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

Author

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  • Wenshuai Wang

    (School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China)

  • Mo Yang

    (School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China)

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.

Suggested Citation

  • Wenshuai Wang & Mo Yang, 2024. "The Nonlinear Flow Characteristics within Two-Dimensional and Three-Dimensional Counterflow Models within Symmetrical Structures," Energies, MDPI, vol. 17(13), pages 1-24, June.
    • Handle: RePEc:gam:jeners:v:17:y:2024:i:13:p:3176-:d:1424192
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    References listed on IDEAS

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    1. Ying, Xuchen & Huang, Weijia & Liu, Wenhua & Liu, Guiliang & Li, Jun & Yang, Mo, 2022. "Asymmetric phenomenon of flow and heat transfer in charging process of thermal energy storage based on an entire domain model," Applied Energy, Elsevier, vol. 316(C).
    2. Li, Zixiang & Miao, Zhengqing & Qiao, Xinqi, 2023. "Effects of structural parameters of a novel burner scheme with annularly combined multiple airflows on performance of a 660 MW tangentially fired boiler," Energy, Elsevier, vol. 280(C).
    3. Li, Zixiang & Qiao, Xinqi & Miao, Zhengqing, 2021. "A novel burner arrangement scheme with annularly combined multiple airflows for wall-tangentially fired pulverized coal boiler," Energy, Elsevier, vol. 222(C).
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