Numerical Studies of Convective Mass Transfer Enhancement in a Membrane Channel by Rectangular Winglets☆

Fluid Dynamics and Transport Phenomena

Numerical Studies of Convective Mass Transfer Enhancement in a Membrane Channel by Rectangular Winglets☆

A R T I C L EI N F O

Article history:

Membrane

Concentration polarization

Mass transfer enhancement

Rectangular winglet

Pumping power

Numerical calculations were conducted to simulate the f l ow and mass transfer in narrow membrane channels with and without f l ow disturbers.The channel consists of an impermeable solid wall and a membrane surface with a spacing of 2.0 mm.The f l ow disturbers studied include rectangular winglets,which are often used as longitudinal vortex generators to enhance heat transfer in heat exchanger applications,as well as square prism,triangular prism,and circular cylinder,which are used here to mimic the traditional spacer f i laments for comparison of their abilities in enhancing the convective mass transfer near the membrane surface to alleviate the concentration polarization.The disturber performance was evaluated in terms of concentration polarization factor versus consumed pumping power,with a largerfactor meaning a more serious concentration polarization. Calculations were carried out for NaCl solution f l ow with Reynolds numbers ranging from 400 to 1000.The results show that the traditional f l ow disturbers can considerably reduce the concentration polarization but cause a substantial pressure drop,while the rectangular winglets can effectively reduce the concentration polarization with a much less pressure drop penalty.The rectangular winglets were optimized in geometry under equal pumping power condition.

©2014TheChemicalIndustry andEngineeringSocietyofChina,andChemicalIndustryPress.Allrightsreserved.

1.Introduction

Ultraf i ltration,nanof i ltration and reverse osmosis are typical membrane processes[1,2].One of the obstacles to more widespread application of these membrane separation processes is the problem of concentration polarization,due to the accumulation of rejected particles/molecules near the membrane surface.Since concentration polarization debases permeate quality and reduces permeate f l ux,its suppression is of great importance.

In spiral-wound and plate-frame membrane modules,wire meshes are often used to separate adjacent membrane sheets to create f l ow passage for feed solution,so they are often called spacers,which also actasf l owdisturbersorturbulencepromoterstoenhancemasstransfer and consequently weaken concentration polarization.In the past decades,many studies have been done to investigate the impacts of various net-type spacers on the f l ow and convective mass transfer in membrane channels[3-14].The cross-sectional shapes of the investigated spacer f i laments included circle[3-13],square[10,11,13,14], triangle[10,11],as well as some other modif i cations[12,13].All results show that spacers augment mass transport but they increase simultaneously f l ow resistance.Since net-type spacers generally cause a signif i cantly higher pressure drop increase than the mass transfer enhancement,they are not effective turbulence promoters in terms of mass transfer enhancement relative to pressure drop penalty.

There is an analogous relation between the heat transfer and the mass transfer.Various enhanced surfaces have been developed for the purpose of heat transfer enhancement in heat exchanger applications. Min and Xu compared the performance of the f i n with winglet-type longitudinal vortex generators(WLVGs)with that of louver f i n,and found that the former had a higher j-to-f factor ratio than the latter [15].There are many studies that support the effectiveness and superiority of WLVG in enhancing heat transfer[16-19].The most attractive character of WLVG is that they can increase the heat transfer coeff i cient with a relatively low pressure drop penalty,as stated by Webb and Kim [20].It is thus interestingto know how WLVGs enhance mass transfer if they are used in a membrane channel for mass transfer.We note that net-type spacers are not always necessary to form membrane channels. Geraldes et al.[21]and de Pinho et al.[22]performed experimental studies of f l ow transfer and mass transfer in an empty membrane channel in nanof i ltration.The channel comprised an impermeable solid wall and a membrane sheet supported by a porous stainless steel plate,so the channel height was maintained without the use of wire meshes.Koutsou et al.[23]investigated numerically the f l ow in a f l at channel containing a periodic array of cylindrical turbulence promoters suspended between the two channel walls,the cylinders thereforeserved only as turbulence promoters rather than spacers.Flow in an empty membrane channel was also studied by Wiley and Fletcher[24].

