Liquid metal battery

Abstract

The present invention relates to a liquid metal battery and a method of exchanging energy with an external device. In particular, the present invention relates to a liquid metal battery comprising a flow inducer configured to induce a swirl flow.

Description

LIQUID METAL BATTERY

[0001] This application claims priority from Australian Provisional Patent Application No. 2023902227 filed 11 July 2023, the content of which is incorporated herein by reference in its entirety. Field of the Invention

[0002] The present invention relates to a liquid metal battery and a method of exchanging energy with an external device. In particular, the present invention relates to a liquid metal battery comprising a flow inducer configured to induce a swirl flow. However, it will be appreciated that the invention is not limited to these particular fields of use. Background of the Invention

[0003] The following discussion of the prior art is provided to place the invention in an appropriate technical context and enable the advantages of it to be more fully understood. It should be appreciated, however, that any discussion of the prior art throughout the specification should not be considered as an express or implied admission that such prior art is widely known or forms part of the common general knowledge in the field.

[0004] Addressing the challenges of global warming requires the decarbonisation of global electricity grids. This energy transition is occurring worldwide via the uptake of renewables, especially wind and solar; in 2021 alone, wind and solar generation capacity grew by 226 GW and for the first time reached a 10.2% share of electricity generation worldwide. While the rapid transition to renewables is necessary, these energy sources present challenges to modern electricity grids. Renewable energy generation is, by nature, intermittent, and peak power generation does not necessarily align with peak power demand. This intermittency necessitates energy storage with durations anywhere from minutes to hours and days to secure the electricity grid. Batteries are well-positioned to supply this storage with a range of discharge durations depending on the technology.

[0005] Liquid metal batteries (LMBs) are a grid-scale energy storage technology developed to enable this transition from carbon-intensive energy sources to renewables. The all-liquid metal battery is typically composed of a less dense negative electrode (anode), a molten salt electrolyte, and a dense positive electrode (cathode). The large differences in density between the immiscible layers result in a gravity-stratified system that does not require any physical separators. This creates cost efficiencies as the cell design is simple and easy to manufacture; typically, the electroactive materials are housed in a stainless-steel 304L cylinder that is sealed with feed-throughs for the current collectors. Beyond low cell construction costs, the batteriesalso have long cycle lifetimes, low material costs, and high-power densities. The Li||Sb-Pb chemistry has been shown to have fade rates as low as 0.002% per cycle and low electrode material costs of $65 USD / kWh. The Li||Te chemistry has power densities of 495 Wh / kg with high discharge voltages of 1.6 V. Additionally, most chemistries have been shown to be able to discharge at current densities up to 1 A / cm2due to the low resistances of the metal electrodes and low activation overpotentials. Owing to these performance characteristics, the technology has gained further interest due to its promise as a grid-scale storage device.

[0006] However, LMBs still have challenges that must be overcome if they are to achieve the stability, robustness, and discharge capacity to be utilised for energy services such as energy arbitrage and load-shifting. The main obstacle for this technology is the mass transport overpotentials that can occur in the battery. Mass transport overpotentials can have significant impacts on a cell's performance.

[0007] Mass transport overpotentials can cause the battery to discharge at lower voltages and reduce the discharge capacity far below the theoretical capacity, limiting the performance of LMBs. It has been identified that discharge time is the most important determinant for a battery technology's commercial success. The reduction in capacity utilisation of the batteries as the capacity, and discharge time, are increased is seemingly a barrier to its commercial competitiveness in the grid-scale market.

[0008] Mass transport overpotentials in the battery are caused by concentration polarisation between the cathode-electrolyte interface and the bulk of the cathode. During discharge, ions migrate from the anode through the electrolyte layer and enter the cathode through the cathode-electrolyte interface forming an alloy in the cathode. The anodic atoms are then transported from the interface by diffusion into the bulk of the cathode. Due to the high discharge current achievable by LMBs, diffusion of species away from the interface occurs at a slower rate than the rate of ions entering the cathode. This causes the concentration of anodic atoms at the cathode-electrolyte interface to be greater than the volumetric concentration in the cathode. This concentration polarisation causes the mass transport overpotentials in the battery.

[0009] It may be advantageous to homogenise the concentration of anodic atoms in the cathode. Owing to the all-liquid composition of the batteries, flows can be generated in the cathode to mix the atoms and extend the operating capacity of the batteries. However, a problematic aspect of these concentration polarisations is that they cause significant density stratifications in the cathode. The anode metal must be less dense than both the electrolyte layer and the cathode for the liquids to stratify appropriately. This means that the alloy at the cathode-electrolyte interface has a much lower density than the rest of the cathode. Theinduced flow must be vigorous enough to break through this density stratification and mix the cathode.

[0010] It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative.

[0011] Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.

[0012] Although the invention will be described with reference to specific examples it will be appreciated by those skilled in the art that the invention may be embodied in many other forms. Summary of the Invention

[0013] According to a first aspect of the present invention there is provided a liquid metal battery, comprising: a negative current collector; a positive current collector; a liquid metal negative electrode in electrical communication with the negative current collector; a liquid metal positive electrode having a height and in electrical communication with the positive current collector; a liquid electrolyte in electrical communication with the negative electrode and the positive electrode; and a flow inducer configured to induce a swirl flow in the positive electrode by generating a magnetic field.

