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Electrolysis stands as a pivotal method for environmentally sustainable hydrogen production. However, the formation of gas bubbles during the electrolysis process poses significant challenges by impeding reactions, diminishing cell efficiency, and dramatically increasing energy consumption. Furthermore, the inherent difficulty in detecting these bubbles arises from the non-transparency of the wall of electrolysis cells. Fortunately, these gas bubbles induce alterations in the cell’s conductivity, leading to corresponding fluctuations in the surrounding magnetic flux density. In this context, we can leverage external magnetic sensors to measure the magnetic flux density fluctuations induced by gas bubbles. Next, by solving the inverse problem of the Biot-Savart Law, we can estimate the conductivity, bubble size, and location within the cell. Nevertheless, reconstructing a high-resolution conductivity map from limited induced magnetic flux density measurements poses a formidable challenge as an ill-posed inverse problem. To overcome this challenge, we employ Invertible Neural Networks (INNs) to reconstruct the conductivity field. The inherent property of INNs, characterized by a bijective mapping between the input and output space, makes them exceptionally well-suited for resolving ill-posed inverse problems. We conducted extensive qualitative and quantitative evaluations to compare the performance of INNs with traditional approaches such as Tikhonov regularization. Our experiments demonstrate that, particularly in the presence of noise in the magnetic sensor data, our INN-based approach outperforms Tikhonov regularization in accurately reconstructing bubble distributions and conductivity fields. We hope that, given the efficacy of INNs shown in this work, they will become an indispensable deep-learning based approach for addressing inverse problems not only in Process Tomography but across various other domains.

Magnetic Particle Tracking is able to track the position and orientation of magnetic particles in opaque media by measuring the magnetic field outside the vessel. This technique was already applied in granular flows with a magnet of 8 mm³ volume [1]. The extension of this technique to flotation, which is used in ore processing and recycling, requires magnetic particles in sub-mm range, which float with the foam. The vessel diameter of 100 mm demands for sensors with a resolution in the order of nT. Thin-film sensors reduce the distance from the sensor to the magnet. We will present in detail a newly developed measurement system with an array of 12 tailored planar Hall magnetoresistive sensors with a measurement range from 300 µT down to 10 nT and demonstrate the reliable detection of the position of a cubic magnet with edge length of 0.4 mm. The sensors consist of single layer permalloy in a 5 ring Wheatstone bridge configuration. Furthermore, we will show preliminary results of an sensor array on a flexible substrate [2], which can be easily and accurately placed around a complex shaped vessel. [1] Buist, et al. AIChE Journal 60.9 (2014): 3133-3142. [2] Granell, et al. npj Flexible Electronics 3.1 (2019): 3.

Inductive flow measurement techniques such as the Contactless Inductive Flow Tomography require sensors that provide a magnetic field resolution of 1 nT while operating in magnetic fields of several mT. With advancements in state-of-the-art magnetoresistive thin-film sensors the required behavior regarding sensitivity, precision and hysteresis can be achieved [1]. Planar Hall Effect sensor have been shown to be one of the leading sensor types in this area. Therefore we present a detailed study on the effect of different sensor layouts, geometries, magnetic flux concentrators and other parameters on the characteristics of single layer Permalloy Planar Hall Effect sensors. [1] Granell, Pablo Nicolás, et al. npj Flexible Electronics 3.1 (2019): 1-6.

Foam processes are essential in many industrial applications e.g., in froth flotation for material separation. A detailed understanding of foam flows is vital for improvements in process efficiency. X- Ray and Neutron imaging can measure flow fields in foam, but require a complex setup and cannot be performed in-situ. Magnetic particle tracking (MPT) is an alternative approach, that measures the trajectory of a small magnetic tracer particle inside the foam as a representation of its movement. Different magnetic field sensors can be applied to detect the magnetic tracer particle. We chose thin film sensors based on the planar Hall effect (PHE) due to their small size, high sensitivity, high signal-to- noise ratio and low cost. Our sensors have a size of only 2 mm x 2 mm and are capable of measuring magnetic fields as low as 10 nT at a sampling frequency of 1 Hz. A sensitivity of 20 V/T at a driving current of 1 mA was achieved by means of sensor bridging. Our PHE-sensors are almost as precise as currently used Fluxgate probes, but offer several advantages due to their reduced size. This includes being installed closer to the area to be measured, enabling finer grids of sensors and decreasing the detection volume, which increases the precision of the MPT as well as other tomographic methods.

