Robust Reconstruction of the Void Fraction from Noisy Magnetic Flux Density Using Invertible Neural Networks.

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 the electrochemical 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. Additionally, these gas bubbles induce alterations in the conductivity of the electrolyte, leading to corresponding fluctuations in the magnetic flux density outside of the electrolysis cell, which can be measured by externally placed magnetic sensors. By solving the inverse problem of the Biot-Savart Law, we can estimate the conductivity distribution as well as the void fraction within the cell. In this work, we study different approaches to solve the inverse problem including Invertible Neural Networks (INNs) and Tikhonov regularization. Our experiments demonstrate that INNs are much more robust to solving the inverse problem than Tikhonov regularization when the level of noise in the magnetic flux density measurements is not known or changes over space and time.

Erratum: Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection [Phys. Rev. Lett. 128, 164501 (2022)].

This corrects the article DOI: 10.1103/PhysRevLett.128.164501.

In-Bulk Temperature Profile Mapping Using Fiber Bragg Grating in Fluids.

The capabilities of Fiber Bragg Grating (FBG) sensors to measure temperature variations in the bulk of liquid flows were considered. In the first step of our research project, reported in this paper, we investigated to what extent the use of thin glass fibers without encapsulation, which only minimally disturb a flow, can fulfill the requirements for robustness and measurement accuracy. Experimental tests were performed in a benchmark setup containing 24 FBG measuring positions, which were instrumented in parallel with thermocouples for validation. We suggest a special assembly procedure in which the fiber is placed under a defined tension to improve its stiffness and immobility for certain flow conditions. This approach uses a single FBG sensor as a reference that measures the strain effect in real time, allowing accurate relative temperature measurements to be made at the other FBG sensor points, taking into account an appropriate correction term. Absolute temperature readings can be obtained by installing another well-calibrated, strain-independent thermometer on the reference FBG. We demonstrated this method in two test cases: (i) a temperature gradient with stable density stratification in the liquid metal GaInSn and (ii) the heating of a water column using a local heat source. In these measurements, we succeeded in recording both spatial and temporal changes in the linear temperature distribution along the fiber. We present the corresponding results from the tests and, against this background, we discuss the capabilities and limitations of this measurement technique with respect to the detection of temperature fields in liquid flows.

Collapse of Coherent Large Scale Flow in Strongly Turbulent Liquid Metal Convection.

The large-scale flow structure and the turbulent transfer of heat and momentum are directly measured in highly turbulent liquid metal convection experiments for Rayleigh numbers varied between 4×10^{5} and ≤5×10^{9} and Prandtl numbers of 0.025≤Pr≤0.033. Our measurements are performed in two cylindrical samples of aspect ratios Γ=diameter/height=0.5 and 1 filled with the eutectic alloy GaInSn. The reconstruction of the three-dimensional flow pattern by 17 ultrasound Doppler velocimetry sensors detecting the velocity profiles along their beam lines in different planes reveals a clear breakdown of coherence of the large-scale circulation for Γ=0.5. As a consequence, the scaling laws for heat and momentum transfer inherit a dependence on the aspect ratio. We show that this breakdown of coherence is accompanied with a reduction of the Reynolds number Re. The scaling exponent ß of the power law Nu∝Ra^{ß} crosses eventually over from ß=0.221 to 0.124 when the liquid metal flow at Γ=0.5 reaches Ra≳2×10^{8} and the coherent large-scale flow is completely collapsed.

Contactless Inductive Flow Tomography for Real-Time Control of Electromagnetic Actuators in Metal Casting.

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 article 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) a 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 computationally heavy matrix inverses for a predefined set of regularization parameters and choosing the optimal one in every measurement frame. Finally, we show that this approach does not hinder the reconstruction quality.

Laboratory Investigation of Tomography-Controlled Continuous Steel 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.

X-ray particle tracking velocimetry in liquid foam flow.

