The influence of the cell inclination on the heat transport and large-scale circulation in liquid metal convection

Lukas Zwirner,Ilya Kolesnichenko,Olga Shishkina,Peter Frick,Alexander Pavlinov,Sergei Mandrykin,Andrei Teimurazov,Andrey Mamykin,Alexander Shestakov,Ruslan Khalilov

doi:10.1017/jfm.2019.935

Abstract

Inclined turbulent thermal convection in liquid sodium is studied at large Rayleigh numbers based on the results of both experimental measurements and high-resolution numerical simulations. For a direct comparison, the considered system parameters are set to be similar: in the direct numerical simulations (DNS), in the large-eddy simulations and in the experiments, while the Prandtl number of liquid sodium is very small ( ). The cylindrical convection cell has an aspect ratio of one; one circular surface is heated, while the other one is cooled. Additionally, the cylinder is inclined with respect to gravity and the inclination angle varies from , which corresponds to Rayleigh–Benard convection (RBC), to , as in a vertical convection (VC) set-up. Our study demonstrates quantitative agreement of the experimental and numerical results, in particular with respect to the global heat and momentum transport, temperature and velocity profiles, as well as the dynamics of the large-scale circulation (LSC). The DNS reveal that the twisting and sloshing of the LSC at small inclination angles periodically affects the instantaneous heat transport (up to of the mean heat transport). The twisted LSC is associated with a weak heat transport, while the sloshing mode that brings together the hot and cold streams of the LSC is associated with a strong heat transport. The experiments show that the heat transport scales as in both limiting cases (RBC and VC) for Rayleigh numbers around , while any inclination of the cell, , leads to an increase of .

Highlights

Elucidation of the mechanisms of turbulent thermal convection in very-low-Prandtlnumber fluids is crucial for our understanding of the universe and the advancement 884 A18-2L
We directly compare the results for inclined convection in a cylindrical container with a diameter-to-height aspect ratio of 1, as they were obtained in the liquid-sodium direct numerical simulations (DNS) for Ra = 1.67 × 107 and Prandtl number (Pr) = 0.0094, large-eddy simulations (LES) for
In our complementary and cross-validating experimental and numerical studies, we have investigated inclined turbulent thermal convection in liquid sodium (Pr ≈ 0.009) in a cylindrical container of aspect ratio one

Summary

Introduction

Elucidation of the mechanisms of turbulent thermal convection in very-low-Prandtlnumber fluids is crucial for our understanding of the universe and the advancement 884 A18-2L. Elucidation of the mechanisms of turbulent thermal convection in very-low-Prandtlnumber fluids is crucial for our understanding of the universe and the advancement 884 A18-2. Turbulent thermal convection takes place, for example, on the surfaces of stars, where the Prandtl number (Pr) varies from 10−8 to 10−4 (Spiegel 1962; Hanasoge, Gizon & Sreenivasan 2016). Turbulent thermal convection in liquid metals (Pr 1) is relevant in engineering applications, especially in cooling systems of tokamaks and fast breeder reactors (Zhilin et al 2009; Belyaev et al 2013). Liquid sodium is of particular interest because of its very low Prandtl number (Pr ≈ 0.009) and it is widely used as cooling agent in fast neutron reactors (Heinzel et al 2017). For reviews on RBC we refer to Bodenschatz, Pesch & Ahlers (2000), Ahlers, Grossmann & Lohse (2009), Lohse & Xia (2010) and Chillà & Schumacher (2012)

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