## Graduation Semester and Year

2021

## Language

English

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy in Mathematics

## Department

Mathematics

## First Advisor

Chaoqun Liu

## Abstract

Although vortex has been studied more than one hundred year, we still have not had universally accepted definition. A few well-known vortex identification methods are introduced ��,∆, ��2,������ criteria to identify coherent vortex structures the last three decades. A new Omega vortex identification method, which is defined as a ratio of the vorticity tensor norm squared over the sum of the vorticity tensor norm squared and deformation norm squared, was proposed in 2016. Two year later, the new vortex vector named Liutex (previously called Rotex) was proposed by Liu et al. with direction of local rotation axis (an eigenvector of velocity gradient tensor) and angular speed (magnitude of Liutex vector) while other identification methods could not give direction of rotation axis. Micro-Vortex Generator (MVG) is a common device for turbulent flow separation control. In this paper, in order to better understand the mechanism of flow control by MVG, the flow data set obtained by an implicit implemented large eddy simulation (ILES) with fifth order WENO spatial discretization at Ma=2.5 and Reθ=5760 is analyzed in details by a proper orthogonal decomposition (POD) method. In this dissertation, the POD method with 120 snapshots using both velocity ( �� , �� , �� ) a nd Liutex vector ( �� �� , �� �� , �� �� ) directly as inputs is applied to analyze the vortex structure behind MVG. From the present study, the first a few POD modes are suitable for the explanation of the vortex structures after MVG. In addition, for the first time, the data loaded directly from Liutex vector instead of velocity are organized as the snapshot matrix and a correlation between the absolute strength of rotation (Liutex) and the cumulative rotation strength (Liutex magnitude) of rotation is discovered. The present result clearly shows the POD modes paring, which is a typical sign of Kevin-Helmholtz (K-H) instability. Furthermore, the mechanism of vortex ring generation caused by the K-H type instability is also presented.

## Keywords

POD, KHI, Liutex

## Disciplines

Mathematics | Physical Sciences and Mathematics

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Trieu, Xuan My, "LIUTEX ANALYSIS BY POD AND DMD IN TURBULENT FLOW AFTER/ IN MICRO VORTEX GENERATOR" (2021). *Mathematics Dissertations*. 135.

https://mavmatrix.uta.edu/math_dissertations/135

## Comments

Degree granted by The University of Texas at Arlington