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The lowest swirling wave mode arising in upright circular cylinders as a response to circular orbital excitation has been widely studied in the last decade, largely due to its high practical relevance for orbitally shaken bioreactors. Our recent theoretical study (Horstmann et al., J. Fluid Mech., vol. 891, 2020, A22) revealed a damping-induced symmetry breaking mechanism that can cause spiral wave structures manifested in the so far widely disregarded higher rotating wave modes. Building on this work, we develop a linear criterion describing the degree of spiralisation and classify different spiral regimes as a function of the most relevant dimensionless groups. The analysis suggests that high Bond numbers and shallow liquid layers favour the formation of coherent spiral waves. This result paved the way to find the predicted wave structures in our interfacial sloshing experiment. We present two sets of experiments, with different characteristic damping rates, verifying the formation of both coherent and overdamped spiral waves in conformity with the theoretical predictions.

We propose a solution to the longstanding problem of experimentally reproducing the metal pad roll instability at room temperature. Combining theoretical arguments with numerical simulations we show that the instability can occur in a centimeter scale set-up, with reasonable values of the magnetic field and electrical current and using either gallium with mercury (immiscible fluid pair) or gallium with GaInSn eutectic alloy (miscible fluid pair).

Liquid metal electrodes are one of the key components of different electrical energy storage technologies. The understanding of transport phenomena in liquid electrodes is mandatory in order to ensure efficient operation. In the present study we focus our attention on the positive electrode of the Li||Bi liquid metal battery. Starting from a real experimental setup, we numerically investigate the charge transfer in a molten salt electrolyte and the mass transport in the positive electrode. The two phenomena are tightly coupled, because the current distribution influences the concentration field in the positive electrode. The cell is studied during charging when compositional convection becomes apparent. First results of compositional convection from a non-uniform current distribution are presented, highlighting its capability to affect the flow in the positive electrode and the cell performance.

Fluid flows in liquid metal batteries can be generated by a number of effects. We start with a short overview of different driving mechanisms and then address questions specific to the metal pad role instabilities in three-layer systems. We focus on the role of the conductivity distribution in the cell, noting at the same time that interfacial tension should be considered as well for smaller cells. Following this discussion, numerical results on the excitation of interfacial waves in two-layer liquid metal systems with miscibility gaps bearing an interface normal electric current are presented. Confirming recent results from the literature, we find that magnetic damping plays a decisive role for strong vertical magnetic fields. In addition, boundary conditions for the electric field strongly influence critical currents and growth rates.

We study numerically localised short circuits in Li | | Bi liquid metal batteries. In the prototype of a classical, three liquid-layer system, we assume a perceptible local deformation of the Li-salt interface. We find that there always exists a critical current at which a Li-droplet is cut off from this hump, and transferred to the Bi-phase. In a second case, we assume that the molten Li is contained in a metal foam, and that a small Li-droplet emerges below this foam due to insufficient wetting. This droplet is deformed by Lorentz forces, until eventually being pinched off. Here, the critical current is slightly lower than in the three-layer system, and both, a droplet transfer and complete short circuits are observed. Finally, we discuss the relevance of our simulations for experimentally observed short circuits and non-faradaic Li-transfer.

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., Comment: 4 pages, 2 figures

We present a new theoretical model describing gravity-capillary waves in orbitally shaken cylindrical containers. Our model can account for both one-layer free surface and two-layer interfacial wave systems. A set of modal equations for irrotational waves is formulated that we complement with viscous damping rates to incorporate energy dissipation. This approach allows us to calculate explicit formulas for the phase shifts between wave and shaker which are practically important for the mixing efficiency in orbitally shaken bioreactors. Resonance dynamics are described using eight dimensionless numbers revealing a variety of different effects influencing the forced wave amplitudes. As an unexpected result, the model predicts the formation of novel spiral wave patterns resulting from a damping-induced symmetry breaking mechanism. For validation we compare theoretical amplitudes, fluid velocities and phase shifts with three different and independent experiments and - when using the slightly deviating experimental values of the resonance frequencies - find a good agreement within the theoretical limits.

