An improved low magnetic Reynolds magnetohydrodynamic method based on computing induced magnetic vector potential by integrating induced current

Abstract

Aming at the applicability of low magnetic Reynolds number method, in this paper we analyze the differences in the application of low magnetic Reynolds number condition and the limitation of full MHD method when it is applied to hypersonic flow. According to the low magnetic Reynolds number magneto-hydrodynamic control numerical simulation method, computing magnetic vector potential through integrating induced current, and considering the reduction of computation domain caused by truncation factors, we propose a low magnetic Reynolds number MHD computation method which is adjusted by the induced magnetic field, and the validation of this method is also presented. Through the numerical simulation of RAM-C blunt cone in flight test condition, we analyze the discrepancy caused by “neglecting induced magnetic field”, and also discuss the principle of the application of low magnetic Reynolds number assumption of hypersonic flow. The obtained results are as follows. (1) The adjusted computation method developed in this paper breaks through the limit of low magnetic Reynolds number, and expands the application range of low magnetic Reynolds number method to hypersonic flow, the numerical simulation result is reliable; Compared with direct integration of Biot-Savart law, the computation efficiency is considerably improved. (2) In the hypersonic flow, the influence of induced magnetic field is presented, thus weakening and distorting the applied magnetic field macroscopically, as a result weakening the effect of magnetic control to some extent. Under the condition of this paper, the low magnetic Reynolds number condition “<i>Re<sub>m</sub></i> < 0.1” is probably too conservative, and it is better to adopt <i>Re<sub>m</sub></i> < 1.0, and the characteristic conductivity and characteristic length should be chosen according to the actual plasma distribution.