Velocity Measurement from Schlieren Images of Compressible Flows Using a Wavelet-Based Optical Flow Algorithm

Abstract 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 method 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 compressible conditions. The method is applied to both a simple turbulent jet and a complex sweeping jet (SWJ). The estimated velocity and vorticity fields are compared with results obtained from an optimized optical flow (OF) method utilizing conventional smoothness constraints. The comparison demonstrates that the WOF method resolves more intricate flow details and exhibits greater robustness to noise. In experiments involving three cases for both the turbulent jet and SWJ, the measured velocities at lower speeds—where the flow can be considered incompressible—agree with theoretical values. Under compressible conditions, compressibility effects lead to energy dissipation due to air expansion or compression, resulting in measured velocities slightly lower than theoretical values but still within an acceptable range. These results indicate that the WOF method is effective for accurately measuring velocity fields in compressible flows.