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Research Papers

Characterization of Surface Roughness Effects on Laminar Flow in Microchannels by Using Fractal Cantor Structures

[+] Author and Article Information
Yongping Chen1

Chengbin Zhang, Panpan Fu, Mingheng Shi

 Key Laboratory of Energy Thermal Conversion and Control,Ministry of Education,School of Energy and Environment,Southeast University,Nanjing, Jiangsu 210096, P.R. China

1

Corresponding author.

J. Heat Transfer 134(5), 051011 (Apr 13, 2012) (7 pages) doi:10.1115/1.4005701 History: Received April 20, 2010; Revised November 23, 2010; Published April 11, 2012; Online April 13, 2012

The fractal characterization of surface topography by using Cantor set structures is introduced to quantify the microchannel surface. Based on this fractal characterization of surface, a model of laminar flow in rough microchannels is developed and numerically analyzed in this paper. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all discussed. The results indicate that the presence of roughness leads to the form of detachment, and the eddy generation is observed at the shadow of the roughness elements. The pressure drop in the rough microchannels along the flow direction is larger than that in the smooth channel. It is no longer in a linear fashion and the fluctuation in pressure drop along the stream due to the vortex near the wall is found. Differing from the smooth channel, the Poiseuille number for laminar flow in rough microchannels is no longer only dependent on the cross-sectional shape of the channel, but also strongly influenced by the Reynolds number, roughness height, and fractal dimension (spectrum) of the surface.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Topography of a rough surface

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Figure 2

Fractal dimension for a rough surface: (a) Topography of a rough surface and (b) Structure function and fractal dimension

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Figure 3

Fractal surface constructed by a Cantor set structure

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Figure 4

Cantor set surface profile (σ = 2 μm, D = 1.5)

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Figure 5

Schematic of microchannel constructed by the Cantor set surface

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Figure 6

Grid generation for local region near the wall

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Figure 7

Local streamlines in the near wall region (Ren  = 1000, D = 1.5, ɛ = 2%)

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Figure 8

Pressure drop along the smooth and rough microchannels (Ren  = 1000)

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Figure 9

Effect of Reynolds number on Poiseuille number

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Figure 10

Effect of relative roughness on Poiseuille number (D = 1.5, Ren  = 1000)

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Figure 11

Effect of fractal dimension on Poiseuille number (ɛ = 2%, Ren  = 1000)

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