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Computational study of desalination by reverse osmosis — Three-dimensional analyses
Desalination 388 (2016) 38–49
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Desalination journal homepage: www.elsevier.com/locate/desal
Computational study of desalination by reverse osmosis — Three-dimensional analyses Ali E. Anqi a,b, Nawaf Alkhamis c, Alparslan Oztekin a,⁎ a b c
Lehigh University, Dept. of Mechanical Engineering & Mechanics, USA King Khalid University, Dept. of Mechanical Engineering, Saudi Arabia King Abdulaziz University, Dept. of Mechanical Engineering, Saudi Arabia
H I G H L I G H T S • • • • •
Characterization of three-dimensional binary fluid flows in a desalination module Membrane performance is enhanced by the presence of spacers. Spacers help in mitigating concentration polarization and fouling buildup. Spacers have more favorable influence on membrane performance at higher flow rates. The net of spacers in the 30° arrangement is the most efficient one.
a r t i c l e
i n f o
Article history: Received 10 January 2016 Received in revised form 20 March 2016 Accepted 24 March 2016 Available online xxxx Keywords: Membrane performance Reverse osmosis Desalination Net of spacers Concentration polarization Fouling buildup
a b s t r a c t A computational study has been conducted to examine three-dimensional steady multicomponent fluid flows in the reverse osmosis membrane module. The module contains a net of spacers. The SST k-ω turbulence model is employed to simulate flow and concentration fields at Re=400 and 800, while the laminar model is employed to characterize flow and concentration fields at Re = 100. Spacer grids with 30°, 45° and 60° are considered as three different geometries. The membrane is treated as a functional surface where water flux, concentration and local pressure are coupled. The nature of concentration polarization in each membrane module is determined. Characteristics of potential fouling buildup are determined from the wall shear stress distribution. Correlations between potential fouling regions and the concentration distribution are presented. The coefficient of performance for each membrane module is determined at all flow rates considered. It has been illustrated that all membrane modules perform better at higher flow rates. The membrane module containing the net of spacers in the 30° arrangement is shown to be the most efficient membrane module. This study proves that the configuration of spacers is an important optimization parameter for the design of reverse osmosis membrane modules. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Reverse Osmosis (RO) is a method which is used around the globe to produce fresh water. This technology is typically used to desalinate seawater or brackish water. Reverse osmosis is capable of producing fresh water by applying high pressure in a feed channel surrounded by a semi-permeable membrane. The applied pressure has to be greater than the osmotic pressure of the solution. The fresh water production rate is dependent on the salt concentration in the feed water and on membrane properties such as the selectivity and the permeability. The greater the value of the selectivity and the permeability, the higher the probability of the occurrence of the salt concentration polarization
⁎ Corresponding author. E-mail address: [email protected] (A. Oztekin).
http://dx.doi.org/10.1016/j.desal.2016.03.017 0011-9164/© 2016 Elsevier B.V. All rights reserved.
along the membrane surface. This is due to the fact that the water permeation through the membrane and the salt accumulation along the membrane surface increase as the selectivity and the permeability of the membrane increase. The occurrence of concentration polarization along the surface of the membrane has two major undesirable effects on the membrane performance. One is the increase of the osmotic pressure as the salt concentration rises so the applied pressure must be increased to keep the water production rate the same. The other is the promotion of a scaling and a fouling along the surface of the membrane at the region where the salt concentration polarization occurs [1–3]. In spiral wound membranes, spacers are placed in the feed channel to maintain the gap between the membranes and to promote momentum mixing. Several investigators studied the influence of spacers on the membrane performance for desalination processes. Karode and Kumar [4] conducted three-dimensional flow simulations and experiments to
A.E. Anqi et al. / Desalination 388 (2016) 38–49
Nomenclature (u ,v , w) Δp hm vw CD h F1 , F2 A Uave D a1 Re c0 Sh cb Sc cp d cw k f p fx CP
components of velocity [m/s] transmembrane pressure difference [Pa] mass transfer coefficient [m/s] water flux [m/s] drag coefficient channel height [m] blending functions membrane permeability [m/s Pa] average inlet velocity [m/s] diffusion coefficient [m2/s] turbulent model parameter Reynolds number, Re =2hUave/ν inlet concentration [kg/m3] Sherwood number, Sh= 2h hm/D bulk concentration [kg/m3] Schmidt number, Sc= ν/D production concentration [kg/m3] spacer diameter [m] membrane salt concentration [kg/m3] turbulent kinetic energy [J/kg] pressure coefficient pressure [Pa] drag force [N] coefficient of performance
Greek letters eddy viscosity [Pa s] μt μ dynamic viscosity [Pa s] kinematic eddy viscosity [m2/s] νt ν kinematic viscosity [m2/s] turbulent model parameter σk1 ρ density [kg/m3] σω ,σω2 turbulent model parameters ω specific dissipation rate [1/s] β, β⁎ turbulent model parameters κ osmotic coefficient [kPa m3/kg] γ turbulent model parameter τ normalized wall shear stress θ strand angle [°] Subscripts i and j index notation w properties along the membrane surface
examine flow characteristics in a feed channel containing different types of commercial spacers. Karode and Kumar [4] have concluded that the turbulent flow structures, the degree of pressure drops and the characteristics of the wall shear stress were strongly influenced by the spacer's types and arrangements. Fimebers-Weihs and Wiley [5] performed steady three-dimensional flows and mass transfer simulations. The membrane was treated as an impermeable wall, and the mass transfer coefficient was determined from an empirical relation. They reported that the pressure drop and the mass transfer coefficient are influenced by the spacer configurations and by the feed flow rate. Koutsou et al. [6] conducted a direct numerical simulation to investigate the flow characteristics inside the feed channel bounded by impermeable walls. They reported that the flow inside the feed channel containing spacers becomes unsteady for values of Reynolds number greater than about 40. Their computational study did not consider the mass transfer.
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Recently, Ishigami and Matsuyama [7] conducted flow and mass transfer simulations in the feed channel containing three-unit cells of meshed spacers. They estimated the salt concentration along the surface of the membrane using an exponential relation. The membrane was treated as an impermeable wall in their work, so the water flux was calculated empirically. Koutsou and Karabelas [8] introduced a novel spacer design by placing spheres at the intersection of the spacer strands. Since spheres touch both membranes, the contact zones between the spacer strands and the membrane is minimized. Numerical simulations and experimental measurements by Koutsou and Karabelas demonstrated that the reduction of contact zones between the spacer and membrane improved the membrane performance and reduced the potential fouling zones. Ma and Song [9] and the present authors [10,11] conducted two-dimensional flow and mass transfer simulations in the feed channel containing spacers. The membranes in these studies were modeled as a functional surface where the mass flux and the concentration are coupled together. Three-dimensional flow and mass transfer simulations in water desalination feed channels containing a net of spacers have not been conducted using an accurate membrane flux model. The present authors perform a computational study to characterize steady three-dimensional velocity and concentration fields in the feed channel containing a net of spacers. The membrane performance is determined for various values of flow rates in a reverse osmosis membrane module with different configurations of mesh of spacers. An accurate membrane flux model is employed to estimate the water permeation through the membrane and the salt accumulation along the surface of the membrane for characterization of concentration polarization. The salt concentration, the pressure and the water flux through the membrane are coupled at the membrane surface. The local Sherwood number is calculated directly from the velocity and the concentration field. Concentration and water flux contours along the surface of the membrane surface are determined to access membrane performance and the concentration polarization. The wall shear stress is calculated to predict regions where the fouling can potentially occur. Moreover, the coefficient of performance for different spacers is calculated at the same pumping power to determine which separation module performs better. This study will aid in design and optimization of reverse osmosis desalination modules containing net type of spacers. 2. Mathematical model The top view of the computational domain is illustrated in Fig. 1. The top and the bottom surfaces represent the reverse osmosis membranes. The gap between the membranes is h = 1.5 mm. Eleven repeated cells are placed along the stream-wise direction in the mid-plane of the feed channel to form a mesh of spacers. The spacer strands diameter (d) is fixed at 1/2 h, and the distance between two successive intersections of strands in the stream-wise direction is also fixed at 6.7 h, as depicted in Fig. 1. The angle between the strands and the stream-wise direction, θ, is varied — 30° , 45° and 60° — to create different geometries of spacers. The cells are symmetrically placed at the mid-plane with their centers along the stream-wise direction, as illustrated in Fig. 1. The length of the inlet and the outlet region is 5 h and 17.67 h, respectively, in order to minimize the effects of the imposed boundary conditions on the velocity and the concentration fields. Reynolds number (Re) is defined as Re = (2h Uave)/ν. Simulations are conducted for values of Re 100 , 400 and 800 for each geometry. Here Uave is the average velocity at the inlet, and ν is the kinematic viscosity (ν = μ/ρ) of the binary solution of salt and water. Velocity and pressure fields in the feed channel are governed by the continuity and momentum equation, and the concentration field is governed by the mass transport equation. The binary solution is assumed to be incompressible with density, ρ, and viscosity, μ. The diffusion coefficient, D, is assumed to be constant. The
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Fig. 1. Schematic of the computational domain. Top view of the feed channel.
