Evaluation of seedless wavelet-based optical flow velocimetry for schlieren images

In harsh flow environments, traditional particle-based velocimetry methods face challenges. This study explores the use of seedless schlieren images for velocimetry through a novel algorithm, namely, wavelet-based optical flow velocimetry (wOFV). Various data term constraints for wOFV were examined. It is found that the data term derived from the integrated continuity equation (ICE) outperformed the conventional displaced frame difference constraint and the schlieren-tailored constraints (SE and SSE). Evaluation based on the root mean square error (RMSE) and turbulence energy spectrum (TES) reveals that the choice of wavelet becomes insignificant for the optimal estimated velocity field when the wavelet support length is sufficiently long. In addition, the implementation of a proper truncation in wOFV shows little dependence of the RMSE on the weighting coefficient, therefore alleviating the uncertainty associated with selecting an appropriate weighting coefficient. It is found that the retrieved flow field from schlieren images approximates a down-sampled result based on available structural scales in images. Considering the prevalence of under-resolved velocity field in practical applications, schlieren-based wOFV offers a reasonable alternative to particle-based velocimetry, particularly in harsh flow environments.