IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v433y2022ics0096300322004891.html
   My bibliography  Save this article

Dynamical and chaotic behaviors of natural convection flow in semi-annular cylindrical domains using energy-conserving low-order spectral models

Author

Listed:
  • Khodakaram-Tafti, Amin
  • Emdad, Homayoun
  • Mahzoon, Mojtaba

Abstract

This paper presents a comprehensive theoretical study on the dynamical behavior of natural convection flow in the confined region between horizontal half-cylinders. For this purpose, a low-order spectral model with three modes will produce for the fluid flow system using the Galerkin technique. It proved that the generated model is physically meaningful, as it conserves energy in the dissipationless limit and has bounded solutions in the phase space. Analytical procedures indicate that the system has three stationary points and the onset of instability in the flow is when the Rayleigh number reaches a critical value. With an appropriate Lyapunov function is proved that for the Rayleigh numbers below the critical value, the flow is globally stable. As the Rayleigh number gets higher and reaches a fixed value, a Hopf bifurcation occurs, and chaotic motion appears in the system. The critical and Hopf Rayleigh numbers relation are derived parametrically based on dynamical system theories. Also, numerical simulations will carry on the presented low-order model. Different dynamical behaviors of this flow and its transition from regular to chaotic motion are explained, with phase portraits and velocity-temperature diagrams obtained by numerical solutions. This parametric study can pave the way for future researchers to determine at around values of critical parameters should an experiment or direct numerical simulation be performed to have more accurate data without resorting to tests at all operating conditions.

Suggested Citation

  • Khodakaram-Tafti, Amin & Emdad, Homayoun & Mahzoon, Mojtaba, 2022. "Dynamical and chaotic behaviors of natural convection flow in semi-annular cylindrical domains using energy-conserving low-order spectral models," Applied Mathematics and Computation, Elsevier, vol. 433(C).
  • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004891
    DOI: 10.1016/j.amc.2022.127415
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322004891
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2022.127415?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Siddheshwar, P.G. & B. N., Shivakumar & Zhao, Yi & C., Kanchana, 2020. "Rayleigh-Bénard convection in a newtonian liquid bounded by rigid isothermal boundaries," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. Roy, D. & Musielak, Z.E., 2007. "Generalized Lorenz models and their routes to chaos. II. Energy-conserving horizontal mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 747-756.
    3. Ahmed, Hamdi E. & Ahmed, Mirghani I., 2017. "Thermal performance of annulus with its applications; A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 71(C), pages 170-190.
    4. Zhang, Fuchen, 2015. "On a model of the dynamical systems describing convective fluid motion in rotating cavity," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 873-882.
    5. Roy, D. & Musielak, Z.E., 2007. "Generalized Lorenz models and their routes to chaos. I. Energy-conserving vertical mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1038-1052.
    6. Roy, D. & Musielak, Z.E., 2007. "Generalized Lorenz models and their routes to chaos. III. Energy-conserving horizontal and vertical mode truncations," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1064-1070.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Khodakaram-Tafti, Amin & Emdad, Homayoun & Mahzoon, Mojtaba, 2024. "Periodicity and chaos of thermal convective flows in annular cylindrical domains using the method of isolation by spectral expansions," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Khodakaram-Tafti, Amin & Emdad, Homayoun & Mahzoon, Mojtaba, 2024. "Periodicity and chaos of thermal convective flows in annular cylindrical domains using the method of isolation by spectral expansions," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    2. Cui, Jialin & Shen, Bo-Wen, 2021. "A kernel principal component analysis of coexisting attractors within a generalized Lorenz model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Garay, B.M. & Indig, B., 2015. "Chaos in Vallis’ asymmetric Lorenz model for El Niño," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 253-262.
    4. Reyes, Tiffany & Shen, Bo-Wen, 2019. "A recurrence analysis of chaotic and non-chaotic solutions within a generalized nine-dimensional Lorenz model," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 1-12.
    5. Duan, Zhisheng & Wang, Jinzhi & Yang, Ying & Huang, Lin, 2009. "Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 848-861.
    6. Ayati, Moosa & Khaloozadeh, Hamid, 2009. "A stable adaptive synchronization scheme for uncertain chaotic systems via observer," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2473-2483.
    7. Xue Chen & Chuang Sun & Xinlin Xia & Rongqiang Liu, 2018. "Numerical Analysis on the Radiation-Convection Coupled Heat Transfer in an Open-Cell Foam Filled Annulus," Energies, MDPI, vol. 11(10), pages 1-20, October.
    8. Husain, Shahid & Adil, Md & Arqam, Mohammad & Shabani, Bahman, 2021. "A review on the thermal performance of natural convection in vertical annulus and its applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 150(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004891. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.