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• BUOYANCY-DRIVEN FLOW TRANSITIONS IN DEEP CAVITIES HEATED FROM BELOW  download article

C. Xia
Dept. of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA

J. Y. Murthy
Dept. of Mechanical Engineering, Carnegie Mellon University, Pittsburgh PA 15213, USA

ABSTRACT

The finite volume method has been used to numerically investigate flow transitions in deep three-dimensional cavities heated from below. The first critical Rayleigh number, Ra_I, below which the flow is at rest, and the second critical Rayleigh number, Ra_II, for transition from steady state to oscillatory flow, have been found for cavities of aspect ratio Ar = 1, 2 and 5. Transitions to chaos have also been examined for these cases. The results show that Ra_I = 3583, 2.545×10⁴ and 5.5× 10⁵ and Ra_II = 4.07× 10⁵, 1.65× 10⁶ and 1.30× 10⁷ for Ar = 1, 2 and 5. The route to chaos is P→QP₂→QP₃→N for Ar = 1 with the Rayleigh number varying from 4.07× 10⁵ to 4.89× 10⁵. The route is P→P₂→I→P→N for Ar = 2 over a Ra range of 1.65× 10⁶ to 1.83× 10⁶. The interval between periodic and chaotic flow is very short for Ar = 5.

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