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Transition to fully developed turbulence in liquid-metal convection facilitated by spatial confinement

Published online by Cambridge University Press:  23 February 2024

Lei Ren Open the ORCID record for Lei Ren [Opens in a new window] ,
Xin Tao Open the ORCID record for Xin Tao [Opens in a new window] ,
Ke-Qing Xia Open the ORCID record for Ke-Qing Xia [Opens in a new window]  and
Yi-Chao Xie Open the ORCID record for Yi-Chao Xie [Opens in a new window]
Lei Ren
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures and School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China
Xin Tao
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures and School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China
Ke-Qing Xia
Affiliation:
Center for Complex Flows and Soft Matter Research, Department of Mechanics and Aerospace Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, PR China
Yi-Chao Xie*
Affiliation:
State Key Laboratory for Strength and Vibration of Mechanical Structures and School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, PR China
*
†Email address for correspondence: yichao.xie@xjtu.edu.cn
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Abstract

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$, implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ($Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$. Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma <1$, the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.

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Turbulent Flows: Turbulent convection

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JFM Rapids
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Journal of Fluid Mechanics , Volume 981 , 25 February 2024 , R2
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© The Author(s), 2024. Published by Cambridge University Press

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Supplementary material: File

Ren et al. supplementary movie 1

Temporal evolution of the large-scale flow structure in a Γ = 1 cell shown in figure 4.
Download Ren et al. supplementary movie 1(File)
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Supplementary material: File

Ren et al. supplementary movie 2

Temporal evolution of the large-scale flow structure in a Γ = 1/2 cell shown in figure 4.
Download Ren et al. supplementary movie 2(File)
File 6.4 MB
Supplementary material: File

Ren et al. supplementary movie 3

Temporal evolution of the large-scale flow structure in a Γ = 1/3 cell shown in figure 4.
Download Ren et al. supplementary movie 3(File)
File 6.2 MB
Supplementary material: File

Ren et al. supplementary movie 4

Temporal evolution of the large-scale flow structure in a Γ = 1/5 cell shown in figure 4.
Download Ren et al. supplementary movie 4(File)
File 5.3 MB
Supplementary material: File

Ren et al. supplementary movie 5

Temporal evolution of the large-scale flow structure in a Γ = 1/10 cell shown in figure 4.
Download Ren et al. supplementary movie 5(File)
File 8.2 MB
Supplementary material: File

Ren et al. supplementary movie 6

Temporal evolution of the large-scale flow structure in a Γ = 1/20 cell shown in figure 4.
Download Ren et al. supplementary movie 6(File)
File 6.8 MB