arXiv subjects

Sven Eckert

Publications and source records attributed to Sven Eckert.

16 recordsLinked to original sources

arXiv2024

Uncertainty Quantification of Super-Resolution Flow Mapping in Liquid Metals using Ultrasound Localization Microscopy

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.

physics.flu-dyn↗

arXiv2024

Learning to reconstruct the bubble distribution with conductivity maps using Invertible Neural Networks and Error Diffusion

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 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.

eess.IV↗

arXiv2023

Oscillatory large-scale circulation in liquid-metal thermal convection and its structural unit

In Rayleigh-Bénard convection (RBC), the size of a flow domain and its aspect ratio $\varGamma$ (a ratio between the spatial length and height of the domain) affect the shape of the large-scale circulation (LSC). For some aspect ratios, the flow dynamics include a three-dimensional oscillatory mode known as a jump-rope vortex (JRV), however, the effects of varying aspect ratios on this mode are not well investigated. In this paper, we study these aspect-ratio effects in liquid metals, for a low Prandtl number $Pr=0.03$. Direct numerical simulations and experiments are carried out for a Rayleigh number range $2.9 \times 10^4 \leq Ra \leq 1.6 \times 10^6$ and square cuboid domains with $\varGamma=2$, $2.5$, $3$ and $5$. Our study demonstrates that a repeating pattern of a JRV encountered at an aspect ratio $\varGamma \approx 2.5$ is the basic structural unit that builds up to a lattice of interlaced JRVs at the largest aspect ratio. The size of the domain determines how many structural units are self-organized within the domain; the number of the realized units is expected to scale as $\varGamma^2$ with sufficiently large and growing $\varGamma$. We find the oscillatory modes for all investigated $\varGamma$, however, they are more pronounced for $\varGamma=2.5$ and $\varGamma=5$. Future studies for large-aspect ratio domains of different shapes would enhance our understanding of how the JRVs adjust and reorganize at such scaled-up geometries, and answer the question of whether they are indeed the smallest superstructure units.

physics.flu-dyn↗

arXiv2022

An image processing pipeline for in-situ dynamic X-ray imaging of directional solidification of metal alloys in thin cells

We present an image processing algorithm developed for quantitative analysis of directional solidification of metal alloys in thin cells using X-ray imaging. Our methodology allows to identify the fluid volume, fluid channels and cavities, and to separate them from the solidified structures. It also allows morphological analysis within the solid fraction, including automatic decomposition into dominant grains by orientation and connectivity. In addition, the interplay between solidification and convection can be studied by characterizing convection plumes in the fluid, and solute concentrations above the developing solidification front. The image filters used enable the developed code (open-source) to work reliably even for single images with low signal-to-noise ratio, low contrast-to-noise ratio, and low image resolution. This is demonstrated by applying the code to several dynamic in situ X-ray imaging experiments with a solidifying gallium-indium alloy in a thin cell. Grain (and global) dendrite orientation statistics, convective plume parameterization, etc. can be obtained from the code output. The limitations of the presented approach are also explained.

cond-mat.mtrl-sci↗

arXiv2022

Synchronizing the helicity of Rayleigh-Bénard convection by a tide-like electromagnetic forcing

We present results on the synchronization of the helicity in a liquid-metal Rayleigh-Bénard (RB) experiment under the influence of a tide-like electromagnetic forcing with azimuthal wavenumber m=2. We show that for a critical forcing strength the typical Large Scale Circulation (LSC) in the cylindrical vessel of aspect ratio unity is entrained by the period of the tide-like forcing, leading to synchronized helicity oscillations with opposite signs in two half-spaces. The obtained experimental results are consistent with and supported by numerical simulations. A similar entrainment mechanism for the helicity in the solar tachocline may be responsible for the astonishing synchronization of the solar dynamo by the 11.07-year triple synodic alignment cycle of the tidally dominant planets Venus, Earth and Jupiter.

