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Research Papers: Fundamental Issues and Canonical Flows

Shape Optimization of Symmetric Cylinder Shape on Buoyancy Using Fourier Series Approximation

[+] Author and Article Information
Hyeongkeun Kim

School of Mechanical Engineering, and Center for Human Interface Nanotechnology (HINT), Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, Koreafaithkim99@skku.edu

Dongmin Choi

School of Mechanical Engineering, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea

Youngjin Kim

School of Mechanical Engineering, SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea

Seunghyun Baik

Department of Energy Science, School of Mechanical Engineering, SKKU Advanced Institute of Nanotechnology (SAINT), Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, Korea

Hyungpil Moon1

School of Mechanical Engineering, Sungkyunkwan University, 300 Cheoncheon-dong, Jangan-gu, Suwon, Gyeonggi-do 440-746, Koreahyungpil@me.skku.ac.kr

1

Corresponding author.

J. Fluids Eng 132(5), 051206 (May 14, 2010) (8 pages) doi:10.1115/1.4001493 History: Received August 11, 2009; Revised March 06, 2010; Published May 14, 2010; Online May 14, 2010

The hydrophobicity of water striders and fisher spiders shows the geometrical property of microsetae with elaborate nanogrooves. Studying such geometrical morphology naturally leads to the question: what is an optimal shape for buoyancy? In this paper, we present a methodology to find suboptimal shapes for star-shaped cross-sectional rods, which maximizes the buoyant force by modeling the cross-sectional shapes with Fourier series representation in the polar coordinate. We provide four suboptimal cross-sectional shapes and their experimental results. Our results support the importance of the geometrical shape for buoyant force and might be helpful in designing water repelling devices.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Coordinate system for a star shape cross section floating on a liquid. The liquid meniscus is also shown as a solid line. V1 is the replaced volume of water due to the meniscus formation and V2 is the volume of the immersed rod.

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Figure 2

Digital images of the PTFE coated rods. The aluminum block was processed using EDM followed by the PTFE coating. The contact angle is 105 deg as shown in the inset image. The rod of (a) circular, (b) triangular, (c) star, and (d) Y-shaped cross section.

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Figure 3

Schematic of the experimental setup to estimate buoyant force

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Figure 4

The photographic images of water meniscus around samples: (a) circular, (b) triangular, (c) star, and (d) Y-shaped cross sections

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Figure 5

Calculation of the buoyant force. Step 1: photographic image. Step 2: outline of water meniscus. Step 3: processed two-dimensional and three-dimensional images.

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Figure 6

Comparison of the nondimensional buoyant force with respect to the nondimensional depth for an equilateral triangular rod, the exact solution (16), the third order, and the seventh order Fourier series approximations (k−1 is the capillary length)

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Figure 7

Shape optimization for buoyancy using Fourier series approximation. Comparisons of the buoyant force of rods with different cross-sectional shapes: (a) optimal shape 1 and (b) optimal shape 2 (cross-sectional area: 5.73 mm2); with respect to equilateral triangle

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Figure 8

Normalized buoyant force, obtained theoretically and experimentally, as a function of the angle θ for (a) circular, (b) triangular, (c) star, and (d) Y-shaped cross sections with corresponding digital images obtained experimentally (cross-sectional area: 50.26 mm2)

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Figure 9

Comparison of the buoyant force between theoretical predictions (Fourier series) and experimental results

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Figure 10

Normalized buoyant force, obtained theoretically and experimentally, as a function of CA: (a) Teflon coated triangular cross section (CA 105 deg), and (b) carbon nanotube (CNT) coated triangular cross section (CA 140 deg)

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