Aiming at a consistent planetary synchronization model of both short-term and long-term solar cycles, we start with an analysis of Schove's historical data of cycle maxima. Their deviations (residuals) from the average cycle duration of 11.07 years show a high degree of regularity, comprising a dominant 200-year period (Suess-de Vries cycle), and a few periods around 100 years (Gleissberg cycle). Encouraged by their robustness, we support previous forecasts of an upcoming grand minimum in the 21st century. To explain the long-term cycles, we enhance our tidally synchronized solar dynamo model by a modulation of the field storage capacity of the tachocline with the orbital angular momentum of the Sun, which is dominated by the 19.86-year periodicity of the Jupiter-Saturn synodes. This modulation of the 22.14 years Hale cycle leads to a 193-year beat period of dynamo activity which is indeed close to the Suess-de Vries cycle. For stronger dynamo modulation, the model produces additional peaks at typical Gleissberg frequencies, which seem to be explainable by the non-linearities of the basic beat process, leading to a bi-modality of the Schwabe cycle. However, a complementary role of beat periods between the Schwabe cycle and the Jupiter-Uranus/Neptune synodic cycles cannot be completely excluded., Comment: 11 pages, 4 figures, final version as published

© 2019 Elsevier Ltd The electrical potential in a battery jumps at each electrode-electrolyte interface. We present a model for computing three-dimensional current and potential distributions, which accounts for such internal voltage jumps. Within the framework of the finite volume method we discretize the Laplace and gradient operators such that they account for internal jump boundary conditions. After implementing a simple battery model in OpenFOAM we validate it using an analytical test case, and show its capabilities by simulating the current distribution and discharge curve of a Li‖Bi liquid metal battery.

Mass and charge transport in liquid metal batteries are closely intertwined because of the fully liquid interior of the cells. We found that charging and discharging cycles may show pronounced asymmetries. They are caused by the presence (charge) or absence (discharge) of solutal convection. While the direction of thermal gradients in the positive electrode of a liquid metal battery depends on boundary conditions and thermodynamics in a non-trivial manner, the solutal gradient predictably changes direction from charge to discharge. The unstable density distribution during charge drives a flow strong enough to prevent any concentration polarization. In contrast, during discharge, the stable density gradient suppresses convection and leads to a substantial mass transport overvoltage. We illustrate this scenario by experimental data, numerical simulations and a physical model. Keywords: Electrorefining, Liquid electrode, Liquid metal batteries, Mass transport, Overvoltage, Solutal convection

We report the design of a low-temperature liquid metal battery (LMB). Li and Ga as the negative and positive electrode, respectively, are used in combination with a room temperature ionic liquid as an electrolyte. 1 mol/L lithium bis(trifluoromethylsulfonyl)imide (Li[TFSI]) in 1-butyl-1-methylpyrrolidinium bis (trifluoromethylsulfonyl)imide ([BMP][TFSI]) is chosen as electrolyte. The battery operates at 220 °C which is a relatively low temperature for a LMB and shows good electrochemical performance at low current density. The cells were cycled for more than 600 h and achieved a round-trip Coulombic efficiency close to 100% and an average voltage efficiency of 66% resulting in an overall energy efficiency of 65%. At higher current densities, however, the system showed up to 75% irreversible capacity loss after three cycles. To understand the origin of this strong deterioration, we characterized the surface and the bulk properties of the Ga cathode using X-ray Photoelectron Spectroscopy. Especially at higher current densities a decomposition of the electrolyte was found. The chemical changes that occurred and the elemental distribution at the Ga cathode are analyzed based on XPS measurements at different stages of the battery charge/discharge cycling.

Liquid metal batteries (LMBs) were recently proposed as cheap large scale energy storage. Such devices are urgently required for balancing highly fluctuating renewable energy sources. During discharge, intermetallic phases tend to form in the cathode of LMBs. These do not only limit the up-scalability, but also the efficiency of the cells. Generating a mild fluid flow in the fully liquid cell will smoothen concentration gradients and minimise the formation of intermetallics. With this application in mind, electro-vortex flow is studied numerically. A recent LMB related experiment is simulated, and it is further discussed how the feeding lines to the cell can be optimised to enhance mass transfer. The Lorentz forces have to overcome the stable thermal stratification in the cathode of the cell; it is shown that thermal effects may reduce electro-vortex flow velocities considerably. Finally, the influence of the Earth magnetic field on the flow is studied.