[0014] The inventors of the present invention have surprisingly found that by having a flow inducer configured to induce a swirl flow in the positive electrode, mass transport overpotentials in the LMBs are effectively reduced and concentration in the positive electrode (cathode) can be homogenised.

[0015] The inventors of the present invention have also surprisingly found that swirl flows induced in accordance with the present invention is advantageous over other fluid motions, including Rayleigh-Bénard convection and electro-vortex flow, in the LMBs. Rayleigh-Bénard convection does not create flows strong enough to impact the concentration stratification.Furthermore, electro-vortex flow is induced by the Lorentz force created from flux concentrations of the current density at the current collectors. Specifically, the current in the battery interacts with its own magnetic field to generate a Lorentz force. The resultant flow consists of an axially oriented jet that expels fluid away from the current collector, penetrating the buoyant and concentration stratified layer reducing concentration polarisation. However, during discharge, electro-vortex flow is suppressed by the growing density stratification, and it will not act for the entire length of discharge. Clearly, electro-vortex flow is not ideal for LMBs.

[0016] The skilled person would understand that the direction of the magnetic field is dependent on the orientation of the flow inducer and / or the liquid metal battery. In one embodiment, the magnetic field is vertical. In another embodiment, the magnetic field is horizontal.

[0017] In one embodiment, the flow inducer is configured to induce a swirl flow in the positive electrode when the battery is discharging. In another embodiment, the flow inducer is configured to induce a swirl flow in the positive electrode when the battery is charging. In yet another embodiment, the flow inducer is configured to induce a swirl flow in the positive electrode when the battery is discharging and charging.

[0018] In some embodiments, the flow inducer is a swirl flow inducer.

[0019] In some embodiments, the flow inducer is embedded in the positive electrode.

[0020] Advantageously, embedding the flow inducer in the positive electrode avoids interference with any existing components of the battery.

[0021] In some embodiments, the flow inducer comprises a metal coil. In some embodiments, the flow inducer is a metal coil.

[0022] In some embodiments, the metal coil is a single loop metal wire.

[0023] The skilled person would appreciate that having a single loop metal wire minimises ohmic overpotentials from the additional wiring.

[0024] In certain embodiments, the metal coil may comprise multiple loops, for example, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 or 20 loops.

[0025] In some embodiments, the metal coil is a copper coil. However, the skilled person would appreciate that other suitable metals can also be used.

[0026] In some embodiments, the flow inducer and / or the positive current collector is at least partially coated with a coating having a magnetic permeability of at least about 1 x 10-4H / m, for example, between about 1 x 10-4to about 1.5 x 10-3H / m. For example, the magneticpermeability may be between 1 x 10-4to about 2 x 10-4H / m, between 2 x 10-4to about 3 x 10-4H / m, between 3 x 10-4to about 4 x 10-4H / m, between 4 x 10-4to about 5 x 10-4H / m, between 5 x 10-4to about 6 x 10-4H / m, between 6 x 10-4to about 7 x 10-4H / m, between 7 x 10-4to about 8 x 10-4H / m, between 8 x 10-4to about 9 x 10-4H / m, between 9 x 10-4to about 1 x 10-3H / m, or between 1 x 10-4to about 1.5 x 10-3H / m.

[0027] In some embodiments, the coating comprises Nickel.

[0028] Advantageously, using a coating with a high magnetic permeability further boosts the magnetic field. This also reduces power consumption of the metal coil while increasing its effectiveness.

[0029] In some embodiments, the flow inducer is in electrical communication with the liquid metal battery. In some embodiments, the flow inducer is in electrical communication with the liquid metal battery to thereby generate the magnetic field from the battery’s discharge current.

[0030] In some embodiments, the flow inducer is connected with the liquid metal battery in series to thereby generate the magnetic field from the battery’s discharge current.

[0031] The skilled person would understand that the magnetic field generated is perpendicular to the direction of the internal current of the flow inducer. In some embodiments, the internal current comprises the battery’s discharge current.

[0032] Advantageously, generating the magnetic field from the battery’s discharge current enables the control of the intensity of the induced swirl flow. The induced swirl flows are controlled by increasing and decreasing the magnitude of the external magnetic field, or conversely by increasing and decreasing the discharge current density.

[0033] In some embodiments, the flow inducer is embedded at about 10% to about 90% of the height of the positive electrode. For example, the flow inducer may be embedded at about 10% to about 90%, about 10% to about 20%, about 30% to about 40%, about 40% to about 50%, about 50% to about 60%, about 60% to about 70%, about 70% to about 80%, about 80% to about 90%, about 10% to about 30%, about 20% to about 40%, about 30% to about 50%, about 40% to about 60%, about 50% to about 70%, about 60% to about 80%, about 70% to about 90%, about 20% to about 80%, about 30% to about 70%, about 20%, about 30%, about 40%, about 50%, about 60%, about 70%, about 80%, or about 90% of the height of the positive electrode.

[0034] In a preferred embodiment, the flow inducer is embedded at about 50% of the height of the positive electrode.

