Effect of Feed Spacer Mesh Length Ratio on Unsteady Hydrodynamics

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Effect of Feed Spacer Mesh Length Ratio on Unsteady Hydrodynamics in 2D Spiral Wound Membrane (SWM) Channel K. K. Lau,*,† M. Z. Abu Bakar,‡ A. L. Ahmad,‡ and T. Murugesan† Department of Chemical Engineering, UniVersiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia, School of Chemical Engineering, Engineering Campus, UniVersiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia

The present work involves the simulation and optimization of the ladder-type spacer mesh length (ML) ratio in spiral wound membranes (SWMs), using a two-dimensional (2D) integrated computational fluid dynamics (CFD) approach. The permeation properties, incorporated with a transient unsteady hydrodynamics modeling approach, were used to analyze and optimize the ML value for SWM feed spacers. The influence of unsteady hydrodynamics on the development of the concentration polarization in the membrane channel was also investigated. The optimum ML ratio was determined to be 3, because of its ability to generate a high intensity of unsteady hydrodynamics with the lowest effective concentration polarization factor and the results were further validated using velocity vector plots, wall shear stress analysis, and the localized concentration polarization factor. 1. Introduction Membrane processes are now commonly considered for wastewater treatment and other specialized separation applications, because of their unique advantages over conventional processes. Among the available configurations, hollow fiber, tubular, plate and frame, and spiral wound modules (SWMs) are commonly employed for separation process. Because of their unique advantages, in terms of better fouling resistance and suitability for wide range of membrane materials,1 SWMs are preferred for commercial applications including the recovery of value-added products from industrial effluents, desalination, water treatment, etc. The use of spacer nets in the SWM could promote the flow instabilities which decreases the fouling and, at the same time, enhances the mass transfer by reducing the concentration polarization. The design and optimization of the feed spacer of these modules requires a systematic analysis of hydrodynamics and mass-transfer characteristics inside the channel. The modeling of hydrodynamics in the spacer-filled SWM channel using computational fluid dynamics (CFD) is necessary for predicting the formation of concentration polarization and fouling phenomena at the membrane interface. Steady-state laminar, transient, and time-averaged turbulent CFD modeling approaches have been applied to model the hydrodynamics in the SWM channel. The steady-state laminar techniques was applied to model the concentration polarization through the solution of the continuity, Navier-Stokes and solute continuity equations.2-4 Later, the work was extended to the modeling of ladder-type spacers by assuming laminar flow structure and concentration distribution in a narrow rectangular channel.5-7 Subramani et al. and Ma et al. have used two-dimensional (2D) laminar simulation to predict the mass transfer and hydrodynamics in the spacer-filled channel,8-10 whereas three-dimensional (3D) laminar simulation was conducted to evaluate the performance * To whom correspondence should be addressed. Tel.: +6053687589. Fax: +605-3656176. E-mail: [email protected]. † Department of Chemical Engineering, Universiti Teknologi Petronas. ‡ School of Chemical Engineering, Engineering Campus, Universiti Sains Malaysia.

of different spacer configurations.11 A study on the effect of curvature on the spacer-filled SWM channel using 2D laminar simulation was also attempted.12 Even though the assumptions of laminar hydrodynamics in the spacer-filled membrane channel are valid under certain circumstances, there are still many researchers who found that the hydrodynamics in the spacerfilled membrane do not represent laminar conditions under relatively low Reynolds numbers (Re < 400).13-16 To model the unsteady hydrodynamics in the spacer-filled membrane channel with lower computational resources, time-averaged turbulent modeling was also applied.15-17 Unsteady transient simulation approaches have been conducted by several researchers to visualize the actual unsteady hydrodynamics in the confined spacer-filled membrane channel. Commercial CFD simulations codes (CFX) were employed by Schwinge et al. and Li et al. to simulate the unsteady hydrodynamics and masstransfer phenomenon in the spacer-filled membrane channel.13,18-21 Koutsou et al. applied periodical transient simulation to study the unsteady hydrodynamics in the spacer-filled membrane channel.14,22 Similar simulation approach was also made by Darcovich et al.23 The usage of this approach offered significant savings in computational time and costs. Inevitably, the usage of transient simulation is a better option to simulate and visualize the actual unsteady hydrodynamics in the spacer-filled membrane channel. However, the abovementioned turbulent and transient CFD studies are limited to the assumption that the membrane is an impermeable wall with zero concentration buildup.13-22 Since the mass transport across the membrane was neglected, the assumption might lead to an incorrect assessment of the concentration polarization phenomenon. To overcome these limitations, a detailed study was made recently, to investigate the unsteady hydrodynamics and permeation properties in a SWM feed channel filled with filaments of different geometries.24 In the present work, an attempt has been made to simulate and optimize ladder-type spacer mesh length ratio using a 2D integrated CFD approach. Permeation properties have also been incorporated in the commercial simulator to simulate the transient unsteady hydrodynamics in the spacer-filled SWM feed channel. Besides, the influence of unsteady hydrodynamics on the development of the concentra-

