Showing papers by "Frank Stefani published in 2017"

Sloshing instability and electrolyte layer rupture in liquid metal batteries

Abstract: Liquid metal batteries (LMBs) are discussed today as a cheap grid scale energy storage, as required for the deployment of fluctuating renewable energies. Built as stable density stratification of two liquid metals separated by a thin molten salt layer, LMBs are susceptible to short-circuit by fluid flows. Using direct numerical simulation, we study a sloshing long wave interface instability in cylindrical cells, which is already known from aluminium reduction cells. After characterising the instability mechanism, we investigate the influence of cell current, layer thickness, density, viscosity, conductivity and magnetic background field. Finally we study the shape of the interface and give a dimensionless parameter for the onset of sloshing as well as for the short-circuit.

Liquid metal batteries - materials selection and fluid dynamics

Abstract: 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.

Metal pad roll instability in liquid metal batteries

Abstract: 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

The Tayler instability at low magnetic Prandtl numbers: Chiral symmetry breaking and synchronizable helicity oscillations

Abstract: 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.

Transitions in a magnetized quasi-laminar spherical Couette Flow

Abstract: First results of a new spherical Couette experiment are presented. The liquid metal flow in a spherical shell is exposed to a homogeneous axial magnetic field. For a Reynolds number Re=1000, we study the effect of increasing Hartmann number Ha. The resulting flow structures are inspected by ultrasound Doppler velocimetry. With a weak applied magnetic field, we observe an equatorially anti-symmetric jet instability with azimuthal wave number m=3. As the magnetic field strength increases, this instability vanishes. When the field is increased further, an equatorially symmetric return flow instability arises. Our observations are shown to be in good agreement with linear stability analysis and non-linear flow simulations.

Thermal convection of liquid metal in the titanium reduction reactor

Abstract: The structure of the convective flow of molten magnesium in a metallothermic titanium reduction reactor has been studied numerically in a three-dimensional non-stationary formulation with conjugated heat transfer between liquid magnesium and solids (steel walls of the cavity and titanium block). A nonuniform computational mesh with a total of 3.7 million grid points was used. The Large Eddy Simulation technique was applied to take into account the turbulence in the liquid phase. The instantaneous and average characteristics of the process and the velocity and temperature pulsation fields are analyzed. The simulations have been performed for three specific heating regimes: with furnace heaters operating at full power, with furnace heaters switched on at the bottom of the vessel only, and with switched-off furnace heaters. It is shown that the localization of the cooling zone can completely reorganize the structure of the large-scale flow. Therefore, by changing heating regimes, it is possible to influence the flow structure for the purpose of creating the most favorable conditions for the reaction. It is also shown that the presence of the titanium block strongly affects the flow structure.

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

Abstract: 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.

On the synchronizability of Tayler-Spruit and Babcock-Leighton type dynamos

Abstract: 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.

Immersed transient eddy current flow metering: a calibration-free velocity measurement technique for liquid metals

Abstract: Eddy current flow meters are widely used for measuring the flow velocity of electrically conducting fluids. Since the flow induced perturbations of a magnetic field depend both on the geometry and the conductivity of the fluid, extensive calibration is needed to get accurate results. Transient eddy current flow metering has been developed to overcome this problem. It relies on tracking the position of an impressed eddy current system that is moving with the same velocity as the conductive fluid. We present an immersed version of this measurement technique and demonstrate its viability by numerical simulations and a first experimental validation.

Stability and instability of hydromagnetic Taylor-Couette flows.

Abstract: Decades ago S. Lundquist, S. Chandrasekhar, P.H. Roberts and R. J.~Tayler first posed questions about the stability of Taylor-Couette flows of conducting material under the influence of large-scale magnetic fields. These and many new questions can now be answered numerically where the nonlinear simulations even provide the instability-induced values of several transport coefficients. The cylindrical containers are axially unbounded and penetrated by magnetic background fields with axial and/or azimuthal components. The influence of the magnetic Prandtl number $Pm$ on the onset of the instabilities is shown to be substantial. The potential flow subject to axial fields becomes unstable against axisymmetric perturbations for a certain supercritical value of the averaged Reynolds number $\overline{Rm}=\sqrt{Re\cdot Rm}$ (with $Re$ the Reynolds number of rotation, $Rm$ its magnetic Reynolds number). Rotation profiles as flat as the quasi-Keplerian rotation law scale similarly but only for $Pm\gg 1$ while for $Pm\ll 1$ the instability instead sets in for supercritical $Rm$ at an optimal value of the magnetic field. Among the considered instabilities of azimuthal fields, those of the Chandrasekhar-type, where the background field and the background flow have identical radial profiles, are particularly interesting. They are unstable against nonaxisymmetric perturbations if at least one of the diffusivities is non-zero. For $Pm\ll 1$ the onset of the instability scales with $Re$ while it scales with $\overline{Rm}$ for $Pm\gg 1$. - Even superrotation can be destabilized by azimuthal and current-free magnetic fields; this recently discovered nonaxisymmetric instability is of a double-diffusive character, thus excluding $Pm= 1$. It scales with $Re$ for $Pm\to 0$ and with $Rm$ for $Pm\to \infty$.