The present research attempts to introduce the longitudinal vortex enhancementtechniqueinto the membrane mass transfer andevaluate the mass transfer enhancement effect of WLVG.It should be noted that the effectiveness of WLVG in augmenting convective mass transfer in a membrane channel is not self-evident,because there are some key differences between the use of WLVGs in heat transfer and that in masstransfer:(1)WLVGsareinstalledindifferentgeometricconf i gurations,(2)the convective mass transfer boundary layer is substantially thinner than the convective heat transfer boundary layer,and(3)a permeate f l ux across the membrane exists in contrast to impermeable heat transfer wall.The present work aims to reveal the mass transfer enhancement effects of winglet-type longitudinal vortex generators in membrane processes.Rectangular winglets are used to enhance convective mass transfer to reduce the concentration polarization in a narrow membrane channel.Quadrangular prism,triangular prism,and circular cylinder,which are used to simulate the traditional spacer f i laments,are also studied for comparison purpose.Numerical calculations are conducted to simulate the f l ow and convective mass transfer in membrane channels with and without the abovementioned f l ow disturbers for channel height based Reynolds numbers ranging from 400 to 1000.The mass transfer enhancement effects are compared in terms of concentration polarization factor versus consumed pumping power.The rectangular winglets are further optimized in geometry under equal pumping power condition.

2.Computational Details

2.1.Physical model

The physical model of the feed channel of a typical plate module is a narrow rectangular channel with an impermeable wall and a membrane,with feed solution fl owing and separating into two parts—permeate and retentate,as illustrated by Fig.1.Fig.2 is a schematic diagram of the basic membrane channel selected for this study,which consists of an impermeable solid wall and a membrane.The channel height is H and the channel length is L=35H.Four kinds of fl ow disturbers,which include the quadrangular prism,triangular prism, circular cylinder,and rectangular winglets,are mounted on the solid bottom wall and located 5H downstream from the channel inlet.The fi rst three strip shape disturbers[(a),(b)and(c)in Fig.2]have a length equal to the channel width,and they are installed in perpendicular to the entering solution fl ow,while the rectangular winglets[Fig.2(d)] are set up with an angle attacking to the entering solution fl ow,they are arranged in pairs to form V or Λ geometry,as illustrated in Fig.3. For convenience,the former is called the convex winglet pair and the latter the concave winglet pair.The typical geometry and arrangement of the rectangular winglets are set as follows:the winglet height h= H/2,theaspectratioσ=l/h=2.0,theattackangleβ=30°,andthedistance between two adjacent winglets W=1.5H,as summarized in Table 1.The winglet thickness is zero.Fig.2 shows that the computational domain is taken to include the channel height in the normal direction(perpendicular to the solid wall and the membrane surface), the entire channel length in the longitudinal(streamwise)direction, and a channel width that just involves one winglet in the transversal (spanwise)direction.Thedomainwidthis equaltothewingletinterval, W.Thecoordinate system adopted in this studyhas anoriginlocatingat the channel inlet on the membrane surface,with the x axis pointing to the streamwise direction,the y axis opposite to the channel height direction,and the z axis to the spanwise direction.

2.2.Numerical simulation

Solution fl ow in membrane channel is assumed to be steady and incompressible with constant properties.Although the solution feed Reynolds number is low,the fl ow may show a feature of turbulence because of the existence of fl ow disturbers in the channel.The renormalization group(RNG)k-ε turbulent fl ow model was developed using the RNG method by Yakhot et al.[25]to renormalize the Navier-Stokes equations to account for the effects of smaller scales of motion.Such a model is considered to be suitable for modeling fl ow in channel with disturbers due to its capacity and accuracy for solving eddy activities at relatively low Reynolds number.The basic idea of the RNG method as applied to turbulence modeling is the elimination of small-scale eddies from governing equations by expressing their effects in terms of larger scale motions and a modi fi ed viscosity[4]. Summarized below are some key equations governing the solution fl ow and solute transport in the membrane channel with use of the RNG model.

