Chapter 11 - Comparison of Liutex and other vortex identification methods

Abstract

In this chapter, several Liutex-based vortex identification methods are applied in different engineering applications to describe the vortex structures. For the swirling jet case, compared with other vortex identification methods, the Omega method shows threshold-insensitive and more capable to capture both strong and weak vortices and Liutex has the outstanding ability to identify more additional secondary small-scale vortices immediately after the bubble vortex breakdown region and in the far downstream. For the turbine rotor passage case, the vortex structures are very complicated due to the coexistence of strong and weak vortices and shears. The case shows the Liutex-Omega method coincides best with streamlines in identifying weak vortices and Liutex is most capable to match the strong vortex with the streamlines. There are a number of marine hydrodynamics cases which have very complicated vortex structures. Compared with the Q-criterion, the modified Liutex-Omega method is proven to correctly describe these complicated vortex structures. For the case of vortex core in the Francis-99 draft tube at off-design conditions, Liutex core line method is applied and demonstrates the Liutex core line method is unique and threshold-free while all other vortex identification methods are threshold dependent although Omega-type methods are insensitive to the threshold selection.