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Nonlinear dynamics and hydrodynamic feedback in two-dimensional double cavity flow

Published online by Cambridge University Press:  17 January 2017

F. Tuerke Open the ORCID record for F. Tuerke [Opens in a new window] ,
L. Pastur ,
Y. Fraigneau ,
D. Sciamarella ,
F. Lusseyran  and
G. Artana
F. Tuerke*
Affiliation:
Laboratorio de Fluidodinámica, Facultad de Ingeniería, Universidad de Buenos Aires, C1063ACV CABA, Argentina CONICET – Consejo Nacional de Investigaciones Científicas y Técnicas, C1425FQD CABA, Argentina Université Paris Sud 11, F-91400 Orsay CEDEX, France
L. Pastur
Affiliation:
Université Paris Sud 11, F-91400 Orsay CEDEX, France LIMSI-CNRS, BP 133, F-91403 Orsay CEDEX, France
Y. Fraigneau
Affiliation:
LIMSI-CNRS, BP 133, F-91403 Orsay CEDEX, France
D. Sciamarella
Affiliation:
LIMSI-CNRS, BP 133, F-91403 Orsay CEDEX, France
F. Lusseyran
Affiliation:
Université Paris Sud 11, F-91400 Orsay CEDEX, France LIMSI-CNRS, BP 133, F-91403 Orsay CEDEX, France
G. Artana
Affiliation:
Laboratorio de Fluidodinámica, Facultad de Ingeniería, Universidad de Buenos Aires, C1063ACV CABA, Argentina CONICET – Consejo Nacional de Investigaciones Científicas y Técnicas, C1425FQD CABA, Argentina
*
†Email address for correspondence: [email protected]
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Abstract

This paper reports results obtained with two-dimensional numerical simulations of viscous incompressible flow in a symmetric channel with a sudden expansion and contraction, creating two facing cavities; a so-called double cavity. Based on time series recorded at discrete probe points inside the double cavity, different flow regimes are identified when the Reynolds number and the intercavity distance are varied. The transition from steady to chaotic flow behaviour can in general be summarized as follows: steady (fixed) point, period-1 limit cycle, intermediate regime (including quasi-periodicity) and torus breakdown leading to toroidal chaos. The analysis of the intracavity vorticity reveals a ‘carousel’ pattern, creating a feedback mechanism, that influences the shear-layer oscillations and makes it possible to identify in which regime the flow resides. A relation was found between the ratio of the shear-layer frequency peaks and the number of small intracavity structures observed in the flow field of a given regime. The properties of each regime are determined by the interplay of three characteristic time scales: the turnover time of the large intracavity vortex, the lifetime of the small intracavity vortex structures and the period of the dominant shear-layer oscillations.

JFM classification

Aerodynamics: Aerodynamics Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 813 , 25 February 2017 , pp. 1 - 22
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Copyright
© 2017 Cambridge University Press 

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