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.

Shadowgraph imaging is a promising technique for volumetric velocity measurements, which features with high framing rate, long depth focus, and a cheap light source. The main objective of current study is to develop a camera calibration algorithm for collimated shadowgraph systems, which is an essential procedure for 3D PTV strategies. First, the optical model of a two-view collimated shadowgraph system is established, which can be described by the orthographic projection model. The image distortion effect is also taken into consideration. Then, the calibration algorithm is developed using a flexible planar-target-based method. Aiming for 3D PTV applications, the extrinsic parameters including rotation and translation relationships between the two camera imaging coordinates have been derived. The ambiguity for sign confirmation of the extrinsic parameters has been solved by introducing extra information from the relative position of the two views. Moreover, extrinsic parameters self-calibration (EPSC) has been implemented to deal with unavoidable camera drifts during the experiments. The results indicate that the EPSC is effective to remove the global system error in the current two-view system. The proposed calibration algorithm has been verified by synthetic images, which has shown a mean reprojection error less than 0.1 pixel. In a water jet experiment, the mean reprojection error is around 0.3 pixel (about 0.019 mm in reality) after the board calibration. The relative error evaluated from the reconstruction points is less than 1%. The reprojection error can be further reduced to less than 0.1 pixel after refining through EPSC algorithm. The results indicate that the proposed calibration procedure is effective and feasible for collimated shadowgraph imaging systems. The 3D-particle positions of a sample frame have been reconstructed successfully. It is believed that the high-quality shadowgraph images can offer high precision measurements for further particle tracking velocimetry.

Determining the time-resolved three-dimensional (3D) three-component (3C) velocity is essential for complex turbulent flow measurements. The current study is an extension of a recently developed temporal-spatial three-dimensional particle tracking velocimetry (TS 3D-PTV) technique established for two-view imaging systems. Two improvements have been embedded in TS 3D-PTV algorithm to improve the accuracy at high particle image densities (up to 0.03 ppp). One is using the neighboring particle information to correct the predicted positions and select the temporal particles with higher probability; the other is to iteratively optimize the 2D particle positions during the tracking process using the temporal and image information. The synthetic particle tests indicate that the correctness can be increased by 4.7-5.8%, to reach a value about 92% with the improved algorithm around 0.03 ppp. The comparative results also indicate that using an advanced particle identification algorithm can improve the correctness over 20%. Two experiments, including a buoyancy jet in water and a transient droplet splashing process, have been conducted with a two-view shadowgraph imaging system. Different tracking algorithms have been conducted to determine the 3D trajectories of seeding particles or secondary droplets comparatively. The new algorithm has shown the best performance with much longer and more reliable trajectories, which indicates the tracking interruption caused by particle overlapping is reduced. The newly developed algorithms have further improved the performance under high seeding density conditions, which makes the two-view shadowgraph 3D PTV system adaptable to more experimental conditions.

The volumetric Lagrangian measurements of droplet or turbulent flow using particle tracking methods have attracted intensive attentions recently. The performance of three-dimensional particle tracking velocimetry (3D PTV) is highly relying on the algorithms. Most of the existing 3D PTV algorithms are developed for multi-view systems, which cannot be applied directly to two-view systems due to the lack of enough geometry constraints. In the current study, three different 3D PTV algorithms applicable for two-view systems have been investigated parametrically using synthetic data. The imaging model is established on a two-view collimated shadowgraph imaging setup, which features with high framing rate, large test volume and long depth focus. The performance of three algorithms has been tested under different image particle densities and displacement-spacing ratios. The correctness of 3D reconstruction and tracking, as well as the number of ghost particles are obtained and compared comprehensively. The results indicate that significant improvement has been achieved through dedicated designed algorithms. The comparative study has revealed the potential of each algorithm with extremely limited geometry constraints in two-view systems, which may serve as guidance for choosing appropriate algorithms under different test conditions.

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