[0035] In some embodiments, the positive current collector extends in the positive electrode to about 10% to about 90% of the height of the positive electrode. For example, the positive current collector may extend in the positive electrode to about 10% to about 90%, about 10% to about 20%, about 30% to about 40%, about 40% to about 50%, about 50% to about 60%, about 60% to about 70%, about 70% to about 80%, about 80% to about 90%, about 10% to about 30%, about 20% to about 40%, about 30% to about 50%, about 40% to about 60%, about 50% to about 70%, about 60% to about 80%, about 70% to about 90%, about 20% to about 80%, about 30% to about 70%, about 20%, about 30%, about 40%, about 50%, about 60%, about 70%, about 80%, or about 90% of the height of the positive electrode.

[0036] In a preferred embodiment, the positive current collector extends in the positive electrode to about 50% of the height of the positive electrode.

[0037] In some embodiments, the flow inducer is embedded at same height of the positive electrode as the positive current collector extends in the positive electrode to.

[0038] In some embodiments, the flow inducer is embedded at about 50% of the height of the positive electrode, and the positive current collector extends in the positive electrode to about 50% of the height of the positive electrode. The skilled person would appreciate that this configuration enables the maximum magnetic field to be generated at 50% of the height of the positive electrode and the current exiting the positive current collector is exposed to this field. Advantageously, having the flow inducer at about 50% of the height allows the flow to flow both over and under the flow inducer without bias.

[0039] In some embodiments, the flow inducer is at least partially insulated from the positive electrode.

[0040] In some embodiments, the positive current collector is at least partially insulated from the positive electrode.

[0041] In some embodiments, the flow inducer and / or the positive current collector is insulated from the positive electrode using a ceramic coating. However, the skilled person would appreciate that other suitable coatings may also be used.

[0042] In some embodiments, the negative electrode comprises an alkali or alkali earth metal.

[0043] In some embodiments, the positive electrode comprises a Group 12 element, Ga, In, Ti, Sn, Pb, Sb, Bi or Te.

[0044] In some embodiments, the electrolyte comprises an alkali metal halide or alkali earth metal halide.

[0045] In some embodiments, the liquid metal battery has a discharge current density of between about 1000 to about 10000 A / m2. For example, the discharge current density is between about 1000 to about 2000 A / m2, between about 2000 to about 3000 A / m2, between about 3000 to about 4000 A / m2, between about 4000 to about 5000 A / m2, between about 5000 to about 6000 A / m2, between about 6000 to about 7000 A / m2, between about 7000 to about 8000 A / m2, between about 8000 to about 9000 A / m2, between about 9000 to about 10000 A / m2, about 1000 A / m2, about 2000 A / m2, about 3000 A / m2, about 4000 A / m2, about 5000 A / m2, about 6000 A / m2, about 7000 A / m2, about 8000 A / m2, about 9000 A / m2, or about 10000 A / m2.

[0046] In some embodiments, the liquid metal battery has a discharge capacity of between about 200 to about 1000 Ah. For example, the discharge capacity is between about 200 to about 300 Ah, between about 300 to about 400 Ah, between about 400 to about 500 Ah, between about 500 to about 600 Ah, between about 600 to about 700 Ah, between about 700 to about 800 Ah, between about 800 to about 900 Ah, between about 900 to about 1000 Ah, about 200 Ah, about 300 Ah, about 400 Ah, about 500 Ah, about 600 Ah, about 700 Ah, about 800 Ah, about 900 Ah, or about 1000 Ah.

[0047] In some embodiments, the liquid metal battery has an areal discharge capacity of between about 1 to about 50 Ah / cm2. For example, the areal capacity is between about 1 to about 10 Ah / cm2, between about 10 to about 20 Ah / cm2, between about 20 to about 30 Ah / cm2, between about 30 to about 40 Ah / cm2, between about 40 to about 50 Ah / cm2, about 1 Ah / cm2, about 5 Ah / cm2, about 10 Ah / cm2, about 15 Ah / cm2, about 20 Ah / cm2, about 25 Ah / cm2, about 30 Ah / cm2, about 35 Ah / cm2, about 40 Ah / cm2, about 45 Ah / cm2, or about 50 Ah / cm2.

[0048] According to a second aspect of the present invention there is provided a plurality of the liquid metal battery according to the first aspect of the present invention.

[0049] According to a third aspect of the present invention there is provided a method of exchanging energy with an external device, comprising the steps of: i) providing an external energy exchanging device; ii) providing the liquid metal battery according to the first aspect of the present invention, or the battery assembly according to the second aspect of the present invention; iii) providing electrical connections connecting the external energy exchanging device to the positive and negative current collectors; iv) inducing a swirl flow in the positive electrode by generating a magnetic field using the flow inducer.

[0050] The skilled person would understand that exchanging energy comprises charging and / or discharging the liquid metal battery or the battery assembly.

[0051] Other aspects of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention. Definitions

[0052] In describing and claiming the present invention, the following terminology will be used in accordance with the definitions set out below. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments of the invention only and is not intended to be limiting. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one having ordinary skill in the art to which the invention pertains.

[0053] Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.