equations governing the fluid motions are the Navier–Stokes equations: ∂ui ¼ 0; ∂xi 2 ∂u 1 ∂p ∂ ui þν : uj i ¼ ∂x j ρ ∂xi ∂x j ∂x j
ð1Þ ð2Þ
The equation governing the mass transport in the feed channel 2
uj
∂c ∂ c ¼D : ∂x j ∂x j ∂x j
ð3Þ
The SST k-ω turbulence mass transport equation is given by: ∂c ∂ uj ¼ ∂x j ∂x j
! μt ∂c Dþ ρ Sct ∂x j
where Sct is the turbulence Schmidt number. The membrane is treated as a functional surface where the local water flux, local salt concentration, and local pressure are coupled together. The solution-diffusion model is used to determine the local water flux and local salt concentration gradient along the surface of the membrane [21,22]. The boundary conditions at the membrane surface are: @y ¼ 0 and h:
Here i and j are the summation indices. x1 = x is the stream-wise direction, x2 = y is the cross-flow direction, and x3 = z is the span-wise direction. u1 = u is the stream-wise component, u2 = v is the cross-flow component, and u3 = w is the span-wise component of the velocity. c is the salt concentration of the binary solution. It is well documented that the flow, temperature and concentration fields in channels containing cylinders are predicted accurately by the shear stress transport (SST) k-ω turbulence model [12–15]. It is also well-documented that flows past arrays of spacers confined in channels have turbulent-like characteristics for Re ≥ 400 [16–19]. The SST k-ω turbulence model is employed by the present computational study to characterize three-dimensional steady turbulent flow structures in the feed channel for Re of 400 and 800. The SST k-ω turbulence momentum transport equation is given by:
uj
∂ui 1 ∂p 1 ∂ ¼ þ ρ ∂xi ρ ∂x j ∂x j
ðμ þ μ t Þ
∂ui ∂x j
! ð4Þ
where μ is the dynamic viscosity and μt is the eddy viscosity, μ t ¼ ρ a1 k maxða1 ω;Ω F 2 Þ.
The equations governing the turbulence kinetic energy, k,
and the specific dissipation rate, ω, are:
ui
∂ðρkÞ ∂u ∂ ∂k ¼ τij i −β ρωk þ ½ðμ þ σ k μ t Þ ; ∂xi ∂x j ∂x j ∂x j
" # ∂ðρωÞ γ ∂ui ∂ ∂ω 2 ðμ þ σ ω μ t Þ ui ¼ τij βρω þ ν t ∂x j ∂xi ∂x j ∂x j 1 ∂k ∂ω þ 2ρð1 F 1 Þσ ω2 ω ∂x j ∂x j
ð5Þ
ð6Þ
where Ω is the vorticity magnitude, a1, β , β⁎, σk, σω, σω2 and γ are closure coefficients, and F1 , F2 are the blending functions. Detailed description of the model can be found in Ref. [20].
ð7Þ
u¼0
;
vw ¼ A Δp−κ cw −cp ∂c D ¼ vw cw −cp ∂y
9 = ; ; ð8Þ
where vw is the local water flux through the membrane, A is the water permeability of the membrane, Δp is the transmembrane pressure difference, κ is the osmotic coefficient, cw is the salt concentration at the membrane surface, and cp is the salt concentration in the production channel. The local water flux at the membrane surface is normalized as vw/(Δ p A). The salt passage through the membrane is neglected, and 100% salt rejection is imposed. At the inlet, the profile of the stream-wise component of the velocity is considered to be parabolic in the cross-flow direction,u = 6Uave[y/h- (y/h)2], while it is assumed to be uniform in the span-wise direction, z. The salt concentration at the inlet is assumed to be constant c0 = 4000 ppm. The inlet concentration selected here is in the range of typical brackish water salinity. For high feed water salinity such as seawater, it is anticipated that the salt concentration polarization along the membrane surface in the production side will affect the membrane performance. Therefore, velocity and concentration field in both feed and production channels need to be characterized to evaluate the membrane performance for seawater desalination processes. The type and the arrangement of spacers providing better membrane performance in seawater desalination modules can be very different than those in brackish water desalination module considered in the present study. No-penetration and no-slip velocity boundary conditions and zero concentration gradient are imposed along the surface of the spacers. At the outlet, zero pressure and constant concentration gradient are applied, and at the side walls periodic conditions on both the velocity and the concentration fields are imposed. The results are presented in various dimensionless flow quantities. The friction coefficient is evaluated from:
f ¼
dp 2h dx ð1=2 Þ ρU 2ave
ð9Þ
A.E. Anqi et al. / Desalination 388 (2016) 38–49 Table 1 Physical parameters used in the simulations. Parameter
Value
Osmotic pressure coefficient: κ Density: ρ Dynamic viscosity: μ Diffusivity: D Schmidt number: Sc Permeability: A Transmembrane pressure: Δp
75 kPa m3/kg 1000 kg/m3 10−3 Pa s 1.5×10−9 m2/s 667 2.3×10−11 m/(s Pa) 1.25 MPa
where dp is the pressure gradient. Sherwood number, Sh, is calculated as: dx
Sh ¼
D
ð2hÞhm D
; hm ¼
∂c ∂y y¼h
ðcb cw Þ
ð10Þ
here hm is the local mass transfer coefficient and cb is the bulk concentration. The drag coefficient, CD, is determined from: CD ¼
2f x ρU 2ave As
;
ð11Þ
where fx is the drag force exerted on the spacer, and As is the projected area of the spacer in the direction perpendicular to the stream-wise direction. 3. Numerical simulations, convergence and validation The commercial software, CFX 14.5, is employed to conduct the numerical simulations. The equations are discretized using the finite volume approach, and the velocity and pressure fields are fully coupled. The boundary conditions at the inlet and along the surface of the membrane are implemented by using CEL expression language. The osmotic pressure coefficient is set to κ = 75 kPa m3/kg. The physical properties of the solution in the feed channel are assumed to be constant. The density is ρ= 1000 kg/m3, and the dynamic viscosity is μ = 10-3 Pa s, the diffusion coefficient is D = 1.5×10-9 m2/s, and the Schmidt number is Sc= ν/D = 667. The membrane considered here for brackish water desalination is a high permeability membrane, A = 2.3 × 10-11 m/(s Pa) [9]. The membrane permeability has strong influence on the membrane flux performance as shown in Eq. (8). It has also strong influence on the concentration polarization since there is more salt accumulation along the surface of the membrane for higher water permeation. The transmembrane pressure is selected to be Δ p = 1.25 MPa. The increase of the feed pressure increases the transmembrane pressure, which in turn increases the fresh water production through the membrane. It is also important to note that the operational cost increases as the feed pressure is increased. In order to calculate the coefficient of performance, CP, for each spacer geometry, numerical simulations are conducted in a feed
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channel without spacers by using the laminar flow model. Membrane parameters and the physical properties of the binary solution are summarized in Table 1. In Ref. [22], the present authors demonstrated the validation of the turbulence model and the numerical method used in the current computational study. Anqi et al. [22] conducted simulations for flows past a cylinder confined in a channel for a blockage ratio of 0.5. They reported CD = 4.482 for two-dimensional flows and CD = 3.995 for threedimensional flows. The drag coefficient reported by Chakraborty et al. [16] (CD = 4.995) for two-dimensional flows past a cylinder agrees well with that documented by the present authors. That helps validating the turbulence model and the numerical method. This method was successfully employed by the present authors to study separation processes using membranes [10,14,15,22]. The present authors also validated the membrane flux model [10] by comparing the water flux and the concentration distribution along the surface of the membrane against results documented by Ma and Song [9], as reported in Ref. [22]. The mesh study is performed for the channel containing the net of spacers in the 60° arrangement. The spatial convergence test employs three mesh sizes: 32 million elements (M1), 48 million elements (M2) and 60 million elements (M3). For three meshes, the profiles of normalized stream-wise velocity component (u/Uave) as a function of the crossflow direction at x/h =8.3 and z/h= 3.9 are shown in Fig. 2a. Fig. 2b and Fig. 2c show profiles of the normalized water flux (vw/(AΔP)) and the normalized concentration (c/c0) along the surface of the top membrane in the span-wise direction, z. Concentration and water flux profiles are obtained at x/h= 8.3. Velocity, concentration and water flux profiles acquired using M2 and M3 meshes differ only slightly (see Fig. 2a–c). This ensures that the spatial convergence is attained with 48 million elements mesh. Results of simulations presented in the current study are obtained by employing M2 mesh. Although, a better spatial resolution can be achieved by refining mesh further, limited computational resources would make the task to be challenging. 4. Results and discussions 4.1. 30° Geometry The iso-surfaces of the stream-wise component of the velocity are shown in Fig. 3a, b and c. Along the iso-surfaces u/Uave = 1.5, the region inside the iso-surfaces u/Uave is greater than 1.5, and the region outside the surfaces u/Uave is lower than 1.5. Iso-surfaces of the normalized ycomponent of the vorticity are illustrated in Fig. 3d, e and f. 1st, 2nd and 3rd rows in Fig. 3 represent iso-surfaces acquired at Re of 100, 400 and 800, respectively. High speed flow is obtained in the middle region of the cell, as illustrated in Fig. 3a for Re = 100. Fluid speed is much higher near the forward stagnation region of the intersection between strands while the backward stagnation region experiences low speed wake flows. Fluid speed becomes much greater in the region between
Fig. 2. (a) Profiles of stream-wise component of the velocity obtained at x/h=8.3 and z/h=3.9, (b) profiles of the normalized water flux through the top membrane obtained at x/h=8.3, and (c) profiles of the normalized concentration obtained at x/h=8.3 along the surface of the top membrane.
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Fig. 3. The iso-surfaces of normalized stream-wise component of the velocity (a, b, c) and normalized y-component of the vorticity (d, e, f). Rows from the top to the bottom denotes isosurfaces at Re = 100, 400 and 800, respectively. The images are acquired in a feed channel containing a mesh of spacers in the 30° arrangement.
