Desalination 284 (2012) 332–340

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Desalination

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A CFD study on the effect of spacer orientation on temperature polarization inmembrane distillation modules

M. Shakaib a,c,⁎, S.M.F. Hasani b, Iqbal Ahmed a, Rosli M. Yunus a

a Faculty of Chemical and Natural Resources Engineering, University Malaysia Pahang, Kuantan, Malaysiab Department of Mechanical Engineering, Al-Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabiac Department of Mechanical Engineering, NED University of Engineering and Technology, Karachi, Pakistan

⁎ Corresponding author at: Faculty of Chemical and NUniversity Malaysia Pahang, Kuantan, Malaysia. Tel.: +

E-mail addresses: shakaib@ump.edu.my, mshakaib@

0011-9164/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.desal.2011.09.020

a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 June 2011Received in revised form 16 August 2011Accepted 6 September 2011Available online 5 October 2011

Keywords:Computational fluid dynamicsTemperature polarizationMembrane distillationSpacer

Computational fluid dynamics (CFD) study in this work examines the effect of spacer orientation, inlet veloc-ity and filament spacing on shear stress distribution and temperature polarization in membrane distillationmodules. The CFD simulations show that spacer orientation affects the temperature polarization and heattransfer rates. If spacer filaments touch the top or bottom surfaces of membrane, the temperature polariza-tion is high which results in low heat transfer rates. When these filaments are detached from the membrane,temperature polarization is lower. The shear stress is also found to be higher and local values of temperaturepolarization index and shear stress are more uniformly distributed in the detached mode making this partic-ular orientation more favorable for use in membrane distillation modules.

atural Resources Engineering,60 9 5492871.live.com (M. Shakaib).

rights reserved.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Membrane distillation is a process that involves temperature gra-dient as the driving force for separation and treatment of fluids. Thisprocess includes a membrane with hot fluid on one side of membraneand cold fluid on the other. The membrane is of hydrophobic naturewhich restricts the water permeation through membrane pores. Afraction of hot fluid initially evaporates within the membrane dueto temperature (or vapor pressure) difference and then condensesto enter the permeate channel. The advantage of membrane distilla-tion (MD) over other membrane processes is that its performance isless sensitive to feed concentration. Further, the MD system is operat-ed at low temperatures and operating pressures and its membranesare more resistant to fouling [1–3].

A phenomenon that reduces the vapor permeation and affects theMD process efficiency is temperature polarization. Temperaturepolarization means that the temperature difference across themembrane surfaces is lower than the difference of the bulk fluidstream temperatures [4]. In MD modules net-type spacers of thetype shown in Fig. 1 are commonly used in feed and permeate flowchannels. The main advantage of spacer is that it disrupts the concen-tration and thermal boundary layers which help in increasing thepermeation rates. The disadvantage, on the other hand is that it alsocreates stagnant zones in the channel. The presence of these stagnant

zones in the membrane channel increases temperature polarizationand decreases the driving force for permeation. The spacer orienta-tion and dimensions are crucial parameters that affect the size and lo-cation of these stagnation regions.

Very few studies exist in the literature that examines the effect ofspacer on the MD module performance. Martínez et al. [4–6]investigated the effect of screen separator (or spacer) and showedthat spacer causes turbulence in membrane channel which reducestemperature polarization. In another paper [7] the same authorscompared temperature and concentration polarization in membranedistillation by using aqueous sodium chloride solution as feed fluid.The effect of temperature polarization was noticed to be moresignificant than concentration polarization on permeate flux reduction.Various other studies compared the spacer-filled channel with emptychannel and reported significant increase in heat transfer coefficientand product flux due to spacers [8–10]. In addition to the experimentalstudies, some CFD studies [11–13] also confirmed that heat transfer canbe augmented by using a spacer in the membrane channels and byincreasing the feed flow rate. Numerous papers included fluid flowand mass transfer analysis in spacer-filled membrane channels[14–18]. These studies were however, focused on spiral woundmodules for ultrafiltration or reverse osmosis processes and heattransfer rates were not determined. The literature review indicatedthat none of the papers investigated the effect of spacer orientation/arrangement in the feed and product channels of MD module which isan important parameter. In the present work, we have hence analyzedthe effect of this parameter on temperature polarization and heat trans-fer rate.