[0054] As used herein, the phrase “consisting of” excludes any element, step, or ingredient not specified in the claim. When the phrase “consists of” (or variations thereof) appears in a clause of the body of a claim, rather than immediately following the preamble, it limits only the element set forth in that clause; other elements are not excluded from the claim as a whole. As used herein, the phrase “consisting essentially of” limits the scope of a claim to the specified elements or method steps, plus those that do not materially affect the basis and novel characteristic(s) of the claimed subject matter.

[0055] With respect to the terms “comprising”, “consisting of”, and “consisting essentially of”, where one of these three terms is used herein, the presently disclosed and claimed subject matter may include the use of either of the other two terms. Thus, in some embodiments not otherwise explicitly recited, any instance of “comprising” may be replaced by “consisting of” or, alternatively, by “consisting essentially of”.

[0056] Other than in the operating examples, or where otherwise indicated, all numbers expressing quantities of ingredients or reaction conditions used herein are to be understood as modified in all instances by the term “about”. The examples are not intended to limit the scope of the invention. In what follows, or where otherwise indicated, “%” will mean “weight %”, “ratio” will mean “weight ratio” and “parts” will mean “weight parts”.

[0057] The term ‘substantially’ as used herein shall mean comprising more than 50% by weight, where relevant, unless otherwise indicated.

[0058] The recitation of a numerical range using endpoints includes all numbers subsumed within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, 5, etc.).

[0059] Further, unless expressly stated to the contrary, “or” refers to an inclusive or and not to an exclusive or. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).

[0060] The terms “preferred” and “preferably” refer to embodiments of the invention that may afford certain benefits, under certain circumstances. However, other embodiments may also be preferred, under the same or other circumstances. Furthermore, the recitation of one or more preferred embodiments does not imply that other embodiments are not useful and is not intended to exclude other embodiments from the scope of the invention.

[0061] It must also be noted that, as used in the specification and the appended claims, the singular forms “a”, “an” and “the” include plural referents unless the context clearly dictates otherwise.

[0062] As used herein, with reference to numbers in a range of numerals, the terms “about,” “approximately” and “substantially” are understood to refer to the range of -10% to +10% of the referenced number, preferably -5% to +5% of the referenced number, more preferably -1 % to +1 % of the referenced number, most preferably -0.1 % to +0.1 % of the referenced number. Moreover, with reference to numerical ranges, these terms should be construed as providing support for a claim directed to any number or subset of numbers in that range. For example, a disclosure of from 1 to 10 should be construed as supporting a range of from 1 to 8, from 3 to 7, from 1 to 9, from 3.6 to 4.6, from 3.5 to 9.9, from 8 to 10, and so forth.

[0063] The term “swirl flow” refers to a flow caused by the Lorentz force generated by the interaction of an externally applied perpendicular magnetic field with the internal current. The external perpendicular magnetic field creates a rotational Lorentz force. This rotational force changes the previously poloidal electro-vortex flow to a toroidally dominant flow.

[0064] The term “current collector” refers to a component of the LMB that connects the battery to external circuits. The current collector conducts the flow of electrons between the active material of the electrode and battery terminals.

[0065] The term “liquid metal negative electrode” refers to the anode or cathode of the LMB when the battery is discharging or charging, respectively, which comprises a liquid metal. The metal is in liquid state when the battery is in operation.

[0066] The term “liquid metal positive electrode” refers to the cathode or anode of the LMB when the battery is discharging or charging, respectively, which comprises a liquid metal. The metal is in liquid state when the battery is in operation.

[0067] The term “liquid electrolyte” refers to the electrolyte of the LMB which comprises a liquid. The electrolyte is in liquid state when the battery is in operation.

[0068] Although exemplary embodiments of the disclosed technology are explained in detail herein, it is to be understood that other embodiments are contemplated. Accordingly, it is not intended that the disclosed technology be limited in its scope to the details of construction and arrangement of components set forth in the following description or illustrated in the drawings. The disclosed technology is capable of other embodiments and of being practiced or carried out in various ways. Brief Description of the Drawing

[0069] A preferred embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawing in which:

[0070] Figure 1 shows an LMB design of an embodiment of the invention.

[0071] Figure 2 shows an experimental setup used for testing an LMB design: (a) Vessel dimensions and layer heights used in the experiment (b) Simplified overview of the experimental setup used during measurements.

[0072] Figure 3 shows instantaneous surface averaged concentration for all experiment cases (a) 0.3 A / cm2(b) 0.5 A / cm2(c) 1 A / cm2(d) Large capacity case at 0.5 A / cm2.

[0073] Figure 4 shows flow dynamics obtained from experiments at 0.5 A / cm2(a) Time evolution of the toroidal and poloidal velocity in the cathode layer; (b) & (c) Instantaneous snap shot of the velocity and concentration fields; (d) Time evolution of the non-dimensionalised interfacial concentration; (e) Characteristic frequencies of the vortex generation in the cathode layer.

[0074] Figure 5 shows PIV results from a lab-scale prototype: (a)-(c) Instantaneous snap shot of the velocity at t=2s, t=4s, t=180s; (d) Experimental averaged velocity and numerical data; (e) Experimental maximum velocity and numerical maximum velocity.

