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Transition to oscillatory flow in a differentially heated cavity with a conducting partition

Published online by Cambridge University Press:  28 November 2011

N. Williamson ,
S. W. Armfield  and
M. P. Kirkpatrick
N. Williamson*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
S. W. Armfield
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
M. P. Kirkpatrick
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Numerical evidence is presented for previously unreported flow behaviour in a two-dimensional rectangular side-heated cavity partitioned in the centre by vertical wall with an infinite conductivity. In this flow heat is transferred between both sides of the cavity through the conducting wall with natural convection boundary layers forming on all vertical surfaces. Simulations have been conducted over the range of Rayleigh numbers at Prandtl number and at aspect ratios of where and are the height and width of the cavity. It was found that the thermal coupling of the boundary layers on either side of the conducting partition causes the cavity flow to become absolutely unstable for a Rayleigh number at which otherwise similar non-partitioned cavity flow is steady but convectively unstable. Additionally, unlike the non-partitioned cavity, which eventually bifurcates to a multi-modal oscillatory regime, this bifurcation is manifested as a single mode oscillation with , where is the temperature difference between the hot and cold walls, is the gravitational acceleration, is the oscillation frequency and and are the fluid viscosity and coefficient of thermal expansion respectively. The critical Rayleigh number for this transition occurs between for and for , indicating that the instability has an aspect ratio dependence.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer stability Convection: Convection in cavities
Type
Papers
Information
Journal of Fluid Mechanics , Volume 693 , 25 February 2012 , pp. 93 - 114
Copyright
Copyright © Cambridge University Press 2011

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Williamson et al. supplementary material

Movie 1: Visualisation of temperature perturbation \phi' at Ra=1.4x10^{10} and A=2 in fully developed flow over t=720-735.

Download Williamson et al. supplementary material(Video)
Video 7.8 MB

Williamson et al. supplementary material

Movie 1: Visualisation of temperature perturbation \phi' at Ra=1.4x10^{10} and A=2 in fully developed flow over t=720-735.

Download Williamson et al. supplementary material(Video)
Video 2.4 MB

Williamson et al. supplementary material

Movie 2: Visualisation of temperature perturbation \phi' at Ra=1.6x10^{10} and A=1 in fully developed flow over t=1200-1211.

Download Williamson et al. supplementary material(Video)
Video 5.9 MB

Williamson et al. supplementary material

Movie 2: Visualisation of temperature perturbation \phi' at Ra=1.6x10^{10} and A=1 in fully developed flow over t=1200-1211.

Download Williamson et al. supplementary material(Video)
Video 1.8 MB