Study on Validity of Low-Magnetic-Reynolds-Number Assumption for Hypersonic Magnetohydrodynamic Control

Abstract

When the magnetic Reynolds number [Formula: see text], the induced magnetic field caused by the applied electric field [Formula: see text] and the applied magnetic field [Formula: see text] can be neglected for magnetohydrodynamic (MHD) control of plasma flows, which is the well-known low-magnetic-Reynolds-number assumption and widely used in the hypersonic MHD numerical simulation. The present study shows whether the induced magnetic field can be neglected depending on not only the magnetic Reynolds number but also the load factor [Formula: see text], where [Formula: see text] is the characteristic velocity. For the MHD accelerator problem, e.g., theoretical and numerical results indicate that the induced magnetic field is proportional to the product of [Formula: see text] and [Formula: see text], and the relative error caused by the induced magnetic field can reach above 25% for the temperature along the channel centerline. Based on the quantitative simulations at different [Formula: see text] and [Formula: see text], an improved criterion [Formula: see text] is proposed in this study to estimate the validity of the low-magnetic-Reynolds-number assumption.