Fig. 1. Spacer-filled membrane distillation channels.

Fig. 2. Nomenclature of spacer orientations considered in this work.

333M. Shakaib et al. / Desalination 284 (2012) 332–340

2. Modeling procedure

The spacer-filled channel contains a large number of cells, howev-er the flow becomes fully developed (of repetitive nature) after pass-ing through the first few cells. It is therefore, practical and convenientto restrict the computational flow and heat transfer analysis to only afew filaments in the fully developed flow region. Hence, for CFDmodeling, the chosen computational domain has an overall channellength of 38 mm. The distance between first and last filament is18 mm, multiple filaments are placed in between the first and last fil-aments. The height of both the feed and the permeate channels is1 mm and the membrane thickness is 0.2 mm. A number of spacerorientations/arrangements are tested; four basic types are given inTable 1. The filaments in the feed and the permeate channels areeither in-line or staggered. This leads to three further orientationtypes as shown in Fig. 2. Two different values of 3 and 4.5 mm for fil-ament spacing/mesh length lm are considered in this work. The no-menclature used for different arrangements in this paper alsoincludes 3 or 45 to indicate the spacing (for example: AI3 means in-line type A spacer with a spacing of 3 mm or BI45 means in-linetype B spacer with a spacing of 4.5 mm).

The flow direction is of counter-flow type for all simulations asshown in Fig. 1. The temperature of hot fluid is 57 °C whereas thecold fluid temperature is set to 27 °C. The fluid is water having con-stant density and thermal conductivity but viscosity varies with tem-perature. The typical permeate fluxes in membrane distillation couldbe as high as 75 kg/m2 h [1]. This leads to a permeation velocity ofonly 2×10−5 m/s that is about 3–4 orders of magnitude smallerthan the feed velocity. For such permeation rates, the velocity profilesremain unaffected in the cross flow channel [18]. The membrane istherefore assumed to be impermeable and no flow connection existsbetween two parallel channels. A constant thermal conductivity of0.2 W/m K is set for the membrane material. The velocity is specifiedat the inlet of the feed and the permeate channels (vh and vp respec-tively) and is varied from 0.05 to 0.35 m/s which corresponds to aReynolds number Re range of 115–800. The computational domainis divided into around 45,000 cells as illustrated in Fig. 3 which is

Table 1Spacer orientations considered in this work.

Orientationtype

Description

A Filaments are in the lower portion of feed and permeate channels.B Filaments in feed channel are in the lower while in permeate

channel are in the upper portion. This means that filaments touchthe membrane surface in both channels.

C Filaments in feed channel are in the upper whereas in permeatechannel they are in the lower portion of the channel. The filamentshence are separated or detached from the membrane.

D Spacer is in feed channel only with filaments in the upper portion ofthe channel and the permeate channel is empty.

found to yield a grid independent solution. The governing equationsare the continuity, the momentum and the energy equations; conver-gence criterion is set to 1×10−6 for residuals of continuity, velocity

Fig. 3. Computational grid for CFD simulations (Type CI).

334 M. Shakaib et al. / Desalination 284 (2012) 332–340

components and energy equation. The flow in spacer-filledmembrane channel is fully laminar and free from instabilities at lowReynolds numbers. When the Reynolds number is high, that exceedsa certain critical value, the flow becomes transient and time-dependent. The critical value for this time-dependent flow is between200 and 800 depending upon the filament spacing and thickness [17].It is well known that for solving the transient flows, the direct methodof solving the Navier Stokes equations or Direct Numerical Simula-tions (DNS) is a suitable approach. However, the drawback of this ap-proach is significantly large computational time. The alternativemethod is to use Reynolds-averaging approach which includes trans-port equations for the mean flow quantities without direct simulationof turbulent/flow fluctuations. The additional fluctuation terms in thegoverning equations are determined through a turbulence model. Forthe simulations in the present work, it is noticed that if velocity is lessthan (or equal to) 0.15 m/s (Re≈350) the solution converges withoutthe need of any turbulence model showing that flow is laminar. Whenthe inlet velocity is higher than 0.15 m/s, the solution diverges whenlaminar model is selected indicating that flow is unsteady.