Magnetic field dynamos and magnetically triggered flow instabilities

Abstract: The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN) An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear In this paper, the main results of these two projects are summarized

Nonmodal analysis of helical and azimuthal magnetorotational instabilities

Abstract: Helical and azimuthal magnetorotational instabilities operate in rotating magnetized flows with relatively steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear, which determine the threshold of modal growth of these instabilities, are continuously connected when some axial electrical current is allowed to pass through the rotating fluid. We investigate the nonmodal dynamics of these instabilities arising from the non-normality of shear flow in the local approximation, generalizing the results of the modal approach. It is demonstrated that moderate transient/nonmodal amplification of both types of magnetorotational instability occurs within the Liu limits, where the system is stable according to modal analysis. We show that for the helical magnetorotational instability this magnetohydrodynamic behavior is closely connected with the nonmodal growth of the underlying purely hydrodynamic problem.

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Abstract: Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI) -- a relative of the standard MRI -- in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that HMRI turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

Numerical simulations of convection in the titanium reduction reactor

Abstract: We introduce a hydrodynamic model of convective flows in a titanium reduction reactor. The reactor retort is a cylindrical vessel with a radius of 0.75 m and a height up to 4 m, filled with liquid magnesium at a temperature of 850°C. The exothermic chemical reaction on the metal surface, cooling of the side wall and heating of the lower part of the retort cause strong temperature gradients in the reactor during the process. These temperature gradients cause intensive convective flows inside the reactor. As a result of the reaction, a block of titanium sponge grows at the retort bottom and the magnesium salt, whose density is close to the density of magnesium, settles down. The process of magnesium salt settling in a titanium reduction reactor was numerically studied in a two-dimensional (full size model) and three-dimensional (30% size of the real model) non-stationary formulation. A detailed analysis was performed for configurations with and without presence of convective flow due to work of furnace heaters. It has been established that magnesium salt is settling in drops with sizes from ≈ 3 cm to ≈ 10 cm. It was shown that convective flow can entrain the drop and carry it with the vortex.

Parametric instability in periodically perturbed dynamos

Abstract: We examine kinematic dynamo action driven by an axisymmetric large-scale flow that is superimposed with an azimuthally propagating non-axisymmetric perturbation with a frequency ω. Although we apply a rather simple large-scale velocity field, our simulations exhibit a complex behavior with oscillating and azimuthally drifting eigenmodes as well as stationary regimes. Within these non-oscillating regimes we find parametric resonances characterized by a considerable enhancement of dynamo action and by a locking of the phase of the magnetic field to the pattern of the perturbation. We find an approximate fulfillment of the relationship between the resonant frequency ω res of the excitation and the eigenfrequency ω 0 of the undisturbed system given by ω res = 2ω 0 , which is known from paradigmatic rotating mechanical systems and our prior study [Giesecke et al., Phys. Rev. E, 86, 066303 (2012)]. We find further, broader, regimes with weaker enhancement of the growth rates but without phase locking. However, this amplification regime arises only in case of a basic (i.e., unperturbed) state consisting of several different eigenmodes with rather close growth rates. Qualitatively, these observations can be explained in terms of a simple low-dimensional model for the magnetic field amplitude that is derived using Floquet theory. The observed phenomena may be of fundamental importance in planetary dynamo models with the base flow being disturbed by periodic external forces like precession or tides and for the realization of dynamo action under laboratory conditions where imposed perturbations with the appropriate frequency might facilitate the occurrence of dynamo action.

Magnetic field dynamos and magnetically triggered flow instabilities

Abstract: The project A2 of the LIMTECH Alliance aimed at a better understanding of those magnetohydrodynamic instabilities that are relevant for the generation and the action of cosmic magnetic fields. These comprise the hydromagnetic dynamo effect and various magnetically triggered flow instabilities, such as the magnetorotational instability and the Tayler instability. The project was intended to support the experimental capabilities to become available in the framework of the DREsden Sodium facility for DYNamo and thermohydraulic studies (DRESDYN). An associated starting grant was focused on the dimensioning of a liquid metal experiment on the newly found magnetic destabilization of rotating flows with positive shear. In this survey paper, the main results of these two projects are summarized.

Nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Abstract: Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. We investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI) in a magnetized Taylor-Couette flow using direct numerical simulations. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter plays a special role for its dynamics and determines its growth rate. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear states remain in all cases nearly axisymmetric suggesting that HMRI turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

The DRESDYN project: planned experiments and present status

Abstract: 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.

Parametric instability in periodically perturbed dynamos

Abstract: We examine kinematic dynamo action driven by an axisymmetric large scale flow that is superimposed with an azimuthally propagating non-axisymmetric perturbation with a frequency $\omega$. Although we apply a rather simple large scale velocity field, our simulations exhibit a complex behavior with oscillating and azimuthally drifting eigenmodes as well as stationary regimes. Within these non-oscillating regimes we find parametric resonances characterized by a considerable enhancement of dynamo action and by a locking of the phase of the magnetic field to the pattern of the perturbation. We find an approximate fulfillment of the relationship between the resonant frequency $\omega_{\rm{res}}$ of the disturbed system and the eigenfrequency $\omega_0$ of the undisturbed system given by $\omega_{\rm{res}}=2\omega_0$ which is known from paradigmatic rotating mechanical systems and our prior study [Giesecke et al., Phys. Rev. E, 86, 066303 (2012)]. We find further -- broader -- regimes with weaker enhancement of the growth rates but without phase locking. However, this amplification regime arises only in case of a basic (i.e. unperturbed) state consisting of several different eigenmodes with rather close growth rates. Qualitatively, these observations can be explained in terms of a simple low dimensional model for the magnetic field amplitude that is derived using Floquet theory. The observed phenomena may be of fundamental importance in planetary dynamo models with the base flow being disturbed by periodic external forces like precession or tides and for the realization of dynamo action under laboratory conditions where imposed perturbations with the appropriate frequency might facilitate the occurrence of dynamo action.