Magnetoconvection and Convection in Liquid Metals

In magnetoconvection (MC), the flow of an electromagnetically conductive fluid is driven by a combination of buoyancy forces, which create the fluid motion due to thermal expansion and contraction, and Lorentz forces, which distort the convective flow structure in the presence of a magnetic field. MC governs most astro- and geophysical systems and is relevant to various engineering applications. The former include, for instance, outer layers of stars and liquid-metal planetary cores, examples of the latter comprise liquid-metal batteries, electromagnetic brakes in continuous casting, liquid-metal cooling for nuclear fusion reactors, and semiconductor crystal growth. One of the key objectives in MC research is to provide scaling relations for the heat transport through the system, represented in dimensionless form by the ratio of total to conductive heat flux, the Nusselt number Nu, as a function of the strength of buoyancy (Rayleigh number Ra) and electromagnetic forces (Hartmann number Ha).
However, the heat transport scaling relations also depend on the flow configuration, including the angle between the magnetic field and gravity, the geometry of the container and the boundary conditions, and whether the buoyancy forces dominate over the Lorentz forces in the system or vice versa.

In A. Teimurazov, M. McCormack, M. Linkmann and O. Shishkina, J. Fluid Mech. 980, R3 (2024) we proposed a theoretical model for the transition between the buoyancy-dominated (BD) and Lorentzforce-dominated (LD) regimes for the case of a static vertical magnetic field applied across a convective fluid layer confined between two isothermal, a lower warmer and an upper colder, horizontal surfaces. When the flow is turbulent with a very weak or no constraining force (BD regime), the heat transport displays a classical Rayleigh–B´enard convection (RBC) power-law dependence Nu ∼ Raγ with the scaling exponent γ. However, when the flow is strongly influenced by a constraining force (LD regime), the heat transport also displays a power-law dependence Nu ∼ (Ha−2Ra)ξ with the scaling exponent ξ. Although these scaling laws in the two extreme regimes appear disconnected, they are intrinsically linked under the assumption that they must overlap at some intermediate region, where the influence of neither the Lorentz force nor the buoyancy force on the convective heat transport can be ignored.
Turbulent thermal convection of a liquid metal (Pr = 0.03) without a presence of any external magnetic fields also exhibits rich dynamics as demonstrated in our study of vertical convection (VC), where two opposite square sidewalls are heated/cooled L. Zwirner, M. S. Emran, F. Schindler, S. Singh, S. Eckert, T. Vogt, and O. Shishkina, J. Fluid Mech. 932, A9 (2022), and RBC A. Teimurazov, S. Singh, S. Su, S. Eckert, O. Shishkina and T. Vogt, J. Fluid Mech. 977, A16 (2023). For some aspect ratios, and at a sufficiently high values of Ra, the flow dynamics includes a 3D oscillatory mode known as a jump rope vortex (JRV).

In A. Teimurazov, S. Singh, S. Su, S. Eckert, O. Shishkina and T. Vogt, J. Fluid Mech. 977, A16 (2023), we investigated the effects of varying domain aspect ratio Γ (a ratio between the spatial length and height of the domain) on this mode, for liquid metals, at a low Prandtl number (Pr = 0.03). DNS and experiments are carried out for a Rayleigh number range (2.9×104 ≤ Ra ≤ 1.6×106) and square cuboid with different aspect ratios varying from 2 to 5. We detected the oscillatory modes for all investigated Γ. The vortices form an orthogonal cross that periodically rotates alternately clockwise and anticlockwise for domains with the aspect ratios Γ = 2.5 and 3. In a Γ = 5 cell, a lattice of four JRVs interlace each other, which oscillate in a synchronised manner.

 

Further reading

Andrei Teimurasov, Matthew McCormack, Moritz Linkmann and Olga Shishkina, Unifying heat transport model for the transition between buoyancy-dominated and Lorentz-force-dominated regimes in quasistatic magnetoconvection, J. Fluid Mech. (2024), vol. 980, R3

Andrei Teimurasov, Sanjay Singh, Sylvie Su, Sven Eckert, Olga Shishkina and Tobias Vogt, Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit, J. Fluid Mech. (2023), vol. 977, A16

Lukas Zwirner, Mohammad S. Emran, Felix Schindler, Sanjay Singh, Sven Eckert, Tobias Vogt and Olga Shishkina, Dynamics and length scales in vertical convection of liquid metals, J. Fluid Mech. (2022), vol. 932, A9

Oleg Zikanov, Yaroslav Listratov, Xuan Zhang and Valentin Sviridov Instabilities in Extreme Magnetoconvection. In: Gelfgat A. (eds) Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics. Computational Methods in Applied Sciences 50 (2019), Springer.
 
Xuan Zhang and Oleg Zikanov. Convection instability in a downward flow in a vertical duct with strong transverse magnetic field. Phys. Fluids 30 (2018), 117101.
 
Xuan Zhang and Oleg Zikanov. Thermal convection in a toroidal duct of a liquid metal blanket. Part II. Effect of axial mean flow. Fusion Eng. and Des. 116 (2017), 40–46.
 
Xuan Zhang and Oleg Zikanov. Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor. J. Fluid Mech. 779 (2015), 36–52.
 
Xuan Zhang and Oleg Zikanov. Mixed convection in a horizontal duct with bottom heating and strong transverse magnetic field. J. Fluid Mech. 757 (2014), 33–56.