physics.flu-dyn↗

arXiv2022

Particle tracking velocimetry and trajectory curvature statistics for particle-laden liquid metal flow in the wake of a cylindrical obstacle

This paper presents the analysis of the particle-laden liquid metal wake flow around a cylindrical obstacle at different obstacle Reynolds numbers. Particles in liquid metal are visualized using dynamic neutron radiography. We present the results of particle tracking velocimetry of the obstacle wake flow using an improved version of our image processing and particle tracking code MHT-X. The latter now utilizes divergence-free interpolation of the particle image velocimetry field used for motion prediction and particle trajectory reconstruction. We demonstrate significant improvement over the previously obtained results by showing the capabilities to assess both temporal and spatial characteristics of turbulent liquid metal flow, and validating the precision and accuracy of our methods against theoretical expectations, numerical simulations and experiments reported in literature. We obtain the expected 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. 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 plans for further research using neutron imaging of particle-laden flow.

physics.flu-dyn↗

arXiv2022

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 $4 \times 10^5$ and $\leq 5 \times 10^9$ and Prandtl numbers of $0.025~\leq~Pr~\leq ~0.033$. 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 beamlines 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 $β$ of the power law $Nu\propto Ra^β$ crosses \FIN{eventually} over from $β=0.221$ to 0.124 when the liquid metal flow at $Γ=0.5$ reaches $Ra\gtrsim 2\times 10^8$ and the coherent large-scale flow is completely collapsed.

physics.flu-dyn↗

arXiv2021

Jump rope vortex flow in liquid metal Rayleigh-Bénard convection in a cuboid container of aspect ratio five

We study the topology and the temporal dynamics of turbulent Rayleigh-Benard convection in a liquid metal with a Prandtl number of 0.03 located inside a box with a square base area and an aspect ratio of five. Experiments and numerical simulations are focused on the moderate Rayleigh number range, where a new cellular flow regime has been reported by a previous study (Akashi et al., Phys. Rev. Fluids, vol.4, 2019, 033501). This flow structure shows symmetries with respect to the vertical planes crossing at the center of the container. The dynamic behaviour is dominated by strong three-dimensional oscillations with a period length that corresponds to the turnover time. Our analysis reveals that the flow structure in the aspect ratio five box corresponds in key features to the jump rope vortex structure, which has recently been discovered in an aspect ratio two cylinder (Vogt et al., Proc. Natl Acad. Sci. USA, vol.115, 2018, 12674-12679). While in the cylinder a single jump rope vortex occurs, the coexistence of four recirculating swirls is detected in this study. %Their cycling movement is restrained by the limited height of the fluid layer in the aspect ratio five box. Their approach to the lid or the bottom of the convection box causes a temporal deceleration of both the horizontal velocity at the respective boundary and the vertical velocity in the bulk, which in turn is reflected in Nusselt number oscillations. The cellular flow regime shows remarkable similarities to properties commonly attributed to turbulent superstructures

physics.flu-dyn↗

arXiv2021

Particle tracking velocimetry in liquid gallium flow about a cylindrical obstacle

This paper demonstrates particle tracking velocimetry performed for a model system wherein particle-laden liquid metal flow about a cylindrical obstacle was studied. We present the image processing methodology developed for particle detection in images with disparate and often low signal- and contrast-to-noise ratios, and the application of our MHT-X tracing algorithm for particle trajectory reconstruction within and about the wake flow of the obstacle. Preliminary results indicate that the utilized methods enable consistent particle detection and recovery of long, representative particle trajectories with high confidence. However, we also underline the necessity of implementing a more advanced particle position extrapolation approach for increased tracking accuracy. We also show that the utilized particles exhibit the Stokes number range that suggests good flow tracking accuracy, and that the particle time scales extracted from reconstructed trajectories are consistent with expectations based a priori estimates.

