An Approach for Suppressing Fluid Instabilities in Liquid Metal Battery with an Internal Structure

The instabilities of fluid in the liquid metal battery (LMB) can easily cause a short circuit and lead to safety accidents, which have become a bottleneck in LMB industrial applications. In this case, a structure named grid-structure (GS) based on the inner cavity of the LMB has been used to suppress the fluid instabilities. Based on OpenFOAM-4 x numerical simulation, we analyzed the critical electric potential in basic structures, which is introduced as the threshold of magnetohydrodynamic (MHD) instabilities. We constructed the GS with a different number of baffles. The simulation results show that the GS can effectively change the spatial distribution of the magnetic field and the flow field. And it can improve the charging/discharging efficiency and enhance the stability of LMB. Simulation results also show that the number of baffles has a positive relationship with the effect of suppressing the instabilities of MHD. This study helps determine the influencing factors of MHD instabilities and proves the universality of the GS.


Introduction
With the increasing proportion of windy energy and solar energy, humanity has had more opportunities to use these clean energy sources, but the intermittent and unstable properties of these renewable sources make them difficult to be connected to the grid.Therefore, seeking high-stability and large-scale energy storage techniques, like the electrochemical energy storage system, has become a research hotspot [1].Compared with other energy storage methods, electrochemical energy storage is independent of the environment, and its energy density and conversion efficiency are higher [2].Among them, as a cheap and efficient energy storage technology, the liquid metal battery (LMB) has the advantages of long service life, high efficiency, stable performance, and fast charging/recharging speed, and it has great application potential in large-scale energy storage.As shown in Figure 1, the positive and negative metal materials, and molten salt of typical LMB are all liquid.Because of their different densities and incompatibility with each other, they are stratified automatically into three layers under the action of gravity.The negative electrode of the upper layer, the positive electrode of the lower layer, and the electrolyte layer in the middle are all liquid.Because the LMB is entirely liquid without other separation structures, it inevitably has many fluid/MHD instabilities, such as Taylor instability.In this case, it is unwise to move it violently.The internal instabilities will cause short circuits and other accidents, which will also affect the service and life of LMB.

Figure 1. Typical LMB structure
There are four types of LMB instabilities, the Tayler instability (TI), the Sloshing instability (SI), the Rayleigh-Bénard instability (R-BI), and the Electro-Vortex Flows (EVF) instability.Concerning the research of TI, Stefani et al. [3] found that the Taylor instability is more likely to occur in LMB of thin and high containers than that of flat.And they proposed a way to suppress the Taylor instability by adding insulated tubes and reverse current to the hollow cylinder in the middle.In SI research, Zikanov [4] simplified the positive and negative electrodes into metal plates.He found that the interface fluctuation mainly depends on the ratio of density jump between the two interfaces.For R-BI research, Kelley and Sadoway [5], by heating the bottom of a single layer of liquid, studied the natural convection phenomenon in liquid metal.They found that with the increase in current density, the electrode mixing time decreased.In the work of Keogh et al. [6], a single-layer electrode was simulated, and their results were compared with experimental data from the literature.The comparison shows that there is a strong interaction between R-BI and EVF in the anodes of discharging.In EVFs research, Denisov et al. [7] found that eddy current usually appears in the place with the highest current density, leading to the increase of local magnetic pressure inside the LMB.
All the above studies were carried out from the aspect of single instability and paid more attention to the mechanism research, but in practical work, many unstable factors work together simultaneously.From the structural point of view, the research [8] put forward a new grid structure (GS), which can suppress the SI, R-BI, and TI.This paper will take the circular section LMB as an example to introduce how the GS suppresses the MHD instabilities.
From our analysis results, we found that the GS can effectively change the spatial distribution of magnetic field and flow field, and suppress various internal instabilities of LMB.We also simulated and analyzed different GSs, and the results proved that the number of baffles is proportional to inhibiting fluid stability.

