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Tuesday 30 Nov 2021Mathematical modelling of free-surface thermoelectric magnetohydrodynamic (TEMHD) flow inside a tokamak reactor

Oliver Bond -

Harrison 101 13:30-15:30

Tokamak Energy, a nuclear fusion company based in Didcot, have built a device known as a tokamak (derived from the Russian word, meaning “toroidal chamber with magnetic field”). It is called ST-40 ( and its aim is to reach 100 million degrees Celsius; temperatures under which nuclear fusion can take place, just like in the core of the Sun. At the top and bottom of ST40 is a component called the divertor. Tokamak Energy are currently exploring ways to incorporate a layer of liquid lithium as a coolant coating the divertor plate, but they want to avoid any regions where the divertor plate is left exposed to the plasma and therefore prone to being damaged in a phenomenon known as dryout. ST40 currently has a piecewise flat divertor plate but Tokamak Energy are investigating using one comprised of a sequence of radial channels or “trenches", inspired by Liquid Metal Infused Trenches (LiMIT), a design created at the University of Illinois at Urbana-Champaign (UIUC). Combined with a toroidal magnetic field, the temperature gradient created by the plasma creates a Lorenz force down the trenches which pushes the liquid lithium down them. This is a direct result of a phenomenon called the Seebeck effect, where a temperature gradient passed along an interface between two electrically conducting materials results in an induced current around that interface. The LiMIT concept exploits the fact that the solid divertor plate and the liquid lithium layer both possess Seebeck coefficients of opposite signs, resulting in current loops around the side walls. The impinging heat flux from the plasma onto the free surface of the liquid lithium results in a temperature gradient which drives the flow.

This project therefore relates to the study of thermoelectric magnetohydrodynamic (TEMHD) flow inside a divertor trench, where the flow is taken to be steady and unidirectional. We provide some asymptotic results and how these draw parallels to classical MHD duct flow problems. We also show some numerical results obtained using COMSOL. Although there is still some work to be done, for example in 3D, even in 2D modelling work we highlight some interesting phenomena.


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