Continuity equation:

Fig.1.Solution splitting in a typical plate membrane module.

Table 1Typical rectangular winglet parameters

Transportequationforturbulentkineticenergyperunitf l uidmass,k:

Fig.2.Membrane channel with various f l ow disturbers.

In these equations,w is the solute mass fraction,D the solute diffusivity,and Sc the Schmidt number.

As boundary conditions,the f l uid inlet velocity is assumed to have a parabolic prof i le along the channel height direction to reduce the inlet velocity inf l uence on mass transfer.Fluid f l owing out of the channel is assumed to exist in a fully developed condition where all changes for the f l ow parameters are equal to zero.Symmetry boundaries are used at both sides of the computational domain shown in Fig.2,with no slip conditions being applied to both the solid wall and the membrane surface.The solute concentration distribution at the membrane surface is determined by the mass balance among the convection,reverse diffusion,and permeate f l ux.

For channel inlet at x=0:

where umis the f l uid mean velocity and w0is the inlet solute mass fraction.

For channel outlet at x=35H,where the f l ow is considered to be fully developed:

Fig.3.Geometry and arrangement of rectangular winglets.

whereJisthepermeatevolumetric fl uxacrossmembraneorthepermeation velocity,and wpis the solute mass fraction at the membrane surfaces on permeate side or the permeate composition.The equation isobtainedfromthesolutemassbalanceatthefeedsolution/membrane interface,that is,the convective fl ux is the sum of the reverse diffusion fl ux and the permeate fl ux.

Foreachsideofthecomputationaldomainatz=0orz=W=1.5H:

whereφexpressesvariousvariablessuchasvelocity,pressureandmass faction.

The governing equations are solved under the boundary conditions using Fluent V6.3 based on the f i nite volume method.The mass balance atthe solution/membraneinterfaceis realized through the user def i ned function(UDF)in Fluent.For each simulation,the numerical grids are ref i ned until a grid independent solution is obtained.

2.3.Data reduction

Based on the numerical simulation results,we can calculate the concentration polarization factor,which is def i ned by

where wbis the solute mass fraction of the bulk fl uid and wwis the solute mass fraction at the feed solution/membrane interface.The bulk fl uid refers to the solution outside the concentration boundary layer, so wbis equal to w0.The magnitude of the concentration polarization factor re fl ects the degree of the concentration polarization,the larger the concentration polarization factor the more serious the concentration polarization problem.The concentration polarization factor averaged over a channel width of W along the spanwise direction at position of x can be represented by

while the concentration polarization factor averaged over a membrane surface area from x1to x2can be expressed as

Considering the position where the f l ow disturbers are located (x=5H)and the feature of the evolution of concentration polarization alongthechannellengthtobeillustratedinthenextsection(Section3), the starting and ending points of the above integral are taken to be x1=3H and x2=13H in the present research.

The f l uid velocity at the channel cross-section perpendicular to the x axis can be represented by

which is the local velocity magnitude of the secondary f l ow.

The total pressure at a channel cross-section perpendicular to the streamwise direction can be calculated from

The pressure drop between the two cross-sections at x1=3H and x2=13H is given by

while the consumed pumping power corresponding to this pressure drop can be obtained from

where V is the volumetric f l ow rate of the feed solution corresponding to a channel width of W.

