(209e) A Novel Position Reconstruction Algorithm for Particle Tracking Based on the Finite Element Method (FEM)

Particle tracking is a non-intrusive velocimetry method that is used to study the hydrodynamics of single and multiphase systems. This technique works by tracking the motion of a single particle that emits gamma-rays. Using an array of detectors placed around the reactor vessel, the number of emitted photons measured by the detectors can be used to reconstruct the position of the particle. In this work, we introduce a new open-source library called Lethe-RPT. Lethe-RPT is a module of Lethe, an open-source Computational Fluid Dynamics (CFD) library. The core of Lethe-RPT is a Monte-Carlo simulation that calculates the number of counts at each position of a given mesh inside the reactor. Lethe-RPT divides the reactor into small cells which form a triangulation. Since the Monte-Carlo method is iterative in nature, the intensity of the radiation has fluctuations in space that are also contained in the calculated position through high -frequency noise from the photon counts. This noise is filtered in Lethe-RPT by using an L2 orthogonal projection (L2P). L2P minimizes the least square error between the photon count obtained from the FEM interpolation and the experimental count for all the detectors in each cell to reconstruct the position of the particle. The reconstruction algorithm locates the particle position by searching through the cells to find the unique cell that satisfies the inverse of the finite element interpolation. This inversion process, albeit not exact, is well-posed.