Commun. Comput. Phys., 12 (2012), pp. 494-514.


Dynamical Motion Driven by Periodic Forcing on an Open Elastic Tube in Fluid

Wanho Lee 1, Sookkyung Lim 2, Eunok Jung 1*

1 Konkuk University, Department of Mathematics, 1 Hwayang-dong, Gwangjin-gu, Seoul, 143-701, Republic of Korea.
2 University of Cincinnati, Department of Mathematical Sciences, 839 Old Chem, Cincinnati, OH 45221, USA.

Received 24 January 2011; Accepted (in revised version) 6 August 2011
Available online 20 February 2012
doi:10.4208/cicp.240111.060811s

Abstract

We present a three dimensional model of an open elastic tube immersed in fluid to understand valveless pumping mechanism. A fluid-tube interaction problem is simulated by the volume conserved immersed boundary method which prevents the generation of spurious velocity field near the tube and local cluster of the tube surface. In order to explain pumping phenomena without valves, average net flow is measured by changing parameter values such as pumping frequency, compression duration, and pumping amplitude. Some frequencies that make the system reach maximal or minimal net flow are selected to study case by case. We also study the effectiveness of fluid mixing using the Shannon entropy increase rate.

AMS subject classifications: 65-04, 65M06, 76D05, 76M20

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Key words: Valveless pumping, volume conserved immersed boundary method, fluid mixing, average net flow.

*Corresponding author.
Email: lwh3958@konkuk.ac.kr (W. Lee), limsk@math.uc.edu (S. Lim), junge@konkuk.ac.kr (E. Jung)
 

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