Flow behavior analysis in boundary layer transition based on the Liutex–shear decomposition

Abstract

The Liutex based vortex identification method is superior to previous methods in that it overcomes the issues of threshold problem, shear contamination, etc., with a clear physical meaning that the direction of the Liutex vector represents the local axis of rotation, while the magnitude is equal to twice the angular velocity of the rigid-rotation part of the flow. The current study focuses on the interaction between the Liutex represented rotation and the residual shear part during the development of Λ vortex and hairpin vortex in boundary layer transition. The temporal–spatial evolution and development of typical vortical structures are analyzed based on the Liutex–shear decomposition with particular attention paid to the position and strength changes of Liutex and shear. Vortex core lines are extracted to investigate the mutual interactions between rotation and shear inside vortices. It is demonstrated that for the Λ vortex, spanwise rotating motions are formed at the head region and can persist for a long time under the influence of surrounding shear, while the tail region of the Λ vortex stretches down near the wall but then becomes weaker due to dissipation. High-shear regions tend to be located on top or below the vortices. When the shear layer formed between the legs gets stronger, it will be rolled up to form new vortices. On the one hand, the vortex legs together with the newly formed spanwise vortex consist of a new hairpin vortex, which, in turn, leads to the generation of the second- and third-level hairpin vortices. On the other hand, it also generates many smaller streamwise vortices in the near wall region. The results show that the interaction between Liutex and shear is very important in the development of vortical structures during transition.