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

Desalination 284 (2012) 332–340

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A CFD study on the effect of spacer orientation on temperature polarization in membrane distillation modules M. Shakaib a, c,⁎, S.M.F. Hasani b, Iqbal Ahmed a, Rosli M. Yunus a a b c

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

a r t i c l e

i n f o

Article history: Received 16 June 2011 Received in revised form 16 August 2011 Accepted 6 September 2011 Available online 5 October 2011 Keywords: Computational fluid dynamics Temperature polarization Membrane distillation Spacer

a b s t r a c t Computational fluid dynamics (CFD) study in this work examines the effect of spacer orientation, inlet velocity and filament spacing on shear stress distribution and temperature polarization in membrane distillation modules. The CFD simulations show that spacer orientation affects the temperature polarization and heat transfer rates. If spacer filaments touch the top or bottom surfaces of membrane, the temperature polarization 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 temperature polarization index and shear stress are more uniformly distributed in the detached mode making this particular orientation more favorable for use in membrane distillation modules. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Membrane distillation is a process that involves temperature gradient as the driving force for separation and treatment of fluids. This process includes a membrane with hot fluid on one side of membrane and cold fluid on the other. The membrane is of hydrophobic nature which restricts the water permeation through membrane pores. A fraction of hot fluid initially evaporates within the membrane due to temperature (or vapor pressure) difference and then condenses to enter the permeate channel. The advantage of membrane distillation (MD) over other membrane processes is that its performance is less sensitive to feed concentration. Further, the MD system is operated at low temperatures and operating pressures and its membranes are more resistant to fouling [1–3]. A phenomenon that reduces the vapor permeation and affects the MD process efficiency is temperature polarization. Temperature polarization means that the temperature difference across the membrane surfaces is lower than the difference of the bulk fluid stream temperatures [4]. In MD modules net-type spacers of the type shown in Fig. 1 are commonly used in feed and permeate flow channels. The main advantage of spacer is that it disrupts the concentration and thermal boundary layers which help in increasing the permeation rates. The disadvantage, on the other hand is that it also creates stagnant zones in the channel. The presence of these stagnant ⁎ Corresponding author at: Faculty of Chemical and Natural Resources Engineering, University Malaysia Pahang, Kuantan, Malaysia. Tel.: + 60 9 5492871. E-mail addresses: [email protected], [email protected] (M. Shakaib). 0011-9164/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.desal.2011.09.020

zones in the membrane channel increases temperature polarization and decreases the driving force for permeation. The spacer orientation and dimensions are crucial parameters that affect the size and location of these stagnation regions. Very few studies exist in the literature that examines the effect of spacer on the MD module performance. Martínez et al. [4–6] investigated the effect of screen separator (or spacer) and showed that spacer causes turbulence in membrane channel which reduces temperature polarization. In another paper [7] the same authors compared temperature and concentration polarization in membrane distillation by using aqueous sodium chloride solution as feed fluid. The effect of temperature polarization was noticed to be more significant than concentration polarization on permeate flux reduction. Various other studies compared the spacer-filled channel with empty channel and reported significant increase in heat transfer coefficient and product flux due to spacers [8–10]. In addition to the experimental studies, some CFD studies [11–13] also confirmed that heat transfer can be augmented by using a spacer in the membrane channels and by increasing the feed flow rate. Numerous papers included fluid flow and mass transfer analysis in spacer-filled membrane channels [14–18]. These studies were however, focused on spiral wound modules for ultrafiltration or reverse osmosis processes and heat transfer rates were not determined. The literature review indicated that none of the papers investigated the effect of spacer orientation/ arrangement in the feed and product channels of MD module which is an important parameter. In the present work, we have hence analyzed the effect of this parameter on temperature polarization and heat transfer rate.

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

333

Fig. 1. Spacer-filled membrane distillation channels.