We present a novel experiment on interfacial wave dynamics in orbitally shaken cylindrical vessels containing two and three fluid layers. The experiment was designed as a hydrodynamical model for liquid metal batteries. It is intended to shed new light into some aspects of the very similar rotational wave motion emerging due to the metal pad roll instability, as the viscous damping behavior or the contact line dynamics. Both issues can be important to better predict instability onsets for upcoming liquid metal batteries and lab-size experiments. Different options are presented to realize stable and measurable multi-layer stratifications. We introduce a new acoustic measurement procedure allowing to reconstruct wave amplitudes also in opaque liquids by tracking ultrasonic pulse echoes reflected at the interfaces. Measurements of resonance curves and phase shifts were conducted for varying interface positions. A strong influence of the top and bottom walls was observed, considerably reducing wave amplitudes and eigenfrequencies, when the interface is getting close. Finally, measured resonance curves were successfully compared with an existing forced wave theory that we extended to two-layer interfacial waves. The comparison stresses the importance to carefully control the boundary condition at the contact line.

We discuss a solar dynamo model of Tayler-Spruit type whose Omega-effect is conventionally produced by a solar-like differential rotation but whose alpha-effect is assumed to be periodically modulated by planetary tidal forcing. This resonance-like effect has its rationale in the tendency of the current-driven Tayler instability to undergo intrinsic helicity oscillations which, in turn, can be synchronized by periodic tidal perturbations. Specifically, we focus on the 11.07 years alignment periodicity of the tidally dominant planets Venus, Earth, and Jupiter, whose persistent synchronization with the solar dynamo is briefly touched upon. The typically emerging dynamo modes are dipolar fields, oscillating with a 22.14 years period or pulsating with a 11.07 years period, but also quadrupolar fields with corresponding periodicities. In the absence of any constant part of alpha, we prove the subcritical nature of this Tayler-Spruit type dynamo. The resulting amplitude of the alpha oscillation that is required for dynamo action turns out to lie in the order of 1 m/s, which seems not implausible for the sun. When starting with a more classical, non-periodic part of alpha, even less of the oscillatory alpha part is needed to synchronize the entire dynamo. Typically, the dipole solutions show butterfly diagrams, although their shapes are not convincing yet. Phase coherent transitions between dipoles and quadrupoles, which are reminiscent of the observed behaviour during the Maunder minimum, can be easily triggered by long-term variations of dynamo parameters, but may also occur spontaneously even for fixed parameters. Further interesting features of the model are the typical second intensity peak and the intermittent appearance of reversed helicities in both hemispheres., Comment: 30 pages, 17 figures, final version

Liquid Metal Batteries (LMBs) are a promising concept for cheap electrical energy storage at grid level. These are built as a stable density stratification of three liquid layers, with two liquid metals separated by a molten salt. In order to ensure a safe and efficient operation, the understanding of transport phenomena in LMBs is essential. With this motivation we study thermal convection induced by internal heat generation. We consider the electrochemical nature of the cell in order to define the heat balance and the operating parameters. Moreover we develop a simple 1D heat conduction model as well as a fully 3D thermo-fluid dynamics model. The latter is implemented in the CFD library OpenFOAM, extending the volume of fluid solver, and validated against a pseudo-spectral code. Both models are used to study a rectangular 10 × 10 cm² Li||Bi LMB cell at three different states of charge.

A numerical model for simulating electro-vortical flows in OpenFOAM is developed. Electric potential and current are solved in coupled solid-liquid conductors by a parent-child mesh technique. The magnetic field is computed using a combination of Biot–Savart’s law and induction equation. Further, a PCG solver with special regularisation for the electric potential is derived and implemented. Finally, a performance analysis is presented and the solver is validated against several test cases.

The design and performance of liquid metal batteries, a new technology for grid-scale energy storage, depend on fluid mechanics because the battery electrodes and electrolytes are entirely liquid. Here we review prior and current research on the fluid mechanics of liquid metal batteries, pointing out opportunities for future studies. Because the technology in its present form is just a few years old, only a small number of publications have so far considered liquid metal batteries specifically. We hope to encourage collaboration and conversation by referencing as many of those publications as possible here. Much can also be learned by linking to extensive prior literature considering phenomena observed or expected in liquid metal batteries, including thermal convection, magnetoconvection, Marangoni flow, interface instabilities, the Tayler instability, and electro-vortex flow. We focus on phenomena, materials, length scales, and current densities relevant to the liquid metal battery designs currently being commercialized. We try to point out breakthroughs that could lead to design improvements or make new mechanisms important., 31 pages, 16 figures, 206 references

