Study on the liquid metal flow transitions behind a circular cylinder under the axial magnetic field

We study the magnetohydrodynamic flow around a circular cylinder confined in a rectangular duct. In this configuration, both the circular cylinder and the walls of the rectangular duct are electrically insulating, while the magnetic field aligns with the axial direction of the cylinder. The experimental measurements are performed by controlling two parameters Re and N (N is the ratio of electromagnetic forces to inertial forces) in the ranges of (180-722) and (0.8-264), respectively. Utilizing the electrical potential method, we employ both movable and wall probes to obtain the local flow velocities in the wake of the cylinder. By analyzing the space correlation of the signals obtained from the wall probes, a distinct transition in the flow behavior is observed, transitioning from a three-dimensional state to a quasi-two-dimensional (Q2D) state when the external magnetic field reaches a sufficient strength (N > 3). Additionally, the Q2D state allows for a further subdivision based on the scaling relationship R e / H a ∼ ( 0.41 - 0.42 ) in the stability map, thereby distinguishing between steady and unsteady flow states, which is consistent with findings from previous studies.