physics.flu-dyn↗

arXiv2021

MHT-X: Offline Multiple Hypothesis Tracking with Algorithm X

An efficient and versatile implementation of offline multiple hypothesis tracking with Algorithm X for optimal association search was developed using Python. The code is intended for scientific applications that do not require online processing. Directed graph framework is used and multiple scans with progressively increasing time window width are used for edge construction for maximum likelihood trajectories. The current version of the code was developed for applications in multiphase hydrodynamics, e.g. bubble and particle tracking, and is capable of resolving object motion, merges and splits. Feasible object associations and trajectory graph edge likelihoods are determined using weak mass and momentum conservation laws translated to statistical functions for object properties. The code is compatible with n-dimensional motion with arbitrarily many tracked object properties. This framework is easily extendable beyond the present application by replacing the currently used heuristics with ones more appropriate for the problem at hand. The code is open-source and will be continuously developed further.

cs.CV↗

arXiv2020

Free-fall velocities and heat transport enhancement in liquid metal magneto-convection

In geo- and astrophysics, low Prandtl number convective flows often interact with magnetic fields. Although a static magnetic field acts as a stabilizing force on such flow fields, we find that self-organized convective flow structures reach an optimal state where the heat transport significantly increases and convective velocities reach the theoretical free-fall limit, i.e. the maximum possible velocity a fluid parcel can achieve when its potential buoyant energy is fully converted into kinetic energy. Our measurements show that the application of a static magnetic field leads to an anisotropic, highly ordered flow structure and a decrease of the turbulent fluctuations. When the magnetic field strength is increased beyond the optimum, Hartmann braking becomes dominant and leads to a reduction of the heat and momentum transport. The results are relevant for the understanding of magneto-hydrodynamic convective flows in planetary cores and stellar interiors in regions with strong toroidal magnetic fields oriented perpendicular to temperature gradients.

physics.flu-dyn↗

arXiv2020

Combined measurement of velocity and temperature in liquid metal convection

Combined measurements of velocity components and temperature in a turbulent Rayleigh-Bénard convection flow at a low Prandtl number of $\mathit{Pr}= 0.029$ and Rayleigh numbers between $10^6 \le \mathit{Ra} \le 6 \times 10^7$ are conducted in a series of experiments with durations of more than a thousand free-fall time units. Multiple crossing ultrasound beam lines and an array of thermocouples at mid-height allow for a detailed analysis and characterization of the complex three-dimensional dynamics of the single large-scale circulation (LSC) roll in the cylindrical convection cell of unit aspect ratio which is filled with the liquid metal alloy GaInSn. We measure the internal temporal correlations of the complex large-scale flow and distinguish between short-term oscillations associated with a sloshing motion in the mid-plane as well as varying orientation angles of the velocity close to the top/bottom plates and the slow azimuthal drift of the mean orientation of the roll as a whole that proceeds on an up to a hundred times slower time scale. The coherent LSC drives a vigorous turbulence in the whole cell that is quantified by direct Reynolds number measurements at different locations in the cell. The velocity increment statistics in the bulk of the cell displays characteristic properties of intermittent small-scale fluid turbulence. We also show that the impact of the symmetry-breaking large-scale flow persists to small-scale velocity fluctuations thus preventing the establishment of fully isotropic turbulence in the cell centre. Reynolds number amplitudes depend sensitively on beam line position in the cell such that different definitions have to be compared. The global momentum and heat transfer scalings with Rayleigh number are found to agree with those of direct numerical simulations and other laboratory experiments.