10.1021/ie9017989  2010 American Chemical Society Published on Web 05/07/2010

Ind. Eng. Chem. Res., Vol. 49, No. 12, 2010 Table 1. Transport Properties for CuSO4 property

value 5

osmotic pressure, π (×10 Pa)

Figure 1. Boundary conditions for periodic unit cell simulation (PUCS).

density, F (kg/m3) viscosity, µ (×10-3 Pa s) diffusion coefficient, DA (×10-9 m2/s)

2.945mA(60.14 - 179.09mA + 1156.22mA2) 997 + 1068mA 0.895(1 + 4.04mA + 15.951mA2) 0.6084(1 - 1.7292mA)b

a Using curve-fitting values taken from ref 27. mA < 0.18.

Figure 2. Boundary condition for permeation properties integrated simulation (PPIS).

tion polarization in the membrane channel has also been investigated. 2. Methodology 2.1. Simulation Approach. Direct Numerical Simulation (DNS) method was used to solve the unsteady 2D hydrodynamics in the spacer-filled membrane channel domain (assuming ladder-type spacers) with a consideration of variation in solute concentration, where the governing equations of Ahmad and Lau24 were used. Since the spacer-filled channels have a streamwise periodic cross-section, the usage of periodic unit cell simulation (PUCS) offers the possibility of resolving small scale features of flow in greater detail without simulating the complete membrane module.15 Nevertheless, it is impossible to integrate the membrane permeation properties in the PUCS using commercial simulators. Since the permeation flux (Jv) is significantly small, in comparison to the inlet velocity (Vin) (Jv < 0.1% of Vin for cross-flow nanofiltration and reverse osmosis), the velocity profile in the PUCS is expected to be identical with the velocity profile in the periodic simulation, which included the permeation properties. Thus, PUCS was applied in the current study to simulate the feed/inlet hydrodynamics for the spacer-filled membrane channel. The hydrodynamics’ structured data generated (which written in “C” language) were applied as the inlet/ feed boundary conditions in permeation properties integrated simulation (PPIS) to simulate the hydrodynamics and the permeation properties in the spacer-filled membrane channel. 2.2. Boundary Conditions. 2.2.1. Boundary Condition for PUCS. The flow inlet and outlet boundary (see Figure 1) were defined as periodic boundary conditions whereby the total mass flow rate and temperature of the feed solution were fixed. The upper and lower membrane walls were treated as nonporous wall, to maintain the overall continuity of the control volume system. The spacer was treated as a nonpermeable wall. PUCS was crucial to providing a reasonable unsteady inlet velocity profile for the multiple cell simulation (PPIS). The purpose of performing PUCS is to reduce the computational time and resources while maintaining the detailed unsteady hydrodynamics calculation. 2.2.2. Boundary Condition for PPIS. After generating the unsteady hydrodynamics structured data using PUCS, these data were applied as the boundary conditions for permeation properties integrated simulation (PPIS) (see Figure 2). A periodic inlet velocity (up and Vp) (obtained from PUCS data) was applied at the entrance of the membrane channel (Boundary 1 in the figure). The top and bottom parts of the channel were treated

