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Research Papers: Fundamental Issues and Canonical Flows

Pumping Flow in a Channel With a Peristaltic Wall

[+] Author and Article Information
Yeng-Yung Tsui

Professor
e-mail: yytsui@mail.nctu.edu.tw

Shi-Wen Lin

Department of Mechanical Engineering,
National Chiao Tung University,
Hsinchu 300, Taiwan

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 4, 2012; final manuscript received October 10, 2013; published online December 18, 2013. Assoc. Editor: Zhongquan Charlie Zheng.

J. Fluids Eng 136(2), 021202 (Dec 18, 2013) (9 pages) Paper No: FE-12-1496; doi: 10.1115/1.4026077 History: Received October 04, 2012; Revised October 10, 2013

Simplified models were widely used for analysis of peristaltic transport caused by contraction and expansion of an extensible tube. Each of these models has its own assumptions, and therefore, weakness. To get rid of the limitations imposed by the assumptions, a numerical procedure is employed to simulate this pumping flow in the present study. In earlier studies, the frame of reference adopted moves with the peristaltic speed of the vibrating wall so that the flow becomes steady. The flow characteristics in a wavelength were the main concern. In our calculations, a channel of finite length with a flexible wall is considered. Pressures are prescribed at the inlet and outlet boundaries. The computational grid is allowed to move according to the oscillation of the wall. Another state-of-the-art technique employed is to construct the grid in an unstructured manner to deal with the variable geometry of the duct. The effects of dimensionless parameters, such as amplitude ratio, wave number, Reynolds number, and back pressure on the pumping performance are examined. Details of the peristaltic flow structure are revealed. Also conducted is the comparison of numerical results with the theoretical predictions obtained from the lubrication model to determine the suitability of this theory.

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References

Figures

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Fig. 1

Schematic sketch of the peristaltic channel

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Fig. 2

Illustration of a typical control volume

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Fig. 3

A control volume adjacent to the open boundary

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Fig. 4

Comparison with theoretical solutions and experiments for two amplitudes

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Fig. 5

Variation of mean flow rate against Reynolds number with ɛ = 0.3 for (a) two wave numbers (Pb = 0) and (b) different back pressures (α = 0.0907)

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Fig. 6

Variation of mean flow rate against amplitude ratio with α = 0.0907 for (a) different Reynolds numbers (Pb = 0) and (b) different back pressures (Re = 20)

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Fig. 7

Variation of mean flow rate against wave number with ɛ = 0.3 for (a) different Reynolds numbers (Pb = 0) and (b) different back pressures (Re = 10)

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Fig. 8

Variation of mean flow rate against back pressure with Re = 10 for (a) two wave numbers (ɛ = 0.3) and (b) two amplitude ratios (α = 0.0907)

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Fig. 9

Streamlines at times t = 0, T/4, T/2, and 3T/4 in a time period for ɛ = 0.3 (a) in wave frame and (b) in laboratory frame (α = 0.0907, Re = 20, and Pb = 1.5)

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Fig. 10

Streamlines at times t = 0, T/4, T/2, and 3T/4 in a time period for ɛ = 1 (a) in wave frame and (b) in laboratory frame (α = 0.0907, Re = 20, and Pb = 1.5)

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Fig. 11

Variation of pressure at the fixed wall for two amplitude ratios (α = 0.0907, Re = 20, and Pb = 1.5)

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Fig. 12

Variation of pressure at the fixed wall for two wave numbers (ɛ = 0.3, Re = 20, and Pb = 1.5)

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Fig. 13

Path lines for three particles (ɛ = 0.3)

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Fig. 14

Velocity profiles along a vertical line in a time period (ɛ = 0.3)

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Fig. 15

Path lines for three particles (ɛ = 1)

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Fig. 16

Velocity profiles along a vertical line in a time period (ɛ = 1)

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