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Three-dimensional stability of natural convection flows in inclined square enclosures

Published online by Cambridge University Press:  13 January 2025

Henry K Shen Open the ORCID record for Henry K Shen [Opens in a new window] ,
Wisam K. Hussam Open the ORCID record for Wisam K. Hussam [Opens in a new window]  and
Gregory J. Sheard Open the ORCID record for Gregory J. Sheard [Opens in a new window]
Henry K Shen*
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
Wisam K. Hussam
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia Department of Mechanical Engineering, College of Engineering, Australian University, West Mishref, Safat 13015, Kuwait
Gregory J. Sheard
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
*
†Email address for correspondence: henry.shen@monash.edu
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Abstract

The three-dimensional stability of two-dimensional natural convection flows in a heated, square enclosure inclined to the horizontal is investigated numerically. First, the computational procedure is validated by comparison of base flow solutions to results reported in literature across a range of inclinations. A bi-global linear stability analysis is then conducted to investigate the stability of these two-dimensional base flows to infinitesimal three-dimensional perturbations, and the effect that buoyancy forces (defined by a buoyancy number $R_N$) and enclosure inclination $\theta$ have on these stability characteristics. The flow is first observed to become three-dimensionally unstable at buoyancy number $R_N = 213.8$ when $\theta$ is $180^\circ$; this increases to $R_N = 2.54 \times 10^4$ at inclination $\theta =58^\circ$. It is found that the two-dimensional base flow is more unstable to three-dimensional perturbations with the critical $R_N$ corresponding to three-dimensional instability being significantly lower than its two-dimensional counterpart across all considered inclinations except $83^\circ \leq \theta \leq 88^\circ$, where the most unstable mode is a two-dimensional oscillatory mode that develops in the boundary layers along the conducting walls. Eight different leading three-dimensional instability modes are identified, with inclinations $58^\circ \leq \theta < 88^\circ$ transitioning through an oscillatory mode, and inclinations $88^\circ \leq \theta \leq 180^\circ$ transitioning through a stationary mode. The characteristics of the primary instability modes corresponding to inclinations $88^\circ \leq \theta \leq 179^\circ$ indicate the presence of a Taylor–Görtler instability.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Convection: Buoyancy-driven instability Convection: Convection in cavities
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1003 , 25 January 2025 , A8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

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Animations of oscillatory instability modes; Mode 1, Mode 2 and Mode 3.
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