Linear biglobal analysis of Rayleigh-Bénard instabilities in binary fluids with and without throughflow - Archive ouverte HAL Access content directly
Journal Articles Journal of Fluid Mechanics Year : 2012

Linear biglobal analysis of Rayleigh-Bénard instabilities in binary fluids with and without throughflow

Abstract

Three-dimensional Rayleigh-Bénard instabilities in binary fluids with Soret effect are studied by linear biglobal stability analysis. The fluid is confined transversally in a duct and a longitudinal throughflow may exist or not. A negative separation factor , giving rise to oscillatory transitions, has been considered. The numerical dispersion relation associated with this stability problem is obtained with a two-dimensional Chebyshev collocation method. Symmetry considerations are used in the analysis of the results, which allow the classification of the perturbation modes as modes (those which keep the left-right symmetry) or modes (those which keep the symmetry of rotation of about the longitudinal mid-axis). Without throughflow, four dominant pairs of travelling transverse modes with finite wavenumbers have been found. Each pair corresponds to two symmetry degenerate left and right travelling modes which have the same critical Rayleigh number . With the increase of the duct aspect ratio , the critical Rayleigh numbers for these four pairs of modes decrease and closely approach the critical value obtained in a two-dimensional situation, one of the mode (a mode called mode A) always remaining the dominant mode. Oscillatory longitudinal instabilities () corresponding to either or modes have also been found. Their critical curves, globally decreasing, present oscillatory variations when the duct aspect ratio is increased, associated with an increasing number of longitudinal rolls. When a throughflow is applied, the symmetry degeneracy of the pairs of travelling transverse modes is broken, giving distinct upstream and downstream modes. For small and moderate aspect ratios , the overall critical Rayleigh number in the small Reynolds number range studied is only determined by the upstream transverse mode A. In contrast, for larger aspect ratios as , different modes are successively dominant as the Reynolds number is increased, involving both upstream and downstream transverse modes A and even the longitudinal mode.
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Dates and versions

hal-00780152 , version 1 (02-10-2013)

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Jun Hu, Daniel Henry, Xie-Yuan Yin, Hamda Ben Hadid. Linear biglobal analysis of Rayleigh-Bénard instabilities in binary fluids with and without throughflow. Journal of Fluid Mechanics, 2012, 713, pp.216-242. ⟨10.1017/jfm.2012.455⟩. ⟨hal-00780152⟩
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