A model and assessments of the effect of transient plasma on liquid metal flows in a fusion blanket

• A model for liquid metal MHD flows driven by the pressure gradient and a transient magnetic field . • 2D analytical solution for a non-conducting rectangular duct and 1D solution for a channel with electrically conducting walls. • New dimensionless parameter Sm , which characterizes the effect of the transient magnetic field on the flow compared to the effect of the pressure gradient . • 2D transient finite-difference numerical code and analysis of MHD flows in a fusion blanjket. • Analysis of liquid metal MHD flows in conditions of plasma disruptions for lead blanket concepts. Rapid changes in the magnetic field associated with the transient plasma in a tokomak are known to induce eddy currents in a liquid metal (LM) breeding blanket. These currents interact with the extant strong reactor magnetic field resulting in large electromagnetic forces. A simplified 2D model for a fully developed LM magnetohydrodynamic flow in a rectangular duct driven by a pressure gradient and transient magnetic field has been proposed to assess the LM flow behavior in conditions when the poloidal component of the magnetic field varies linearly in time while the other two field components are constant. A new dimensionless parameter Sm (characterizes the effect of the transient plasma on the LM flow compared to the effect of the pressure gradient) has been identified and calculated for the lead LM blanket concepts. Two analytical solutions for a steady-state flow and a transient finite-difference numerical code have been developed and applied to LM MHD flows for various Sm (up to 50), Hartmann numbers (up to 10 000) and wall conductance ratios. The characteristic feature of the flow driven by the transient magnetic field at high Sm is the formation of the cross-sectional current loop in the LM with the induced currents flowing in the thin boundary layers resembling the classical Hartmann layers. The interaction of these currents with the constant in time toroidal magnetic field results in a special antisymmetric velocity profile. The high maximum velocities in such a flow occur near the Hartmann walls on the order of 10° m/s for the conventional segmented blanket and 10 1 –10 2 m/s for a toroidally symmetric banket. The transition time needed to achieve the steady state decreases quickly with the toroidal field. For the field > 4 T, the transition time was found to be comparable with the plasma disruption time ∼ 10–20 ms.