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a

b

Applicability range:

as permeable membrane walls (Boundaries 3 and 4 in the figure). Fluid flowing out of the channel was assumed to be in a fully developed condition (parabolic profile), where all changes for the flow parameters (velocity and concentration) were set to zero (Boundary 2 in the figure). No-slip conditions (u ) 0) were fixed for the wall and membrane interface. The user-defined function (UDF) was incorporated in the membrane boundary condition to model the concentration profile and permeation flux for the membrane interface.24,26 The boundary conditions for PPIS computational domain are represented by the following equations: Boundary 1: u ) up(x, y, t); V ) Vp(x, y, t); mA ) mA0

(1)

Boundary 2: ∂u ) 0; ∂x

∂V ) 0; ∂x

∂mA )0 ∂x

(2)

Boundary 3 (upper membrane wall): u ) 0; V ) Jv ) Lp{∆P - σ[(mAw) - π(Rt′mAw)]}; mA ) mAw ) exp

( )

Jvδc 1 × × mAc DA Rt + Rt′ exp(Jvδc/DA)

(3)

Boundary 4 (lower membrane wall): u ) 0;

V ) -Jv ) -Lp{∆P - σ[(mAw) - π(Rt′mAw)]};

mA ) mAw ) exp

( )

Jvδc 1 × × mAc (4) DA Rt+Rt′ exp(Jvδc/DA)

2.3. Simulation Condition. For the feed material conditions, those for CuSO4 and water were defined before executing the simulation loops. The physical transport properties for CuSO4 are listed in Table 1. These physical properties were correlated using the reference data27 and are represented as a function of solute concentration (mass fraction). Hydraulic permeability and reflection coefficient for the membrane (NF90, membrane sample from Dow Chemical Corp., USA) was set to 4.72 × 10-11 m/(Pa s) and 0.98, respectively. These data were generated by curve-fitting method using the experimental permeation data of CuSO4 in an empty membrane channel operated at a pressure range of 200-1100 kPa. The transmembrane pressure used in all the simulations for the present study was 1100 kPa. CuSO4 was selected for the present study, because of its capacity to produce significant osmotic pressure and a concentration polarization effect within the range of pressure studied in the present work. Spacer mesh length (ML) ratio is an important design and optimization parameter for the SWM module. The spacer mesh length ratio (ML ) lm/h) is the distance between two consecutive spacer filaments (lm), relative to channel height (h). For the

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Figure 5. Preliminary simulation test of the optimum grid resolution for a spacer-filled SWM channel (Nc ) number of cells, Ref ) 300, mean velocity magnitude for a vertical sampling line between two spacer filaments).

Figure 3. Computational domain for spacer mesh length (ML) ratio analysis.

present study, ML ratios were varied from 2 to 7 (Figure 3). Generally, ML ratios of >7 are not feasible in practice, since it fails to support the membrane envelope, whereas, ML ratios of 0.0001 s has failed to meet the convergence

Figure 4. Computational domain for 2D spacer-filled membrane channel.

Figure 6. Area-averaged concentration polarization factor development for the membrane wall in the membrane channel filled with spacer ML3 between 0 and 1 s.

criteria for the solution of continuity equation (with a residual error of >10-5), a smaller time step (tstep ) 0.0001 s) was used for the present unsteady simulation. This time step is crucial to simulate the details of unsteady hydrodynamics and the overall continuity of the fluid flowing in the spacer-filled membrane channel. 2.4. Experimental Setup for Model Validation. Polyamide (nylon) filaments were used to fabricate feed spacers. The constructions of feed spacers from polyamide (nylon) filaments were aided by the spacer fabrication frame. This frame was fabricated with polyethermide (with 30% carbon). Fine holes (0.5 mm) in one line were made on the four sides of the frame. These holes were used to hold the polyamide filaments for the formation of the feed spacer structure. The polyamide filaments were attached together by applying adhesive at the joint of the filaments. Spacers ML3, ML4.5, and ML6 were fabricated for model validation using the above-mentioned method. The details of the experimental procedures have been described in our previous work.26 3. Results and Discussion 3.1. CFD Model Validation. The CFD-simulated hydrodynamics and permeation properties in a spacer-filled membrane channel were validated using a series of present experimental

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Figure 7. Comparison of simulated and experimental channel pressure drop for different types of spacer-filled membrane channels.

