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The Nonlinear Flow Characteristics within Two-Dimensional and Three-Dimensional Counterflow Models within Symmetrical Structures.

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Title: The Nonlinear Flow Characteristics within Two-Dimensional and Three-Dimensional Counterflow Models within Symmetrical Structures.
Authors: Wang, Wenshuai1 (AUTHOR) wangwen.shuai@163.com, Yang, Mo2 (AUTHOR) yangm@usst.edu.cn
Source: Energies (19961073). Jul2024, Vol. 17 Issue 13, p3176. 22p.
Subjects: Three-dimensional modeling, Counterflows (Fluid dynamics), Three-dimensional flow, Two-dimensional models, Fluid flow, Symmetry breaking
Abstract: In this paper, we investigate the nonlinear characteristics of the flow in a two-dimensional and a three-dimensional counterflow model with symmetrical structures. Through numerical simulations, we obtain the velocity fields of the fluid flow in these models for different Re. The numerical results are analyzed to understand the nonlinear characteristics and differences between the two-dimensional and three-dimensional models. The findings indicate that, when Re varies, both the two-dimensional and three-dimensional models exhibit solution bifurcations and nonlinear phenomena such as symmetry breaking, self-sustained oscillations, and chaos. As Re increases, the two-dimensional counterflow model displays a unique solution, an asymmetric solution, and an oscillating solution. Specifically, when Re < 4320, both the laminar and turbulent models show a unique, symmetric, and steady-state velocity distribution. For 4652 < Re < 8639, the two-dimensional model solutions are not unique, presenting a pair of antisymmetric, asymmetric solutions that nevertheless remain steady-state. When Re > 8639, the solution becomes oscillatory and unsteady. The three-dimensional counterflow model exhibits a two-dimensional solution independent of the Z-axis. At Re = 4652, both the three-dimensional and two-dimensional models produce the same unique, symmetric, and steady-state velocity distribution with no three-dimensional flow (W = 0). At Re = 8639, the three-dimensional model solutions are not unique, showing a pair of antisymmetric, asymmetric solutions, while still being steady and time-independent. At Re = 87,627, the three-dimensional model solution becomes oscillatory and unsteady. By elucidating the flow characteristics and nonlinear features of both models, this study compares the differences between the two-dimensional and three-dimensional flows, thereby laying the groundwork for simplification of the problem and further theoretical research. [ABSTRACT FROM AUTHOR]
Copyright of Energies (19961073) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: The Nonlinear Flow Characteristics within Two-Dimensional and Three-Dimensional Counterflow Models within Symmetrical Structures.
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– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we investigate the nonlinear characteristics of the flow in a two-dimensional and a three-dimensional counterflow model with symmetrical structures. Through numerical simulations, we obtain the velocity fields of the fluid flow in these models for different Re. The numerical results are analyzed to understand the nonlinear characteristics and differences between the two-dimensional and three-dimensional models. The findings indicate that, when Re varies, both the two-dimensional and three-dimensional models exhibit solution bifurcations and nonlinear phenomena such as symmetry breaking, self-sustained oscillations, and chaos. As Re increases, the two-dimensional counterflow model displays a unique solution, an asymmetric solution, and an oscillating solution. Specifically, when Re &lt; 4320, both the laminar and turbulent models show a unique, symmetric, and steady-state velocity distribution. For 4652 &lt; Re &lt; 8639, the two-dimensional model solutions are not unique, presenting a pair of antisymmetric, asymmetric solutions that nevertheless remain steady-state. When Re &gt; 8639, the solution becomes oscillatory and unsteady. The three-dimensional counterflow model exhibits a two-dimensional solution independent of the Z-axis. At Re = 4652, both the three-dimensional and two-dimensional models produce the same unique, symmetric, and steady-state velocity distribution with no three-dimensional flow (W = 0). At Re = 8639, the three-dimensional model solutions are not unique, showing a pair of antisymmetric, asymmetric solutions, while still being steady and time-independent. At Re = 87,627, the three-dimensional model solution becomes oscillatory and unsteady. By elucidating the flow characteristics and nonlinear features of both models, this study compares the differences between the two-dimensional and three-dimensional flows, thereby laying the groundwork for simplification of the problem and further theoretical research. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: &lt;i&gt;Copyright of Energies (19961073) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.3390/en17133176
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        Text: English
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        PageCount: 22
        StartPage: 3176
    Subjects:
      – SubjectFull: Three-dimensional modeling
        Type: general
      – SubjectFull: Counterflows (Fluid dynamics)
        Type: general
      – SubjectFull: Three-dimensional flow
        Type: general
      – SubjectFull: Two-dimensional models
        Type: general
      – SubjectFull: Fluid flow
        Type: general
      – SubjectFull: Symmetry breaking
        Type: general
    Titles:
      – TitleFull: The Nonlinear Flow Characteristics within Two-Dimensional and Three-Dimensional Counterflow Models within Symmetrical Structures.
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            NameFull: Wang, Wenshuai
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            NameFull: Yang, Mo
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          Dates:
            – D: 01
              M: 07
              Text: Jul2024
              Type: published
              Y: 2024
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            – TitleFull: Energies (19961073)
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