Theoretical modeling of a vortex-type liquid metal MHD generator for energy harvesting applications

The use of liquid metals (LM) in energy harvesting is gaining attention due to their unique properties. The DC vortex magnetohydrodynamic (MHD) generator is a suitable and robust option among the different approaches in which LM can be used for energy scavenging. In this device, the LM is driven in a cylindrical chamber to produce a swirling flow, which interacts with an external magnetic field, inducing electric currents that can be extracted to power an external electric system. In turn, the electrical resistance of this system highly affects the dynamics of the flow and the electric variables. In this work, two analytical models for the total voltage, electric current, electric and fluid power are developed. One model considers an inviscid fluid performing a rigid solid rotation. The second model considers a real fluid, for which the velocity distribution is also determined. For this latter case, MHD induced effects are modeled. These solutions are also obtained in dimensionless form in terms of the interaction parameter, Reynolds number and Hartmann number. In addition, 2D and 3D numerical models were implemented. These models are compared with reported experimental results, obtaining a good qualitative and quantitative agreement (differences ⩽13.5%) with numerical and analytical results.