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Flow structures and heat transport in Taylor–Couette systems with axial temperature gradient

Published online by Cambridge University Press:  15 June 2021

X.-Y. Leng ,
D. Krasnov ,
B.-W. Li  and
J.-Q. Zhong Open the ORCID record for J.-Q. Zhong [Opens in a new window]
X.-Y. Leng
Affiliation:
School of Physics Science and Engineering, Tongji University, 200092Shanghai, PR China
D. Krasnov
Affiliation:
Fakultät für Maschinenbau, Technische Universität Ilmenau, Postfach 100565, 98684Ilmenau, Germany
B.-W. Li
Affiliation:
School of Energy and Power Engineering, Dalian University of Technology, 116024Dalian, PR China
J.-Q. Zhong*
Affiliation:
School of Physics Science and Engineering, Tongji University, 200092Shanghai, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the heat transfer and coherent structures in Taylor–Couette (TC) flows that undergo thermal convection driven by an axially applied temperature gradient. Direct numerical simulations are performed in a Rayleigh number range $10^6 \leq Ra \leq 3 \times 10^8$ for Prandtl number $Pr = 4.38$ and with the shear Reynolds number up to $Re = 10^4$. When the rotation number $R_f$ increases, the flows undergo a transition from buoyancy-dominated ($R_f<1$) to shear-dominated convection ($R_f>1$). In the buoyancy-dominated regime with weak rotations, the flow features are similar to those in Rayleigh–Bénard (RB) convection with large-scale plumes emanating from the thermal boundary layers. In this regime, the $Re$-dependence of heat transport $Nu$ is sensitive to $Ra$. We find that for low $Ra$, $Nu$ decreases with increasing $Re$ and becomes independent of $Re$ at high $Ra$. In the shear-dominated regime, the flow structures are characterised by Taylor vortices (TVs), which effectively enhance the heat transport. With sufficiently high Reynolds number for $2000< Re \le 10\,000$, the flow structures are dominated by turbulent TVs, and the transport scaling laws of heat and angular velocity fluxes become independent of buoyancy. We report that in this turbulent regime the axial heat-transport scaling $(Nu\sim Re^{0.578\pm 0.018})$ is consistent with the scaling of radial angular-momentum transport $(Nu_{\omega }\sim Re^{0.581\pm 0.026})$.

JFM classification

Turbulent Flows: Turbulent convection Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A42
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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