Overall mass transfer in swirling decaying flow in annular electrochemical cells

Mass transfer coefficients between an electrolyte solution and the inner cylinder of an annulus were determined experimentally, using the electrochemical technique, for both laminar and turbulent swirling flows of a liquid induced by means of a tangential inlet in the annular gap. The average mass transfer coefficients were determined as a function of the axial distance from the entrance, for various diameters of the inlet duct and thicknesses of the annular space, for a Reynolds number range of 100 to 5900. Enhancement of mass transfer up to 400% was achieved in comparison to that obtained in fully developed axial flow. Correlations of the experimental data, taking into account the geometrical and hydrodynamic parameters influencing the overall mass transfer, are presented.Nomenclature A Cathode surface area - C Potassium ferricyanide concentration - D Ferricyanide ion diffusion coefficient - d Tube diameter - e=R ₂–R₁ Thickness of the annular gap - ERR Mean square error between experimental and calculated data - F Faraday's constant - f(N) Function of the geometrical parameters - h Local heat transfer coefficient - l ₁ Limiting diffusional current - k Mass transfer coefficient - L,L ₁,L ₂ Axial distances from the inlet - L/2e Reduced axial coordinate - N=R ₁ /R ₂ Radii ratio of the annular gap - n Number of electrons involved in the electrochemical reaction - Nu _x =hx/ Local Nusselt number - Q Volumic flow rate - R ₁ External radius of the inner cylinder - R ₂ Internal radius of the outer cylinder - Re=2eU/ Reynolds number - Re _x =Ux/ Local Reynolds number - S ₀=U /U Initial swirl intensity - Sc=/D Schmidt number - Sh=2ek/D Sherwood number obtained in swirling flow - Sh_a=2ek/D Sherwood number obtained in fully developed axial flow - Sh _x Local Sherwood number - U Mean axial velocity in the annular gap - U Axial velocity in the inlet duct - x Axial coordinate Greek letters , , , , Correlation parameters - Diameter of the tangential inlet - Thermal conductivity - Kinematic viscosity of the electrolyte - Density of the working solution     

Electrochemical study of mass transfer in decaying annular swirl flow

This paper describes an investigation of local mass transfer behaviour at the inner rod and outer pipe wall of an annular test section in decaying annular swirl flow generated by axial vane-type swirl generators. Four swirl generators with vane angles of between 15–60° to the axis of the duct were used. The experiments were carried out in the Reynolds number range 3300–50 000 and at a Schmidt number of 1650. The axial distribution of the local mass transfer coefficients at both the inner rod and the outer wall were measured using an electrochemical technique. Current fluctuations were also recorded to gain information on the turbulence characteristics in the vicinity of the local electrodes. This paper was presented at the International Workshop on Electrodiffusion Diagnostic's of Flows held in Dourdan, France, May 1993.     

Mass transfer in an annular electrodialysis cell in pulsating flow

The effect of pulsating flow on the mass transfer in an annular electrodialysis cell has been studied in terms of the limiting current. The results indicate that the limiting current is influenced by the fluid velocity, the pulsation amplitude and the pulsation frequency, giving an increase of 400% with respect to the steady state. For a given amplitude, the dimensionless velocity, 0 (0 = a/v), can be taken as a representative parameter of the pulsation effect on the mass transfer. The fractional increase in the Sherwood number in pulsating flow with respect to the steady state has been correlated in terms of the dimensionless velocity, 0, and the Stokes number, 1 (1 = Deq (/)1/2), giving the correlation:     

Electrochemical study of mass transfer in decaying annular swirl flow Part II: Correlation of mass transfer data

This paper presents correlations of local mass transfer at the inner rod and the outer wall in annular decaying swirl flow generated by axial vane swirl generators. Four swirl generators with vane angles in the range 15–60° to the duct axis were used and experiments were carried out in a Reynolds number range 3300–50000 and at a Schmidt number of 1650. The results were correlated in the general form Sh _x = 0.0204 Re _x ^0.86 (1 + tan _i )^0.53 Sc ^1/3, for the inner rod, and Sh _x = 0.0224 Re _x ^0.86 (1 + tan _o)^0.55 Sc ^1/3, for the outer pipe. Comparison is made with heat transfer data for work with a similar entry configuration.     

