We investigate turbulent Rayleigh-B & eacute;nard convection (RBC) in a convection cell with square cross section and aspect ratio Gamma = width/height = 25 filled with the liquid metal alloy GaInSn at Prandtl number Pr approximate to 0.03. A dense array of thermocouples and ultrasonic Doppler velocimetry is employed to measure the temperature distributions at the top of the convection cell and horizontal velocity profiles, respectively, in the Rayleigh number range 3.27 & times; 10(4) less than or similar to Ra less than or similar to 2.17 & times; 10(5). Conspicuous thermal structures manifest themselves in the two-dimensional temperature fields and closely resemble the turbulent superstructures predicted in numerical simulations. The velocity data reveal flow features that indicate the presence of "jump rope vortices" (JRV). This can be seen in characteristic oscillations that permeate the entire 3D flow structure. The measured frequencies, f0 correspond very well with the empirical scaling f(0) proportional to Ra-0.419.The results thus provide experimental evidence that the jump-rope vortex, which has previously been identified as the striking dynamical feature of large-scale convection (LSC) in geometries with moderate aspect ratios (1.4 <= Gamma <= 5), also persists as a robust, three-dimensional mode embedded within turbulent convective superstructures at very large aspect ratios.

A clear understanding of the dynamics of rising bubbles in liquid metals under a horizontal magnetic field (MF) is essential for improving the steelmaking processes. In this study, the motion of bubble chains rising in a gallium alloy was experimentally investigated using ultrasonic tomography. By systematically varying the inter-bubble distances, bubble diameters, and horizontal MF strengths, the combined effects of the wake caused by the leading bubbles and electromagnetic forces on the bubble motion are evaluated. The bubble oscillating motions in the chain bubbles are classified into five modes based on their magnitude and direction. Without the MF and at large inter-bubble distances, the bubbles exhibit random oscillations, whereas the application of a horizontal MF constrains their motion to two-dimensional planes depending on the MF strength. When the electromagnetic force becomes dominant, the bubbles rise nearly linearly. However, at small inter-bubble distances, anisotropic oscillations perpendicular to the MF direction appear, which are not observed in the case of single bubbles. Moreover, the anisotropy of bubble oscillation under a strong MF is more pronounced for larger bubble diameters than for small bubbles. Under these conditions, the motion directions of the bubbles become consistent, and successive bubbles rise along similar trajectories. These findings suggest that the motion of the trailing bubbles is influenced by the asymmetric wake vortices shed by the leading bubbles under horizontal MFs, resulting in differences in their rising trajectories. Our results provide valuable insights into the dynamics of bubbly flows in liquid metals under the influence of horizontal MFs.

Computational ultrasound imaging has become a powerful tool in technical and medical applications. It enables visualization through complex scattering media such as skull bone or engineered waveguides. In this context, waveguides for ultrasound imaging in hot melts are necessary to shield the transducers from the hot environment. Published works on the topic of ultrasonic testing usually deal with single-mode waveguides. These waveguides support only a single mode within the submerged environment; therefore, imaging can be performed only by time-consuming point-by-point mechanical scanning. Instead of a single-mode waveguide, a multimode waveguide supports several modes and was proposed for real-time ultrasound imaging without the need for 2-D or 3-D scanning. Meanwhile, the use of multimode waveguides presents several challenges, such as modal dispersion that distorts wavefronts and scrambles spatial information, for which additional signal processing schemes are necessary to compensate for them. The goal of the present work is to create an optimization model for multimodal waveguide-based ultrasound imaging in hot melts. This model allows for a tradeoff between the number of reflected signals returned from the scatterer, attenuation of waves, and the desired bulk wave types, which is governed by the selected depth between the bottom surface of the waveguide and the scatterer position. Therefore, the optimal depth will always depend on the respective fluid-waveguide combination. First, we compute and visualize the paths that return from different positions of the scatterer immersed in the hot melts using a numerical method. Second, the optimal angles of the guided modes in the waveguide are calculated based on the ordinary differential equation (ODE) method and Snell-Descartes law. Accordingly, the guided and bulk waves propagating within the waveguide can be distinguished, where a classification into six types of signals is introduced. Experimental results carried out confirm the feasibility of the proposed optimization model, which achieves a tradeoff between the number of reflected signals returned from the scatterer, attenuation of waves, and the desired bulk wave types to maintain a reasonable signal-to-noise ratio (SNR) value. The present measurement system achieves 0.27 mm axial resolution and 25 ms temporal resolution. The unique advantage of the present physics model of multimode waveguide-based ultrasound imaging is its ability to improve SNR, as well as it can be transferred to several applications such as skull bone imaging in the medical field, where ultrasound imaging of the brain is obstructed by the aberrating skull bone, as well as in energy applications.

