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.     

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     

气液螺旋环状流压降特性研究

考虑旋流衰减的影响,对气液螺旋环状流的压降特性进行研究并推导出了螺旋环状流压降预测模型。定义压降旋-直比系数为气液两相螺旋环状流和气液两相直流的压降之比,以此来表征旋流衰减对压降的影响。基于量纲分析的方法对压降旋-直比系数进行分析,推导出其表达式,压降旋-直比系数依赖于Lockhart-Martinelli 参数和气相Froude数变化。最终,得出了气液两相螺旋环状流的压降预测模型。在50 mm内径的水平管内对螺旋环状流的压降特性进行了实验研究,其中气相表观流速变化范围为10~16 m/s,体积含液率（LVF）变化范围为0.6%~4.8%。通过与实验数据进行对比,压降预测模型的相对误差在±15%以内,为工程应用提供了参考。     

Study on pressure drop characteristics of gas-liquid swirl annular flow

Considering the influence of swirl attenuation, the pressure drop characteristics of gas-liquid spiral annular flow are studied, and the pressure drop prediction model of spiral annular flow is deduced. The swirl-straight ratio of pressure drop is defined as the ratio of pressure drop of swirl flow to straight flow, used to characterize the effect of swirl decay on pressure drop. The expression of swirl-straight ratio of pressure drop is derived by the method of dimensional analysis, and it has a strongly dependence on Lockhart-Martinelli coefficient and gas phase Froude number. Finally, the prediction model of pressure drop for gas-liquid swirl annular flow is obtained. The pressure drop characteristics of the swirl annular flow are experimentally studied in a horizontal tube with an inner diameter of 50 mm. The range of the gas superficial velocity is 10—16 m/s and the range of the liquid volume fraction (LVF) is 0.6%—4.8%. Through comparison with experimental data, the relative error of the pressure drop prediction model is within ±15%, which provides a method reference for engineering applications.     

Experimental study of mass transfer limited reaction—Part II: Existence of cross-over phenomenon

In Part II, we extend the inverse methodology which is discussed in Part I to various experiments performed in a tubular reactor to infer mass transfer coefficients. Mass transfer coefficients, inferred from the concentrations of the reactants which are extracted from the absorbance of the reaction mixture using multicomponent spectrum analysis, are then used to solve the convection-diffusion-reaction equations for the concentrations of the reactants in the bulk phase and in the dispersed phase, to explore the possibility of cross-over for a mass transfer limited reaction. Experiments are performed incorporating the asymmetry in the transport rates of the premixed reactants, which is the potential reason for the existence of cross-over. The different mass transfer coefficients of the two premixed reactants indeed indicate a switch in the concentration of the reactants in the dispersed phase, which is termed as “cross-over”. The experimental results are further analysed by validating the theoretical criterion proposed by Mchedlov-Petrossyan et al. (2003, Chem. Eng. Sci. 58, 3005-3023 & 2691-2703) to obtain the parametric space for the existence of cross-over, in order to optimize the length of the tubular reactor.     

Electrodiffusional determination of momentum transfer in annular flows: Axial developing and swirling decaying flows

Two types of developing flows were studied: the axial developing flow occuring downstream of fixed beds of spheres, and the swirling decaying flow induced by a tangential inlet. In both flows, the momentum transfer was investigated for different axial distances and for a Reynolds number range of 90 to 3780 using an electrochemical method. Measurement of the wall shear stress was achieved by means of the limiting electrodiffusional current on circular microelectrodes. Comparisons of swirling flow and axial developing and developed flows are made in terms of velocity gradients and friction factors.Notation A microcathode surface area - C _s potassium ferricyanide concentration - d microelectrode diameter - e=R ₂–R ₁ thickness of the annular gap - F Faraday constant - f _ax,f _df,f _e friction factors - I _L limiting diffusional current - k _F local mass transfer coefficient - L _e entrance length - R ₁ external radius of the inner cylinder - R ₂ internal radius of the outer cylinder - Reynolds number - S _ax,S _df,S _e velocity gradients - U _m mean axial velocity - x axial coordinate - kinematic viscosity This paper was presented at the Workshop on Electrodiffusion Flow Diagnostics, CHISA, Prague, August 1990.     

