Quantitative comparison of vortex identification methods in three-dimensional fluid flow around bluff bodies

Abstract

The identification of vortices remains a critical yet unresolved challenge in fluid mechanics, as no universally accepted definition of a vortex exists. This study compares several vortex detection methods applied to the simulation of three-dimensional fluid flows around a cylinder and a rectangular cuboid at various Reynolds numbers and angles of attack, including a highly turbulent flow case. The methods under investigation include traditional Eulerian local criteria – $\omega$-criterion, $Q$-criterion, and ${\lambda }_2$-criterion – as well as more recent approaches such as the $\Omega$-method, Rortex method, Omega-Liutex method, and the Lagrangian-averaged vorticity deviation (LAVD). Classification metrics and visualization methods are used to quantify and compare the performance of each method. While traditional criteria and the Rortex method demonstrated accuracy only with carefully chosen parameters, the $\Omega$-, and Omega-Liutex methods achieved reliable results with consistent uncertainty using threshold values near the suggested value of 0.52. In highly three-dimensional turbulent flows, all methods encountered challenges with shear contamination, though the LAVD method was the most robust. However, the LAVD method’s reliance on two-dimensional plane-based analysis limits its ability to capture the full volumetric nature of vortices in such flows, which contributed to reduced accuracy. The LAVD method is threshold independent, and can provide accurate results, however, only on the cost of high computational time. It is concluded that for applications with limited computational resources, simpler methods like the $\Omega$-method may be preferable. However, in scenarios requiring high accuracy, the LAVD method, despite its longer processing time, could be more effective.