Analytical Analysis of Flow in a Magnetohydrodynamic Pump (MHD)

The interaction of moving conducting fluids with electric and magnetic fields provides the magnetohydrodynamic (MHD) phenomenon. Based on this principle, MHD pump uses the "Lorentz Force" to move fluid. The railgun channel is one important segment in an electromagnetic launcher. As known one of the possible ways to increase the EML efficiency is to segment the working channel. For this purpose MHD flow study is necessary. It is required to have the knowledge of the flow field to design a magnetohydrodynamic pump. The purpose of this study is to analytically investigate the effect of Hartman number as well as magnetic and electrical angular frequency on the velocity distribution in a magnetohydrodynamic pump. To solve the governing differential equation, initially a velocity profile is guessed and then the Navier-Stokes is solved. Results show that as Hartman number approaches zero the velocity profile becomes similar to that of fully developed flow in a pipe. Furthermore, for frequency over 10pi rad/sec the flow can be treated as steady state. However below angular frequency of 10pi rad/sec velocity oscillates constantly. Therefore flow can not be treated as steady state.