There are several turbulence models that are used for complexflow problems. The Spalart–Allmaras (SA) model is used here inwhich additional transport equation for turbulent viscosity is solved.Previous CFD study by the present authors [19] for obstructed narrowchannels has shown qualitative and quantitative agreement of SAmodel with DNS in terms of velocity contours and pressure drops. An-other CFD study [20] showed good agreement of reattachmentlengths predicted by this model with the ones obtained experimen-tally as well as using DNS approach. Further, the trials using other tur-bulence models showed that results of SA model are similar to resultsobtained using two-equation model k-ω (SST). In addition, lesscomputational time is needed with Spalart Allmaras model whencompared to two-equation models and convergence is achievedwithin 2500 iterations for the cases considered in this paper.

The governing equations are solved using the CFD code FLUENT6.3. For discretization of momentum equations, a higher orderscheme QUICK (Quadratic Upstream Interpolation for ConvectionKinetics) whereas a relatively simple Power law scheme is usedfor energy and turbulence equations. This selection is based onsome preliminary results that showed negligible difference if thePower law is chosen instead of QUICK for energy and turbulenceequations. This will be discussed in more detail in Results anddiscussions section. However, for momentum equations, the differ-ence is relatively higher if Power law is used. Pressure–velocitycoupling is made through SIMPLE (Semi-Implicit Method forPressure Linked Equations) algorithm.

The spacer performance is evaluated in terms of temperaturepolarization index ϕ. The definition used in this paper is:

ϕ ¼ Th−TcThm−Tcm

: ð1Þ

In Eq. (1) Th and Tc are inlet temperatures in hot and cold channelsrespectively whereas Thm and Tcm are the temperatures at themembrane wall on hot (top) and cold (bottom) sides respectively. Alower value of ϕ is desirable. The present CFD results are comparedwith experimental correlation (Eq. (2)) available in literature forheat transfer in spacer-filled channel [10]. This correlation is given as:

Nu ¼ α 4:36þ 0:036RePr dh=Lð Þ1þ 0:0011 RePr dh=Lð Þð Þ0:8

" #ð2Þ

where

α ¼ 1:88dfhch

� �−0:039

sinθð Þ1:33x exp �4:05 lnεεm

� �� �2� �� �:

In Eq. (2) dh is hydraulic diameter, L is channel length, df isfilament diameter, hch is channel height, θ is flow attack angle, ε isvoidage of feed or permeate channel and εm is voidage of membrane.The Reynolds number Re, Prandtl number Pr and Nusselt number Nuare defined as:

Re ¼ ρvdhμ

ð3Þ

Nu ¼ hdhk

ð4Þ

where

h ¼ qwTh−Thm

or

h ¼ qwTcm−Tc

ð5Þ

Pr ¼ μCp

k: ð6Þ

In Eqs. (3–6), qw is heat flux, ρ is density, μ is viscosity, k is thermalconductivity, Cp is specific heat and h is heat transfer coefficient.

3. Results and discussions

The effect of various spacer orientations on velocity and tempera-ture profiles is shown in Fig. 4. These profiles cover the regionbetween three filaments labeled as 0, 1 and 2. In the top channel,hot feed flows from left to right while in the bottom channel, coldpermeate flows in the opposite direction. The inlet velocity is setequal (vh=vc=0.05 m/s) in both the feed and the permeate chan-nels. The figure shows an increase in local velocity in the narrowarea above and below the spacer filaments while a subsequent de-crease in velocity behind the filaments is observed for all orientations.In type AI, velocity is higher in the top portion and a recirculation re-gion exists in the bottom portion of the two channels. The top surfaceof membrane layer is in contact with low velocity (recirculation) andreattachment regions whereas the bottom portion of membrane isexposed to a higher local velocity zone. Since velocity and shear stressare directly related to each other, it can thus be noticed in Fig. 5a thatthe top side of the membrane in hot channel experiences low shearstress due to the low velocity recirculation zone. On the bottommem-brane wall (in cold channel) the shear stress is high above each fila-ment which drops sharply in the central portion between the twofilaments. In type BI the flow recirculation takes place near the topas well as near the bottom of the membrane. In type CI, the high ve-locity region is on both sides of the membrane. The shear stress onbothmembrane sides in type BI is identical to the profile on topmem-brane side in type AI while in type CI the profiles are nearly the sameas the ones seen for the bottom side in type AI. The shear rate peaks inBI, however become noticeable in Fig. 5b because the spread of shearstress values is small and the selected range of the axis is narrow.

