In this paper, multiple-particle tracking, a new method that enables us to track more than one particle, is presented. Thus, to track multiple particles, the tracers are labelled with different radioactive levels, so that the number of g -rays received from each tracer is significantly different. The most active tracer can be located while the trajectories from the remaining tracers are regarded as corrupt trajectories. The location of the strongest tracer is the point which minimises the sum of perpendicular distances to the various trajectories. This procedure is iterative, in that, having calculated the minimum distance point for a set of trajectories as a first approximation, those passing furthest away are discarded and the minimum distance point recalculated using the remaining subset. The iteration procedure continues until it is believed that all corrupt trajectories have been discarded. Trajectories passing close to the located tracer are then removed from the dataset. The location of the second tracer is then calculated supposing that the trajectories from the third strongest tracer are corrupted. The location of the third tracer is calculated similarly.
Three typical examples are presented in this paper, one for tracking two stationary particles, one for tracking three stationary particles, and another for tracking three moving particles.
For two stationary particles, tracers were fixed on a metal stick on which the separation distance of particles could be adjusted. The stick was mounted approximately at the centre of the field of view of the detectors for each of the 72 runs. The separation distance of particles was varied over the range from 1.5mm to 13mm. The technique was validated by comparison of the distance obtained from PEPT measurements to the actual one. As the separation distance increased, the error decreased. Even when the separation distance is down to 3mm, the tracked distance error is only ± 0.7mm.
For testing three stationary particles, 12 tests have been performed. Three tracers were fixed at the corners of each of a set of wooden cubes which had different dimensions and were mounted in turn approximately at the centre of the field of view of the detectors. The dimension of the cubes varied from 5mm to 20mm. For each cube, the location algorithm was used to determine repeated sets of locations for the three tracers, and the consistency was determined by calculating the standard deviations within each set. The results show that the variations are reasonable. For example, the variations are 1.1mm and 1.6mm when the separation distances between three tracers are 28 mm and 7 mm respectively.
For moving particles, nine experiments have been taken with three tracers fixed on a cube having a dimension of 17 mm. The cube was mounted on a turntable rotating at constant speeds. The cube speeds varied from 3.5mm/s to 240mm/s. From the trajectories of the tracers, calculated by the multiple-particle tracking techniques, the three dimensional images of the cube can be reconstructed at any time, giving the rotational information of the cube. The latter, is an invaluable for understanding the relative movement of solids in various industrial applications. The results show that the errors of location and speed are acceptable. The r.m.s. location errors are only 1.8mm and 6mm, and the r. m. s. speed errors are 2mm/s and 25mm/s when the tracer speeds are 3.5mm/s and 240mm/s respectively.
Once the technique was validated three non restricted tracers were placed in a 150 mm fluidized bed filled with 500 mm glass beads. Parameters such as occupancy and tracer velocity vectors, circulation times were used. The results indicated that there was no apparent difference between the data obtained from different tracers.
The multiple-particle tracking technique has shown that it can not only track positions of particles but also provides the rotation information of solids with any regular shapes. The examples have been shown to give valuable and accurate results for stationary and moving particles rotating at speeds up to 240mm/s which are relevant to many industrial applications. The procedure is relatively simple and can be implemented for fundamental research as well as industrial applications.
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