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.     

Mass transfer in a magnetoelectrolytic flow cell

The effect of natural convection and forced flow on dc electrolysis in a superimposed uniform magnetic field was studied in a range of low Reynolds numbers. The critical magnetic field strength for limiting currents is lowered by increasing electrolyte flow rate and concentration. The dimensionless equation

Full-size image (<1K)

adequately correlates relative mass transfer rates with the pertinent process parameters.     

Mass transfer in smooth and rough annular ducts under developing flow conditions

Rates of solid–liquid mass transfer were measured at the inner surface of an annular duct by the electrochemical technique under developing flow conditions. Variables studied were physical properties of the solution, velocity, length of the annulus, inlet port diameter and surface roughness. Inlet port diameter was found to have no effect on the rate of mass transfer. For smooth annuli the laminar flow data fit the equation:Sh = 1.029Sc0.33Re0.55(L/d)-0.472The turbulent flow data fit the equation: Sh = 0.095Sc0.33Re0.85(L/d)-0.472Surface roughness in the form of V-threads normal to the flow was found to have a negligible effect on the rate of mass transfer in the laminar flow region while in the turbulent region the data fit the equation: Sh = 0.167Sc0.33Re(L/d)-0.472(e/d)0.33Under the present conditions, where the dimensionless roughness height e+ lies between 0.5 and 22, the rate of mass transfer was found to increase by an amount ranging from 10% to 200% depending on e+.     

Mass transfer in the entrance region for axial and swirling annular flow

Rates of mass transfer to the inner core of an annular flow system have been determined for the mass transfer entry region using the limiting current density method. Both in laminar and turbulent flow, the hydrodynamic and concentration boundary layers were not fully developed. The variation of the mass transfer coefficients with length of core section has been demonstrated, and the data for swirling flow correlated by the equation for 1500<Re < 14000, 1500 < Sc < 6200 and 1.75 < L/D^e < 10.14. The data for axial flow in the entry region have been correlated by the equation. for 1800 < Re < 12500 and Sc = 2604. Mass transfer enhancement in the entry region due to swirl when compared to axial flow-systems with a jetting transverse inlet is only noticeable for Re > 6000, but is very significant compared to systems with fully developed boundary layers in axial or swirling flow.     

Mass transfer in a rotating annular gap

The mass transfer in a rotating annular gap is theoretically calculated. The calculation results are compared with experimental data on the desorption of carbon dioxide from an aqueous solution into air.     

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 fluid flow and electrochemical mass transfer in an annular duct with an obstruction

A so-called blockage geometry consisting of a rod with a fin positioned concentrically within a pipe is used to asses the capabilities of numerical turbulent flow and mass transfer models to predict the turbulent mass transfer coefficients. Measurements of the mass transfer coefficient have been performed for a range of fin diameters and flow rates. The limiting diffusion current measurements were performed using the ferri-ferrocyanide system and nickel electrodes. Different mass transfer turbulence models are used for the calculations and the results are compared with the measurements. The influence of flow rate and fin diameter on the mass transfer rate is examined.     

Mass transfer in annular electrolytic cells with gas stirring

Mass transfer towards the inner electrode and the wall electrode was studied in an annular cell stirred with an inert gas bubble flow. Experimental data obtained for the wall electrode follow the relationship found previously for circular cells; namely $$Sh = 0.231(ScGa)^{1/3} (L/D_e )^{ - 0.194_\varepsilon0.246}$$ Study of the influence of gas hold-up on the mass transfer rate towards the inner wall electrode has yielded the following relationship: $$Sh_\infty= 0.315(ScGa)^{1/3_\varepsilon0.231}$$      

Mass transfer around prolate spheroidal drops in an extensional flow

Mass transfer in the continuous phase around a small eccentricity prolate spheroidal drop in an axisymmetric extensional creeping flow and at large Peclet numbers was investigated theoretically. The results show that, at very short times, the total quantity of solute transferred to or from the drop represents, at O(Ca¹), mass transfer by diffusion only around a sphere. For long times, or at steady‐state, the total quantity of solute transferred is, at O(Ca¹), slightly smaller than that of a spherical drop, and it decreases with an increase of the capillary number or the viscosity ratio. © 2012 Canadian Society for Chemical Engineering     