Figure 8. Comparison of simulated and experimental permeation fluxes for membrane channels filled with spacer ML3 under different pressures at a feed Reynolds number of Ref ) 350. (Notation: (4) experimental data, ( · · · ) simulation data.)

data. Periodic feed conditions (which were coupled with PPIS) were employed in model validation simulation to avoid entrance transition effect. For the validation of hydrodynamics, simulated channel pressure drop (∆pch) was compared with the experimental data obtained using cylindrical feed spacers ML3, ML4.5, and ML6 (see Figure 7), for different feed Reynolds numbers, (Ref). Figure 8 shows the comparison of simulated permeation fluxes under different transmembrane pressures (at Ref ) 350), relative to the experimental data (feed spacer ML3). Both Figures 7 and 8 show satisfactory agreement of the simulated hydrodynamic and permeation properties with the respective experimental results. 3.2. Unsteady Hydrodynamics Analysis for Spacer-Filled SWM Feed Channel. The hydrodynamics in the porous structure of feed spacer can achieve unsteady-state behavior under relatively low Reynolds number (Ref ) 200-400).13-15,18 The existence of unsteady hydrodynamics subsequently promotes the generation of vortices (moving eddies) in the membrane channel and, hence, suppress the formation of concentration polarization and fouling. 3.2.1. Unsteady Entrance Transition Effect in SpacerFilled SWM Feed Channel. As discussed in our earlier work using different filament geometries,24 the emergence of unsteady hydrodynamics in the spacer-filled membrane channel could be detected only downstream of the spacer-filled membrane channel. A similar approach was extended for different ML ratios. Figure 9 demonstrates the instantaneous membrane wall shear stress along the membrane channel length generated by different spacer configurations with ML ratios in the range of 2-7.

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Generally, wall shear stress along the spacer-filled membrane channel would exhibit periodical evolution trend in the steady hydrodynamics region, as shown in Figure 9. The emergence of unsteady hydrodynamics would disturb this periodical evolution trend and produces fluctuation of the wall shear stress in a disordered manner, as shown in the unsteady hydrodynamics region depicted in Figure 9. The distance from the channel inlet to the point where the unsteady hydrodynamics formed will give the transition length for different spacers to achieve unsteady hydrodynamics. Based on Figure 9, spacer ML3 achieved unsteady hydrodynamics with the shortest transition length, which was 0.01 m from the channel entrance, followed by spacer ML2 (0.0125 m). The entrance transition lengths generated by spacers ML4, ML5, ML6, and ML7 were in ascending order. The reduction of porosity and hydraulic diameter increases the flow resistance in the membrane channel, which potentially triggered the unsteady hydrodynamics in the spacer-filled membrane channel. However, the usage of spacers with ML ratios smaller than the optimum mesh length would also delay the generation of unsteady hydrodynamics, because the flow disturbance was subsequently dampened by the close packing of the spacer filaments (see Figure 9). This reasoning was supported by the simulation results where spacer ML3 generated the shortest transition entrance length, instead of spacer ML2 and, subsequently, the rest of the spacers. The above-simulated results exhibited the presence of an entrance transitions effect in the spacer-filled SWM channel. To reduce this effect during the comparison of spacer performance (with different ML ratio), the present study was conducted, using periodic feed conditions to avoid the usage of a large simulation domain, which requires massive computational resources. 3.2.2. Effect of Different Mesh Length Ratios on Unsteady Hydrodynamics. To quantify the unsteady hydrodyj) namics as discussed earlier, the mean velocity magnitude (V and root-mean-square (rms) of velocity fluctuation magnitude (VRMS′) were computed for the hydrodynamics in the spacerfilled membrane channel under different ML ratios. The mean velocity magnitude indicates the average value for the fluctuating instantaneous velocity magnitude, which is represented by j ) 1 × V t

