Analysis of intermittent trailing edge vortex shedding using recurrence plots

Abstract

Time-resolved particle image velocimetry is conducted in the wake of a trailing-edge separated flow past a NACA4415 airfoil at a fixed angle of attack beyond the static stall angle to analyze the formation and temporal evolution of the wake coherent structures. Under the presented experimental circumstances, intermittent trailing-edge vortex shedding occurs. A flow diagnostic analysis combining the proper orthogonal decomposition method with a recurrence plot and quantification analysis reveals that the occurrence and duration of vortex-shedding interruptions are random and that the durations of the interruptions are shorter than the intervals of regular shedding. Furthermore, a recurrence-based conditional averaging strategy is proposed that preserves the instantaneous dynamics of the wake flow and allows for successful separation of the coherent and turbulent contributions to the flowfield fluctuations. Based on the recurrence-based conditional averaged flowfields, the spatiotemporal evolution of the wake centerline is visualized and the wake convection speed is calculated. The latter is found to be distributed normally around 0.66 of the freestream velocity. Classic vortex detection and tracking reveals a formation length of ≈20% of the airfoil chord length downstream of the trailing edge before alternating trailing edge vortex shedding can occur through mutual interactions of the upper and lower shear layers.