Linear stability analysis of Rayleigh-Bénard convection of cold water near its density maximum in a vertically heated annular container
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In order to understand the onset of Rayleigh-Bénard convection of cold water near its density maximum in a vertical annular container heated from below and cooled from above, the instability of the static diffusive state was investigated by linear stability analysis. Two kinds of thermal boundary conditions, perfect insulating and conducting sidewalls, were used. The aspect ratio and radius ratio of the annular container varied from 0.5 to 4.5 and 0.1 to 0.8, respectively. Results indicate that the critical Rayleigh number and the critical wave number increase with the increase of density inversion parameter. There are some new flow modes with large azimuthal wave number near the convection onset for cold water with density maximum, which are not observed in Rayleigh-Bénard convection of the Boussinesq fluids. The stratified flow phenomenon in cold water with density maximum is certified. The larger the density inversion parameter is, the more obvious the stratified flow phenomenon becomes. With the increase of the aspect ratio, the critical Rayleigh number decreases, but the critical wave number increases. However, with the increase of the radius ratio, both the critical Rayleigh number and the critical wave number increase continuously. Furthermore, the effect of thermal boundary conditions at the sidewalls on the convection stability is also validated.
KeywordsLinear stability analysis Rayleigh-Bénard convection Density inversion parameter Instability Annular container
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