高超声速MHD球头激波脱体距离理论求解

高超声速飞行器强激波后高温气体形成具有导电性的等离子体流场, 电离气体为磁场应用提供了直接工作环境, 磁流体流动控制技术利用外加磁场影响激波后的离子或电子运动规律, 这可以有效改善高超声速飞行器气动特性. 激波脱体距离作为高超声速磁流体流动控制较为直观的气动现象, 受到研究者重点关注; 磁场添加后激波脱体距离发生变化, 其变化幅度直接反映磁控效果, 然而基于高超声速磁流体流动控制的相关理论模型较少, 需要进一步发展. 本文基于低磁雷诺数假设和偶极子磁场分布的条件, 通过对连续方程沿径向积分以及对动量方程采用分离变量的方法, 推导了高超声速磁流体流动控制下的球头激波脱体距离解析表达式. 理论分析结果表明, 激波脱体距离随着磁相互作用系数的增加而变大; 随着来流速度的增加, 磁相互作用系数变为影响激波脱体距离大小的主要因素. 本文理论模型可以达到快速评估磁控效果的目的, 对高超声速磁流体流动控制实验方案设计和结果分析具有一定的指导意义. 

THEORETICAL ANALYSIS ON HYPERSONIC MHD SHOCK STAND-OFF DISTANCE OF BLUNT BODY

High speed and shock compression behind the bow shock of an aircraft head result in very high temperature, which would subsequently lead to a conductivity plasma flowfield around the vehicle. The plasma gas provides a direct working environment for the application of magnetic field. The magnetohydrodynamic (MHD) flow control, which uses the magnetic field to alter the trajectory of ions or electrons, can improve the aerodynamic characteristics of hypersonic vehicles effectively. As an intuitive aerodynamic phenomenon in the field of hypersonic MHD flow control, shock stand-off distance has attracted close attention from researchers. Under the influence of the applied magnetic field, the shock stand-off distance will change with it, of which the value can directly reflect the effect of the MHD flow control. However, the relevant theoretical models are still limited, and further development in this field is consequently needed. Focusing on dealing with this problem, MHD hypersonic shock stand-off distance of the spherical model is theoretically studied in this paper. By means of radially integrating the continuity equation and applying mathematical method of variable separation to the momentum equation, the analytical expression of MHD shock stand-off distance is obtained. The theoretical analysis was performed under the assumption of low magnetic Reynolds number, and the common-used dipole distribution of magnetic field as applied. The results show that the MHD stand-off distance of shock increases with the increase of magnetic interaction parameter. Moreover, the regularity can be found that as the speed of inflow becomes higher, magnetic interaction parameter can be viewed as the primary impact factor of shock stand-off distance under hypersonic condition. The theoretical model in this work can rapidly evaluate the effect of MHD control, and it can provide theoretical guidance to the design of experiment scheme and the analysis of results.