2. Modeling procedure The spacer-filled channel contains a large number of cells, however the flow becomes fully developed (of repetitive nature) after passing through the first few cells. It is therefore, practical and convenient to restrict the computational flow and heat transfer analysis to only a few filaments in the fully developed flow region. Hence, for CFD modeling, the chosen computational domain has an overall channel length of 38 mm. The distance between first and last filament is 18 mm, multiple filaments are placed in between the first and last filaments. The height of both the feed and the permeate channels is 1 mm and the membrane thickness is 0.2 mm. A number of spacer orientations/arrangements are tested; four basic types are given in Table 1. The filaments in the feed and the permeate channels are either in-line or staggered. This leads to three further orientation types as shown in Fig. 2. Two different values of 3 and 4.5 mm for filament spacing/mesh length lm are considered in this work. The nomenclature used for different arrangements in this paper also includes 3 or 45 to indicate the spacing (for example: AI3 means inline type A spacer with a spacing of 3 mm or BI45 means in-line type B spacer with a spacing of 4.5 mm). The flow direction is of counter-flow type for all simulations as shown in Fig. 1. The temperature of hot fluid is 57 °C whereas the cold fluid temperature is set to 27 °C. The fluid is water having constant density and thermal conductivity but viscosity varies with temperature. The typical permeate fluxes in membrane distillation could be as high as 75 kg/m 2 h [1]. This leads to a permeation velocity of only 2 × 10 −5 m/s that is about 3–4 orders of magnitude smaller than the feed velocity. For such permeation rates, the velocity profiles remain unaffected in the cross flow channel [18]. The membrane is therefore assumed to be impermeable and no flow connection exists between two parallel channels. A constant thermal conductivity of 0.2 W/m K is set for the membrane material. The velocity is specified at the inlet of the feed and the permeate channels (vh and vp respectively) and is varied from 0.05 to 0.35 m/s which corresponds to a Reynolds number Re range of 115–800. The computational domain is divided into around 45,000 cells as illustrated in Fig. 3 which is

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

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

Table 1 Spacer orientations considered in this work. Orientation Description type A B

C

D

Filaments are in the lower portion of feed and permeate channels. Filaments in feed channel are in the lower while in permeate channel are in the upper portion. This means that filaments touch the membrane surface in both channels. Filaments in feed channel are in the upper whereas in permeate channel they are in the lower portion of the channel. The filaments hence are separated or detached from the membrane. Spacer is in feed channel only with filaments in the upper portion of the channel and the permeate channel is empty.

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

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components and energy equation. The flow in spacer-filled membrane channel is fully laminar and free from instabilities at low Reynolds numbers. When the Reynolds number is high, that exceeds a certain critical value, the flow becomes transient and timedependent. The critical value for this time-dependent flow is between 200 and 800 depending upon the filament spacing and thickness [17]. It is well known that for solving the transient flows, the direct method of solving the Navier Stokes equations or Direct Numerical Simulations (DNS) is a suitable approach. However, the drawback of this approach is significantly large computational time. The alternative method is to use Reynolds-averaging approach which includes transport equations for the mean flow quantities without direct simulation of turbulent/flow fluctuations. The additional fluctuation terms in the governing equations are determined through a turbulence model. For the simulations in the present work, it is noticed that if velocity is less than (or equal to) 0.15 m/s (Re ≈ 350) the solution converges without the need of any turbulence model showing that flow is laminar. When the inlet velocity is higher than 0.15 m/s, the solution diverges when laminar model is selected indicating that flow is unsteady. There are several turbulence models that are used for complex flow problems. The Spalart–Allmaras (SA) model is used here in which additional transport equation for turbulent viscosity is solved. Previous CFD study by the present authors [19] for obstructed narrow channels has shown qualitative and quantitative agreement of SA model with DNS in terms of velocity contours and pressure drops. Another CFD study [20] showed good agreement of reattachment lengths predicted by this model with the ones obtained experimentally as well as using DNS approach. Further, the trials using other turbulence models showed that results of SA model are similar to results obtained using two-equation model k-ω (SST). In addition, less computational time is needed with Spalart Allmaras model when compared to two-equation models and convergence is achieved within 2500 iterations for the cases considered in this paper. The governing equations are solved using the CFD code FLUENT 6.3. For discretization of momentum equations, a higher order scheme QUICK (Quadratic Upstream Interpolation for Convection Kinetics) whereas a relatively simple Power law scheme is used for energy and turbulence equations. This selection is based on some preliminary results that showed negligible difference if the Power law is chosen instead of QUICK for energy and turbulence equations. This will be discussed in more detail in Results and discussions section. However, for momentum equations, the difference is relatively higher if Power law is used. Pressure–velocity coupling is made through SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The spacer performance is evaluated in terms of temperature polarization index ϕ. The definition used in this paper is: ϕ¼

