Dynamics and length scales in vertical convection of liquid metals

Zwirner, Lukas; Emran, Mohammad S.; Schindler, Felix; Singh, Sanjay; Eckert, Sven; Vogt, Tobias; Shishkina, Olga

doi:10.1017/jfm.2021.977

Cited by 19 publications

(9 citation statements)

References 61 publications

(64 reference statements)

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“…Due to rotational symmetry, most experiments and many numerical investigations have been conducted in upright cylinders, hence the aspect ratio Γ = D/H between cylinder diameter D = 2R and height H is a parameter quantifying the geometrical constraints. The height H is a good length scale in RBC only for sufficiently large Γ because only then is Nu independent of Γ (Ahlers et al 2022;Zwirner et al 2021). Nevertheless, most experiments are conducted in cylinders of Γ close to 1 in order to maximize H, and in this way Ra.…”

Section: Introductionmentioning

confidence: 99%

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Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

et al. 2022

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We report on the presence of the boundary zonal flow in rotating Rayleigh–Bénard convection evidenced by two-dimensional particle image velocimetry. Experiments were conducted in a cylindrical cell of aspect ratio $\varGamma =D/H=1$ between its diameter ( $D$ ) and height ( $H$ ). As the working fluid, we used various mixtures of water and glycerol, leading to Prandtl numbers in the range $6.6 \lesssim \textit {Pr} \lesssim 76$ . The horizontal velocity components were measured at a horizontal cross-section at half height. The Rayleigh numbers were in the range $10^8 \leq \textit {Ra} \leq 3\times 10^9$ . The effect of rotation is quantified by the Ekman number, which was in the range $1.5\times 10^{-5}\leq \textit {Ek} \leq 1.2\times 10^{-3}$ in our experiment. With our results we show the first direct measurements of the boundary zonal flow (BZF) that develops near the sidewall and was discovered recently in numerical simulations as well as in sparse and localized temperature measurements. We analyse the thickness $\delta _0$ of the BZF as well as its maximal velocity as a function of Pr, Ra and Ek, and compare these results with previous results from direct numerical simulations.

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Section: Introductionmentioning

confidence: 99%

“…2022; Zwirner et al. 2021). Nevertheless, most experiments are conducted in cylinders of close to 1 in order to maximize , and in this way .…”

Section: Introductionmentioning

confidence: 99%

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

et al. 2022

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“…However, it is recognised widely that the mean velocity profile in wall shear flows cannot be applied to describe vertical convection (VC), due to the effect of buoyancy (Ke et al 2020). The VC is the buoyancy-driven flow along a vertical heated wall, and it usually includes three configurations (Hölling & Herwig 2005;Howland et al 2022): (a) a single heated vertical plate immersed in an ambient fluid (Tsuji & Nagano 1988a,b;Wells & Worster 2008;Ke et al 2020), abbreviated as 'plate VC' hereafter; (b) a closed cavity with two opposite sidewalls heated at different temperatures (Shishkina 2016;Jiang et al 2019;Wang et al 2021;Zwirner et al 2022), abbreviated as 'cavity VC' hereafter; (c) a vertical infinite channel with periodic boundary conditions in the wall-parallel directions (Pallares et al 2010;Ng et al 2013Ng et al , 2015Howland et al 2022;Ching 2023), abbreviated as 'channel VC' hereafter. This study focuses on the last configuration of VC, as shown in figure 1(a).…”

Section: Introductionmentioning

confidence: 99%

“…2021; Zwirner et al. 2022), abbreviated as ‘cavity VC’ hereafter; ( c ) a vertical infinite channel with periodic boundary conditions in the wall-parallel directions (Pallares et al. 2010; Ng et al.…”

Section: Introductionmentioning

confidence: 99%

Mean velocity and temperature profiles in turbulent vertical convection

Li,

Jia,

Liu

et al. 2023

J. Fluid Mech.

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In this study, mean velocity and temperature profiles for turbulent vertical convection (VC) confined in an infinite channel are investigated theoretically. The analysis starts from the governing equations of the thermal flow, with Reynolds shear stress and turbulent heat flux closed by the mixing length theory. Employing a three-sublayer description of the mean fields, the mean velocity and temperature profiles are found to be linear laws near the channel wall (viscosity-dominated sublayer), and they follow power laws close to the channel centre (turbulence-dominated sublayer). The characteristic scales of velocity, temperature and length in the present profiles arise naturally from the system normalisation, rather than from scaling analyses, thus ensuring a sound mathematical description. The derived profiles are verified fully via various literature data available in the classical regime; further, they are compared with the reported profiles, and the results indicate that the present profiles are the only ones with the ability to interpret data accurately from different sources, demonstrating much better versatility. Meanwhile, we provide analytical arguments showing that in the ultimate regime, the mean profiles in VC may remain in power laws, rather than the log laws inferred by analogy with Rayleigh–Bénard convection (RBC) systems. The power profiles recognised in this study are induced by the effect of buoyancy, which is in parallel with the mean flow in VC and contributes to the streamwise momentum transport, whereas in RBC systems, buoyancy is perpendicular to the mean flow, and does not influence the streamwise momentum transport, resulting in log profiles, being similar to the case of wall shear flows.

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“…The work devoted to the study of natural convection in liquid gallium for the crystal growth applications can be distinguished as one of the early ones [20]. In some studies on inclined convection, the position of a cylindrical container at the extreme horizontal point will also correspond to the case of vertical convection [8,9] The most complete study from the fluid mechanics point of view on vertical convection of liquid metal in a box-shaped container was published in [21].…”

Section: Introductionmentioning

confidence: 99%

Interaction of Vertical Convection with an Electromagnetically Forced Flow

Shvydkiy¹,

Smolyanov²,

Baake³

2022

Preprint

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Heat and momentum transfer of low-Prandtl-number fluid (P r = 0.029) in a closed rectangular cavity (100 × 60 × 10 mm 3 ) heated at one side and cooled at the opposite side are analyzed. The electromagnetic forces into the liquid metal are generated by the travelling magnetic field inductor and directed towards buoyancy forces. Large eddy simulations are performed with the Grashof number Gr from 1.9 • 10 5 to 7.6 • 10 7 and the electromagnetic forcing parameter F from 2.6 • 10 4 to 2.6 • 10 6 . An experimental validation of the simulation results of vertical convection and electromagnetically driven flow using GaInSn alloy has been performed. Three types of flow patterns are obtained for different interaction parameters N = F/Gr: counterclockwise flow, clockwise flow, and coexistence of two vortices. Analysis of the Reynolds number shows that the transition zone from natural convection to electromagnetic stirring lies in the range 0.02 < F/Gr < 0.07 and two braking modes are found. The transition point between the convective heat transfer regimes is found for F/Gr around 1. The analysis of isotherms deformation showed that in such convective systems it is possible to achieve minimum deviation of the isotherm shape from a straight line in the range of 0.05 < F/Gr < 0.2.

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Dynamics and length scales in vertical convection of liquid metals

Cited by 19 publications

References 61 publications

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection

Mean velocity and temperature profiles in turbulent vertical convection

Interaction of Vertical Convection with an Electromagnetically Forced Flow

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