Contents lists available at SciVerse ScienceDirect
Desalination
j ourna l homepage: www.e lsev ie r .com/ locate /desa l
Effect of feed spacer arrangement on flow dynamics through spacer filled membranes
Asim Saeed, Rupa Vuthaluru, Yanwu Yang, Hari B. Vuthaluru ⁎School of Chemical and Petroleum Engineering, Curtin University, GPO Box 1987, Perth Western Australia 6845, Australia
Article history:Received 23 August 2011Accepted 27 September 2011Available online 26 October 2011
Keywords:CFDMembraneSpacersPressure dropShear stressPower number
Operational issues arising from scaling and fouling of membranes are addressed by pre-treatment processesand alternative membrane or membrane secondary structures. In the present work the flow patterns associ-ated with fluids within the membrane module are investigated using Computational Fluid Dynamics (CFD)tools. The effects on flow patterns through a spacer filled Reverse Osmosis (RO) membrane with the second-ary structure of the membranes (feed spacer filaments) at various angles with the inlet flow are analyzed. Thepresence of the feed spacers in membrane module appears to generate secondary flow patterns enhancingthe prospects for self induced backwashing increasing the allowable operational time and membrane effi-ciency. The flow visualization in the present study is useful in understanding the complex flow patterns gen-erated in spacer filled RO membrane modules and could possibly lead to developing a new RO membranewhich is more efficient, economical and appears to be a practically viable solution to reduce costs associatedwith the maintenance of RO membranes.
Reverse Osmosis operations are often confronted with challengesassociated with periodic maintenance of membranes due to signifi-cant material build-up on the surfaces. Operational issues arisingfrom scaling and fouling primarily include: increased membrane re-sistance, decreased permeate flow, increased energy requirementand decreased membrane life. These issues have been addressed byseveral researchers, in a limited way, by proposing better pre-treatment processes. However, there appears a need to change mem-brane or membrane secondary structures to alter the flow patternsassociated with fluids within the membrane module. To visualizeflow through RO membranes Computational Fluid Dynamics (CFD)tools have been used extensively by various researchers. Literaturereview reveals that CFD tools have been used quite accurately to pre-dict the flow behavior through RO membranes [1–4].
Spiral wound membrane module (SWM) is regarded as one of themost commonly used assemblies for water treatment usingmembrane separation processes. Fig. 1 represents a SWM in partlyunwounded state. In case of Spiral Wound Module (SWM) a numberof flat membrane sheets are glued together, in pair arrangement, onthree sides forming a pocket and a permeate spacer is introducedbetween the membranes pocket. The fourth open end of the mem-brane pocket is connected to a common permeate collector tube.The membrane pockets are rolled around the tube with feed spacersbetween each pocket [5,6]. As a result of the design alternating feed
haluru).
11 Published by Elsevier B.V. All rig
and permeate channels are developed. Feed enters through one sideof the module and is forced through the membrane. Retentate leavesthe module from the opposite side of the feed inlet, whereas perme-ate is collected in the common permeate tube.
The net spacer in the feed channel not only keep the membranelayers apart, thus providing passage for the flow, but also significantlyaffects the flow and concentration patterns in the feed channel.Spacers are not only responsible for the pressure drop and limitedflow zones (dead zones) creation but also promote mixing betweenthe fluid bulk and fluid elements adjacent to the membrane surface.In other words they are intended to keep the membranes clean by en-hancing mass transfer and disrupting the solute concentrationboundary layer. In the past several experimental and theoretical stud-ies were carried out to shed light on these phenomena and to opti-mize spacer configuration [7–12]. So it is quite understandable thatthe presence of these spacers promote directional changes in theflow which reduces membrane fouling and concentration polariza-tion. Hence the efficiency of a membrane module depends heavilyon the efficacy of the spacers to increase mass transport away fromthe membrane surface into the bulk fluid by increasing shear rate atthe membrane surface [13].
Spiral wound membranes have tightly wrapped structures whichcannot be opened easily for chemical cleaning or cannot be backflushed by operating in reverse direction. For these reasons, the foul-ing control methods for SWM are limited to hydrodynamics, pretreat-ment of the feed and operational controls [15]. The fouling issues canbe addressed to a large extent by varying the hydrodynamic condi-tions prevailing in spiral wound membrane. The feed spacers can beoriented to generate high cross flow velocities or secondary flow pat-terns which can develop higher scouring forces on the membrane
Fig. 1. Schematic diagram of SWM in partly unwound state, adapted from [14].
