Seedless Velocimetry in a Turbulent Jet using Schlieren Imaging and a Wavelet-based Optical Flow Method

Velocity measurements were made in a turbulent jet of carbon dioxide issuing into air using a wavelet-based optical flow velocimetry (wOFV) method applied to schlieren image pairs. Schlieren image pairs were acquired with a two-camera setup using a single conventional Z-type schlieren system. The mean axial velocity shows good agreement with PIV data in the same jet after application of an Abel transformation. The applicability of Abel transforms for schlieren image velocimetry (SIV) in turbulent flows is discussed in general, and it is demonstrated that it is only appropriate to apply the Abel transform to the mean velocity field rather than instantaneous velocity fields, schlieren images, or other higher-order statistics. These restrictions apply regardless of the velocimetry approach (i.e., correlation-based analysis or wOFV) due to the path-integrated nature of the current Schlieren measurement. Due to these limitations, it is not clear whether a high-resolution technique such as wOFV provides additional benefits compared to correlation-based methods for the current Schlieren measurements.