Computational Magnetohydrodynamics (MHD) for Nuclear Fusion Blanket Studies

HyPerComp Incompressible MHD solver for Arbitrary Geometry
HIMAG is a pioneering complex geometry modeling software for incompressible two-phase magnetohydrodynamics (MHD) flows at fusion-relevant conditions.

HIMAG is used to model the flow of liquid metals and other flows occurring in fusion reactors where strong interactions with the magnetic field produce numerous effects that are unique to this brand of flows.

HIMAG and VTBM are developed under funding from the U.S. Department of Energy. For availability and enquiries concerning MHD and free surface modeling research at HyPerComp, please email:
Liquid Lithium reacts with neutrons to breed Tritium, an essential fuel for the fusion reaction. Lithium flow in a fusion reactor (e.g. ITER shown right) in strong magnetic fields is an important prediction hurdle in fusion reactor design. The Hartmann number (ratio of MHD force to viscous force) is often used to quantify the relative importance of MHD effects. HIMAG demonstrated for the first time in published literature the feasibility of very high Hartmann number (>10,000) calculations on complex geometries, validated against experiments and analysis. fusion reactor
In MHD flows, the applied magnetic field B induces closed electric current loops shown in the cross section of a square duct with conducting walls in the adjacent diagram. As the magnetic field intensity increases, the current lines cluster densely towards the wall perpendicular to the field and form “Hartmann layers”. Fluid momentum migrates towards the walls where the normal magnetic field component is lower, and the classic M-shaped profiles of the velocity u are observed. velocity profile

Sumary of HIMAG Capabilities

  • Three dimensional incompressible flow solver (second order accurate in space and time)
  • Free surface capture using the level set technique
  • Arbitrary mesh structure (hexahedral / tetrahedral / prismatic cells)
  • Well tested parallel code environment
  • Electric potential as well as induced magnetic field formulations for MHD
  • Point implicit scheme, solved in an iterative manner
  • Multiple strategies to account for mesh skewness (non-orthogonality)
  • Ability to include multiple solid walls of different conductivity and contact resistance
  • Heat transfer and natural convection


Various MHD Flows
Circular Duct Square Duct
Flow in a circular duct (above), at a Hartmann number of 6640, emerging from a region of strong magnetic field, and a similar flow in a square duct (above right). Computed data is shown compared with experiments. (Experimental data for comparison obtained from: Reed, C.B., Picologlou, B.D., Huan T.Q., Walker, J.S., "ALEX results - A comparison of measurements from a round and rectangular duct with 3-D code predictions," presented at the 12th IEEE symposium on Fusion Engineering, Monterey, CA, October 12-16, 1987)

Blanket Physics Modeling with HIMAG

The structure immediately surrounding the fusion plasma that forms a plasma chamber (referred to as a blanket,) serves a vital role in fusion energy systems by providing Tritium fuel self-sufficiency, radiation shielding of the vacuum vessel and efficient power extraction. A very promising candidate for a liquid breeder blanket for future reactors, is a Dual Coolant Lead-Lithium (DCLL) concept. DCLL uses the liquid metal eutectic alloy Lead-Lithium as a breeder and coolant, flowing in the presence of a strong plasma-confining magnetic field. Decades of research on the nature of such flows has revealed their enormous complexity, to the extent that no single analytical technique or experiment is presently available, which can accurately and economically represent the entire fluid dynamic-electromagnetic-thermal phenomena that are present.

Flow in the DCLL Module

Flow in the DCLL module computed using HIMAG, showing pressure profiles at various locations (above left) and velocity profiles (above right). Seen below are streamlines, with natural convection currents forming recirculation regions


Flow Channel Inserts (FCI, shown with dotted lines in the sketch above) are proposed as means to insulate the core of the liquid metal flow from the conducting steel walls, thus reducing pressure drop caused by MHD. (This will make it easier to pump the liquid metal into the reactor.) In the illustration to the right, we see the three dimensional effects of dividing the FCI midway in the DCLL channel, showing electric potential contours and electric current loops computed by HIMAG.

Continuous FCL

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