Even though the inlet velocity is same in hot and cold channels,the comparison of velocity contours in feed and permeate channelsshows that sizes of high velocity and recirculation regions are largerin the feed channel. The reason for this is that the fluid temperaturein the feed channel is higher and hence has lower viscosity which in-creases recirculation and reattachment length. The same explanationis true for Fig. 5b and c in which the magnitude of shear stress is notthe same in the two channels (types BI and CI).

In types AI, BI and CI, the filaments are in-line vertically in the twochannels. The high and low velocity zones are hence aligned in the

Fig. 4. Velocity and temperature distributions in spacer types AI (a, e), BI (b, f), CI (c, g) and AS (d, h).

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same way. The difference between in-line and staggered arrange-ments can be seen by comparing Fig. 4a with Fig. 4d. In the cold chan-nel of type AI (Fig. 4a), at location 0, the bottom portion of membraneis exposed to the high velocity zone but at the top side of membrane(at the same location 0), a dead zone exists due to presence offilament. In staggered arrangement AS, maximum velocity in thecold channel occurs halfway between locations 0 and 1. At thislocation on the hot side of membrane, a low velocity zone is present.Similar differences are observed in the flow behavior of orientationtypes BI and CI when compared with types BS and CS respectively.The difference in flow patterns on the two sides of membrane forin-line and staggered arrangements leads to dissimilar distributionof temperature polarization which will be explained later in thediscussion of Fig. 6.

The temperature contours and line plots are illustrated in Figs. 4e–h and 5e–h respectively. It must be pointed out that lower tempera-tures in the hot channel indicate a higher degree of temperature po-larization, which is undesirable. In the same way, high temperaturesare not beneficial in the cold channel. When filaments are in contactwith the membrane surface in one or both channels such as in typesAI (hot channel) or BI, temperature polarization is seen to be highclose to the filaments which are the dead locations with almost zerovelocity or shear stress values. The local temperatures are relativelyhigher in the center of the filaments where shear stress rises(Fig. 5a). In the cold channel type AI, in which spacer filaments donot touch the membrane, thermal polarization is noted to be less di-rectly above the filaments. The difference between local temperaturesof hot and cold sides in AI and BI is highest approximately in the cen-ter of the filaments which means low temperature polarization. Inchannels of type CI, the thermal polarization is comparatively lessabove and below the filaments. The temperature contours in typeAS are same as in AI except for the fact that several temperature re-gions are shifted horizontally in the cold channel due to staggered ar-rangement. A comparison of Fig. 5a with d shows that staggering offilaments does not affect the shear stress distribution. The local tem-perature values are however found to be more uniform on the bottomside of membrane in the staggered type (Fig. 5h).

The effect of spacer orientation and spacing on temperature polar-ization index ϕ, calculated from Eq. (1) is illustrated in Fig. 6. Thecurve for in-line arrangement AI45 shows that ϕ index drops from ahigh value of 3.5 to approximately 2 and then again rises rapidly atlocations 1 and 2. The decrease in filament spacing does not signifi-cantly change the ϕ distribution as can be seen for spacer type AI3.The shape of ϕ curve in type AS45 is symmetrical and the minimumvalue of ϕ index lies in the middle of locations 0 and 1 (or 1 and 2).The B type orientation, in which the filaments touch the membraneon both sides, is found to have considerably higher ϕ values. Particu-larly for the in-line spacer type BI, ϕ value reaches up to 6, implyingsignificant reduction in thermal driving force. The trend is relativelybetter in BS45 in which ϕ index values remain between 2 and 3.Five peaks are observed for temperature polarization in BS45; threein the hot channel and two in the cold channel due to the formationof stagnant zones in the vicinity where filaments are present. Thetype C has better profiles since the temperature polarization isnoticed to be lower than in types A and B. In all C types, ϕ indexshows minimum variation and its value remains below 2 which isan advantageous feature. When spacer is used only in one (hot) chan-nel such as type D, the ϕ index values are higher than the onesobtained for type C but are lower than those obtained in types Aand B. This can be clearly seen in the ϕ plots for types D45 and D3.