Physical models
We take circular cross sections for example, and a cylindrical physical model with an aspect ratio of Γ= H/D=4.5 (in which the height H=450 mm and diameter D=100 mm) is established for calculation.The thickness of the positive electrode, electrolyte, and negative electrode materials are 200 mm, 50 mm, and 200 mm respectively.Among them, the negative electrode-electrolyte-positive electrode materials are Li||LiCl-KCl||Pb-Bi.Table 1 lists the physical parameters of the three materials at the working temperature of 500℃, and Superscripts (1), (2), and (3) represent positive electrode, electrolyte, and negative electrode respectively.Figure 2 shows the structural diagram after adding baffles, and positive and negative current collectors are respectively arranged at the lower and upper ends of positive and negative materials.Coefficient of viscosity The GS is arranged inside the LMB shell and it consists of baffles that cross each other and are parallel to the axis.The baffles used have the characteristics of electric insulation and magnetic insulation.At the same time, to avoid the generation of solid metallic compounds at the electrolytepositive interface when the LMB works, a certain EVF is necessary for the positive electrode, so the bottom of the GS cannot extend to the positive electrode current collector.

Mathematical models
For the fluid flow, the general governing equations are Navier-Stokes (N-S) ones for different layers: (1) The continuity equation is: ⋅   0.
(2) The potential equation is: (3) The magnetic vector potential equation is: .
(5) Current density is: The Volume of Fluid (VOF) model of Eulerian multiphase flow is adopted to capture the interfaces of different layers.In the incompressible VOF model, the phase equation is expressed as follows:

Assumptions
To execute the numerical simulation successfully, the following assumptions are made: (1) All solid-liquid boundaries are non-slip; (2) The side walls of the container and the GS composed of baffles are electrically insulated and magnetically insulated, but the top and bottom walls are good electrical conductors; (3) Viscous dissipation is neglected; (4) The Joule heat is neglected; (5) All physical parameters are constants, as shown in Table 1; (6) The thickness of the baffles can be ignored compared with the whole volume of the container.

Initial and boundary conditions
The initial conditions in the present problem are as follows: (1) The initial values of velocity , pressure p, current density J, electric potential E, magnetic field strength , and magnetic vector potential A are zero; (2) The surface tension coefficient of the liquid-liquid contact interface is the same and constant, and its value is 0.07; (3) The solid-liquid interface contact angle is 90°.We continue the above assumptions, and the boundary conditions for the circular section are as follows.

Numerical methods and process
Based on OpenFOAM, the grid systems are generated by a structure grid, as shown in Figure 3.The solvers are based on the multiphase Inter Foam solver, and the PIMPLE algorithm is adopted, which can be regarded as a combination of the PISO algorithm and SIMPLE algorithm.

Instability of LMB
In the simulation, the calculation data is output every 0.1 seconds by applying different voltages.Figure 4 is the 3D morphological diagram of the electrolyte layer at a certain critical time, and Figure 5 is the streamlined diagram of the middle section of the container in the vertical direction when different voltages are applied.It can be found that the fluctuation first occurs at the interface between the negative electrode and the electrolyte, and with the extension of the working time, the interface between the electrolyte layer and the positive electrode also begins to fluctuate, but its fluctuation speed is far less than that at the interface of the former.As can be seen from Figure 4 (a) and Figure 5 (a), when the applied voltage is ≤ 95 V and the observation time is 60 s, the electrolyte layer is still stable; when the voltage is increased to 96 V, as shown in Figure 4 (b) and Figure 5 (b), the electrolyte layer loses its original shape after 38 s and begins to fluctuate like waves.From the streamlined diagram of the middle section of the container in the vertical direction, the eddy current is about to break through the interface of the electrolyte layer, and part of the electrolyte has flowed into the area of the positive and negative liquid metal layer.This is mainly due to the change in the direction and magnitude of the current density and the imbalance of the Lorentz force.If the LMB continues to work at this time, its positive and negative electrodes may contact directly to cause short circuits.At the same time, the internal temperature rises sharply, which is prone to safety accidents.Therefore, the critical voltage is 96 V.When the voltage is increased to 120 V, as shown in Figure 4 (c) and Figure 5 (c), the electrolyte layer deforms in 1.2 s, and the deformation accelerates.The three liquids have been completely mixed, resulting in short circuits of the LMB.

