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Research Papers: Fundamental Issues and Canonical Flows

Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel

[+] Author and Article Information
Semyung Wang

e-mail: smwang@gist.ac.kr
School of Mechatronics,
Gwangju Institute of Science and
Technology (GIST),
261 Cheomdan-gwagiro, Buk-gu,
Gwangju 500-712, China

Joon Ha Kim

e-mail: joonkim@gist.ac.kr
School of Environmental
Science and Engineering,
GIST, 261 Cheomdan-gwagiro, Buk-gu,
Gwangju 500-712, China

1Corresponding authors.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 19, 2013; final manuscript received September 1, 2013; published online November 22, 2013. Assoc. Editor: Ali Beskok.

J. Fluids Eng 136(2), 021201 (Nov 22, 2013) (13 pages) Paper No: FE-13-1097; doi: 10.1115/1.4025680 History: Received February 19, 2013; Revised September 01, 2013

The objective of this study is to design spacers using topology optimization in a two-dimensional (2D) crossflow reverse osmosis (RO) membrane channel in order to improve the performance of RO processes. This study is the first attempt to apply topology optimization to designing spacers in a RO membrane channel. The performance was evaluated based on the quantity of permeate flux penetrating both the upper and lower membrane surfaces. Here, Navier–Stokes and convection-diffusion equations were employed to calculate the permeate flux. The nine reference models, consisting of combinations of circle, rectangle, and triangle shapes and zig-zag, cavity, and submerged spacer configurations were then simulated using finite element method so that the performance of the model designed by topology optimization could be compared to the reference models. As a result of topology optimization with the allowable pressure drop changes in the channel, characteristics required of the spacer design were determined. The spacer design based on topology optimization was then simplified to consider manufacturability and performance. When the simplified design was compared to the reference models, the new design displayed a better performance in terms of permeate flux and wall concentration at the membrane surface.

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References

Joyce, A., Loureiro, D., Rodrigues, C., and Castro, S., 2001, “Small Reverse Osmosis Units Using PV Systems For Water Purification In Rural Places,” Desalination, 137(1–3), pp. 39–44. [CrossRef]
Sutzkover, I., Hasson, D., and Semiat, R., 2000, “Simple Technique For Measuring The Concentration Polarization Level In A Reverse Osmosis System,” Desalination, 131(1–3), pp. 117–127. [CrossRef]
Parekh, B. S., 1988, Reverse Osmosis Technology: Application For High-Purity-Water Production, Marcel Dekker, New York.
Song, L., and Yu, S., 1999, “Concentration Polarization In Cross-Flow Reverse Osmosis,” AIChE J., 45(5), pp. 921–928. [CrossRef]
Bellucci, F., and Pozzi, A., 1975, “Numerical and Analytical Solutions For Concentration Polarization In Hyperfiltration Without Axial Flow,” Int. J. Heat Mass Transfer, 18(7–8), pp. 945–951. [CrossRef]
Kim, S., and Hoek, E. M. V., 2005, “Modeling Concentration Polarization In Reverse Osmosis Processes,” Desalination, 186(1–3), pp. 111–128. [CrossRef]
Ma, S., Song, L., Ong, S. L., and Ng, W. J., 2004, “A 2-D Streamline Upwind Petrov/Galerkin Finite Element Model For Concentration Polarization In Spiral Wound Reverse Osmosis Modules,” J. Membrane Sci., 244(1–2), pp. 129–139. [CrossRef]
Ahmad, A. L., Lau, K. K., and Abu Bakar, M. Z., 2005, “Impact of Different Spacer Filament Geometries On Concentration Polarization Control In Narrow Membrane Channel,” J. Membrane Sci., 262(1–2), pp. 138–152. [CrossRef]
Song, L., and Ma, S., 2005, “Numerical Studies of the Impact of Spacer Geometry on Concentration Polarization in Spiral Wound Membrane Modules,” Ind. Eng. Chem. Res., 44(20), pp. 7638–7645. [CrossRef]
Ma, S., and Song, L., 2006, “Numerical Study On Permeate Flux Enhancement By Spacers In A Crossflow Reverse Osmosis Channel,” J. Membrane Sci., 284(1–2), pp. 102–109. [CrossRef]
Subramani, A., Kim, S., and Hoek, E. M. V., 2006, “Pressure, Flow, And Concentration Profiles In Open And Spacer-Filled Membrane Channels,” J. Membrane Sci., 277(1–2), pp. 7–17. [CrossRef]
Santos, J. L. C., Geraldes, V., Velizarov, S., and Crespo, J. G., 2007, “Investigation of Flow Patterns And Mass Transfer In Membrane Module Channels Filled With Flow-Aligned Spacers Using Computational Fluid Dynamics (CFD),” J. Membrane Sci., 305(1–2), pp. 103–117. [CrossRef]
Radu, A. I., Vrouwenvelder, J. S., van Loosdrecht, M. C. M., and Picioreanu, C., 2010, “Modeling the Effect Of Biofilm Formation On Reverse Osmosis Performance: Flux, Feed Channel Pressure Drop And Solute Passage,” J. Membrane Sci., 365(1–2), pp. 1–15. [CrossRef]
Bendsøe, M. P., and Kikuchi, N., 1988, “Generating Optimal Topologies In Structural Design Using A Homogenization Method,” Comput. Methods Appl. Mech. Eng., 71(2), pp. 197–224. [CrossRef]
Bendsøe, M. P., and Sigmund, O., 2003, Topology Optimization-Theory, Method And Application, Springer, Berlin, Chap. 2, pp. 71–158.
Borrvall, T., and Petersson, J., 2003, “Topology Optimization Of Fluids In Stokes Flow,” Int. J. Numer. Methods Fluids, 41(1), pp. 77–107. [CrossRef]
Evgrafov, A., 2005, “The Limits of Porous Materials in the Topology Optimization of Stokes Flows,” Appl. Math. Optim., 52(3), pp. 263–277. [CrossRef]
Aage, N., Poulsen, T., Gersborg-Hansen, A., and Sigmund, O., 2008, “Topology Optimization Of Large Scale Stokes Flow Problems,” Struct. Multidisc. Optim., 35(2), pp. 175–180. [CrossRef]
Andreasen, C. S., Gersborg, A. R., and Sigmund, O., 2009, “Topology Optimization Of Microfluidic Mixers,” Int. J. Numer. Methods Fluids, 61(5), pp. 498–513. [CrossRef]
Van Gauwbergen, D., and Baeyens, J., 1997, “Macroscopic Fluid Flow Conditions In Spiral-Wound Membrane Elements,” Desalination, 110(3), pp. 287–299. [CrossRef]
Larson, R. E., Cadotte, J. E., and Petersen, R. J., 1981, “The FT-30 Seawater Reverse Osmosis Membrane–Element Test Results,” Desalination, 38, pp. 473–483. [CrossRef]
Reddy, J. N., and Gartling, D. K., 2001, The Finite Element Method In Heat Transfer And Fluid Dynamics, CRC Press, Boca Raton, FL, Chap. 4, pp. 149–253.
Codina, R., 1998, “Comparison of Some Finite Element Methods For Solving The Diffusion-Convection-Reaction Equation,” Comput. Methods Appl. Mech. Eng., 156(1–4), pp. 185–210. [CrossRef]
Tezduyar, T. E., and Osawa, Y., 2000, “Finite Element Stabilization Parameters Computed From Element Matrices And Vectors,” Comput. Methods Appl. Mech. Eng., 190(3–4), pp. 411–430. [CrossRef]
Onate, E., and Manzan, M., 2000, “Stabilization Techniques For Finite Element Analysis Of Convection-Diffusion Problems,” International Center For Numerical Methods In Engineering, p. 183.
Olesen, L. H., Okkels, F., and Bruus, H., 2006, “A High-Level Programming-Language Implementation Of Topology Optimization Applied To Steady-State Navier–Stokes Flow,” Int. J. Numer. Methods Eng., 65(7), pp. 975–1001. [CrossRef]
Svanberg, K., 1987, “The Method Of Moving Asymptotes—A New Method For Structural Optimization,” Int. J. Numer. Methods Fluids, 24(2), pp. 359–373. [CrossRef]
Sigmund, O., and Petersson, J., 1998, “Numerical Instabilities In Topology Optimization: A Survey On Procedures Dealing With Checkerboards, Mesh-Dependencies And Local Minima,” Struct. Optimiz., 16(1), pp. 68–75. [CrossRef]
Tortorelli, D. A., and Michaleris, P., 1994, “Design Sensitivity Analysis: Overview and Review,” Inv. Problems Eng., 1(1), pp. 71–105. [CrossRef]
Stover, R. L., 2006, “Energy Recovery Devices for Seawater Reverse Osmosis,” Everything About Water, pp. 40–45. Available at: http://67.199.53.244/index.cfm/0/0/55/0/start/31.