164 A. Saeed et al. / Desalination 285 (2012) 163–169
surface to reduce fouling and concentration polarization. However,this approach will need higher pumping energy to compensate losseswithin the membrane module. Hence the feed spacers must be opti-mized to reduce the buildup on the membrane surface with moderateenergy loss.
Literature review to date reveals that for the same type of spacers,spacer-filled flat channels and SWM channels show similar flow char-acteristics [16,17]. Studies of Ranade and Kumar [18] in another studyconcluded that the transition from laminar to turbulent flow regimefor most of the spacer-filled channels occurs at Reynolds numbers of300–400 (based on hydraulic diameter) for packed beds. In the pre-sent study we have used laminar flow model as channel's Reynoldsnumber (Rech) which was kept between 100 and 125 for all thecases. In the present work, an attempt has been made to study the ef-fect on flow patterns through a spacer filled RO membrane when thesecondary structures of the membranes (feed spacer filaments) areset at various angles with the inlet flow. Three cases were analyzedto investigate the effect of feed spacer orientation, with respect tothe inlet flow, on wall shear stress, pressure drop and power number.
2. CFD simulation
2.1. Geometric parameters for spacers
Geometry of spacers used in SWM can be characterized with thehelp of some important parameters shown in Fig. 2. In the figure db
and dt represent diameters of bottom and top filaments, whereas lb
Fig. 2. Geometric characterization of spacer.
and lt represents the mesh size of bottom and top filaments respec-tively. The flow attack angles that top and bottom filament makeswith the y-axis are represented by θ1 and θ2 respectively. Whereasα is angle between the top and bottom crossing filaments. It is evi-dent from the geometry description that the available channel heighthch is sum of the filaments diameters in top and bottom layers. In thecurrent study we have considered symmetric spacers having same di-ameter and mesh size for both top and bottom filaments, i.e.d=db=dt and l=lb=lt. Spacer parameters are non-dimensionalizedby using channel height (hch). The ratio of filament diameter to thechannel height (D=d/hch) is set at 0.5 whereas for filament meshsize to the channel height (L=l/hch) is kept at 3.6. Angle betweenthe top and bottom filaments (α) was kept at 90° for the first twocases and 45° for the third case study.
Computational domain comprising of six bottom and four top fila-ments was created using bottom up approach in Gambit®. Booleanoperations (unite, subtract and intersect) and split functions wereused extensively for that purpose. The geometry was further decom-posed into several volumes to have a structured mesh. Fig. 3 showsthe diamond spacers arrangement in which the orientation of thebottom filament is transverse to the flow direction, whereas the topfilaments are in axial direction to the flow hence making the flow at-tack angle (with Y-axis of flow direction) for the top and bottom fila-ments to be 90° and 0° respectively.
2.2. Modelling procedure and assumptions
For all the cases Rech was kept below the defined range of chan-nel's critical Reynolds number for spacer filled channels to enablelaminar flow model to simulate flow through the computational do-main. Water is used as working fluid having constant density(998.2 kg/m3), viscosity (0.001 kg/(ms)) and solute diffusivity(1.54×10−9 m2/s). The filament surfaces are defined as walls. Sincefor most of the membrane processes the feed velocity is 3–4 timeshigher than the permeation velocity, the membrane walls are as-sumed to be impermeable walls with no-slip conditions [19,20]. Fur-thermore, translational periodic boundary condition was defined forthe two vertical surfaces parallel to top filaments. Due to low perme-ation rate through the membranes the variation of local concentra-tion along the flow direction is neglected and hence top and bottommembrane walls are set to be at higher fixed values of concentrationthan at the inlet [20].
QUICK ( Quadratic Upstream Interpolation for convective Kinetics)scheme is used for discretizing momentum equations, whereas SIM-PLEC (Semi-Implicit Method for Pressure linked Equations, Consis-tent) algorithm is used for pressure velocity coupling [20,21].
