Stability Of Conducting Fluid Flow Under A Vertical Magnetic Field

The instability of flow has been one of the most hot and difficult problems in fluid mechanics.The characteristics of flow will change when the fluid is conducting and flowing in the magnetic field,and the stability of the fluid flow is more difficult to predict,which is so-called MHD flow instability problem and has received a lot of concern and study from scholars.In this paper,the stability of conducting fluid flow in a perfectly conducting channel and a model of MHD duct flow with perfecting conducting walls under a vertical magnetic field were investigated using non-normal modal stability analysis and numerical simulation,respectively.The amplification and distribution of optimal primary perturbations are obtained by solving iteratively the direct and corresponding adjoint governing equations with respect of perturbations,and its effect on the stability problem is also considered.The stability analysis of conducting fluid flow in a perfectly conducting channel is performed.The results show that when the Hartmann number Ha is larger than 8,the two opposite Hartmann boundary layers are essentially independent of each other;however,when the Hartmann number Ha is smaller than 8,the suppression effect of the magnetic field on the antisymmetric vortices is more significant and there are still interactions between the two opposite Hartmann boundary layers to some extent,which has influences on the stability of the flow.By comparing the growth characteristics and spatial distribution of the primary disturbance in the case of conducting and insulting parallel channel walls,the influence of the wall conductivity on the stability of flow was explored.The results show that the growth of disturbances and spatial distributions of primary perturbations in the conducting walls case is similar to the one in the insulating walls case.When the walls are conducting,the suppression effect of the magnetic field on the disturbances is more significant.A model of MHD duct flow with perfecting conducting walls under a vertical magnetic field was also considered.The results show that two weak jets appear in the centre of the duct at a relatively magnetic field and the velocity of the jet increases while the thickness of the side layer decreases,with the increase of the intensity of the magnetic field.When Ha is small,the optimal streamwise wavenumber ?_opt is the same for the four modes,while the maximum amplification of perturbation energy G_max is different.When Ha is large enough,the vortices at the opposite walls are effectively separated by the center flow,the G_max and ?_opt are identical for different type of mode of perturbations.When Ha is mediate,some perturbations in the type of mode I,grows surprisingly with a very low exponential growth rate and may destabilize the mean flow considering time is sufficiently large.