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Highlights • Drag of steady flow through and around arrays of cylinders are numerically investigated. • A novel formula for the drag force is proposed. • Macroscopic permeability is estimated from microscopic flow results via Darcy's law. • Drag ratio computed is in a good agreement with previous porous media model results. Abstract The drag properties of flow through and around square arrays of 10 × 10 evenly spaced circular cylinders with a wide range of solid fraction ϕ from 9.69 × 10 - 11 to 0.785 and Reynold number of the array Re from 1 to 50 are investigated numerically. The purpose of the present study is to better understand the phenomena of flow through and around permeable bodies that appear in bioreactors and fluid–solid reactors, for example. Instead of using the semi-empirical porous medium model, the direct numerical simulation is employed in order to investigate the flow mechanism from a microscopic point of view. A peak in drag coefficient is observed for the range of ϕ investigated, which appears at a smaller ϕ as Re increases. Three flow regimes are identified based on the shape effects quantified via the averaged velocity within the array, and the drag property in each regime is analyzed. A novel drag formula is also found by investigating the dependence of drag on ϕ and R (Reynolds number based on the mean velocity within the array). Finally, the dimensionless macroscopic permeability Da is estimated via the Darcy's law. The drag ratio computed is in a good agreement with the previous results from porous media models. [ABSTRACT FROM AUTHOR]

Though bubble column reactors are widely used in industry, the present design practice is still closer to an art than a desired state of science because of the complexity of its fluid mechanics. The empiricism can be reduced by understanding detailed flow pattern, turbulence characteristics and turbulent structures and their effects on the performance such as mixing and axial mixing in both the phases and rate of heat and mass transfer. For this purpose, in the present work, CFD simulations have been undertaken by using standard k-ε, RSM and LES turbulence models. The cylindrical column having a computational height of H D = 900 mm with inside diameter of D = 150 mm was employed as a bubble column operated at three superficial gas velocities (20, 40 and 100 mm/s). The instantaneous three dimensional velocity field is obtained by means of two phase Eulerian-Eulerian Large Eddy Simulations (LES). The conservation equations for turbulent kinetic energy (k) and the turbulent energy dissipation rate (ε) have been derived from the two fluid governing equations using the Reynolds averaging procedure. This enabled accurate estimation of convective transport, diffusive transport, turbulent transport, production and dissipation of k and ε. These estimations have been compared with the modelled terms of the standard k-ε and Reynolds stress models. The difference in values gives an idea about the severity of assumptions made in these models. An attempt has been made to bring out the implications of simplifying assumptions. [ABSTRACT FROM AUTHOR]

Gas–liquid two phase flows are widely encountered in industry. The design parameters include two phase pressure drop, mixing and axial mixing in both the phases, effective interfacial area, heat and mass transfer coefficients. Currently, there is a high degree of empiricism in the design process of such reactors owing to the complexity of coupled flow and reaction mechanism. Hence, we focus on synthesizing recent advances in computational and experimental techniques that will enable future designs of such reactors in a more rational manner by exploring a large design space with high-fidelity models (computational fluid dynamics) that are validated with high-fidelity measurements (hot film anemometry (HFA), Laser Doppler anemometry (LDA), particle image velocimetry (PIV), etc.) to provide a high degree of rigor. Understanding the spatial distributions of dispersed phases and their interaction during scale up are key challenges that were traditionally addressed through pilot scale experiments, but now can be addressed through advanced modelling. For practically complete knowledge of the fluid mechanical parameters, it is desirable to implement direct numerical simulations (DNS). However, the current computational power does not permit full DNS for real bubble columns. Therefore, we have been using simplified turbulence models (such as large eddy simulation, Reynolds stress, k – ε , etc.) which need the knowledge of turbulence parameters. For the estimation of these parameters, currently semi-empirical procedures are being used pending the knowledge of turbulence. Further, the formulation of governing equations in all the CFD models (except DNS), the knowledge of interface forces (drag, lift, virtual mass, Basset, etc.) is needed and for their estimations empirical correlations are being employed, again pending the knowledge of fluid mechanics under turbulent conditions in bubble columns. In gas–liquid dispersions, the gas is sparged in the form of bubbles. During the bubble rise, the mechanism of wake detachment creates turbulence which can be called as wake generated turbulence. In addition, energy gets transferred from the gas phase to liquid phase. The quantitative amounts are negligible when bubble motion is not hindered and the gas–liquid dispersion is homogenous. The amounts increase with an increase in the extent of hindrance. However, in the homogenous regime, even under extreme conditions, the extent of energy transfer in the bulk gas–liquid dispersions (volume other than wake volume) is fairly limited. On contrast, in the heterogeneous regime, the rates of energy transfer become sizeable. The energy received by the liquid (in both the regimes) also creates turbulent motion and termed as bulk generated turbulence. In turbulent flows a compendium of eddies (flow structures) of different length and time scales contribute towards improved/enhanced mixing, momentum transfer, heat transfer, and mass transfer (transport phenomena). Hence, a proper understanding of the dynamics of these turbulent flow structures, and their role in the transport phenomena, can bring substantial improvement in the scale-up and design procedures. The present paper brings out the current status of knowledge on bubble generated turbulence. All the published literature in experimental measurements and DNS simulations has been critically analysed and coherently presented. [ABSTRACT FROM AUTHOR]

[Display omitted] • Single and multiphase CFD of a small-scale crystallizer with two stirrer types. • Indications when each stirrer is preferably used based on hydrodynamics. • X-ray CT applied in mixing studies used for the validation of the CFD simulations. Although small-scale crystallizers have gained increasing importance in recent years, their hydrodynamic properties have not yet been thoroughly studied. The purpose of this work is to characterize an intensively stirred small-scale crystallizer and to analyze whether its fluid mechanics behavior deviates from being homogeneously well-mixed. To this aim, single and multiphase computational fluid dynamics (CFD) simulations have been conducted. Two types of stirrers, including one overhead stirrer (OS) and one magnetic stirrer (MS), were compared. The single-phase CFD simulations showed that the mixing characteristics of the two stirrers differ significantly, thereby leading to variations in the distribution of solids. The MS is an axial flow type impeller, which is better at handling solid suspensions than the OS. The simulations were complemented by X-ray computed tomography measurements, which confirmed that spatial variations in solid distribution occur and that assuming a homogeneous suspension might lead to errors when modeling crystallization processes. [ABSTRACT FROM AUTHOR]

