Real-Time Identification of Vortex Shedding in the Wake of a Circular Cylinder

Abstract

Lagrangian saddles, identified as nonparallel intersections of finite-time Lyapunov exponent (FTLE) ridges, have previously been shown to indicate the timing of von Kármán vortex shedding in the wake of a circular cylinder using two-dimensional simulation data. To expand the application of this method, two-dimensional, two-component velocity data were collected in the wake of a circular cylinder using particle image velocimetry at a Reynolds number of 19,000. This experimental data, as well as three-dimensional simulation data at a Reynolds number of 400, were used to calculate FTLE fields. The Lagrangian saddle found upstream of a forming vortex was shown to accelerate away from the cylinder surface as the vortex begins to shed for both cases, in agreement with the previous work. These saddles are impossible to track in real time, however, because future flowfield data are needed for the computation of the FTLE fields. To detect the Lagrangian saddle acceleration without using FTLE, the saddle dynamics are connected to physical quantities measurable in real time. The acceleration of the Lagrangian saddle occurs simultaneously with a maximum in lift in the numerical case and with a minimum in the static pressure at a location slightly upstream of the mean separation location in both cases, albeit with a lag time in the experimental case. This allows the time at which the von Kármán vortex sheds, determined objectively by the acceleration of the Lagrangian saddle away from the circular cylinder, to be identified by distinct signatures in the spatiotemporal evolution of the pressure distribution on the cylinder surface.