∫ V(t) dt t

(5)

0

whereas the rms of the velocity magnitude fluctuation (VRMS′) measures the degree of unsteady hydrodynamics in the spacerfilled SWM channel: VRMS′ )

1t × ∫ V′(t) t

0

(

)2

dt

(6)

where V is the velocity magnitude (m/s) and V′ is the velocity j ). magnitude fluctuation (V′ (m/s) ) V - V j ) and rms of velocity The mean velocity magnitude (V magnitude fluctuation (VRMS′) generated in the membrane channel filled by spacers with different mesh length ratio (ML) are presented in Table 2. It is obvious that the reduction of mesh j and VRMS′ length ratio from ML7 to ML3 increased both the V values of the flow in the spacer-filled membrane channel. However, further reduction of mesh length ratio after ML3 only j value, while reducing the value of VRMS′. The increased the V reduction in the degree of unsteady hydrodynamics (VRMS′) could be attributed to the fact that an ML value of 300), the increment of VRMS′ was relatively moderate (based on the comparison between the consecutive Ref values that produce unsteady hydrodynamics), which was typically 105 Pa/m is not desirable in a SWM, since the pumping costs and the loss of driving force become too large in array operation.13 Hence, setting the range of λ from 2000 Pa s to 50000 Pa s (where λ ) ∆Pch/(lu)) is sufficient to fulfill the criterions for most practical applications. j versus λ (see Figure 12), the specific Based on the plot of Γ design that produces the lowest value of Ψ was selected as the optimal spacer ML ratio. Hence, optimization of the spacer ML ratio is based on the effective minimum concentration polarization factor (Ψ) (between the range of study of 2000 < λ < 50000 Pa s), using the following objective function:

where x is the ML ratio.

1 × t

λ2

(14)

The value of cτ, jτRMS′, cτe, and (τje′)rms were determined numerically using the trapezoidal rule. For the confirmation of the optimum spacer design parameter, the velocity contour plot profile and localized concentration polarization factor (which was based on channel length at any specific time) were also considered. The optimal spacer ML ratio is to be determined based on the tradeoff between concentration reduction ability and specific power consumption j) (λ). Figure 12 exhibits the average concentration factor (Γ generated by spacers with different ML ratios for a specific range of λ (2000 < λ < 50000). Based on the figure, spacer ML3 apparently generated the lowest average concentration polarization factor, followed by spacer ML4. Based on the figure, spacer ML2 obviously produced the highest concentration factor, compared to other spacer filaments. Spacers with ML ratios of 5-7 generated relatively comparable concentration factors for the current range of λ that has been covered in the present study. Effective concentration polarization factors (Ψ) were comj versus λ. Figure 13 puted based on the area under the plot of Γ depicts the effective concentration polarization factor (Ψ) generated by spacers with different ML ratios, which indicates that spacer ML3 generated the lowest Ψ value, compared to the other spacer filaments. The reduction of mesh length ratio from 7 to 5 did not significantly reduce the Ψ. Further decreases in the ML ratio from 5 to 3 exhibited a considerable reduction

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Figure 13. Effective concentration polarization factor (Ψ) generated by spacers with different ML ratios. Figure 15. Time-distance-averaged wall shear stress (τc) generated by spacers with different ML ratios under a specific range of λ (2000-50000).

Figure 14. Velocity contour plot for spacers with different ML ratios at Ref ) 400: (a) ML7, (b) ML6, (c) ML5, (d) ML4, (e) ML3, and (f) ML2.

