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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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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