Numerical Study of the Routes toward Chaos of Natural Convection within an Inclined Enclosure

Authors

  • F. Kieno University of Ouagadougou
  • A. Ouedraogo University of Ouagadougou
  • O. M. Zongo University of Ouagadougou
  • J. D. Bathiebo University of Ouagadougou
  • B. Zeghmati Unversity of Perpignan

DOI:

https://doi.org/10.3329/jsr.v5i1.10709

Keywords:

Natural convection, Limit point, Limit cycle, T2 torus, Poincaré section, Lyapunov exponent, Chaos

Abstract

Two-dimensional numerical study of transient natural convection in an inclined cubic cavity filled with air using stream function-vorticity form for the Navier-Stokes equations has been carried out to explore the route toward chaos. The hot and cold vertical walls are maintained isothermal at temperature Tc and Th respectively and the other walls are adiabatic.  Two angles of inclination of the cavity 25° and 65° are considered. Transfers equations are solved using finite-difference discretization procedures. The study predicts various critical Rayleigh numbers for the two tilted angles characterizing the variation of the attractor behaviour and shows that the larger the Rayleigh number is, the more sensitive the attractor becomes to time step and meshes size. The routes toward the chaos followed by the attractor are: limit point / limit cycle / T2 torus / cycle fitted on a T2 torus / chaos / T2 torus / cycle fitted on a T2 torus / chaos when the Rayleigh number increases. The analysis confirms also the bifurcation of the attractor from a limit point to a limit cycle via an overcritical Hopf bifurcation for a Rayleigh number between 1.95x106 and 1.96x106.

© 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.

doi: http://dx.doi.org/10.3329/jsr.v5i1.10709        J. Sci. Res. 5 (1), 105-117 (2013)

 

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Author Biographies

F. Kieno, University of Ouagadougou

Departement de Physique

Professeur

A. Ouedraogo, University of Ouagadougou

Département de Physique

Professeur

O. M. Zongo, University of Ouagadougou

Département de Physique

Professeur

J. D. Bathiebo, University of Ouagadougou

Departement de Physique

Professeur

B. Zeghmati, Unversity of Perpignan

Departement de Physiue

Professeur

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Published

2012-12-26

How to Cite

Kieno, F., Ouedraogo, A., Zongo, O. M., Bathiebo, J. D., & Zeghmati, B. (2012). Numerical Study of the Routes toward Chaos of Natural Convection within an Inclined Enclosure. Journal of Scientific Research, 5(1), 105–117. https://doi.org/10.3329/jsr.v5i1.10709

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Section

Section A: Physical and Mathematical Sciences