A study of ionic transfer in electrodialysis process with laminar flow

The concentration profile in a laminar flow of the diluent of a parallel-plate electrodialysis stack is derived by assuming operation at the limiting current density. The Nusselt mass transfer number is found to depend on the Reynolds number, the Schmidt number and the dimensionless hydraulic equivalent diameter according to (Nu)_theo. = 3.7 · (Re · Sc · de/L)^1/3. An empirical correlation of the Reynolds number, the Schmidt number, and the shape factor of the electrodialysis cell, with the ionic mass transfer rate in ion exchange membrane electrodialysis is obtained by measuring the limiting current densities at various conditions. The resulting empirical mass-transfer correlation, (Nu)_exp. = 3.91 · Re^0.333 · Sc^0.328 · (de/L)^0.352, holds for sodium acetate as dialysate at concentrations ranging from 0.0106 to 0.0508 kmol/m³, viscosities ranging from 0.608 to 0.926 mPa · s, temperatures ranging from 15 to 55°C, axial velocities ranging from 0.341 to 4.55 cm/s, and for cell thicknesses of 0.32 and 0.94 cm, and is found to be in agreement with the equation obtained from theory. The effects of concentration, flow rate and temperature on the limiting current density are also studied. The relationship between the thicknesses of the diffusion layer and the Reynolds number has been analyzed.     

Mass transfer in cylindrical couette flow

Theoretical equations for mass transfer to a section of the inner cylinder for laminar cylindrical couette flow are presented. The effects of curvature, the non-linear velocity profile, and the elliptic nature of the convective diffusion equation are included to extend the result of a previous treatment by Gabe and Robinson. The equations indicate that the correction to the result of Gabe and Robinson is dominated by elliptic effects for short electrodes and by curvature and velocity profile effects as the electrode comprises a larger proportion of the inner cylindrical circumference.     

基于电渗析的溶液再生传质模型及性能分析

电渗析溶液再生与传统热再生相比具有较大的节能潜力,近年来受到了越来越多的关注。目前有关电渗析溶液再生的研究主要都集中在系统层面的分析,而缺乏对电渗析传质机理的认识。为此,建立了描述电渗析在高浓度下的传质理论模型,并试验探究了不同电流密度、体积比及初始浓度对系统性能的影响。结果表明,模型和试验结果吻合很好,误差小于±4%。体积比越大时,系统再生性能越好,但溶液产量也越低;电流密度越大时,系统再生性能越好,但系统能耗也越高;初始浓度越高时,系统电流效率和再生性能越低,同时膜堆中浓差极化系数也越低。在实际应用时应权衡以上因素以实现更高的系统性能和效率。     

Enhancement of mass transfer at a spherical electrode in pulsating flow

The effect of pulsation on the overall mass transfer coefficient between a sphere and a liquid at low Reynolds number (Re < 6.36) has been studied. When there is no flow reversal, pulsations have a negative effect on the mass transfer coefficient, it being minimum when the dimensionless group α = a/u ₀ = 1. When flow reversal occurs the mass transfer coefficient increases with both frequency, f, and amplitude, a, of the pulse and decreases with the mean fluid velocity, u ₀. The variation of the mass transfer coefficient has been studied with a model based on the quasisteady-state assumption. In this way two correlations have been obtained for the mass transfer coefficient: $$\operatorname{Re} < 20\user1{ }Sh = 1.23Sc^{1/3} \operatorname{Re} ^{0.23} $$ $$\operatorname{Re} < 20\user1{ }Sh = 0.39Sc^{1/3} \operatorname{Re} ^{0.58} $$      

