1. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Schematic representation of the domain (Ω) and boundary (Γ)

2. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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.

3. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Mesh used in the simulation of truncated open channel

4. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Convergence study w.r.t. number of degrees of freedom

5. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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.

6. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Flow chart of the topology optimization algorithm

7. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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

8. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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.

9. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Mesh convergence study for accuracy of numerical model (a) submerge, (b) zig-zag, and (c) cavity

10. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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

11. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Velocity streamline of three types of spacer (submerged, cavity, and zig-zag)

12. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Comparisons of (a) wall concentration: cbottom+ctop and (b) wall shear rate: ∂u/∂y depending on the shape of the zig-zag-type spacer

13. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Results of the topology optimization with respect to the pressure drop (black: spacer)

14. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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

15. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
New design model considering manufacturability

16. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
Mesh convergence study for accuracy of the numerical model

17. Date of download: 10/26/2017
Copyright © ASME. All rights reserved.
From: Novel Spacer Design Using Topology Optimization in a Reverse Osmosis Channel
J. Fluids Eng. 2013;136(2): doi: /
Figure Legend:
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