A numerical investigation was carried out to study the mixing behavior of Stokes flows in a rectangular cavity stirred by three square rods. The square loops of the rods move in such a way that a pseudo-Anosov map can be built in the flow domain in the augmented phase space. The finite volume method was used, and the flow domain was meshed by staggered grids with the periodic boundary conditions of the rod motion being imposed by the mesh supposition technique. Fluid particle tracking was carried out by a fourth-order Runge–Kutta scheme. Tracer stretches from different initial positions were used to evaluate interface prediction by a pseudo-Anosov map. The colored short period Poincaré section was obtained to reveal the size of the domain in which the pseudo-Anosov map was in effect. Dye advection patterns were used to analyze chaotic advection of passive tracer particles using statistical concepts such as “variances” and “complete spatial randomness.” For the fluid in the core region of the cavity, tracer interface stretches experienced exponential increases and had the same power index as that predicted by the pseudo-Anosov map matrix.
Skip Nav Destination
Article navigation
March 2015
Research-Article
Topological Chaos by Pseudo-Anosov Map in Cavity Laminar Mixing
Baiping Xu,
Baiping Xu
Technology Development Center
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
e-mail: xubaiping2003@163.com
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
Guangdong Industry Technical College
,Guangzhou 510641
, China
e-mail: xubaiping2003@163.com
Search for other works by this author on:
Lih-Sheng Turng,
Lih-Sheng Turng
1
Polymer Engineering Center,
e-mail: turng@engr.wisc.edu
University of Wisconsin–Madison
,Madison, WI 53706
e-mail: turng@engr.wisc.edu
1Corresponding author.
Search for other works by this author on:
Huiwen Yu,
Huiwen Yu
Technology Development Center
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
Guangdong Industry Technical College
,Guangzhou 510641
, China
Search for other works by this author on:
Meigui Wang
Meigui Wang
Technology Development Center
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
Guangdong Industry Technical College
,Guangzhou 510641
, China
Search for other works by this author on:
Baiping Xu
Technology Development Center
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
e-mail: xubaiping2003@163.com
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
Guangdong Industry Technical College
,Guangzhou 510641
, China
e-mail: xubaiping2003@163.com
Lih-Sheng Turng
Polymer Engineering Center,
e-mail: turng@engr.wisc.edu
University of Wisconsin–Madison
,Madison, WI 53706
e-mail: turng@engr.wisc.edu
Huiwen Yu
Technology Development Center
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
Guangdong Industry Technical College
,Guangzhou 510641
, China
Meigui Wang
Technology Development Center
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
for Polymer Processing Engineering
of Guangdong Colleges and Universities,
Guangdong Industry Technical College
,Guangzhou 510641
, China
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received December 2, 2013; final manuscript received January 27, 2014; published online January 12, 2015. Assoc. Editor: Stefano Lenci.
J. Comput. Nonlinear Dynam. Mar 2015, 10(2): 021013 (8 pages)
Published Online: March 1, 2015
Article history
Received:
December 2, 2013
Revision Received:
January 27, 2014
Online:
January 12, 2015
Citation
Xu, B., Turng, L., Yu, H., and Wang, M. (March 1, 2015). "Topological Chaos by Pseudo-Anosov Map in Cavity Laminar Mixing." ASME. J. Comput. Nonlinear Dynam. March 2015; 10(2): 021013. https://doi.org/10.1115/1.4026634
Download citation file:
Get Email Alerts
Cited By
Investigation of Nonlinear Dynamic Behaviors of Vertical Rotor System Supported by Aerostatic Bearings
J. Comput. Nonlinear Dynam (January 2025)
Electric Circuit Analogs of First-Order Dual-Phase-Lag Diffusion
J. Comput. Nonlinear Dynam
Related Articles
Buoyancy-Driven Flow Transitions in Deep Cavities Heated From Below
J. Heat Transfer (August,2002)
Nonintegrability of an Infinite-Degree-of-Freedom Model for Unforced and Undamped, Straight Beams
J. Appl. Mech (September,2003)
A Coupled Motion of the Thermally Induced Fluid Convection and the Membrane Motion
J. Comput. Nonlinear Dynam (July,2008)
Computation of the Statistics of Forced Response of a Mistuned Bladed Disk Assembly via Polynomial Chaos
J. Vib. Acoust (August,2006)
Related Proceedings Papers
Related Chapters
Global-Local Multisalce Modelling of Sandwich Structures by Using Arlequin Method
Proceedings of the 2010 International Conference on Mechanical, Industrial, and Manufacturing Technologies (MIMT 2010)
Efficient Estimation of the High Dimensional Model Representation for Non-Linear Models (PSAM-0402)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
An Approach to Use BDD during the Fault Tree Editing and Analyzing (PSAM-0142)
Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)