Three-dimensional particle tracking algorithm based on the special ellipsoids

A 3D PTV algorithm based on the minimum volume enclosing ellipsoid (MVEE) and the inertia-equivalent ellipsoid (IEE) is proposed. Firstly, different versions of this algorithm are proposed by incorporating the features of MVEE and Voronoi polyhedron through weighted summation. Secondly, according to the test by homemade particle flows, among these versions, the Voronoi polyhedron feature expressed by IEE has the best performance, thus leading to a completely ellipsoid-based version named E-PTV. Thirdly, a series of tests and analyses are conducted to compare E-PTV with some classical and newly developed 3D PTV algorithms. The results show that, E-PTV is parameter-independent and optimally efficient in addition to being close to these algorithms in accuracy. Finally, combining E-PTV with the volumetric 3-component velocimetry (V3V) system successfully reconstructs an actual 3D vortex ring flow, thereby confirming the practicality of E-PTV.