If mankind were to successfully replicate nuclear fusion reactions like those fueling the sun, it would have access to a clean, safe, and virtually unlimited source of carbon-free energy. To achieve this aim, the Tokamak constitutes the most promising concept (see e.g. [1] for more details). It consists of a vessel where a plasma is magnetically confined and heated to extremely high temperatures, allowing the ionized gas to undergo high-energy collisions that result in nuclear fusion reactions. A pivotal milestone in the pursuit of fusion energy will be reached when ITER begins operation and starts collecting experimental data [2].

In a Tokamak fusion power plant, a blanket system is essential for capturing neutrons emitted during fusion reactions. This system serves two main purposes: breeding the tritium needed to sustain the reaction and collecting heat, which is used to produce steam that drives turbines and generators to produce electricity.

Among the various blanket system designs, several feature duct assemblies through which liquid metal circulates. The flow then takes place within a region immersed in the intense magnetic field needed to confine the fusion plasma. Consequently, electric currents are induced within the liquid, significantly altering its dynamics compared to a purely hydrodynamic flow.

The branch of physics describing the behavior of electrically conducting flows and their interaction with electromagnetic fields is called Magnetohydrodynamics (MHD) [3]. It has a very broad range of applications, ranging from astrophysics to laboratory flows. In the case of liquid-metal flows relevant for blanket systems, a simplified version of the MHD equations, known as the quasi-static (QS) approximation [4], may be used. In this formulation, the confinement magnetic field strongly influences the flow, but the flow does not, in turn, affect the magnetic field. Its main effects are an increased heat dissipation and an anisotropic modification of flow structures.

Liquid metal flows subject to strong magnetic fields, such as those occurring in blanket systems, are notoriously challenging to compute numerically. This is a result of the existence within the flow of extremely thin boundary layers, requiring very refined meshes in some parts of the computational domain. As of today, no computational fluid dynamics (CFD) code can provide complete and accurate solutions to tackle the full complexity of blanket systems like that foreseen in ITER. Although significant progress has been made in recent years, the main bottleneck remains the huge computational costs associated to solve the flow equations through direct numerical simulation.

In this project, we aim to improve currently available methods by further developing our in-house MHD module for the yales2 solver [5, 6], and test several grid optimization strategies to produce grids of sufficient resolution with the least number of grid nodes.

The CFD code yales2, developed under the leadership of the CORIA laboratory, is a massively parallel code using the finite volume discretization. In this method, the computational domain is divided into small volumes and the flow equations are integrated on all of them to produce a discrete system. As a result, yales2 can accommodate complex geometries by utilizing hybrid grids made up of various shapes, such as hexahedrons, tetrahedrons, pyramids, and more. 

In the initial phase of this project, we intend to enhance the MHD module in yales2 by implementing various skewness correction methods and by analyzing the performance of different linear solvers based on the correction’s formulation. Skewness corrections are essential for solving MHD flows subjected to strong magnetic fields, as the necessary computational grids are generally highly stretched and skewed.

In the second phase of the project, grid optimization strategies will be tested in various canonical geometries to better understand how to cluster grid points at various locations in the flow to reduce the necessary number of grids points and achieve higher accuracy for flows subjected to intense magnetic fields.

Finally, thanks to the gained expertise in simpler geometries, we will test the methods developed for the simulation of mock-up blanket systems under fusion relevant conditions.

[1] https://euro-fusion.org

[2] https://www.iter.org

[3] Davidson PA. An Introduction to Magnetohydrodynamics. Cambridge University Press, 2001.

[4] Müller, U and Bühler, L. Magnetofluiddynamics in Channels and Containers. Springer, 2001

[5] https://www.coria-cfd.fr/index.php/YALES2

[6] https://difusion.ulb.ac.be/vufind/Record/ULB-DIPOT:oai:dipot.ulb.ac.be:…