MATHEMATICAL APPROACH OF LIUTEX CORE LINE AND LIUTEX CORE TUBE FOR VORTEX STRUCTURE VISUALIZATION

Abstract

During the past decades, many vortex identification methods have been published to present a clear definition and identification of the vortex. However, all these methods are failed to offer a unique identification method, and they also cannot answer the six essential issues for vortex identification methods, which are: 1) absolute strength, 2) relative strength, 3) rotational axis, 4) vortex core center location, 5) vortex core size, and 6) vortex boundary. In this work, two vortex identification methods, which are never affected by the threshold, will be proposed. Moreover, this study will address two critical questions: 1) Where is the rotational axis? 2)what is vortex core size? Liutex as a new physical quantity concept opens an era of turbulence research because Liutex introduces a scalar form and provides vector and tensor forms too. The Liutex vector represents the rotation part of fluid motion in isolation of the shear contamination. Depending on a clear and reasonable mathematical approach, an exact Liutex core line and Liutex core tube algorithm will propose in this research. The results proved that the Liutex core line is the only vortex identification method unique so far. In addition, the result shows that

both the Liutex core line and Liutex core tube can expose the strength of the vortex, unlike the previous methods, which are iso-surface based. Since both methods, the Liutex core line and Liutex core tube, have been extracted by Liutex lines, they both get another advantage showing the vortex direction. Even though the Liutex core tube is not a unique vortex identification method, comparing the Liutex core tube and the iso-surface-based methods displays the superiority of the Liutex core tube in showing the strong and weak spots of the vortex structure clearly. The proposed algorithms have been implemented on the Direct Numerical Simulation (DNSUTA) data of flow transition in boundary layers, which is pre-processed and validated by researchers from UTA and NASA Langley.