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Numerical characterization of a liquid metal magnetohydrodynamic alternate generator in the laminar-regime under inductionless approximation
Author(s): Jose Amilcar Rizzo Sierra, Cesar Isaza, Jonny Paul Zavala de Paz, Ely Karina Anaya Rivera
Keywords: Magnetohydrodynamics, Oscillatory liquid metal flow, Laminar fully developed regime, Inductionless approximation, Navier-Stokes equation, Spectral collocation method, Alternative power generation
Performance characterization of a liquid metal magnetohydrodynamic alternate generator is numerically investigated by calculating its electric isotropic efficiency. The alternate generator model consists of a harmonically driven liquid metal oscillatory flow confined to a thin-walled closed rectangular channel interacting with a uniform magnetic field transverse to its motion and attached to a load resistance. Spectral collocation method is used to solve the properly boundary-conditioned Navier-Stokes equation under \textit{inductionless} approximation for the magnetic field with implementation of gradient formulation for the electric field. Flow is considered fully developed in the direction perpendicular to the applied uniform magnetic field (i.e., motion direction), incompressible, viscous, and laminar in regime. Numerical results are cross-referenced with analytical results from a one-dimensional analytical model, finding reasonable correspondence. Equally comparable analytical models or purely experimental results to this problem's conditions are not viable or available, hence the need of computational treatment and the absence of an equally termed analytical/numerical validation. Characterization is developed in terms of an unreported dimensionless group of parameters defining the problem: Hartmann number, oscillatory interaction parameter, duct aspect ratio, and load resistance. This paper presents another stage in the development and testing of a set of physical/numerical models applicable to both magnetohydrodynamics and power generation aspects of Cartesian-symmetric liquid metal flow. Antecedents focus on the magnetohydrodynamics of oscillatory rectangular channel flow, whereas this focuses on a system set as generator with the attachment of a load resistance. Dimensional estimates on the power production of prospective mesoscale devices having in mind household application are provided for different liquid metals as well. Calculations presented might be useful in different magnetohydrodynamic (alternative) power generation contexts.