Systematic flow measurements are conducted in a 1:6 fluid-dynamic model of the continuous steel slab casting process. The focus is on the impact of various traveling magnetic fields on the flow in the mold. The HZDR mini-LIMMCAST facility provides a controlled and reproducible environment, ensuring accurate and reproducible experiments. The GaInSn alloy is chosen as the modeling fluid, because it remains liquid at room temperature due to its low melting point. Our study focuses on three different configurations of traveling fields: inward, outward, and rotational stirring. In each configuration, magnetic flux density and frequency were varied to understand their respective impact on the flow behavior. The horizontal velocity at the mold’s middle plane and two parallel side planes were measured using Ultrasound Doppler Velocimetry (UDV). Additionally, the vertical velocities at the mold’s middle plane were measured by the same method. The results demonstrated a significant influence on the velocities in the upper mold region under the impact of each traveling field configuration. This study significantly contributes to the existing knowledge about the impact of the traveling magnetic field on the liquid steel flow in the continuous casting of steel.

We present measurements of temperature fields and flow structures in a liquid metal Rayleigh–Bénard convection at a low Prandtl number, which were carried out for the first time using embedded fiber Bragg grating sensors (FBG) in combination with ultrasonic Doppler velocimetry (UDV). The FBG sensors enable minimally invasive, spatially resolved temperature measurements in optically opaque and electrically conductive liquids, thereby overcoming significant limitations of conventional thermocouples and optical techniques. This approach was applied in a cuboid Rayleigh–Bénard cell with an aspect ratio $$\Gamma = 5$$ Γ = 5 filled with GaInSn. In this paper, we present measurements at two Rayleigh numbers, $$\textrm{Ra} = 6.8 \times 10^4$$ Ra = 6.8 × 10 4 and $$2.1 \times 10^5$$ 2.1 × 10 5 . At the lower Rayleigh number, a coherent three-roll structure is observed with low-frequency modulation of thermal fluctuations. At the higher Rayleigh number, a cellular convection regime emerges, featuring checkerboard-like temperature patterns in the mid-plane and periodic plume emissions. Spectral analysis reveals a dominant oscillation frequency near $$f = 0.029$$ f = 0.029 Hz, while autocorrelation and extremum tracking highlight strong temporal coherence near the center and more volatile plume behavior near the sidewalls. The results of the temperature measurements and the UDV velocity measurements are consistent, thus confirming the capability of FBG sensors as a robust tool for investigating the spatio-temporal dynamics in convective systems.

The effect of a horizontal magnetic field on heat transport and flow structures in vertical liquid metal convection (Prandtl number $Pr \approx 0.03$ ) is investigated experimentally. The experiments are carried out for Rayleigh numbers in the range of $1.48 \times 10<^>6 \leqslant Ra \leqslant 3.54 \times 10<^>{7}$ and Chandrasekhar numbers in the range of $2 \times 10<^>2 \leqslant Q \leqslant 1.86 \times 10<^>6$ , as well as for the non-magnetic case ( $Q=0$ ). Measurements of the heat transport show a rise in the Nusselt number at low and moderate magnetic field strengths up to an optimum value of $Q$ , before a further increase in the magnetic field leads to a decrease in the transport properties. By applying simultaneous velocity and temperature measurements, we are able to identify three different oscillatory flow regimes for $10<^>{-5}\lt Q/Ra \lt 0.5$ and assign them to the respective heat transfer characteristics. In the range $10<^>{-5}\gt Q/Ra\gt 10<^>{-3}$ , first evidence of a transition to anisotropic flow structures caused by the magnetic field is visible. Two strongly oscillatory regimes are identified, where the energy is either distributed around a dominant frequency ( $10<^>{-3}\gt Q/Ra\gt 10<^>{-2}$ ), or strongly concentrated on a single frequency ( $10<^>{-2}\gt Q/Ra\gt 0.5$ ). The dominating frequency increases with the Rayleigh number according to $Ra<^>{0.71\pm 0.02}$ . This flow structure based regime separation correspond to changes of both the heat transfer through the Nusselt number and mass transfer through the Reynolds number.

