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Efficient mixing by swirling electrovortex flows in liquid metal batteries

Published online by Cambridge University Press:  11 March 2021

W. Herreman Open the ORCID record for W. Herreman [Opens in a new window] ,
C. Nore Open the ORCID record for C. Nore [Opens in a new window] ,
L. Cappanera Open the ORCID record for L. Cappanera [Opens in a new window]  and
J.-L. Guermond Open the ORCID record for J.-L. Guermond [Opens in a new window]
W. Herreman*
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400Orsay, France
C. Nore
Affiliation:
Université Paris-Saclay, CNRS, Laboratoire Interdisciplinaire des Sciences du Numérique, 91400Orsay, France
L. Cappanera
Affiliation:
Department of Mathematics, University of Houston, Houston, TX77204-3008, USA
J.-L. Guermond
Affiliation:
Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX77843-3368, USA
*
†Email address for correspondence: wietze.herreman@limsi.fr
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Abstract

Using direct numerical simulations, we show that swirling electrovortex flows significantly enhance the mixing of the bottom layer alloy in liquid metal batteries during discharge. By studying the flow in various parameter regimes, we identify and explain a novel scaling law for the intensity of these swirling electrovortex flows. Using this scaling law and the model described in Herreman et al. (Phys. Rev. Fluids, vol. 5, 2020, 074501), we estimate the minimal intensity of the external magnetic field that is needed for the swirling electrovortex to enhance the mixing of the alloys in the bottom electrode of arbitrary liquid metal batteries.

JFM classification

Flow Control: Mixing enhancement Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A17
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Herreman et al. supplementary movie 1

Swirling electrovortex flow intensity in axisymmetric simulation of Figure 4, from time t=0 s to 12s with intervals of 0.1 s.

Download Herreman et al. supplementary movie 1(Video)
Video 1.9 MB

Herreman et al. supplementary movie 2

Molar fraction in axisymmetric simulation of Figure 4, from time t=0 s to 12s with intervals of 0.1 s.

Download Herreman et al. supplementary movie 2(Video)
Video 1 MB

Herreman et al. supplementary movie 3

Evolution of the molar fraction with time in the three-dimensional simulation reported in Figure 5(b). Successive snapshots are not uniformly sampled in time: snapshots 1 to 6 (t = 1s to 6 s, every 1s), snapshots 7 to 23 (t = 6.5s to 14.5s, every 0.5s), snapshots 24 to 35 (t = 14.75s to 17.5s, every 0.25s), snapshots 36 to 42 (t=17.625s to 18.375s, every 0.125s).

Download Herreman et al. supplementary movie 3(Video)
Video 3.3 MB

Herreman et al. supplementary movie 4

Evolution of the molar fraction with time in the three-dimensional simulation reported in Figure 6(a). Successive snapshots are not uniformly sampled in time: snapshots 1 to 6 (t = 1s to 6 s, every 1s), snapshots 7 to 23 (t = 6.5s to 14.5s, every 0.5s), snapshots 24 to 35 (t = 14.75s to 17.5s, every 0.25s), snapshots 36 to 42 (t=17.625s to 18.375s, every 0.125s).

Download Herreman et al. supplementary movie 4(Video)
Video 4 MB

Herreman et al. supplementary movie 5

Evolution of the flow intensity in the three-dimensional simulation of swirling electrovortex flow without solutal buoyany, reported in Figure 12. Time varies from t=15s to 20s, every 0.2s.

Download Herreman et al. supplementary movie 5(Video)
Video 1.5 MB