perfectly mixed. The thermal conductivity of wet particles is modelled using a serial and parallel circuit. The moisture diffusion in wet particles was simulated using a numerical finite volume method. Applying a simplified lumped model to a single solid particle, the heat and mass transfer between the interstitial gas and solid phase is taken into account during the whole drying process as three drying rate periods: warming-up, constant rate and falling-rate. The effects of the process parameters, such as particle size, gas velocity, inlet gas temperature and relative humidity, on the moisture content of solids in the bed have been studied by numerical computation using this model. The results are in good agreement with experimental data of heat and mass transfer in fluidised bed dryers. The model will be employed for online simulation of a fluidised bed dryer and for online control. [Copyright &y& Elsevier]