Hydromagnetic stability of current-induced flow in a small gap between concentric rotating cylinders

被引:5
作者
Chang, MH [1 ]
Chen, CK [1 ]
机构
[1] Natl Cheng Kung Univ, Dept Mech Engn, Tainan 701, Taiwan
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1998年 / 454卷 / 1975期
关键词
Taylor number; Hartmann number; hydromagnetic stability; Lorenz force; axisymmetric disturbance; non-axisymmetric disturbance;
D O I
10.1098/rspa.1998.0237
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
The stability analysis of the flow of a viscous electrically conducting fluid between concentric rotating cylinders in the presence of an axial magnetic field is extended to the case where the primary flow includes a pressure gradient acting in the azimuthal direction. The pressure gradient is produced electromagnetically by the interaction of a superimposed radial current and the uniform axial magnetic field. The assumption of small gap approximation is made and the governing equations with respect to both axisymmetric and non-axisymmetric three-dimensional disturbances are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of Q, the Hartmann number which represents the strength of axial magnetic field, and beta, a parameter characterizing the ratio of induced current and rotation velocities, is conducted for weakly conducting cylinders and the situation of practical interest where the outer cylinder is stationary and the inner cylinder is rotating. The area where the onset mode is non-axisymmetric is shown in the plane (beta, Q). It is found that the most stable state occurs approximately along a critical curve (beta + 4.3)Q(2) + 56 250(beta + 3.75) = 0 and the critical axial wavenumber always has discontinuity when the parameters Q and beta cross this curve. The critical mode transition of the onset of instability will, be demonstrated in detail and results for the critical wavenumber and the critical Taylor number are presented. The corresponding values of the radial current density required for the appearance of secondary flow are also determined.
引用
收藏
页码:1857 / 1873
页数:17
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