In Figs. 5 and 6, the inlet velocity is set to 0.05 m/s in both channels.The effect of inlet velocity is shown in Fig. 7 in which three cases areconsidered: (a) vh=vc=0.15 m/s, (b) vh=0.35 m/s, and vc=0.15 m/s(c) vh=vc=0.35 m/s. As expected, it is observed that magnitudes oftemperature polarization index ϕ are lower for higher velocities. Thedifferences in the trends of ϕ distribution are however minor for mostof the cases. In type AI45, for case (a) when vh=vc=0.15 m/s, the ϕindex from a peak value at filament 0 continuously declines, reachesminimum value somewhere before the filament at location 1 and thenincreases rapidly. For cases (b) and (c), when inlet velocity is higher inhot or both channels, a small sized extra peak is also present down-stream of the filament. The reason for this peak to show up is the factthat at low velocity only a single large recirculation region exists behindthe filaments. However, when velocity is high as in cases (b) and (c),

Fig. 5. Shear stress and temperature profiles in AI (a, e), BI (b, f), CI (c, g) and AS (d, h).

336 M. Shakaib et al. / Desalination 284 (2012) 332–340

velocity fields (not shown) reveal that secondary vortices appear on thedownstream side very close to the filaments. The point where two recir-culation regions merge creates another stagnant zone which locally

raises the temperature polarization. This minor peak is also present intypes AS, BI and BS for cases (b) and (c) due to the same reason. Intypes CI and CS, the inlet velocity though affects the magnitude of local

Fig. 6. Temperature polarization in various spacer types.

337M. Shakaib et al. / Desalination 284 (2012) 332–340

temperature polarization index ϕ but the shapes of ϕ curves are same.This shows that locations of high and low temperature polarizationindex are not changed due to inlet velocity variation in type C.

To evaluate the modeling approach in this work, a comparison oftemperature polarization index ϕ is done at two different grid sizes,discretization schemes used in energy equation modeling and usingtwo different turbulence models. The results are given in Fig. 8 whichshows that ϕ distribution is same for the four situations and the curvesalmost overlap. The difference in average temperature polarizationindex obtained with 45,000 cells when compared with 80,000 cells isabout 0.5% for spacer CI3 at an inlet velocity of 0.35 m/s. The differencein average ϕ index is around 0.7% when QUICK scheme is used insteadof Power law scheme for energy and Spalart Allmaras model. Similarlythe difference in average ϕ is less than 0.5% if k-ω (SST) model is usedinstead of Spalart Allmaras model. The negligible difference in average

ϕ shows that number of cells, differencing methods and turbulenceequation chosen in this work are sufficient to produce reliable results.

The average and standard deviation of temperature polarizationindex ϕ are given in Table 2. The inlet velocity in hot channel isequal to the inlet velocity in cold channel in the table. The results re-veal that among the orientations considered, C types have lowest av-erage ϕ values. The ϕ index values in the staggered orientation CS areequal to the values obtained for the in-line CI arrangement. The typeD has second lowest ϕ index. A smaller spacing of 3 mm (D3) is foundto perform a little better than 4.5 mm (D45) for type D due to lowertemperature polarization. In orientations A and B, a higher spacingof 4.5 mm is more suitable than 3 mm as can be noticed from thesummarized results in Table 2. Also, the staggered orientations ASand BS are found to be superior to the in-line arrangements AI andBI respectively because of lower ϕ index values. The table also

Fig. 7. Effect of inlet velocity on temperature polarization.

Fig. 8. Effect of grid, discretization scheme and turbulence model on ø distribution.

338 M. Shakaib et al. / Desalination 284 (2012) 332–340

includes results for empty (hot and cold) channel. In the empty chan-nel temperature polarization is smaller than in type A when inlet ve-locities are low (0.05 and 0.15 m/s). This phenomenon is howeverreversed and the ϕ values in the empty channel become larger thanin type A when inlet velocities are high (0.25 and 0.35 m/s). Thetype B is therefore an improper arrangement as its all subtypes resultin higher temperature polarization index when compared withempty channel at almost all inlet velocities. In addition to average,the standard deviations (normalized by average) of ϕ index valuesare also calculated for the tested orientations. A smaller value of stan-dard deviation is desirable as it indicates equal permeation ratesthrough various portions of the membrane surface. The standard de-viation results show that empty channel has negligible variation inlocal temperature polarization index values. The orientation type Dhas lowest deviations followed by type C. The types A and B havemuch higher standard deviations of temperature polarization index.A comparison of filament spacings indicates that in type C, a 3 mmspacing results in lower standard deviations or more uniform distri-bution of ϕ than 4.5 mm. In types A and B, a spacing of 4.5 mm haslower standard deviations than 3 mm for most of the inlet velocities.The staggering is useful in types A and B since standard deviations are

Table 4Pressure drop in membrane distillation channels.