The dynamics of the thermal boundary layer are studied experimentally in turbulent Rayleigh-B & eacute;nard convection at 3 x 107 <= Ra <= 3 x 109. The local boundary layer (BL) height and the flow structures are measured in the ternary alloy GaInSn (Prandtl number Pr = 0.03) contained in a cylindrical sample with an aspect ratio of Gamma = 0.5. The data, which are recorded at two measurement positions in the center of the plate and near the side wall, reveal disruptive disturbances of the thermal BL at the top plate, the intensity and frequency of which vary with the Rayleigh number Ra. We observe the occurrence of pronounced peaks in the BL thickness, whereby the number of these events relative to the free-fall time tff decreases with increasing Ra while their mean duration increases. The events of this intermittent significant broadening of the thermal boundary layer are detectable in the temporal behavior of the Nusselt number and correlate strongly with the occurrence of a vertical flow moving away from the plate surface. This suggests that the peaks in the thermal BL height coincide with the formation and detachment of thermal plumes on the copper plate. An interesting aspect of our measurements is the observation of BL disturbances at the measurement position in the center of the plate, which is dominated by a wall-parallel shear flow of large-scale circulation (LSC), just as frequently as in the region near the side wall, where impingement or detachment of thermal plumes should occur.

A weakly turbulent buoyancy-driven flow is studied experimentally and numerically in a liquid metal cylinder with small height-to-diameter ratio. The cell represents a model of the Czochralski crystal growth process and includes heating at the bottom and non-uniform cooling at the top. Transition to a non-axisymmetric roll-like flow structure (wind) is observed experimentally under conditions, which still produce a nearly axisymmetric flow in the computations. It is shown that the contradiction can be explained by the flow sensitivity to temperature boundary conditions at the cell bottom. It is made of a massive copper disk to approximate isothermal temperature conditions. Due to a finite heat conductivity, the bottom is unable to sufficiently equalize the temperature over large distances. This deviation from isothermal conditions is amplified in a separate experiment by a thin heat barrier at the cell's bottom. In this case, the transition to wind is observed at a nearly ten times lower heat flux both in numerics and experiment. The transition then produces a very long-period flow oscillation as the wind erratically changes flow direction.

Solidification of a ternary Ga-In-Bi alloy under a thermal gradient approximate to 1.8 K/mm with a moderate cooling rate 0.01 K/s was performed with in-situ observation using X-ray radiography. Similar to the solidification of a binary GaIn alloy, buoyancy convection developed in the system due to a large density difference between the alloy components. Yet, it was found that contrary to the binary system, the primary arms of the ternary solid structure not only adapt their velocity to the variation of the local concentration ahead of their tips but may also change continuously or abruptly their growth direction. A closer look on the system revealed that the deviation of the growth direction happened via branching. Alternatively, some of primary arms demonstrated multiple splitting and intense yet retarded growth of the secondary arms.

Understanding the crystallization of metallic cores is necessary to constrain the structure and thermal evolution of terrestrial bodies in our solar system and beyond. Core cooling is also closely related to the generation and sustainability of a magnetic field. The core crystallization regime depends primarily on the depth of intersection of the core temperature with the liquidus ([1], and refs therein). Core composition, pressure, and thermal profile are the major parameters controlling the depth of intersection. If the temperature gradient across the core is steeper than that of the liquidus, solidification starts at the top, the “top-down” crystallization regime. At low pressure (≤10 GPa) relevant to small terrestrial planets, moons, and possibly some asteroids, the eutectic temperature decreases with increasing pressure (e.g., [2] for the Fe-S system), favoring an onset of crystallization at the top of the core. Top-down crystallization has been proposed to exist in several planets and moons in the Solar System, such as Mercury [2], [3], Mars ([4], [5]), and Ganymede [6], [7], [8], [9].In this study, which was performed by the International Space Science Institute (ISSI) Team “A new non-equilibrium model of iron snow in planetary cores”, we investigate the effect of non-equilibrium as well as the effect of the core composition on top-down crystallization. We find that the time scale of phase relaxation is significantly shorter than the time scales usually employed in one-dimensional evolution models. Consequently, the assumption of equilibrium in these models remains valid. Nevertheless, the time scales associated with crystallization, melting, and crystal settling may be similar to the phase relaxation time scale, which warrants a closer investigation. Additionally, if the amount of supercooling required to initiate nucleation is large [11], non equilibrium could play a much larger role. In terms of core chemistry we studied two different core alloys (Fe-S and Fe-C) motivated by silicate-metal partitioning experiments (reviewed by [12]) at various concentrations in the framework of the equilibrium top-down crystallization model. We find that the time scales of growing either the snow zone (iron-rich compositions) or the flotation crust (iron-poor compositions) can vary significantly between the Fe-S and Fe-C system. Furthermore, the exact concentration of sulfur or carbon has an impact on the thermodynamic parameters, subsequently affecting the entropy available to the dynamo.References:[1] Breuer et al., 2015. [2] Chen et al., 2008. [3] Dumberry & Rivoldini, 2015. [4] Stewart et al., 2007. [5] Davies & Pommier, 2018. [6] Hauck et al., 2006. [7] Christensen, 2015. [8] Rückriemen et al., 2015. [9] Rückriemen et al., 2018. [10] Loper, 1992. [11] Huguet et al., 2018. [12] Pommier et al., 2022.

