Three-dimensional numerical simulations of magnetohydrodynamic flow around a confined circular cylinder under low, moderate, and strong magnetic fields

This paper presents three-dimensional direct numerical simulations of liquid metal flow around a circular cylinder placed symmetrically in a rectangular duct, under a wide range of magnetic field intensities. Results are presented for values of the Hartmann number (based on the duct width) in the range of 0 ⩽ Ha ⩽ 1120, and the Reynolds number (based on the cylinder diameter and centerline velocity) in the range 0 ⩽ Re_c ⩽ 5000. The generated flow regimes and the associated critical values of parameters are investigated in detail through full three-dimensional simulations. The effect of the magnetic field on the wake structure is discussed in relation to the possible mechanisms for the generation or suppression of vortices, and to previous attempts to model magnetohydrodynamic flows using simplified two-dimensional models. Present results reveal a non-monotonic dependance of the critical Reynolds number for the onset of vortex shedding, with respect to the Hartmann number. For certain combinations of Ha and Re values, this work confirms the onset of a new flow regime, the existence of which has been recently suggested based on quasi-two-dimensional simulations. Unexpectedly, the spanwise distribution of the force coefficients along the cylinder is found to become more three-dimensional with increasing Ha. Furthermore, the three-dimensional nature of the present simulations reveals additional counter-intuitive features of the new regime that could not possibly had been captured by quasi-two-dimensional models. One such feature, shown here for the first time, is an increase in the flow unsteadiness with increasing intensity of the magnetic field.