Type/velocity Pressure drop (Pa)

0.05 0.15 0.25 0.35

AI3 93 382 985 1793BI3 94 384 995 1808CI3 94 383 991 1802D3 60 227 618 1097AI45 78 348 949 1735BI45 79 352 957 1746CI45 78 411 954 1742D45 54 217 605 1071AS3 89 362 948 1733BS3 90 365 957 1747CS3 90 364 955 1743AS45 74 388 911 1678BS45 75 391 917 1688CS45 75 392 916 1684Empty 34 114 207 313

Table 2Average and standard deviation of temperature polarization index for spacerorientations.

Type/velocity Average temperaturepolarization index

Standard deviation oftemperature polarization index

0.05 0.15 0.25 0.35 0.05 0.15 0.25 0.35

AI3 2.40 1.93 1.60 1.45 0.192 0.223 0.213 0.166BI3 3.03 2.35 1.82 1.65 0.403 0.391 0.357 0.333CI3 1.82 1.52 1.38 1.31 0.027 0.008 0.008 0.008D3 1.96 1.63 1.48 1.40 0.014 0.006 0.007 0.007AI45 2.33 1.90 1.58 1.43 0.227 0.184 0.184 0.133BI45 2.82 2.26 1.76 1.60 0.465 0.372 0.330 0.306CI45 1.89 1.51 1.38 1.31 0.052 0.027 0.027 0.027D45 2.10 1.65 1.49 1.41 0.031 0.010 0.021 0.018AS3 2.37 1.86 1.54 1.40 0.215 0.204 0.195 0.149BS3 2.74 2.16 1.68 1.53 0.193 0.215 0.196 0.178CS3 1.83 1.52 1.38 1.31 0.022 0.008 0.007 0.007AS45 2.24 1.66 1.50 1.38 0.254 0.175 0.159 0.123BS45 2.41 1.85 1.61 1.49 0.216 0.171 0.167 0.160CS45 1.89 1.51 1.38 1.30 0.038 0.031 0.028 0.023Empty 2.16 1.78 1.65 1.57 0.001 0.001 0.001 0.001

339M. Shakaib et al. / Desalination 284 (2012) 332–340

lowered (in comparison to in-line) but in type C the difference is notsignificant between types CI and CS.

The shear stress and pressure drops for all orientations are deter-mined and summarized in Tables 3 and 4. Higher shear stress is usefulto prevent accumulation of particles on the membrane while a higherpressure drop is undesirable as it increases the energy to move fluidsacross the membrane channel. Higher shear stress averages andlower standard deviations are seen in C type arrangements. Type Ahas higher average shear stress than D but the distribution is non-uniform as indicated by the high standard deviation values. The ori-entation B is again found to be unsuitable due to the lowest averageshear stress. The pressure drop is almost same in types A, B and C.In type D or empty channel the pressure drop is lower due to absenceof filaments in one or both channels. The filament spacing also affectsthe shear rates. In orientations A and C, the 3 mm spacing results inhigher average shear stress than 4.5 mm. In type B, on the otherhand, spacing of 4.5 mm gives better results than 3 mm. The overallcomparison of staggered and in-line orientations indicates that stag-gered orientations such as CS3 and CS45 are superior since it resultsin higher average shear stress and lower standard deviations andpressure drop for majority of the cases.

The Nusselt number Nu and Reynolds number Re are also deter-mined from Eqs. (3) and (4). The CFD results are compared with theexperimental correlation suggested by Phattaranawik et al. [10] andgiven as Eq. (2) in this paper. The simulated Nu values are compared

Table 3Average and standard deviation of shear stress for spacer orientations.

