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DOI: 10.1615/ICHMT.2008.CHT.1500
page 12

Sabiha Aklouche
Laboratoire des Transferts Polyphasiques et des Milieux Poreux Faculté de génie mécanique et génie des procèdes. Algérie

Belkacem Zeghmati
Laboratoire de Mathématiques et de Physique, Université de Perpignan Via Domitia, Perpignan, France

Khedidja Bouhadef
USTHB, Faculty of Mechanical and Process Engineering (FGMGP), Laboratory of Multiphase Transport and Porous Media (LTPMP), Algeria

Madjid Tata
Laboratoire des Transferts Polyphasiques et des Milieux Poreux Faculté de génie mécanique et génie des procèdes. Algérie


In this study, we numerically investigated transient natural convection in an air filled rectangular cavities where the horizontal sides were adiabatic and the vertical walls were composed of two regions of same size maintained at different temperatures. We have studied two ratios aspects, A=1 and A=2. The flow was assumed to be laminar and two-dimensional. The dimensionless governing equations, expressed in terms of stream function and vorticity, have been solved using the Alternating Direction Implicit Method (ADI) and the GAUSS elimination method. We analysed the effects of the Rayleigh number and the ratio aspect on the route to chaos borrowed by the system. For A=1 the Calculations are performed for air (Pr=0.71) and Rayleigh number varying between 2.5·105 and 1.5·107. The first transition has been from steady-state to oscillatory flow and the second is a subharmonic bifurcation as the Rayleigh number is increased further. For sufficiently small Rayleigh numbers our results show that the flow is characterized by four cells. The attractor bifurcates from a stable fixed point to a limit cycle for a Rayleigh number varying between 2.5·105 and 3·105. A limit cycle settle from Ra=3·105 and persist until Ra=5·105. As Rayleigh number increases, the flow become unstable and bifurcates to a time periodic solution at a critical Rayleigh number between 2.53·105 and 2.54·105. After the first HOPF bifurcation the oscillatory flow undergoes several bifurcations and ultimately evolves into a chaotic flow.

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