Liutex Analysis By Pod And Dmd For Vortex Formations In Boundary Layer Transition

Vortices are considered as the building blocks of turbulent flows. To study how one type of vortex becomes another type especially in flow transition is one way to get better understanding about turbulence. In this dissertation, two types of vortex formations, i.e., the hairpin vortex formation and the formation of vortex structure from symmetry to asymmetry, are studied by the direct numerical simulation. According to Liu et al. (2019), Liutex has been proposed as a new physical quantity with scalar, vector and tensor forms. A Liutex vector is defined as a rotation part of fluid motion without shear contamination. The purpose of this work is to apply Liutex and other Liutex-based methods to analyze and identify the vortex structures in the flow transition. Moreover, the proper orthogonal decomposition and dynamic mode decomposition are applied to extract the whole structures into coherent structures. In this work, the hairpin vortex formation in early transition is analyzed by the new mathematical definition of vortex core based Liutex definition. The results apparently show that the Lambda vortex is not self-deformed to the hairpin vortex as many literatures suggested. Then, the POD result demonstrates that fluctuating modes are in pairs and share the same characteristics such as eigenvalues, eigenvectors, amplitudes, mode shapes and time evolutions. It can be implied that the Lambda vortex is not self deformed to a hairpin vortex, but it is formed by the K-H instability during the formation of Lambda vortex and hairpin vortex in boundary layer flow transition. In addition, in late flow transition, which is more complex than the early stage, the symmetric and asymmetric areas are compared to identify the vortex structures. The new findings from Liutex analysis are obtained as follows. 1) Asymmetry of vortex structure starts from the bottom not the middle or the top part of wall normal direction. 2) Asymmetry of vortex structure is measured strong in the bottom, moderate in the middle and weak on the top.3) Flow fluctuations are closely related to the Liutex or fluid rotation. 4) Flow fluctuations are closely correlated with the loss of symmetry of vortex structures. 5) The high frequency modes represent small-scale structures. 6) The low-frequency modes that possess the high Liutex magnitudes represent large-scale structures of hairpin vortices, whereas the low-frequency modes that possess the low Liutex magnitudes represent large-scale structures of streamwise vortices.

This book collects papers presented in the Invited Workshop, “Liutex and Third Generation of Vortex Definition and Identification for Turbulence,” from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference. Liutex is a new physical quantity introduced by Prof. Chaoqun Liu of the University of Texas at Arlington. It is a vector and could give a unique and accurate mathematical definition for fluid rotation or vortex. The papers in this volume include some Liutex theories and many applications in hydrodynamics, aerodynamics and thermal dynamics including turbine machinery. As vortex exists everywhere in the universe, a mathematical definition of vortex or Liutex will play a critical role in scientific research. There is almost no place without vortex in fluid dynamics. As a projection, the Liutex theory will play an important role on the investigations of the vortex dynamics in hydrodynamics, aerodynamics, thermodynamics, oceanography, meteorology, metallurgy, civil engineering, astronomy, biology, etc. and to the researches of the generation, sustenance, modelling and controlling of turbulence.