Instability of LMB with GS
Due to the huge difference between the thickness of the baffles and the size of the LMB, it is ignored in the calculation process, and the insertion depth of the GS into the positive electrode layer is set to half of the height of the positive electrode layer, as shown in Figure 6.By applying different voltages, the calculated data are output every 0.1 seconds for different GS.According to the 3D morphological diagram of the electrolyte layer at different times and the streamlined diagram of the middle section of the container in the vertical direction, it can be obtained that the critical voltage of instability is 118 V when there are three baffles, and 163 V when there are four baffles.In this way, after adding the GS, the charging/discharging voltage is increased obviously, thus shortening the time required for charging/discharging the LMB.

Inhibition mechanism of instability
The main reason for the instability of MHD in LMB is the interaction between charge and discharge current and its induced magnetic field.According to Faraday's law of electromagnetic induction, the internal charging and discharging will generate an induced magnetic field, and its magnetic field distribution is concentric circles with the axis, as shown in Figure 7 (a).Most tangential currents and the maximum induced magnetic field are distributed near the container wall.At this time, the tangential currents and the induced magnetic field will produce Lorentz force in the vertical direction.When the Lorentz force is greater than the viscous force of liquid metal, LMB instabilities begin to occur, and the peak of instability is near the interface edge, that is, near the side wall.The GS can change the distribution of the flow field and circumferential magnetic field.We take four added baffles as an example, as shown in Figure 7 (b).At this time, the magnetic field distribution is uniformly divided into four sectors by the GS.The magnetic field distribution is symmetrical, with the cylinder axis as the symmetrical center, and the magnetic field strength decreases by one order of magnitude.In addition, the distribution of Lorentz force also changes with the magnetic field distribution.Figure 8 shows the Lorentz force distribution with and without GS.We found that the Lorentz force with adding GS decreases by 2 orders of magnitude.

Conclusions and prospects
By numerical simulation, a method to suppress the MHD flow instability in LMB by adding GS is proposed.Through simulation analysis, we draw the following conclusions: (1) The critical voltages for different shapes of LMBs with and without GS are evaluated successfully, which are of utmost importance for the charging/discharging fluently working conditions; (2) The proposed GS device can separate the whole section of the container into many smaller sections, therefore efficiently suppressing many instabilities in LMBs for different shapes LMBs, further improving the working efficiency of LMBs; (3) Numerical simulation results verified the functions of GS in suppressing different instabilities for LMBs with different sections.
Next, we will further study the effect of grating on instability suppression and the comprehensive evaluation of LMB capacity loss caused by it.And we will explore the combination of the GS and series mode, which is anticipated to significantly improve charging/discharging efficiency.

Figure 2 .
Figure 2. Schematic diagram of the overall structure of the GS for an LMB: (a) the main view; (b) the top view with 3 built-in baffles.

Figure 4 .Figure 5 .
Figure 4.A 3D morphology diagram of the electrolyte layer at a certain critical moment when different voltages are applied (a) the applied voltage is 48 V~95 V, t=60 s; (b) the applied voltage is 96 V, t=38 s; (c) the applied voltage is 120 V, t=1.2 s

Figure 6 .
Figure 6.The LMB of the built-in 4 partitions Figure 7. (a) the induced magnetic field without baffle on z=0.23;(b) the induced magnetic field on z=0.23 plane with 4 baffles

Table 1 .
Physical parameters of a three-layer LMB system Li||LiCl-KCl|| Pb-Bi at an operating