The contactless inductive flow tomography is a procedure that enables the reconstruction of the global three-dimensional flow structure of an electrically conducting fluid by measuring the flow-induced perturbation of an applied static magnetic field and by subsequently solving the associated linear inverse problem. The method enables the visualisation of the dynamics of a large-scale circulation in the modified Rayleigh-Bénard experiment.

Contactless Inductive Flow Tomography (CIFT) is a flow measurement technique allowing for visualizing the global flow in electrically conducting fluids. The method is based on the precise measurement of very weak induced magnetic fields arising from the fluid motion under the influence of one or several primary excitation magnetic field(s). The simultaneous use of more than one excitation magnetic field is necessary to fully reconstruct three-dimensional liquid metal flows, yet is not trivial as the scalar values of induced magnetic field at the sensors need to be disentangled for each contribution of the excitation fields. Another approach is to multiplex the excitation fields. Here the temporal resolution of the measurement needs to be kept as high as possible. We apply two trapezoidal-shaped excitation magnetic fields with perpendicular direction to each other to a mechanically driven liquid metal flow. The consecutive application by multiplexing enables to determine the flow structure in the liquid with a temporal resolution down to 3 s with the existing equipment.

Electrolysis is crucial for eco-friendly hydrogen production, but gas bubbles generated during the process hinder reactions, reduce cell efficiency, and increase energy consumption. Additionally, these gas bubbles cause changes in the conductivity inside the cell, resulting in corresponding variations in the induced magnetic field around the cell. Therefore, measuring these gas bubble-induced magnetic field fluctuations using external magnetic sensors and solving the inverse problem of Biot-Savart’s Law allows for estimating the conductivity in the cell and, thus, bubble size and location. However, determining high-resolution conductivity maps from only a few induced magnetic field measurements is an ill-posed inverse problem. To overcome this, we exploit Invertible Neural Networks (INNs) to reconstruct the conductivity field. Our qualitative results and quantitative evaluation using random error diffusion show that INN achieves far superior performance compared to Tikhonov regularization.

A novel concept of a measurement technology for the localization and determination of the size of gas bubbles is presented, which is intended to contribute to a further understanding of the dynamics of efficiency-reducing gas bubbles in electrolyzers. A simplified proof-of-concept (POC) model is used to numerically simulate the electric current flow through materials with significant differences in electrical conductivity. Through an automated approach, an extensive data set of electric current density and conductivity distributions is generated, complemented with determined magnetic flux densities in the surroundings of the POC cell at virtual sensor positions. The generated data set serves as testing data for various reconstruction approaches. Based on the measurable magnetic flux density, solving Biot-Savart’s law inversely is demonstrated and discussed with a model-based solution of an optimization problem, of which the gas bubble locations are derived.

Mit der kontaktlosen induktiven Strömungstomografie (CIFT) lassen sich Geschwindigkeitsfelder in elektrisch leitfähigen Flüssigkeiten global bestimmen. Kenntnisse über den Strömungszustand in Metallschmelzen sind für industrielle Prozesse, wie das Stranggießen von Stahl, von immenser Bedeutung und können auch in der Grundlagenforschung nutzbringend angewendet werden, z.B. zur Analyse von konvektiven Flüssigmetallströmungen als Modellsysteme des Wärmetransportes. Das Verfahren beruht auf der präzisen Messung kleinster Magnetfeldänderungen durch geeignete Sonden und der nachfolgenden Rekonstruktion der Strömungsstruktur durch die Lösung eines linearen inversen Problems. In dieser Veröffentlichung geben wir einen Überblick über die Entwicklungen der letzten Dekade und diskutierten je einen Anwendungsfall für CIFT aus der grundlegenden und der angewandten Fluiddynamik. >>Contactless Inductive Flow Tomography (CIFT) is a flow measurement technique that can reconstruct the global 3D flow in electrically conducting fluids. Knowledge of the flow conditions in liquid metals is of outmost importance for industrial processes as continuous casting of steel. CIFT can also be applied to fundamental research, e.g. to measure convective liquid metal flows. The technique is based on the precise measurement of very small magnetic field changes and the subsequent reconstruction of the flow field by solving the linear inverse problem. This publication illustrates one use-case from fundamental and applied fluid mechanics each.