membrane, located adjacent to the spacer and suppressed the formation of concentration polarization. Further reductions in the ML ratio from 6 to 5 exhibited the absence of steady recirculation and reattachment flow. Only unsteady vortices can be observed in membrane channel filled with spacer ML5. A similar observation was also reported by Schwinge et al.,13 indicating that the reattachment flow could only be detected at higher ML ratios. The absence of recirculation and reattachment flow in the channel filled with spacer ML5 slightly increased the value of Ψ for spacer ML5, compared to spacers ML6 and ML7 (see Figure 13). The membrane channel fileld with spacer ML4 clearly demonstrates three unsteady vortices (see Figure 14). Since spacer ML4 possessed a relatively smaller mesh length, compared to those of spacers ML5, ML6, and ML7, the existence of triple unsteady vortices in spacer ML4 was sufficient to generate lower Ψ, compared to other spacers (Figure 13 and 14). For spacer ML3, a highly unsteady vortex (separated from the upper unsteady hydrodynamics) and two unsteady vortices can be observed in the membrane channel. Since spacer ML3 possessed smaller mesh length as compared to the previous spacers, the presence of the highly unsteady hydrodynamics (one highly unsteady vortex and two unsteady vortices) was adequate to generate the lowest Ψ value, compared to other spacers (ML4-ML7). In the channel filed with spacer ML2, a significantly close arrangement of spacer filaments generated only a single low-magnitude unsteady vortex near to the spacer filament. The presence of this low-magnitude

in Ψ. In contrast, a reduction in ML ratio from 3 to 2 showed an increase in Ψ. Based on the results, ML3 was identified as the optimum spacer ML ratio, because further increases or decreases in mesh length ratio produced higher Ψ values. The reasons for the generation of the lowest Ψ value for spacer ML3 are discussed in detail. 3.4.1. Velocity Vector Plot Study. To further confirm the optimum spacer (ML3) based on the minimum Ψ, the velocity vector plot for different types of spacers in the SWM channel were studied. Figure 14 shows the velocity vector plot generated by spacers with different ML ratios at Ref ) 400, where a steady recirculation and reattachment flows can be seen for spacers ML6 and ML7. Reattachment flow occurs when the high velocity profile (generated by the spacers) comes into contact with the membrane adjacent to the spacer, whereas recirculation flow occurs because of the presence of steady vortex. These phenomena significantly increased the wall shear stress on the

Figure 16. Root-mean-square (rms) of the distance-averaged wall shear stress fluctuation (τjrms′) generated by spacers with different ML ratios under a specific range of λ (2000-50000).

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Table 3. Effective Time-Distance-Averaged Wall Shear Stress (τce) and Effective rms of the Distance-Averaged Wall Shear Stress Fluctuation ((τje′)RMS) Generated by Spacers with Different ML Ratios

mesh length ratio

effective time-distance averaged wall shear stress, cτe (Pa)

effective rms of distanceaveraged wall shear stress fluctuation, (τje′)rms (Pa)

ML2 ML3 ML4 ML5 ML6 ML7

6.37 8.54 9.20 9.22 9.87 9.94

1.83 4.91 0.94 0.47 0.94 0.73

unsteady vortex was insufficient to produce lower Ψ values, compared to other spacers with different ML ratios. Detailed simulation results for different spacers, in terms of the localized concentration factor generated under these conditions, will be discussed in section 3.4.3. 3.4.2. Wall Shear Stress Analysis. Further validation for the optimum ML ratio was made based on the wall shear stress analysis, to study the actual hydrodynamic conditions adjacent to the membrane wall for spacers with different ML ratios. Figures 15 and 16 depict the time-distance-averaged wall shear

stress (τc) and the rms of distance-averaged wall shear stress fluctuation (τjrms′) generated by spacers with different ML ratios under specific range of λ. Based on Figure 15, spacer ML2 generated the lowest cτ value, followed by spacer ML3. Other spacers yielded relatively comparable cτ values. Based on the (τjrms′ value (Figure 16), spacer ML3 generated a significantly higher magnitude jτrms′ value, compared to other spacers with different ML ratios. Spacer ML2 generated the second highest jτrms′ value, after that observed for spacer ML3. The effective time-distance-averaged shear stress (τje′) and the effective rms of the distance-averaged wall shear stress fluctuation ((τje′)rms) were computed based on the area under the plots in Figures 15 and 16. An increment in ML ratio increased the cτe value, as given in Table 3. Although spacer ML3 generated cτe values that were ∼5%-12% lower than other spacers with higher ML ratios, yet it produced (τje′)rms values that were ∼500% higher than other spacers with higher ML ratios. Under highly unsteady hydrodynamics (the highest (τje′)rms value), spacer ML3 produced the lowest Ψ value, compared to other spacers with different ML ratios (Figure 13). These results also proved that unsteady hydrodynamics was more dominant in influencing the optimization result of the ML ratio, compared

