Optimal Transient Disturbances Preceding Vortex Shedding in Magneto-Hydrodynamic Flow past a Circular Cylinder in a Duct

Abstract – Flow of liquid metal in an electrically insulated rectangular duct past a circular cylinder under a strong axial magnetic field is investigated in the subcritical regime, below the onset of von Kármán vortex shedding. In this configuration, the flow is quasi-two-dimensional and can be solved over a two-dimensional domain. A transient energy growth analysis of optimal linear perturbations is carried out. Parameters are considered for Reynolds numbers 50 ≤ Re ≤ 2500, Hartmann numbers 500 ≤ Ha ≤ 1200, and blockage ratios 0.1 ≤ β ≤ 0.4. Transient growth is determined as a function of the evolution time of disturbances. For all β, the energy amplification of the disturbances was found to decrease significantly with increasing Ha and the peak growths shift towards smaller times. The nature of the disturbance does not vary with the blockage ratios. Index Terms – transient growth, magnetohydrodynamic