Contactless inductive flow tomography (CIFT) can reconstruct the global 3D flow field in liquid metals. The technique is based on measuring very small magnetic fields induced by currents in the conducting liquid arising from the fluid motion under the influence of two primary excitation fields and solving the according linear inverse problem [1]. We present experimental results of CIFT measurements on a large cylindrical vessel with a height of 640 mm and a diameter of 320 mm, i.e. aspect ratio 0.5, filled with the eutectic alloy GaInSn. The liquid metal is heated from the bottom and cooled from the top, i.e. a so-called Rayleigh-Bénard (RB) convection cell. The temperature gradient drives a complex flow, that varies spatially and temporally [2-5]. The experimental set-up includes a number of Fluxgate sensors for highly sensitive measurements of the induced magnetic field in the order of 10 nT [6] as well as Ultrasound-Doppler velocimetry probes, that directly measure the velocity of the flow along their line-of-sight. Our preliminary measurements used only the excitation field in vertical direction, yet show a very high agreement of the time-dependent velocity profiles measured by UDV and the according CIFT data, projected onto the line-of-sight of the UDV sensors. Acknowledgement This work was supported by the German Research Foundation (DFG) under project no. 374994652. T.V. and F.S. also thank the DFG for support under the grant VO 2331/1. REFERENCES [1] Stefani F., Gundrum T., Gerbeth G., Physical Review E 70: 056306. 2004. [2] Akashi M. et al., J. Fluid Mech. 932 (2022). [3] Zürner T. et al., J. Fluid Mech. 876 (2019). [4] Vogt T. et al., PNAS 115 (2018). [5] Mitra R. et al., Magnetohydrodynamics, vol. 58 (2022) [accepted for publication]. [6] Sieger M. et al., Magnetohydrodynamics, vol. 58 (2022) [accepted for publication].

Contactless inductive flow tomography (CIFT) is a flow measurement technique developed at Helmholtz-Zentrum Dresden-Rossendorf that can reconstruct the global 3D flow field in electrically conducting fluids such as liquid metals. The velocity field of the moving fluid can be reconstructed by solving the underlying inverse problem using appropriate regularization methods. This publication introduces the key concept and mathematical foundation of the method and illustrates the measurement capability of CIFT on two examples: continuous casting of steel in applied fluid dynamics and Rayleigh-Bénard convection as a paradigmatic system in fundamental fluid dynamics.

The Eddy Current Flow Meter is an inductive velocity sensor which can be used in liquid metal applications, such as liquid metal cooled fast reactors. There it can be used as part of the safety instrumentation in order to monitor the coolant flow through subassemblies under normal operating conditions or to detect and locate blockages in case of a local freezing of the coolant. Typically the Eddy Current Flow Meter is used in pipe flows where the flow is mostly parallel to the sensor axis, whereas the flow angle may change significantly above subassemblies in a liquid metal cooled reactor. In the first part, the paper therefore deals with investigating the influence of varying flow angles on the performance of the Eddy Current Flow Meter. By performing measurements in a model experiment, the effect of different flow angles on the measured velocities will be demonstrated. In the second part of the paper, multiple Eddy Current Flow Meters in an array are used to detect and locate blockages in an array of seven subassemblies in the same model experiment. All experiments are carried out at room temperature with a liquid alloy of gallium, indium and tin.

The development of closed control loops for electromagnetic actuators in continuous casting based on the current flow conditions of the liquid steel in the mold is challenging due to the opaqueness and the high temperature of the melt. In this work we will investigate the applicability of Contactless Inductive Flow Tomography (CIFT) as a real-time measurement technique for controlling the strength of a ruler type Electromagnetic Brake (EMBr) in a model of a continuous caster. Because CIFT relies on the measurement of the small flow induced perturbation of an applied magnetic field, the measurement system is very sensitive to changes of the strength the EMBr. We will shortly delineate the developed compensation method that is able to cope with the non-linearity of the ferromagnetic yoke of the brake. In combination with the real-time reconstruction algorithm for solving the linear inverse problem, CIFT is able to visualize the flow structure in the mold in real-time with a time resolution of 1 Hz. As a proof of concept of a closed control loop, we implemented a simple controller which switches the EMBr off, when the impingement positions of the jets at the narrow faces are below a critical threshold. The implemented controller and the experiment will be described in detail.