Figure 17. Concentration factor Γ generated by spacers with different ML ratios at Ref ) 400: (a) Spacer ML2 - ML4 and (b) Spacer ML5 - ML7. (Membrane located opposite to the spacers, data sampling at a simulation time of 1.0000 s, vertical dotted lines indicate the location of the specific spacer (except for spacer ML2).)

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Figure 18. Concentration factor Γ generated by spacer with different mesh length ratios at Ref ) 400 (membrane located adjacent to the spacers, data sampling at simulation time 1.0000s, vertical dotted lines indicate the location of the specific spacer (except for spacer ML2)): (a) spacers ML2-ML4 (b) and spacers ML5-ML7.

to steady hydrodynamics. Although spacer ML2 generated significantly higher (τje′)rms values, compared to other spacers (except for spacer ML3) (Table 3) values, however, the occurrence of delayed unsteady hydrodynamics in the membrane channel has reduced its concentration reduction ability. At low Ref, the rapid formation of concentration polarization could easily be disrupted by the existence of unsteady wall shear stress. Based on Figure 16, spacer ML2 only exhibited a higher magnitude of jτrms′ above λ > 20000. At higher Ref (λ > 20000), the development of concentration polarization was basically suppressed by the higher static wall shear stress, whereas a rapid increase in the jτrms′ value, under these conditions, did not promote significant reduction in concentration factor. Hence, based on Figures 13 and 16, the increase in jτrms′ at λ > 20000 did not significantly reduce the effective concentration polarization factor Ψ generated by the spacer ML2. 3.4.3. Localized Concentration Polarization Factor Study. To understand the development of localized concentration polarization factor (Γ), the Γ generated by spacers with different

ML ratios were analyzed along the membrane wall. The results for the localized concentration polarization factor for different spacers were simulated using the same hydrodynamics conditions that were applicable for the velocity vector plot study (section 3.4.1). Figure 17 depicts the concentration factor generated by spacers with different ML ratios at Ref ) 400 for cases where the membrane was located opposite to the spacers. Based on the figure, spacer ML3 generated the lowest Γ, compared to other spacers. Obvious concentration factor peaks were detected between spacer ML4 and spacer ML7. Besides that, spacer ML2 was determined to produce a higher magnitude of Γ, which increased along the membrane channel. Figure 18 demonstrates the concentration factor Γ generated by spacers with different ML ratios (at Ref ) 400) for cases where the membrane was located adjacent to the spacers. The figure shows that the spacers with higher ML ratios (ML5-ML7) produced wider concentration development regions before and after the spacer filaments (see Figure 18b). The area of concentration development region for spacers ML3 and ML4 was obviously

