A qualitative computational study of mass transfer in upward bubble train flow through square and rectangular mini-channels

In this paper we present a new method for numerical simulation of conjugate mass transfer of a dilute species with resistance in both phases and an arbitrary equilibrium distribution coefficient. The method is based on the volume-of-fluid technique and accounts for the concentration jump at the interface by transforming the discontinuous physical concentration field into a continuous numerical one. The method is validated by several test problems and is used to investigate the mass transfer in upward bubble train flow within square and rectangular channels. Computations are performed for a single flow unit cell and a channel hydraulic diameter of 2 mm. The simulations consider the transfer of a dilute species from the dispersed gas into the continuous liquid phase. Optionally, the mass transfer is accompanied by a first-order homogeneous chemical reaction in the liquid phase or a first-order heterogeneous reaction at the channel walls. The results of this numerical study are qualitative in nature. First, because periodic boundary conditions in axial direction are not only used for the velocity field but also for the concentration field and second, because the species diffusivity in the liquid phase is arbitrarily increased so that the liquid phase Schmidt number is 0.8 and the thickness of the concentration and momentum boundary layer is similar. Two different equilibrium distribution coefficients are considered, one where the mass transfer is from high to low concentration, and one where it is vice versa. The numerical study focuses on the influence of the unit cell length, liquid slug length and channel aspect ratio on mass transfer. It is found that for the exposure times investigated the liquid film between the bubble and the wall is saturated and the mass transfer occurs by the major part through the bubble front and rear so that short unit cells are more efficient for mass transfer. Similar observations are made for the homogeneous reaction and for the heterogeneous reaction when the reaction is slow. In case of a fast heterogeneous reaction and when the main resistance to mass transfer is in the gas phase, it appears that for square channels long unit cells are more efficient, while large aspect ratio rectangular channels are more efficient than square channels, suggesting that for these conditions they might be more appropriate for use in monolithic catalysts.     

Diffusion limitation effects in the washcoat of a catalytic monolith reactor

In monolith reactors with catalytic washcoat, intraphase diffusion effects have often been underestimated. This paper presents numerical simulations of diffusion/reaction in the washcoat of a catalytic monolith reactor. The problem is solved in two dimensions for the washcoat geometry obtained in a 1-mm square monolith channel, as revealed by scanning electron microscopy. For the oxidation of carbon monoxide, propane or methane diffusion limitation can be substantial at typical operating conditions. The two-dimensional solution is compared to a one-dimensional approximation. The latter approximation for the real washcoat is valid provided that the characteristic length is selected carefully. This value is different from the characteristic length of the two-dimensional washcoat. The characteristic length of a two-dimensional geometry is not sufficient in itself to describe all washcoat geometries. It is predicted that the application of a diffusion barrier of 4–6 μm of inactive washcoat may be used to lower the rate of reaction in the inlet region of the monolith reactor.     

The effect of washcoat geometry on mass transfer in monolith reactors

This paper reports the results of a numerical investigation of the diffusion and reaction in the washcoat of a catalytic monolith reactor. Both idealized shapes and real geometries are tested. It is shown that for non-uniform washcoat thickness, the Sherwood number varies along the channel/washcoat interface. The internal diffusion resistance, expressed in terms of an effectiveness factor, cannot be represented in terms of a unique curve using the generalized Thiele modulus approach. The most significant deviation occurs when the washcoat has the greatest variation in thickness. The internal diffusion affects the magnitude of the external mass transfer resistance. Three factors significantly affect the rates and role of mass transfer. These are (1) the washcoat thickness, (2) the channel radius, including its non-uniformity around the channel, and (3) the angular diffusion in the washcoat caused by variable thickness.     

Investigation of convection and diffusion during biodiesel production in packed membrane reactor using 3D simulation

The 3D simulation of convection and diffusion phenomena within a ceramic membrane during transesterification reaction was the aim of this study. The ceramic membrane was a tubular micro porous TiO₂/Al₂O₃ packed with the heterogeneous catalyst. The Navier–Stokes, Brinkman and Stephan–Maxwell equations were applied for investigation of fluid flow reaction and mass transfer within the system. The value of the convection was generally between 10⁴ and 10⁷ times higher than diffusion. It depends on concentration component, the diffusion coefficient and components velocity. A good agreement was found with the maximum deviation of 8% from experimental data.     

