Spectral Analysis of Chaos Transition in a Dynamic System: Application to Backward Facing Step Flow in Mixed Convection

  • Héctor Barrios-Piña
  • Stéphane Viazzo
  • Claude Rey
  • Hermilo Ramírez-León
Chapter
Part of the Environmental Science and Engineering book series (ESE)

Abstract

This work focuses on the study of the transition from steady to chaotic behavior in mixed convection flow over a backward-facing step. Direct numerical simulations are performed in a two-dimensional horizontal channel of expansion ratio ER = 2 at step level. The effects of the temperature difference between the heated bottom wall and the inflow temperature are investigated by keeping constant the Richardson number at 1. The covered range of Grashof and Reynolds numbers is respectively 3.31 × 104 ≤ Gr ≤ 2.72 × 105 and 182.03 ≤ Re ≤ 521.34. The thermodynamic instabilities which cause the onset of unsteady flow are described in detail. A spectral and phase portrait analysis of the temperature time series allows us to observe that the transition from steady to chaotic flow occurs by period-doubling bifurcations.

Keywords

Fundamental Frequency Direct Numerical Simulation Chaotic Behavior Richardson Number Temperature Time Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Héctor Barrios-Piña
    • 1
  • Stéphane Viazzo
    • 2
  • Claude Rey
    • 2
  • Hermilo Ramírez-León
    • 1
  1. 1.Explotación de Campos en Aguas ProfundasInstituto Mexicano del PetróleoMexicoMexico
  2. 2.Laboratoire M2P2UMR 6181 CNRS - Universités d’Aix-Marseille, Technopôle Château-GombertMarseilleFrance

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