Proper Orthogonal Decomposition Analysis of Coherent Structure in a Turbulent Flow after a Micro-vortex Generator

Abstract

A micro-vortex generator (MVG) is a common device used for turbulent flow separation control. In this study, in order to better understand the flow control mechanism using an MVG, we analyzed the flow data set obtained by implicit large eddy simulation with fifth order weighted essentially nonoscillatory scheme spatial discretization at Ma = 2.5 and Reθ = 5760 in detail by using the proper orthogonal decomposition (POD) method. The POD method was applied with 120 snapshots using both the velocity (u, v, w) and Liutex vector (Lx, Ly, Lz) directly as inputs to analyze the vortex structure behind the MVG. According to the results, the first six POD modes were suitable for explaining the vortex structures behind the MVG. In addition, for the first time, the data loaded directly from the Liutex vector instead of velocity were organized in a snapshot matrix and the correlation was determined between the absolute strength of rotation (Liutex) and cumulative rotation strength (Liutex magnitude). Vortex pairing and merging of co-rotating vortices were found in both data input cases with the velocity and Liutex. When the modes were ranked by energy, the first six modes were paired and the streamwise structures were dominant in modes 1–2. When the modes were ranked by Liutex strength, the first two modes mixed by streamwise and spanwise vortices were not paired, but modes 3–4 and 5–6 were paired, and they were all spanwise-structure dominant. Comparisons also showed that the spanwise vortices had higher frequencies.