2.4.Model validation

Calculations were implemented to simulate the concentration polarization in a membrane channel in nanof i ltration investigated by de Pinho et al.[22],who studied NaCl solution f l ow and mass transfer in an empty membrane channel having a height of 0.7 mm,a width of 30 mm,and a length of 200 mm.They performed both experimental and numerical studies and obtained the concentration polarization factor by combining the experimental data on the solute mass fraction of the bulk solution and permeate composition with the twodimensional numerical results on the solute mass fraction at the feed solution/membrane interface.Fig.4 illustrates the longitudinal concentration polarization prof i le for w0=2.0×10−4kg·kg−1feed solute mass fraction,J=1.36×10−5m·s−1permeate f l ux,and wp=3.7× 10−5kg·kg−1permeate composition.The feed Reynolds number is Re=1300,which corresponds to an entering velocity of 1.658 m·s−1, this value is substantially greater than the permeation velocity of 1.36×10−5m·s−1.Fig.4 compares our calculation with that in de Pinho et al.[22].Note that our results were obtained by using a grid system of 50×400 grid points for the computational domain.Two grid systems of 50×400 and 80×750 were tested to examine the grid-independence of the numerical result,and the relative error between the two meshes was 1.6%for the averaged concentration polarization factor.Fig.4 shows that our result is in good agreement with the de Pinho data,supporting the reliability of our numerical procedure.

Fig.4.Comparison of the present results and the literature simulation.

3.Results and Discussion

Consider NaCl solution fl ow in the present membrane channel that has a height of H=2.0 mm and a length of L=35H=70 mm.Calculations were fi rst conducted on an empty channel to show the effects of Reynolds number,which is de fi ned by Re=2Humρ/μ.The simulations used w0=0.2×10−3kg·kg−1,J=1.36×10−5m·s−1and wp= 3.7×10−5kg·kg−1,with the Reynolds numbers ranging from 400 to 1000,which correspond to the entering solution velocities of 0.1786-0.4464 m·s−1.The NaCl solution physical and transport properties are given in Table 2.

Fig.5 depicts the evolution of the concentration polarization along the channel length for Reynolds numbers of Re=400,600,800 and 1000,which correspond to the entering solution velocities of 0.1786, 0.2679,0.3572 and 0.4464 m·s−1,respectively.The coordinate is the local concentration polarization factor(Гx)and the abscissa is the dimensionless longitudinal distance from the channel inlet(x/H).The fi gure shows that the concentration polarization factor increases with increasing dimensionless distance of x/H,with a larger Reynolds number yielding a smaller concentration polarization factor.This is becausealargerReynoldsnumbermeansalargervelocity,whichcauses an enhanced mass transfer and consequently a reduced concentration polarization.

3.1.Performance comparison of rectangular winglets with traditional fl ow disturbers

Calculations were then conducted to investigate the effects of various fl ow disturbers,which include the traditional two-dimensional (2D) fl ow disturbers of square prism,triangular prism and circular cylinder,andthespecialthree-dimensional(3D) fl owdisturberofrectangular winglets,whose geometry and arrangement are presented in Table 1.Same as above,the simulations used w0=0.2×10−3kg·kg−1, J=1.36×10−5m·s−1and wp=3.7×10−5kg·kg−1.

Fig.6 illustrates the evolution of the concentration polarization along the channel length for channels with and without fl ow disturbers for Re=600.The coordinate is the local concentration polarization factor(Гx)and the abscissa is the dimensionless longitudinal distance from the channel inlet(x/H).The data for the empty channel are also incorporated to serve as a baseline to better show the concentration polarization suppressing effects of various fl ow disturbers.Fig.6 showsthatthethreetraditionaldisturberscauseasubstantiallyreduced concentration polarization factor over a region in which the disturbers are located,but their concentration polarization suppressing effect weakens with increasing dimensionless distance of x/H.Although the rectangular winglets cause only a moderately reduced concentration polarization factor over a region in which the winglets are placed, their concentration polarization suppressing effect tends to strengthen with increasing dimensionless distance of x/H.Concretely speaking,in theregionof 3＜x/H＜8,thetraditional disturbers yield a lowerconcentrationpolarizationfactorthantherectangularwinglets;intheregionof x/H＞10,however,the rectangular winglets give a lower concentration polarization factor than the traditional disturbers.The three traditional disturbers are basically comparable in reducing concentration polarization.

