Abstract
The stability of magnetohydrodynamic flow in a duct with perfectly conducting walls is investigated in the presence of a homogeneous and constant static magnetic field. The temporal growth and spatial distribution of perturbations are obtained by solving iteratively the direct and adjoint governing equations with respect of perturbations, based on nonmodal stability theory. The effect of the applied magnetic field, as well as the aspect ratio of the duct on the stability of the magnetohydrodynamic duct flow is taken into account. The computational results show that, weak jets appear near the sidewalls at a moderate magnetic field and the velocity of the jet increases with the increase of the intensity of the magnetic field. The duct flow is stable at either weak or strong magnetic field, but becomes unstable at moderate intensity magnetic field, and the stability is invariance with the aspect ratio of the duct. The instability of magnetohydrodynamic duct flow is related with the exponential growth of perturbations evolving on the fully developed jets. Transient growth of perturbations is also observed in the computation and the optimal perturbation is found to be in the form of streamwise vortices and localized within the sidewall layers. By contrast, the Hartmann layer perpendicular to the magnetic field is irrelevant to the stability issue of the magnetohydrodynamic duct flow.
Highlights
The problem of magnetohydrodynamic (MHD) flow through ducts has become important because of several industrial applications, such as design of the cooling blankets for nuclear fusion reactor, MHD pumps, measurement of blood flow, etc [1,2,3]
As the aspect ratio r is increased, the amplification factor G is getting closer to the limit Gmax % 1800, which corresponds to r ! 1, i. e., the channel case
A static and homogeneous magnetic field is imposed along the height of the duct, which is kept constant while the width of the duct is varied
Summary
The problem of magnetohydrodynamic (MHD) flow through ducts has become important because of several industrial applications, such as design of the cooling blankets for nuclear fusion reactor, MHD pumps, measurement of blood flow, etc [1,2,3]. Nonmodal stability analysis in the Hartmann flow reported similar structures in the form of streamwise vortices, which are confined in the Hartmann layers [10,11,12] Based on these ideas, Krasnov et al [19] performed direct numerical simulation (DNS) on MHD channel flow to explore a two-step transition scenario including the evolution of streamwise vortices into streaks and breakdown of streaks to subsequent transition. After performing normal mode stability analysis, Priede et al [21] demonstrated that the flow in a square duct become unstable at Ha = 9.6 They have shown that for high value of Ha, Instability occurred in the form of strongly non-uniform vortices aligned with the magnetic field.
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