Magnetic Field Effects on Backward-Facing Step Flow of Ferrofluids

Backward-facing step (BFS) flow is a benchmark case study in fluid mechanics. Its control by means of electromagnetic actuation has attracted great interest in recent years. This paper focuses on the effects of a uniform stationary magnetic field on the laminar ferrofluid BFS flows for the Reynolds number range $0.1≤Re≤400$ and different expansion ratios. The coupled ferrohydrodynamic equations, including the microscopically derived magnetization equation, for a two-dimensional domain are solved numerically by an openfoam solver after validation and a test of accuracy. The application of a magnetic field causes the corner vortices in the concave corner behind the step to be retracted compared with their positions in the absence of a magnetic field. The maximum percentage of the normalized decrease in length of these eddies reaches 41.23% in our simulations. For small Reynolds numbers (<10), the flow separation points on the convex corner are lowered in the presence of a magnetic field. Furthermore, the dimensionless total pressure drop between the channel inlet and outlet decreases almost linearly with Reynolds number $Re$⁠, but the drop is greater when a magnetic field is applied. On the whole, the normalized recirculation length of the corner vortex increases nonlinearly with increasing magnetic Reynolds number $Rem$ and Brownian Péclet number $Pe$⁠, but it tends to constant values in the limits $Rem≪1$ and $Rem≫1$⁠.