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smaller and mostly limited to the stagnant zones. Spacer ML3 was determined to produce the lowest concentration factor, compared to other spacers. Based on the simulated results, ML3 was determined to be the optimum ML ratio, because it yielded the lowest effective concentration polarization factor (Ψ), compared to other spacers with lower or higher ML ratios (see Figure 13). Further study on this optimum ML ratio also proved that spacer ML3 was capable of generating highest degree of unsteady hydrodynamics (adjacent to membrane wall) with the presence of significantly higher values of the effective rms of the distance-averaged wall shear stress fluctuation ( jτe′)rms (Table 3). This unique criterion effectively suppressed the alleviation of concentration polarization in the spiral wound membrane channel while maintaining minimum power losses. 4. Conclusion The emergence of unsteady hydrodynamics in the spacerfilled spiral wound membrane (SWM) feed channel can only be detected after a certain transition length from the channel entrance. To avoid an entrance transition effect, the performance comparison for spacer filaments was conducted, using periodic simulation. Using the two-dimensional (2D) integrated computational fluid dynamics (CFD) approach, a mesh length (ML) ratio of 3 was determined to be optimum, because this ML ratio yielded the lowest effective concentration polarization factor (Ψ), which was further validated using velocity vector plots, wall shear stress analysis, and the localized concentration polarization factor. Furthermore, it was also proved that spacer ML3 was capable of generating a high intensity of unsteady conditions in the hydrodynamics (adjacent to the membrane) with the presence of significantly high value of the effective root-mean-square (rms) of distance-averaged wall shear stress fluctuation ((τje′)rms). Nomenclature dh ) hydraulic diameter (m) DA ) binary mass diffusion coefficient (m2/s) h ) channel height (m) Jv ) permeate flux (m/s) l ) membrane channel length (m) lm ) spacer mesh length (m) Lp ) hydraulic permeability (m/(Pa s)) ML ) spacer mesh length ratio (dimensionless); ML ) lm/h mA ) solute mass fraction (kg solute/kg solution) p ) pressure (Pa) PPIS ) permeation properties integrated simulation PUCS ) periodic unit-cell simulation Rt ) true rejection (dimensionless); Rt ) (mAw - mAp)/mAw Rt′ ) 1 - Rt (dimensionless) Ref ) feed Reynolds number (dimensionless); Ref ) Fu0h/µ Rech ) channel Reynolds number (dimensionless); Rech ) Fu0dh/µ Sc ) Schmidt number (dimensionless); Sc ) µ/FDA t ) time (s) u ) velocity in the x-direction (m/s) up ) periodic velocity in the x-direction (m/s) V ) velocity in the y-direction (m/s) Vp ) periodic velocity in the y-direction (m/s) V ) velocity magnitude (m/s) j ) mean velocity magnitude; V j ) (1/t)∫t0V(t) dx V j V′ ) fluctuation of velocity magnitude; V′ ) V - V VRMS′ ) root mean square (rms) of velocity magnitude fluctuation; VRMS′ ) [(1/t)∫t0(V′)2(t) dt]1/2

x ) x-axis coordinate (m) y ) y-axis coordinate (m) Greek Symbols Γ ) concentration factor (concentration polarization factor) (dimensionless); Γ ) (mAw/mA0) - 1 j ) average concentration polarization factor (dimensionless); Γ j ) (1/L)∫L0 Γ(x) dx Γ λ ) specific power consumption (Pa/s); λ ) ∆pu/l σ ) reflection coefficient (dimensionless) δ ) boundary layer thickness (m) δc ) distance between membrane wall and adjacent cell centroid value (m) π ) osmotic pressure (Pa) F ) density (kg/m3) τ ) instantaneous wall shear stress (Pa) jτ ) distance-averaged wall shear stress (Pa); jτ ) (1/l)∫ll12τ(l) dl cτ ) time-distance-averaged wall shear stress (Pa); cτ ) (1/t)∫t0jτ(t) dt jτ′ ) distance-averaged wall shear stress fluctuation (Pa); jτ′ ) jτ - cτ jτRMS′ ) root mean square (rms) of distance-averaged wall shear stress fluctuation (Pa); jτRMS′ ) [(1/t)∫t0(τj′)2(t) dt]1/2 cτe ) effective time-distance-averaged wall shear stress (Pa); cτe ) (1/∆λ)∫λλ12cτ(λ) dλ (τj′e)rms ) effective rms of distance-averaged wall shear stress fluctuation (Pa); (τj′e)rms ) (1/∆λ)∫λλ12jτRMS′(λ) dλ j (λ) Ψ ) effective concentration polarization factor; Ψ ) (1/∆λ)∫λλ12Γ dλ µ ) viscosity (kg/(m s)) ∆P ) transmembrane pressure (Pa) ∆pch ) cross-channel pressure drop (Pa/m) Subscripts 0 ) feed solution c ) centroid value of the cell adjacent to the membrane wall p ) permeate side/periodical w ) membrane wall

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ReceiVed for reView November 13, 2009 ReVised manuscript receiVed April 6, 2010 Accepted April 23, 2010 IE9017989