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

TL;DR

This paper presents a finite volume and Levenberg-Marquardt optimization framework for benchmarking magnetohydrodynamic flows over backward-facing steps, highlighting magnetic field effects on flow reattachment and vortex behavior.

Contribution

It introduces a combined finite volume and Levenberg-Marquardt optimization approach for MHD flow analysis, with validation against experimental and numerical data.

Findings

Magnetic field reduces reattachment point as its magnitude increases.

Magnetic field angle of π/2 has the greatest influence on flow.

Magnetic field can significantly diminish the main vortex.

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 $\varphi = \pi/2$. In several cases, the magnetic field could substantially reduce the main flow vortex leading to a shifted reattachment point.