[0075] Figure 6 shows a cell module design with the coil embedded in the cathode and the design incorporated into a cell stack (assembly). Detailed Description of the Invention Liquid Metal Battery Design

[0076] As shown in Figure 1, an LMB of the present invention is designed to comprise three layers housed inside a cylindrical steel vessel made from stainless steel 304L. The wall thickness is 6.5 mm and the inner radius is 0.5 ^^ = ^^ = 50.14 mm. The cathode is isolated from the anode by a hollow Al2O3 cylinder with a wall thickness of 5 mm. The anodic current collector is also made from stainless steel with a copper wire in electrical contact via a feed-through in the vessel. The electrolyte layer is 10 mm high.

[0077] A coil is embedded inside the cathode to generate a vertical magnetic field to induce a swirl flow. Embedding the coil inside the cathode layer eliminates interference with any existing components of a battery module. The coil is connected in series to the battery allowing the battery’s own discharge current to create the magnetic field. A strong field is generated using a single small loop of copper wire which minimises the ohmic overpotentials from the additional wiring. The coil is embedded at half the height of the cathode layer; therefore, the maximum vertical magnetic field is also generated at this height. The current collector inside the battery was raised to this height so that the current exiting the current collector is exposed to this field. Finally, the coil and current collector are insulated from the cathode where required using a ceramic coating. Evaluating Liquid Metal Battery Design

[0078] A two-dimensional (2D) axisymmetric model was developed to evaluate the proposed design. A lab-scale prototype was constructed and tested using a layer of Galinstan and a seeded layer of HCl, and the resulting flow was analysed using particle image velocimetry (PIV). Numerical study design

[0079] The chemistry chosen to test the design was the lithium-lead chemistry, Li||Pb. This chemistry has the strongest density stratification owing to the low density of lithium, 487 kg / m3, and the high density of lead, 10,433 kg / m3. The material properties of the pure layers are also well defined at an exemplary operating temperature of the cell, ^^ = 500oC, as well as the material properties of the cathode alloy at different molar fractions of lithium. In all cases, the material properties used are for Pb(Li) at a molar fraction of ^^^^ ^^( ^^ ^^)= 0.25. This intermediate molar fraction used was between 0.17 < ^^^^ ^^( ^^ ^^)< 0.6 the density of the cathode alloy varieslinearly with increasing concentrations of lithium. This means that the Boussinesq approximation can be used to capture the changes in density during discharge. The electrolyte modelled was LiF-LiCl-LiI (3.2-13-83.8). The electrical conductivities, ^^, of steel and copper are required for computation of the electric and magnetic fields and at ^^ = 500oC they are 19,794,166 and 1,370,000 S / m respectively. The material properties of the layers are provided in Table 1. Table 1. Material properties at ^^ = ^^ ^^ ^^^^^^ Component Material Property Value Density ^^ (kg / m3) 489 Volumetric thermal expansion coefficient ^^^^ℎ2.05x10-4(1 / K) Lithium Anode Kinematic viscosity ^^ (m2 / s) 6.72 x10-7Heat capacity ^^^^(J / kgK) 4,210 Thermal conductivity ^^ (W / mK) 53.5 Electrical conductivity ^^ (S / m) 2,62,000 Density ^^ (kg / m3) 2,690 Volumetric thermal expansion coefficient ^^^^ℎ3.17x10-4LiF-LiCl-LiI (1 / K) (3.2-13-83.8) Kinematic viscosity ^^ (m2 / s) 7.77 x10-7Electrolyte Heat capacity ^^^^(J / kgK) 1,220 Thermal conductivity ^^ (W / mK) 0.248 Electrical conductivity ^^ (S / m) 288 Density ^^ (kg / m3) 8,960 Volumetric thermal expansion coefficient ^^^^ℎ1.37 x10-4(1 / K) Pb(Li) Cathode Solutal thermal expansion coefficient ^^^^(m3 / kg) 1.31 x10-3Diffusion coefficient ^^ (m2 / s) 8x10-9Kinematic viscosity ^^ (m2 / s) 1.61x10-7Heat capacity ^^^^(J / kgK) 147 Thermal conductivity ^^ (W / mK) 14.9 Electrical conductivity ^^ (S / m) 1,380,000

[0080] The two capacities considered are 240.64 Ah and 481.28 Ah. These capacities correspond to real capacities, the capacity per unit area, of 3.75 Ah / cm2and 7.5 Ah / cm2. These capacities are ideal for long-duration energy storage and will be required in grid-scale installations of LMBs. The corresponding layer heights are provided in Table 2 and the dimensions can be matched to Figure 1. Table 2. Layer heights (in mm) for the numerical geometries modelled in this work. Variable cell dimensions in Figure 1 240.64 Ah 481.28 AhNumerical model

[0081] The numerical model uses a multi-region approach where domains are coupled at shared interfaces. It uses the quasi-static approximation, which is only valid if the magnetic Reynolds number is small, typically ^^^^≪ 1. The magnetic Reynolds number is given by ^^^^= ^^ ^^0^^ ^^(1)in which ^^ is the electrical^^0is the magnetic permeability of the medium, taken as the vacuum permeability in this case, u is a characteristic velocity, and ^^ is a characteristic length scale. This dimensionless number estimates the importance of the advection and diffusion of the magnetic field. If the magnetic Reynolds number is small, then the magnetic field is well determined by the boundary conditions and any perturbations to the field due to the fluid velocity are insignificant. Using a ^^^^value of 0.01, taking the electrical conductivity of lead from Table 2 and the height of the lead layer in the largest case, ^^ = 0.02 m, it was found that so long as the velocity was less than 0.268 m / s this limit was met. A typical velocity found in the computations was 0.067 m / s and so these computations fall in the low ^^^^limit. • Static and induced electric and magnetic fields