Abstract: The blood viscosity uncertainty is investigated in an idealized portal-vein flow and its effect is propagated in the 3D Navier–Stokes equations and quantified on the quantities of interest, such as wall shear, pressure and mass flow split. The variability of the random blood viscosity is investigated in detail assuming that the true blood viscosity is given in the range covered by four Carreau blood viscosity model variants. Three different characterizations of the associated Probability Density Functions (PDFs) were considered: (i) a single blood Carreau model with random parameters that covers the variability range under consideration; (ii) the assumption that there is equal probability of sampling each of the four different Carreau model variants; and (iii) the assumption of a bi-linear composition of the four Carreau models affected by random coefficients. These assumptions result in different inlet blood viscosity PDFs that were propagated in the Navier–Stokes solution with the application of a non-intrusive stochastic collocation method based on the generalized polynomial chaos expansion. The stochastic simulations have quantified the uncertainty of random viscosity model parameters on the interested flow parameters wall shear stress and pressure for two Reynolds numbers: Re=212 and Re=21. The results include error bars of these variables and hierarchy impact of the random variables on the solution. [Copyright &y& Elsevier]

A detailed numerical study on the interaction between two consecutive Taylor bubbles rising through vertical columns of stagnant Newtonian liquids is reported in this work. The CFD method used is based on the VOF technique implemented in the commercial package ANSYS FLUENT. Simulations were made for a large set of flow conditions, within the laminar regime, covering a range of Morton number of 4.72×10−5–104 and an interval of Eötvös number between 15 and 575. The changes in the shape of the bubbles interface were followed throughout the approach process, and the main hydrodynamic features characterizing the liquid film and the wake region of the trailing bubble were determined as the separation distance became smaller. Numerical data on the velocity ratio between the trailing and the leading bubble are presented, and two distinct regions are identified (acceleration and deceleration) in the corresponding evolution curves. The velocity ratio curves produced for several flow conditions were fitted to equations describing the acceleration and the deceleration behaviour of the trailing bubble. These equations together with the fitting parameters obtained here can be very useful to improve simulators of continuous slug flow. [ABSTRACT FROM AUTHOR]

Abstract: Microtiter plates are one of the most widely used platforms for biofilm studies. However, these systems have been used rather blindly without knowledge of the flow characteristics inside them. Plates with 96-wells were used to study flow dynamics and its influence on Escherichia coli JM109(DE3) biofilm formation. Two different glucose concentrations (1gL−1 and 0.25gL−1) and two different shaking conditions were tested using incubators with orbital diameters of 50 and 25mm. Biofilm growth was monitored for 60h and the hydrodynamics were simulated by computational fluid dynamics. These simulations have shown that wall shear stress was higher near the air/liquid interface and average values of 0.070 and 0.034Pa were obtained for the largest and smallest orbital diameter. For the high glucose concentration, the maximum biofilm amount was attained at 24h and similar values were obtained in both incubators. For the low glucose concentration, lower values were attained. Numerical simulations indicated that microtiter plates can adequately model biofilm formation in relevant biomedical systems. [Copyright &y& Elsevier]

Abstract: We performed Direct Numerical Simulation (DNS) of a gas-fluidized bed using the Immersed Boundary method combined with traditional Computational Fluid Dynamics. We have compared the individual fluid–particle force with the force as evaluated in an unresolved Discrete Element Model (DEM) simulation using closures for the gas–solid force for one fluidisation condition. We find that the average DEM gas–solid force is about 33% smaller than the “true” value which follows from the DNS model. For more realistic DEM simulations, a modification of the gas–solid force calculation is required, for instance by adding fluctuations or including the effect of the granular temperature. [Copyright &y& Elsevier]

Abstract: Among many research studies on fluidized bed membrane reactors, only very few focus on the details of the effects of gas permeation through the membranes on the hydrodynamic properties of the membrane-assisted fluidized bed. For this reason, in the first part of this paper, a novel hybrid Immersed Boundary Method (IBM) Discrete Particle Model (DPM) has been developed. In the second part of the paper, this model is employed to investigate fluidized bed membrane reactors in more detail. Simulations without membrane inserts (having vertical membranes at the side walls instead), with membrane tubes in an in-line arrangement and membranes in a staggered arrangement are compared with each other. The time-averaged particle fraction maps display a lower bed height for the simulations with inserts. A very important aspect of the simulation with gas extraction/addition via the side walls is the solids circulation; an inversion of the solids circulation is observed when gas is added via the side walls with altered bubble properties. Because of this phenomenon, the bubble size counter-intuitively decreases when gas is added, and increases slightly when gas is extracted. The latter is a result of the existence of compacted zones near the membranes. For the simulation cases with membrane inserts, the solids circulation and bubble properties are different; in these cases they mainly depend on the local fluidization velocity, and not so much on the extent of permeation itself. Although the arrangement of the membrane tubes plays only a minor role in this matter, their presence has a pronounced influence on the bubble size. The system''s energy and energy dissipation are both smaller for the simulations with inserts compared to those with permeation via the side walls. Also in this respect, the local fluidization velocity is found to be more important than the extent of permeation. [Copyright &y& Elsevier]

Abstract: The micromechanics of different particle–fluid flow regimes, such as fixed, expanded and fluidized beds, in gas fluidization is investigated for group A and B powders. To establish the connection between macroscopic and microscopic descriptions of complex particle–fluid flows, focus is given to the following two aspects: the formation of a stable expanded bed in relation to the interparticle cohesive, sliding and rolling frictional forces, and the correlation between coordination number (CN) and porosity (ε). The method employed is the combined approach of three-dimensional (3D) discrete element method (DEM) and two-dimensional (2D) computational fluid dynamics. The results show that compared to 2D DEM, 3D DEM is more reliable in investigating the micromechanics of granular media, although both can capture key features of different flow regimes. The roles of various forces between particles and between particles and fluid are examined, and the origin of different flow regimes is discussed. It is shown that the cohesive force is critical to the formation of a static expanded bed, while the sliding and rolling frictional forces also play a role here. The criterion for bed expansion is analyzed at bulk and particle scales, and the deficiency at a bulk scale is identified. CN, as a key measure of local structure, is analyzed. It is found that the CN–ε relationship for group A powders has a transitional point between the expanded and fluidized bed flow regimes at a bulk scale, unlike group B powders. A new phase diagram is established in terms of CN–ε relationship that has two branches representing expanded and fluidized (bed) states, which corresponds to the one in terms of interparticle forces. [Copyright &y& Elsevier]

Abstract: Scale-up of a crystallizer is an extremely difficult and unsolved issue up till now, mainly because of the complexity of occurring phenomena from kinetic and fluid-dynamics point of view. In this paper the attempt was made to deal with this problem with the use of computational fluid dynamics (CFD). The expectations of the mentioned process and possibilities from fluid-dynamics point of view were discussed with aid of primary circulation time. Consideration involved full and partial geometrical similarity as well as two selected scale-up criteria, i.e.: constant unit power input and propeller tip speed. In general, geometric similarity is not recommended for scale-up. [Copyright &y& Elsevier]

