三维方腔内导电流体第1次Hopf分叉

Abstract

Abstract:

The unstable transition of conducting fluid caused by Hopf bifurcation under the action of 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 magnetohydrodynamics (MHD) governing equations under the subcritical flow state directly. The Fourier analysis is employed to calculate the spectral distribution of 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 Ha. The results show that the magnetic field strongly suppresses velocity oscillation and significantly increases the critical Reynolds number Re_cr for the first Hopf bifurcation. With the increase of Ha from 0 to 5， the decay of velocity amplitude increases sharply in a parabolic form. The Re_cr also increases in a parabolic form， from 1 916.6 to 2 040.1. However， the velocity oscillations with different Ha only have a unique dominant dimensionless angular frequency （ω=0.575 2）. 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 (MHD), oscillatory flow, instability analysis, spectral collocation method

CLC Number:

V211.1

Jingkui ZHANG, Jiapeng CHANG, Miao CUI, Qifen LI, Hongbo REN, Yongwen YANG. First Hopf bifurcation of conducting fluid in three-dimensional square cavity[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 128328-128328.

Figures/Tables 10

Table 1

Prediction of critical parameters by the first Hopf bifurcation in a three-dimensional square cavity

研究者	临界雷诺数 $R e c r$	临界无量纲角频率 $ω$
Feldman和Gelfgat^［4］	1 914	0.575
Kuhlmann和Albensoeder^［5］	1 915.5	0.586
Loiseau等^［19］	1 914
Gelfgat^［20］	1 914.6	0.586
Zhang等^［21］	1 916.6	0.575 2
Liberzon等^［22］	1 700~1 970	0.472~0.651
Chang等^［23］	1 750~1 950
Anupindi等^［24］	2 100~2 250

Table 1

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First Hopf bifurcation of conducting fluid in three-dimensional square cavity

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