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Onset of convection induced by centrifugal buoyancy in a rotating cavity

Published online by Cambridge University Press:  04 August 2017

Diogo B. Pitz Open the ORCID record for Diogo B. Pitz [Opens in a new window] ,
Olaf Marxen  and
John W. Chew
Diogo B. Pitz*
Affiliation:
Department of Mechanical Engineering Sciences, University of Surrey, Guildford, GU2 7XH, UK
Olaf Marxen
Affiliation:
Department of Mechanical Engineering Sciences, University of Surrey, Guildford, GU2 7XH, UK
John W. Chew
Affiliation:
Department of Mechanical Engineering Sciences, University of Surrey, Guildford, GU2 7XH, UK
*
†Email address for correspondence: [email protected]
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Abstract

Flows induced by centrifugal buoyancy occur in rotating systems in which the centrifugal force is large when compared to other body forces and are of interest for geophysicists and also in engineering problems involving rapid rotation and unstable temperature gradients. In this numerical study we analyse the onset of centrifugal buoyancy in a rotating cylindrical cavity bounded by two plane, insulated disks, adopting a geometrical configuration relevant to fundamental studies of buoyancy-induced flows occurring in gas turbine’s internal air systems. Using linear stability analysis, we obtain critical values of the centrifugal Rayleigh number $Ra$ and corresponding critical azimuthal wavenumbers for the onset of convection for different radius ratios. Using direct numerical simulation, we integrate the solutions starting from a motionless state to which small sinusoidal perturbations are added, and show that nonlinear triadic interactions occur before energy saturation takes place. At the lowest Rayleigh number considered, the final state is a limit-cycle oscillation affected by the presence of the disks, having a spectrum dominated by a certain mode and its harmonics. We show that, for this case, the limit-cycle oscillations only develop when no-slip end walls are present. For the largest $Ra$ considered chaotic motion occurs, but the critical wavenumber obtained from the linear analysis eventually becomes the most energetic even in the turbulent regime.

JFM classification

Convection: Buoyancy-driven instability Geophysical and Geological Flows: Rotating flows Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 484 - 502
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Copyright
© 2017 Cambridge University Press 

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