Direct numerical simulation study on the mechanisms of the magnetic field influencing the turbulence in compressible magnetohydrodynamic flow

The magnetohydrodynamic (MHD) control has great potential in the applications of hypersonic vehicles. Typically, the MHD flowfield in these applications is low magnetic Reynolds (Re_m) compressible turbulent flow, which is different from that without magnetic field and within the high Re_m range. This paper investigated the low Re_m compressible MHD isotropic turbulence in different Taylor-scale Reynolds numbers and interaction parameters via the Direct Numerical Simulation (DNS), and the influence of the magnetic field on the turbulence is researched. Results indicate that the normal Reynolds stress decreases in the direction perpendicular to the magnetic field. Moreover, the eddies are stretched in the direction parallel to the magnetic field. Besides, the Joule dissipation quicken the decay of the turbulent kinetic energy, and occurs mainly in large scale vortex. Based on the DNS data, the correlation between fluctuating electric intensity and velocity is studied. Results indicate that the electric intensity agrees well with the first-order approximate solution of the electric potential equation. Accordingly, an improved closure model of the correlation terms is established, where a coefficient related to the local turbulent Mach number is proposed. Comparisons with the DNS results reveal that the proposed model could correctly predict the correlation terms.