physics.flu-dyn↗

arXiv2020

Flow regimes of Rayleigh-Bénard convection in a vertical magnetic field

The effects of a vertical static magnetic field on the flow structure and global transport properties of momentum and heat in liquid metal Rayleigh-Bénard convection are investigated. Experiments are conducted in a cylindrical convection cell of unity aspect ratio, filled with the alloy GaInSn at a low Prandtl number of $\mathit{Pr}=0.029$. Changes of the large-scale velocity structure with increasing magnetic field strength are probed systematically using multiple ultrasound Doppler velocimetry sensors and thermocouples for a parameter range that is spanned by Rayleigh numbers of $10^6 \le \mathit{Ra} \le 6\times 10^7$ and Hartmann numbers of $\mathit{Ha} \le 1000$. Our simultaneous multi-probe temperature and velocity measurements demonstrate how the large-scale circulation is affected by an increasing magnetic field strength (or Hartmann number). Lorentz forces induced in the liquid metal first suppress the oscillations of the large-scale circulation at low $\mathit{Ha}$, then transform the one-roll structure into a cellular large-scale pattern consisting of multiple up- and downwellings for intermediate $\mathit{Ha}$, before finally expelling any fluid motion out of the bulk at the highest accessible $\mathit{Ha}$ leaving only a near-wall convective flow that persists even below Chandrasekhar's linear instability threshold. Our study thus proves experimentally the existence of wall modes in confined magnetoconvection. The magnitude of the transferred heat remains nearly unaffected by the steady decrease of the fluid momentum over a large range of Hartmann numbers. We extend the experimental global transport analysis to momentum transfer and include the dependence of the Reynolds number on the Hartmann number.

physics.flu-dyn↗

arXiv2017

Local Lorentz force and ultrasound Doppler velocimetry in a vertical convection liquid metal flow

We report velocity measurements in a vertical turbulent convection flow cell that is filled with the eutectic liquid metal alloy gallium-indium-tin by the use of local Lorentz force velocimetry (LLFV) and ultrasound Doppler velocimetry (UDV). We demonstrate the applicability of LLFV for a thermal convection flow and reproduce a linear dependence of the measured force in the range of micronewtons on the local flow velocity magnitude. Furthermore, the presented experiment is used to explore scaling laws of the global turbulent transport of heat and momentum in this low-Prandtl-number convection flow. Our results are found to be consistent with theoretical predictions and recent direct numerical simulations.

physics.flu-dyn↗

arXiv2017

The DRESDYN project: planned experiments and present status

The Dresden sodium facility for dynamo and thermohydraulic studies (DRESDYN) is a platform for large-scale liquid sodium experiments devoted to fundamental geo- and astrophysical questions as well as to various applied problems related to the conversion and storage of energy. Its most ambitious part is a precession driven dynamo experiment comprising 8 tons of liquid sodium supposed to rotate with up to 10 Hz and to precess with up to 1 Hz. Another large-scale set-up is a Tayler-Couette experiment with a gap width of 0.2 m and a height of 2 m, whose inner cylinder rotates with up to 20 Hz. Equipped with a coil system for the generation of an axial field of up to 120 mT and two different axial currents through the center and the liquid sodium, this experiment aims at studying various versions of the magnetorotational instability and their combinations with the Tayler instability. We discuss the physical background of these two experiments and delineate the present status of their technical realization. Other installations, such as a sodium loop and a test stand for In-Service-Inspection experiments will also be sketched.

physics.flu-dyn↗

arXiv2017

Visualization of the global flow structure in a modified Rayleigh-Benard setup using contactless inductive flow tomography

Rayleigh-Benard convection is not only a classical problem in fluid dynamics but plays also an important role in many metallurgical and crystal growth applications. The measurement of the flow field and of the dynamics of the emerging large-scale circulation in liquid metals is a challenging task due to the opaqueness and the high temperature of the melts. Contactless inductive flow tomography is a technique to visualize the mean three-dimensional flow structure in liquid metals by measuring the flow induced magnetic field perturbations under the influence of one or several applied magnetic fields. In this paper, we present first measurements of the flow induced magnetic field in a Rayleigh-Benard setup, which are also used to investigate the dynamics of the large-scale circulation. Additionally, we investigate numerically the quality of the reconstruction of the three-dimensional flow field for different sensor configurations.

physics.flu-dyn↗