Electrochemical study of mass transfer in Li-Mg and Li-Mg-Al alloys

The interdiffusion coefficients in Li-Mg alloys and Li-Mg-Al alloys were evaluated using transient techniques such as chronopotentiometry and chronoamperometry. Anodic or cathodic pulses were imposed on the alloy electrodes under galvanostatic and potentiostatic conditions. Taking into account charging of the double layer, ohmic drop, adsorption of diffusing species and electrolyte-electrode boundary shift, the diffusion coefficients of lithium in Li-Mg alloys (α-phase and β-phase) and in Li-Mg-Al alloys were estimated at around 420°C. In the case of Li-Mg α-phase alloys, the values of the diffusion coefficients,D _Li, can be represented in a polynomial expansion of the composition of the alloy,X _Li (mol%) as follows: $$ln D_{Li} = - 19.850 - 0.4294X_{Li} + 0.0249X_{Li}^2$$ The diffusion coefficients of lithium in Li-Mg (β-phase) alloys show extremely large values (?10^?6 cm²s^?1) as also in the Li-Al β-phase alloys.     

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.     

An experimental investigation of heat transfer to water in film flow Part II – boiling runs with and without induced swirl

In the previous paper, (Part I)⁽¹⁾, the results were presented of an investigation of heat transfer to non-boiling falling films of water in an electrically heated copper tube of 0.948-in. i.d. and 8-ft. long. Comparative measurements of heat transfer in full tube flow were also given, and the effect of a simple swirl-type turbulence promoter was studied for both full tube and film-type flow. The present paper presents the results of an investigation of boiling heat transfer in the same apparatus.     

Electrochemical study of liquid-solid mass transfer in packed bed electrodes with upward and downward co-current gas-liquid flow

Hydrodynamic and mass transfer parameters (pressure drop, gas and liquid hold-up, liquid-solid mass transfer coefficients) have been measured for porous electrodes with upward or downward co-current gas-liquid flow by means of several electrochemical techniques. The influence of the most important parameters (packing diameter, gas and liquid flow rates) and of the hydrodynamic flow regimes, has been studied. It is found that in the trickle flow regime the limiting current densities depend only on the liquid flow rates (with no measurable influence of the gas). In the upward flow configuration, the strong turbulence generated by the ascending gas bubbles leads to a sharp increase of current densities with the gas flow rate. A comparison between both configurations is presented.     

Heat and mass transfer in multicylinder drying: Part I. Analysis of machine data

A mathematical model describing the heat and mass transfer in the dryer section of a paper machine has been applied to the production data from four paper machines. Model predictions for the machine speed are compared to actual machine speeds for a total of 163 data sets. The mathematical model assumes that the temperature and moisture content remain homogeneous in the thickness direction of the sheet. For three paper machines producing paper with basis weights ranging from 0.056 to 0.159 kg d.s./m² the model predictions are adequate. For the paper machine producing the heaviest grades with basis weights ranging from 0.189 to 0.390 kg d.s./m² the model predictions are flawed by a systematic error. For low machine velocities/high basis weights the machine velocity is over-predicted and for high machine velocities/low basis weights the machine velocity is under-predicted. This systematic error is caused by the assumption of homogeneous moisture content and temperature within the sheet being severely in error for thick sheets.     

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.     

