In blankets of a fusion power reactor, liquid metal (LM) breeders, such as pure lithium or lead-lithium alloy, circulate in complex shape blanket conduits for power conversion and tritium breeding in the presence of a strong plasma-confining magnetic field. The interaction of the magnetic field with induced electric currents in the breeder results in various magnetohydrodynamic (MHD) effects on the flow. Of them, high MHD pressure losses in the LM breeder flows is one of the most important feasibility issues. To design new feasible LM breeding blankets or to improve the existing blanket concepts and designs, one needs to identify and characterize sources of high MHD pressure drop, to understand the underlying physics of MHD flows and to eventually define ways of mitigating high MHD pressure drop in the entire blanket and its sub-components. This article is a comprehensive review of earlier and recent studies of MHD pressure drop in LM blankets with a special focus on: (1) physics of LM MHD flows in typical blanket configurations, (2) development and testing of computational tools for LM MHD flows, (3) practical aspects associated with pumping of a conducting liquid breeder through a strong magnetic field, and (4) approaches to mitigation of the MHD pressure drop in a LM blanket.

Three classic MHD problems are revisited assuming hydrodynamic slip condition at the interface between the electrically conducting fluid and the insulating wall: (1) Hartmann flow; (2) fully developed flow in a rectangular duct; and (3) quasi-two-dimensional (Q2D) turbulent flow. The first two problems have been solved analytically. Additionally to the Hartmann number (Ha), a new dimensionless parameter S, the ratio of the slip length to the thickness of the Hartmann layer, has been identified. One of the most important conclusions of the paper is that the duct flows with the slip still exhibit Hartmann layers, whose thickness scales as 1/Ha, while the thickness of the side layers is a function of both Ha and S. In the case of Q2D flows, a new expression for the Hartmann braking time has been derived showing its increase at Ha >> 1 by factor (1+ S). Numerical simulations performed for a flow with the “M-shaped” velocity profile show that in the presence of the slip, a Q2D flow becomes more irregular as vortical structures experience less Joule and viscous dissipation in the Hartmann layers.

Direct numerical simulations of turbulent pipe flow have been carried out in a constant transverse magnetic field. The Reynolds number based on bulk velocity and pipe diameter is set to Reb = 5300 for three Hartmann numbers, Ha, 5, 10 and 20. The skin friction velocity, velocity profiles, turbulent intensities and turbulent kinetic energy budget along the circumferential direction of the pipe have been obtained and a turbulent streaky structure has been investigated via computational flow visualization. The skin friction coefficient decreases in cases of Ha = 5 and 10; however, it increases in case of Ha = 20. The velocity profile becomes more rounded in the near-wall region at Π = π/2, and the velocity acceleration appears at the top of the pipe (Π = 0), especially for Ha = 20. This clearly shows that the ‘Hartmann effect' mainly occurs at Π = 0. It is also shown that all turbulent intensities and turbulent kinetic energy budget decrease at Π = 0 and remain at other positions (Π = π/4, π/2). The behavio...

In “An Approach to Verification and Validation of MHD Codes for Fusion Applications” [S. Smolentsev et al., Fusion Eng. Des., Vol. 100, p. 65 (2015)], an effort for verification and validation of computer codes for liquid metal flows in a magnetic field for fusion cooling/breeding applications was initiated. The current study continues that effort. A group of experts in computational magnetohydrodynamics from several institutions in the United States and Europe performed a code-to-code comparison for the selected reference case of a mixed-convection buoyancy-opposed magnetohydrodynamic flow of eutectic lead-lithium (PbLi) alloy in a thin-wall conducting square duct at Hartmann number Ha = 220, Reynolds number Re = 3040, and Grashof number Gr = 2.88 × 10⁷. As shown, the reference flow demonstrates a boundary layer separation in the heated region and formation of a reversed flow zone. The results of the comparison suggest that all five solvers predict well the key flow features but have moderate quantitative differences, in particular, in the location of the separation point. Also, two of the codes are more computationally dissipative, showing no velocity and temperature oscillations.

The generation of vorticity in the two-dimensional creeping flow of an incompressible, electrically conducting viscous fluid past a localized magnetic field distribution is analyzed under the low magnetic Reynolds number approximation. It is shown that the Lorentz force produced by the interaction of the induced electric currents with the nonuniform magnetic field acts as an obstacle for the flow, creating different steady flow patterns that are reminiscent of those observed in the flow past bluff bodies. First, analytic solutions are obtained for a creeping flow past a magnetic point dipole, modeled as a Gaussian distribution. Using a perturbation scheme, the vorticity is expressed as an expansion in the small Reynolds number, and first- and second-order approximations are calculated. The induced magnetic field, pressure, and stream function are also determined. Further, full numerical finite difference solutions are obtained for a uniform creeping flow past a finite size magnetic field distribution produced by a square magnetized plate. Hartmann numbers in the range $1⩽\mathrm{Ha}⩽100$ are explored. Depending on the strength of the magnetic force, stagnation zones or steady vortical structures are obtained. The analysis contributes to the understanding of flows in nonuniform magnetic fields and flows produced by localized forces.

Predicting 3D magnetohydrodynamic (MHD) pressure losses associated with liquid metal flows in complex geometry ducts is required to design breeding blankets for fusion reactors. Of such components, manifolds exhibit major pressure losses. Recent correlations [T. Rhodeset al. Magnetohydrodynamic pressure drop and flow balancing of liquid metal flow in a prototypic fusion blanket manifold. Phys. Fluids. 2018; 30: 057101.] demonstrate promise for predicting pressure drops in electrically insulated inlet manifolds. In the present work, the extend to which these correlations can be applied to outlet manifolds, which feature sudden contractions, is investigated in both viscous-electromagnetic (VE) and inertial-electromagnetic (IE) regimes for Reynolds numbers 50 < Re < 1500, Hartmann numbers 2500 < Ha < 5475, and expansion/contraction ratio 10. Numerical computations have shown that the MHD pressure drops in the eutectic lead-lithium (PbLi) flows in contractions are almost identical to those in the flows featuring expansion with slightly higher magnitudes in the contraction cases. The small discrepancy in the MHD pressure drop between contractions and expansions (<8%) suggests that the earlier obtained correlations for the 3D MHD pressure drop in a duct flow with a sudden expansion can also be applied to flows with a sudden contraction.