Abstract: The aim of this study was to find models for turbulent fragmenting forces in the high-pressure homogeniser from data available in Computational Fluid Dynamics (CFD) simulations with Reynolds Averaged Navier Stokes (RANS) turbulence models. In addition to the more common RANS k–ε turbulence models, a Multi-scale k–ε model was tested since experimental investigations of the geometry imply large differences in behaviour between turbulent eddies of different length-scales. Empiric models for the driving hydrodynamic factors for turbulent fragmentation using the extra information given by multi-scale simulations were developed. These models are shown to give a more reasonable approximation of local fragmentation than models based on the previously used RANS k–ε models when comparing to hydrodynamic measurements in an experimental model. [Copyright &y& Elsevier]

Abstract: This paper presents the state of the art regarding the understanding of axial mixing in pulsed columns. Residence Time Distribution (RTD) experiments carried out mainly between 1986 and 2002 are reviewed in connection with fluid mechanics studies and CFD simulations. Based on prior work by Buratti (1988), a new model is established to correlate the continuous phase axial dispersion coefficient with the operating conditions in a wide range of operating (pulse intensity up to 7.5cms−1) and geometric conditions (0.17≤H/D≤1.33), thereby reducing the estimation error from 143% to 21% in the case of small-aspect ratio columns (H/D<1), such as those used in nuclear research, and from 95% to 27% in the case of (possibly annular) industrial size columns. Experimental results are relatively well reproduced by RANS-type computational fluid dynamics (CFD) simulations, provided a low-Reynolds model is used for the turbulent viscosity estimation. [Copyright &y& Elsevier]

Abstract: Micromixing of viscous systems in a stirred-tank reactor with Rushton turbine is investigated numerically. It is characterized by the product selectivity of parallel competitive reactions. Flow fields inside the reactor are determined by the Reynolds Stress Model (RSM). A computational fluid dynamics (CFD) method combining the standard E model and Finite-Rate/Eddy-Dissipation (FR/ED) model is implemented and is validated using experimental data in the literature. The simulations show that a higher agitation speed, a lower fluid viscosity and/or a feeding location closer to the discharge area of the impeller favor micromixing and the reaction rate. The trajectory of the reaction plume also influences the micromixing performance. The value of the FR/ED model parameter determined by lab-scale experiments decreases with increasing fluid viscosity. However, it is little affected by the agitation speed. These results provide useful guidelines for the scale-up of industrial reactors with complex chemical reactions. [Copyright &y& Elsevier]

Abstract: The flow field in T-jets mixers is studied experimentally for different geometrical parameters using Planar Laser Induced Fluorescence (PLIF). A particular chaotic flow regime is reported for the first time from experimental work. It is shown that two geometrical parameters, the ratio of the mixing chamber width to the injectors’ width, and chamber''s width to the chamber''s depth, have an impact on the flow dynamics as important as the jets Reynolds numbers that were here studied over a range of values from 50 to 500. The values of the geometrical parameters and operation Reynolds number that mark the transitions of flow regime in the T-jets mixers are reported, and the impact of the geometry on such transitions is analyzed. The main features of the flow regimes are related with the mixing efficiency in T-jets mixers. Computational Fluid Dynamics (CFD) simulations for a particular case are shown in order to reveal the 3D flow structure of chaotic flow regime. [Copyright &y& Elsevier]

Abstract: Since the emulsification in the High-Pressure Homogenizer (HPH) is controlled by hydrodynamic forces, the turbulent flow field in the valve region is of significant interest. Computational Fluid Dynamics (CFD) simulations have been used for this in many studies. However, there are reasons to question if the utilized turbulence models, with their inherent assumptions and simplifications, could accurately describe the influential aspects of the flow. This study compares CFD simulations using the methods from previous studies with experimental measurements in a model HPH valve. The results show that the region upstream of the gap can be described accurately regardless of turbulence model and that the gap region can be captured by using one of the more refined k−ε models. None of the studied turbulence models were able to describe the details of the highly turbulent region downstream of the gap. The obtained results are also discussed in relation to generalizability and limitations in using CFD simulations for understanding the emulsification in the HPH. [Copyright &y& Elsevier]

Abstract: Flow behavior of particles is simulated using an Eulerian–Eulerian two-fluid model based on the kinetic theory of rough spheres. The interactions of the short and fast collisions of particles are incorporated to consider the redistribution of momentum and kinetic energy between the collision and friction interactions. The fluctuating kinetic energy by collisions of particles has taken the transfer of particle kinetic energy between the rotational and translational degrees of freedom and also the energy losses into account. Two coefficients, normal restitution coefficient and tangential restitution coefficient, are used to characterize the collisions of particles. The friction coefficient is used to predict the frictional stresses caused by the enduring contacts of particles. The collisional and frictional constitutive relations are used to predict the stresses of rough spheres. The solid pressure and viscosity are obtained in terms of the normal and tangential restitution coefficients and empirical friction constants. Distributions of concentrations and velocities of particles are predicted in the 2-D bubbling fluidized bed. The influence of bed temperature and particle diameter on fluctuation kinetic energy is analyzed in the bubbling fluidized beds. Simulated results are compared with measured axial velocity of particles and bubble diameter published in literature. [Copyright &y& Elsevier]

Abstract: Large Eddy Simulations (LESs) were performed for a confined rectangular liquid jet with a co-flow and compared in detail with particle image velocimetry (PIV) measurements. A finite-volume CFD library, OpenFOAM, was used to discretize and solve the filtered Navier–Stokes equation. The effects of grid resolution, numerical schemes and subgrid models on the LES results were investigated. The second and fourth order schemes gave similar performance, while the fourth order scheme costs much more computationally. Subgrid model comparison showed that the locally dynamic procedure is necessary for complex flow simulation. Model validation was performed by comparing LES data for the point-wise velocity statistics such as the mean and the root-mean-square velocity, shear stress, correlation coefficient, velocity skewness and flatness with the PIV data. In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data. Good agreement was observed leading to the conclusion that the LES velocity field accurately captures the important characteristics of all the turbulent length scales present in the flow, from the fully resolved energy-containing eddies to the subgrid-scale dissipative eddies. [Copyright &y& Elsevier]

Abstract: This paper proposes that a diesel oxidation catalyst (DOC) operating within the fully turbulent flow regime is an efficient means of reducing the contents of particulate matter in the exhaust gases. The suggested mode of operation is in contrast to the fact that the DOCs are typically operated within the laminar flow regime. In the paper, the particle trapping efficiency and pollutant conversion in turbulent ceramic DOCs are calculated using both mass-transfer correlations available in the literature and computational fluid dynamics (CFD). It is shown that a turbulent DOC substantially increases the removal of small particulates from the exhaust gases. This indicates the potential of the aftertreatment system to comply with the forthcoming number-based emission legislations on particulate matter. In addition, the turbulent DOC can be used to optimize the overall performance of a combined system consisting of a DOC and a diesel particulate filter. [Copyright &y& Elsevier]

