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Lagrangian analysis on structure evolution and mass transport of circular and noncircular turbulent synthetic jets

圆和非圆湍流合成射流结构演化和质量输运的拉格朗日方法分析

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Abstract

Fluid entrainment is of particular significance for the applications of synthetic jets in flow control. We investigate the structure evolution and transient fluid entrainment by the vortex rings in turbulent synthetic jets. Two orifice configurations of circular and rectangular with the aspect ratio of 3 are examined at the same parameters. Time-resolved tomographic particle image velocimetry is used to acquire the three-dimensional flow field information. The analysis based on Lagrangian coherent structures is used to visualize topology deformation of the vortex ring, describe mass transport and quantify entrainment by successive vortex rings. Particularly, the traditional method of the moving reference frame of the vortex ring cannot be effectively applied to the rectangular case due to non-uniform azimuthal translational velocity on the vortex ring. A new approach based on identifying the vortex boundaries by the finite-time Lyapunov exponent ridges is adopted to estimate the volume of the vortex bubble and thus to calculate entrainment and kinetic energy fractions. The results show that the rectangular case generally entrains more ambient fluids, resulting in larger vortex strength than the circular case. Furthermore, more kinetic energy from the ejected fluids is absorbed by the rectangular case to sustain the axis switching of the vortex ring. That could be beneficial for jet mixing enhancement. The current study develops the mathematic description of the dynamics of vortex rings, which can provide an important reference for quantifying fluid entrainment by the vortex rings in flow control applications.

摘要

旋涡卷吸特性对合成射流的流动控制应用具有重要意义. 为了研究湍流合成射流涡环的结构演化和瞬态卷吸特性, 采用时间解析层析粒子图像测速技术, 测量了相同参数下, 圆形和长宽比为3的矩形合成射流的三维流场. 利用拉格朗日拟序结构方法, 刻画了涡环的三维拓扑变形和质量输运过程, 并量化了连续涡环的卷吸特性. 特别是对矩形涡环, 由于涡环的对流速度沿周向分布不均匀, 导致传统的移动参考系方法无法有效计算卷吸. 针对该问题, 采用基于有限时间李雅普诺夫指数“脊线”辨识旋涡边界的方法, 估计涡泡体积, 从而计算涡环的卷吸和动能转换效率. 结果表明, 矩形涡环能够卷吸更多的周围流质, 产生比圆形涡环更大的涡旋强度; 此外, 矩形涡环从孔口喷出的流质中获得了更多动能, 以维持涡环的轴系转换, 这些特征有利于增强射流掺混. 上述工作通过发展旋涡动力学的数学描述, 为量化流动控制中的旋涡卷吸特性提供了重要参考.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12102029, 11902019 and 11721202), and the Postdoctoral Science Foundation Grant of China (Grant No. 2021M690301).

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Authors and Affiliations

  1. Fluid Mechanics Key Laboratory of Education Ministry, Beijing University of Aeronautics and Astronautics, Beijing, 100191, China

    Lei Wang  (王雷), Lihao Feng  (冯立好) & Yang Xu  (徐杨)

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  1. Lei Wang  (王雷)
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  2. Lihao Feng  (冯立好)
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  3. Yang Xu  (徐杨)
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Correspondence to Lihao Feng  (冯立好).

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Author contributions

Lei Wang designed the research and developed the methodology. Lei Wang and Yang Xu wrote the first draft of the manuscript. Lei Wang and Yang Xu set up the experiment set-up and processed the experiment data. Lihao Feng helped organize the manuscript. Lei Wang and Lihao Feng revised and edited the final version.

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Wang, L., Feng, L. & Xu, Y. Lagrangian analysis on structure evolution and mass transport of circular and noncircular turbulent synthetic jets. Acta Mech. Sin. 39, 322294 (2023). https://doi.org/10.1007/s10409-022-22294-x

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