Figures

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Fig. 1

Schematic representation of the domain (Ω) and boundary (Γ)

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Fig. 2

Numerical instability of convection-diffusion equation at membrane surface (αopt = 1.0). In this simulation, Reynold (Re) number is 100 and Peclet (Pew) number is 273.

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Fig. 3

Mesh used in the simulation of truncated open channel

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Fig. 4

Convergence study w.r.t. number of degrees of freedom

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Fig. 5

Nine spacer-filled reference channel models. Channel length: 20 mm, channel height: 1 mm, diameter of circle spacer: 0.5 mm, length of rectangle spacer: 0.5 mm, length of the base and height of triangle spacer: 0.5 mm, distance between spacers: 4 mm.

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Fig. 6

Flow chart of the topology optimization algorithm

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Fig. 7

Conceptual illustration of material distribution based topology optimization for pipe-bend and rugby ball [16]. (a) Initial pipe bend problem to minimize pressure drop, (b) optimal pipe bend design, (c) initial rugby ball problem to minimize drag, and (d) optimal rugby ball design

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Fig. 8

Reverse osmosis membrane channel and design domain. The design domain is defined by four subdomains (green combed pattern: 0.5 mm × 1.0 mm) in which the distance between subdomains is 4 mm.

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Fig. 9

Mesh convergence study for accuracy of numerical model (a) submerge, (b) zig-zag, and (c) cavity

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Fig. 10

Comparisons of (a), (b) wall shear rate: ∂u/∂y, (c) total permeate flux: |vw|bottom+|vw|top, and (d) wall concentration: cbottom+ctop with different configurations of rectangle spacers along the channel

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Fig. 11

Velocity streamline of three types of spacer (submerged, cavity, and zig-zag)

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Fig. 12

Comparisons of (a) wall concentration: cbottom+ctop and (b) wall shear rate: ∂u/∂y depending on the shape of the zig-zag-type spacer

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Fig. 13

Results of the topology optimization with respect to the pressure drop (black: spacer)

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Fig. 14

Three major components of a fully developed spacer design obtained via topology optimization. (a) Fully developed spacer design, (b) component 1 attached to the membrane surface, (c) component 2 located at the entrance of the subdomain, and (d) component 3 located at the center of subdomains

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Fig. 15

New design model considering manufacturability

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Fig. 16

Mesh convergence study for accuracy of the numerical model

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Fig. 17

Comparisons of (a) total permeate flux: |vw|bottom+|vw|top, (b) wall concentration: cbottom+ctop, (c) wall shear rate on bottom membrane surface, and (d) top membrane surface, respectively, ∂u/∂y

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