In this work, we introduce a novel approach to measure the flow velocity of liquid foam by tracking custom-tailored 3D-printed tracers in X-ray radiography. In contrast to optical observations of foam flow in flat cells, the measurement depth equals 100 mm in the X-ray beam direction. Light-weight tracers of millimetric size and tetrapod-inspired shape are additively manufactured from stainless steel powder by selective laser melting. Matching with the foam structure and bubble size, these tracers follow the foam flow. An X-ray beam passes through the radiotransparent foam channel and is detected by an X-ray image intensifier. The X-ray transmission images show the two-dimensional projections of the radiopaque tracers. Utilizing particle tracking velocimetry algorithms, the tracer trajectories are measured with both high spatial (0.2 mm) and temporal (25 fps) resolution. Fine and coarse liquid foam flow of different velocities are studied in a partly curved channel with rectangular cross section. The simultaneous time-resolved measurements of the tracers' translational motion and their intrinsic rotation reveal both the local velocity and vorticity of the foam flow. In the semi-circular curved channel section, the rigid-body-like flow pattern is investigated. Moreover, a relaxation of the foam structure in the transition zone between straight and curved section is observed.

Experimental Validation of an Inductive System for Magnesium Level Detection in a Titanium Reduction Reactor.

In order to precisely determine the magnesium level in a titanium reduction retort by inductive methods, many interfering influences have to be considered. By using a look-up-table method, the magnesium level can be reliably identified by taking into account the interfering effects of the titanium sponge rings forming at the walls with their unknown geometrical and electrical parameters. This new method uses a combination of numerical simulations and measurements, whereby the simulation model is calibrated so that it represents the experimental setup as closely as possible. Previously, purely theoretical studies on this method were presented. Here, the practical feasibility of that method is demonstrated by performing measurements on a model experiment. The method is not limited to the production of titanium but can also be applied to other applications in metal production and processing.

A Parallel Cellular Automata Lattice Boltzmann Method for Convection-Driven Solidification.

This article presents a novel coupling of numerical techniques that enable three-dimensional convection-driven microstructure simulations to be conducted on practical time scales appropriate for small-size components or experiments. On the microstructure side, the cellular automata method is efficient for relatively large-scale simulations, while the lattice Boltzmann method provides one of the fastest transient computational fluid dynamics solvers. Both of these methods have been parallelized and coupled in a single code, allowing resolution of large-scale convection-driven solidification problems. The numerical model is validated against benchmark cases, extended to capture solute plumes in directional solidification and finally used to model alloy solidification of an entire differentially heated cavity capturing both microstructural and meso-/macroscale phenomena.

Contactless Inductive Bubble Detection in a Liquid Metal Flow.

The detection of bubbles in liquid metals is important for many technical applications. The opaqueness and the high temperature of liquid metals set high demands on the measurement system. The high electrical conductivity of the liquid metal can be exploited for contactless methods based on electromagnetic induction. We will present a measurement system which consists of one excitation coil and a pickup coil system on the opposite sides of the pipe. With this sensor we were able to detect bubbles in a sodium flow inside a stainless steel pipe and bubbles in a column filled with a liquid Gallium alloy.

Prediction of postnatal outcomes in fetuses with isolated congenital diaphragmatic hernias using different lung-to-head ratio measurements.

OBJECTIVES: The purpose of this study was to compare different methods for measuring the fetal lung area-to-head circumference ratio and to investigate their prediction of postpartum survival and the need for neonatal extracorporeal membrane oxygenation (ECMO) therapy in fetuses with isolated congenital diaphragmatic hernias. METHODS: This prospective study included 118 fetuses of at least 20 weeks' gestation with isolated left-sided congenital diaphragmatic hernias. The lung-to-head ratio was measured with 3 different methods (longest diameter, anteroposterior diameter, and tracing). To eliminate the influence of gestational age, the observed-to-expected lung-to-head ratio was calculated. Receiver operating characteristic (ROC) curves were calculated for the statistical prediction of survival and need for ECMO therapy by the observed-to-expected lung-to-head ratio measured with the different methods. RESULTS: For survival and ECMO necessity 118 and 102 cases (16 neonates were not eligible for ECMO) were assessed, respectively. For prediction of postpartum survival and ECMO necessity, the areas under the ROC curves and 95% confidence intervals showed very similar results for the 3 methods for prediction of survival (tracing, 0.8445 [0.7553-0.9336]; longest diameter, 0.8248 [0.7360-0.9136]; and anteroposterior diameter, 0.8002 [0.7075-0.8928]) and for ECMO necessity (tracing, 0.7344 [0.6297-0.8391]; longest diameter, 0.7128 [0.6027-0.8228]; and anteroposterior diameter, 0.7212 [0.6142-0.8281]). Comparisons between the areas under the ROC curves showed that the tracing method was superior to the anteroposterior diameter method in predicting postpartum survival (P = .0300). CONCLUSIONS: Lung-to-head ratio and observed-to-expected lung-to-head ratio measurements were shown to accurately predict postnatal survival and the need for ECMO therapy in fetuses with left-sided congenital diaphragmatic hernias. Tracing the limits of the lungs seems to be the favorable method for calculating the fetal lung area.

