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Residence-time distributions for chaotic flows in pipes

Mezić, Igor and Wiggins, Stephen and Betz, David (1999) Residence-time distributions for chaotic flows in pipes. Chaos, 9 (1). pp. 173-182. ISSN 1054-1500. http://resolver.caltech.edu/CaltechAUTHORS:MEZchaos99

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Abstract

In this paper we derive two rigorous properties of residence-time distributions for flows in pipes and mixers motivated by computational results of Khakhar et al. [Chem. Eng. Sci. 42, 2909 (1987)], using some concepts from ergodic theory. First, a curious similarity between the isoresidence-time plots and Poincaré maps of the flow observed in Khakhar et al. is resolved. It is shown that in long pipes and mixers, Poincaré maps can serve as a useful guide in the analysis of isoresidence-time plots, but the two are not equivalent. In particular, for long devices isoresidence-time sets are composed of orbits of the Poincaré map, but each isoresidence-time set can be comprised of many orbits. Second, we explain the origin of multimodal residence-time distributions for nondiffusive motion of particles in pipes and mixers. It is shown that chaotic regions in the Poincaré map contribute peaks to the appropriately defined and rescaled axial distribution functions.


Item Type:Article
Additional Information:Copyright © 1999 American Institute of Physics. Received 13 April 1998; accepted for publication 30 December 1998. This research was partially supported by ONR. Grant No. N00014-98-1-0056 and AFOSR Grant No. F49620-97-1-0293 to I.M. and ONR Grant No. N00014-97-1-0071 to S.W.
Subject Keywords:pipe flow; chaos; flow instability; Poincaré mapping
Record Number:CaltechAUTHORS:MEZchaos99
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:MEZchaos99
Alternative URL:http://dx.doi.org/10.1063/1.166388
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1705
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:13 Feb 2006
Last Modified:26 Dec 2012 08:45

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