Electrochemical mass transfer studies in open cavities

Experimental measurements on free convection mass transfer in open cavities are described. The electrochemical deposition of copper at the inner surface of a cathodically polarized copper cylinder, open at one end and immersed in acidified copper sulphate was used to make the measurements. The effects on the rate of mass transfer of the concentration of the copper sulphate, the viscosity of the solution, the angle of orientation, and the dimensions of the cylinder were investigated. The data are presented as an empirical relation between the Sherwood number, the Rayleigh number, the Schmidt number, the angle of orientation and the ratio of the diameter to the depth of the cylinder. Comparison of the results with the available heat transfer data was not entirely satisfactory for a number of reasons that are discussed in the paper.Nomenclature C _b bulk concentration of Cu⁺⁺ (mol cm^–3) - C _b bulk concentration of H₂SO₄ (mol cm^–3) - C _o concentration of Cu⁺⁺ at cathode (mol cm^–3) - C _o concentration of H₂SO₄ at cathode (mol cm^–3) - D cavity diameter (cm) - D diffusivity of CuSO₄ (cm² s^–1) - D diffusivity of H₂SO₄ (cm² s^–1) - Gr Grashof number [dimensionless] (=Ra/Sc) - g acceleration due to gravity (=981 cm s^–2) - H cavity depth (cm) - h coefficient of heat transfer (Wm ^–2 K^–1) - i _L limiting current density (mA cm^–2) - K mass transfer coefficient (cm s^–1) - K ₁,K ₂ parameters in Equation 1 depending on the angle of orientation () of the cavity (see Table 3 for values) [dimensionless] - k thermal conductivity (W m^–1 K^–1) - L ^* characteristic dimension of the system (=D for cylindrical cavity) (cm) - m exponent on the Rayleigh number in Equation 1 (see Table 3 for values) [dimensionless] - Nu Nusselt number (=hL ^* k^–1) [dimensionless] - n exponent on the Schmidt number in Equation 1 (see Table 3 for values) [dimensionless] - Pr Prandtl number (=v/k) [dimensionless] - Ra Rayleigh number (defined in Equation 2) [dimensionless] - Sc Schmidt number (=v/D) [dimensionless] - Sh Sherwood number (=KD/D) [dimensionless] - ^t H⁺ transference number for H⁺ [dimensionless] - ^t Cu⁺⁺ transference number for Cu⁺⁺ [dimensionless] - specific densification coefficient for CuSO₄ [(1/)/C] (cm³ mol^–1) - specific densification coefficient for H₂SO₄ [(1/)/C] (cm³ mol^–1) - k thermal diffusivity (cm² s^–1) - dynamic viscosity of the electrolyte (g cm^–1 s^–1) - kinematic viscosity of the electrolyte (= /)(cm² s^–1) - density of the electrolyte (g cm^–3) - angle of orientation of the cavity measured between the axis of the cavity and gravitational vector (see Fig. 1) [degrees] - parameter of Hasegawaet al. [4] (=(2H/D))5/4 Pr^{– 1/2}) [dimensionless]     

A heat transfer relation for swirl flow in a vortex tube

An experimental investigation was made to study the heat transfer behavior of a water-cooled vortex tube with air as the working medium. The vortex flow was generated by leading the compressed air to enter the vortex tube tangentially. The pressures of the inlet air were 300 to 500 kPa gauge. For each of these inlet pressures, the heat transfer performance of the vortex tube was studied at different cold mass flow ratios. New experimental data are presented. An empirical correlation for the prediction of the air-side Nusselt number is established. It was shown that the air-side Nusselt number for the swirl flow in this vortex tube can be up to 30 times higher than that for a flow without swirl in the same tube.     

同心环形管强迫流动与传热实验研究

在高温高压沸腾二相流实验系统上,实验研究了窄缝为2.05 mm的同心环形管,在不同加热条件下水的流动阻力与传热特性。2种加热方式为单内管或单外管电加热,通过处理实验测量的管壁温度获得传热系数。得到了以下结果:层流向紊流转变的临界雷诺数为2 300;环形管内的流动阻力系数小于普通圆管,外管加热时的摩擦系数小于非加热条件时的数值;窄缝环形管内换热有一定强化,高于相同条件下的圆管内紊流换热;内外管同时加热时,相比仅外管加热而言,外管的换热得到了抑制;得到了环形管内流动摩擦阻力系数与传热系数的实验关联式。     

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:     

缩放管内带衰减性自旋流的复合强化传热研究

以水、质量分数50%和85%的甘油为工质,对缩放管内分别插入的10种不同结构形式旋流片的传热性能进行实验研究.结果表明:相同实验流量范围内,以传热强化综合因子η为目标,在水为介质下,η均小于1,不适用.在质量分数50%甘油为工质下,旋流片的扭率为2.52,旋转角为180°,间距为383 mm时,η最大,在1.08-1....     

Electrochemical wall mass transfer in liquid particulate systems

Ionic mass transfer coefficients between the wall of a 2.081 inch tube and liquid fluidized beds of lead glass, soda glass and lucite spheres have been measured using the diffusion-controlled reduction of ferricyanide ion at a nickel cathode for porosities 0.90 to 0.45 and Schmidt numbers 580 to 2100. The developed fluidization mass transfer coefficient for 41 < D_T/d_p < 105 were correlated by i_D E = 0.274 Re_H^?0.38 for 10 < Re_H <1600 and by J_D E = 0.455 Re_H^?0.44 for 16.7 < D_T/d_p < 27 and 50 < Re_H < 3500. Re_H is the hydraulic Reynolds number = d_H up/μ_E and d_H is D_T E/[1 + (3/2) ((1–E)) (D_T/d_p)). The distinct effect of D_T/d_p ratio is attributed to wall effects and the non-particulate behaviour of the fluidized bed for D_T/d_p < 27. Measurements in the open pipe and packed bed agreed very well with literature values. The packed bed gives highest mass transfer coefficients at given Re_H.