Abstract: This work presents a comprehensive study of different turbulence models, including the k–ε, SST, SSG–RSM and the SAS–SST models, for simulating turbulent flow in a baffled tank stirred with a Rushton turbine. All the turbulence models tested predict the mean axial and tangential velocities reasonably well, but under-predict the decay of mean radial velocity away from the impeller. The k–ε model predicts poorly the generation and dissipation of turbulence in the vicinity of the impeller. This contrasts with the SST model, which properly predicts the appearance of maxima in the turbulence kinetic energy and turbulence energy dissipation rate just off the impeller blades. Curvature correction improves the SST model by allowing a more accurate prediction of the magnitude and location of these maxima. However, neither the k–ε nor the SST model is able to properly capture the chaotic and three-dimensional nature of the trailing vortices that form downstream of the blades of the impeller. In this sense, the SAS–SST model produces more physical predictions. However, this model has some drawbacks for modelling stirred tanks, such as the large number of modelled revolutions required to obtain good statistical averaging for calculating turbulence quantities. Taking into consideration both accuracy and solution time, the SSG–RSM model is the least satisfactory model tested for predicting turbulent flow in a baffled stirred tank with a Rushton turbine. [Copyright &y& Elsevier]

Abstract: Fluid dynamic gauging (FDG) was developed to measure, in situ and in real time, the thickness of a soft deposit layer immersed in a liquid without contacting the surface of the layer. An analysis based on the lubrication assumption for the flow patterns in the space between the nozzle and the surface being gauged yielded analytical expressions for the relationships between the main flow variables and system parameters. Nozzle shapes for particular pressure, pressure gradient and shear stress profiles could then be identified. The effect of flow rate, nozzle geometry and nozzle position on the pressure beneath the nozzle and shear stress on the gauged surface showed very good agreement with computational fluid dynamics (CFD) simulations. Case studies presented include nozzle shapes for uniform pressure and shear stress profiles, which are useful for measuring the strength of soft deposit layers. [Copyright &y& Elsevier]

Abstract: Foreseen standards regarding microorganism content for drinking water require assessment of the capability of existing plants to reach the upcoming requirements. This paper presents the development of a tool to assess this capability in a commonly encountered key step of water disinfection: ozonation. In this paper, this tool is applied to the test case of an ozonation channel of the Belgian drinking water producer Vivaqua. This tool is based on a mathematical model of the momentum and mass transport phenomena in an ozonation channel. The gas–liquid flow is coupled to ozone mass transfer and kinetics describing the ozone and microorganisms concentrations decay. The degradation of Bacillus subtilis spores, as a representative of resistant microorganisms, is implemented in the model. The model takes explicitly into account the bubble size variation and its impact on mass transfer. Bubbles sizes and kinetics parameters are estimated based on dedicated experiments. The model is partially validated by comparing simulations results, obtained using computational fluid dynamics, to experimental residence time distributions, residual ozone concentration and Bacillus subtilis spores degradation efficiency measurements obtained on the studied ozonation channel. It is shown that, at the industrial scale, bubble diameter variation has a significant impact on ozone concentration in the liquid at the reactor exit. Using the tool, it is also shown that, the ozonation channel of Vivaqua can be used to achieve degradation of resistant microorganisms but only with its maximal flow rate and concentration of ozone injection. Moreover, at low operating temperature, some microorganisms that present latency towards reaction with dissolved ozone might hardly be destroyed. [Copyright &y& Elsevier]

Abstract: The degree of mixing was first proposed by Danckwerts and further discussed by Zwietering more than 50 years ago to measure mixing performance of a continuous flow system. Although the measure has been widely discussed in mixing literature, there has never been a method to compute its value for a general continuous flow. In this paper, a method is developed to compute this measure for a general steady continuous flow system for the first time. The method is based on the recently developed mean age theory. The governing equations for the mean age and higher moments of age are also derived for different types of tracer introduction other than pulse input in the current mean age theory. [Copyright &y& Elsevier]

Abstract: An experimental study and numerical investigation of thermal mixing are carried out on tandem twin jets in cross flow. Experiments were carried out for velocity ratios 1, 2 and 4 for 15°C temperature difference between main pipe and jet fluid. Velocity and temperature fields are measured using Hot Film Anemometer (HFA). Three dimensional steady state Computational Fluid Dynamics (CFD) simulations have been carried out to predict the velocity and temperature fields. The predicted velocity and temperature fields are in good agreement with the experimental measurements. Temperature fluctuations have been predicted using temperature variance model. The effect of jet spacing for different velocity ratios is studied. For jet spacing equal to twice the jet diameter, both the jets influence each other. Increase in the jet spacing decreases the effect of jets on each other. [Copyright &y& Elsevier]

Abstract: Dry pressure drop in columns equipped with structured packings is considered to involve two components: drag force due to the direction changes near the column walls and in the transition region between two packing layers rotated to each other by 90°, and friction force between the different gas flows inside the crossing triangular channels and with the packing solid walls. It is believed that in a packed bed with compact sheet density and large packing surface area (above 250m2/m3), the major contribution of the pressure drop is generated by the friction component. In this paper, a model is proposed to determine the dry pressure drop friction component. The gas is assumed to establish a fully developed turbulent flow inside the structured packing channels. The structured packing geometry consists of a combination of periodic elements. It is shown that the reproduction of one periodic element aerodynamics leads to determine the gas distribution and pressure drop inside the packed bed. Therefore, modeling the dry pressure drop through one periodic element is a meaningful representation of the dry pressure drop over the packing. CFD simulations are carried out on periodic elements using different turbulence models: RNG , realizable , and SST . The best results that agree with the experimental data in the literature are obtained with the SST model. The CFD model proposed is used to study the impact of packing geometry variations on the dry pressure drop and to bring up a correlation for the pressure drop with respect to changes of packing geometry: channel height dimension, channel opening angle, and corrugation angle. [Copyright &y& Elsevier]

Abstract: A mechanical separation process in a hydrocyclone is described in which disperse water droplets are separated from a continuous diesel fuel phase. This separation process is influenced by droplet–droplet interaction effects like droplet breakup and coalescence resulting in a change of droplet size distribution. A simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics with population balances. The droplet size distribution is discretized and each discrete droplet size fraction is assumed to be an individual phase within a multiphase-mixture model. The droplet breakup and coalescence rates are defined as mass transfer rates between the discrete phases by the aid of user-defined functions. All model equations are solved with the CFD software package FLUENT™. The investigations show the impact of the cyclone geometry on the coupled population and separation dynamics. Cyclone separators with an optimized geometry show less steep velocity gradients increasing the coalescence rates and improving the separation efficiency. The calculated droplet size distributions at the cyclone overflow and at the underflow show good accordance with experimental data. The basic modeling approach can be extended and adapted to other disperse multiphase flow systems. [Copyright &y& Elsevier]

