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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Schematic representation of the domain (Ω) and boundary (Γ)

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):021201-021201-13. doi:10.1115/1.4025680 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.

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Mesh used in the simulation of truncated open channel

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Convergence study w.r.t. number of degrees of freedom

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):021201-021201-13. doi:10.1115/1.4025680 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.

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Flow chart of the topology optimization algorithm

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):021201-021201-13. doi:10.1115/1.4025680 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

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):021201-021201-13. doi:10.1115/1.4025680 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.

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Mesh convergence study for accuracy of numerical model (a) submerge, (b) zig-zag, and (c) cavity

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):021201-021201-13. doi:10.1115/1.4025680 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

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Velocity streamline of three types of spacer (submerged, cavity, and zig-zag)

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):021201-021201-13. doi:10.1115/1.4025680 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

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Results of the topology optimization with respect to the pressure drop (black: spacer)

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):021201-021201-13. doi:10.1115/1.4025680 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

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: New design model considering manufacturability

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):021201-021201-13. doi:10.1115/1.4025680 Figure Legend: Mesh convergence study for accuracy of the numerical model

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):021201-021201-13. doi:10.1115/1.4025680 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