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Evaporation-driven turbulent convection in water pools

Published online by Cambridge University Press:  08 October 2020

William A. Hay Open the ORCID record for William A. Hay [Opens in a new window]  and
Miltiadis V. Papalexandris Open the ORCID record for Miltiadis V. Papalexandris [Opens in a new window]
William A. Hay*
Affiliation:
Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering, B1348 Louvain-la-Neuve, Belgium
Miltiadis V. Papalexandris
Affiliation:
Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering, B1348 Louvain-la-Neuve, Belgium
*
†Email address for correspondence: [email protected]
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Abstract

In this paper we study turbulent thermal convection driven by free-surface evaporation at the top and a uniformly heated wall at the bottom. More specifically, we report on direct numerical simulations over 1.25 decades of Rayleigh number, Ra. At the top of the cubic domain, a shear-free boundary condition acts as an approximation of a free surface, and different evaporation rates form the basis of a temperature gradient assigned as a non-zero Neumann boundary condition. The corresponding lower wall temperature is fixed and we assess the thermal mixing on the water side of the air–water interface. The set-up is considered a simplified model of the turbulent natural convection in the upper volumes of spent-fuel pools of nuclear power plants. Surface temperatures are investigated over a range of 40 K, resulting in a sixteenfold increase in evaporation rates. Our work allows, for the first time, analysis of the features and mean flow statistics of this particular thermal convection configuration. Results show that a shear-free surface increases heat transfer within the domain; however, the exponent in the diagnosed power-law relation between the Nusselt and Rayleigh numbers, $Nu = 0.178Ra^{0.301}$, is similar to that of classical turbulent Rayleigh–Bénard convection. Further, the free slip accelerates the fluid after impingement on the upper boundary, significantly affecting the structure of the large-scale circulation in the container. Analysis of the flow statistics then shows how the shear-free surface introduces inhomogeneities in thermal boundary layer heights. Overall, the investigated turbulent convection configuration shows unique traits, borrowing from both turbulent Rayleigh–Bénard convection and evaporative cooling.

JFM classification

Convection: Convection in cavities Turbulent Flows: Turbulent convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A14
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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