|
|
- 2016
侧壁非对称的方管MHD流动的线性稳定性分析
|
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.
| [1] | <p> Smolentsev S, Moreau R, Abdou M. Characterization of key magnetohydrodynamic phenomena in PbLi flows for the US DCLL blanket[J]. Fusion Engeering and Design, 2008, 83(5): 771-783. |
| [2] | Pothérat A. Quasi-two-dimensional perturbations in duct flows under transverse magnetic field[J]. Physics of Fluids, 2007, 19(7): 319-345. |
| [3] | Shatrov V, Gerbeth G. Marginal turbulent magnetohyd-rodynamic flow in a square duct[J]. Physics of Fluids, 2010, 22(8): 585-591. |
| [4] | Priede J, Aleksandrova S, Molokov S. Linear stability of magnetohydrodynamic flow in a perfectly conducting rectangular duct[J]. Journal of Fluid Mechanics, 2012, 708: 111-127. |
| [5] | Hunt J C R. Magnetohydrodynamic flow in rectangular ducts[J]. Journal of Fluid Mechanics, 1965, 21(4): 577-590. |
| [6] | Shercliff J A. Steady motion of conducting fluids in pipes under transverse magnetic fields[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1953 (1): 136-144. |
| [7] | Tao Z, Ni M J. Analytical solutions for MHD flow at a rectangular duct with unsymmetrical walls of arbitrary conductivity[J]. Science China Physics, Mechanics Astronomy, 2015, 58(2): 024701. |
| [8] | Priede J, Aleksandrova S, Molokov S. Linear stability of Hunt's flow[J]. Journal of Fluid Mechanics, 2010, 649: 115. |
| [9] | Smolentsev S, Vetcha N, Moreau R. Study of instabilities and transitions for a family of quasi-two-dimensional magnetohy-drodynamic flows based on a parametrical model[J]. Physics of Fluids, 2012, 24(2): 024101. |
| [10] | Krasnov D, Zikanov O, Rossi M, et al. Optimal linear growth in magnetohydrodynamic duct flow[J]. Journal of Fluid Mechanics, 2010, 653(6): 273-299. |
| [11] | Jun H, Henry D, Yin X Y, et al. Linear biglobal analysis of Rayleigh-Bénard instabilities in binary fluids with and without throughflow[J]. Journal of Fluid Mechanics, 2012, 713(6): 216-242.</p> |