Th −Tc : Thm −Tcm

ð1Þ

In Eq. (1) Th and Tc are inlet temperatures in hot and cold channels respectively whereas Thm and Tcm are the temperatures at the membrane wall on hot (top) and cold (bottom) sides respectively. A lower value of ϕ is desirable. The present CFD results are compared with experimental correlation (Eq. (2)) available in literature for heat transfer in spacer-filled channel [10]. This correlation is given as: " Nu ¼ α 4:36 þ

0:036RePrðdh =LÞ 1 þ 0:0011ðRePrðdh =LÞÞ0:8

#

where  −0:039    2  df ε 1:33 ð sinθÞ x exp 4:05 ln : α ¼ 1:88 εm hch

ð2Þ

In Eq. (2) dh is hydraulic diameter, L is channel length, df is filament diameter, hch is channel height, θ is flow attack angle, ε is voidage of feed or permeate channel and εm is voidage of membrane. The Reynolds number Re, Prandtl number Pr and Nusselt number Nu are defined as: Re ¼

ρvdh μ

ð3Þ

Nu ¼

hdh k

ð4Þ

where h¼

qw Th −Thm

or h¼

qw Tcm −Tc

ð5Þ

μCp : k

ð6Þ

Pr ¼

In Eqs. (3–6), qw is heat flux, ρ is density, μ is viscosity, k is thermal conductivity, Cp is specific heat and h is heat transfer coefficient. 3. Results and discussions The effect of various spacer orientations on velocity and temperature profiles is shown in Fig. 4. These profiles cover the region between three filaments labeled as 0, 1 and 2. In the top channel, hot feed flows from left to right while in the bottom channel, cold permeate flows in the opposite direction. The inlet velocity is set equal (vh = vc = 0.05 m/s) in both the feed and the permeate channels. The figure shows an increase in local velocity in the narrow area above and below the spacer filaments while a subsequent decrease in velocity behind the filaments is observed for all orientations. In type AI, velocity is higher in the top portion and a recirculation region exists in the bottom portion of the two channels. The top surface of membrane layer is in contact with low velocity (recirculation) and reattachment regions whereas the bottom portion of membrane is exposed to a higher local velocity zone. Since velocity and shear stress are directly related to each other, it can thus be noticed in Fig. 5a that the top side of the membrane in hot channel experiences low shear stress due to the low velocity recirculation zone. On the bottom membrane wall (in cold channel) the shear stress is high above each filament which drops sharply in the central portion between the two filaments. In type BI the flow recirculation takes place near the top as well as near the bottom of the membrane. In type CI, the high velocity region is on both sides of the membrane. The shear stress on both membrane sides in type BI is identical to the profile on top membrane side in type AI while in type CI the profiles are nearly the same as the ones seen for the bottom side in type AI. The shear rate peaks in BI, however become noticeable in Fig. 5b because the spread of shear stress 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 channels shows that sizes of high velocity and recirculation regions are larger in the feed channel. The reason for this is that the fluid temperature in the feed channel is higher and hence has lower viscosity which increases recirculation and reattachment length. The same explanation is true for Fig. 5b and c in which the magnitude of shear stress is not the same in the two channels (types BI and CI). In types AI, BI and CI, the filaments are in-line vertically in the two channels. The high and low velocity zones are hence aligned in the

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335

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

same way. The difference between in-line and staggered arrangements can be seen by comparing Fig. 4a with Fig. 4d. In the cold channel of type AI (Fig. 4a), at location 0, the bottom portion of membrane is 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 of filament. In staggered arrangement AS, maximum velocity in the cold channel occurs halfway between locations 0 and 1. At this location on the hot side of membrane, a low velocity zone is present. Similar differences are observed in the flow behavior of orientation types BI and CI when compared with types BS and CS respectively. The difference in flow patterns on the two sides of membrane for in-line and staggered arrangements leads to dissimilar distribution of temperature polarization which will be explained later in the discussion 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 temperatures in the hot channel indicate a higher degree of temperature polarization, which is undesirable. In the same way, high temperatures are not beneficial in the cold channel. When filaments are in contact with the membrane surface in one or both channels such as in types AI (hot channel) or BI, temperature polarization is seen to be high close to the filaments which are the dead locations with almost zero velocity or shear stress values. The local temperatures are relatively higher in the center of the filaments where shear stress rises (Fig. 5a). In the cold channel type AI, in which spacer filaments do not touch the membrane, thermal polarization is noted to be less directly above the filaments. The difference between local temperatures of hot and cold sides in AI and BI is highest approximately in the center of the filaments which means low temperature polarization. In channels of type CI, the thermal polarization is comparatively less above and below the filaments. The temperature contours in type AS are same as in AI except for the fact that several temperature regions are shifted horizontally in the cold channel due to staggered arrangement. A comparison of Fig. 5a with d shows that staggering of filaments does not affect the shear stress distribution. The local temperature values are however found to be more uniform on the bottom side of membrane in the staggered type (Fig. 5h).