Liquid metal batteries (LMBs) are discussed today as a cheap grid scale energy storage, as required for the deployment of fluctuating renewable energies. LMBs incorporate stratified three-layer fluid systems consisting of two liquid metal electrodes separated by a thin molten salt electrolyte (see sketch below). Due to the large electrical conductivities of the liquid metals, LMBs are highly susceptible to become unstable by interactions of induced or external magnetic fields with internal cell currents. Several different types of instabilities have been identified as to be crucial for the LMB operation. Besides the Tayler instability and electrovortex flows, the metal pad roll (MPR) instability, originally known from aluminium reductions cells (ARCs), emerged as a key instability mechanism capable to cause short-circuits by exciting interfacial gravity-capillary waves. The MPR instability can be induced only by the interaction of a homogeneous vertical magnetic field with horizontal compensation currents arising due to small perturbations of the interfaces. While this mechanism is well understood in the case of ARCs, in LMBs an additional interface is present that may strongly influence the global stability depending on several parameters. Both interfaces can be closely coupled for thin salt-layers such that they both may excite each other and may be connected by different oscillating modes. The analysis of the coupling behavior is the main target of this study. As the main part of this talk I will present an analytical analysis using linear wave theory describing coupled gravity-capillary waves enclosed in cylindrical containers. We have derived a fourth-order dispersion relation containing two different coupling modes. Further, we found that the global coupling behavior can be completely described by only two dimensionless parameters. On this basis, we suggest a coupling criterion predicting for which parameter regimes both interfaces can be considered as to be fully decoupled such that two-layer stability analysis becomes sufficient. Our study is further accompanied by both numerical simulations and experiments. For highly coupled cases we discovered different kinds of interface displacements not known from ARCs. Some of the found states cannot be explained by the MPR instability mechanism alone and probably involve some new physical aspects.

The solar cycle appears to be remarkably synchronized with the gravitational torques exerted by the tidally dominant planets Venus, Earth and Jupiter. Recently, a possible synchronization mechanism was proposed that relies on the intrinsic helicity oscillation of the current-driven Tayler instability which can be stoked by tidal-like perturbations with a period of 11.07 years. Inserted into a simple alpha-Omega dynamo model these resonantly excited helicity oscillations led to a 22.14 years dynamo cycle. Here, we assess various alternative mechanisms of synchronization. Specifically we study a simple time-delay model of Babcock-Leighton type dynamos and ask whether periodic changes of either the minimal amplitude for rising toroidal flux tubes or the Omega effect could eventually lead to synchronization. In contrast to the easy and robust synchronizability of Tayler-Spruit dynamo models, our answer for those Babcock-Leighton type models is less propitious., Comment: 21 pages, 11 figures

Water electrolysis is a promising technique for energy conversion and is one of the key technologies to ensure an efficient and clean energy management in the future. However, the efficiency of this process is limited by overpotentials arising from - among other things - the high bubble coverage at the electrode surface. The influence of a magnetic field on the bubble behavior during electrolysis, in particular the bubble detachment from the electrodes, shows great potential for improving the efficiency of the process. In this study experiments and numerical simulations were carried out to investigate the effect of an electrode-normal magnetic field on the bubble detachment. Astigmatism Particle Tracking Velocimetry (APTV) was used to measure the magnetohydrodynamic (MHD) flow field around a magnetized sphere mimicking an electrolytic bubble. Complementary simulations gave further insight into the corresponding pressure field. The experimental and numerical results demonstrate that the pressure reduction formerly assumed to be responsible for the accelerated bubble detachment in the magnetic field is too weak to cause this effect. However, the flow over an arrangement of magnets was additionally measured by Particle Image Velocimetry (PIV), showing that the formation of bubble groups on the electrode surface gives rise to a stronger global flow which may have a substantial influence on the bubble behavior.

Liquid metal batteries are possible candidates for massive and economically feasible large-scale stationary storage and as such could be key components of future energy systems based mainly or exclusively on intermittent renewable electricity sources. The completely liquid interior of liquid metal batteries and the high current densities give rise to a multitude of fluid flow phenomena that will primarily influence the operation of future large cells, but might be important for today's smaller cells as well. The paper at hand starts with a discussion of the relative merits of using molten salts or ionic liquids as electrolytes for liquid metal cells and touches the choice of electrode materials. This excursus into electrochemistry is followed by an overview of investigations on magnetohydrodynamic instabilities in liquid metal batteries, namely the Tayler instability and electromagnetically excited gravity waves. A section on electro-vortex flows complements the discussion of flow phenomena. Focus of the flow related investigations lies on the integrity of the electrolyte layer and related critical parameters.