Contactless Inductive Flow Tomography (CIFT) is a flow measurement technique that is able to reconstruct the time-dependent three-dimensional velocity field in electrically conducting fluids, e.g., liquid metals, from magnetic field measurements. The paper describes the design of a specific CIFT measurement set-up for flow studies in liquid metal Rayleigh-Benard convection (RBC) in a large cylinder of aspect ratio (diameter/height) of Gamma = 0.5 filled with the ternary alloy GaInSn as model fluid. An optimized configuration for the CIFT excitation system and magnetic field sensor layout under consideration of the specific requirements for the application in turbulent RBC is determined by numerical simulations. The new experimental CIFT-RBC system resulting from the design process is constructed and a preliminary experiment at a Rayleigh number of Ra = 2.13 x 10(7) and a Prandtl number of Pr = 0.03 is performed and evaluated.

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.

Contactless inductive flow tomography (CIFT) is a flow measurement technique allowing for visualization of the global flow in electrically conducting fluids. The method is based on the principle of induction by motion: very weak induced magnetic fields arise from the fluid motion under the influence of a primary excitation magnetic field and can be measured precisely outside of the fluid volume. The structure of the causative flow field can be reconstructed from the induced magnetic field values by solving the according linear inverse problem using appropriate regularization methods. The concurrent use of more than one excitation magnetic field is necessary to fully reconstruct three-dimensional liquid metal flows. In our laboratory demonstrator experiment, we impose two excitation magnetic fields perpendicular to each other to a mechanically driven flow of the liquid metal alloy GaInSn. In the first approach, the excitation fields are multiplexed. Here, the temporal resolution of the measurement needs to be kept as high as possible. Consecutive application by multiplexing enables determining the flow structure in the liquid with a temporal resolution down to 3 s with the existing equipment. In another approach, we concurrently apply two sinusoidal excitation fields with different frequencies. The signals are disentangled on the basis of the lock-in principle, enabling a successful reconstruction of the liquid metal flow.

In this experimental study, we explore the dynamics of the thermal boundary layer in liquid metal Rayleigh-Benard convection, covering the parameter ranges of 0.026 <= Prandtl numbers (Pr) <= 0.033 and Rayleigh numbers (Ra) up to 2.9 x 10(9). Our research focuses on characterising the thermal boundary layer near the top plate of a cylindrical convection cell with an aspect ratio of 0.5, distinguishing between two distinct regions: the shear-dominated region around the centre of the top plate and a location near the side wall where the boundary layer is expected to be affected by the impact or ejection of thermal plumes. The dependencies of the boundary layer thickness on Ra at these positions reveal deviating scaling exponents with the difference diminishing as Ra increases. We find stronger fluctuations in the boundary layer and increasing deviation from the Prandtl-Blasius-Pohlhausen profile with increasing Ra, as well as in the measurements outside the centre region. Our data illustrate the complex interplay between flow dynamics and thermal transport in low-Pr convection.

