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TECHNICAL PAPERS

# Modeling of Laminar Flows in Rough-Wall Microchannels

[+] Author and Article Information
R. Bavière

Laboratory of Geophysical and Industrial Flows, Grenoble University, UJF-INPG-CNRS BP 53X, 38041 Grenoble Cedex 9, France and Centre de Recherches sur les Très Basses Températures, CNRS B.P. 166, 38042 Grenoble Cedex 09, France

G. Gamrat, S. Le Person

Laboratory of Geophysical and Industrial Flows, Grenoble University, UJF-INPG-CNRS, BP 53X, 38041 Grenoble Cedex 9, France

M. Favre-Marinet1

Laboratory of Geophysical and Industrial Flows, Grenoble University, UJF-INPG-CNRS, BP 53X, 38041 Grenoble Cedex 9, FranceMichel.Favre-Marinet@hmg.inpg.fr

1

Corresponding author.

J. Fluids Eng 128(4), 734-741 (Nov 22, 2005) (8 pages) doi:10.1115/1.2201635 History: Received April 15, 2005; Revised November 22, 2005

## Abstract

Numerical modeling and analytical approach were used to compute laminar flows in rough-wall microchannels. Both models considered the same arrangements of rectangular prism rough elements in periodical arrays. The numerical results confirmed that the flow is independent of the Reynolds number in the range 1–200. The analytical model needs only one constant for most geometrical arrangements. It compares well with the numerical results. Moreover, both models are consistent with experimental data. They show that the rough elements drag is mainly responsible for the pressure drop across the channel in the upper part of the relative roughness range.

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## Figures

Figure 1

Computational domain and arrangement of the rough elements

Figure 2

Sketch of a control volume over the rough surface. Side view.

Figure 10

Poiseuille number. Comparison of numerical computations and analytical model with experimental results. ◆ Experimental results; 엯 Numerical computations, k=5μm; analytical model, dotted lines indicate k=6.2μm, thick lines indicate 7.2μm, dashed lined indicate 8.2μm, dash-dotted lines indicate Po=24.

Figure 3

Surface open for flow. Top view.

Figure 4

Distribution of the drag law coefficient K along a rough element. k*=d*=Lr*∕2=lr*∕2=0.2, β=0.75, Re=200.

Figure 5

Velocity profiles. k*=0.1, d*=Lr*∕2=lr*∕2=0.2, β=0.75, Re=1; semirough channel, plus indicates numerical computations, thin lines indicate analytical model; fully rough channel, open circle indicate numerical computations, thick lines indicate analytical model; smooth channel, dotted lines indicate Poiseuille flow.

Figure 6

Contribution of viscous and drag forces to the pressure gradient. d*=Lr*∕2=lr*∕2=0.2, β=0.75. Solid diamonds and dotted lines indicate friction on the bottom wall: Fνw∕FT, solid circles and dash-dotted lines indicate friction at the top of the rough elements: Fνt∕FT, solid triangles and dashed lines indicate drag force: FD∕FT. Solid symbols correspond to numerical computations, continuous lines correspond to the analytical model.

Figure 7

Influence of the roughness element height on the channel height reduction. d*=lr*∕2=lr*∕2=0.2, β=0.75. Open circles indicate numerical computations, thick lines indicate analytical model, dotted lines indicate HWL’s results, dashed-dotted lines indicate 1−Hr∕H=2k*.

Figure 8

Influence of the roughness element side length on the channel height reduction. k*=Lr*∕2=lr*∕2=0.2. Dashed lines indicate β. Open circles indicate Numerical computations, analytical model, dashed-dotted lines indicate K2=0, thick line indicate K2=0.5, dotted lines indicate HWL’s results.

Figure 9

Influence of the roughness element spacing on the channel height reduction. k*=d*=0.2. Same symbols as in Fig. 8.

## Errata

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