Fig. 4. (a, b, c) Contours of the normalized concentration along the surface of the top membrane (left column) and (d, e, f) contours of the normalized water flux through the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 30° arrangement.
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Fig 5. (a, b, c) Contours of Sherwood number along the surface of the top membrane (left column) and (d, e, f) contours of the normalized wall shear stress along the top membrane (right column). Rows from the top to the bottom denotes contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 30° arrangement.
Fig. 6. Iso-surfaces of normalized stream-wise component of the velocity (a, b, c) and normalized y-component of the vorticity (d, e, f). Rows from the top to the bottom denote iso-surfaces at Re = 100, 400 and 800, respectively. The images are acquired in a feed channel containing a mesh of spacers in the 45° arrangement.
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spacers and membranes as Re is increased. High speed flow region in the middle of the cell shrinks, and it extends from the backward stagnation area to the forward stagnation area, as shown in Fig. 3b for Re = 400. The high speed region inside the cell shrinks further while the high speed region between the strands and the membranes grows as Re is increased to 800, as depicted in Fig. 3c. Low level of vorticity is obtained inside the cell at Re= 100, as indicated in Fig. 3d. Uniform distribution of the vorticity is confined to the boundary layers of the strand. This implies that low level of mixing is present inside the cell at low flow rates. The vortices spread to the region inside the cell by extending from the rear stagnation region to the middle region of the cells, as shown in Fig. 3e for Re = 400. The region where high level of vortical activities grows, and the magnitude of the vorticity increases as Re is raised to 800. This is an indication that mixing is strongly enhanced inside the cells as the flow rate is increased. It is anticipated that the presence of the spacers in the feed channel influences the membrane performance and the concentration polarization. Contours of the normalized local concentration (c/c0) and the normalized local water flux (vw/(Δp A)) along the surface of the top membrane are shown in Fig. 4 for Re of 100, 400 and 800. Images on the left and the right columns denote concentration contours and water flux contours, respectively. Images at rows from the top to the bottom denote contours at Re of 100, 400 and 800. Concentration polarization occurs in a repeated pattern along the stream-wise direction. For each flow rate, it occurs in the regions away from the intersection of strands. The concentration polarization region follows similar patterns at all flow rates with a slim alterations at Re= 800. The level of concentration polarization is the highest at Re= 100, and it decreases significantly as Re is increased to 800, as shown in Fig. 4c. The presence of spacers in
the feed channel reduces the magnitude of concentration polarization significantly at all flow rates. Mitigation of concentration polarization is much greater at higher flow rates. This is directly attributed to the mixing in the feed channel induced by spacers. The vorticity field clearly indicates that mixing in the feed channel is much greater at higher flow rates. More than 40% reduction in the maximum concentration along the surface of the membrane is obtained as Re is increased from 100 to 800. The water flux distributions along the surface of membrane follow very similar characteristics as the concentration distributions. The lowest rate of water passage through the membrane is obtained in regions where concentration polarization occurs, as shown in Fig. 4d, e, and f. The water flux increases significantly as the flow rate is increased. It is documented by several investigators that the water flux increases and the concentration polarization decreases as the feed flow rate increases [23,24]. The membrane module performs much more efficiently at higher flow rate. It is important to note that the pressure drop can significantly be higher at higher flow rates. In order to access the membrane performance properly the coefficient of performance including the influence of pressure drop should be calculated and compared for different configurations at different operating conditions. Contours of the local Sherwood number and the normalized local wall shear stress along the surface of the top membrane are shown in Fig. 5 for Re of 100, 400 and 800. Images on the left denote contours of Sherwood number and images on the right denote contours of wall shear stress at Re of 100 (the top row), 400 (the middle row) and 800 (the bottom row). The wall shear stress is normalized by the maximum value of the shear stress for each value of Re. The maximum value of the wall shear stress is 0.7, 3.1 and 7.4 Pa, respectively, for Re of 100, 400 and 800. Regions where Sherwood number assumes low values coincides
Fig. 7. (a, b, c) Contours of the normalized concentration along the surface of the top membrane (left column) and (d, e, f) contours of the normalized water flux through the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 45° arrangement.
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with regions where the concentration polarization occurs, as illustrated in Fig. 4a–c and Fig. 5a–c. The maximum value of Sherwood number is attained in the region above the intersection of strands. That region also coincides with the low concentration regions of the membrane. Sherwood number increases more than four folds as Re is increased from 100 to 800, as depicted in Fig. 5a–c. It is previously documented that fouling potentially occurs in regions of low wall shear stress [22, 25,26]. The low shear region along the membrane coincides with regions of low Sherwood number. It is deducted from these results that regions where concentration polarization occurs are strongly correlated with regions where potential fouling could occur. The intensity of local wall stress increases drastically as Re is increased to 800, implying the probability of occurrence of fouling is much lower at higher flow rates. It is also important to note that the presence of grid of spacers increases the intensity of wall shear stress. Therefore, the occurrence of fouling buildup is less likely in the separation module containing a net of spacers. In fact, it is documented by Park et al. [27] that the spacer arrangement strongly influences the characteristics of the fouling buildup along the surface of the membrane in a desalination module. 4.2. 45° Geometry Fig. 6 shows the iso-surfaces of the normalized stream-wise component of the velocity and the normalized y-component of vorticity in a feed channel containing a net of spacers in the 45° arrangement. The high speed flow is observed in the middle section of the cell and above the strands of spacers at low flow rates. As Re is increased, the high speed flow region in the middle of cell shrinks while the high
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speed flow region above strands grows. The intensity of the vorticity is greater near the forward and the backward stagnation regions of strands at Re = 100. The intensity of vorticity in the middle region of cell increases as Re is increased to 800, as shown in Fig. 6b. Flow structures in the feed channel containing net spacers in the 45° arrangement are similar to those in the feed channel containing a net of spacers in the 30° arrangement. The only noticeable difference is that the high vorticity region in the feed channel with 45° spacer grid is confined to the middle section of the cell. This implies that the mixing in this geometry may not be as effective as in the case for spacer grid with 30°. In this geometry, strands of spacer face the flow more directly, which results in acceleration of fluid toward the center region. That will increase the drag forces exerted by the fluid on the strand of the spacers. Fig. 7 illustrates contours of the normalized salt concentration and the water flux along the surface of the top membrane. The distribution of salt concentration in the geometry with θ = 45° exhibits strikingly different patterns compared to that with θ = 30° at Re = 100, as shown in Fig. 7a and Fig. 4a. Concentration polarization occurs everywhere in the cell except along the centerline and at regions above the strands. This is proving that the mixing is not as effective in this geometry at Re= 100. As Re is increased to 400 and 800, distribution of concentration along the surface of the membrane becomes similar to that with 30° grid. There is a clear indication that enhanced mixing at high flow rates helps reducing the level of concentration polarization, as depicted in Fig. 7b and c. Water flux is lower in the region where concentration polarization occurs. In a similar manner, the water flux distribution is strongly influenced by the spacer arrangement. Bands of low water flux region extend in the stream-wise direction, as depicted in
Fig. 8. (a, b, c) Contours of Sherwood number along the surface of the top membrane (left column) and (d, e, f) contours of the normalized wall shear stress along the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 45° arrangement.
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Fig. 7d–f. The rate at which water passes through the membrane increases drastically as Re is increased from 100 to 800. Contours of the local Sherwood number and the normalized local wall shear stress are illustrated in Fig. 8. The maximum value of the wall shear stress along the surface of the top membrane is 0.9, 4.3 and 10.6 Pa, respectively, for Re = 100 , 400 and 800. The intensity of wall shear stress is greater in this geometry compared to that in the geometry with 30°. Sherwood number overall increases more than five folds as Re is increased from 100 to 800, as shown in Fig. 8a–c. High Sherwood number regions correlate directly with regions of low concentration polarization. Regions of low wall shear stress also directly correlate with regions of high concentration polarization. The probability of occurrence of fouling is greatly reduced as flow rate is increased, as illustrated in Fig. 8. 4.3. 60° Geometry Iso-surfaces of the stream-wise component of the velocity and the ycomponent of the vorticity are plotted in Fig. 9 in a feed channel containing a net of spacers in the 60° arrangement. Iso-surfaces of both velocity and vorticity at Re =100 are similar to those for geometries with 30° and 45°. At higher flow rates a flow transition occurs. Iso-surfaces of the velocity and the vorticity become streaky in the span-wise direction as a manifestation of flow transitions. The flow transition observed in this geometry is very similar to that observed in the feed channel containing arrays of spacers situated perpendicular to primary flows, as documented in Ref. [22] by the present authors. The geometry that was considered in Ref. [22] is similar to the geometry contains a net of spacer in the 90° arrangement, and it is referred as the ladder-type
spacer arrangement. The streaks are not perfectly periodic as in the geometry of ladder-type spacer. The intensity of vorticity and velocity is greater near the middle of cells. Flow field is three-dimensional even at low flow rates unlike the flow structure obtained in the feed channel with ladder type spacers, as depicted in Fig. 9. Fig. 10 shows contours of the local salt concentrations and the local water flux along the surface of the top membrane in the geometry with 60°. At Re =100, high concentration polarization is obtained inside the cell. Low concentration region is right above the strands of spacers and the lowest concentration regions are seen in the region near the intersection of strands. At higher flow rates, high concentration regions become streaky in the span-wise direction, as illustrated in Fig. 10a–c. Streaky patterns are also seen in the contours of water flux at higher flow rates, as shown in Fig. 10f. This is again manifestation of the flow transition observed in this geometry at higher flow rates. Streaks seen in both concentration and water flux distribution along the surface of the membrane are induced by the secondary flows resulted from flow transitions. The concentration polarization diminishes as Re is increased to 800, but the level of reduction is less compare to those in other two geometries. The patterns of the local water flux are inversely proportional to the patterns of concentration distribution. High flux regions coincide with regions of low concentration while low flux regions coincide with regions of high concentration. Sherwood number is nearly uniform along the surface of the membrane at Re = 100 (see Fig. 11a). It is slightly elevated in the regions above the strands of spacers. Sherwood number becomes streaky at Re of 400 and 800, as seen in Fig. 11b and c. Sherwood number increases significantly as Re is increased. The intensity of wall shear stress is immensely larger in the regions above the strands of spacers compared
Fig. 9. Iso-surfaces of normalized stream-wise component of the velocity (a, b, c) and normalized y-component of the vorticity (d, e, f). Rows from the top to the bottom denote iso-surfaces at Re = 100, 400 and 800, respectively. The images are acquired in a feed channel containing a mesh of spacers in the 60° arrangement.