环形通道内层流入口段换热及流体变物性的影响

采用SIMPLER算法对环形通道内二维定常轴对称入口段流动与换热进行了数值计算, 研究了两种边界条件下的层流流动与换热规律, 给出了不同Prandtl数以及半径比率下沿程Nusselt数的变化曲线,同时还给出了流体物性随温度变化对流动与换热的影响, 最后还拟合出了不同半径比率下平均Nusselt数的关联式.计算结果还表明,环形通道能强化传热,强化程度随半径比率减小而增大,且入口段的换热强化与其较高的径向速度有关.     

Heat and mass transfer in non-newtonian fluid flow with power function velocity profiles

Heat and mass transfer in laminar and turbulent non-Newtonian fluids is investigated in this work using the power function velocity profiles. Analytical solutions are presented for cases of mass transfer in laminar non-Newtonian fluid flows, namely for a flat velocity profile (plug flow), for the case of a constant velocity gradient at the solid boundary (Couette flow), and for the velocity distribution within a laminar boundary layer on a flat plate, and these are illustrated by rotating disks and cylinders in laminar Ostwald-de Waele fluids. Further, turbulent mass transfer processes (tubular flow, rotating disk, and rotating cylinder) in non-Newtonian fluids (Ostwald-de Waele fluid and drag-reducing fluid) at low and large Schmidt numbers are also discussed using the solutions of mass transfer in flows with power function velocity profiles. Reasonable agreement is found between the predictions of this work and the available experimental data and correlations.     

电化学反应器流动和传质特性的仿真研究

提出了一种基于双面BDD电极的平行板结构的电化学反应器,它通过阳极和阴极交替排列引导污水多通道蜿蜒流动,实现了三维传质的增强。利用OpenFOAM分析了四阳极结构反应器的流动特性和传质特性,结果表明该结构的反应器在低入口流体雷诺数下传质系数低,分布不均,当入口雷诺数大于500时流体出现不稳定,传质增强。     

Developing and fully developed turbulent flow of drag reducing fluids in an annular duct

Velocity profiles for the inner and outer flow regions of annuli are proposed for the turbulent flow of drag reducing fluids. Theoretical expressions for friction factors are developed. From the shear stress equations and the velocity profiles, estimates for the entrance lengths are given.     

Turbulent heat and mass transfer in dilute polymer solutions

A new model based on Levich's three-zone model is developed to discuss the turbulent heat and mass transfer in drag-reducing solutions. The proposed model, which has no adjustable parameters and is represented in an explicit form, provides satisfactory predictions of the maximum heat and mass transfer reduction in smooth and rough pipes. The mass transfer to a disk rotating in drag-reducing solutions is also discussed using the proposed model.     

