A Finite Volume and Levenberg-Marquardt Optimization Framework for Benchmarking MHD Flows over Backward-Facing Steps

Abstract

This study examines the hydrodynamic and magnetohydrodynamic numerical solution of an electrically conducting fluid flow in a backward facing step (BFS) geometry under the influence of an external, uniform magnetic field applied at an angle. The numerical results are obtained utilizing the Finite Volume Method in a collocated grid configuration whereas the resulting system is solved directly using a Newton-like method in contrast to iterative approaches. The computed hydrodynamic results are validated with experimental and numerical studies for an expansion ratio of two. The magnetohydrodynamic case is also validated for Reynolds number $Re=380$ and Stuart number $N=0.1$ with previous numerical studies. Some applications of BFS flow under the influence of a magnetic field include metallurgical processes, cooling of nuclear reactors, plasma confinement, and biomedical applications in arteries. One of the most important findings of this study is the reduction of the reattachment point in contrast to the increase of pressure as the magnitude of the magnetic field is amplified. The magnetic field angle with the greatest influence on fluid flow has been observed to be at an angle of $\varphi = π/2$. In several cases, the magnetic field could substantially reduce the main flow vortex leading to a shifted reattachment point.

Figures (15)

• Figure 1: The geometry of BFS with the recirculation zone, the secondary recirculation region where a second smaller vortex exists and the potential flow where the velocity is equal to $u_{\infty}.$
• Figure 2: Backward-facing step for a uniform magnetic field of an angle $\varphi < \pi/2$.
• Figure 3: $u$-velocity contours for $Re=200, \ 400, \ 600$ and $800$, respectively.
• Figure 4: Pressure distribution contours for $Re=200, \ 400, \ 600$ and $800$, respectively.
• Figure 5: BFS for $u$-velocity zoomed with streamlines in the lower bubble (left) and upper bubble (right). Pressure distribution in the second figure. Figures correspond to $Re = 800$.