The magnetohydrodynamic (MHD) control has great potential in the applications of hypersonic vehicles. Typically, the MHD flowfield in these applications is low magnetic Reynolds (Rem ) compressible turbulent flow, which is different from that without magnetic field and within the high Rem range. This paper investigated the low Rem 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.

中文翻译：

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磁场影响可压缩磁流体动力流动湍流机制的直接数值模拟研究

磁流体动力学（MHD）控制在高超音速飞行器的应用中具有巨大的潜力。通常，这些应用中的 MHD 流场是低磁雷诺 (Rem) 可压缩湍流，这与没有磁场的情况不同，处于高 Rem 范围内。本文通过直接数值模拟(DNS)研究了不同泰勒级雷诺数和相互作用参数下的低Rem可压缩MHD各向同性湍流，并研究了磁场对湍流的影响。结果表明，法向雷诺应力在垂直于磁场的方向上减小。此外，涡流在平行于磁场的方向上被拉伸。此外，焦耳耗散加速了湍动能的衰减，并且主要发生在大尺度涡旋中。基于DNS数据，研究了脉动电场强度与速度的相关性。结果表明，电场强度与电势方程的一阶近似解吻合得很好。据此，建立了相关项的改进闭合模型，提出了与局部湍流马赫数相关的系数。与 DNS 结果的比较表明，所提出的模型可以正确预测相关项。建立了相关项的改进闭合模型，提出了与局部湍流马赫数相关的系数。与 DNS 结果的比较表明，所提出的模型可以正确预测相关项。建立了相关项的改进闭合模型，提出了与局部湍流马赫数相关的系数。与 DNS 结果的比较表明，所提出的模型可以正确预测相关项。