Turbulent mass transfer in small radius ratio annuli

Mass transfer in annuli for both fully developed laminar and turbulent flow conditions has been studied with respect to available experimental data. It is shown that prediction of the Sherwood number for the inner annular wall based on the hypothesis of coincidence of the zero shear stress position for laminar and turbulent flows leads to serious error in the case of small radius ratio. Also it is shown that in contrast with plain tubes the curvature in small radius ratio annuli should be taken into account for the case of small Reynolds numbers. In consequence, the well-known Leveque equation can be used for the calculation of the mass transfer coefficient in annuli only under certain conditions. Possibilities of electrodiffusion diagnostics for the precise determination of the zero shear stress position in annuli are discussed.List of symbols A cross-section flow area (m²) - a =r ₁/r ₂ annular radius ratio (–) - mean fluctuation and bulk concentration (mol m^–3) - D molecular diffusivity (m²s^–1) - d _b hydraulic diameter (m) - f,f ₁,f ₂ overall, inner and outer wall friction factors (–) - f = ₁/ near wall velocity gradient (s^–1) - pressure drop per unit of length (Pam^–1) - K _L average mass transfer coefficient (ms^–1 ) - k =r ₀/r _0,L ratio of zero shear stress position in turbulent and laminar flows (–) - L mass transfer surface length (m) - L _D diffusion leading edge length (m) - L _ent diffusion entrance length (m) - P _W wetted perimeter (m) - Re =U _av d _h/ Reynolds number (–) - r radial distance from conduit axis (m) - r ₀,r _o,L radial distance of zero shear stress position in turbulent and laminar flows (m) - r ₁,r ₂ radius of inner and outer annular cylinders (m) - Sc = /D molecular Schmidt number (–) - Sh =K _L d _h/D Sherwood number (–) - U _av average liquid velocity (ms^–1) - u,u mean and fluctuation axial velocity (ms^–1) - , mean and fluctuation radial velocity (ms^–1) - y = r – r ₁ distance from the inner wall (m) - y = (/₁)^1/2 dynamic length (m) - Z distance in direction of the flow (m) Greek symbols _D diffusion layer thickness (m) - µ dynamic viscosity (Pa s) - kinematic viscosity (m²s^–1) - density (kgm^–3) - shear stress (Pa) - _W wall shear stress for tube and plate channel (Pa) - ₁, ₂ wall shear stress for inner and outer annular cylinders (Pa) - Geometrical factor with respect to k-function (–) - _R, _K geometrical factor with respect to Rothfus or Kays-Leung equations (–) - ratio of radial distance of zero shear stress position to outer radius in laminar flow (–)     

Turbulent mass transfer from a rotating disk

A new model based on the surface renewal concept was proposed to discuss the turbulent mass transfer from a rotating disk. The proposed model, in which the proportionality constants are determined by using hydrodynamic data rather than mass transfer data and no adjustable parameters are included, was in excellent agreement with the available experimental data for Newtonian fluids. The mass transfer from a disk rotating in dilute polymer solutions and power-law fluids was also investigated using the proposed model. Good agreement was found between the model and the experimental data for dilute polymer solutions and power-law fluids.     

Mixed convection mass transfer studies of opposing and aiding flow in a parallel plate electrochemical flow cell

Studies of combined natural and forced convection in a vertical parallel plate electrochemical cell in laminar conditions in cases of opposing and aiding flow are reported. In an ongoing project it was necessary to identify conditions in which natural convection had no significant influence on mass transfer rates at the cell walls so that data could be validly compared with purely laminar flow computational models. For the different electrode lengths investigated, natural convection dominated at low Reynolds number and there was no Reynolds number dependence. At high Reynolds number the data approached the laminar flow solution. At intermediate Reynolds number, however, there existed a distinct region where free and forced convection were significant. At high electrolyte concentrations data did not merge with laminar flow equations until Re=1000 and low electrolyte concentration data for the large plate could not be compared with numerical predictions below Re of 250. An attempt was made to compare the data with those of other workers on combined forced and natural convection heat and mass transfer.     

