磁场作用下三维方腔内导电流体第一次Hopf分叉流动转变研究

doi:10.7527/S1000-6893.2023.28328

Abstract

Abstract: The unstable transition of conducting fluid caused by Hopf bifurcation under magnetic field has not been studied. In this work, the numerical method SCM-ACM which combines the spectral collocation method and artificial compressibility method developed by our research group, is used to solve the MHD governing equations directly. The Fourier analysis is employed to calculate the spectral distribution of the velocity oscillation. The first Hopf bifurcation of a conducting fluid from a steady state flow to an unsteady periodic oscillatory flow in a three-dimensional square cavity is studied with a range of Hartmann number . The results show that the magnetic field strongly suppresses the velocity oscillation and significantly increases the critical Reynolds number for the first Hopf bifurcation. With the increase of from 0 to 5, the decay velocity of velocity amplitude increases sharply in a parabolic form. The also increases in a parabolic form, from 1916.6 to 2040.1. However, the velocity oscillations only have a unique dominant dimensionless angular frequency (ω=0.5752) under different . The present research method and results on Hopf bifurcation can provide reference for the engineering design and operation control.

Key words: first Hopf bifurcation, magnetohydrodynamics, oscillatory flow, instability analysis

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Study on the Flow Transition by first Hopf bifurcation of conducting fluid in three-dimensional square cavity under magnetic field

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