Influence of Prandtl number on the chaos transition for pure natural and Rayleigh-Benard convections inside a rectangular cavity

초록

A peculiar flow instability known as multiple chaos transitions was recently reported for the free convection in an enclosure where the direction of the temperature gradient changes continuously; it has been explained to be attributed to the competition for dominance between pure natural and Rayleigh - Be <acute accent>rnard convections. In this study, the chaos transition of free convection is investigated when a horizontal or vertical temperature gradient forms in a rectangular cavity. Analyses are conducted under a laminar flow regime, with Prandtl numbers ranging from 0.01 to 50 and Rayleigh numbers up to 10 9 . In the horizontal temperature gradient, the chaostransition Rayleigh number increases monotonically with the Prandtl number. However, under vertical temperature gradient conditions, it reaches the maximum value at approximately Pr = 0.5. Contrary to the general knowledge that higher-Prandtl number fluids effectively stabilize natural convection, a free convection in a vertical temperature gradient initiates a new flow instability when the Prandtl number is over 1.0, where momentum and thermal diffusions balance each other. The oscillation pattern, 2D phase trajectory, power spectral density, and Poincare <acute accent> point of equivalent thermal conductivity are used to assess the free -convection flow instability.

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