Abstract: Hydrodynamic properties of open-cell metallic foams are analyzed at the pore scale on a microtomographied sample from creeping flow to unsteady inertial flow. The influence of the anisotropy, obtained by shearing the initial sample, is also analyzed. The simulations show that the Darcy–Forchheimer law is valid at and that the inertial coefficient tensor can be asymmetric as proved by Whitaker [1996. The Forchheimer equation: a theoretical development. Transp. Porous Media 25, 27–61] and checked by the lattice Boltzmann method. Despite this property, the eigen vectors are nearly orthogonal to each other and their orientation follows the shear angle. To evaluate the accuracy of the results, the analysis of the REV leads to a REV size lower than for the velocity and is lower than for the inertial flow permeability tensor. It is shown also that the CFD approach, validated by MRI investigation [Graf von den Schulenburg et al., 2007. Flow through an evolving porous media-compressed foam. J. Mater. Sci. 42 6541–6548], matches the 3D-Brinkman–Forchheimer model if the effective viscosity is close to two. [Copyright &y& Elsevier]

Abstract: Non-ideal aerosol reactors for synthesizing nano- and micro-metal-oxide powders can currently be accurately designed by means of computational fluid dynamics (CFD) models instead of an expensive trial-and-error experimental technique. According to a multi-scale approach, fluid dynamics of the reacting volume is modeled by an appropriate population balance equation (PBE) coupled to momentum, energy and chemical species conservative equations. The present work refers to the modeling of non-ideal vapor-phase aerosol reactors, in particular to the numerical investigation on the effects of feeding nozzle arrangement, where the most significant gradients and aerosol phenomena occur. The described aerosol CFD model, which a priori assumes a log-normal particle size distribution (PSD), has been validated against both an experimental and an industrial case, and therefore it has been applied to the study of new reactor configurations. Numerical results show that traditional axial-symmetric and jet-opposed nozzle arrangements can be improved adopting a tangential geometry. [Copyright &y& Elsevier]

Abstract: In this work, a three-dimensional PEM fuel cell model has been developed and is used to investigate the effects of water flooding on cell performance parameters. The presence of liquid water in the cathode gas diffusion layer (GDL) limits the flow of reactants to the cathode catalyst layer, thereby reducing the overall reaction rate and curtailing the maximum power that can be derived from the cell. To characterize the effects of water flooding on gas diffusion, effective diffusivity models that account for the tortuosity and relative water saturation of the porous fuel cell electrodes have been derived from percolation theory and coupled with the CFD model within a single phase flow skeleton. The governing equations of the overall three-dimensional PEM fuel cell model, which are a representative of the coupled CFD and percolation theory based effective diffusivity models, are then solved using the finite volume method. Parametric studies have been conducted to characterize the effects of GDL permeability, inlet humidity and diffusivity of the reactants on the various cell performance parameters such as concentration of reactants/products and cell current densities. It is determined that the GDL permeability has little or no effect on the current densities due to the diffusion dominated nature of the gas flow. However, through the incorporation of percolation theory based effective diffusivity model; a marked reduction in the cell performance is observed which closely resembles published experimental observations. This is a reasonable approximation for effects of water flooding which has been inherently used for further parametric studies. [Copyright &y& Elsevier]

Abstract: The mixing behavior in laminar flow in microchannels is investigated using numerical and experimental approaches. The concept of residence-time distribution (RTD) was applied to indirectly characterize flow and mixing in a T-junction microchannel chosen as a model microchannel mixer/reactor. The residence-time distribution used in this study, although a well-known method for characterizing mixing behavior in conventional macro mixers/reactors, is still a novel measure for the characterization of mixing in microchannels. The standard T-junction microchannel and one of its modifications were studied for their mixing characteristics by performing computational fluid dynamics (CFD) simulations of pulse tracer experiments. Experimentally, RTD measure in conjunction with a UV–vis absorption spectroscopy detection technique was used to characterize flow and mixing quality in the microchannels studied. The moments of the RTD and coefficient of variation were used to quantify the mixing behavior. Two flow models, namely the well-known axial dispersion model (ADM) and a semi-empirical model (SEM), were used to obtain model descriptions for the RTD of the microchannel. As expected, the SEM fits better the experimental data than the ADM since the SEM with its characteristic asymmetric distribution predicts better the strong laminar flow behavior in the microchannels than the ADM. The results from the simulations and experiments are in very good agreement thus establishing the validity of the mathematical model and the associated solution algorithm implemented in the CFD simulations. The CFD code in conjunction with the RTD measure can then be used as a predictive tool in the design, evaluation, and optimization of microscale flow systems. [Copyright &y& Elsevier]

Abstract: This paper discusses the aerodynamic behaviors of a gas mask canister with a complex inner structure and two porous materials in the filter layer and the activated carbon layer. The effects of the distribution and area of holes in the main sieve diaphragm and the thickness of the activated carbon layer on the pressure drop and the flow structure were determined using computational fluid dynamic (CFD) tools. The momentum loss of porous flow calculated by Forchheimer''s equation was added to the source term in the momentum equation. Streakline flow visualization was employed to observe gas flow structures within the empty canister and to identify the shortcomings of the prototype canister. Simulation results for the estimated inertial and viscosity parameters in Forchheimer''s equation agree closely with experimental values. The porosity of the canister for intake flows of 15–135L/min causes the flow behavior to transition gradually from linear (viscous effect) to slight non-linear behavior (slight inertia effect). This study uses air age as an index of the time that air resides within the canister to displace the adsorption time of toxic gas. This approach conveniently elucidates overall filter capacity and the positions of dead zones in the activated carbon layer. The simulation results reveal that the channel design of the main sieve diaphragm dominates the aerodynamic behavior of the fluid within the activated carbon layer. Better hole distribution and a larger hole area correspond to a lower pressure drop, a smaller dead zone, and a higher adsorption time. The results in this study provide a valuable reference for designing channels in the main sieve diaphragm, and will be helpful in designing gas mask canisters. [Copyright &y& Elsevier]

Abstract: This work is aimed at investigating the capability of a computational fluid dynamics (CFD) approach to reliably predict the fluid dynamic and the separation performances of inorganic membranes modules for gas mixture separation. The simulations are based on the numerical solution of the Navier–Stokes equations on the three dimensional domain representing quite closely the selected module geometry. The membrane is modelled as a selective layer, which allows the permeation of different components as a function of the transport mechanism and the driving force. The computational strategy is strictly evaluated by comparing the results with available experimental data. The simulation predictions show fairly good agreement with the measured permeation data and allow to recognise the critical local fluid dynamic features of the separation module. [Copyright &y& Elsevier]

