Lagrangian sensors drift with the fluid and measure the conditions inside a chemical reactor. They have shown promise to improve the awareness of operators about the state of a reactor, but tracking them in three dimensions remains a mostly unsolved challenge.
The authors explore a setup in which sensors simulated on the computer, based on a recently proposed design for a real sensor, are tracked using the data of an accelerometer and a magnetometer from the inertial measurement unit inside the sensor. Filtering algorithms, which use a dynamical model developed for this purpose, process these readings into estimates of the position.
The tracking performance of an extended Kalman filter, of a particle filter and of the unscented Kalman filter implemented in the pykalman library is compared. The numerical experiments follow particles that move in an analytically given vortex in three dimensions and in the experimentally measured flow field of a stirred tank reactor on laboratory scale, which is agitated by two Rushton turbines. The movement of the inertial particles is described by the Maxey-Riley-Gatignol equations, which serve as the ground truth.
The extended Kalman filter and the particle filter reconstruct the trajectories from noisy synthetic data with mean relative errors below 3 percent, which makes them suitable candidates for the tracking of such sensors.
The study is a collaboration between the Chair of Computational Mathematics at the Institute of Mathematics at Hamburg University of Technology and the Heinrich Blasius Institute at the Hamburg University of Applied Sciences, carried out within the Collaborative Research Centre CRC 1615 (SMART Reactors).
Vamika Rathi, Fatima Sehar, Finn Sommer, Sebastian Götschel, Eike Steuwe, Alexandra von Kameke, Daniel Ruprecht (2026). Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor. Computers & Chemical Engineering, 109911.