Type/velocity Average shear stress Standard deviation of shearstress

0.05 0.15 0.25 0.35 0.05 0.15 0.25 0.35

AI3 0.35 1.30 2.75 4.80 1.136 0.988 0.859 0.751BI3 0.07 0.31 1.03 1.95 0.775 0.887 0.999 0.942CI3 0.53 1.99 4.16 6.71 0.546 0.363 0.310 0.326D3 0.35 1.23 2.49 3.95 0.530 0.512 0.609 0.692AI45 0.28 1.18 2.56 4.12 1.422 1.192 1.126 1.185BI45 0.09 0.37 1.14 1.99 0.748 0.632 0.780 0.813CI45 0.41 1.72 3.60 5.53 0.844 0.740 0.817 0.844D45 0.30 1.03 2.12 3.36 0.745 0.573 1.007 1.091AS3 0.36 1.39 2.96 4.85 1.047 0.889 0.711 0.664BS3 0.07 0.33 1.08 2.07 0.770 0.789 0.922 0.897CS3 0.53 2.01 4.19 6.76 0.502 0.348 0.300 0.320AS45 0.28 1.28 2.63 4.23 1.286 1.027 0.988 1.059BS45 0.09 0.49 1.23 2.18 0.702 0.728 0.829 0.855CS45 0.42 1.76 3.53 5.68 0.844 0.727 0.782 0.854Empty 0.21 0.64 1.08 1.54 0.201 0.224 0.222 0.216

with those obtained from Eq. (2) and are presented in Fig. 9. Since thecorrelation was developed from experiments and considered validonly in the Re range of 400–1000, the Nu is obtained only for veloci-ties (0.25 and 0.35 m/s) which fall in the same Re range. Furthermore,details about spacer orientations were not provided in the experi-mental work. Therefore the Nu values obtained for the three in-lineorientations AI, BI and CI have been included in Fig. 9 which showsthat the simulated values are in close agreement with the onesobtained from the experimental correlation. In Fig. 9, it is assumedthat experimental work [10] included in-line arrangement. Due tosatisfactory agreement with experiments, it is suitable to calculateNusselt number of other arrangements such as staggered types, typeD and empty channel. The Nusselt numbers Nu for these arrange-ments are shown in Fig. 10. The Nusselt numbers in Figs. 9 and 10show that the trends are approximately similar as were seen inTable 2 for average ϕ index.

4. Conclusions

The detailed study carried out to examine the effect of spacer ori-entation on temperature polarization and shear rate in a membrane

Fig. 9. Comparison of CFD results with experiments.

Fig. 10. Nusselt number values in various spacer arrangements.

340 M. Shakaib et al. / Desalination 284 (2012) 332–340

distillation process reveals that when the spacer filaments are in con-tact with the membrane surface, recirculation and stagnant zones arecreated near the membrane. The presence of a recirculation region isbeneficial for the process as it reduces temperature polarization indexwhile the stagnant zone has a negative effect because it increases thisindex. When the spacer filaments are not touching the membrane,high velocity zone at the membrane layer enhances shear stress andheat transfer rate by decreasing temperature polarization. Thedistribution of local values of temperature polarization index andshear stress is also uniform in this orientation. The in-line and stag-gered arrangements are also compared in terms of these two param-eters. The staggered arrangement is found better, in particular for theorientations that include filaments touching the membrane. The Nus-selt numbers obtained through CFD simulations have been found tobe in close agreement with experimental results, thus expandingthe scope of this technique for other spacer orientations which havenot been considered and tested yet.

NomenclatureCp specific heat (J/kg K)df filament diameter (m)dh hydraulic diameter (m)h heat transfer coefficient (W/m2 K)hch channel height (m)k thermal conductivity (W/m K)k-ω turbulence model, turbulent kinetic energy (m2/s2) and

specific dissipation rate (1/s)L channel length (m)lm mesh length/filament spacing (m)Nu Nusselt numberPr Prandtl numberqw heat flux (W/m2)Re Reynolds numberv average velocity (m/s)Tc inlet temperature of cold fluid (K)Tcm temperature at membrane surface in cold channel (K)Th inlet temperature of hot fluid (K)

Thm temperature at membrane surface in hot channel (K)ρ density (kg/m3)ϕ temperature polarization indexμ viscosity (kg/m s)ε voidage of feed or permeate channelεm voidage of membraneθ flow attack angle

Acknowledgments

The authors acknowledge the support provided by UniversityMalaysia Pahang for this work.

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