Abstract: This is a pioneering paper that deals with the semi-steady-state liquid film thickness on a rotating drum partially submerged in liquid using CFD. The CFD predictions have been compared with both experimental results and analytical solutions. The liquid film thickness and the film rising on a circular curved wall were monitored for various rpm of the rotating drum. The 2D simulations were performed neglecting the end effects (assuming the rotating drum is very long). As the rotating drum speed was increased, the film thickness was found to increase at the film rising side and at the minimum film thickness point (top of the rotating drum). There was never been a steady-state condition reached, the opposite was expected as a wiper is used in the CFD calculation (same as the experimental investigation). The liquid that leaves the domain by the wiper (as outflow boundary condition) is forced to enter to the domain from far end to keep the level of the free surface constant. [Copyright &y& Elsevier]

Abstract: Industrial bubble column reactors for Fischer–Tropsch (FT) synthesis include complex hydrodynamic, chemical and thermal interaction of three material phases: a population of gas bubbles of different sizes, a liquid phase and solid catalyst particles suspended in the liquid. In this paper, a CFD model of FT reactors has been developed, including variable gas bubble size, effects of the catalyst present in the liquid phase and chemical reactions, with the objective of predicting quantitative reactor performance information useful for design purposes. The model is based on a Eulerian multifluid formulation and includes two phases: liquid–catalyst slurry and syngas bubbles. The bubble size distribution is predicted using a Population Balance (PB) model. Experimentally observed strong influence of the catalyst particles concentration on the bubble size distribution is taken into account by including a catalyst particle induced modification of the turbulent dissipation rate in the liquid. A simple scaling modification to the dissipation rate is proposed to model this influence in the PB model. Additional mass conservation equations are introduced for chemical species associated with the gas and liquid phases. Heterogeneous and homogeneous reaction rates representing simplified FT synthesis are taken from the literature and incorporated in the model. Hydrodynamic effects have been validated against experimental results for laboratory scale bubble columns, including the influence of catalyst particles. Good agreement was observed on bubble size distribution and gas holdup for bubble columns operating in the bubble and churn turbulence regimes. Finally, the complete model including chemical species transport was applied to an industrial scale bubble column. Resulting hydrocarbon production rates were compared to predictions made by previously published one-dimensional semi-empirical models. As confirmed by the comparisons with available data, the modeling methodology proposed in this work represents the physics of FT reactors consistently, since the influence of chemical reactions, catalyst particles, bubble coalescence and breakup on the key bubble–fluid drag force and interfacial area effects are accounted for. However, heat transfer effects have not yet been considered. Inclusion of heat transfer should be the final step in the creation of a comprehensive FT CFD simulation methodology. A significant conclusion from the modeling results is that a highly localized FT reaction rate appears next to the gas injection region when the syngas flow rate is low. As the FT reaction is exothermal, it may lead to a highly concentrated heat release in the liquid. From the design perspective, the introduction of appropriate heat removal devices may be required. [Copyright &y& Elsevier]

Abstract: Three-compartment model was used to study non-homogeneity of mixing in a fully baffled stirred tank. Multiple reference frame (MRF) technique was used for calculations. Calculations were performed to study the effects of agitator speed, impeller diameter, baffle width and distance of impeller from bottom of the tank on turbulent flow field. Three different zones of the vessel, that were a small zone near the impeller, another zone around the baffles, and a relatively large zone far from the impeller and baffles, named circulation zone, were investigated. Boundaries of these zones were determined using two different methods. The first method used gradient of energy dissipation rate while the other method used cumulative energy dissipation rate to determine the zone boundaries. Zone boundaries determined by both methods were comparable. The turbulent kinetic energy dissipation rate gradient was the preferred method due to its simplicity. Turbulent kinetic energy dissipation rate increased with agitator speed in all zones. Both turbulent kinetic energy dissipation rate and turbulent kinetic energy showed considerable change with impeller diameter at impeller zone, while no remarkable change was observed at baffle and circulation zones. Three-compartment model parameters, impeller and baffle energy dissipation ratios λ i, λ b, impeller and baffle volume ratios μ i, μ b and impeller and baffle exchange flow rates Q i, Q b were obtained from CFD simulations. Impeller energy dissipation ratio, impeller exchange flow rate and baffle exchange flow rate increased while baffle volume ratio decreased with agitation rate and impeller diameter. Baffle energy dissipation ratio and impeller volume ratio showed no considerable change with agitation rate and impeller diameter. [Copyright &y& Elsevier]

Abstract: Understanding and modelling the dynamic behaviour of particulate systems has been a major research focus worldwide for many years. Discrete particle simulation plays an important role in this area. This technique can provide dynamic information, such as the trajectories of and transient forces acting on individual particles, which is difficult to obtain by the conventional experimental techniques. Consequently, it has been increasingly used by various investigators for different particulate processes. In spite of the large bulk volume, little effort has been made to comprehensively review and summarize the progress made in the past. To overcome this gap, we have recently completed a review of the major work in this area in two separate parts. The first part has been published [Zhu, H.P., Zhou, Z.Y., Yang, R.Y., Yu, A.B., 2007. Discrete particle simulation of particulate systems: theoretical developments. Chemical Engineering Science 62, 3378–3392.], which reviews the major theoretical developments. This paper is the second one, aiming to provide a summary of the studies based on discrete particle simulation in the past two decades or so. The studies are categorized into three subject areas: particle packing, particle flow, and particle–fluid flow. The major findings are discussed, with emphasis on the microdynamics including packing/flow structure and particle–particle, particle–fluid and particle–wall interaction forces. It is concluded that discrete particle simulation is an effective method for particle scale research of particulate matter. The needs for future research are also discussed. [Copyright &y& Elsevier]

Abstract: Eddy viscosity models (EVM) constitute a powerful approach for turbulence modeling in engineering applications. However, the correct formulation of EVM models is still subject to discussion, in particular the impact of model parameters on the practical relevance of models in different classes of application scenarios is not fully understood. A systematic approach for assessing parameter impact involves optimization methods for computational fluid dynamics that allow for quantitative model analysis by rigorous comparison with experimental data. In order to illustrate this systematic approach, the – turbulence model is analyzed on the basis of laser Doppler velocimetry measurements for the flow between two plates. It is shown that ad hoc approaches for adapting parameter values for the – model may easily fail due to over-parameterization of the underlying model or insufficient data. Therefore, an a priori method for the identification of potential problems is important which is based on the sensitivity coefficients of the measurements with respect to the model parameters. The commercial software package FLUENT employed in our application is augmented using the automatic differentiation system ADIFOR for efficient sensitivity computation. Taken together, this results in reliable a priori methods for model assessment and calibration. Noteworthy, the choice of turbulence parameters on the basis of the formal a priori analysis agrees well with the physical understanding of the – model. [Copyright &y& Elsevier]