[0082] The quasi-static approximation assumes that there are two components to the electric field. A stationary component from the applied field that remains fixed throughout the computations, and an induced component from the fluid velocity without a time derivative. The magnetic field remains fixed, and this field has no induced components. Thus, the electric potential and current density are considered as summations of the static and induced components^^ = ^^^^+ ^^^^(3) in which ^^ is the electric potential, ^^ is the current flux vector and the subscripts a and i indicate whether the field is applied or induced. The Laplace equation for electric potential is used to calculate the applied potential ∇ ^^ ∇ ^^^^= 0 (4) with boundary conditions ^^^^= 0 (5)applied at opposing current collectors. From the electric potential, the current density is determined using^^^^= − ^^ ∇ ^^^^(7)

[0083] The magnetic field is then computed with the magnetic vector potential formulation using a coulomb gauge which ensures the field is divergence-free ∇2^^ = − ^^0^^ (8) in which A is the magnetic vector potential. The magnetic flux vector is obtained from the curl of the magnetic vector potential such that ^^ = ∇ × ^^ (9) which gives the corresponding magnetic field to the current inside the cell and embedded coil. To simplify the computations, the current density inside the coil is assumed to be homogenous and solely in the azimuthal direction. These fields make up the static component of the electric field. The induced components of the electric fields are calculated using ∇ ^^∇ ^^^^= ∇ ∙(^^( ^^ × ^^))(10) ^^^^= ^^(−∇ϕi+ ^^ × ^^) (11)in which u is the fluid velocity vector. A reference point is used to set a zero-reference potential and the field is then solely calculated from the fluid velocity and the background magnetic field found using equation (9). The potential fields are coupled between regions using a Dirichlet-Neumann boundary condition such that the potential at the interface is given byin^^is the potential at the interface, ^^^^ ^^is the potential at the cell centre adjacent to the interface, ^^^^ ^^is the electrical conductivity at the cell centre adjacent to the interface, ^^^^ ^^is the distance from the interface to the cell centre, and the subscript i and j indicate the fluid on either side of the interface. • Mass transfer

[0084] The approach used by in this numerical model to calculate mass transfer in the battery is the same as has been used extensively in the literature. A scalar transport equation,in which ^^ is the mass concentration of lithium, captures the essential characteristics of the convection and diffusion of lithium into lead as ions are transported into the cathode. The key assumption when using this approach is that the height of the cathode changes by a small enough height during the computations that it can be neglected. This limits the timeframe of the computations to changes in molar fractions of no more than ∆ ^^^^ ^^= 0.1. If this condition is satisfied then the discharge voltages of the battery can be captured with errors as low as 0.5%.

[0085] Since there are no changes in height, the electric field does not change during the computations. The flux of ions, or gradient of the concentration field, can then be calculated using the current flux from the applied electric field. Faraday's law is applied at the cathode- electrolyte interfacein which ^^ is Faraday's constant, ^^^^ ^^is the molar mass of lithium and ^^̂ is the normal direction vector. • Heat transfer

[0086] In this model, the only source of heat is the joule heating from the discharge current. In a discharging LMB, the electrochemical reactions act as additional sources and sinks for heat; however, these are not well defined and accounting only for joule heating gives an accurate estimate for the temperature gradients in the battery. The energy equation is used to this end,in which ^^ is the thermal conductivity, ^^0is the reference density and ^^^^is the specific heat capacity. This equation is coupled between regions with a Dirichlet-Neumann boundary condition such that the temperature at the interface is given byin which ^^^^is the temperature at the interface, ^^^^ ^^is the temperature at the cell centre adjacent to the interface and ^^^^ ^^is the thermal conductivity at the cell centre adjacent to the interface. To solve this equation, it was assumed that the sidewalls of the LMB are thermally non-conducting, an assumption easily justified by the low thermal conductivity of Al2O3, andthat the top and bottom boundary maintain a constant temperature equivalent to the operating temperature of the battery, ^^ = 500oC. • Fluid dynamics

[0087] The incompressible formulation of the Navier-Stokes and continuity equations are used to model the fluid flow in the layers,)∇ ∙ ^^ = 0 (18) in which ^^ is pressure, ^^^^is the Lorentz body force, z is the coordinate vector and g is the gravitational acceleration vector. The Lorentz body force is given by ^^^^= ^^ × ^^ (19)

[0088] These equations are solved by assuming that the interfaces between the layers are impermeable and unmoving. This assumption appears to be valid as in the experiment there was no visible deformation or vibration of the interface. The state of each layer is solved individually on its own mesh with momentum transferred between the layers through a boundary condition at the interface that accounts for the viscous coupling between layers. For completeness, it is given as follows; the coupled velocity at an interface is given by ^^^^ ^^= ^^^^ ^^(22)^^ ∙ ^^ = 0(23)^^1∇ ^^^^ ^^∙ ^^^^= ^^2∇ ^^^^ ^^∙ ^^^^(24)in which ^^^^is the velocity at the coupled interface, ^^^^is the tangential velocity at the cell centre adjacent to the interface, ^^^^ ^^is the tangential velocity at the face, n is the normal vector and ^^ is the dynamic viscosity. Combining equation (23) and (24) gives ^^^^ ^^− ^^^^ ^^^^^^ ^^− ^^ ^^1= ^^^^ ^^2(25) ^^1^^2

