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Numerical simulation of turbulent flow in FlowCube platform under a strong magnetic field

强磁场下FlowCube中湍流流动的数值模拟

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Abstract

The investigation of magnetohydrodynamic (MHD) flow has been carried out through a two-dimensional approximation known as the PSM model within the FlowCube platform (Pothérat and Klein, 2014). The platform itself is a cubic vessel featuring alternating positive and negative electrodes that are uniformly located on its bottom. The flow is driven by the Lorentz force, which is induced by injected currents and imposed magnetic fields. The energy spectrum of two-dimensional flow agrees well with our three-dimensional one, confirming the two-dimensionality of MHD turbulence under strong magnetic fields. For quasi-two-dimensional (Q2D) flow in FlowCube, the energy spectrum displays ∼ k−3 and ∼ k2 slopes, corresponding to direct enstrophy cascade from forcing scale li to small scale and statistical equilibrium state of large scale (> li), where li is electrodes space in FlowCube. Moreover, a comprehensive study has been conducted on the transition from a laminar state to a turbulent state, revealing various flow states, including periodic, quasi-periodic, and chaotic states. Furthermore, under the same driving force, the periodic network of alternating vortices, which are typical structures in the FlowCube configuration, display different flow states. This observation may correspond to a large-scale intermittency in MHD flows due to the complex interaction between the driving force and dissipation.

摘要

本文借助PSM 模型(Pothérat and Klein, 2014)研究了FlowCube 构型中磁流体动力学(MHD)的准二维(Q2D)流动问题.FlowCube的底壁均匀布置着正负相间的点电极, 内部充满液态金属, 在外加均匀磁场作用下, 通过注入恒定电流驱动流体流动. 计算结果表明: 在强磁场作用下, 准二维流动的能谱与三维计算结果吻合较好, 证实了强磁场下MHD湍流的二维性. 此外, 对于FlowCube中的准二维流动, 能谱图呈现k−3和k2的斜率, 分别对应于从驱动尺度l i 向小尺度的拟涡能级串和大尺度结构(>li)的统计平衡态, 其中l i 是FlowCube中的相邻点电极间距. 随着驱动力的逐渐增加, 我们对流动从层流到湍流状态的转变进行了详细讨论, 揭示了从周期、准周期再到混沌的变化规律. 最后, 在相同的驱动力下, 不同的初始流场将产生不同的流动状态, 这与FlowCube中大尺度结构的间歇性可能是相对应的.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52076204 and 51927812), and Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

  1. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 101408, China

    Zhao-Bo Wang  (王赵波), Long Chen  (陈龙) & Ming-Jiu Ni  (倪明玖)

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  1. Zhao-Bo Wang  (王赵波)
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  2. Long Chen  (陈龙)
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Contributions

Author contributions Ming-Jiu Ni designed the research. Zhao-Bo Wang and Long Chen wrote the first draft of the manuscript. Zhao-Bo Wang set up the numerical simulation set-up and processed the data. Long Chen helped organize the manuscript. Ming-Jiu Ni and Long Chen revised and edited the final version.

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Correspondence to Long Chen  (陈龙).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Wang, ZB., Chen, L. & Ni, MJ. Numerical simulation of turbulent flow in FlowCube platform under a strong magnetic field. Acta Mech. Sin. 39, 323143 (2023). https://doi.org/10.1007/s10409-023-23143-x

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