A.E. Anqi et al. / Desalination 388 (2016) 38–49
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Fig. 10. (a, b, c) Contours of the normalized concentration along the surface of the top membrane (left column) and (d, e, f) contours of the normalized water flux through the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 60° arrangement.
to the center region of cells. The streaky patterns in the wall stress distribution is clearly present at Re = 800, as depicted in Fig. 11f. These results demonstrate that fouling could also occur with a streaky pattern in this geometry inside the cells. It is abundantly clear that a grid of spacers in the feed channel creates strong three-dimensional flows. That in turn induces robust momentum mixing. As a result the membrane performance such as the water flux, concentration polarization and the potential fouling buildup is immensely altered. It is also important to note that binary fluid flows studied here could be transient. The effects of such transient flows on the membrane performance could also be significant. Present authors are investigating transient nature of the flows and its
influence on the membrane performance for few selected geometries and flow rates. Results of these simulations will be published in a full paper in the future. 4.4. Coefficient of performance The coefficient of performance, CP, is introduced to compare performance of membrane modules: CP ¼
Sh Shs
13 fs f
ð12Þ
48
A.E. Anqi et al. / Desalination 388 (2016) 38–49
Fig. 11. (a, b, c) Contours of Sherwood number along the surface of the top membrane (left column) and (d, e, f) contours of the normalized wall shear stress along the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 60° arrangement.
Table 2 The average friction factor, the average Sherwood number and the coefficient of performance of all geometries at various flow rates. Channel without spacer
θ = 30°
θ = 45°
θ = 60°
Re
fs
Shs
f
Sh
CP
f
Sh
CP
f
Sh
CP
100 400 800
0.187 0.051 0.027
31 46 57
0.986 0.352 0.235
50 131 215
0.94 1.51 1.85
1.007 0.386 0.274
41 106 201
0.76 1.18 1.64
1.067 0.439 0.321
39 82 155
0.72 0.87 1.20
Here Sh is the Sherwood number averaged along the surface of the membrane, and f is the friction factor averaged over 38 ≤ x/h ≤ 76.7 across the spacer bank. Shs and fs are Sherwood number and the friction factor calculated in the feed channel without spacers. The coefficient of performance, also referred as the merit number, measures membrane mass flux performance for the same pumping power. Membrane module containing three different spacer grids are evaluated at Re of 100, 400 and 800. Table 2 lists the average friction coefficient, the average Sherwood number and the coefficient of performance for each grid at different flow rates. For all geometries, the friction factor decreases rapidly as the flow rate increases. It is also shown that Sherwood number
A.E. Anqi et al. / Desalination 388 (2016) 38–49
increases with increasing flow rates in all channels. As θ increases, the average friction factor increases and the average Sherwood number decreases at all flow rates. The mass flux is greatly improved for modules containing a net of spacers at all flow rate considered in this study. This enhancement comes with a penalty of increasing pressure drop or increasing pumping power. In order to claim that membrane module with a net of spacers is an effective design the merit number should be greater than unity. All membrane modules considered in the study have the merit number less than unity at Re = 100. For Re = 400 the merit number is greater than unity in geometries with 30° and 45°, but it is less than unity for the geometry with 60°. The net of spacers with 30° is the most effective design among all modules studied here at all flow rates. The coefficient of performance for all geometries increases as the flow rate is increased, as listed in Table 2. The merit number or the coefficient of performance discussed here only considers the mass flux in determining the membrane performance. Concentration polarization and characteristics of fouling buildup have to be incorporated in determining the performance characteristics of the membrane modules. It is shown above that all these geometries help in mitigating the concentration polarization and the fouling buildup at all flow rates compared to modules without spacers. 5. Conclusions Simulations have been conducted to characterize three-dimensional multicomponent fluid flows in a feed channel of a reverse osmosis membrane module. The feed channel consists of a net of spacers in different arrangements. Computational fluid dynamics simulations are performed for Re of 100, 400 and 800 in geometries with strand angle of 30°, 45° and 60°. The laminar model is employed to characterize flow structures at Re = 100, while the SST k-ω turbulence model is employed to determine flow structures at Re= 400 and 800. The membrane is treated as a functional surface where the water flux and the concentration gradient are determined from the local pressure and the concentration. The present study illustrates that three-dimensional flows induced by the spacers in the feed channel have profound influence on the membrane performance. The high concentration polarization regions coincide with low flux regions, and these regions also correlate directly with low shear regions where potential fouling buildup occurs. The presence of net of spacers in the feed channel aids in mitigating the concentration polarization and aids in minimizing potential fouling buildup. The membranes with all geometries perform much better at higher flow rates. The grid of spacers in the 30° arrangement offers the most efficient membrane modules at all flow rates considered. The coefficient of performance based on efficient mass transfer indicates that the angle of spacer with 30° is very effective at Re of 400 and 800. This study clearly demonstrates that the spacer arrangement should be an integral part of the optimization process of membrane modules in desalination systems. References [1] S.S. Shenvi, A.M. Isloor, A.F. Ismail, A review on RO membrane technology: developments and challenges, Desalination 368 (2015) 10–26, http://dx.doi.org/10.1016/j. desal.2014.12.042. [2] L. Malaeb, G.M. Ayoub, Reverse osmosis technology for water treatment: state of the art review, Desalination 267 (2011) 1–8, http://dx.doi.org/10.1016/j.desal.2010.09. 001. [3] K.P. Lee, T.C. Arnot, D. Mattia, A review of reverse osmosis membrane materials for desalination—development to date and future potential, J. Membr. Sci. 370 (2011) 1–22, http://dx.doi.org/10.1016/j.memsci.2010.12.036.
