Jingkui Zhang , Jiapeng Chang , Miao Cui , Yi Fan , Qifen Li , Cheng Peng
{"title":"Study on the steady-oscillatory transition of three-dimensional (3D) natural convection via Hopf bifurcation","authors":"Jingkui Zhang , Jiapeng Chang , Miao Cui , Yi Fan , Qifen Li , Cheng Peng","doi":"10.1016/j.euromechflu.2024.01.009","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>The transition from steady-state flow to periodic oscillatory flow<span> for the natural convection by </span></span>Hopf bifurcation<span> is investigated in a three-dimensional (3D) cavity. The spectral collocation method (SCM) in combination with the artificial compressibility<span> method (ACM), which is developed by ourselves as a numerical method SCM-ACM with high accuracy, is employed to solve the governing equations directly instead of linear stability analysis<span> method that is commonly used for the research on flow instability. The results show that the amplitude decays exponentially with time and the decay rate is linear with the Grashof number (</span></span></span></span><em>Gr</em>). The critical Grashof number for steady-oscillatory transition is obtained as <em>Gr</em><sub><em>cr</em></sub> = 3.423 × 10<sup>6</sup>. The dimensionless angular frequency <em>ω</em><sub><em>cr</em></sub><span> = 0.24 is also determined by Fourier analysis. In this work, we also examine the heat-momentum interactions within the boundary layers, visualize the periodic oscillations of temperature and velocity amplitudes, and analyze the origin of instability from multiple angles. The results show that large oscillations of velocity and temperature are observed near the isothermal<span> walls. The oscillation is enhanced by the increase of thermal boundary layer thickness and flow velocity at both ends of isothermal walls. The maximum velocity and temperature amplitudes appear at the lower left and upper right corners of the mid-plane (</span></span><em>Z</em><span> = 0.5), where are the origin of instability, and the spanwise walls are almost independent of oscillations. The oscillatory flow of natural convection in three-dimensional cavity originates from the continuously increasing buoyancy force, and its transition occurs by Hopf bifurcation. Moreover, the temperature amplitude exhibits a wavy distribution on the mid-plane (</span><em>X</em> = 0.5) and strongly depends on the depth <em>Z</em><span>. These results provide benchmark data for future numerical studies and engineering application.</span></p></div>","PeriodicalId":11985,"journal":{"name":"European Journal of Mechanics B-fluids","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Mechanics B-fluids","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0997754624000177","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The transition from steady-state flow to periodic oscillatory flow for the natural convection by Hopf bifurcation is investigated in a three-dimensional (3D) cavity. The spectral collocation method (SCM) in combination with the artificial compressibility method (ACM), which is developed by ourselves as a numerical method SCM-ACM with high accuracy, is employed to solve the governing equations directly instead of linear stability analysis method that is commonly used for the research on flow instability. The results show that the amplitude decays exponentially with time and the decay rate is linear with the Grashof number (Gr). The critical Grashof number for steady-oscillatory transition is obtained as Grcr = 3.423 × 106. The dimensionless angular frequency ωcr = 0.24 is also determined by Fourier analysis. In this work, we also examine the heat-momentum interactions within the boundary layers, visualize the periodic oscillations of temperature and velocity amplitudes, and analyze the origin of instability from multiple angles. The results show that large oscillations of velocity and temperature are observed near the isothermal walls. The oscillation is enhanced by the increase of thermal boundary layer thickness and flow velocity at both ends of isothermal walls. The maximum velocity and temperature amplitudes appear at the lower left and upper right corners of the mid-plane (Z = 0.5), where are the origin of instability, and the spanwise walls are almost independent of oscillations. The oscillatory flow of natural convection in three-dimensional cavity originates from the continuously increasing buoyancy force, and its transition occurs by Hopf bifurcation. Moreover, the temperature amplitude exhibits a wavy distribution on the mid-plane (X = 0.5) and strongly depends on the depth Z. These results provide benchmark data for future numerical studies and engineering application.
期刊介绍:
The European Journal of Mechanics - B/Fluids publishes papers in all fields of fluid mechanics. Although investigations in well-established areas are within the scope of the journal, recent developments and innovative ideas are particularly welcome. Theoretical, computational and experimental papers are equally welcome. Mathematical methods, be they deterministic or stochastic, analytical or numerical, will be accepted provided they serve to clarify some identifiable problems in fluid mechanics, and provided the significance of results is explained. Similarly, experimental papers must add physical insight in to the understanding of fluid mechanics.