侧壁非对称的方管MHD流动的线性稳定性分析

doi:10.7523/j.issn.2095-6134.2016.01.007

中国科学院大学学报 ›› 2016, Vol. 33 ›› Issue (1): 42-49.DOI: 10.7523/j.issn.2095-6134.2016.01.007

侧壁非对称的方管MHD流动的线性稳定性分析

刘婵, 张年梅, 倪明玖

中国科学院大学物理学院, 北京 101408

收稿日期:2015-03-27 修回日期:2015-05-08 发布日期:2016-01-15
通讯作者: 倪明玖
基金资助:
国家自然科学基金(51376175)和973ITER项目(2013GB114001)资助

Linear stability analysis of MHD flow in square duct with unsymmetrical side walls

LIU Chan, ZHANG Nianmei, NI Mingjiu

School of Physics, University of Chinese Academy of Sciences, Beijing 101408, China

Received:2015-03-27 Revised:2015-05-08 Published:2016-01-15

摘要/Abstract

摘要：

研究垂向磁场作用下,压差驱动下的金属流体在方截面通道中充分发展流动的线性稳定性问题.此流动中,垂直于磁场的两壁面理想导电,平行于磁场的左壁面为理想导电,右壁面绝缘.根据线性稳定性理论得到广义特征值问题,并采用2D-Chebyshev配置法求解该特征值问题,得到扰动的增长率曲线和扰动速度在通道截面上的分布.结果表明,当Ha数变化时,流动中有2种不稳定模态依次起主导作用.这2种模态的交替发生在Ha数介于20至21之间某值.当Ha≤20时,拐点不稳定性起主导作用;当Ha≥21时,不稳定性由速度拐点、侧层内的速度剪切及射流沿z方向速度的不均匀性共同作用引起.

关键词: 线性稳定性, 垂向磁场, 不对称侧壁

Abstract:

Linear stability of liquid metal flow driven by pressure gradient in a square duct is investigated under the influence of a transverse magnetic field. In this study, the duct walls perpendicular to the magnetic field and the left parallel wall are perfectly conducting,whereas the right parallel wall is insulating. Generalized eigenvalue problem was obtained and solved by 2D-Chebyshev collocation method. Growth rate curves and distributions of perturbations are obtained for different Hartmann numbers. There are two different modes that lead to the linear instability of the flow. The dominant unstable mode alters from one to the other during the increase of Ha from 20 to 21. When Ha≤20, the flow is destabilized by the inflectional instability. When Ha≥21, the instability is caused by a combined effect by the inflection point, shear in side layer, and the non-uniformity of the velocity along the z direction.

Key words: linear stability, transverse magnetic field, unsymmetrical side walls

中图分类号:

O361.5

刘婵, 张年梅, 倪明玖. 侧壁非对称的方管MHD流动的线性稳定性分析[J]. 中国科学院大学学报, 2016, 33(1): 42-49.

LIU Chan, ZHANG Nianmei, NI Mingjiu. Linear stability analysis of MHD flow in square duct with unsymmetrical side walls[J]. , 2016, 33(1): 42-49.

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侧壁非对称的方管MHD流动的线性稳定性分析

Linear stability analysis of MHD flow in square duct with unsymmetrical side walls

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