Lorentz Force Transient Response at Finite Magnetic Reynolds Numbers

Abstract

In this paper, we investigate the transient response of Lorentz force at finite magnetic Reynolds numbers $ {R_{m}}$ on an electrically conducting rectangular bar that is strongly accelerated in the presence of a localized magnetic field. This is done through numerical simulations utilizing a coupled finite-difference boundary element approach. The results show good qualitative agreement with existing experiments with a circular cylinder. The Lorentz force rise time is seen to be a linear function of $ {R_{m}}$ . The linear dependence of Lorentz force on $ {R_{m}}$ is found to be valid only for low values of $ {R_{m}}$ , after which the slope decays leading to an apparent saturation in the Lorentz force at sufficiently large values of $ {R_{m}}$ . Our results provide important information for the development of Lorentz force flow meters for transient flow applications.