A spatial-temporal algorithm for three-dimensional particle tracking velocimetry using two-view systems

In the present study, a novel temporal three-dimensional particle tracking velocimetry (3D PTV) algorithm for flow measurements with only two views is developed and validated with synthetic particles. The spatial information in image and object spaces, as well as the temporal predictions, are strongly coupled to improve the particle tracking accuracy. A well-designed cost function, simultaneously penalizing the reconstruction and tracking processes, is minimized to determine the most reliable traces. The algorithm shows a correctness over 98% up to 0.0273 ppp (particles per pixel) when using ideal synthetic particle positions, which is superior to several artificial intelligence methods. Moreover, an improved particle identification algorithm is proposed to handle overlapped particles and reduce the error introduced into the 3D PTV scheme. The algorithm adopts a particle position shifting process to tackle the correct particle numbers iteratively, which shows better performance than some other methods. A comparative study indicates that particle identification accuracy has a significant effect on the subsequent 3D reconstruction and tracking processes. The 3D PTV and particle identification algorithms show good consistencies under two types of flow conditions: a homogeneous isotropic turbulent flow and a vortex ring flow. Comparing with multiple-view setups, two-view systems are more compact and cost-effective, especially in conditions requiring high-speed cameras. With the newly established algorithms, a two-view system is now able to handle higher particle-seeding densities and thus can resolve higher spatial resolutions, which is significant for applications in turbulent flow and particle motion measurements. (paper)