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Large Scale Liquid Metal Batteries

Liquid metal batteries are possible candidates for large scale energy storage offering a possible breakthrough of intermittent wind and solar energy exploitations. The major concern over their practical implementation is the operation at elevated temperatures and sensitivity to liquid motion. The concept of liquid metal battery bears a close similarity to aluminium electrolytic production cells. The two liquid layer MHD effects can be projected to the three liquid layer self-segregated structure of the batteries. This paper presents numerical models for the three density-stratified electrically conductive liquid layers using 3D and shallow layer approximation accounting for specific MHD effects during periods of battery activity. It is demonstrated that a stable operation of these batteries can be achieved if reusing an infrastructure of existing aluminium electrolysis pot lines. The basic principles of the MHD processes in the cells are illustrated by the numerical example cases.


Introduction
With the growing renewable energy production comes a requirement to store the intermittently produced electrical energy to be available at peak consumption times. The traditional battery storage is not well suited for a large scale capacity comparable to the needs of industrial or urban electrical grids. Liquid metal batteries are possible candidates for such large scale energy storage [1]. The attraction of liquid batteries lies in the fast kinetics at liquid metal-electrolyte interfaces, simple assembly and recycling, while the major difficulties to implementation are their sensitivity to liquid motion and operation at elevated temperatures [2]. Important features of the liquid only cells are the continuous renewal of the liquid metal electrodes upon charge-discharge cycling, as well as their insensitivity to micro-structural degradation mechanisms, which are a major limitation to the majority of solid battery types [3,4]. The concept of liquid metal battery bears a close similarity to aluminium electrolytic production cells containing two horizontal liquid layers, for which reliable mathematical models are available, see for instance [5] and the references therein. The two liquid layer MHD effects can be easily extended to the three liquid layer self-segregated structure of the batteries. The modern trend in gaining efficiency for commercial aluminium electrolysis cells is to increase their size instead of operating a large number of parallel small ones. We assume the same tendency will held for the efficient and practical implementation of large scale liquid metal battery cells having a large horizontal surface area and a small depth of the liquid metal electrodes and the electrolyte (which is the major electrical resistivity in the battery). The operation of the batteries needs to clarify if the layered structure will be overly sensitive to liquid motion caused mainly by electromagnetic forces, which potentially may lead to the top and bottom liquid metal electrode short-circuiting, accompanied by associated electrochemical and thermal problems [2]. The instability could result from interaction of the electric currents with the total magnetic field from all the current supply, connection lines and the self-induced magnetic field of the current in the cell. In order to prevent the most dangerous electromagnetically driven long wave instabilities [5,6], the electrolyte layer thickness should be above a certain critical limit, however the maximum thickness of electrolyte layer is limited by the requirement that the voltage loss in the electrolyte must not exceed a significant portion of the available thermodynamic driving force (open circuit voltage) [1]. For the relevant combination of metals and salts, this means that the electrolyte thickness should not exceed a few centimetres, while the horizontal extent of the liquid layers may reach several meters. This paper presents numerical models for the three density-stratified electrically conductive liquid layers using both 3D and shallow layer approximation to account for specific MHD effects during periods of battery charging and discharging cycles. After considering a simple and straightforward battery design we arrive to the conclusion that a more complex magnetic stabilisation is required to make the batteries suitable for practical implementation. The knowledge accumulated in designing magnetically stable aluminium production cells [5,6] permits to investigate a possibility of reusing the infrastructure of an existing aluminium electrolysis pot-line. Such 'redundant' pot-lines are increasingly available due to the present overproduction of aluminium raw materials. The mathematical model for a typical aluminium electrolysis line of 180 kA cells is extended to the battery 3 liquid layer case while preserving the plant infrastructure arrangements. It is demonstrated that a reasonably stable operation of charging and discharging of these batteries can be achieved.

Problem set up and governing equations
The battery consists of the three liquid electrically conducting layers naturally stratified due to their density (see the Figure 1 for the notation to be used in this paper). The electric current from an external circuit is flowing upwards or downwards depending on the charge/discharge cycle. The liquid electrodes are highly conductive molten metals (about 10 6 S/m), while the molten salt electrolyte has the conductivity of up to 300 S/m. The electric current enters and exits the cell via the metallic collectors connected to the external circuit.
The current distribution in the cell is fully 3 dimensional. The problem can be solved by means of spectral algorithm based on Fourier and Chebyshev polynomial expansions: Figure 1. Schematic representation and the notation used for the liquid metal battery model.
The advantage of using the trigonometric expansion in the horizontal coordinate functions in (2) is that it satisfies the condition of insulating side-walls, while the given collector currents are imposed as the boundary conditions at the top and bottom electrode areas at z=H0 and z=H3. The interface conditions between the layers are the continuity of the normal electric current and the electric potential at the deformed liquid surfaces. The magnetic field (from the currents in the cell and the supply lines) is computed numerically using the Biot-Savart law for the volume current distribution in the cell and in the external circuit [5]: The respective electromagnetic force distribution f(x,y,z,t) = j × B is recomputed at each time step due to the electric current change in time with the interface H1(x,y,t) and H2(x,y,t) variation according to the hydrodynamic wave model. The wave model for the three coupled layers can be represented efficiently using the assumption of a small wave amplitude A and the shallow layer approximation. The following non-dimensional parameters are introduced: where the depth The boundary conditions for the waves are derived from the zero normal velocity condition at the side walls: The horizontal depth average force Fk(x,y,t) and the velocity components Uk (k=1,2) appearing in the wave equations are computed after the depth averaging procedure [5] is

Single collector cell
The   The long term simulation of the interface wave development with the fully coupled electromagnetic interaction demonstrates that the bottom heavier metal interface is stable to the perturbation effects. The top metal and the electrolyte interface is easily destabilized, due to the small density difference for the selected combination of materials, leading to the wave amplitude growth in a typical rotating wave instability [5]. The cell with the single current collectors can be stabilized only when reducing the magnitude of the total current I from 100 kA to 75 kA, or alternatively increasing the electrolyte thickness from 0.05 m to 0.08 m.

Multiple collector battery cell
An improvement in efficiency (by reducing the thickness of the electrolyte layer) can be achieved by optimizing the current supply path in such a way that the vertical magnetic field is reduced in magnitude and its distribution permits to avoid the MHD wave instability.
The commercial aluminium electrolysis cells were developed following such stringent guidelines. Hence, we attempted to reuse one of the existing optimized bus bar configurations    The respective computed velocities are of smaller magnitude (Figure 9) if compared to the previous case, and the interface waves are stable after the initial perturbation dies out even at the full current of 100 kA, Figure 10. When the critical electrolyte thickness is reduced from 0.05 to 0.025 m, and further to the low value of 0.02 m. This means that it is possible to reach the stable discharge of this battery at a reasonable voltage drop of 0.29 V for the Mg/Bi metal combination (having the EDS = 0.4 V). The maximum current in the latter case is 75 kA. An additional advantage in this case is that the minimum thickness of the metal layers can be safely reduced to 0.1 m while maintaining the 3 layer battery completely stable in the MHD sense. After the initial perturbation is damped the interfaces are slightly deformed in a stationary shapes as shown in the Figure 11, however the deviation from the flat surface is just a couple of millimeters at most.

Conclusions
The MHD model for the large scale liquid metal battery demonstrates that it is possible to design a stable operating cell relative to dynamic perturbations if using the optimized bus bar configuration with multiple current collectors. For the Mg/Sb metal combination the bottom heavier metal layer is always stable to perturbations, leaving the top lighter metal (Mg, Li, Ca) interface stability as the critical step to control.