The solute mass fraction distributions at the feed solution/ membrane interface in channels with and without fl ow disturbers for Re=600 are illustrated in Fig.7.The channels with the traditional fl ow disturbers including the square prism,triangular prism and circular cylinder provide a simple mass fraction distribution because these channels have a conf i guration that has a 2D feature,while the channel with the rectangular winglets produces a more complicated mass fraction distribution because this channel has a conf i guration that has a 3D feature.Different mass fraction distributions exist in the regions that contain the convex and concave winglet pairs,which are def i ned in Fig.3.A large mass fraction is observed in the region that contains theconvex winglet pairwhilea small massfraction is seen intheregion that contains the concave winglet pair.Note that large mass fraction means serious concentration polarization.The convex and concave winglet pairs work together to yield a longitudinal concentration polarization prof i le like that shown in Fig.6.

Fig.8 illustrates the f l uid velocity contours at plane of z=0.75H for channels with and without f l ow disturbers for Re=600.Since the traditional f l ow disturbers including the square prism,triangular prism and circular cylinder considerably block the f l ow passage,they produce a larger maximum velocity,which appears in a region close to the membrane surface and slightly downstream from the disturbers. AlargevelocitymaycauseasmallmassfractionasobservedinFig.7(b), (c)and(d)and further to a reduced concentration polarization as seen in Fig.6.This trend is also illustrated in Fig.5.Since the rectangular winglets have only a limited f l ow blocking effect,they cause only a moderateincreaseinf l uidvelocityandyieldamaximumvelocitysignificantly smaller than that by the traditional f l ow disturbers.

Table 2NaCl solution physical and transport properties

Fig.5.Longitudinal concentration polarization prof i les in an empty channel for various Reynolds numbers.

Fig.6.Evolutionsofconcentrationpolarizationalongchannellengthforchannelswithand without f l ow disturbers(Re=600).

Fig.7.Solute mass fraction contours at membrane surface for channels with and without f l ow disturbers(Re=600).

Fig.8.Fluid velocity contours at plane of z=0.75H for channels with various f l ow disturbers(Re=600).

Fig.9.Fluid velocity vector plot at cross-section of x/H=6 for channel with rectangular winglets(Re=600).

Fig.10.Fluid velocity contours at cross-sections of x/H=6,7,8 and 9 for channel with rectangular winglets(Re=600).

Fig.9 is a vector plot of f l uid velocityat a cross-section of x/H=6 for channel with the rectangular winglets for Re=600.The f i gure shows that each winglet produces one vortex,with the concave winglet pair generating two counter-rotating vortices that f l ow up to wash the membrane surface while the convex winglet pair generating two counter-rotatingvortices thatf l ow down to wash thesolid wall surface. The f l ow-up vortices thin the concentration boundary layer near the membranesurface,causinganenhancedmasstransferandconsequently a small mass fraction at the membrane surface as observed in Fig.7(e), whereas the f l ow-down vortices thicken the concentration boundary layer near the membrane surface,causing a reduced mass transfer and consequently a large mass fraction at the membrane surface as seen in the same f i gure.

Fig.10 depicts the evolution of f l uid velocity contours at a series of consecutive channel cross-sections of x/H=6,7,8 and 9 for channel equipped with the rectangular winglets for Re=600.The magnitude of the f l uid velocity,which is given by Eq.(14),ref l ects the strength of the secondary f l ow.The f i gure shows that the vortices can effectively move downstream,supporting the fact that the rectangular winglets are able to extend their concentration polarization suppressing effect to a space further away downstream from the position at which they are located, as seen in Fig.6.

Fig.11.Evolutions of pressure along channel length for channels with and without f l ow disturbers(Re=600).