The effect of spacer orientation and spacing on temperature polarization index ϕ, calculated from Eq. (1) is illustrated in Fig. 6. The curve for in-line arrangement AI45 shows that ϕ index drops from a high value of 3.5 to approximately 2 and then again rises rapidly at locations 1 and 2. The decrease in filament spacing does not significantly change the ϕ distribution as can be seen for spacer type AI3. The shape of ϕ curve in type AS45 is symmetrical and the minimum value 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 membrane on both sides, is found to have considerably higher ϕ values. Particularly for the in-line spacer type BI, ϕ value reaches up to 6, implying significant reduction in thermal driving force. The trend is relatively better in BS45 in which ϕ index values remain between 2 and 3. Five peaks are observed for temperature polarization in BS45; three in the hot channel and two in the cold channel due to the formation of stagnant zones in the vicinity where filaments are present. The type C has better profiles since the temperature polarization is noticed to be lower than in types A and B. In all C types, ϕ index shows minimum variation and its value remains below 2 which is an advantageous feature. When spacer is used only in one (hot) channel such as type D, the ϕ index values are higher than the ones obtained for type C but are lower than those obtained in types A and 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 are considered: (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 of temperature polarization index ϕ are lower for higher velocities. The differences in the trends of ϕ distribution are however minor for most of the cases. In type AI45, for case (a) when vh = vc = 0.15 m/s, the ϕ index from a peak value at filament 0 continuously declines, reaches minimum value somewhere before the filament at location 1 and then increases rapidly. For cases (b) and (c), when inlet velocity is higher in hot or both channels, a small sized extra peak is also present downstream of the filament. The reason for this peak to show up is the fact that at low velocity only a single large recirculation region exists behind the filaments. However, when velocity is high as in cases (b) and (c),

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

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

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

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337

Fig. 6. Temperature polarization in various spacer types.

temperature polarization index ϕ but the shapes of ϕ curves are same. This shows that locations of high and low temperature polarization index are not changed due to inlet velocity variation in type C. To evaluate the modeling approach in this work, a comparison of temperature polarization index ϕ is done at two different grid sizes, discretization schemes used in energy equation modeling and using two different turbulence models. The results are given in Fig. 8 which shows that ϕ distribution is same for the four situations and the curves almost overlap. The difference in average temperature polarization index obtained with 45,000 cells when compared with 80,000 cells is about 0.5% for spacer CI3 at an inlet velocity of 0.35 m/s. The difference in average ϕ index is around 0.7% when QUICK scheme is used instead of Power law scheme for energy and Spalart Allmaras model. Similarly the difference in average ϕ is less than 0.5% if k-ω (SST) model is used instead of Spalart Allmaras model. The negligible difference in average

ϕ shows that number of cells, differencing methods and turbulence equation chosen in this work are sufficient to produce reliable results. The average and standard deviation of temperature polarization index ϕ are given in Table 2. The inlet velocity in hot channel is equal to the inlet velocity in cold channel in the table. The results reveal that among the orientations considered, C types have lowest average ϕ values. The ϕ index values in the staggered orientation CS are equal to the values obtained for the in-line CI arrangement. The type D has second lowest ϕ index. A smaller spacing of 3 mm (D3) is found to perform a little better than 4.5 mm (D45) for type D due to lower temperature polarization. In orientations A and B, a higher spacing of 4.5 mm is more suitable than 3 mm as can be noticed from the summarized results in Table 2. Also, the staggered orientations AS and BS are found to be superior to the in-line arrangements AI and BI respectively because of lower ϕ index values. The table also

