497 POD analysis on vortical structures in MVG wake by Liutex core line identification * Xiang-rui Dong 1, 2 , Xiao-shu Cai 1, 2 , Yinlin Dong 3 , Chaoqun Liu 4 1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China 2. Key Laboratory of Multiphase Flow and Heat Transfer in Shanghai Power Engineering, Shanghai 200093, China 3. Department of Mathematics, University of Central Arkansas, Conway 72035, USA 4. Department of Mathematics, University of Texas at Arlington, Arlington 76019, USA (Received March 21, 2020, Revised May 13, 2020, Accepted May 14, 2020, Published online June 28, 2020) ©China Ship Scientific Research Center 2020 Abstract: The Liutex core line method, first combined with the snapshot proper orthogonal decomposition (POD), is utilized in a supersonic micro-vortex generator (MVG) wake flow at = 2.5 Ma and = 5 760 Re  to reveal the physical significance of each POD mode of the flow field. Compared with other scalar-based vortex identification methods, the Liutex core line identification is verified to be the most appropriate approach that is threshold-free and provides full information of a fluid rotation motion. Meanwhile, the Liutex integration is employed to quantitatively track the evolution of the vortices in MVG wake and is applied to the determination of the effective control section of the MVG wake for the optimization study of MVG design. The physical mechanism of each POD mode for multi-scale and multi-frequency vortical structures is investigated by using Liutex core line identification to give some revelations. For the mean mode (mode 0) indicating the time-averaged velocity flowfield of the MVG wake flow, a pair of primary counter-rotating streamwise vortices and another pair of secondary vortices is uniquely identified by two pairs of Liutex core lines with Liutex magnitude. In contrast, mode 1 is featured by a fluctuated roll-up motion of streamwise vortex, and the streamwise component of the MVG wake is demonstrated to be dominant in terms of the total kinetic energy contribution. Meanwhile, a dominant shedding frequency of = 0.072 St is detected from the temporal behavior of mode 2, which has the organized arc-shaped vortex structures shedding from MVG induced by the K-H instability. Additionally, mode 4 subjects to low-frequency oscillations of the wall vortices and thus takes a relatively lower frequency of = 0.044 St . Key words: Proper orthogonal decomposition (POD), vortex identification, Liutex, vortex core lines, micro-vortex generator (MVG) Introduction Flows such as turbulent boundary layers, blunt-wakes, jets, and separated flows are dominantly characterized by some coherent structures with various spatial and temporal scales, which are posited to be responsible for significant portions in mass and heat transfer, turbulent mixing, flow noises and aerodynamic drag, etc., and thus, these flow structures are always considered the major objective of flow control and optimal design for aircraft designers. In particular, for supersonic flows, the presence of unsteady and viscous effects such as shock waves, turbulence, and their interactions may lead to flow * Biography: Xiang-rui Dong (1991-), Female, Ph. D., E-mail: dongxr1154@126.com Corresponding author: Chaoqun Liu, E-mail: cliu@uta.edu distortion, flow separation or aerodynamic force fluctuations, resulting in the performance of aircraft deteriorating and causing body oscillation. As a convenient and effective passive device for most control of shock-induced flow separation, micro- vortex generator (MVG) is of particular interest in many industrial applications. Due to its importance in both scientific research and engineering applications, many efforts on the study of the control mechanism of the MVG wake and the distinct coherent structures (vortices) have been devoted over the past decades. Coherent structures are organized with large-scale structures that persistently appear, disappear, and reappear with a characteristic temporal lifespan, although they are not explicitly steady in space or time [1] . They also play an important role in random and chaotic fluctuations with small scales, due to the redistribution and partitioning of the turbulent kinetic energy. Thus, it is obvious that a complete and precise description of the characteristics of canonical coherent Available online at https://link.springer.com/journal/42241 http://www.jhydrodynamics.com Journal of Hydrodynamics, 2020, 32(3): 497-509 https://doi.org/10.1007/s42241-020-0037-x