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

doi:10.7523/j.issn.2095-6134.2016.01.007

›› 2016, Vol. 33 ›› Issue (1): 42-49.DOI: 10.7523/j.issn.2095-6134.2016.01.007

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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 Online:2016-01-15

Abstract

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

CLC Number:

O361.5

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

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