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Theoretical analysis of quasi-one-dimensional compressible magnetohydrodynamic channel flow
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2021-07-15 , DOI: 10.1016/j.amc.2021.126500
Ke Xu 1 , Xiang Li 1 , Zhenxun Gao 1, 2, 3 , Chongwen Jiang 1, 2, 3 , Chun-Hian Lee 1
Affiliation  

A theoretical analysis of quasi-one-dimensional, steady, inviscid, compressible channel flow at a low magnetic Reynolds number with variable cross-section is performed in this paper. A second-order nonlinear dynamical system describing the variation of physical parameters is investigated in the phase plane. The characteristics of all possible channel flow with a constant electromagnetic field are obtained by the phase plane and the isomorphism of labeled graphs. It is revealed that the magnetic interaction number novelly derived from the variation rate of the cross-sectional area could significantly affect the phase trajectory in the phase plane of dimensionless velocity and Mach number. Meanwhile, the phase trajectory is only dependent on this magnetic interaction number. Further analysis of the second-order dynamical system discovers five critical values in the range of the magnetic interaction number. These five critical values can divide the whole range into eight subsets under the isomorphism of labeled graphs, forming eight equivalence classes of the phase plane. The study of such eight equivalence classes reveals that the variable cross-section flow in the phase plane can be viewed as a linear superposition of constant cross-section magnetohydrodynamic flow and isentropic flow, the weight ratio being exactly the magnetic interaction number. Consequently, for the divergent channel, the acceleration region in the supersonic zone is larger than that of the constant cross-section flow, while for the convergent channel, only the acceleration region in the subsonic zone is larger than that of the constant cross-section flow.



中文翻译:

准一维可压缩磁流体动力通道流的理论分析

本文对具有变截面的低磁雷诺数下准一维、稳定、无粘性、可压缩通道流进行了理论分析。在相平面上研究了描述物理参数变化的二阶非线性动力系统。通过相平面和标记图的同构得到具有恒定电磁场的所有可能通道流动的特征。结果表明,由横截面积变化率新推导出的磁相互作用数可以显着影响无量纲速度和马赫数相平面中的相轨迹。同时,相轨迹仅取决于此磁相互作用数。对二阶动力系统的进一步分析发现了磁相互作用数范围内的五个临界值。这五个临界值可以在标记图的同构下将整个范围划分为八个子集,形成相平面的八个等价类。对这八个等价类的研究表明,相平面中的变截面流可以看作是等截面磁流体动力学流和等熵流的线性叠加,权重比正是磁相互作用数。因此,对于发散通道,超音速区的加速区域大于等截面流的加速区域,而对于收敛通道,

更新日期:2021-07-15
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