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

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

includes results for empty (hot and cold) channel. In the empty channel temperature polarization is smaller than in type A when inlet velocities are low (0.05 and 0.15 m/s). This phenomenon is however reversed and the ϕ values in the empty channel become larger than in type A when inlet velocities are high (0.25 and 0.35 m/s). The type B is therefore an improper arrangement as its all subtypes result in higher temperature polarization index when compared with empty channel at almost all inlet velocities. In addition to average, the standard deviations (normalized by average) of ϕ index values are also calculated for the tested orientations. A smaller value of standard deviation is desirable as it indicates equal permeation rates through various portions of the membrane surface. The standard deviation results show that empty channel has negligible variation in local temperature polarization index values. The orientation type D has lowest deviations followed by type C. The types A and B have much higher standard deviations of temperature polarization index. A comparison of filament spacings indicates that in type C, a 3 mm spacing results in lower standard deviations or more uniform distribution of ϕ than 4.5 mm. In types A and B, a spacing of 4.5 mm has lower standard deviations than 3 mm for most of the inlet velocities. The staggering is useful in types A and B since standard deviations are

M. Shakaib et al. / Desalination 284 (2012) 332–340 Table 2 Average and standard deviation of temperature polarization index for spacer orientations. Type/velocity

AI3 BI3 CI3 D3 AI45 BI45 CI45 D45 AS3 BS3 CS3 AS45 BS45 CS45 Empty

Average temperature polarization index

Table 4 Pressure drop in membrane distillation channels. Type/velocity

Pressure drop (Pa)

Standard deviation of temperature polarization index

0.05

0.15

0.25

0.35

0.05

0.15

0.25

0.35

2.40 3.03 1.82 1.96 2.33 2.82 1.89 2.10 2.37 2.74 1.83 2.24 2.41 1.89 2.16

1.93 2.35 1.52 1.63 1.90 2.26 1.51 1.65 1.86 2.16 1.52 1.66 1.85 1.51 1.78

1.60 1.82 1.38 1.48 1.58 1.76 1.38 1.49 1.54 1.68 1.38 1.50 1.61 1.38 1.65

1.45 1.65 1.31 1.40 1.43 1.60 1.31 1.41 1.40 1.53 1.31 1.38 1.49 1.30 1.57

0.192 0.403 0.027 0.014 0.227 0.465 0.052 0.031 0.215 0.193 0.022 0.254 0.216 0.038 0.001

0.223 0.391 0.008 0.006 0.184 0.372 0.027 0.010 0.204 0.215 0.008 0.175 0.171 0.031 0.001

0.213 0.357 0.008 0.007 0.184 0.330 0.027 0.021 0.195 0.196 0.007 0.159 0.167 0.028 0.001

0.166 0.333 0.008 0.007 0.133 0.306 0.027 0.018 0.149 0.178 0.007 0.123 0.160 0.023 0.001

lowered (in comparison to in-line) but in type C the difference is not significant between types CI and CS. The shear stress and pressure drops for all orientations are determined and summarized in Tables 3 and 4. Higher shear stress is useful to prevent accumulation of particles on the membrane while a higher pressure drop is undesirable as it increases the energy to move fluids across the membrane channel. Higher shear stress averages and lower standard deviations are seen in C type arrangements. Type A has higher average shear stress than D but the distribution is nonuniform as indicated by the high standard deviation values. The orientation B is again found to be unsuitable due to the lowest average shear 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 absence of filaments in one or both channels. The filament spacing also affects the shear rates. In orientations A and C, the 3 mm spacing results in higher average shear stress than 4.5 mm. In type B, on the other hand, spacing of 4.5 mm gives better results than 3 mm. The overall comparison of staggered and in-line orientations indicates that staggered orientations such as CS3 and CS45 are superior since it results in higher average shear stress and lower standard deviations and pressure drop for majority of the cases. The Nusselt number Nu and Reynolds number Re are also determined from Eqs. (3) and (4). The CFD results are compared with the experimental correlation suggested by Phattaranawik et al. [10] and given as Eq. (2) in this paper. The simulated Nu values are compared