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[4] S.K. Karode, A. Kumar, Flow visualization through spacer filled channels by computational fluid dynamics I.: pressure drop and shear rate calculations for flat sheet geometry, J. Membr. Sci. 193 (2001) 69–84, http://dx.doi.org/10.1016/S03767388(01)00494-X. [5] G.A. Fimbres-Weihs, D.E. Wiley, Numerical study of mass transfer in threedimensional spacer-filled narrow channels with steady flow, J. Membr. Sci. 306 (2007) 228–243, http://dx.doi.org/10.1016/j.memsci.2007.08.043. [6] 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, http://dx.doi.org/10.1016/j.memsci.2006.12.032. [7] T. Ishigami, H. Matsuyama, Numerical modeling of concentration polarization in spacer-filled channel with permeation across reverse osmosis membrane, Ind. Eng. Chem. Res. 54 (2015) 1665–1674, http://dx.doi.org/10.1021/ie5039665. [8] C.P. Koutsou, A.J. Karabelas, A novel retentate spacer geometry for improved spiral wound membrane (SWM) module performance, J. Membr. Sci. 488 (2015) 129–142, http://dx.doi.org/10.1016/j.memsci.2015.03.064. [9] S. Ma, L. Song, Numerical study on permeate flux enhancement by spacers in a crossflow reverse osmosis channel, J. Membr. Sci. 284 (2006) 102–109, http://dx. doi.org/10.1016/j.memsci.2006.07.022. [10] A.E. Anqi, N. Alkhamis, A. Oztekin, Numerical simulation of brackish water desalination by a reverse osmosis membrane, Desalination 369 (2015) 156–164, http://dx. doi.org/10.1016/j.desal.2015.05.007. [11] A.E. Anqi, N. Alkhamis, M.F. Alrehili, A. Oztekin, Numerical study of brackish water desalination using reverse osmosis, Proc. IDA World Congr. Desalination Water Reuse, San Diego, 2015. [12] W. Changcharoen, S. Eiamsa-ard, Numerical investigation of turbulent heat transfer in channels with detached rib-arrays, Heat Transf. Asian Res. 40 (2011) 431–447, http://dx.doi.org/10.1002/htj.20357. [13] A. Chaube, P.K. Sahoo, S.C. Solanki, Analysis of heat transfer augmentation and flow characteristics due to rib roughness over absorber plate of a solar air heater, Renew. Energy 31 (2006) 317–331, http://dx.doi.org/10.1016/j.renene.2005.01.012. [14] N. Alkhamis, D.E. Oztekin, A.E. Anqi, A. Alsaiari, A. Oztekin, Numerical study of gas separation using a membrane, Int. J. Heat Mass Transf. 80 (2015) 835–843, http:// dx.doi.org/10.1016/j.ijheatmasstransfer.2014.09.072. [15] N. Alkhamis, A.E. Anqi, A. Oztekin, Computational study of gas separation using a hollow fiber membrane, Int. J. Heat Mass Transf. 89 (2015) 749–759, http://dx.doi. org/10.1016/j.ijheatmasstransfer.2015.05.090. [16] J. Chakraborty, N. Verma, R.P. Chhabra, Wall effects in flow past a circular cylinder in a plane channel: a numerical study, Chem. Eng. Process. Process Intensif. 43 (2004) 1529–1537, http://dx.doi.org/10.1016/j.cep.2004.02.004. [17] N. Kanaris, D. Grigoriadis, S. Kassinos, Three dimensional flow around a circular cylinder confined in a plane channel, Phys. Fluids 23 (2011) 064106, http://dx.doi.org/ 10.1063/1.3599703. [18] F. Rehimi, F. Aloui, S.B. Nasrallah, L. Doubliez, J. Legrand, Experimental investigation of a confined flow downstream of a circular cylinder centred between two parallel walls, J. Fluids Struct. 24 (2008) 855–882, http://dx.doi.org/10.1016/j.jfluidstructs. 2007.12.011. [19] M.D. Griffith, J. Leontini, M.C. Thompson, K. Hourigan, Vortex shedding and threedimensional behaviour of flow past a cylinder confined in a channel, J. Fluids Struct. 27 (2011) 855–860, http://dx.doi.org/10.1016/j.jfluidstructs.2011.02.007. [20] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (1994) 1598–1605. [21] J. Wijmans, R. Baker, The solution-diffusion model: a review, J. Membr. Sci. 107 (1995) 1–21. [22] A.E. Anqi, A. Oztekin, N. Alkhamis, Steady three dimensional flow and mass transfer analyses for brackish water desalination by reverse osmosis membranes, Int. J. Heat Mass Transf. (2015) (under review). [23] J. Schwinge, D.E. Wiley, A.G. Fane, R. Guenther, Characterization of a zigzag spacer for ultrafiltration, J. Membr. Sci. 172 (2000) 19–31. [24] S. Sablani, M. Goosen, R. Al-Belushi, M. Wilf, Concentration polarization in ultrafiltration and reverse osmosis: a critical review, Desalination 141 (2001) 269–289, http://dx.doi.org/10.1016/S0011-9164(01)85005-0. [25] C.P. Koutsou, S.G. Yiantsios, A.J. Karabelas, A.J. Karabelas, Membrane module performance optimization using CFD simulation of flow through narrow channels with spacers, Proc. IDA World Congr. Desalination Water Reuse 2007, pp. 21–26. [26] A.I. Radu, M.S.H. van Steen, J.S. Vrouwenvelder, M.C.M. van Loosdrecht, C. 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Contents lists available at ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Computational study of desalination by reverse osmosis — Three-dimensional analyses Ali E. Anqi a,b, Nawaf Alkhamis c, Alparslan Oztekin a,⁎ a b c
Lehigh University, Dept. of Mechanical Engineering & Mechanics, USA King Khalid University, Dept. of Mechanical Engineering, Saudi Arabia King Abdulaziz University, Dept. of Mechanical Engineering, Saudi Arabia
H I G H L I G H T S • • • • •
Characterization of three-dimensional binary fluid flows in a desalination module Membrane performance is enhanced by the presence of spacers. Spacers help in mitigating concentration polarization and fouling buildup. Spacers have more favorable influence on membrane performance at higher flow rates. The net of spacers in the 30° arrangement is the most efficient one.
a r t i c l e
i n f o
Article history: Received 10 January 2016 Received in revised form 20 March 2016 Accepted 24 March 2016 Available online xxxx Keywords: Membrane performance Reverse osmosis Desalination Net of spacers Concentration polarization Fouling buildup
a b s t r a c t A computational study has been conducted to examine three-dimensional steady multicomponent fluid flows in the reverse osmosis membrane module. The module contains a net of spacers. The SST k-ω turbulence model is employed to simulate flow and concentration fields at Re=400 and 800, while the laminar model is employed to characterize flow and concentration fields at Re = 100. Spacer grids with 30°, 45° and 60° are considered as three different geometries. The membrane is treated as a functional surface where water flux, concentration and local pressure are coupled. The nature of concentration polarization in each membrane module is determined. Characteristics of potential fouling buildup are determined from the wall shear stress distribution. Correlations between potential fouling regions and the concentration distribution are presented. The coefficient of performance for each membrane module is determined at all flow rates considered. It has been illustrated that all membrane modules perform better at higher flow rates. The membrane module containing the net of spacers in the 30° arrangement is shown to be the most efficient membrane module. This study proves that the configuration of spacers is an important optimization parameter for the design of reverse osmosis membrane modules. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Reverse Osmosis (RO) is a method which is used around the globe to produce fresh water. This technology is typically used to desalinate seawater or brackish water. Reverse osmosis is capable of producing fresh water by applying high pressure in a feed channel surrounded by a semi-permeable membrane. The applied pressure has to be greater than the osmotic pressure of the solution. The fresh water production rate is dependent on the salt concentration in the feed water and on membrane properties such as the selectivity and the permeability. The greater the value of the selectivity and the permeability, the higher the probability of the occurrence of the salt concentration polarization
⁎ Corresponding author. E-mail address: [email protected] (A. Oztekin).
http://dx.doi.org/10.1016/j.desal.2016.03.017 0011-9164/© 2016 Elsevier B.V. All rights reserved.
along the membrane surface. This is due to the fact that the water permeation through the membrane and the salt accumulation along the membrane surface increase as the selectivity and the permeability of the membrane increase. The occurrence of concentration polarization along the surface of the membrane has two major undesirable effects on the membrane performance. One is the increase of the osmotic pressure as the salt concentration rises so the applied pressure must be increased to keep the water production rate the same. The other is the promotion of a scaling and a fouling along the surface of the membrane at the region where the salt concentration polarization occurs [1–3]. In spiral wound membranes, spacers are placed in the feed channel to maintain the gap between the membranes and to promote momentum mixing. Several investigators studied the influence of spacers on the membrane performance for desalination processes. Karode and Kumar [4] conducted three-dimensional flow simulations and experiments to
A.E. Anqi et al. / Desalination 388 (2016) 38–49
Nomenclature (u ,v , w) Δp hm vw CD h F1 , F2 A Uave D a1 Re c0 Sh cb Sc cp d cw k f p fx CP
components of velocity [m/s] transmembrane pressure difference [Pa] mass transfer coefficient [m/s] water flux [m/s] drag coefficient channel height [m] blending functions membrane permeability [m/s Pa] average inlet velocity [m/s] diffusion coefficient [m2/s] turbulent model parameter Reynolds number, Re =2hUave/ν inlet concentration [kg/m3] Sherwood number, Sh= 2h hm/D bulk concentration [kg/m3] Schmidt number, Sc= ν/D production concentration [kg/m3] spacer diameter [m] membrane salt concentration [kg/m3] turbulent kinetic energy [J/kg] pressure coefficient pressure [Pa] drag force [N] coefficient of performance
Greek letters eddy viscosity [Pa s] μt μ dynamic viscosity [Pa s] kinematic eddy viscosity [m2/s] νt ν kinematic viscosity [m2/s] turbulent model parameter σk1 ρ density [kg/m3] σω ,σω2 turbulent model parameters ω specific dissipation rate [1/s] β, β⁎ turbulent model parameters κ osmotic coefficient [kPa m3/kg] γ turbulent model parameter τ normalized wall shear stress θ strand angle [°] Subscripts i and j index notation w properties along the membrane surface
examine flow characteristics in a feed channel containing different types of commercial spacers. Karode and Kumar [4] have concluded that the turbulent flow structures, the degree of pressure drops and the characteristics of the wall shear stress were strongly influenced by the spacer's types and arrangements. Fimebers-Weihs and Wiley [5] performed steady three-dimensional flows and mass transfer simulations. The membrane was treated as an impermeable wall, and the mass transfer coefficient was determined from an empirical relation. They reported that the pressure drop and the mass transfer coefficient are influenced by the spacer configurations and by the feed flow rate. Koutsou et al. [6] conducted a direct numerical simulation to investigate the flow characteristics inside the feed channel bounded by impermeable walls. They reported that the flow inside the feed channel containing spacers becomes unsteady for values of Reynolds number greater than about 40. Their computational study did not consider the mass transfer.
