A schlieren motion estimation method for water flow velocimetry

In the present study, a schlieren motion estimation algorithm is proposed for two-dimensional seedless water flow measurement. A physical constraint is derived combining the schlieren intensity and continuity equations. The space smoothness constraint adopts the second-order div-curl regularizer. Based on the two constraints, the global cost function is derived and minimized to resolve the velocity field using the variation method. As an example, a buoyant plume in the water tank is tested using a Z-type schlieren imaging system. The sample images are calculated using a correlation algorithm in PIVlab, an optimized optical flow algorithm, and the newly proposed schlieren motion estimation algorithm. The results show that the new algorithm can resolve more details of the flow field with higher spatial resolution, while the velocity gradient is consistent with the continuity characteristics. It also features with good robustness without obvious outlier mistakes. The schlieren setup is simple and cost effective in setup. The proposed algorithm has shown great potentials for velocity measurement in more complex configurations.