CONVECTIVE DIFFUSION IN HETEROGENEOUS CATALYTIC DUCT REACTORS WITH NONCIRCULAR CROSS SECTION AND NONUNIFORM CATALYST ACTIVITY

Steady-state simulations of convection, diffusion and first-order irreversible heterogeneous chemical reaction are presented for catalytic channels with rectangular cross section and nonuniform catalyst activity. Finite difference results from the microscopic three-dimensional mass transfer equation also satisfy the cross-section-averaged one-dimensional form of the same equation. Comparisons between viscous flow and plug flow in square cross-section channels suggest how previous inferences of surface-averaged reaction velocity constants from plug flow simulations should be modified when convective diffusion in the mass transfer boundary layer adjacent to the catalytic surface is modeled correctly. Over the following range of Damkohler numbers (i.e., 20 to 10³), viscous flow in rectangular ducts with aspect ratios between two and three can be approximated by the corresponding problem in tubes with the same effective diameter. For Damkohler numbers between 0.5 and 10³, aspect ratios greater than 20 are required to simulate viscous flow between two parallel plates with catalyst coated on both walls. At low Damkohler numbers where reactant diffusion toward the catalytic surface is not the rate-limiting step, nonuniform activity profiles suggest that most of the catalyst should be deposited in regions that are easily accessible to the reactants. However, this strategy for converting reactants to products is not more effective than uniform deposition in the diffusion-limited regime.     

Calculating effectiveness factors in non-uniform washcoat shapes

This paper describes a method for the determination of effectiveness factors in a monolith washcoat of non-uniform thickness. The method is based on the previously reported slice concept, in which the monolith is divided into a series of slices, each of which is analysed using a one-dimensional approach. In each one-dimensional slice, an apparent characteristic length is used to compute the Thiele modulus. In the approach described here, the apparent characteristic length is determined by conducting a single two-dimensional simulation for a first-order reaction in the kinetically controlled region. The characteristic length is then calculated from the flux at the surface using an analytical solution. Results are shown for the idealized circular washcoat in a square channel, as well as for a real washcoat in a square channel and a sinusoidal shape. Results for first-order and LHHW kinetics show good agreement between the one-dimensional approximation and the true solution. Both average and local effectiveness factors can be calculated within acceptable range for monolith reactor simulations.     

Conjugate heat and mass transfer model for predicting thin-layer drying uniformity in a compact,crossflow dehydrator

Abstract

A conjugate heat and mass transfer model was implemented into a commercial CFD code to analyze the convective drying of corn. The Navier–Stokes equations for drying air flow were coupled to diffusion equations for heat and moisture transport in a corn kernel during drying. Model formulation and implementation in the commercial software is discussed. Validation simulations were conducted to compare numerical results to experimental, thin-layer drying data. The model was then used to analyze drying performance for a compact, crossflow dehydrator. At low inlet air temperatures, the drying rate in the compact dehydrator matched the thin-layer drying rate. At higher temperatures, heat losses through the external walls resulted in temperature and moisture variations across the dehydrator.     

Modeling the evolution and rupture of stretching pendular liquid bridges

A simplified mathematical model and numerical simulations of the governing Navier–Stokes equations are used to predict the shape evolution, rupture distance, and liquid distribution of stretching pendular liquid bridges between two equal-sized spherical solid particles. In the simplified model, the bridge shape is approximated with a parabola, and it is assumed that the surface tension effects dominate the viscous, inertial, and gravitational effects. For the numerical simulations, a commercial Computational Fluid Dynamics (CFD) software package – FLUENT – is used. The rupture distance predictions obtained with both models are compared with experimental data and a reasonable agreement is found. The results of the numerical investigations show that for simulations with negligible viscous, inertial, and gravitational effects, the rupture distance approaches an asymptotic value, which is close to the value predicted by the simplified model. The bridge profiles predicted using the simplified model and the numerical simulation are compared. It is found that a second-order polynomial appropriately represents the stable bridge shape for particles with identical contact angles; however, for liquid bridges between particles with different contact angles, the numerical simulations of the governing Navier–Stokes equations should be used.     

CFD simulation for biomagnetic separation involving dilute suspensions

Full‐Eulerian simulation of the separation of magnetic particles carried by a Newtonian fluid through a planar channel under the influence of a magnetic field is presented. The simulation is based on the application of the Navier–Stokes and concentration equations. The scheme for the magnetic separation of particles is achieved by applying an external magnetic dipole field. The hydrodynamic and magnetophoretic interactions between the particles and the carrier fluid are analysed. Analysis of the competing tendencies of mass transfer indicates that the magnetophoresis migration of magnetic particles is dominant over the molecular diffusion. This dominance becomes more evident at lower diffusivities leading to a drastic magnetic separation confined within a small region in the proximity of the magnetic field source. © 2012 Canadian Society for Chemical Engineering     

Experimental study of mass transfer limitations in Fe- and Cu-zeolite-based NH3-SCR monolithic catalysts

