Contact

Dr. Thomas Wondrak

Head Inductive measurement techniques
Process Diagnostics
t.wondrakAthzdr.de
Phone: +49 351 260 2489

Lukas Krause

l.krauseAthzdr.de
Phone: +49 351 260 3867

Current Tomography

The spatial and temporal distribution of the electrical conductivity inside a current-conducting reaction vessel acts as key feature of the process state. Through the electric current density, the electrical conductivity is linked to the magnetic flux density, which can be measured precisely by sensors outside the reactor. The current tomography as a measurement method for the ­magnetic field-based reconstruction of the electric conductivity in conducting liquids enables efficient process control for water electrolysis, pyrolysis and further industrial applications.

Foto: Wasserelektrolyse – Prinzipskizze ©Copyright: Lukas Krause

Fig. 1: Schematic representation of the water electrolysis as use case for the current tomography.

Functional principle

The current density distribution j inside a current-conducting reactor is depending on electric conductivity σ within the vessel (Fig. 2: → Ohm´s law). The electric currents are generating a weak magnetic field (→ Biot Savart law, forward problem) that can be measured outside of the reaction vessel with magnetic field sensors. By solving the associated invers problem based on these measurements, the inner conductivity distribution of the reactor can be reconstructed (→ inverse problem).

The method consists of two steps:

  1. (Contactless) measurement of the distribution of the magnetic field outside the vessel
  2. Reconstruction of the distribution of the current density or the conductivity inside the vessel by solving the invers problem.
Foto: Stromtomografie – Inverses Problem und Funktionsprinzip ©Copyright: Lukas Krause

Fig. 2: Relation of the distribution of electric conductivity, current density and magnetic flux density.

Proof-of-concept

The applicability of the measurement method was investigated in a coupled numerical and experimental study. The magnetic field sensors are located below a nearly two-dimensional conductor (Fig. 3). The distribution of the current density distribution in highly conductive media (GaInSn, Cu) is influenced by therein inserted electrically non-conducting cylinders, modeling gas bubbles in a water electrolyzer.

Foto: Current Tomography – Proof-of-concept setup ©Copyright: Lukas Krause

Fig. 3: Proof-of-concept setup.

For solving the invers problem, an Invertible Neural Network (INN) was trained based on a numerically generated dataset containing distributions of conductivity, current density and magnetic flux density. Moreover, additional models not included in the training data were simulated and replicated for experimental validation. Figure 4 shows the simulated distribution of the current density and the corresponding relative conductivity distribution, reconstructed by the trained INN based on experimental measurements.

Foto: Current Tomography – simulated current density distribution with bubbles and reconstructed conductivity ©Copyright: Lukas Krause

Fig. 4: left: Simulated current density distribution with exemplary gas bubbles / right: corresponding INN prediction of the relative conductivity distribution.