339

AI3 BI3 CI3 D3 AI45 BI45 CI45 D45 AS3 BS3 CS3 AS45 BS45 CS45 Empty

0.05

0.15

0.25

0.35

93 94 94 60 78 79 78 54 89 90 90 74 75 75 34

382 384 383 227 348 352 411 217 362 365 364 388 391 392 114

985 995 991 618 949 957 954 605 948 957 955 911 917 916 207

1793 1808 1802 1097 1735 1746 1742 1071 1733 1747 1743 1678 1688 1684 313

with those obtained from Eq. (2) and are presented in Fig. 9. Since the correlation was developed from experiments and considered valid only in the Re range of 400–1000, the Nu is obtained only for velocities (0.25 and 0.35 m/s) which fall in the same Re range. Furthermore, details about spacer orientations were not provided in the experimental work. Therefore the Nu values obtained for the three in-line orientations AI, BI and CI have been included in Fig. 9 which shows that the simulated values are in close agreement with the ones obtained from the experimental correlation. In Fig. 9, it is assumed that experimental work [10] included in-line arrangement. Due to satisfactory agreement with experiments, it is suitable to calculate Nusselt number of other arrangements such as staggered types, type D and empty channel. The Nusselt numbers Nu for these arrangements are shown in Fig. 10. The Nusselt numbers in Figs. 9 and 10 show that the trends are approximately similar as were seen in Table 2 for average ϕ index.

4. Conclusions The detailed study carried out to examine the effect of spacer orientation on temperature polarization and shear rate in a membrane

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

AI3 BI3 CI3 D3 AI45 BI45 CI45 D45 AS3 BS3 CS3 AS45 BS45 CS45 Empty

Average shear stress

Standard deviation of shear stress

0.05

0.15

0.25

0.35

0.05

0.15

0.25

0.35

0.35 0.07 0.53 0.35 0.28 0.09 0.41 0.30 0.36 0.07 0.53 0.28 0.09 0.42 0.21

1.30 0.31 1.99 1.23 1.18 0.37 1.72 1.03 1.39 0.33 2.01 1.28 0.49 1.76 0.64

2.75 1.03 4.16 2.49 2.56 1.14 3.60 2.12 2.96 1.08 4.19 2.63 1.23 3.53 1.08

4.80 1.95 6.71 3.95 4.12 1.99 5.53 3.36 4.85 2.07 6.76 4.23 2.18 5.68 1.54

1.136 0.775 0.546 0.530 1.422 0.748 0.844 0.745 1.047 0.770 0.502 1.286 0.702 0.844 0.201

0.988 0.887 0.363 0.512 1.192 0.632 0.740 0.573 0.889 0.789 0.348 1.027 0.728 0.727 0.224

0.859 0.999 0.310 0.609 1.126 0.780 0.817 1.007 0.711 0.922 0.300 0.988 0.829 0.782 0.222

0.751 0.942 0.326 0.692 1.185 0.813 0.844 1.091 0.664 0.897 0.320 1.059 0.855 0.854 0.216

Fig. 9. Comparison of CFD results with experiments.

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Thm ρ ϕ μ ε εm θ

temperature at membrane surface in hot channel (K) density (kg/m 3) temperature polarization index viscosity (kg/m s) voidage of feed or permeate channel voidage of membrane flow attack angle

Acknowledgments The authors acknowledge the support provided by University Malaysia Pahang for this work. References

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

distillation process reveals that when the spacer filaments are in contact with the membrane surface, recirculation and stagnant zones are created near the membrane. The presence of a recirculation region is beneficial for the process as it reduces temperature polarization index while the stagnant zone has a negative effect because it increases this index. When the spacer filaments are not touching the membrane, high velocity zone at the membrane layer enhances shear stress and heat transfer rate by decreasing temperature polarization. The distribution of local values of temperature polarization index and shear stress is also uniform in this orientation. The in-line and staggered arrangements are also compared in terms of these two parameters. The staggered arrangement is found better, in particular for the orientations that include filaments touching the membrane. The Nusselt numbers obtained through CFD simulations have been found to be in close agreement with experimental results, thus expanding the scope of this technique for other spacer orientations which have not been considered and tested yet. Nomenclature Cp specific heat (J/kg K) df filament diameter (m) dh hydraulic diameter (m) h heat transfer coefficient (W/m 2 K) hch channel height (m) k thermal conductivity (W/m K) k-ω turbulence model, turbulent kinetic energy (m 2/s 2) and specific dissipation rate (1/s) L channel length (m) lm mesh length/filament spacing (m) Nu Nusselt number Pr Prandtl number qw heat flux (W/m 2) Re Reynolds number v 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)

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