In the present study channel's Reynolds number defined earlier bySchock and Miquel [17] is used and presented in Eq. (1).
165A. Saeed et al. / Desalination 285 (2012) 163–169
In the equation dh represents the hydraulic diameter of the chan-nel and defined by the following equation for a spacer-filled channeldh
dh ¼ 4�2
hchþ 1−�ð ÞSv;sp
ð2Þ
Where hch is the channel height, � is the porosity of the spacerrepresented by Eq. (3) and Sv;sp represents specific surface of the ofthe spacer represented by Eq. (4)
� ¼ 1−Spacer volumeTotal volume
ð3Þ
Sv;sp ¼ Wetted surface of pacerVolume of pacer
: ð4Þ
In membrane systems, cost associated with pumping the fluid isone of the most important factors. Power number, which relates re-sistance force to inertia force, is evaluated to compare the results ofthe present study with the data available in literature. Earlier Li etal. [4] defined dimensionless power number (Pn) to compare energyconsumption of different spacer, used later by Skakaib et al. [19] intheir study. The same definition is used for the present study andrepresented by the following equation:
Pn ¼ SPCρ2h4
ch
μ3
!ð5Þ
where SPC is the specific power consumption and is given by thefollowing relation
SPC ¼ uavΔPLc
: ð6Þ
In the above expressions, Lc and ΔP are the channel length andpressure drop over the channel respectively, whereas uav, μ and ρare the average velocity, dynamic viscosity and density respectively.Dimensionless pressure drop is calculated by using the following rela-tion and the results are compared to those published by Koutsou et al.[22] and Skakaib et al. [19].
ΔP� ¼ ΔPLc
d3
Re2cylρν
2
!ð7Þ
3. Results and discussion
Three case studies were carried out to investigate the effect of feedspacer orientation (with respect to the inlet flow) on shear stress,power number and pressure drop by changing the flow attack angles(θ1 and θ2) and angle between the crossing filaments (α). The results
Table 1Comparison of average shear stresses on walls and pressure drop at Rech=100 withavailable data [4,19].
Parameters a Shakaibet al. [19]
b Li et al.[4]
Presentstudy
Average Shear stress on top wall (N/m2) 1 – 1.15Shear stress on bottom wall (N/m2) 0.16 – 0.20Pressure drop*10−3 (Pa/m) 5 – 6.29Power number *10−5 – 1.7 1.80Dimensionless pressure drop – – 0.32
a Interpolated value from the plot between filament spacing vs avg shear stress onwalls and linear pressure drop.
b Values reported for L=4.
of first two case studies and comparison with previous studies arepresented in Tables 1 and 2.
In the third case study angle between the crossing filaments wasset to 45° and the flow attack angles θ1and θ2 were set as 135° and0° respectively. The results are shown in Table 3. To the best ofauthors knowledge, flow through such configuration has never beeninvestigated in previous studies and no results are available in theliterature apart from the outcomes of current work.
In the first case study the orientation of the top and bottom filamentwith the flow direction was set in such a manner that top filamentswere in axial directionwhereas the bottomfilamentswere in transversedirection, that is θ1=90°and θ2=0°.
Variation in shear stress values on bottom and top membrane wallalong the flow direction are shown in Fig. 4. a and b respectively.Since the shear stress distribution is mainly dependent on the veloc-ity field, so for the bottom membrane wall it is zero near the bottomfilaments and reaches a maximum values close to the center of thetwo consecutive bottom filaments along the flow direction. Whenthe fluid flows through narrow space above the bottom filaments itis accelerated and hence the peak value for shear stress on the topmembrane is observed just above the bottom filaments and it reachesits lowest value at the center of the two consecutive bottomfilaments.
In the present work the dimensionless filament spacing (L) wasset to 3.6. The shear stress distribution on walls can be explained byFig. 7. which represents velocity vectors on a plane in the vicinity ofbottom wall. Two distinct flow regions are prominent near the bot-tom wall. In the first region, extending from the center of the twoconsecutive transverse filaments to the next bottom filament in thenormal flow direction, flow appears to reattach to the bottom surfaceand accelerates in the normal flow direction in a diverging manner.Whereas in the second region which extends from the center tonext transverse filament (in opposite flow direction) the flow tendsto reverse and recirculate.
