The interaction between a uniform magnetic field and a conducting duct highlights a fundamental phenomenon in electromagnetism, bearing considerable consequences for both theoretical research and practical applications. A uniform magnetic field, defined by its constant magnitude and direction, applies forces on moving charges within conductive materials, resulting in phenomena such as electromagnetic induction and the creation of Lorentz forces. These interactions are crucial in technologies such as magnetohydrodynamic generators, electromagnetic flow meters, and advanced cooling mechanisms in nuclear reactors. Comprehending these implications not only enhances our understanding of electromagnetic principles but also drives innovation in engineering and industrial processes. This is where validating a paper becomes important using ANSYS Fluent MHD module. This study is conducted based on the paper titled” Effect of Hartmann layer resolution for MHD flow in a straight, conducting duct at high Hartmann numbers”.

• Reference [1]: Subramanian, Sharanya, et al. “Effect of Hartmann layer resolution for MHD flow in a straight, conducting duct at high Hartmann numbers.” Sadhana40 (2015): 851-861.

Figure 1: Uniform Magnetic Field CFD Simulation using MHD module

Simulation Process

A square duct and a rectangular duct with cross-sections of 25 mm by 25 mm and 25 mm by 50 mm, respectively, and a length of 500 mm have been designed. Accordingly, a structured, non-uniform mesh—coarse in the central region of the flow and increasingly finer towards the walls—was utilized (figure 2), resulting in 2040000 hexagonal cells. The Magnetic Induction and Electric Potential methods are employed to resolve MHD equations. Given that Ha/Re >> 1/300 for the geometries under investigation, the laminar model was selected for the numerical solution. The entrance velocity for all scenarios was 0.01 m/s, established by a Velocity entrance boundary condition, while a Pressure Outlet boundary condition was employed to set the channel outlet gauge pressure to 0 atm. A No-slip boundary condition was implemented on all inner wall surfaces, treating these walls as connected to guarantee the continuation of the normal component of current density and electric potential. The external surfaces of the wall were designed as insulating barriers to prevent the passage of electric current through these limits.

Figure 2: Structured non-uniform grid produced for Uniform Magnetic Field Effect CFD Simulation Using MHD

Post-processing

The numerical results show significant agreement with the benchmark data from Subramanian et al., as seen by the velocity profile comparison in the graph. The CFD simulation (shown by the solid line) closely matches the actual data points across the whole duct width, with a particularly strong correlation in the central region where the z-velocity reaches its maximum of approximately 0.03 m/s. This validation demonstrates the accuracy of our computational method as well as the dependability of the electromagnetic coupling integration in the solver.

Figure 3: Validation graph of Uniform Magnetic Field Effect CFD Simulation Using MHD

The distribution of the electromagnetic field, as seen by the magnitude plots of the E and B fields, follows distinct patterns throughout the conductor. The electric field (E) is evenly distributed along the length of the duct; however, the magnetic field (B) shows significant striations with alternate intensity bands ranging from 7.76e-6 to 1.15e-5 Tesla. The field patterns quickly alter the flow structure, resulting in the symmetric velocity profile typical of MHD channel flows. The maximal field strengths are placed near the duct walls, where electromagnetic coupling effects are strongest, resulting in the observed velocity profile formation.

Figure 4: Magnitude of a) Magnetic Field b) Electric field in  Uniform Magnetic Field Effect CFD Simulation Using MHD