Convection of liquid metals drives large natural processes and is important in technical processes. Model experiments are conducted for research purposes where simulations are expensive and the clarification of open questions requires novel flow mapping methods with an increased spatial resolution. In this work, the method of Ultrasound Localization Microscopy (ULM) is investigated for this purpose. Known from microvasculature imaging, this method provides an increased spatial resolution beyond the diffraction limit. Its applicability in liquid metal flows is promising, however the realization and reliability is challenging, as artificial scattering particles or microbubbles cannot be utilized. To solve this issue an approach using nonlinear adaptive beamforming is proposed. This allowed the reliable tracking of particles of which super-resolved flow maps can be deduced. Furthermore, the application in fluid physics requires quantified results. Therefore, an uncertainty quantification model based on the spatial resolution, velocity gradient and measurement parameters is proposed, which allows to estimate the flow maps validity under experimental conditions. The proposed method is demonstrated in magnetohydrodynamic convection experiments. In some occasions, ULM was able to measure velocity vectors within the boundary layer of the flow, which will help for future in-depth flow studies. Furthermore, the proposed uncertainty model of ULM is of generic use in other applications.

The most ambitious project within the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) is the set-up of a precession-driven dynamo experiment. After discussing the scientific background and some results of water pre-experiments and numerical predictions, we focus on the numerous structural and design problems of the machine. We also outline the progress of the construction work and give an outlook for the upcoming experimental campaigns.

In this paper, we present numerical and experimental results on helicity oscillations in a liquid-metal Rayleigh-Bénard (RB) convection cell, with an aspect ratio of 0.5. We find that helicity oscillations occur during transitions of flow states that are characterised by significant changes in the Reynolds number. Moreover, we also observe helicity oscillations at flow conditions where the temporal gradient of the change in the Reynolds number is significantly smaller than that of the helicity. Notably, the helicity oscillations observed during the transient double-roll state exhibit characteristics remarkably similar to those associated with the Tayler Instability.

Understanding the behavior of rising bubbles in a liquid metal under the influence of a magnetic field (MF) is crucial for optimizing continuous casting processes. The study experimentally investigated the effects of a horizontal MF on the behavior of bubble chains in a gallium alloy. High-speed ultrasonic computed tomography was used to measure the instantaneous bubble crossing positions in a cylindrical column with an inner diameter of 50 mm. With an increase in the MF strength, the oscillations of the bubbles were suppressed, resulting in the crossing position being concentrated in a certain area of the cross-section. The fluctuations in the time intervals of the chain bubbles decreased. These effects were more pronounced when the magnetic interaction parameter (or Stuart number) was greater than 1. The distribution of bubbles in the direction perpendicular to the MF was widespread slightly compared to that in the direction parallel to the MF; this was noticeable at higher flow rates. The suppression of the wake turbulence induced by the Lorentz force was larger in the direction parallel to the MF than that in the direction perpendicular to the MF. Our results have the potential to be used for the direct verification of numerical models.

This paper presents the analysis of particle-laden liquid metal flow around a cylindrical obstacle at different obstacle Reynolds numbers. Particles in liquid metal are imaged using dynamic neutron radiography. We present the results of particle tracking velocimetry of the obstacle wake flow and demonstrate the capabilities to assess both temporal and spatial characteristics of turbulent liquid metal flow, validating our methods against theoretical expectations, numerical simulations and experiments reported in the literature. We obtain the expected linear vortex shedding frequency scaling with the obstacle Reynolds number and correctly identify the universal algebraic growth laws predicted and observed for trajectory curvature in isotropic homogeneous two-dimensional turbulence. To our knowledge, this is the first such result for liquid metals. Particle residence times within the obstacle wake and velocity statistics are also derived and found to be physically sound. Finally, we outline potential improvements to our methodology and plan for further research using neutron imaging of particle-laden flow.

We present an evaluation study on the characterization of bubbles rising in liquid sodium by applying two-plane ultrafast X-ray computed tomography (UFXCT). It includes a new method for determining the three-dimensional shape and velocity vector of each individual bubble. In the experimental part, argon gas was injected through a single nozzle located slightly above the bottom of a cylindrical vessel filled with liquid sodium. The gas flow rate was varied between 10 and 635 cm3/min to obtain a chain of individual bubbles. In this parameter range, collisions of bubbles, coalescence or breakup are not expected. Measurements were carried out in a wide spatial range starting near the nozzle up to a height of about 200 mm above it. It was convincingly demonstrated that two-plane UFXCT imaging, in combination with the data processing presented here, allows a reliable characterization of the size, shape and velocity of bubbles with a size of a few millimeters in a sodium column of 54 mm diameter. Moreover, a reproducible fluctuation of shape, position and velocity has been observed in the experiments in the lower part of the column.