Similar flow behavior and shear stress distribution has beenreported by Shakaib et al. [20] in their study. Their computational do-main comprised of six bottom and one top filaments. Their study re-flects the effect of dimensionless filament spacing on velocity,pressure and shear stress. However, they carried out the simulationsat integer values (L=2, 3, 4 and 6) for the dimensionless filamentspacing and reported that there is considerable change in fluid flowbehavior when the spacing is changed from 3 to 4, especially for thebottom filaments as they are present in transverse direction to thenormal flow. According to their study when L is set to 3 for the trans-verse filaments the portion of the flow striking the bottom filamentshows complete recirculation without flow reattachment. But whenthe spacing is increased to 4 two distinct regions (flow reattachmentand recirculation) appear near the bottom wall.
Shear stress distribution in Fig. 4. a and b indicates that the shearstress values at the membrane walls are not equal for the first few fil-aments but then tend to become equal for succeeding filaments re-vealing the signature of fully developed and periodic flow. Similar
Table 2Comparison of current and previous studies at flow attack angle of 45° and Rech=100.
aShakaibet al. [19]
bKoutsouet al. [22]
bLi et al.[4]
Presentwork
Average shear stress on walls (pa) 0.70 – – 0.69Pressure drop×10−3 (pa/m) 5.20 – – 6.46Dimensionless pressure drop 0.32 0.35 – 0.33Power Number×10−5 2.60 2.0 2.40 1.91
a Interpolated value from the plot between filament spacing vs avg shear stress,linear pressure drop, dimensionless pressure drop at θ1=θ2 45°.
b Values reported at L=4.
Table 3Shear stress, pressure drop, dimensionless pressure drop and power number atflow attack angle θ1=135° and θ2=0° at Rech=100.
Average shear stress on top wall (pa) 0.9Average shear stress on bottom wall (pa) 0.7Pressure drop×10−3 (pa/m) 11.84Dimensionless pressure drop 0.605Power Number×10−5 3.36
Fig. 5. X-Velocity contours.
166 A. Saeed et al. / Desalination 285 (2012) 163–169
results were reported by Yuan et al. [23] in their research work andshowed that the flow and heat transfer in channels with periodiccross-section becomes periodic and fully-developed after few cells.Later Li at al [24] validated its use for non-woven net spacers. Our re-sults are also in fair accordance with their findings as can be seenfrom the shear stress distribution trends. Furthermore profiles ob-served in the current study for shear stress are found to be similarto previous two-dimensional CFD studies by Cao et al. [25] and thethree-dimensional CFD studies by Shakaib et al [20].
Fig. 5 represents the x-velocity contours of the fluid flowingthrough the membrane. It is quite evident from the figure that thefluid is accelerated at the narrow space available above the transversefilament. Moreover, it also shows the areas behind the bottom fila-ments where the velocity is opposite to the normal flow direction(negative values) which essentially means the flow reversal andrecirculation. It is also evident that a portion of the fluid after strikingthe bottom filaments changes its direction and tends to accelerate inthe direction opposite to that of the normal flow and reaches a max-imum negative velocity (direction opposite to normal flow) some-where in the middle of the two consecutive transverse filaments. Asa result of this flow pattern the highest local negative shear stressvalues at the bottom wall towards the central portion of the two con-secutive transverse filaments can be seen in Fig. 6. Two distinct
Fig. 4. Shear stress distribution on bottom (a) and top (b) wall (Note: Vertical linesindicate center lines of bottom filaments).
regions of high positive shear stress are also apparent just beforethe transverse filaments and in the vicinity of the crossing of trans-verse and axial filaments. Development of those regions can beexplained by Fig. 7. representing the velocity vectors on a plane justabove the bottom membrane at 0.05 hch. The flow is seen to be accel-erated in normal flow direction in a diverging manner thus explainingthe generation of those distinct zones of higher positive shear stress.In addition to that, another region of peak negative shear stress is alsoevident just beneath the axial filament. Since it is evident from Fig. 5that the fluid is accelerated as a result of narrow space availabilityover the bottom filaments and consequently results in shear stresspeaks on the top wall above bottom transverse filaments as shownin Fig. 8.
