Magnetohydrodynamic flow regimes in an annular channel

One method and two results have contributed to the complete understanding of magnetohydrodynamic laminar flow in an annular channel with a transverse magnetic field in this paper. In terms of the method, a computationally cheap semi-analytic algorithm is developed based on the spectral method and perturbation expansion. By virtue of the fast computation, dense cases with almost continuous varying Hartmann number M, Reynolds number Re, and cross section ratio eta are calculated to explore the flow patterns that are missed in previous research. In terms of the results of the inertialess regime, we establish the average velocity map and electric-flow coupling delimitation in eta-M space. Seven phenomenological flow patterns and their analytical approaches are identified. In terms of the results of the inertial regime, we examine the law of decreasing order-of-magnitude of inertial perturbation on primary flow with increasing Hartmann number. The proposed semi-analytic solution coincides with the Re-2/M-4 suppression theory of J. A. Baylis and J. C. R. Hunt [ "MHD flow in an annular channel; theory and experiment, " J. Fluid Mech. 43, 423-428 (1971)] in the case of M < 40. When M > 40, the pair of trapezoid vortices of secondary flow begins to crack, and there is, therefore, a faster drop in inertial perturbation as Re-2/M-5, which is a new suppression theory. When M > 80, the anomalous reverse vortices are fully developed near Shercliff layers resulting in the weaker suppression mode of Re-2/M-2.5, which confirms the theoretical prediction of P. Tabeling and J. P. Chabrerie [ "Magnetohydrodynamic secondary flows at high Hartmann numbers, " J. Fluid Mech. 103(1), 225-239 (1981)].