39
Recently, Ishigami and Matsuyama [7] conducted flow and mass transfer simulations in the feed channel containing three-unit cells of meshed spacers. They estimated the salt concentration along the surface of the membrane using an exponential relation. The membrane was treated as an impermeable wall in their work, so the water flux was calculated empirically. Koutsou and Karabelas [8] introduced a novel spacer design by placing spheres at the intersection of the spacer strands. Since spheres touch both membranes, the contact zones between the spacer strands and the membrane is minimized. Numerical simulations and experimental measurements by Koutsou and Karabelas demonstrated that the reduction of contact zones between the spacer and membrane improved the membrane performance and reduced the potential fouling zones. Ma and Song [9] and the present authors [10,11] conducted two-dimensional flow and mass transfer simulations in the feed channel containing spacers. The membranes in these studies were modeled as a functional surface where the mass flux and the concentration are coupled together. Three-dimensional flow and mass transfer simulations in water desalination feed channels containing a net of spacers have not been conducted using an accurate membrane flux model. The present authors perform a computational study to characterize steady three-dimensional velocity and concentration fields in the feed channel containing a net of spacers. The membrane performance is determined for various values of flow rates in a reverse osmosis membrane module with different configurations of mesh of spacers. An accurate membrane flux model is employed to estimate the water permeation through the membrane and the salt accumulation along the surface of the membrane for characterization of concentration polarization. The salt concentration, the pressure and the water flux through the membrane are coupled at the membrane surface. The local Sherwood number is calculated directly from the velocity and the concentration field. Concentration and water flux contours along the surface of the membrane surface are determined to access membrane performance and the concentration polarization. The wall shear stress is calculated to predict regions where the fouling can potentially occur. Moreover, the coefficient of performance for different spacers is calculated at the same pumping power to determine which separation module performs better. This study will aid in design and optimization of reverse osmosis desalination modules containing net type of spacers. 2. Mathematical model The top view of the computational domain is illustrated in Fig. 1. The top and the bottom surfaces represent the reverse osmosis membranes. The gap between the membranes is h = 1.5 mm. Eleven repeated cells are placed along the stream-wise direction in the mid-plane of the feed channel to form a mesh of spacers. The spacer strands diameter (d) is fixed at 1/2 h, and the distance between two successive intersections of strands in the stream-wise direction is also fixed at 6.7 h, as depicted in Fig. 1. The angle between the strands and the stream-wise direction, θ, is varied — 30° , 45° and 60° — to create different geometries of spacers. The cells are symmetrically placed at the mid-plane with their centers along the stream-wise direction, as illustrated in Fig. 1. The length of the inlet and the outlet region is 5 h and 17.67 h, respectively, in order to minimize the effects of the imposed boundary conditions on the velocity and the concentration fields. Reynolds number (Re) is defined as Re = (2h Uave)/ν. Simulations are conducted for values of Re 100 , 400 and 800 for each geometry. Here Uave is the average velocity at the inlet, and ν is the kinematic viscosity (ν = μ/ρ) of the binary solution of salt and water. Velocity and pressure fields in the feed channel are governed by the continuity and momentum equation, and the concentration field is governed by the mass transport equation. The binary solution is assumed to be incompressible with density, ρ, and viscosity, μ. The diffusion coefficient, D, is assumed to be constant. The
40
A.E. Anqi et al. / Desalination 388 (2016) 38–49
Fig. 1. Schematic of the computational domain. Top view of the feed channel.
equations governing the fluid motions are the Navier–Stokes equations: ∂ui ¼ 0; ∂xi 2 ∂u 1 ∂p ∂ ui þν : uj i ¼ ∂x j ρ ∂xi ∂x j ∂x j
ð1Þ ð2Þ
The equation governing the mass transport in the feed channel 2
uj
∂c ∂ c ¼D : ∂x j ∂x j ∂x j
ð3Þ
The SST k-ω turbulence mass transport equation is given by: ∂c ∂ uj ¼ ∂x j ∂x j
! μt ∂c Dþ ρ Sct ∂x j
where Sct is the turbulence Schmidt number. The membrane is treated as a functional surface where the local water flux, local salt concentration, and local pressure are coupled together. The solution-diffusion model is used to determine the local water flux and local salt concentration gradient along the surface of the membrane [21,22]. The boundary conditions at the membrane surface are: @y ¼ 0 and h:
Here i and j are the summation indices. x1 = x is the stream-wise direction, x2 = y is the cross-flow direction, and x3 = z is the span-wise direction. u1 = u is the stream-wise component, u2 = v is the cross-flow component, and u3 = w is the span-wise component of the velocity. c is the salt concentration of the binary solution. It is well documented that the flow, temperature and concentration fields in channels containing cylinders are predicted accurately by the shear stress transport (SST) k-ω turbulence model [12–15]. It is also well-documented that flows past arrays of spacers confined in channels have turbulent-like characteristics for Re ≥ 400 [16–19]. The SST k-ω turbulence model is employed by the present computational study to characterize three-dimensional steady turbulent flow structures in the feed channel for Re of 400 and 800. The SST k-ω turbulence momentum transport equation is given by:
uj
∂ui 1 ∂p 1 ∂ ¼ þ ρ ∂xi ρ ∂x j ∂x j
ðμ þ μ t Þ
∂ui ∂x j
! ð4Þ
where μ is the dynamic viscosity and μt is the eddy viscosity, μ t ¼ ρ a1 k maxða1 ω;Ω F 2 Þ.
The equations governing the turbulence kinetic energy, k,
and the specific dissipation rate, ω, are:
ui
∂ðρkÞ ∂u ∂ ∂k ¼ τij i −β ρωk þ ½ðμ þ σ k μ t Þ ; ∂xi ∂x j ∂x j ∂x j
" # ∂ðρωÞ γ ∂ui ∂ ∂ω 2 ðμ þ σ ω μ t Þ ui ¼ τij βρω þ ν t ∂x j ∂xi ∂x j ∂x j 1 ∂k ∂ω þ 2ρð1 F 1 Þσ ω2 ω ∂x j ∂x j
ð5Þ
ð6Þ
where Ω is the vorticity magnitude, a1, β , β⁎, σk, σω, σω2 and γ are closure coefficients, and F1 , F2 are the blending functions. Detailed description of the model can be found in Ref. [20].
ð7Þ
u¼0
;
vw ¼ A Δp−κ cw −cp ∂c D ¼ vw cw −cp ∂y
9 = ; ; ð8Þ
where vw is the local water flux through the membrane, A is the water permeability of the membrane, Δp is the transmembrane pressure difference, κ is the osmotic coefficient, cw is the salt concentration at the membrane surface, and cp is the salt concentration in the production channel. The local water flux at the membrane surface is normalized as vw/(Δ p A). The salt passage through the membrane is neglected, and 100% salt rejection is imposed. At the inlet, the profile of the stream-wise component of the velocity is considered to be parabolic in the cross-flow direction,u = 6Uave[y/h- (y/h)2], while it is assumed to be uniform in the span-wise direction, z. The salt concentration at the inlet is assumed to be constant c0 = 4000 ppm. The inlet concentration selected here is in the range of typical brackish water salinity. For high feed water salinity such as seawater, it is anticipated that the salt concentration polarization along the membrane surface in the production side will affect the membrane performance. Therefore, velocity and concentration field in both feed and production channels need to be characterized to evaluate the membrane performance for seawater desalination processes. The type and the arrangement of spacers providing better membrane performance in seawater desalination modules can be very different than those in brackish water desalination module considered in the present study. No-penetration and no-slip velocity boundary conditions and zero concentration gradient are imposed along the surface of the spacers. At the outlet, zero pressure and constant concentration gradient are applied, and at the side walls periodic conditions on both the velocity and the concentration fields are imposed. The results are presented in various dimensionless flow quantities. The friction coefficient is evaluated from:
f ¼
dp 2h dx ð1=2 Þ ρU 2ave
ð9Þ
A.E. Anqi et al. / Desalination 388 (2016) 38–49 Table 1 Physical parameters used in the simulations. Parameter
Value
Osmotic pressure coefficient: κ Density: ρ Dynamic viscosity: μ Diffusivity: D Schmidt number: Sc Permeability: A Transmembrane pressure: Δp
75 kPa m3/kg 1000 kg/m3 10−3 Pa s 1.5×10−9 m2/s 667 2.3×10−11 m/(s Pa) 1.25 MPa
where dp is the pressure gradient. Sherwood number, Sh, is calculated as: dx
Sh ¼
D
ð2hÞhm D
; hm ¼
∂c ∂y y¼h
ðcb cw Þ
ð10Þ
here hm is the local mass transfer coefficient and cb is the bulk concentration. The drag coefficient, CD, is determined from: CD ¼
2f x ρU 2ave As
;
ð11Þ
where fx is the drag force exerted on the spacer, and As is the projected area of the spacer in the direction perpendicular to the stream-wise direction. 3. Numerical simulations, convergence and validation The commercial software, CFX 14.5, is employed to conduct the numerical simulations. The equations are discretized using the finite volume approach, and the velocity and pressure fields are fully coupled. The boundary conditions at the inlet and along the surface of the membrane are implemented by using CEL expression language. The osmotic pressure coefficient is set to κ = 75 kPa m3/kg. The physical properties of the solution in the feed channel are assumed to be constant. The density is ρ= 1000 kg/m3, and the dynamic viscosity is μ = 10-3 Pa s, the diffusion coefficient is D = 1.5×10-9 m2/s, and the Schmidt number is Sc= ν/D = 667. The membrane considered here for brackish water desalination is a high permeability membrane, A = 2.3 × 10-11 m/(s Pa) [9]. The membrane permeability has strong influence on the membrane flux performance as shown in Eq. (8). It has also strong influence on the concentration polarization since there is more salt accumulation along the surface of the membrane for higher water permeation. The transmembrane pressure is selected to be Δ p = 1.25 MPa. The increase of the feed pressure increases the transmembrane pressure, which in turn increases the fresh water production through the membrane. It is also important to note that the operational cost increases as the feed pressure is increased. In order to calculate the coefficient of performance, CP, for each spacer geometry, numerical simulations are conducted in a feed
41
channel without spacers by using the laminar flow model. Membrane parameters and the physical properties of the binary solution are summarized in Table 1. In Ref. [22], the present authors demonstrated the validation of the turbulence model and the numerical method used in the current computational study. Anqi et al. [22] conducted simulations for flows past a cylinder confined in a channel for a blockage ratio of 0.5. They reported CD = 4.482 for two-dimensional flows and CD = 3.995 for threedimensional flows. The drag coefficient reported by Chakraborty et al. [16] (CD = 4.995) for two-dimensional flows past a cylinder agrees well with that documented by the present authors. That helps validating the turbulence model and the numerical method. This method was successfully employed by the present authors to study separation processes using membranes [10,14,15,22]. The present authors also validated the membrane flux model [10] by comparing the water flux and the concentration distribution along the surface of the membrane against results documented by Ma and Song [9], as reported in Ref. [22]. The mesh study is performed for the channel containing the net of spacers in the 60° arrangement. The spatial convergence test employs three mesh sizes: 32 million elements (M1), 48 million elements (M2) and 60 million elements (M3). For three meshes, the profiles of normalized stream-wise velocity component (u/Uave) as a function of the crossflow direction at x/h =8.3 and z/h= 3.9 are shown in Fig. 2a. Fig. 2b and Fig. 2c show profiles of the normalized water flux (vw/(AΔP)) and the normalized concentration (c/c0) along the surface of the top membrane in the span-wise direction, z. Concentration and water flux profiles are obtained at x/h= 8.3. Velocity, concentration and water flux profiles acquired using M2 and M3 meshes differ only slightly (see Fig. 2a–c). This ensures that the spatial convergence is attained with 48 million elements mesh. Results of simulations presented in the current study are obtained by employing M2 mesh. Although, a better spatial resolution can be achieved by refining mesh further, limited computational resources would make the task to be challenging. 4. Results and discussions 4.1. 30° Geometry The iso-surfaces of the stream-wise component of the velocity are shown in Fig. 3a, b and c. Along the iso-surfaces u/Uave = 1.5, the region inside the iso-surfaces u/Uave is greater than 1.5, and the region outside the surfaces u/Uave is lower than 1.5. Iso-surfaces of the normalized ycomponent of the vorticity are illustrated in Fig. 3d, e and f. 1st, 2nd and 3rd rows in Fig. 3 represent iso-surfaces acquired at Re of 100, 400 and 800, respectively. High speed flow is obtained in the middle region of the cell, as illustrated in Fig. 3a for Re = 100. Fluid speed is much higher near the forward stagnation region of the intersection between strands while the backward stagnation region experiences low speed wake flows. Fluid speed becomes much greater in the region between
Fig. 2. (a) Profiles of stream-wise component of the velocity obtained at x/h=8.3 and z/h=3.9, (b) profiles of the normalized water flux through the top membrane obtained at x/h=8.3, and (c) profiles of the normalized concentration obtained at x/h=8.3 along the surface of the top membrane.