An experimental study of steady-state selective catalytic reduction (SCR) of NO_x with NH₃ on both Fe-ZSM-5 and Cu-ZSM-5 monolithic catalysts was carried out to investigate the extent of mass transfer limitations in various SCR reactions. Catalysts with different washcoat loadings, washcoat thicknesses and lengths were synthesized for this purpose. SCR system reactions examined included NO oxidation, NH₃ oxidation, standard SCR, fast SCR and NO₂ SCR. Comparisons of conversions obtained on catalysts with the same washcoat volumes but different washcoat thicknesses indicated the presence of washcoat diffusion limitations. NH₃ oxidation, an important side reaction in SCR system, showed the presence of washcoat diffusion limitations starting at 350 °C on Fe-zeolite and 300 °C on Cu-zeolite catalysts. Washcoat diffusion limitations were observed for the standard SCR reaction (NH₃+NO+O₂) on both Fe-zeolite (≥350 °C) and Cu-zeolite (≥250 °C). For the fast (NH₃+NO+NO₂) and NO₂ SCR (NH₃+NO₂) reactions, diffusion limitations were observed throughout the temperature range explored (200–550 °C). The experimental findings are corroborated by theoretical analyses. Even though the experimentally observed differences in conversions clearly indicate the presence of washcoat diffusion limitations, the contribution of external mass transfer was also found to be important under certain conditions. The transition temperatures for shifts in controlling regimes from kinetic to washcoat diffusion to external mass transfer are determined using simplified kinetics. The findings indicate the necessity of inclusion of mass transfer limitations in SCR modeling, catalyst design and optimization.     

Two‐dimensional model of methane thermal decomposition reactors with radiative heat transfer and carbon particle growth

A two‐dimensional model of methane thermal decomposition reactors is developed which accounts for coupled radiative heat and polydisperse carbon particle nucleation, growth, and transport. The model uses the Navier–Stokes equations for the fluid dynamics, the radiative transfer equation for methane and particle species radiation absorption, the advection–diffusion equation for gas and particle species transport, and a sectional method for particle species nucleation, heterogenous growth, and coagulation. The model is applied to a tubular laminar flow reactor. The simulation results indicate the development of a reaction boundary layer inside the reactor, which results in significant variation of the local particle size distribution across the reactor. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2545–2556, 2012     

Analysis of a Two‐Layer Nozzle‐and‐Diffuser Electroosmotic Micromixer

An electroosmotic micromixer with two‐layer microchannels of a nozzle‐and‐diffuser structure was proposed. Numerical analysis of the flow and mixing was performed using the three‐dimensional Poisson‐Boltzmann and Navier‐Stokes equations with a diffusion‐convection model for the species concentration. A parametric analysis of the microchannels was performed using three geometric parameters, i.e., length of the nozzle section, length of the diffusion section, and width of the nozzle end, to investigate the impact of each parameter on the mixing performance, which was quantified by a quantitative measure based on the mass variance. The numerical results were used to improve the design of the proposed micromixer, leading to a far better mixing performance with a much shorter channel length compared to an existing electroosmotic micromixer.     

One + One‐Dimensional Modeling of Monolithic Catalytic Converters

The inclusion of a washcoat model into monolithic catalyst simulations in order to create a one + one‐dimensional framework using a minimum number of parameters is reviewed. All assumptions and numerical methods are presented while ensuring the prevention of excessive temperature excursions. Parametric studies illustrate the influence of model parameters (porosity, wall thickness, pore diameter) on the conversion of carbon monoxide during a light‐off experiment using a uniform washcoat. Moreover, simulating a layered washcoat of dissimilar catalytic materials demonstrates a significant influence on conversion characteristics depending on the order of the layers. As a result, employing a washcoat requires careful consideration of the advection of the gas, the reactions occurring in each catalytic material, material layering, the diffusion properties of the different species, and the characteristics of the washcoat.     

Contact dynamic modeling of a liquid droplet between two approaching porous materials

A computational fluid dynamics model based on a finite difference solution to mass and momentum conservation equations (Navier–Stokes equations) for a liquid droplet transport between two porous or nonporous contacting surfaces (CSs) is developed. The CS dynamic (equation of motion) and the spread of the incompressible liquid available on the primary surface for transfer are coupled with the Navier–Stokes equations. The topologies of the spread dynamic between and inside both surfaces (primary and CSs) are compared with experimental data. The amount of mass being transferred into the CS, predicted by the model, is also compared to the experimental measurements. The impact of the initial velocity on the spread topology and mass transfer into the pores is addressed. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2346–2353, 2014     

Numerical simulation of mass transfer in a liquid–liquid membrane contactor for laminar flow conditions

Liquid–liquid phase membrane contactors are increasingly being used for mixing and reaction. The principle is the following: component A flows through the membrane device inlet to mix/react with component B which comes from the membrane pores. This study presents a numerical simulation using computational fluid dynamics (CFD) of momentum and mass transfer in a tubular membrane contactor for laminar flow conditions. The velocity and concentration profiles of components A–C are obtained by resolution of the Navier-Stokes and convection-diffusion equations. The numerical simulations show that mixing between A and B is obtained by diffusion along the streamlines separating both components. The mixing/reaction zone width is within the region of a few hundred of microns, and depends on the diffusion coefficients of A and B. Hollow fiber membrane devices are found to be of particular interest because their inner diameter is close to the mixing zone width.     

