Numerical simulations of flow past a backward-facing step under a strong transverse magnetic field

The flow of liquid metal over a backward-facing step (BFS) exhibits unique flow characteristics due to the influence of strong magnetic field. In this study, direct numerical simulation of the BFS flow under a strong magnetic field is conducted based on a quasi-two-dimensional model (with a large interaction number, N ≫ 1 , and a large Hartmann number, H a ≫ 1 ). The Reynolds number (Re), Hartmann number (Ha), and expansion ratio (ER) are investigated within the ranges of [ 100 − 80 000 ] , [ 100 − 40 000 ] , and [ 1.67 − 5 ] , respectively. Three typical flow regimes are defined based on the evolution of the free shear layer vortices and the separation state of the boundary layer. Furthermore, a comprehensive flow regime map is presented for different ER, revealing a positive correlation between the critical Reynolds number ( R e c 1 ) and Ha at the onset of instability. Specifically, R e c 1 is proportional to H a 0.5 , H a 0.54 , and H a 0.56 for ER = 5, 2.5, and 1.67, respectively. Moreover, the maximum relative thickness of the free shear layer at H a c 1 appears in the range of approximately 0.7 - 0.78 L r for ER = 5, while for ER = 2.5, it appears in the range of approximately 0.80 - 0.85 L r , indicating that the instability position of the free shear layer occurs earlier for large ER. Our numerical investigation also demonstrates that an increase in the transverse magnetic field compresses the free shear layer and delays the process of vortex pairing, thereby suppressing the oscillatory behavior of the shear layer.