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Ha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Re_(cr)。随Ha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,Recr也呈抛物线形式增加,由1916.6增加至2040.1。然而,不同Ha条件下,速度振荡均仅有唯一主导的无量纲角频率(ω=0.5752)。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。
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 re⁃sults show that the magnetic field strongly suppresses velocity oscillation and significantly increases the critical Reyn⁃olds number Re_(cr) for the first Hopf bifurcation.With the increase of Ha from 0 to 5,the decay of velocity amplitude in⁃creases sharply in a parabolic form.The Recr also increases in a parabolic form,from 1916.6 to 2040.1.However,the velocity oscillations with different Ha only have a unique dominant dimensionless angular frequency(ω=0.5752).The present research method and results on Hopf bifurcation can provide reference for the engineering design and op⁃eration control.
作者
张敬奎
常家鹏
崔苗
李琦芬
任洪波
杨涌文
ZHANG Jingkui;CHANG Jiapeng;CUI Miao;LI Qifen;REN Hongbo;YANG Yongwen(College of Energy and Mechanical Engineering,Shanghai University of Electric Power,Shanghai 200090,China;State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)
出处
《航空学报》
EI
CAS
CSCD
北大核心
2023年第18期132-142,共11页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(12172078)。
