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Time-resolved, four-pulse and two-pulse pairs of synthetic particle images with different particles per pixel (PPP) values created by four virtual camera views of tracer particles in the turbulent boundary layers flow are provided along with the calibration data to challenge the latest developments of the LPT code. The challenge synthetic dataset was computed by Large Eddy Simulation (LES) of a cylinder embedded in a turbulent boundary layer flow over a plate. More details of the LPT challenge is available in "http://cfdforpiv.dlr.de/".
LCTI was implemented to run the whole 4D-PTV process (see this link). LCTI (KLPT-LCTI) was examined on the time-resolved data from the LPT challenge at four particle densities (i.e., concentrations) from 0:005 up to 0:08 ppp. The challenge cases were obtained from the wall-bounded wake flow behind a cylinder at a momentum thickness Reynolds number Re around 4500. In terms of turbulence length scales, particle concentration of the mentioned four cases varied between 2*10^-7 and 3*10^-6 pp_etta^3. The domain of interest was set at 100*50*30 mm^3 downstream of the cylinder. The image acquisition rate was equal to 600 ls, resulting in dt/(Kolmogorov timescale)=2:68 temporal scale. At the lowest ppp, the proposed method managed to reconstruct over 99% of true particles accurately. Percentage of true particles maintained over 99% for higher densities (i.e., 0.025, 0.05, and 0:08 ppp). Accordingly, missed and ghost particles were less than 1%. The case studies of the LPT challenge revealed that the positional Root-Mean-Square error (RMSE) of KLPT-LCTI increased linearly with ppp, but it remained below 0:0041 mm for all four particle densities. This illustrates the reliable performance of the LCTI at particle densities lower than 0:08 ppp, knowing that most of the 4D-PTV real experiments perform at 0:05 ppp particle density or lower.
FIG. 1. LCTI trajectory results for the LPT challenge wake flow at 0:12 ppp (a) slice view in y direction of particle trajectories in gray and the target track in red and (b) cluster of coherent tracks with the target track in red.
FIG. 2. Sensitivity of the 4D-PTV convergence to the number of initialized tracks for the LPT challenge high-density case at 0:12 ppp over the first 30 time steps. Number of initialized tracks after the first four frames varies from 12 000 to 60 000.
For densities higher than 0:08 ppp, a more accurate initialization technique could prevent the 4D-PTV algorithm from failing or improve its convergence speed. We highlighted that KLPT featuring LCTI succeeded in reconstructing tracks at the density of 0:12 ppp, while KLPT featuring NNI failed to converge. Fig 1 shows an example of coherent motion detection by LCTI at the density of 0:12 ppp. The particle trajectories obtained from the proposed method are shown in Video. 1. Questions have been raised about the 4D-PTV sensitivity to the number of initialized particles at the beginning. We illustrated this issue in the LPT challenge case with 0:12 ppp and over 120 000 particles. As shown in Fig. 2, the KLPT-LCTI process reaches no more than 85 000 (i.e., 70%) final tracks if the process starts with any number below 30000 initialized tracks. However, starting with 60 000 initialized tracks leads to cover over 99% of final trajectories after 30 time steps at 0:12 ppp. The evidence from this study indicates that the number of initialized tracks is one deterministic contributor to the 4D-PTV convergence at high-density scenarios. Without a proper track initialization algorithm, a 4D-PTV scheme would not be able to recover the majority of tracks eventually.
VIDEO. 1. LPT challenge results of wall-bounded wake flow behind a cylinder. Tracking over 120000 particles using time-resolved particle tracking velocimetry (4D-PTV).
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Cite as: Ali Rahimi Khojasteh, Yin Yang, Dominique Heitz, and Sylvain Laizet , "Lagrangian coherent track initialization", Physics of Fluids 33, 095113 (2021) https://doi.org/10.1063/5.0060644
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