We discuss how to derive a force or a force density from a measured velocity field. The first part focuses on the integral force a fluid exerts on a body, e.g. lift and drag on an airfoil. Obtaining the correct pressure is crucial; however, it cannot be measured within the flow non-intrusively. Using numerical and experimental test cases, we compare the accuracy achievable with three methods: pressure reconstruction from velocity fields via (1) the differential momentum equation, or (2) the Poisson equation, furthermore, (3) Noca’s momentum equation [Noca, JFS 13(5), 1999], which does not require pressure explicitly. The latter gives the best results for the lift, whereas the first or second approach should be used for the drag. The second part deals with obtaining the distribution of a body force density generated by an actuator. Using a stream function ansatz, we obtain a Laplace equation that allows us to compute the solenoidal part of the force distribution; however, the irrotational part is lost. Furthermore, the wall pressure must be known. We validate this approach using numerical data from a wall jet flow in a rectangular box, driven by a fictitious, solenoidal body force. Reconstructing the force distribution yields an error of less than 10−2 for most of the domain.

Lorentz force-based flow control in materials with low electrical conductivity has a long history back to the first half of the 19th century. This review will focus on developments during the last two decades, collecting results from numerical simulations and laboratory experiments. Typically, the actuators consist of permanent magnets and electrodes flush-mounted with the surface, generating Lorentz forces in the fluid layers adjacent to the wall. We will discuss the application of Lorentz forces to reduce friction drag in turbulent boundary layers and to delay boundary layer transition. The control of separated flows and shear layers is another key aspect of the review. Energetic efficiency, one of the main criteria for flow control, and its relation to typical operating conditions will be analyzed as well. Lorentz forces can be successfully used to control a broad range of flow phenomena and are a versatile tool for basic fluid dynamics research. However their current applicability in large scale systems is hampered by the low electrical to mechanical efficiency intrinsic to actuators based on the magnetic fields delivered by today’s permanent magnets.

The DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) is intended as a platform both for large scale experiments related to geo- and astrophysics as well as for experiments related to thermohydraulic and safety aspects of liquid metal batteries and liquid metal fast reactors. The most ambitious projects in the framework of DRESDYN are a homogeneous hydromagnetic dynamo driven solely by precession and a large Taylor-Couette type experiment for the combined investigation of the magnetorotational instability and the Tayler instability. In this paper we give a short summary about the ongoing preparations and delineate the next steps for the realization of DRESDYN., Comment: 10 pages, 6 figures, submitted to Magnetohydrodynamics

The effect of a uniform magnetic field on the hydrogen evolution reaction (HER) during water electrolysis in 0.1 M Na 2 SO 4 solution was investigated. Irrespective of the magnetic field orientation with respect to the electrode surface, the desorption of hydrogen is enhanced by the presence of the magnetic field. This effect is displayed by a reduction of the mean bubble size as well as a narrower bubble size distribution in a magnetic field. Moreover, it is shown that in the presence of an external magnetic field the fractional bubble coverage is strongly retarded. As a consequence the current density is increased since more active sites are available for the reduction processes. These effects are discussed with respect to the Lorentz force driven convection induced by a magnetic field. In order to resolve further the influence of a magnetic field applied in the perpendicular-to-electrode configuration, where the bulk Lorentz force is negligible, a numerical study has been performed. This revealed the mechanism of the improved desorption of a hydrogen bubble from the electrode surface. The numerical study has been validated by a model experiment. Most importantly, it is clearly demonstrated that a magnetic field superposed during water decomposition is a very effective method to intensify hydrogen evolution processes, and it should be possible to significantly improve the energetic efficiency of the hydrogen production via water electrolysis in a magnetic field.

In electrochemical reactions, Lorentz forces due to external homogeneous magnetic fields may lead to increased mass transfer as additional convection is forced (MHD effect). A careful analysis shows that often a three-dimensional modeling of this effect is necessary. We present numerical simulations of copper electrolysis in cuboid cells under the influence of homogeneous magnetic fields of vertical direction in the limiting current regime. The Lorentz force is found to drive horizontal counter-rotation which is stronger than the natural convection. Experimental results confirm the numerical findings.

