三维方腔内导电流体第1次Hopf分叉

流体力学与飞行力学

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三维方腔内导电流体第1次Hopf分叉

张敬奎¹, 常家鹏¹, 崔苗²(), 李琦芬¹, 任洪波¹, 杨涌文¹

^1.上海电力大学能源与机械工程学院，上海 200090
^2.大连理工大学工业装备结构分析优化与CAE软件全国重点实验室，大连 116024

收稿日期:2022-11-28 修回日期:2023-01-29 接受日期:2023-03-17 出版日期:2023-09-25 发布日期:2023-04-03
通讯作者: 崔苗 E-mail:miaocui@dlut.edu.cn
基金资助:
国家自然科学基金(12172078)

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

Jingkui ZHANG¹, Jiapeng CHANG¹, Miao CUI²(), Qifen LI¹, Hongbo REN¹, Yongwen YANG¹

^1.College of Energy and Mechanical Engineering，Shanghai University of Electric Power，Shanghai 200090，China
^2.State Key Laboratory of Structural Analysis，Optimization and CAE Software for Industrial Equipment，Dalian University of Technology，Dalian 116024，China

Received:2022-11-28 Revised:2023-01-29 Accepted:2023-03-17 Online:2023-09-25 Published:2023-04-03
Contact: Miao CUI E-mail:miaocui@dlut.edu.cn
Supported by:
National Natural Science Foundation of China(12172078)

摘要/Abstract

摘要：

磁场作用下导电流体由Hopf分叉引起的不稳定转变还未有研究涉及。采用课题组开发的配置点谱方法与人工压缩法相结合的数值方法SCM-ACM直接求解次临界流动状态下的磁流体控制方程，采用Fourier分析法获得速度振荡的频谱分布，研究了一定哈特曼数 $H a$ 条件下三维方腔内导电流体由稳态流动转变为非稳态周期性振荡流动的第1次Hopf分叉。结果显示，磁场强烈抑制了速度振荡，显著增加了第1次Hopf分叉的临界雷诺数 $R e c r$ 。随 $H a$ 从0增加至5，速度振幅的衰减速度呈抛物线形式急剧增加。同时， $R e c r$ 也呈抛物线形式增加，由1 916.6增加至2 040.1。然而，不同 $H a$ 条件下，速度振荡均仅有唯一主导的无量纲角频率（ $ω = 0.575 2$ ）。所提Hopf分叉的方法和相关结果，能够为工程设计和运行控制提供参考。

关键词: 第1次Hopf分岔, 磁流体力学（MHD）, 振荡流动, 不稳定性分析, 配置点谱方法

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

中图分类号:

V211.1

张敬奎, 常家鹏, 崔苗, 李琦芬, 任洪波, 杨涌文. 三维方腔内导电流体第1次Hopf分叉[J]. 航空学报, 2023, 44(18): 128328-128328.

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.

图/表 10

表 1

三维方腔内由第1次Hopf分叉的临界参数预测结果

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

表 1

图 1

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图 9

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E-mail：hkxb@buaa.edu.cn

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三维方腔内导电流体第1次Hopf分叉

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

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