From the literature review [19,20] it is quite evident that majorportion of the fluid flows in main flow direction (x-direction) incase of spacer filled SWM. However, the presence of net spacersgives rise to strong three-dimensional effects. Two separate zonesare defined near the top wall where the flow patterns are influencedby the presence of axial filament. Flow tends to shift towards the topfilament in the vicinity of top and bottom filament intersection andgets diverted away from the top filament somewhere in the middleof two consecutive transverse filaments. The two distinct zones,namely, flow attachment and separation are quite evident in Figs. 9and 10. Fig. 9 represents the velocity vectors at top wall showingthe two distinct zones, whereas Fig. 10 represents the contours of ve-locity over-layed by the velocity magnitude at a plane surface veryclose to the top wall. Since it is reported in literature that for largetransverse filament dimensionless spacing (L=4), high fluid velocity
167A. Saeed et al. / Desalination 285 (2012) 163–169
and shear stress is observed near the top wall right above the trans-verse filament and the values decrease considerably near the centerof two consecutive transverse filaments. All flow patterns, shearstress and velocity distribution represented in this study are in fair ac-cordance with results available in literature [19,20].
Fig. 11 (a and b) represents different views of path lines of velocityreleasing from the inlet. The figure shows the bottom view of the flowdomain. It can be clearly seen from the figure that flow tends to recir-culate in the region near the vicinity of the bottom membrane in thedirection opposite to that of the normal flow and tends to reattach tothe bottom surface somewhere in the middle. However the severityof recirculation dampens along flow direction. Fig. 11 c representsthe top view of the domain where the flow tends to move towardsthe top filament at the intersection of the two filaments (flow reat-tachment) and shifts away from the top filament as it moves aheadin the normal flow direction (flow separation). Our study further re-veals that for this type of spacer (L=3.6, D=0.5, θ1=90°, θ2=0°,Rech=125) the average value of shear stress on top wall is nearly 5times high than that at the bottom wall. The ratio was further crosschecked by making a very finely meshed geometry comprising of 6bottom and one top filaments. Boundary conditions were kept exactlythe same and the ratio obtained was 5.02, indicating an error lessthan 0.5%. The average shear stress value for the top and bottomwalls were respectively 1.8 and 0.32 N/m2. To compare our valueswith those reported in literature [4,19], simulation was carried out
Fig. 8. X-Shear stress contours on top wall.
at Rech=100. Table 1 shows the comparison of the results neglectingthe entrance and exit effects. Our reported values are in fair agree-ment with the reported ones.
In the second case study the filaments were oriented at an anglewith the inlet flow instead of being axial or transverse. Flow attackangles that top and bottom filament makes with y-axis and repre-sented by θ1 and θ2 in Fig. 2 were set to 45°. However the ratio offilament diameter to the channel height (D=d/hch) was kept 0.5and that for filament mesh size to the channel height (L=l/hch)was also kept 3.6. However, channel Reynolds number was set to100 to compare our results with already available in literature[4,19,22]. Numerically obtained pressure drop value in the study isfurther used to calculate Power number defined by Eq. (5) anddimensionless pressure drop defined by Eq. (7). The results of thestudy show reasonable agreement with those available in literatureand are reported in Table 2.
In the third case study the angle between the top and bottom fil-aments (α) was changed to 45° and the flow attack angles θ1 and θ2were set 135° and 0° respectively. In this case the bottom filamentsare again in transverse direction however the top filaments are in-clined towards the channel axis. It should be noted that flow throughsuch configuration has never been investigated in previous studiesand no results are available in literature.
Fig. 11. Pathlines of Velocity realizing from the inlet (a) and (b) bottom view, (c) top view.
168 A. Saeed et al. / Desalination 285 (2012) 163–169
Fig. 12 a represents the contours of velocity at plane close to thebottom membrane, whereas Fig. 12 b represents the contours of ve-locity at a plane close to the top membrane. It is evident fromFig. 12 a that the fluid tends to accelerate at the narrow space avail-able below the top filament in the vicinity of the bottom wall,where as the fluid velocity in the vicinity of the top membrane is onhigher side above the bottom filaments.
The values for average shear stress on top and bottom wall,pressure drop and Power number are listed in Table 3.