Effect of gas evolution on mass transfer in an electrochemical reactor

Experiments were conducted to study the effect of gas bubbles generated at platinum microelectrodes, on mass transfer at a series of copper strip segmented electrodes strategically located on both sides of microelectrodes in a vertical parallel-plate reactor. Mass transfer was measured in the absence and presence of gas bubbles, without and with superimposed liquid flow. Mass transfer results were compared, wherever possible, with available correlations for similar conditions, and found to be in good agreement. Mass transfer was observed to depend on whether one or all copper strip electrodes were switched on, due to dissipation of the concentration boundary layer in the interelectrode gaps. Experimental data show that mass transfer was significantly enhanced in the vicinity of gas generating microelectrodes, when there was forced flow of electrolyte. The increase in mass transfer coefficient was as much as fivefold. Since similar enhancement did not occur with quiescent liquid, the enhanced mass transfer was probably caused by a complex interplay of gas bubbles and forced flow.List of symbols A electrode area (cm²) - a constant in the correlation (k = aRe ^m , cm s^–1) - C _{R, bulk} concentration of the reactant in the bulk (mol^–1 dm^–3) - D diffusion coefficient (cm² s^–1) - d _h hydraulic diameter of the reactor (cm) - F Faraday constant - Gr Grashof number =gL ³/² (dimensionless) - g gravitational acceleration (cm s^–2) - i _g gas current density (A cm^–2) - i _L mass transfer limiting current density (A cm^–2) - k mass transfer coefficient (cm s^–1) - L characteristic length (cm) - m exponent in correlations - n number of electrons involved in overall electrode reaction, dimensionless - Re Reynolds number =Ud _h^–1 (dimensionless) - Sc Schmidt number = D ^–1 (dimensionless) - Sh Sherwood number =kLD ^–1 (dimensionless) - U mean bulk velocity (cm s^–1) - x distance (cm) - _N equivalent Nernst diffusion layer thickness (cm) - kinematic viscosity (cm² s^–1) - density difference = (_L – ), (g cm^–3) - _L density of the liquid (g cm^–3) - average density of the two-phase mixture (g cm^–3) - void fraction (volumetric gas flow/gas and liquid flow)     

泡沫金属内流体流动沸腾热质传递过程的模拟

为了了解泡沫金属内流体流动沸腾热质传递机理,建立了泡沫金属内流体流动沸腾的理论模型。建模中采用Mixture多相流模型,通过引入泡沫金属的渗透率、有效热导率等参数,以体现泡沫金属区别于传统多孔介质的特点;通过在动量方程中增加达西项与惯性力项以体现泡沫金属对两相流动中动量传递的影响;通过增加固体能量方程,并与流体能量方程耦合,以体现泡沫金属内传热过程的热不平衡性。将本文建立的理论模型与已有文献中的数据进行对比,结果表明模型预测值和已有的实验数据吻合较好。     

Computer modeling of multiscale fluid flow and heat and mass transfer in engineered spaces

Design and analysis of fluid flow and heat and mass transfer in engineered spaces require information of spatial scales ranging from to and time scales from to . The studies of such a multiscale problem often use multiple computer models, while each of computer models is applied to a small range of spatial and time scales. Accurate solution normally requires exchanging information between a macroscopic model and a microscopic model that can be done by coupling the two models. With the approach, it is possible to obtain an informative solution with the current computer memory and speed.This paper used a few examples of fluid flow and heat and mass transfer in engineered spaces to conclude that a coupled macroscopic and microscopic model is likely to have a solution and the solution is unique. A stable solution for the coupled model can be obtained if some criteria are met. The information transfer between the macroscopic and microscopic models is mostly two ways. A one-way assumption can be accepted when the impact from small scale on large scale is not very significant.     

Mass transfer in annular cylindrical reactors in laminar flow

Radial diffusional mass transfer is studied in a fluid flowing in fully developed laminar flow in an annular cylindrical reactor in which a first order heterogeneous reaction is taking place at the wall. The asymptotic behaviour of the concentration decrease far from the reactor inlet is especially investigated. Limiting values of Sherwood numbers are numerically determined and represented by semi-empirical expressions. Additivity relationships between homogeneous and heterogeneous contributions are established. Theoretical results are found in excellent agreement with those yielded by a new experimental method based on heterogeneous decomposition of ozone. Annular reactors exhibit a mass transfer efficiency which is noticeably higher than that of empty tubes. This efficiency may be characterized by three criteria related to inner space utilization, catalytic surface utilization and/or mechanical energy degradation.     

