Liquid metal flow analysis in a duct with sudden expansion under an inclined magnetic field

Liquid metal flow studies pertaining to liquid breeder blankets typically assume a unidirectional magnetic field, often transverse to the flow. In contrast to this simplified picture, in a Tokamak, the toroidal magnetic field alone makes a shallow angle to the liquid flow. Additionally, a poloidal magnetic field can be further superimposed, leading to an overall higher inclination angle of the magnetic field. Sudden expansion is one of the prevalent geometrical entities present in all typical fusion blanket designs. In the present work, numerical simulations have been carried out to understand the liquid metal flow, undergoing a sudden expansion, in the presence of various magnetic-field inclination angles and wall conductivity ratios. The numerical approach has been first validated against the experimental data available in the literature. Then, the validated model is used for further numerical computations across various parameter ranges (125 < Stuart number < 7455). The three-dimensional (3D) pressure drop across the sudden expansion is found to follow an inverted S curve with an increase in inclination angle of the magnetic field, for which a correlation has been proposed. The influence of the inclination angle on the recirculation region has been investigated. Twisting of fluid is observed after the expansion for intermediate inclination angles, which is generally absent for completely transverse magnetic fields. With an increase in wall conductance ratio, the pressure drop still follows the inverted S curve, but its steepness depends upon the value of the wall conductance ratio. The present findings, together with the proposed 3D pressure drop correlation, provide valuable information for the design and optimization of liquid breeder blankets.