Recent years have seen an increased interest in the question of whether the gravitational action of planets could have an influence on the solar dynamo. Without discussing the observational validity of the claimed correlations, we ask for a possible physical mechanism that might link the weak planetary forces with solar dynamo action. We focus on the helicity oscillations that were recently found in simulations of the current-driven, kink-type Tayler instability, which is characterized by an m=1 azimuthal dependence. We show how these helicity oscillations can be resonantly excited by some m=2 perturbation that reflects a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation induced by the Venus--Earth--Jupiter system may lead to a 1:1 resonant excitation of the oscillation of the alpha-effect. Finally, in the framework of a reduced, zero-dimensional alpha--Omega dynamo model we recover a 22.14-year cycle of the solar dynamo., Comment: 18 pages, 7 figures, accepted by Solar Physics

The flow structure and lift response of a separated flow over an airfoil that is subjected to an impulsive type of pitching motion are compared to the response produced by a localized pulse disturbance at the leading edge of an airfoil. Time-resolved PIV data are used to obtain the velocity field on the suction side of the airfoil. POD analysis shows that the majority of energy is contained within the first four modes. Strong similarities in the shapes of the POD basis functions are found, especially for the second mode, irrespective of the type of actuation (global or local). The time-varying coefficient of this second POD mode tracks the negative of the lift coefficient or circulation in each case. Basis functions from the localized actuation data were projected on the velocity field of the globally actuated flow to obtain a hybrid set of coefficients. The hybrid coefficients matched reasonably well with the coefficients obtained from the original POD analysis for the globally excited flow. Both types of actuation were found to generate very similar Lagrangian flow structures. The results suggest a certain degree of universality in the POD modes/flow structures for the separated flow over an airfoil, irrespective of the type of excitation.

The current-driven, kink-type Tayler instability (TI) is a key ingredient of the Tayler-Spruit dynamo model for the generation of stellar magnetic fields, but is also discussed as a mechanism that might hamper the up-scaling of liquid metal batteries. Under some circumstances, the TI involves a helical flow pattern which goes along with some alpha effect. Here we focus on the chiral symmetry breaking and the related impact on the alpha effect that would be needed to close the dynamo loop in the Tayler-Spruit model. For low magnetic Prandtl numbers, we observe intrinsic oscillations of the alpha effect. These oscillations serve then as the basis for a synchronized Tayler-Spruit dynamo model, which could possibly link the periodic tidal forces of planets with the oscillation periods of stellar dynamos., Comment: 10 pages, 4 figures, extended proceedings paper of the PAMIR 2016 conference

International audience; The increasing deployment of renewable energies requires three fundamental change to the electric grid: more transmission lines, a flexibilization of the demand and grid scale energy storage. Liquid metal batteries (LMBs) are considered these days as a promising means of stationary energy storage. Built as a stable density stratification of two liquid metals separated by a liquid salt, LMBs have three main advantages: a low price, a long life-time and extremely high current densities. In order to be cheap, LMBs have to be built large. However, battery currents of the order of kilo-amperes may lead to magnetohydrodynamic (MHD) instabilities, which – in the worst case – may short-circuit the thin electrolyte layer. The metal pad roll instability, as known from aluminium reduction cells, is considered as one of the most dangerous phenomena for LMBs. We develop a numerical model, combining fluid- and electrodynamics with the volume-of-fluid method, to simulate this instability in cylindrical LMBs. We explain the instability mechanism similar to that in aluminium reduction cells and give some first results, including growth rates and oscillation periods of the instability

In two different cylindrical electrochemical cells, copper deposition and dissolution in the presence of a magnetic field mostly parallel to the electric field has been investigated. Particle image velocimetry measurements show that even under such a field configuration where Lorentz forces are often a priori neglected in fact they may dominate the flow. Further on, depending on the electrode radius a reversal of the secondary flow has been found. This feature can be explained by the different Lorentz force configurations calculated from the magnetic field and the primary current distributions. The components of the magnetic field have been determined by means of a traversed Hall probe as well as calculated by a commercial finite element package. Experimentally and numerically determined field distributions match very well. A good agreement between the measured and calculated velocity distributions has also been found, suggesting that in the present case the effect of the Lorentz force alone is sufficient to explain the magnetic field influence on the flow.

