Effect of radius of toroidal square duct on the transition of electromagnetically driven liquid metal flow

Abstract

Toroidal magnetohydrodynamic flows are important for fusion technology because of the blanket surrounding the core of the fusion machine. The effect of the radius of toroidal square ducts on flow transition of an electromagnetically driven liquid metal is assessed. The flow governing equations are solved numerically using direct numerical simulation. Critical Reynolds (Re) numbers where transition occurs are obtained for Hartmann (Ha) numbers in the range of 3 < Ha < 500. The results are compared with previous experimental and numerical results of toroidal square ducts of various radii. It is shown that, independent of the toroidal duct mean radius (r), the transition occurs in three regimes: in the sub-magnetohydrodynamic regime for very low Ha numbers, in a plateau regime for 10 < Ha < 20 and in a higher Ha regime. By increasing the radius of the torus, a transition occurs at higher Reynolds numbers as turbulent fluctuations are developing inside the boundary layers of the cylindrical side walls. The results indicate that transition occurs at RerH̃a-3.39 in the sub-magnetohydrodynamic regime and at RerH̃a-1.4 in the magnetohydrodynamic one. The boundary layer thickness at the Hartmann walls were found to scale as Ha-0.8.