New objective Liutex vector based on an optimization procedure

Abstract

The objectivity of a vortex identification method, which is critical in capturing vortices in rotating machineries, requires that the visualized vortical structures are independent of the movement of the observer. However, the common methodology to objectivize an Eulerian vortex identification method with relative/net vorticity or relative/net velocity gradient suffers from the issues of requirement to select a spatial volume to do vorticity average and inconsistency with the non-objective counterpart in an inertial reference frame. In this regard, a new objective Liutex vector method to visualize vortices is developed in the current study, which is based on the observed intermittency of Liutex represented vortices in turbulence. The intermittency indicates that a large volume fraction of the considered domain is void of Liutex, and the rotating motion of the observer is very likely to decrease this volume fraction. Therefore, an optimization procedure is proposed to approximate the rotating angular velocity of the observer by maximizing the zero Liutex volume percentage. With the known angular velocity to offset the rotational effects of the observer’s reference frame, objective version of Eulerian vortex identification methods can be introduced. As an example, the new objective Liutex method has been applied to turbulent channel flow at Reτ=180 in arbitrarily rotating coordinate systems, and the results show that the new method is both objective, i.e. independent of observer’s motion including translation and rotation and consistent with the original Liutex method in an inertial reference frame.