Lagrangian Visualization and Real-Time Identification of the Vortex Shedding Time in the Wake of a Circular Cylinder
Date of Award
Doctor of Philosophy (PhD)
Mechanical and Aerospace Engineering
Melissa A. Green
cylinder, fluid mechanics, FTLE, vortex
The flow around a circular cylinder, a canonical bluff body, has been extensively studied in the literature to determine the mechanisms that cause the formation of vortices in the cylinder wake. Understanding of these mechanisms has led to myriad attempts to control the vortices either to mitigate the oscillating forces they cause, or to augment them in order to enhance mixing in the near-wake. While these flow control techniques have been effective at low Reynolds numbers, they generally lose effectiveness or require excessive power at Reynolds numbers commonly experienced in practical applications. For this reason, new methods for identifying the locations of vortices and their shedding time could increase the effectiveness of the control techniques. In the current work, two-dimensional, two-component velocity data was collected in the wake of a circular cylinder using a planar digital particle image velocimetry (DPIV) measurement system at Reynolds numbers of 9,000 and 19,000. This experimental data, as well as two-dimensional simulation data at a Reynolds number of 150, and three-dimensional simulation data at a Reynolds number of 400, is used to calculate the finite-time Lyapunov exponent (FTLE) field. The locations of Lagrangian saddles, identified as non-parallel intersections of positive and negative time FTLE ridges, are shown to indicate the timing of von Kármán vortex shedding in the wake of a circular cylinder. The Lagrangian saddle found upstream of a forming and subsequently shedding vortex is shown to clearly accelerate away from the cylinder surface as the vortex begins to shed. This provides a novel, objective method to determine
the timing of vortex shedding. The saddles are impossible to track in real-time, however, since future flow field data is needed for the computation of the FTLE fields. In order to detect the Lagrangian saddle acceleration without direct access to the FTLE, the saddle dynamics are connected to measurable surface quantities on a circular cylinder in crossflow. The acceleration of the Lagrangian saddle occurs simultaneously with a maximum in lift in both numerical cases, and with a minimum in the static pressure at a location slightly upstream of the mean separation location in the numerical cases, as well as the experimental data at a Reynolds number of 19,000. This allows the von Kármán vortex shedding time, determined objectively by the acceleration of the Lagrangian saddle away from the circular cylinder, to be detected by a minimum in the static pressure at one location on the cylinder, a quantity that can be measured in real-time using available pressure sensors. These results can be used to place sensors in optimal locations on bluff bodies to inform closed-loop flow control algorithms of the timing of von Kármán vortex shedding.
Rockwood, Matthew, "Lagrangian Visualization and Real-Time Identification of the Vortex Shedding Time in the Wake of a Circular Cylinder" (2017). Dissertations - ALL. 679.