Velocity measurement from schlieren images of subsonic flows using a wavelet-based optical flow algorithm

Schlieren imaging is a highly sensitive and flexible technique widely used for flow visualization in high-speed fluid flow investigations. However, there is a lack of robust methods for extracting quantitative velocity from Schlieren images. In this study, a wavelet-based optical flow (WOF) algorithm incorporating a viscous regularization term is employed to compute velocity fields from Schlieren images under subsonic conditions. The method is applied to both a steady turbulent jet and an unsteady sweeping jet (SWJ). The estimated velocity and vorticity fields are compared with results obtained from an optimized optical flow (OF) method. The comparison demonstrates that the WOF method resolves more intricate flow details and exhibits greater resistance to noise. In experiments involving three different scenarios for both the turbulent jet and the SWJ, the measured velocities at lower speeds—where the flow can be considered incompressible—show good agreement with the theoretical values. However, under compressible conditions, the effects of compressibility and the internal flow oscillation mechanisms of the sweeping jet actuator (SJA) lead to energy dissipation, resulting in measured velocities lower than the theoretical values. These results confirm the effectiveness of the WOF method for velocity measurement in subsonic flows and represent the first validation of its application to high-subsonic SWJ flows.