Abstract: Rapid precipitation of both organic and inorganic compounds at high supersaturation requires homogenous mixing to control the particle size distribution. We present the design and characterization of a new multi-inlet vortex mixer (MIVM). The four-stream MIVM allows control of both the supersaturation and the final solvent quality by varying stream velocities. The design also enables the separation of reactive components prior to mixing. Finally, the design enables mixing of streams of unequal volumetric flows, which is not possible with alternate confined impinging jet mixing geometries. We characterize the mixing performance of the MIVM using competitive fast reactions (the so-called “Bourne reactions”). Adequate micromixing is obtained with a suitably defined Reynolds number when . The experimental results are compared to computational fluid dynamics (CFD) simulations of the fluid mechanics and parallel reactions in the MIVM. Excellent correspondence is found between the simulation and the experimental results with no adjustable parameters. The CFD simulations provide a powerful tool for the optimization of these complex mixing geometries. [Copyright &y& Elsevier]

Abstract: Electrical resistance tomography (ERT) provides a non-intrusive technique to examine, in three dimensions, the homogeneity and flow pattern inside the mixing tank. In this study, a 4-plane 16-sensor ring ERT system was employed to study the shape and the size of cavern generated around a radial-flow Scaba 6SRGT impeller in the mixing of xanthan gum solution, which is a pseudoplastic fluid possessing yield stress. The size of cavern measured using ERT was in good agreement with that calculated using Elson''s model (cylindrical model). The 3D flow field generated by the impeller in the agitation of xanthan gum was also simulated using the commercial computational fluid dynamics (CFD) package (Fluent). The CFD model provided useful information regarding the impeller pumping capacity, flow pattern, and the formation of cavern around the impeller. CFD results showed good agreement with the experimental data and theory. [Copyright &y& Elsevier]

Abstract: Computational fluid dynamics (CFD) was used to simulate non-reacting heat transfer in a steam reforming packed reactor tube of tube-to-particle diameter ratio () equal to 4, with cylindrical multi-hole catalyst particles. These simulations extend those of our previous study [Nijemeisland, M., Dixon, A.G., Stitt, E.H., 2004. Catalyst design by CFD for heat transfer and reaction in steam reforming. Chemical Engineering Science 59, 5185–5191] to provide accurate tube wall temperatures, runs at constant pressure drop in addition to those at constant mass flow rate and simulations of particles with different sizes of holes. At constant pressure drop, particles with higher void fractions allowed higher mass flow rates, resulting in tube wall temperatures and radial temperature profiles in order: solid cylinders one-hole particles multi-hole particles. Little difference was seen between three-hole and four-hole particles. The particles with multiple holes gave a substantial reduction in tube wall temperature, with only a small decrease in core tube heat transfer. The effect of hole size was small, for the cases investigated in this study. [Copyright &y& Elsevier]

The phenomenon of drop spreading is important to several process engineering applications. In the present work, numerical simulations of the dynamics of drop impact and spreading on horizontal and inclined surfaces were carried out using the volume of fluid (VOF) method. For the horizontal surfaces, the dynamics of impact and spreading of glycerin drops on wax and glass surfaces was investigated for which the experimental measurements were available [Šikalo, Š., Tropea, C., Ganic, E.N., 2005a. Dynamic wetting angle of a spreading droplet. Experimental Thermal and Fluid Science 29, 795–802; Šikalo, Š., Tropea, C., Ganic, E.N., 2005b. Impact of droplets onto inclined surfaces. Journal of Colloid and Interface Science 286, 661–669]. The influence of surface wetting characteristics was investigated by using static contact angle (SCA) and dynamic contact angle (DCA) models. The dynamics of drop impact and spreading on inclined surfaces and the different regimes of drop impact and spreading process were also investigated. In particular, the effects of surface inclination, surface wetting characteristics, liquid properties and impact velocity on the dynamics of drop impact and spreading were investigated numerically and the results were verified experimentally. It was found that the SCA model can predict the drop impact and spreading behavior in quantitative agreement with the experiments for less wettable surfaces . However, for more wettable surfaces , the DCA observed at initial contact times were order of magnitude higher than SCA values and therefore the DCA model is needed for the accurate prediction of the spreading behavior. [Copyright &y& Elsevier]

Abstract: Free convection effects of heat and mass transfer are of prime importance when modeling the behavior of supercritical fluids in packed bed reaction equipment and in solid extractors. Density gradients, caused by temperature or composition variations, tend to control the overall flow pattern of the fluid, making the buoyancy terms of the Navier–Stokes equations an important term to model when doing a computational fluid dynamics (CFD) simulation under the described conditions. The purpose of this work is to visualize by means of CFD techniques the influence of the buoyancy forces over flow patterns and the convective flow in a packed bed filled with a supercritical fluid, because the experimental option is very expensive and time demanding. Computations were made using a three-dimensional CFD modeling strategy. Carbon dioxide in the supercritical conditions was selected as a flowing fluid. Its transport properties at high pressure were incorporated within a CFD commercial code in order to estimate them online within the simulation process. Particle-to-fluid mass transfer in supercritical conditions was analyzed, and transport coefficients were obtained and validated. Recently, Guardo et al. [2006. CFD study on particle-to-fluid heat transfer in fixed bed reactors: convective heat transfer at low and high pressure. Chemical Engineering Science 61, 4341–4353] have presented a correlation for particle-to-fluid heat transfer in supercritical conditions based on an analogy with the correlation proposed by Stüber et al. [1996. Supercritical fluid extraction of packed beds: external mass transfer in upflow and downflow operation. Industrial & Engineering Chemistry Research 35, 3618–3628] for mass transfer. The obtained numerical results presented in this work validate the idea that the modified correlation presented by Guardo et al. [2006. CFD study on particle-to-fluid heat transfer in fixed bed reactors: convective heat transfer at low and high pressure. Chemical Engineering Science 61, 4341–4353] can be used to describe heat transfer phenomena in a packed bed under mixed convection regime at high pressures. [Copyright &y& Elsevier]

Abstract: Computational fluid dynamics (CFD) is applied to the study of the catalytic hydrogenation of sunflower oil in the presence of a supercritical solvent. A 2D CFD model of a single Pd-based catalyst pellet is presented. Intra-particle concentration profiles for all species present in the mixture (oil fatty acids and hydrogen) are obtained and compared against experimental results. Different particle sizes are studied and external mass transfer and intra-particle diffusional effects are analyzed. External mass transfer coefficients are obtained and presented. Fitting of the intra-particle concentration profiles allowed to verify the kinetic reaction model. The verified kinetic reaction model and intra-particle diffusion coefficients were utilized in a 3D packed bed reactor model, and conversion profiles are obtained. [Copyright &y& Elsevier]

