Research Papers: Design Automation

An Optimum Design Method for a Thermal-Fluid Device Incorporating Multiobjective Topology Optimization With an Adaptive Weighting Scheme

[+] Author and Article Information
Yuki Sato

Department of Mechanical Engineering
and Science,
Graduate School of Engineering,
Kyoto University,
Kyoto 615-8540, Japan
e-mail: satou.yuuki.87x@st.kyoto-u.ac.jp

Kentaro Yaji

Department of Mechanical Engineering,
Graduate School of Engineering,
Osaka University,
Suita 565-0871, Japan
e-mail: yaji@mech.eng.osaka-u.ac.jp

Kazuhiro Izui

Department of Mechanical Engineering
and Science,
Graduate School of Engineering,
Kyoto University,
Kyoto 615-8540, Japan
e-mail: izui@me.kyoto-u.ac.jp

Takayuki Yamada

Department of Mechanical Engineering
and Science,
Graduate School of Engineering,
Kyoto University,
Kyoto 615-8540, Japan
e-mail: takayuki@me.kyoto-u.ac.jp

Shinji Nishiwaki

Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 615-8540, Japan e-mail: shinji@prec.kyoto-u.ac.jp

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 23, 2017; final manuscript received September 29, 2017; published online January 10, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 140(3), 031402 (Jan 10, 2018) (12 pages) Paper No: MD-17-1359; doi: 10.1115/1.4038209 History: Received May 23, 2017; Revised September 29, 2017

This paper proposes an optimum design method for a two-dimensional microchannel heat sink under a laminar flow assumption that simultaneously provides maximal heat exchange and minimal pressure drop, based on a topology optimization method incorporating Pareto front exploration. First, the formulation of governing equations for the coupled thermal-fluid problem and a level set-based topology optimization method are briefly discussed. Next, an optimum design problem for a microchannel heat sink is formulated as a bi-objective optimization problem. An algorithm for Pareto front exploration is then constructed, based on a scheme that adaptively determines weighting coefficients by solving a linear programming problem. Finally, in the numerical example, the proposed method yields a Pareto front approximation and enables the analysis of the trade-off relationship between heat exchange and pressure drop, confirming the utility of the proposed method.

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Grahic Jump Location
Fig. 1

Fixed design domain D in which Ω represents a fluid domain and Γin, Γout, and Γwall are the inlet, outlet, and wall, respectively

Grahic Jump Location
Fig. 3

Adaptive weighted sum method: (a) setting a desired point, (b) determining weighting coefficients, and (c) update nondominated solutions

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Fig. 2

Flowchart of the proposed method, the main algorithm

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Fig. 4

Design model and fixed design domain D

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Fig. 6

Obtained Pareto front approximation for N = 2

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Fig. 7

Histogram of fluid volume fraction in obtained Pareto-optimal solutions

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Fig. 8

Optimal configurations on the Pareto front approximation: (a) P1, (b) P2, (c) P3, (d) P4, (e) P5, (f) P6, (g) P7, (h) P8, (i) P9, and (j) P10

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Fig. 9

Comparison of the proposed method to a conventional weighted sum method and our previous method

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Fig. 10

Optimal configurations obtained by the conventional weighted sum method: (a) w¯=(0.900,0.100), (b) w¯=(0.831,0.169), and (c) w¯=(0.646,0.354): (a) W1, (b) W2, and (c) W3

Grahic Jump Location
Fig. 11

Velocity magnitudes: (a) W2, (b) P5, and (c) P6

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Fig. 12

Temperature distributions: (a) W3, (b) P5, and (c) P6

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Fig. 13

Intermediate and obtained Pareto front approximations

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Fig. 5

Obtained Pareto front approximation for various settings of parameter N



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