Pressure drop in spacer filled modules depends on the resistanceoffered by the filaments to flow, which in turn depends on the flowattack angles. Pressure drop will be at the higher side when theflow will hit more filaments in an upright fashion. It can be seenthat when the flow attack angle θ1and θ2 were set at 90° and 0° re-spectively the bottom filaments were perpendicular to the flow direc-tion providing maximum resistance to flow where as the topfilaments were along the flow direction and hence provide quiteless resistance. When the flow attack angles θ1and θ2 was set to 45degree the bottom filaments were moved outwards the channel axis( providing less resistance than the previous case) and the top fila-ments were moved inwards to the channel axis (hence providing
more resistance as compared to the previous case). As a result pres-sure drop for the two filament arrangements do not differ to a largeextent. However when the flow attack angle θ1and θ2 was set to135° and 0° degree, the bottom filaments are in perpendicular direc-tion to the flow where as the top filaments were moved further in-wards to the channel axis and hence providing maximum pressuredrop and maximum power number for the arrangement.
4. Conclusion
In the present work, an attempt has been made to study the effecton flow patterns through a spacer filled RO membrane when thesecondary structures of the membranes (feed spacer filaments) areset at various angles with the inlet flow. Due to the presence of feedspacers secondary flow patterns are developed in spacer filled mem-brane modules and can be helpful for self sustaining backwashing andhence increasing membrane efficiency. Post processing revealed thatthe alignment of the feed spacers with the flow direction have greatinfluence on the generation of secondary flow patterns through thespacer filled channels. Optimization of the feed spacers orientationcan lead to desirable flow patterns generation within the membranemodule eventually leading to enhanced membrane performance.
Shear stress values were found to be not equal for the first fewfilaments but tend to become equal for the succeeding filaments(after 2–3 filaments) in flow direction revealing the signature offully developed and periodic flows. Spacer having filaments orientedin transverse and axial direction (θ1=90°, θ2=0°) induce highshear stress on the top wall than on the bottom wall. The nature offlow is of more complex nature in the vicinity of bottom wall wheretwo distinct zones (flow reversal and reattachment) are apparent.However near the top membrane flow tends to shift towards thetop filament at the vicinity of top and bottom filament intersectionand divert away from the top filament as it progress in the normalflow direction somewhere in the middle of transverse filaments.
Pressure drop in spacer filled SWM appears to depend largely onthe filament orientation based on current investigations. Pressuredrop and power number will be higher if the filaments are inclinedmore towards the channel axis. Pressure drop and power numberfor the first two cases did not differ significantly, whereas in thethird case study the bottom filaments are perpendicular to the flowdirection and the top filaments were further moved inwards to the
169A. Saeed et al. / Desalination 285 (2012) 163–169
channel axis resulting in maximum pressure drop and powernumber.
Flow visualizations carried out in the current study appears to bevery valuable in understanding the complex flow patterns generatedin spacer filled RO membrane modules which could potentially leadto the development of efficient membrane modules with optimumspacer arrangements.
Nomenclatured filament thickness (m)db bottom filament thickness (m)hch channel height (m)dh hydraulic diameter (m)dt top filament thickness (m)D dimensionless filament thicknesslb bottom filament spacing (m)lt top filament spacing (m)L dimensionless filament spacingLc channel length (m)Pn Power numberΔP pressure drop (Pa)ΔP* dimensionless pressure dropRech channel Reynolds numberRecyl cylinder Reynolds numberSPC specific power consumption (Pa/s)uav average velocity
Greek lettersα angle between the crossing filamentsθ1 angle between top filament and y-axis (flow attack angle)θ2 angle between bottom filament and y-axis (flow attack
angle)μ dynamic viscosity (Pa s)υ kinematic viscosity (m2/s)ρ density (kg/m3)
References
[1] R. Ghidossi, D. Veyret, P. Moulin, Computational fluid dynamics applied tomembranes:State of the art and opportunities, Chem. Eng. Process. 45 (2006) 437–454.
[2] S.K. Karode, A. Kumar, Flow visualization through spacer filled channels bycomputational fluid dynamics I.: Pressure drop and shear rate calculations forflat sheet geometry, J. Membr. Sci. 193 (2001) 69–84.