Liquid metal batteries, i.e. batteries in which both electrodes as well as the electrolyte are in the liquid state are usable for grid-scale energy storage and have received considerable attention recently. However, in completely liquid systems, fluid dynamic instabilities have to be considered. We focus here on the current driven Tayler instability and present results of a numerical study using a finite volume code for the calculation of the fluid flow coupled to a Biot-Savart integration to obtain the magnetic field. Growth rates of the instability as well as the magnetic field structure of the saturated instability fit very well to the experimental findings.

Chemical energy storage systems, e.g., in the form of hydrogen or methanol, have a great potential for the establishment of volatile renewable energy sources due to the large energy density. The efficiency of hydrogen production through water electrolysis is, however, limited by gas bubbles evolving at the electrode’s surface and can be enhanced by an accelerated bubble detachment. In order to characterize the complex multi-phase flow near the electrode, simultaneous measurements of the fluid velocities and the size and trajectories of hydrogen bubbles were performed in a water electrolyzer. The liquid phase velocity was measured by PIV/PTV, while shadowgraphy was used to determine the bubble trajectories. Special measurement and evaluation techniques had to be applied as the measurement uncertainty is strongly affected by the high void fraction close to the wall. In particular, the application of an advanced PTV scheme allowed for more precise fluid velocity measurements closer to electrode. Based on these data, stability characteristics of the near-wall flow were evaluated and compared to that of a wall jet. PTV was used as well to investigate the effect of Lorentz forces on the near-wall fluid velocities. The results show a significantly increased wall parallel liquid phase velocity with increasing Lorentz forces. It is presumed that this enhances the detachment of hydrogen bubbles from the electrode surface and, consequently, decreases the fractional bubble coverage and improves the efficiency. In addition, the effect of large rising bubbles with path oscillations on the near-wall flow was investigated. These bubbles can have a strong impact on the mass transfer near the electrode and thus affect the performance of the process.

Electromagnetic body forces, i.e. Lorentz forces, have been used to modify the boundary layer around a circular cylinder in cross flow. Depending on the polarity of the applied electric field different effects on the flow can be obtained. Lorentz forces directed with the mean flow are able to prevent the boundary layer from separation. Therefore flow separation as well as the von Karman vortex trail can be suppressed. When the momentum gain produced by the Lorentz forces in the boundary layer is high enough, thrust is produced, which results in a jet flow originated from the cylinder's backside. If the Lorentz forces are directed opposite to the mean flow, the separation points are shifted towards the front stagnation point, the recirculation region broadens and the von Karman vortex trail is modified. The described technique gives a variety of opportunities to control the flow around the cylinder and the flow structure of the cylinder wake. Results from flow visualizations and numerical calculations are presented.

The Tayler instability is a kink-type flow instability which occurs when the electrical current through a conducting fluid exceeds a certain critical value. Originally studied in the astrophysical context, the instability was recently shown to be also a limiting factor for the upward scalability of liquid metal batteries. In this paper, we continue our efforts to simulate this instability for liquid metals within the framework of an integro-differential equation approach. The original solver is enhanced by multi-domain support with Dirichlet-Neumann partitioning for the static boundaries. Particular focus is laid on the detailed influence of the axial electrical boundary conditions on the characteristic features of the Tayler instability, and, secondly, on the occurrence of electro-vortex flows and their relevance for liquid metal batteries., Comment: 26 pages, 16 figures

The use of liquid metal batteries is considered as one promising option for electric grid stabilisation. While large versions of such batteries are preferred in view of the economies of scale, they are susceptible to various magnetohydrodynamic instabilities which imply a risk of short-circuiting the battery due to the triggered fluid flow. Here we focus on the current driven Tayler instability and give critical electrical currents for its onset as well as numerical estimates for the appearing flow structures and speeds. Scaling laws for different materials, battery sizes and geometries are found. We further discuss and compare various means for preventing the instability., 9 pages, 14 figures

The response of a separated flow over a two-dimensional wing to a short duration disturbance from a Lorentz force leading-edge actuator is presented. The transient flow structures and lift force measurements were obtained from PIV measurements. The dependence of the lift response on actuator pulse duration, pulse amplitude, and direction of actuation was documented. The flow structures in the separated shear layer were identified using Finite Time Lyapunov Exponent (FTLE) method. The direction of the actuator pulse had a significant effect on the initial development of the shear layer, but the larger scale envelope of the separated flow had essentially the same response, irrespective of the direction of actuation.

