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Research Papers: Design Automation

Topology Optimization of Fixed-Geometry Fluid Diodes

[+] Author and Article Information
Sen Lin

Department of Civil Engineering,
Johns Hopkins University,
Baltimore, MD 21218
e-mail: slin@jhu.edu

Longyu Zhao

Department of Materials Science
and Engineering,
Johns Hopkins University,
Baltimore, MD 21218

James K. Guest

Associate Professor
Department of Civil Engineering,
Johns Hopkins University,
Baltimore, MD 21218

Timothy P. Weihs

Professor
Department of Materials Science
and Engineering,
Johns Hopkins University,
Baltimore, MD 21218

Zhenyu Liu

Professor
Changchun Institute of Optics,
Fine Mechanics and Physics,
Chinese Academy of Sciences,
Changchun, Jilin 130033, China

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received November 10, 2014; final manuscript received March 25, 2015; published online June 8, 2015. Assoc. Editor: Kazuhiro Saitou.

J. Mech. Des 137(8), 081402 (Aug 01, 2015) (8 pages) Paper No: MD-14-1730; doi: 10.1115/1.4030297 History: Received November 10, 2014; Revised March 25, 2015; Online June 08, 2015

This paper proposes using topology optimization to design fixed-geometry fluid diodes that allow easy passage of fluid flowing in one direction while inhibiting flow in the reverse direction. Fixed-geometry diodes do not use movable mechanical parts or deformations, but rather utilize inertial forces of the fluid to achieve this flow behavior. Diode performance is measured by diodicity, defined as the ratio of pressure drop of reverse flow and forward flow, or equivalently the ratio of dissipation of reverse and forward flow. Diodicity can then be maximized by minimizing forward dissipation while maximizing reverse dissipation. While significant research has been conducted in topology optimization of fluids for minimizing dissipation, maximizing dissipation introduces challenges in the form of small, mesh dependent flow channels and that artificial flow in solid region becomes (numerically) desirable. These challenges are circumvented herein using projection methods for controlling the minimum length scale of channels and by introducing an additional penalty term on flow through intermediate porosities. Several solutions are presented, one of which is fabricated by 3D printing and experimentally tested to demonstrate the diodelike behavior.

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Figures

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Fig. 1

Fixed-geometry fluid diodes with flat-walled structures: (a) Tesla valve and (b) diffuser

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Fig. 2

Streamline of original Tesla valve (Re = 300): (a) forward flow and (b) reverse flow

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Fig. 3

Demonstration of the control volume Ω, shown as dashed line

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Fig. 4

Reproduction of the Tesla valve created using topology optimization (Re = 100; Da = 4.4 × 10–7; WF = 0; Rmin = 0.25 L). The white circle shows projection diameter and the red lines represents streamlines of reverse flow. (a) Pentagon design domain with inclined inlet and outlet. (b) Optimization result using projection method on fluid phase. (c) Demonstration of mesh independency of projection method. Projection radius: L/5; mesh size: L/6 (left) and L/20 (right).

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Fig. 5

Demonstration of the rectangular design domain

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Fig. 6

Optimization results for different aspect ratio (Re = 300, Da = 3 × 10−5, W = 0.1). (a) Aspect ratio 2:3; (b) aspect ratio 4:3; and (c) aspect ratio 9:3.

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Fig. 7

Streamlines of the optimized fluid diode shown in Fig. 6(c) (Re = 300, Da = 3 × 10−5, aspect ratio = 9:3). (a) Forward flow and (b) reverse flow.

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Fig. 8

Comparison of diodicity of channel-like diode and published works (simulation result)

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Fig. 9

Optimization result with expanding channel (Re = 300, Da = 3 × 10−5, W = 0.1, aspect ratio 4:3). (a) Design domain and (b) optimization result.

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Fig. 10

Streamlines of optimized diffuser-type diode (Re = 300, Da = 3 × 10−5). (a) Forward flow and (b) reverse flow.

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Fig. 11

Fabricated fluid diode specimen. (a) Geometry for 3D printing (b) 3D representation of the void (fluid) space for the experiment, with locations of pressure measurement marked as red.

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Fig. 12

Diodicity versus Reynolds number calculated via interpolation of experimental measurements (red curve) and computational simulations for the three-dimensional extruded sample with distanced pressure measurement locations (blue curve). The experimental error bars represent the combination of variation from three experimental trials and the accuracy of the instruments.

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Fig. 13

Demonstration of the impact of fabrication errors at Re = 300. Small perturbations in channel sizes lead to loss in diodicity, with smaller channel sizes (over deposition of 3D printed material) leading to a 50% loss in diodicity. (a) Dilation, Di = 7.41; (b) Original, Di = 8.87; (c) Erosion, Di = 4.24.

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