An input/output approach to the optimal concentration transition control problem of a certain type of distributed chemical reactors is proposed based on the concept of residence time distribution, which can be determined in practice by using data from experimental measurements or computer simulations. The main assumptions for the proposed control method to apply are that the thermal and fluid flow fields in the reactor are at pseudo-steady-state during transition and that the component whose concentration is to be controlled participates only in first-order reactions. Using the concept of cumulative residence time distribution, the output variable is expressed as the weighted sum of discretized inputs or input gradients in order to construct an input/output model, on the basis of which a constrained optimal control problem, penalizing a quadratic control energy functional in the presence of input constraints, is formulated and solved as a standard least squares problem with inequality constraints. The effectiveness of the proposed optimal control scheme is demonstrated through a continuous-stirred-tank-reactor (CSTR) network and a tubular reactor with axial dispersion and a first-order reaction. It is demonstrated through computer simulations that the proposed control method is advantageous over linear quadratic regulator (LQR) and proportional-integral (PI) control in terms of control cost minimization and input constraint satisfaction. [Copyright &y& Elsevier]

Abstract: Liquid-phase turbulent transport in a confined rectangular wake was investigated for a Reynolds number of 37,500 based on bulk velocity and the hydraulic diameter of the test section and a Schmidt number of 1250 using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). The velocity and concentration field data were analyzed for flow statistics such as the mean velocity, Reynolds stresses, turbulent kinetic energy, turbulent dissipation rate, mixture-fraction mean, mixture-fraction variance and one-point composition probability density functions (PDF). Computational fluid dynamics (CFD) models, including a two-layer – turbulence model, a scalar gradient-diffusion model and a scalar dissipation rate model were validated against PIV and PLIF data collected at six downstream locations. Low-Reynolds-number effects on turbulent transport were taken into consideration through the mechanical-to-scalar time-scale ratio. The experimental and computational results were found to be in satisfactory agreement. [Copyright &y& Elsevier]

Abstract: The mixing efficiency in a curved tube is a complex function of the Reynolds number, Schmidt number, curvature ratio and tube pitch, therefore, the relative effectiveness of a helical tube is quite complicated and challenging over a straight tube. A state of art review on mixing of two miscible liquids in curved tubes revealed that the mixing in coils of circular cross section has not been reported in the literature. In the present work a computational fluid dynamics study is performed in curved tubes of circular cross-section of finite pitch under laminar flow conditions to examine the scalar mixing of two miscible fluids using scalar transport technique. In the present study the phenomenon of mixing by convection and diffusion of two flow streams with inlet scalar concentrations of zero and unity in the two halves of a tube perpendicular to the plane of curvature has been reported. The mixing efficiency has been quantified with concentration distributions and unmixedness coefficient at different cross-sections and process conditions (Reynolds number, Schmidt number and curvature ratio) in the straight and curved tube of circular cross-section. The result shows that, in curved tube, for higher Schmidt number fluids, mixing is considerably improved at moderately low Reynolds numbers , but is not affected for Reynolds number of the order of 0.1. It is also reported that mixing in the curved tube is higher at low values of curvature ratio as compared to the higher curvature ratio. [Copyright &y& Elsevier]

Abstract: In order to model the complex hydrodynamic phenomena prevailing in industrial scale gas–solid bubbling fluidised bed reactors and especially the macro-scale emulsion phase circulation patterns induced by bubble–bubble interactions and bubble coalescence, a discrete bubble model (DBM) has been developed. In the DBM, the (larger) bubbles are modelled as discrete elements and are tracked individually during their rise through the emulsion phase, which is considered as a continuum. The DBM, originally developed for the description of gas–liquid flows, has been adapted to cope with bubbles with a diameter larger than the size of an Eulerian cell, which is required in view of the large bubble size distribution at higher gas flow rates. Moreover, a new drag model for a single bubble rising in a fluidised bed derived from empirical correlations has been implemented, as well as a simple model to account for bubble coalescence and break-up. The strong advantage of the DBM compared to other models previously reported in the literature for the description of large-scale fluidised beds is that it fully accounts for the two-way coupling between the bubbles and the emulsion phase, which enables direct computation of the emulsion phase velocity profiles. Comparison of the results of simulations ignoring bubble coalescence and simulations taking bubble coalescence properly into account demonstrated the significant effect of bubble coalescence on the large-scale circulation patterns prevailing in bubbling fluidised beds. The simulation results for the lateral profiles of the visible bubble flow rate have been compared qualitatively with experimental results reported by Werther [1974. Influence of the bed diameter on the hydrodynamics of gas fluidized beds. A.I.Ch.E. Symposium Series 70(141), 53–62]. The effect of the superficial gas velocity on the velocity and porosity profiles has been studied. In general, it can be concluded that the DBM is able to capture the salient features of the hydrodynamics of bubbling fluidised beds. However, further research is required to improve the closure equations for the bubble behaviour, bubble–bubble interactions and bubble coalescence and break-up to enable a complete quantitative description. [Copyright &y& Elsevier]

Abstract: The numerical solutions for different formulations of the conservation equations based on the dependent variables, pressure , enthalpy , density , entropy and flow velocity for highly transient flows are presented. The models are each in turn applied for simulating the transient fluid flow dynamics following the rupture of a real and a number of hypothetical pipelines containing liquid, flashing liquid, two-phase and a permanent gas. In the case of the flashing liquid and two-phase pipelines, a significant reduction in the computational run time for the Phu and Psu based simulations as compared to the conventional formulation is observed. The above effect is found to be much less pronounced for the liquid and permanent gas inventories. [Copyright &y& Elsevier]

Abstract: In the present work attempts were made to investigate the hydrodynamics and heat transfer characteristics of tube-in-tube helical heat exchanger at the pilot plant scale. The experiments were carried out in counter current mode operation with hot fluid in the tube side and cold fluid in the annulus area. The outer tube was fitted with semicircular plates to support the inner tube and also to provide high turbulence in the annulus region. Overall heat transfer coefficients were calculated and heat transfer coefficients in the inner and outer tube were determined using Wilson plots. A commercial Computational Fluid Dynamics package [FLUENT User''s Guide, release 6.0, Fluent Inc., Lebnon, NH, 1994] was used to predict the flow and thermal development in tube-in-tube helical heat exchanger. The Nusselt number and friction factor values in the inner and outer tubes were compared with the experimental data collected in the present study as well as reported in the literature. The CFD simulations were in agreement with the present experimental data. In case of literature data a reasonable comparison was found even though the boundary conditions in the present work were different. [Copyright &y& Elsevier]