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Fig. 3. The iso-surfaces of normalized stream-wise component of the velocity (a, b, c) and normalized y-component of the vorticity (d, e, f). Rows from the top to the bottom denotes isosurfaces at Re = 100, 400 and 800, respectively. The images are acquired in a feed channel containing a mesh of spacers in the 30° arrangement.
Fig. 4. (a, b, c) Contours of the normalized concentration along the surface of the top membrane (left column) and (d, e, f) contours of the normalized water flux through the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 30° arrangement.
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Fig 5. (a, b, c) Contours of Sherwood number along the surface of the top membrane (left column) and (d, e, f) contours of the normalized wall shear stress along the top membrane (right column). Rows from the top to the bottom denotes contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 30° arrangement.
Fig. 6. Iso-surfaces of normalized stream-wise component of the velocity (a, b, c) and normalized y-component of the vorticity (d, e, f). Rows from the top to the bottom denote iso-surfaces at Re = 100, 400 and 800, respectively. The images are acquired in a feed channel containing a mesh of spacers in the 45° arrangement.
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spacers and membranes as Re is increased. High speed flow region in the middle of the cell shrinks, and it extends from the backward stagnation area to the forward stagnation area, as shown in Fig. 3b for Re = 400. The high speed region inside the cell shrinks further while the high speed region between the strands and the membranes grows as Re is increased to 800, as depicted in Fig. 3c. Low level of vorticity is obtained inside the cell at Re= 100, as indicated in Fig. 3d. Uniform distribution of the vorticity is confined to the boundary layers of the strand. This implies that low level of mixing is present inside the cell at low flow rates. The vortices spread to the region inside the cell by extending from the rear stagnation region to the middle region of the cells, as shown in Fig. 3e for Re = 400. The region where high level of vortical activities grows, and the magnitude of the vorticity increases as Re is raised to 800. This is an indication that mixing is strongly enhanced inside the cells as the flow rate is increased. It is anticipated that the presence of the spacers in the feed channel influences the membrane performance and the concentration polarization. Contours of the normalized local concentration (c/c0) and the normalized local water flux (vw/(Δp A)) along the surface of the top membrane are shown in Fig. 4 for Re of 100, 400 and 800. Images on the left and the right columns denote concentration contours and water flux contours, respectively. Images at rows from the top to the bottom denote contours at Re of 100, 400 and 800. Concentration polarization occurs in a repeated pattern along the stream-wise direction. For each flow rate, it occurs in the regions away from the intersection of strands. The concentration polarization region follows similar patterns at all flow rates with a slim alterations at Re= 800. The level of concentration polarization is the highest at Re= 100, and it decreases significantly as Re is increased to 800, as shown in Fig. 4c. The presence of spacers in
the feed channel reduces the magnitude of concentration polarization significantly at all flow rates. Mitigation of concentration polarization is much greater at higher flow rates. This is directly attributed to the mixing in the feed channel induced by spacers. The vorticity field clearly indicates that mixing in the feed channel is much greater at higher flow rates. More than 40% reduction in the maximum concentration along the surface of the membrane is obtained as Re is increased from 100 to 800. The water flux distributions along the surface of membrane follow very similar characteristics as the concentration distributions. The lowest rate of water passage through the membrane is obtained in regions where concentration polarization occurs, as shown in Fig. 4d, e, and f. The water flux increases significantly as the flow rate is increased. It is documented by several investigators that the water flux increases and the concentration polarization decreases as the feed flow rate increases [23,24]. The membrane module performs much more efficiently at higher flow rate. It is important to note that the pressure drop can significantly be higher at higher flow rates. In order to access the membrane performance properly the coefficient of performance including the influence of pressure drop should be calculated and compared for different configurations at different operating conditions. Contours of the local Sherwood number and the normalized local wall shear stress along the surface of the top membrane are shown in Fig. 5 for Re of 100, 400 and 800. Images on the left denote contours of Sherwood number and images on the right denote contours of wall shear stress at Re of 100 (the top row), 400 (the middle row) and 800 (the bottom row). The wall shear stress is normalized by the maximum value of the shear stress for each value of Re. The maximum value of the wall shear stress is 0.7, 3.1 and 7.4 Pa, respectively, for Re of 100, 400 and 800. Regions where Sherwood number assumes low values coincides
Fig. 7. (a, b, c) Contours of the normalized concentration along the surface of the top membrane (left column) and (d, e, f) contours of the normalized water flux through the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 45° arrangement.
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with regions where the concentration polarization occurs, as illustrated in Fig. 4a–c and Fig. 5a–c. The maximum value of Sherwood number is attained in the region above the intersection of strands. That region also coincides with the low concentration regions of the membrane. Sherwood number increases more than four folds as Re is increased from 100 to 800, as depicted in Fig. 5a–c. It is previously documented that fouling potentially occurs in regions of low wall shear stress [22, 25,26]. The low shear region along the membrane coincides with regions of low Sherwood number. It is deducted from these results that regions where concentration polarization occurs are strongly correlated with regions where potential fouling could occur. The intensity of local wall stress increases drastically as Re is increased to 800, implying the probability of occurrence of fouling is much lower at higher flow rates. It is also important to note that the presence of grid of spacers increases the intensity of wall shear stress. Therefore, the occurrence of fouling buildup is less likely in the separation module containing a net of spacers. In fact, it is documented by Park et al. [27] that the spacer arrangement strongly influences the characteristics of the fouling buildup along the surface of the membrane in a desalination module. 4.2. 45° Geometry Fig. 6 shows the iso-surfaces of the normalized stream-wise component of the velocity and the normalized y-component of vorticity in a feed channel containing a net of spacers in the 45° arrangement. The high speed flow is observed in the middle section of the cell and above the strands of spacers at low flow rates. As Re is increased, the high speed flow region in the middle of cell shrinks while the high
45
speed flow region above strands grows. The intensity of the vorticity is greater near the forward and the backward stagnation regions of strands at Re = 100. The intensity of vorticity in the middle region of cell increases as Re is increased to 800, as shown in Fig. 6b. Flow structures in the feed channel containing net spacers in the 45° arrangement are similar to those in the feed channel containing a net of spacers in the 30° arrangement. The only noticeable difference is that the high vorticity region in the feed channel with 45° spacer grid is confined to the middle section of the cell. This implies that the mixing in this geometry may not be as effective as in the case for spacer grid with 30°. In this geometry, strands of spacer face the flow more directly, which results in acceleration of fluid toward the center region. That will increase the drag forces exerted by the fluid on the strand of the spacers. Fig. 7 illustrates contours of the normalized salt concentration and the water flux along the surface of the top membrane. The distribution of salt concentration in the geometry with θ = 45° exhibits strikingly different patterns compared to that with θ = 30° at Re = 100, as shown in Fig. 7a and Fig. 4a. Concentration polarization occurs everywhere in the cell except along the centerline and at regions above the strands. This is proving that the mixing is not as effective in this geometry at Re= 100. As Re is increased to 400 and 800, distribution of concentration along the surface of the membrane becomes similar to that with 30° grid. There is a clear indication that enhanced mixing at high flow rates helps reducing the level of concentration polarization, as depicted in Fig. 7b and c. Water flux is lower in the region where concentration polarization occurs. In a similar manner, the water flux distribution is strongly influenced by the spacer arrangement. Bands of low water flux region extend in the stream-wise direction, as depicted in
Fig. 8. (a, b, c) Contours of Sherwood number along the surface of the top membrane (left column) and (d, e, f) contours of the normalized wall shear stress along the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 45° arrangement.
