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Liutex and Proper Orthogonal Decomposition for Coherence Structure in the Wake of Micro Vortex Generator

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Liutex and Third Generation of Vortex Definition and Identification

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Abstract

In 2016, a new criterion called Omega vortex identification was proposed by Liu et al., which has many advantages according to several studies. However, all the existing vortex identification methods are just a scalar and they are contaminated by shear. For the first time in history, a new vortex vector with both local rotation axis and rotation strength - called Liutex (with no shear) was introduced by Liu et al. in 2018. In this study, we load data directly from Liutex vector (Lx, Ly, Lz) instead of velocity (u, v, w). Moreover, proper orthogonal decomposition (POD) method is applied to analyze the coherent structure of the first eighth POD modes in the wake of micro vortex generator at Ma = 2.5 and Reθ = 5760 by using Liutex. Pairing of POD modes is clearly found, which is the sign of Kevin-Helmholtz instability. The observation of the mode paring strongly supports the new mechanism of MVG for reduction of flow separation, which is the interaction between the shock and the spanwise vortex rings generated by K-H instability.

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Acknowledgments

The authors are grateful to TACC (Texas Advanced Computation Center) for providing CPU hours to this research project. The computation is performed by using MPI code “LESUTA” which was developed by Drs. Qin Li and Chaoqun Liu.

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Authors and Affiliations

  1. University of Texas at Arlington, Arlington, TX, USA

    Xuan My Trieu & Chaoqun Liu

  2. Department of Mathematics and Statistical Science, Jackson State University, Jackson, MI, USA

    Yonghua Yan

Authors
  1. Xuan My Trieu
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  2. Yonghua Yan
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  3. Chaoqun Liu
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Corresponding author

Correspondence to Xuan My Trieu .

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Editors and Affiliations

  1. University of Texas at Arlington, Arlington, TX, USA

    Chaoqun Liu

  2. Soochow University, Suzhou, Jiangsu, China

    Yiqian Wang

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Trieu, X.M., Yan, Y., Liu, C. (2021). Liutex and Proper Orthogonal Decomposition for Coherence Structure in the Wake of Micro Vortex Generator. In: Liu, C., Wang, Y. (eds) Liutex and Third Generation of Vortex Definition and Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-70217-5_14

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