[0089] Rearranging for ^^^^ ^^gives ^^^^ ^^= ^^ ∙ ^^^^ ^^+(1 − ^^)∙ ^^^^ ^^(26)in which w is the weighting factor given by)

[0090] Since a tangential velocity can be defined as^^^^= ^^ ∙(^^ − ^^ ^^) (28)The boundary condition for the velocity at the interface can then be written as= ( ^^ − ^^ ^^) ∙ ( ^^ ∙ ^^^^+ (1 − ^^) ∙ ^^^^) (29) in which I is the identity matrix. For all other surfaces, a no-slip boundary condition is used. Explicitly estimating cell potential

[0091] Estimation of the electrochemical performance of the cell is quantitatively determined by explicitly estimating the cell potential from the interfacial concentration. Since the electrochemical potential of batteries is an interfacial phenomenon, the first step is to determine the average interfacial concentration which can be defined asin which 〈ψ〉^^is the instantaneous average interfacial concentration, ^^^^is the radius of the cathode, and ^^^^indicates that the integral is taken at the cathode-electrolyte interface. The next step is to determine the molar fraction of lithium at the interface where)is the molar fraction of lithium and n is the number of moles. This requires the computation of the number of moles in each cell volume which is unknown. However, the concentration at each cell volume is computed so substituting for the concentration usingin which ^^^^is the cell volume gives)which can be computed since an operating principle of the numerical model is that the lead concentration remains the same throughout the volume in time. The open circuit voltage (OCV) is then interpolated data determined at molar fractions of lithium in lead ( ^^^^ ^^) between 0.025 and 0.965. The nominal voltage of the battery can be determined by taking the time integral of the surface concentration data using:

[0092] Another key parameter is the volume averaged concentration which can be determined by taking the volume integral of the concentration field:)which then allows the divergence of the interfacial concentration from the volume concentration to be computed usingIn a similar manner the mass transport overpotentials can be estimated by substituting the surface and volumetric potentials into equation (33). So that the additional parasitic losses of the coil can be quantified and used to estimate a true performance of the modified design the ohmic overpotentials of the coil are calculated usingin which ^^^^ ^^ ^^ ^^is the length of the coil which is taken as 0.0768 m and can be estimated from Figure 1. Convergence

[0093] The convergence of the numerical model was determined by comparing the divergence of the concentration at the cathode-electrolyte interface from the volumetric concentration for 160 seconds of computation time for three different mesh sizes in the model with a 10 mm cathode layer height. Table 3 shows that a mesh with quadrilaterals with a side length 1.25 × 10−4m is converged for interfacial concentration. This mesh was used to analyse the performance of the battery. The non-uniform mesh has better resolution particularly around the current collector and so this discretisation was used to analyse the dynamics of the flow. For each case the mesh was purely quadrilateral and structured with five additional layers applied around the walls to resolve the boundary layer. Table 3. Convergence study for the numerical modelling. The mesh in the electrolyte and anode were similarly refined during each study. Number of cellsPercent in the cathode difference (%) Cell side length (m) layer 1.5 × 10−427,000 13.132 - 1.25 × 10−437,000 13.482 2.63 8.5 × 10−5− 1.35 × 10−4 46,000 13.495 0.1

[0094] Table 5 shows the mesh sizes used for the additional cases. Since the numerical domain was complex, a variable time step was used to ensure efficient use of computational resources. So that the computations remained fully resolved in time, two constraints were set on the timestep size; the courant number was limited to a value of 0.5, and the maximum timestep that could be taken was ^^ = 2.5 × 10−4^^. Due to these constraints on the step size typical courant numbers were found to be in the range of 0.2-0.4. A second order accurate discretisation scheme was used with linear interpolation for all terms and the backwards Euler time scheme and a convergence criterion of 1 × 10−8. The concentration fields were solved with a fourth order cubic scheme. The PIMPLE method, which is a combination of the semi- implicit method for pressure linked equations and pressure-implicit with splitting of operator’s method, was used to solve the pressure equation. Owing to the explicit coupling with the velocity fields, at every time step the equations in each region were solved three times with two pressure corrector steps during each solution. Table 5. Mesh size used for the computation of each case Case Cell side length (m) 5,000 A / m21.25x10-43,000 A / m21.25x10-410,000 A / m27.50x10-55,000 A / m2Large Capacity 1.25x10-4Axisymmetric Experiment 6.5x10-5Experiment

[0095] The design was tested using a lab-scale prototype and PIV with the setup illustrated in Figure 2. The coil in the experiment was machined from copper and mounted in an acrylic fitting with the copper current supply. Both the copper current supply and coil were isolated from the working fluid using an acrylic vinyl coating. The diameter of both the coil and current supply were ^^ = 3.2 mm and the thickness of the acrylic vinyl coating was determined as being 0.2 mm. The coil and current supply were then connected in series such that the current delivered to the current supply travelled through the coil first, generating a vertical magnetic field. The acrylic fitting was mounted in a copper plate using an interference fit. The copper plate served as the current collector and the current was forced to enter the working fluid owing to the insulation provided by the acrylic fitting and acrylic vinyl coating before exiting through the copper plate. The vessel, which was made from cast Plexiglas with an internal diameter of ^^ = 44 mm, was mounted directly on top of the copper current collector.

