Direct Lagrangian method to characterize entrainment dynamics using particle residence time: a case study on a laminar separation bubble

Abstract

This study demonstrates the feasibility of characterizing small-scale flow dynamics using path-specific Particle Residence Time (PRT). PRT, defined as the time a parcel of fluid spends in a region of interest, is a clear indicator of stagnation and recirculation. To test the concept, two-dimensional particle tracking velocimetry is used to measure a laminar separation bubble (LSB) on the suction side of an SD7003 airfoil at $$Re=60,000$$ . Extended pathlines are calculated from the Lagrangian data such that fluid parcels entering the region of interest are tracked continuously. PRT is then directly calculated and used to quantify the entrainment process across the LSB. Using convential Eulerian quantities, the flow field around the LSB is divided into outer (free stream) and inner layers—separated by the local minimum velocity magnitude line. Entrainment, initiated by the formation of vortices near the reattachment point, is quantified according to the trajectories of fluid parcels crossing into the inner flow layer. The PRT values of entrained fluid parcels are significantly increased compared to the bulk flow. Variations of the mean PRT of entrained fluid reveal unsteady features, including the transition and reattachment of the LSB. The path-dependent indicators of separation, transition and reattachment are shown to closely agree with Eulerian-based benchmark measurements.