[3] K.K. Lau, M.Z. Abu Bakar, A.L. Ahmad, T. Murugesan, Feed spacer mesh angle: 3Dmodeling, simulation and optimization based on unsteady hydrodynamic inspiral wound membrane channel, J. Membr. Sci. 343 (2009) 16–33.
[4] F. Li, W. Meindersma, A.B. de Haan, T. Reith, Experimental validation of CFD masstransfer simulations in flat channels with non-woven net spacers, J. Membr. Sci.232 (2004) 19–30.
[5] C. Fritzmann, J. Lowenberg, T. Wintgens, T. Melin, State-of-the-art of reverseosmosis desalination, Desalination 216 (2007) 1–76.
[6] T. Peters, Membrane technology for water treatment, Chem. Eng. Technol. 33(2010) 1233–1240.
[7] J. Fárková, The pressure drop in membrane module with spacers, J. Membr. Sci. 64(1991) 103–111.
[8] V. Geraldes, V. Semião, M.N. de Pinho, Flow management in nanofiltration spiralwound modules with ladder-type spacers, J. Membr. Sci. 203 (2002) 87–102.
[9] V. Geraldes, V. Semião, M.N. de Pinho, The effect of the ladder-type spacersconfiguration in NF spiral-wound modules on the concentration boundary layersdisruption, Desalination 146 (2002) 187–194.
[10] V. Geraldes, V. Semião, M. Norberta Pinho, Hydrodynamics and concentrationpolarization in NF/RO spiral-woundmoduleswith ladder-type spacers, Desalination157 (2003) 395–402.
[11] C.C. Zimmerer, V. Kottke, Effects of spacer geometry on pressure drop, masstransfer, mixing behavior, and residence time distribution, Desalination 104(1996) 129–134.
[12] S.G. Chatterjee, G. Belfort, Fluid flow in an idealized spiral wound membranemodule, J. Membr. Sci. 28 (1986) 191–208.
[14] Y.-L. Li, K.-L. Tung, CFD simulation of fluid flow through spacer-filled membranemodule: selecting suitable cell types for periodic boundary conditions, Desalina-tion 233 (2008) 351–358.
[15] A. Fane, P. Beatson, H. Li, Membrane fouling and its control in environmentalapplications, Water Sci. Technol. (2000) 303–308.
[16] V.V. Ranade, A. Kumar, Comparison of flow structures in spacer-filled flat andannular channels, Desalination 191 (2006) 236–244.
[17] G. Schock, A. Miquel, Mass transfer and pressure loss in spiral wound modules,Desalination 64 (1987) 339–352.
[18] V.V. Ranade, A. Kumar, Fluid dynamics of spacer filled rectangular and curvilinearchannels, J. Membr. Sci. 271 (2006) 1–15.
[19] M. Shakaib, S.M.F. Hasani, M. Mahmood, Study on the effects of spacer geometryin membrane feed channels using three-dimensional computational flow model-ing, J. Membr. Sci. 297 (2007) 74–89.
[20] M. Shakaib, S.M.F. Hasani, M. Mahmood, CFD modeling for flow and mass transferin spacer-obstructed membrane feed channels, J. Membr. Sci. 326 (2009)270–284.
[21] F. I. Fluent V 6.3 User's Guide, , 2006.[22] C.P. Koutsou, S.G. Yiantsios, A.J. Karabelas, Direct numerical simulation of flow in
spacer-filled channels: Effect of spacer geometrical characteristics, J. Membr. Sci.291 (2007) 53–69.
[23] Z.-X. Yuan, W.-Q. Tao, Q.-W. Wang, Numerical prediction for laminar forcedconvection heat transfer in parallel-plate channels with streamwise-periodicrod disturbances, Int. J. Numer. Methods Fluids 28 (1998) 1371–1387.
[24] F. Li, W. Meindersma, A.B. de Haan, T. Reith, Optimization of commercial netspacers in spiral wound membrane modules, J. Membr. Sci. 208 (2002) 289–302.
[25] Z. Cao, D.E. Wiley, A.G. Fane, CFD simulations of net-type turbulence promoters ina narrow channel, J. Membr. Sci. 185 (2001) 157–176.