A semi-analytical model for gas flow in pleated filters

A semi-analytical model of gas flow in pleated fibrous filters is developed for large filtration velocities. This case presents two main new and distinguishing features compared to the low filtration velocity situations studied in previous works: the velocity profiles are not parabolic within the pleat channels and the filtration velocity is not uniform along the pleated filter element and this has a great impact on the filter loading. The model relies on similarity solutions to the Navier–Stokes equations in the channels formed by pleating the filter medium. After validation by comparison with direct CFD simulations and experimental data, the model is used to determine the optimal pleat density, i.e. the pleat density minimizing the overall pressure drop across the filter for given flow rate, pleat length and given filter medium properties. As illustrated in the paper, this model greatly facilitates the study of flow within the pleated filter compared to a standard CFD approach. It represents an excellent basis for the more involved problem of filter loading computation. In particular, no remeshing across the width of the pleated filter entrance channels is needed when a filtration cake forms at the channel walls.     

Mathematical analysis of effects on the electrostatic double layer of nanoscale surfaces in microfluidic channels

The effects of microfluidics on the electrostatic double layer (EDL) of a nano‐structured electrode are investigated through numerical modelling. The parameters of interest are the height and spacing of nanostructures, specifically, nanowire and “nanopillar” pairs rising from an idealised sensor substrate perpendicular to the fluid flow. A direct comparison of the EDL thicknesses at the peaks and valleys of this nanostructure are reported for variations in fluid velocity, nanowire spacing, and height under fixed conditions of combined pressure‐driven and electro‐osmotic driving forces. In a microchannel based on the Navier–Stokes and Helmholtz–Smoluchoswki flow models, numerical simulations provide insight into the practical design of chemically selective nanomaterial electrodes for potentiometric detection of ions in water.     

运动颗粒对传质过程影响的格子Boltzmann模拟

颗粒的主动运动对传质过程有重要影响.以表面恒浓度的二维球形颗粒为研究对象,采用耦合传质的格子Boltzmann方法(LBM)模拟了颗粒在自旋和振动两种情况下的相间传质过程.选择浸入运动边界法和非平衡态外推法处理运动颗粒边界,研究了颗粒自旋速度、颗粒振幅及振动频率对传质过程的影响.结果表明,中等雷诺数的自旋颗粒绕流中,随...     

整体式床层中液体分布与气-液传质的关系

With a particular focus on the connection between liquid flow distribution and gas-liquid mass transfer in monolithic beds in the Taylor flow regime, hydrodynamic and gas-liquid mass transfer experiments were carried out in a column with a monolithic bed of cell density of 50 cpsi with two different distributors (nozzle and packed bed distributors). Liquid saturation in individual channels was measured by using self-made micro-conductivity probes. A mal-distribution factor was used to evaluate uniform degree of phase distribution in monoliths. Overall bed pressure drop and mass transfer coefficients were measured. For liquid flow distribution and gas-liquid mass transfer, it is found that the superficial liquid velocity is a crucial factor and the packed bed distributor is better than the nozzle distributor. A semi-theoretical analysis using single channel models shows that the packed bed distributor always yields shorter and uniformly distributed liquid slugs compared to the nozzle distributor, which in turn ensures a better mass transfer performance. A bed scale mass transfer model is proposed by employing the single channel models in individual channels and incorporating effects of non-uniform liquid distribution along the bed cross-section. The model predicts the overall gas-liquid mass transfer coefficient with a relative error within ±30%.     

A generalized CFD model for evaluating catalytic separation process in structured porous materials

A hybrid multiphase model is developed to simulate the simultaneous momentum, heat and mass transfer and heterogeneous catalyzed reaction in structured catalytic porous materials. The approach relies on the combination of the volume of fluid (VOF) and Eulerian–Eulerian models, and several plug-in field functions. The VOF method is used to capture the gas–liquid interface motion, and the Eulerian–Eulerian framework solves the temperature and chemical species concentration equations for each phase. The self-defined field functions utilize a single-domain approach to overcome convergence difficulty when applying the hybrid multiphase for a multi-domain problem. The method is then applied to investigate selective removal of specific species in multicomponent reactive evaporation process. The results show that the coupling of catalytic reaction and interface species mass transfer at the phase interface is conditional, and the coupling of catalytic reaction and momentum transfer across fluid–porous interface significantly affects the conversion rate of reactants. Based on the numerical results, a strategy is proposed for matching solid catalyst with operating condition in catalytic distillation application.