New formulas for calculating the lung-to-head ratio in healthy fetuses between 20 and 40 weeks' gestation.

OBJECTIVES: The purpose of this study was to develop new formulas for the expected fetal lung area-to-head circumference ratio in normal singleton pregnancies between 20 and 40 weeks' gestation. METHODS: The lung-to-head ratio and complete fetal biometric parameters of 126 fetuses between 20 and 40 weeks' gestation were prospectively measured. The lung-to-head ratio was measured by 3 different methods (longest diameter, anteroposterior diameter, and tracing). Formulas for predicting right and left lung-to-head ratios with regard to gestational age and biometric parameters were derived by stepwise regression analysis. RESULTS: New formulas for calculating right and left lung-to-head ratios by each measurement method were derived. The formulas included gestational age only and no biometric parameters. CONCLUSIONS: The new formulas for estimating the expected lung-to-head ratio by the 3 different methods in normal singleton pregnancies up to 40 weeks' gestation may help improve the prognostic power of observed-to-expected lung-to-head ratio assessment in fetuses with congenital diaphragmatic hernias.

Prediction of mortality and the need for neonatal extracorporeal membrane oxygenation therapy by 3-dimensional sonography and magnetic resonance imaging in fetuses with congenital diaphragmatic hernias.

OBJECTIVES: To compare different rotation angles for assessment of fetal lung volume by 3-dimensional (3D) sonography with magnetic resonance imaging (MRI) regarding prediction of mortality and the need for neonatal extracorporeal membrane oxygenation (ECMO) therapy in fetuses with congenital diaphragmatic hernias. METHODS: One hundred patients with fetal congenital diaphragmatic hernias between 22 and 39 weeks' gestation were examined by 3D sonography and MRI. Sonographic contralateral fetal lung volumes were assessed by the rotational technique (virtual organ computer-aided analysis) at 3 different rotation angles: 6°, 15°, and 30°. The MRI fetal lung volumes were calculated based on multiplanar T2-weighted MRI. To eliminate the influence of gestational age, the observed to expected contralateral fetal lung volume on sonography and the observed to expected fetal lung volume on MRI were calculated. Receiver operating characteristic (ROC) curves were calculated for the statistical prediction of survival and need for ECMO therapy by the observed to expected contralateral fetal lung volume (sonography) and observed to expected fetal lung volume (MRI). RESULTS: One hundred cases were assessed for survival and 89 for ECMO necessity (11 neonates were not eligible for ECMO). For prediction of postpartum survival and ECMO necessity, the areas under the ROC curves (AUCs) showed very similar results for MRI and 3D sonography: observed to expected fetal lung volume by MRI, 0.819 (95% confidence interval, 0.730-0.909) and 0.835 (0.748-0.922), respectively; 6° sonography, 0.765 (0.647-0.883) and 0.820 (0.734-0.905); 15° sonography, 0.784 (0.672-0.896) and 0.811 (0.719-0.903); and 30° sonography, 0.732 (0.609-0.855) and 0.772 (0.671-0.872). Comparisons between the AUCs revealed no statistical differences. CONCLUSIONS: We have shown the good prognostic value of 3D sonography in fetuses with congenital diaphragmatic hernias compared with MRI, particularly when using small rotation angles. Therefore, it can be an appropriate diagnostic tool when counseling patients for congenital diaphragmatic hernias.

Influence of different rotation angles in assessment of lung volumes by 3-dimensional sonography in comparison to magnetic resonance imaging in healthy fetuses.