Heavy-liquid metals (HLMs), such as lead and lead–bismuth eutectic (LBE), are proposed as primary coolants in accelerator driven systems and next-generation fast reactors. In Europe, the reference systems using HLMs are MYRRHA (LBE) and ALFRED (lead). Extensive R&D programs have been established for supporting their detailed design and safety assessment, including thermal–hydraulic experiments at representative operating conditions in an HLM environment. These experiments aim both at a design verification and at the validation of numerical models, which allow an extrapolation of the results. Advanced instrumentation, capable of sustaining high temperatures and corrosion, is necessary for accurate measurements, often in compact geometries. This article presents an overview of recent experiences and ongoing activities on pool-type and loop-type HLM experiments. Pool tests include the measurement of forced- and natural-circulation flow patterns in several scenarios representative of nominal and decay heat removal conditions. Loop tests are focused on the evaluation of specific components, like mockups of the fuel assembly, control rod and heat exchangers. They involve the measurement of global variables, such as flow rate and pressure difference, and local quantities like temperature, velocity and vibrations. In addition to traditional techniques, other instrumentation based on optical fibers, ultrasonic and electromagnetic methods are discussed.

Flow control of liquid metals based on the actual flow condition is important in many metallurgical applications. For instance, the liquid steel flow in the mould of a continuous caster strongly influences the product quality. The flow can be modified by an electromagnetic brake (EMBr). However, due to the lack of appropriate flow measurement techniques, the control of those actuators is usually not based on the actual flow condition. This paper describes the recent developments of the Contactless Inductive Flow Tomography (CIFT) towards a real-time monitoring system, which can be used as an input to the control loop for an EMBr. CIFT relies on measuring the flow-induced perturbation of an applied magnetic field and the solution of an underlying linear inverse problem. In order to implement the CIFT reconstructions in combination with EMBr, two issues have to be solved: (i) compensation of the effects of the change in EMBr strength on the CIFT measurement system and (ii) real-time solution of the inverse problem. We present solutions of both problems for a model of a continuous caster with a ruler-type EMBr. The EMBr introduces offsets of the measured magnetic field that are several orders of magnitude larger than the very flow-induced perturbations. The offset stems from the ferromagnetic hysteresis exhibited by the ferrous parts of the EMBr in the proximity of the measurement coils. Compensation of the offset was successfully achieved by implementing a numerical model of hysteresis to predict the offset. Real-time reconstruction was achieved by precalculating the computationaly-heavy matrix inverses for a predefined set of regularization parameters and choosing the optimal every measurement frame. Finally, we show that this approach does not hinder the reconstruction quality.

Contactless inductive flow tomography (CIFT) can reconstruct the complex 3-dimensional flow structure of the large scale circulation in liquid metal filled Rayleigh-Bénard (RB) convection cells. The method relies on the precise measurement of weak magnetic fields induced by currents in the conducting liquid arising from the fluid motion in combination with primary excitation fields. The velocity distribution is reconstructed from the magnetic field measurements by solving a linear inverse problem using the Tikhonov regularization and L-curve method. A number of technical challenges have to be overcome to reach the desired accuracy of the measurement signals. In this paper we will describe our design of a new CIFT set-up for a large RB vessel with a diameter of 320 mm and a height of 640 mm. We outline the major factors perturbing the measurement signal of several tens of nanoteslas and describe solutions to decrease mechanical drifts by thermal expansion to a sub-critical level to enable CIFT measurements for high-Rayleigh number flows.

Lack of appropriate flow measurement techniques for liquid steel during continuous casting limits the application of control strategies that could improve the quality of the end product. Contactless Inductive Flow Tomography (CIFT) is a promising measurement technique that can provide information about the flow structure in the mould to a real time controller. On this basis, electromagnetic actuators can be used to react on undesired flow conditions in the mould. However, because of their nature, these actuators pose a significant challenge for inductive measurement methods. In this work we describe the influence of an electromagnetic brake on CIFT in a laboratory environment. We also show how this influence can be fully compensated, which facilitates the viability of CIFT as a key ingredient of real time control of continuous casting.

More than 96% of steel in the world is produced via the method of continuous casting. The flow condition in the mould, where the initial solidification occurs, has a significant impact on the quality of steel products. It is important to have timely, and perhaps automated, control of the flow during casting. This work presents a new concept of using contactless inductive flow tomography (CIFT) as a sensor for a novel controller, which alters the strength of an electromagnetic brake (EMBr) of ruler type based on the reconstructed flow structure in the mould. The method was developed for the small-scale Liquid Metal Model for Continuous Casting (mini-LIMMCAST) facility available at the Helmholtz-Zentrum Dresden-Rossendorf. As an example of an undesired flow condition, clogging of the submerged entry nozzle (SEN) was modelled by partly closing one of the side ports of the SEN; in combination with an active EMBr, the jet penetrates deeper into the mould than when the EMBr is switched off. Corresponding flow patterns are detected by extracting the impingement position of the jets at the narrow faces of the mould from the CIFT reconstruction. The controller is designed to detect to undesired flow condition and switch off the EMBr. The temporal resolution of CIFT is 0.5 s.