Fig.11 illustrates the evolution of f l uid pressure(P)along the channel length for channels with and without f l ow disturbers for Re=600. Comparison of the channels equipped with different f l ow disturbers suggests that the triangular prism yields the maximum pressure drop while the rectangular winglets give the minimum pressure drop.This is consistent with Fig.8 result,which shows that the triangular prism yields the largest maximum velocity while the rectangular winglets give the smallest maximum velocity.

Fig.12 is a graph of the area-averaged concentration polarization factor(ГA)plotted against the consumed pumping power(E)for channels with and without f l ow disturbers.For each channel,there are four data points,which correspond to the cases of Re=400,600,800 and 1000,respectively.Fig.12 shows that for a given pumping power,the channels with the traditional f l ow disturbers yield the largest concentration polarization factor while that with the rectangular winglets give the smallest concentration polarization factor,with the empty channel providing an intermediate value.The results support that the rectangularwingletsaremuchmoreeffectiveinsuppressingconcentration polarization than the traditional f l ow disturbers.

Fig.12.Variations of area-averaged concentration polarization factor with pumping power for channels with and without f l ow disturbers(400≤Re≤1000).

Fig.13.Effects of winglet height on concentration polarization factor and pressure (Re=600).

Fig.14.Variations of area-averaged concentration polarization factor with pumping power for various winglet heights(400≤Re≤1000).

Fig.15.Effects of attack angle on concentration polarization factor and pressure (Re=600).

Fig.16.Variations of area-averaged concentration polarization factor with pumping power for various attack angles(400≤Re≤1000).

Fig.17.Effects of aspect ratio on concentration polarization factor and pressure (Re=600).

Fig.19.Effects of winglet interval on concentration polarization factor and pressure (Re=600).

3.2.Parametric optimization of rectangular winglets

Calculations were f i nally implemented to investigate the effects of the winglet geometry and arrangement on the winglet performance for the purpose of winglet optimization.As stated previously,there are four key parameters to def i ne the winglet geometry and arrangement,which include the winglet height h,the aspect ratio σ=l/h,the attack angle β,and the distance between two adjacent winglets W. The values taken for these parameters for typical rectangular winglets are h=H/2,σ=2.0,β=30°and W=1.5H,as presented in Table 1. Calculations were made with these data as a base.In each calculation, onlyoneparameterwasvariedwithotherparametersbeingunchanged. Also,the simulations used w0=0.2×10−3kg·kg−1,J=1.36× 10−5m·s−1and wp=3.7×10−5kg·kg−1.

Fig.13 shows the effects of the winglet height(h)on the concentration polarization and pressure drop characteristics for Re=600.As expected,when the winglet height is increased,the concentration polarization factor decreases while the pressure drop increases.Fig.14 depicts the variations of the area-averaged concentration polarizationfactor(ГA)with the consumed pumping power(E)for various winglet heights.For each height,there are four data points,which correspond to the cases of Re=400,600,800 and 1000,respectively.For a fi xed pumping power,comparison of the results for h=4H/6 and h=5H/6 shows that the former gives a slightly lower concentration polarization factorthanthelatter,suggestingthath=4H/6isthebestwingletheight.

Fig.15 shows the effects of the winglet attack angle(β)on the concentration polarization and pressure drop characteristics for Re= 600.As the attack angle increases,the concentration polarization factor decreases while the pressure drop increases.Fig.16 illustrates the variations of the area-averaged concentration polarization factor with the consumed pumping power for various attack angles.For a fi xed pumping power,the winglets having a 30°attack angle yields the smallest concentration polarization factor,suggesting that the best attack angle is β=30°.This can be explained as follows.When the angle is small,the increase of the angle is very effective in improving the concentration polarization,at the same time it causes only a moderate increase in the pressure drop;when the angle is large,however,further increase of the angle is not so effective in suppressing the concentration polarization,at the same time it causes a substantial increase in the pressure drop.As a result,the minimum concentration polarization factor takes place at β=30°.

