A flow of an electrically conducting fluid in the form of a round jet entering a square duct subjected to a transverse magnetic field is studied using direct numerical simulations. The complex dynamics of the jet, determined by the effects of Joule dissipation, the flow's transformation into anisotropic states, the Kelvin–Helmholtz instability leading to the development of large-scale fluctuations, and the constraints imposed by the duct's walls, is revealed through analysis of the fields of velocity, pressure, and electric currents. The results show a good qualitative agreement with earlier experiments and provide an explanation for the experimental findings. In particular, the simulations confirm the hypothesized existence of two distinct regimes of the flow: an unstable central jet at low-to-moderate Stuart numbers N and a macrovortex shedding large-scale quasi-two-dimensional eddies at large N. The system is also used as a benchmark for the exploration of possible sources of uncertainty in experimental and numerical analysis of liquid-metal magnetohydrodynamics (MHD). A detailed comparison between the results of the simulations and the experimental data, as well as a parametric study of the effects of the model assumptions, allows us to identify and quantitatively assess the main such sources: the accuracy of velocity measurement by the electric potential sensors, the uncertain electric conductivity of the walls, the velocity profile and perturbations at the inlet, and the time of averaging required for accurate evaluation of mean flow properties in the presence of large-scale eddies typical for MHD flows.
Listratov et al. (Wed,) studied this question.
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