We observe electrolysis with gas evolution, a phenomenon occurring in a number of industrial scale electrochemical processes. Here, water electrolysis takes place in a small undivided electrolysis cell consisting of vertical electrodes embedded in a larger glass vessel which contains a dilute NaOH solution. Fluid flow velocities are measured by Particle Image Velocimetry with fluorescent tracers, while size distribution and velocities of the bubbles are determined from bubble shadow images obtained with a high speed camera. Coalescence phenomena are observed in the flow and explain the relatively wide distribution of bubble sizes. Depending on the gap width and the current density, bubbles ascending near the electrodes form two discernible bubble curtains (low average void fraction, wide gaps) or a flow profile more akin to a channel flow (high average void fraction, small gaps). If the flow consists of separate bubble curtains, instabilities develop not unlike to that of a single phase wall jet. Finally, the influence of different wall parallel Lorentz force configurations on the velocity distribution in the cell is investigated. These Lorentz forces are generated by permanent magnets mounted behind the electrodes. Depending on gap width, current density, and magnet configuration, liquid phase velocities can be increased by several times compared to the baseline case.

Magnetic fields are applied to electrically conducting fluids in order to influence electrochemical processes through the magnetohydrodynamic effect. Various phenomena, e.g. on electrodeposited metal layers, which can be attributed to forced convections were observed. To provide information about acting forces, the laser Doppler velocity profile sensor was applied to measure the transition layer of a Lorentz force influenced flow over a backward-facing step and the velocity boundary layer during copper deposition. With this sensor, the electrolyte convection within < 500 μm of the front of an electrode is measured with a spatial resolution down to 15 μm. The interaction of buoyancy, Lorentz and magnetic field gradient forces is studied by measuring the velocities down to 10 μm in front of the cathode. Inside the concentration boundary layer, complex electrolyte convection is induced, which varies not only in time but also in its structure, depending on the forces present and their influence over time. In inhomogeneous magnetic field configurations, the magnetic field gradient force dominates the velocity boundary layer at steady state and transports electrolyte toward regions of high magnetic gradients, where maximum deposit thicknesses are found. In this way, the measurements confirm the predicted influence of the magnetic field gradient force on the structuring of copper deposits.

Liquid metal batteries (LMBs) consist of two liquid metal electrodes and a molten salt ionic conductor sandwiched between them. The density ratios allow for a stable stratification of the three layers. LMBs were already considered as part of energy conversion systems in the 1960s and have recently received renewed interest for economical large-scale energy storage. In this paper, we concentrate on the magnetohydrodynamic aspects of this cell type with special focus on electro-vortex flows and possible effects of the Tayler instability.

In the current-driven, kink-type Tayler instability (TI) a sufficiently strong azimuthal magnetic field becomes unstable against nonaxisymmetric perturbations. The TI has been discussed as a possible ingredient of the solar dynamo mechanism and a source of the helical structures in cosmic jets. It is also considered as a size-limiting factor for liquid metal batteries. We report on a liquid metal TI experiment using a cylindrical column of the eutectic alloy GaInSn to which electrical currents of up to 8 kA are applied. We present results of external magnetic field measurements that indicate the transient occurrence of the TI in good agreement with numerical predictions. The interference of TI with the competing large-scale convection, resulting from Joule heating, is also discussed.

The separated flow around inclined airfoils can be controlled by unsteady actuation near the leading edge (LE), increasing the maximum lift coefficient without the need for heavy and complex high lift devices such as flaps. Zero net mass flow devices (ZNMF) are often used for this purpose. While certainly favorable for industrial application, actuation via ZNMF faces some problems. In particular, to independently control both amplitude and frequency of the excitation is considered a ``great challenge'' This is even more severe when the wave form of the actuation is non-sinusoidal, i.e., contains more than one frequency component. Lorentz forces do not suffer from such limitations; driven by an electric current, arbitrary wave forms can be generated easily. The main purpose here is to identify possibly different mechanisms triggered by different wave forms. In particular, we investigate electromagnetic excitation using a) a sinusoidal wave and b) rectangular waves at duty cycles of DC=1/4 and DC=1/8.