The Laminar-Turbulence Transition in Wall-Bounded Incompressible Magnetohydrodynamic Flows

Abstract

Understanding the laminar-turbulence transition mechanism in wall-bounded incompressible magnetohydrodynamic (MHD) flows is particularly important for liquid metal blankets of fusion reactors. However, this physical mechanism is still not thoroughly clear until now, especially there is a lack of quantitative analysis results to indicate where within the channel the transition process is likely to occur first. Moreover, the Hartmann layer thickness-based Reynolds number (R) has been found as a single parameter to control the transition process in MHD flows, but a mathematical explanation about this parameter is still absent. In this work, the turbulence transition phenomenon of the wall-bounded incompressible MHD flow is studied by a method called the energy gradient analysis. It points out that the ratio of the total mechanical energy density gradient in the transverse direction to that in the streamwise direction of the main flow (defined by a dimensionless parameter K) characterizes the development of the disturbance in the flow field. We have found that the distance between the initial turbulence transition position in the Hartmann layer and the Hartmann wall is always 69.31% of the thickness of the Hartmann layer, independent of the value of the Hartmann number (Ha). The effects of the Hartmann number and the wall conductance ratio on the initial turbulence transition position in the side layer are also investigated. At last, the reason why the Hartmann layer thickness-based Reynolds number (R) plays the role as a single control parameter in the transition process of MHD flows is explained mathematically.