Fig.17 shows the effects of the winglet aspect ratio(σ)on the concentration polarization and pressure drop characteristics for Re=600. Note that the winglet aspect ratio,which is de fi ned as the winglet length-to-height ratio,is varied,with the winglet surface area being kept unchanged in the calculations.Fig.17 shows that as the aspect ratio increases,the concentration polarization factor tends to decrease while the pressure drop increases.Fig.18 depicts the variations of the area-averaged concentration polarization factor with the consumed pumping power for various aspect ratios.The fi gure shows that for a fi xed pumping power,the winglets having aspect ratios of σ=2.0 and σ=2.8 provide almost the same concentration polarization factor, which is much lower than that generated by the winglet having an aspect ratio of σ=1.2.Since σ=2.0 is a typical value for the winglet aspect ratio,it is thus taken as the best aspect ratio.

Fig.19showstheeffectsofthedistancebetweentwoadjacentwinglets(W)on theconcentrationpolarization and pressure drop characteristicsforRe=600.The fi gureshowsthatwhenthewingletinterval(W) is reduced,the concentration polarization factor decreases while the pressure drop increases.Fig.20 illustrates the variations of the areaaveraged concentration polarization factor with the consumed pumping power for various winglet intervals.The fi gure shows that, for a f i xed pumping power,a winglet interval of W=1.5H yields the lowest concentration polarization factor,suggesting that the best interval is W=1.5H.

The summary of the above results supports that the optimal geometric parameters for the rectangular winglets are h=4H/6, β=30°,σ=2.0,and W=1.5H.As compared to the typical values listed in Table 1,the only difference is that the winglet height changes from h=3H/6 to h=4H/6.This change leads to a signif i cant reduction in the area-averaged concentration polarization factor under the equal pumping power condition,as shown in Fig.14.

Fig.20.Variations of area-averaged concentration polarization factor with pumping power for various winglet intervals(400≤Re≤1000).

4.Conclusions

Numerical calculations were carried out to simulate the solution fl owandsolutetransportinnarrowmembranechannelswithandwithout fl ow disturbers for reducingconcentration polarization under equal pumping power condition.The conclusions are as follows:

(1)The traditional f l ow disturbers including the square prism,triangular prism and circular cylinder can considerably reduce the concentration polarization factor but they simultaneously cause a substantially increased pressure drop,while the rectangular winglets can effectively reduce the concentration polarization factor with a much less pressure drop penalty.Under equal pumping power condition,the use of the traditional disturbers worsens the concentration polarization while the use of the rectangular winglets improves the concentration polarization.

(2)Two adjacent rectangular winglets that form a concave winglet pair generate two counter-rotating vortices f l owing up to wash the membrane surface,causing a thinned concentration boundary layer near the membrane surface and consequently a reduced concentration polarization factor,while two adjacent rectangular winglets that form a convex winglet pair generate two counter-rotating vortices f l owing down to wash the solid wall surface,leading to a thickened concentration boundary layer near the membrane surface and consequently an increased concentration polarization factor.

(3)Parametric optimization of the rectangular winglets under equal pumpingpowercondition suggests that the winglet heightis 2/3 of the channel height,the aspect ratio is 2.0,the attack angle is 30°,and the winglet interval is 3/2 of channel height.

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Jingchun Min*,1,Bingqiang Zhang21School of Aerospace,Tsinghua University,Beijing 100084,China2Beijing Key Laboratory of Space Thermal Control Technology,Beijing 100094,China

5 January 2014

☆SupportedbyTsinghuaUniversityInitiativeScientif i cResearchProgram (20131089319).

*Corresponding author.

E-mail address:minjc@tsinghua.edu.cn(J.C.Min).

http://dx.doi.org/10.1016/j.cjche.2014.09.004

1004-9541/©2014 The Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

Received in revised form 12 June 2014

Accepted 22 August 2014

Available online 6 September 2014