With the ongoing digitalization of industry, imaging sensors are becoming increasingly im-portant for industrial process control. In addition to direct imaging techniques such as those provided by video or infrared cameras, tomographic sensors are of interest in the process indus-try where harsh process conditions and opaque fluids require non-intrusive and non-optical sensing techniques. Because most tomographic sensors rely on complex and often time-multiplexed excitation and measurement schemes and require computationally intensive image reconstruction, their application in the control of highly dynamic processes is often hindered. This article provides an overview of the current state of the art in fast process tomography and its potential for use in industry.

A new experimental facility has been designed and constructed which represents a 1:5.25 model of an industrial 185 t steel ladle. This setup is intended for systematic investigations of complex liquid metal multiphase flows created by gas blowing from the bottom. Two tons of a Sn40wt.%Bi alloy are employed as working fluid, its thermophysical properties are very similar to those of liquid steel. The relatively low operating temperatures (T~200°C) compared to the real industrial process allow the use of powerful measuring techniques for characterizing the behavior of the gas phase and resulting flow regimes. Argon gas is injected through diverse plug systems into a cylindrical fluid vessel which is equipped with a pressure tight lid to achieve low-pressure conditions for vacuum processing. This paper presents first measurements of the gas distribution close to the free liquid metal surface for various gas flow rates, plug positions and types. Moreover, the pressure in the vessel has been varied between 1 mbar and ambient pressure. The experiments provide a copious data base about the flow regimes, void fraction, liquid and bubble velocities, and bubble properties, which can be used to provide so far unknown boundary conditions for numerical simulations of various metallurgical reactors such as steelmaking converters or steelmaking ladles.

The Eddy Current Flow Meter is a reliable and robust inductive sensor for the measurement of flowrates in liquid metal flows. This kind of sensor is usually being used in pipe flows where the flow is mostly parallel to the sensor axis. When this sensor is used as part of the safety instrumentation above the subassemblies in liquid metal cooled fast reactors, the flow angle may change rapidly according to the conditions within the reactor. In this paper we investigate the performance of the Eddy Current Flow Meter in flows inclined to the sensor axis by numerical simulations as well as model experiments. We demonstrate that the Eddy Current Flow Meter yields reliable results for flow angles up to 30° while the sensitivity of the sensor is significantly reduced for larger angles.

The time dependent behaviour of the large-scale circulation in a Rayleigh-Bénard convection cell exhibits a rich set of different three-dimensional flow features like rotations or torsional modes. In this paper, the applicability of the contactless inductive flow tomography (CIFT) to visualise these flow features in a cylindrical cell filled with GaInSn is investigated numerically. The simulated flow in the cylinder with a diameter of 320 mm and a height of 640 mm serves as a basis to investigate the quality of the reconstructed velocity field by CIFT.

In the present study, we have performed a series of numerical simulations of the turbulent liquid metal flow in a laboratory-scale setup of the continuous casting. The liquid metal flow was subjected to an external non-uniform magnetic field reproducing a realistic electromagnetic brake (EMBr) effect. The focus of this research was on the effects of the finite electrical conductivity of Hartmann walls on the flow and turbulence in the mold. To be able to simulate distributions of the electric potential and current in both the fluid and solid wall domains, we applied our recently developed and validated in-house conjugate MHD solver based on the open-source code OpenFOAM. The dynamic Large Eddy Simulation (LES) method was used to simulate the turbulent flow. The results obtained for the neutral (non-MHD) and MHD cases over a range of the imposed EMBr strengths – all for the perfectly electrically insulated walls – were compared with the available Ultrasound Doppler Velocimetry (UDV) measurements. A good agreement between simulations and experiments was obtained for all simulated cases. Next, we completed a series of simulations including a wide range of the finite electric conductivities (ranging from a weakly to perfectly conducting wall conditions) of the Hartmann walls for a fixed value of the imposed EMBr. The obtained results demonstrated a significant influence of the electric wall conductivities on the flow and turbulence reorganization. It is expected that here provided insights can be applicable for the new generation of the laboratory- and real-scale continuous casting setups.

Dataset containing the raw and post-processed data used for in the associated publication. Dataset contains the measurements of the flow-induced magnetic field for identification of the compensation parameters and the test data used to validate the model. It also contains the down-sampled velocity profile generated from the numerical simulations, and the reconstructions of the same velocity profile.

Dataset containing the raw and post-processed data used for in the associated publication. Scripts for evaluating the data are attached.