高超声速飞行器磁控热防护霍尔电场数值方法研究  

Numerical solution procedure for Hall electric field of the hypersonic magnetohydrodynamic heat shield system

作　　者：李开[1] 柳军[1] 刘伟强[1] 

机构地区：[1]国防科学技术大学航天科学与工程学院,长沙410073

出　　处：《物理学报》2017年第8期179-188,共10页Acta Physica Sinica

基　　金：湖南省自然科学基金(批准号:13JJ2002);国家自然科学基金(批准号:90916018)资助的课题~~

摘　　要：作为一种新概念高超声速热防护手段,磁控热防护系统在实际应用中往往需要考虑霍尔效应的影响.为了在真实气体环境下求解霍尔电场,采用交替隐式近似因子分解法建立并验证了热化学非平衡流体域电场数值求解方法.分析了电场虚拟步进因子和收敛性的关系以及影响步进因子取值的因素,提出了当地变步进因子加速电场收敛方法.研究表明,存在一个最优的步进因子a_p使得霍尔电场收敛速度最快,并且随网格尺度的减小和霍尔系数的增加,最优步进因子a_p变大,电势场收敛速率变慢.对于局部加密网格而言,当地变步进因子法的电势收敛性明显优于常规的定步进因子法.Magnetohydrodynamic（MHD） heat shield system is a novel-concept thermal protection technique for hypersonic vehicles,which has been proved by lots of researchers with both numerical and experimental methods.Most of researchers neglect the Hall effect in their researches.However,in the hypersonic reentry process,the Hall effect is sometimes so significant that the electric current distribution in the shock layer can be changed by the induced electric field.Consequently,the Lorentz force as well as the Joule heat is varied,and thus the efficiency of the MHD heat shield system is affected.In order to analyze the influence of Hall effect,the induced electric field must be taken into consideration.According to the weakly-ionized characteristics of hypersonic flow post bow shock,the magneto-Reynolds number is assumed to be small.Therefore,the Maxwell equations are simplified with the generalized Ohm＇s law,and the induced electric field is governed by the potential Possion equation.Numerical methods are hence established to solve the Hall electric field equations in the thermochemical nonequilibrium flow field.The electric potential Poisson equation is of significant rigidity and difficult to solve for two reasons.One is that the coefficient matrix may not be diagonally dominant when the Hall parameter is large in the shock layer,and the other is that this matrix including the electric conductivity is discontinuous across the shock.In this paper,a virtual stepping factor is included to strengthen the diagonal dominance and improve the computational stability.Moreover,approximate factor and alternating direction implicit method are employed for further improving the stability.With these methods,a FORTRAN code is written and validated by comparing the numerical results with the analytical ones as well as results available from previous references.After that,relation between the convergence property and the virtual stepping factor is revealed by theoretical analysis and numerical simulations.Based on these work,a loca

关 键 词：磁流体控制 热防护 霍尔效应 泊松方程 

分 类 号：V244.1[航空宇航科学与技术—飞行器设计]