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Research Papers: Flows in Complex Systems

Fluid Flow in Trapezoidal Silicon Microchannels With 3D Random Rough Bottoms

[+] Author and Article Information
Renqiang Xiong

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611

J. Fluids Eng 133(3), 031102 (Mar 16, 2011) (7 pages) doi:10.1115/1.4003423 History: Received December 31, 2009; Revised January 06, 2011; Published March 16, 2011; Online March 16, 2011

Abstract

In this paper, a bottom-up approach is used to construct random rough bottom walls for trapezoidal silicon microchannels with hydraulic diameters $Dh$ from $47 μm$ to $241 μm$. The top and side walls are set to be smooth. A computational fluid dynamics solver is used to solve the 3D Navier–Stokes equations for the water flow through the rough trapezoidal microchannels. No-slip and periodic boundary conditions are applied to achieve the fully developed flow characteristics. The effects of Reynolds number Re (75–600), relative roughness height $H/Dh$ (1.66–5.39%), aspect ratio $β$ (0.13–1), and base angle $θ$ (30–90 deg) on the Poiseuille number Po are investigated. It is found that the roughness strongly affects the flow near the bottom wall but does not have significant effect on the center flow. The Po number in the developing flow region increases with the Re number and in the fully developed region tends to be independent of the Re number. The entrance length $Le$ is found to be smaller than that in smooth channels because the roughness reduces hydraulic diameter $Dh$ of the microchannel. It is also observed that with a certain $H/Dh$, the Po number has a larger deviation from the theoretical value with a smaller $β$, and with the same $H/Dh$ and $β$, $θ$ can also change the Po number, especially at small base angles.

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Figures

Figure 1

A trapezoidal microchannel with a 3D random rough bottom wall created by Coons surface

Figure 2

Simulated surface asperities; H=4 μm and 13 μm and Dh=241 μm

Figure 3

Velocity contours along the length of rough and smooth microchannels (H/Dh=2.49%)

Figure 4

Velocity profiles (a) near the wall and (b) at the center (H/Dh=2.49%)

Figure 5

Effect of Re number on the Po number (H/Dh=2.49%)

Figure 6

Entrance length of the rough trapezoidal microchannel (H/Dh=2.49%)

Figure 7

Comparison of the Po number at developing and fully developed flow regions (H/Dh=2.49%)

Figure 8

Effect of relative roughness height H/Dh on the Po number

Figure 9

Effect of aspect ratio β on the Po number (H/Dh=5.39%)

Figure 10

Effect of base angle θ on the Po number (H/Dh=5.39%)

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