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Turbulent convection for different thermal boundary conditions at the plates

Published online by Cambridge University Press:  25 November 2020

Najmeh Foroozani Open the ORCID record for Najmeh Foroozani [Opens in a new window] ,
Dmitry Krasnov  and
Jörg Schumacher Open the ORCID record for Jörg Schumacher [Opens in a new window]
Najmeh Foroozani*
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, P.O.Box 100565, D-98684Ilmenau, Germany
Dmitry Krasnov
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, P.O.Box 100565, D-98684Ilmenau, Germany
Jörg Schumacher
Affiliation:
Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, P.O.Box 100565, D-98684Ilmenau, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The influence of the different thermal boundary conditions at the bottom and top plates on the dynamics and statistics of a turbulent Rayleigh–Bénard convection flow is studied in three-dimensional direct numerical simulations. The flow evolves in a closed cylinder with an aspect ratio of $\varGamma =1/2$ in air for a Prandtl number $Pr=0.7$ and a Rayleigh number $Ra=10^7$ and in the liquid metal alloy GaInSn at $Pr=0.033$ and $Ra=10^7$, $10^8$. We apply for each case three different thermal boundary conditions at the top and bottom of the fluid volume while leaving the solid sidewall thermally insulated: (i) fixed temperature, (ii) fixed heat flux and (iii) conjugate heat transfer which couples the temperature and heat flux in the working fluid to that of the finitely thick, solid plates enclosing the turbulent flow. The global heat transfer is enhanced by up to 19 % for the conjugate heat transfer case in comparison to that of isothermal plates. The differences decrease for the lower of the two Prandtl numbers; they remain generally smaller for the global turbulent momentum transfer. Mean temperature profiles and root mean square velocity fluctuations are surprisingly weakly affected. The largest difference appears for the distribution of local thermal boundary scales when the cases of fixed temperature and of conjugate heat transfer are compared. We also discuss our results in view to experimental uncertainties in liquid metal experiments.

JFM classification

Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 907 , 25 January 2021 , A27
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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