Vortex convection velocity determination methods and application in the flow near airfoil trailing edge

The convection velocity is an important parameter for characterizing traveling vortices in turbulent flow, and its calculation methods are evolving with the measurement technologies. Using high-frequency particle image velocimetry and the synchronized far field sound pressure measurements, different methods are explored to calculate the convection velocity, i.e., the velocity decomposition, the velocity cross correlation, the vortex time trajectory, the frequency-wave number contour, as well as the time delay between velocity and noise signal methods. The methods have been applied on a test case of airfoil trailing edge with vortex shedding, which includes laminar separation bubble, acoustic feedback loop, and tonal noise generation phenomena. A relative standard deviation of 2.71% of the convection velocities has been noticed from the five methods under the same flow condition. The cross correlation methods show the advantage of convection velocity determination along the chordwise direction. The frequency-wave number method seems the most robust method for its global calculation in terms of spatial and time domain. At the end, all the methods have been applied to investigate the trend of convection velocity vs free stream velocity and angle of attack. The convection velocity increases as the angle of attack decreases and flow speed increases, which is ascribed to the separation bubble moving upstream.