OBJECTIVES: Three-dimensional (3D) sonographic volumetry is established in gynecology and obstetrics. Assessment of the fetal lung volume by magnetic resonance imaging (MRI) in congenital diaphragmatic hernias has become a routine examination. In vitro studies have shown a good correlation between 3D sonographic measurements and MRI. The aim of this study was to compare the lung volumes of healthy fetuses assessed by 3D sonography to MRI measurements and to investigate the impact of different rotation angles. METHODS: A total of 126 fetuses between 20 and 40 weeks' gestation were measured by 3D sonography, and 27 of them were also assessed by MRI. The sonographic volumes were calculated by the rotational technique (virtual organ computer-aided analysis) with rotation angles of 6° and 30°. To evaluate the accuracy of 3D sonographic volumetry, percentage error and absolute percentage error values were calculated using MRI volumes as reference points. Formulas to calculate total, right, and left fetal lung volumes according to gestational age and biometric parameters were derived by stepwise regression analysis. RESULTS: Three-dimensional sonographic volumetry showed a high correlation compared to MRI (6° angle, R(2) = 0.971; 30° angle, R(2) = 0.917) with no systematic error for the 6° angle. Moreover, using the 6° rotation angle, the median absolute percentage error was significantly lower compared to the 30° angle (P < .001). The new formulas to calculate total lung volume in healthy fetuses only included gestational age and no biometric parameters (R(2) = 0.853). CONCLUSIONS: Three-dimensional sonographic volumetry of lung volumes in healthy fetuses showed a good correlation with MRI. We recommend using an angle of 6° because it assessed the lung volume more accurately. The specifically designed equations help estimate lung volumes in healthy fetuses.

Assessment of lung volume by 3-dimensional sonography and magnetic resonance imaging in fetuses with congenital diaphragmatic hernias.

OBJECTIVES: The purpose of this study was to evaluate the influence of different rotation angles in assessment of the contralateral lung volume by 3-dimensional (3D) sonography in comparison to magnetic resonance imaging (MRI) in fetuses with congenital diaphragmatic hernias. METHODS: A total of 126 measurements by 3D sonography and MRI were conducted in 81 patients between 18 and 39 weeks' gestation. The 3D sonographic volumes of the contralateral fetal lung were calculated by the rotational technique (virtual organ computer-aided analysis) with rotation angles of 6°, 15°, and 30°. Transverse multiplanar T2-weighted MRI was performed for the MRI measurements. To compare the accuracy of 3D sonographic volumetry using different rotation angles, MRI assessment was taken as the reference method, and percentage errors and limits of agreement were calculated for each angle. RESULTS: Three-dimensional sonographic volume measurements showed a high correlation with MRI (6° angle, R(2) = 0.86; 15° angle, R(2) = 0.78; 30° angle, R(2) = 0.68). The mean percentage error showed no systematic error. With regard to random error, the 6° step had significantly lower values than the larger angles 30° step (R = 0.472) and the narrowest limits of agreement. CONCLUSIONS: Especially when using a small rotation angle, assessment of the contralateral fetal lung volume by 3D sonography in congenital diaphragmatic hernias is a reliable alternative to MRI.

Phased Array Ultrasound System for Planar Flow Mapping in Liquid Metals.

Controllable magnetic fields can be used to optimize flows in technical and industrial processes involving liquid metals in order to improve quality and yield. However, experimental studies in magnetohydrodynamics often involve complex, turbulent flows and require planar, two-component (2c) velocity measurements through only one acoustical access. We present the phased array ultrasound Doppler velocimeter as a modular research platform for flow mapping in liquid metals. It combines the pulse wave Doppler method with the phased array technique to adaptively focus the ultrasound beam. This makes it possible to resolve smaller flow structures in planar measurements compared with fixed-beam sensors and enables 2c flow mapping with only one acoustical access via the cross beam technique. From simultaneously measured 2-D velocity fields, quantities for turbulence characterization can be derived. The capabilities of this measurement system are demonstrated through measurements in the alloy gallium-indium-tin at room temperature. The 2-D, 2c velocity measurements of a flow in a cubic vessel driven by a rotating magnetic field (RMF) with a spatial resolution of up to 2.2 mm are presented. The measurement results are in good agreement with a semianalytical simulation. As a highlight, two-point correlation functions of the velocity field for different magnitudes of the RMF are presented.

Regular flow reversals in Rayleigh-Bénard convection in a horizontal magnetic field.

Magnetohydrodynamic Rayleigh-Bénard convection was studied experimentally using a liquid metal inside a box with a square horizontal cross section and aspect ratio of five. Systematic flow measurements were performed by means of ultrasonic velocity profiling that can capture time variations of instantaneous velocity profiles. Applying a horizontal magnetic field organizes the convective motion into a flow pattern of quasi-two-dimensional rolls arranged parallel to the magnetic field. The number of rolls has the tendency to decrease with increasing Rayleigh number Ra and to increase with increasing Chandrasekhar number Q. We explored convection regimes in a parameter range, at 2×10^{3}