Electrolysis in an annular flow cell with gas generation

A cylindrical electrochemical cell with axial flow in the annulus, formed by the inner indifferent anode tube and the outer cathode tube, is analysed in terms of various reactor models. One alternative characterization, the radial dispersion model, allows the estimation of an apparent radial dispersion on the basis of experimental conversion data.Nomenclature a ratio of the inner electrode radius to the outer electrode radius - c active ion concentration;c _o same in bulk - d _e equivalent (or hydraulic) diameter - D _i ionic diffusion coefficient - D _r radial dispersion coefficient - F Faraday's constant - i _z current density distribution along the cathode - J _n Bessel function of the first kind, ordern - I current flow between the electrodes;I _m its mean value - L length of the cathode - n number of electrons transferred in the cathode reaction - p eigenvalue set in the Annular Hankel Transform - Q volumetric flow rate of electrolyte - r radius - R _i radius of the inner electrode (anode) - R _o radius of the outer electrode (cathode) - (Re) Reynolds number (characteristic length: hydraulic diameter) - S dimensionless radius,r/R _o - S _i stoichiometric number - (Sc) Schmidt number - u _m mean value of electrolyte linear velocity - x conversion, defined as (c _o-c)/c ₀;x _E average exit conversion;x_E:x _E computed from a regression line;x_w conversion at the cathode tube - y dimensionless axial variable,z/L - Y _n Bessel function of the second kind, ordern - z axial coordinate - degree of dissociation - lumped parameter in radial dispersion model - geometric-aspect parameter in annulus flow theory - electrolyte residence time in cell     

Turbulent particle mass flux in a two-phase shear flow

This paper presents measurements of mean and rms of fluctuations of concentration, particle turbulent velocities, shear stress and covariance of the fluctuations of particle number density and particle velocities in a horizontal plane shear layer. Particle Image Velocimetry (PIV) was used to obtain simultaneously particle velocities and number densities to evaluate models for the prediction of particle dispersion in Reynolds-Averaged Navier-Stokes calculation approaches. The flow was horizontal with the low speed side on top and laden with nearly mono-dispersed 55 and 90 µm glass beads, which were injected at the upper, low speed side of the flow. The Stokes number of the particles was in the range of 0.41 to 4.3 and the drift parameter due to gravity was in the range 0.18 to 1.5. The experimental results quantified how particle ‘centrifuging’ by the large fluid vortices influenced the measured quantities. The turbulent particle mass flux was compared with models based on the gradient of mean particle concentration. Different dispersion coefficients were evaluated by introducing the measured quantities into the model equation and it was found that dispersion coefficients based on the fluid eddy diffusivity performed poorly leading to an order of magnitude errors. A dispersion coefficient in tensor form, based on the product of particle shear stress and particle integral time scale, led to good agreement with measured turbulent particle mass fluxes with errors between 0 and 50%.     

Ionic mass transfer in parallel plate electrochemical cells

Experimental investigations have been made of ionic mass transfer in a parallel plate electrochemical cell under both laminar and turbulent flow. The results obtained in the laminar flow region were found to be well represented by a Leveque-type equation modified to include the cell aspect ratio as an additional parameter. The influence of decreased mass transfer at the edges of the electrodes due to changes in the velocity profile was found to be small. For the turbulent region, there is a correlation of the mass transfer coefficient with Reynolds number to an exponent of 0.875 and Schmidt number to exponent of 0.21. This is in accord with existing correlations for heat and mass transfer in similar geometries over the range studied.     

Two-phase flow and mass transfer in scrubbers

Experimental investigations were carried out in spray scrubbers of different sizes with cocurrent flow of gas and liquid. Of special interest were the local processes in the mass transfer zone. The scrubber was operated with warm water/air system (cooling tower) to obtain detailed information about mass transfer. Air is being humidified with water vapour, which in turn leads to a temperature drop in the liquid. The liquid temperatures are relatively easy to measure and are shown as liquid isotherms. In the case of plug flow, the liquid isotherms should be straight horizontal lines. In reality, significant deviations from plug flow are caused by the transfer of liquid to the walls. A large part of the liquid forms a film flow at the wall. Furthermore, nearly all the mass transfer is completed in the zone of liquid atomization immediately beneath the nozzle. The number of measured transfer units was between 0.5 and 2.0 and was significantly influenced by the liquid flow rate. Based on the improved knowledge of the proceses inside the scrubber, a simplified model has been developed. Since the model simulates all the essential processes inside the mass transfer zone, liquid distribution and mass transfer efficiency can be approximately predicted.