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Fig. 7d–f. The rate at which water passes through the membrane increases drastically as Re is increased from 100 to 800. Contours of the local Sherwood number and the normalized local wall shear stress are illustrated in Fig. 8. The maximum value of the wall shear stress along the surface of the top membrane is 0.9, 4.3 and 10.6 Pa, respectively, for Re = 100 , 400 and 800. The intensity of wall shear stress is greater in this geometry compared to that in the geometry with 30°. Sherwood number overall increases more than five folds as Re is increased from 100 to 800, as shown in Fig. 8a–c. High Sherwood number regions correlate directly with regions of low concentration polarization. Regions of low wall shear stress also directly correlate with regions of high concentration polarization. The probability of occurrence of fouling is greatly reduced as flow rate is increased, as illustrated in Fig. 8. 4.3. 60° Geometry Iso-surfaces of the stream-wise component of the velocity and the ycomponent of the vorticity are plotted in Fig. 9 in a feed channel containing a net of spacers in the 60° arrangement. Iso-surfaces of both velocity and vorticity at Re =100 are similar to those for geometries with 30° and 45°. At higher flow rates a flow transition occurs. Iso-surfaces of the velocity and the vorticity become streaky in the span-wise direction as a manifestation of flow transitions. The flow transition observed in this geometry is very similar to that observed in the feed channel containing arrays of spacers situated perpendicular to primary flows, as documented in Ref. [22] by the present authors. The geometry that was considered in Ref. [22] is similar to the geometry contains a net of spacer in the 90° arrangement, and it is referred as the ladder-type
spacer arrangement. The streaks are not perfectly periodic as in the geometry of ladder-type spacer. The intensity of vorticity and velocity is greater near the middle of cells. Flow field is three-dimensional even at low flow rates unlike the flow structure obtained in the feed channel with ladder type spacers, as depicted in Fig. 9. Fig. 10 shows contours of the local salt concentrations and the local water flux along the surface of the top membrane in the geometry with 60°. At Re =100, high concentration polarization is obtained inside the cell. Low concentration region is right above the strands of spacers and the lowest concentration regions are seen in the region near the intersection of strands. At higher flow rates, high concentration regions become streaky in the span-wise direction, as illustrated in Fig. 10a–c. Streaky patterns are also seen in the contours of water flux at higher flow rates, as shown in Fig. 10f. This is again manifestation of the flow transition observed in this geometry at higher flow rates. Streaks seen in both concentration and water flux distribution along the surface of the membrane are induced by the secondary flows resulted from flow transitions. The concentration polarization diminishes as Re is increased to 800, but the level of reduction is less compare to those in other two geometries. The patterns of the local water flux are inversely proportional to the patterns of concentration distribution. High flux regions coincide with regions of low concentration while low flux regions coincide with regions of high concentration. Sherwood number is nearly uniform along the surface of the membrane at Re = 100 (see Fig. 11a). It is slightly elevated in the regions above the strands of spacers. Sherwood number becomes streaky at Re of 400 and 800, as seen in Fig. 11b and c. Sherwood number increases significantly as Re is increased. The intensity of wall shear stress is immensely larger in the regions above the strands of spacers compared
Fig. 9. Iso-surfaces of normalized stream-wise component of the velocity (a, b, c) and normalized y-component of the vorticity (d, e, f). Rows from the top to the bottom denote iso-surfaces at Re = 100, 400 and 800, respectively. The images are acquired in a feed channel containing a mesh of spacers in the 60° arrangement.
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Fig. 10. (a, b, c) Contours of the normalized concentration along the surface of the top membrane (left column) and (d, e, f) contours of the normalized water flux through the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 60° arrangement.
to the center region of cells. The streaky patterns in the wall stress distribution is clearly present at Re = 800, as depicted in Fig. 11f. These results demonstrate that fouling could also occur with a streaky pattern in this geometry inside the cells. It is abundantly clear that a grid of spacers in the feed channel creates strong three-dimensional flows. That in turn induces robust momentum mixing. As a result the membrane performance such as the water flux, concentration polarization and the potential fouling buildup is immensely altered. It is also important to note that binary fluid flows studied here could be transient. The effects of such transient flows on the membrane performance could also be significant. Present authors are investigating transient nature of the flows and its
influence on the membrane performance for few selected geometries and flow rates. Results of these simulations will be published in a full paper in the future. 4.4. Coefficient of performance The coefficient of performance, CP, is introduced to compare performance of membrane modules: CP ¼
Sh Shs
13 fs f
ð12Þ
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Fig. 11. (a, b, c) Contours of Sherwood number along the surface of the top membrane (left column) and (d, e, f) contours of the normalized wall shear stress along the top membrane (right column). Rows from the top to the bottom denote contours at Re = 100, 400 and 800, respectively. The contours are determined in a feed channel containing a mesh of spacers in the 60° arrangement.
Table 2 The average friction factor, the average Sherwood number and the coefficient of performance of all geometries at various flow rates. Channel without spacer
θ = 30°
θ = 45°
θ = 60°
Re
fs
Shs
f
Sh
CP
f
Sh
CP
f
Sh
CP
100 400 800
0.187 0.051 0.027
31 46 57
0.986 0.352 0.235
50 131 215
0.94 1.51 1.85
1.007 0.386 0.274
41 106 201
0.76 1.18 1.64
1.067 0.439 0.321
39 82 155
0.72 0.87 1.20
Here Sh is the Sherwood number averaged along the surface of the membrane, and f is the friction factor averaged over 38 ≤ x/h ≤ 76.7 across the spacer bank. Shs and fs are Sherwood number and the friction factor calculated in the feed channel without spacers. The coefficient of performance, also referred as the merit number, measures membrane mass flux performance for the same pumping power. Membrane module containing three different spacer grids are evaluated at Re of 100, 400 and 800. Table 2 lists the average friction coefficient, the average Sherwood number and the coefficient of performance for each grid at different flow rates. For all geometries, the friction factor decreases rapidly as the flow rate increases. It is also shown that Sherwood number
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increases with increasing flow rates in all channels. As θ increases, the average friction factor increases and the average Sherwood number decreases at all flow rates. The mass flux is greatly improved for modules containing a net of spacers at all flow rate considered in this study. This enhancement comes with a penalty of increasing pressure drop or increasing pumping power. In order to claim that membrane module with a net of spacers is an effective design the merit number should be greater than unity. All membrane modules considered in the study have the merit number less than unity at Re = 100. For Re = 400 the merit number is greater than unity in geometries with 30° and 45°, but it is less than unity for the geometry with 60°. The net of spacers with 30° is the most effective design among all modules studied here at all flow rates. The coefficient of performance for all geometries increases as the flow rate is increased, as listed in Table 2. The merit number or the coefficient of performance discussed here only considers the mass flux in determining the membrane performance. Concentration polarization and characteristics of fouling buildup have to be incorporated in determining the performance characteristics of the membrane modules. It is shown above that all these geometries help in mitigating the concentration polarization and the fouling buildup at all flow rates compared to modules without spacers. 5. Conclusions Simulations have been conducted to characterize three-dimensional multicomponent fluid flows in a feed channel of a reverse osmosis membrane module. The feed channel consists of a net of spacers in different arrangements. Computational fluid dynamics simulations are performed for Re of 100, 400 and 800 in geometries with strand angle of 30°, 45° and 60°. The laminar model is employed to characterize flow structures at Re = 100, while the SST k-ω turbulence model is employed to determine flow structures at Re= 400 and 800. The membrane is treated as a functional surface where the water flux and the concentration gradient are determined from the local pressure and the concentration. The present study illustrates that three-dimensional flows induced by the spacers in the feed channel have profound influence on the membrane performance. The high concentration polarization regions coincide with low flux regions, and these regions also correlate directly with low shear regions where potential fouling buildup occurs. The presence of net of spacers in the feed channel aids in mitigating the concentration polarization and aids in minimizing potential fouling buildup. The membranes with all geometries perform much better at higher flow rates. The grid of spacers in the 30° arrangement offers the most efficient membrane modules at all flow rates considered. The coefficient of performance based on efficient mass transfer indicates that the angle of spacer with 30° is very effective at Re of 400 and 800. This study clearly demonstrates that the spacer arrangement should be an integral part of the optimization process of membrane modules in desalination systems. References [1] S.S. Shenvi, A.M. Isloor, A.F. Ismail, A review on RO membrane technology: developments and challenges, Desalination 368 (2015) 10–26, http://dx.doi.org/10.1016/j. desal.2014.12.042. [2] L. Malaeb, G.M. Ayoub, Reverse osmosis technology for water treatment: state of the art review, Desalination 267 (2011) 1–8, http://dx.doi.org/10.1016/j.desal.2010.09. 001. [3] K.P. Lee, T.C. Arnot, D. Mattia, A review of reverse osmosis membrane materials for desalination—development to date and future potential, J. Membr. Sci. 370 (2011) 1–22, http://dx.doi.org/10.1016/j.memsci.2010.12.036.
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