Numerical Calculations of Liquid-Metal Magnetohydrodynamic Flows in Rectangular Ducts with Sudden Contractions

For the design of the liquid-metal blanket in a fusion reactor, numerical calculations have been carried out on liquid-metal magnetohydrodynamic flows in rectangular ducts with sudden contractions. Conservation equations of fluid mass and fluid momentum and the Poisson equation for electrical potential have been solved numerically. The numerical calculations have been conducted for a Hartmann number of ~10 000; a Reynolds number of ~10 000; and contraction ratios (CRs) of 2, 3, and 4. The pressure loss through the contraction has been estimated by the loss coefficient ζ divided by the interaction parameter N, i.e. ζ/N. The loss coefficient ζ/N through the contraction parallel to the magnetic field is much larger than that through the corresponding contraction perpendicular to the magnetic field. The loss coefficient ζ/N increases consistently with the CR and does not change very much with N. While ζ/N also does not change very much with the wall conductance ratio for the contraction parallel to the magnetic field, ζ/N increases gradually with the wall conductance ratio for the contraction perpendicular to the magnetic field.