层流中脉动气流横掠平板强化传热

为研究脉动气流下等热流密度平面的换热特性,搭建了脉动气流强化传热实验台架,进行了不同雷诺数（Re=433～1733）的脉动气流下高温共烧陶瓷发热片组的换热实验研究,脉动气流的脉动频率f固定为30 Hz,脉动振幅prms固定为165 Pa。结果表明,在合适的脉动参数下（f=30 Hz, prms=165 Pa）,脉动气流有效地强化了等热流密度平面的换热性能,本文获得的强化换热效率介于9.7%和10.8%之间,随着雷诺数的增加轻微地线性增加。另外,结果揭示了在层流流动中,不管在稳定气流下还是在脉动气流下,等热流密度平面的换热性能都随着雷诺数的增加而线性地增加,但脉动气流下线性拟合的结果的斜率较大,为稳定气流下的斜率的1.26倍。最后,结果显示了在稳定气流中加入脉动分量能迅速增大换热面下游的温度水平,预示着脉动气流在强化传热的同时,也增强了气流内部的热传递。     

微通道内气-液传质研究

以CO₂-H₂O为模型体系，实验考察了当量直径为667 μm的单通道和16个并行通道内的气-液传质行为.实验发现，液体表观速度增加，单通道内液侧体积传质系数明显提高;同一液体表观速度下，液侧体积传质系数随气体表观速度增加而增加;在实验数据基础上关联了液侧体积传质系数与气-液两相流参数间的关系.微通道内的液侧体积传质系数较常规尺度气-液接触设备至少高1～2个数量级.并讨论了并行微通道内气-液两相流分配特性对整体传质性能的影响，表明合理设计气、液流动分布结构，可保证微通道内优异的传质特性.     

Non-ideal flow in an annular photocatalytic reactor

This study deals with the modelling of non-ideal flow in a tubular photocatalytic reactor with thin layer of TiO₂ photocatalyst. The objective was to analyse different level of mixing in the photoreactor applying basic principles of chemical reaction engineering. For this purpose photocatalytic oxidation of toluene was used as the model reaction. Photocatalytic reactor was operated in two different flow modes: classic type of an annular reactor with basically ideal (plug) flow with some extent of dispersion and annular flow reactor acted as stirred tank reactor with mixing of reaction mixture accomplished by recirculation. A series of experiments with step input disturbance at the entrance of the reactor with different air flow was performed in order to achieve better understanding of the reactor hydrodynamics. Several reactor models are applied, such as one dimensional model of tubular reactor at the steady state conditions, axial dispersion model at non-stationary conditions and the model of the continuous non-stationary stirred tank reactor. Numerical methods necessary for solving model equations and parameter estimation were described.     

Modeling an annular flow tubular reactor

A stochastic model representing annular flow in a tubular reactor is proposed. Numerical simulation was utilized to generate sample paths fitting the residence time distributions (RTD) of the system. The model was constructed from basic diffusion equations with the additional consideration of random effects disturbing the system, thus yielding a stochastic partial differential equation. The stochastic model is simulated using the Euler–Maruyama procedure. Experimental data from three tubular polymerization reactors were well fitted by the model. The model encompassed the two deterministic parameters, mean residence time and Peclet number, as well as three stochastic parameters: stochastic relevance (b), updated time (ΔT) and the seed that begins the Wiener process. The satisfactory results indicate that the model constitutes an important step toward comprehending the complex fluid dynamics of tubular flow systems.     

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 from bubbles in cocurrent flow

An experimental study has been made of liquid phase mass transfer from bubbles travelling cocurrently with liquid in a horizontal pipe. A simple model of the process based on streams of spherical bubbles has been developed and solved in the form of fractional absorption as a function of dimensionless groups. The derivation of and results obtained from this model are presented and explained. Experimental absorption rates measured in turbulent liquid flow over very wide ranges of bubble frequencies support the predictions of this model. A very effective bubble-frequency counter has also been developed capable of counts as high as 1600/min.     

Modeling of transfer in electrodialysis systems

The mass electrotransfer in an electrodialysis cell that desalinates and concentrates a salt solution is mathematically modeled with consideration of water transfer.