Numerical Simulations on the Fully Developed Liquid-metal MHD Flow at High Hartmann Numbers in the Rectangular Duct

Abstract

Numerical simulation on the liquid metal mangetohydrodynamic (MHD) flow is a very attractive way to study the MHD flow problems. The two-level radial point interpolation method is applied to study the fully developed MHD flow in this work. With the method, numerical simulations of the MHD flows at Hartmann numbers up to 10 4 in a duct with arbitrary wall conductance ratios, namely, from thin conducting to insulated wall ducts, are conducted. The non-dimensional flowrate for different electrical conductivities of the duct wall are listed and compared with the exact solutions, showing a good accuracy. These results also indicate that the higher electrical conductivity of the duct wall, the lower non-dimensional flowrate, which is consistent with the well-known MHD flow behavior. Numerical simulations for insulated walls with conducting cracks or different orientation of external applied magnetic field are also carried out with the two-level radial point interpolation method.