[0096] The working fluid used was the alloy Galinstan at a composition of Ga67In20.5Sn12.5. The laboratory temperature during the experiments was determined as ^^ = 22.6oC at the time of the experiments. The material properties of Galinstan at this temperature are ^^ =3.27 × 106S / m, ^^ = 6440 kg / m3, ^^ = 3.302 × 10−7m2 / s. Upon exposure to the atmosphere, liquid metals form an oxide coating on the external surfaces which gives boundary conditions close to no-slip. To dissolve this oxide coating a thin layer of 6.4% HCl solution was added to the surface. This concentration was used as it enables the oxide formed on the surface of the liquid metal to be dissolved at a rate faster than the rate of reaction with any oxygen absorbed in the acid solution. The material properties of HCl at this temperature are ^^ = 1045.14 kg / m3and ^^ = 1.016 × 10−6m2 / s.

[0097] To take the PIV measurements the HCl was seeded with silver coated glass microspheres with a diameter of 12 − 15 μm and a density of 1.00 g / cm3. The silver coated glass microspheres are particularly well suited to being the seeding particle in HCl as silver will not react with low concentrations of HCl. A laser light was directed through the HCl layer allowing the silver coated particles to scatter light during the experiment. A Nikon D850 was mounted perpendicular to the layer and footage of the fluid was taken at a frame rate of 120 frames per second, fps, with a shutter speed of 1 / 240 s, and an fstop of 2.8. The footage from the D850 was corrected for both tangential and radial distortion using 450 images of a checkerboard pattern taken before each run. These images were also used to determine the pixel to distance ratio. The height of the checkerboard pattern was ℎ = 11 mm from the top surface of the copper current collector which means that the camera was focussed at ℎ = 11 mm, or the mid-height of the HCl layer, during the experiment. After correction, the images were analysed in PIVlab using interrogation windows of 128x128, 64x64, 48x48 and 32x32 pixels with 50% overlap. Linear correlation was used, and the final pass was repeated until the quality slope of the correlation coefficient was 0.025. After the frames were analysed, spurious data was removed using two filters: a standard deviation filter and a local median filter. Following this any vectors that remained with a low correlation coefficient were removed and interpolation was performed from the surrounding data. These filters only removed a limited number of vectors per frame, and these were often located around the perimeter of the Galinstan where the high surface tension of the fluid caused strong curvature which created either reflections or a drop in luminosity depending on the location of the laser. Key Parameters

[0098] All simulations performed in this work are axisymmetric. That is to say that the z-axis is taking to be the axis of rotational symmetry and the velocity components are ^^( ^^, ^^, ^^). This allows key global parameters to be defined as follows:where u is the volume averaged velocity magnitude. The poloidal velocity magnitude can be defined as:where ^^^^and ^^^^are the flow components parallel and perpendicular to the axisymmetric axis. Considering that the axisymmetric axis is vertical, the poloidal flow is important for mass transfer as it is responsible for the removal of ions from the cathode-electrolyte interface. The toroidal velocity magnitude is defined as:where ^^^^is the component of flow that rotates around the axisymmetric axis. Finally, the improvement of the old design over the new design is expressed using the formula for percent change × 100 % (41)in which ^^ is the value and the subscripts 1 and 2 represent the old and new values respectively. Results and discussion • Performance

[0099] The computations were performed at current densities of 0.3, 0.5, and 1 A / cm2. For the 0.3 and 0.5 A / cm2cases the computations reached a change in molar fraction, ∆ ^^^^ ^^, of 0.1. The 1 A / cm2and the large capacity case were considerably more computationally expensive and were only computed until the behaviour of the interfacial concentration could be resolved. In all cases, the discharge current was determined using the interfacial area of the cathode- electrolyte interface. The current was then applied to the coil with a simplifying assumption that the current was homogenous and completely azimuthal. This means that as the current in the cases changed, the magnetic field also changed proportionally. The reference cases were computed by assuming that there was no flow in the electrode.

[0100] In the reference cases, once the computations began the interfacial concentration diverged from the volumetric concentration sharply. Indeed in Figures 3(a) – (d), throughout the time computed, the gradient of the interfacial concentration was always higher than that of the volume-averaged concentration. That is to say that the surface averaged interfacial concentration increased faster than the volumetric averaged concentration. In LMBs, the ionicdiffusion coefficient is small, in the order of ~ 1 × 10−8m2 / s. This means that the diffusion of ions away from the interface is slow. In fact, it is much slower than the mass flux of ions into the cathode which is typically high in the batteries because of the low ohmic overpotentials and fast reaction kinetics. As the discharge current of the battery increased, the divergence of the interfacial concentration from the volumetric concentration also increased. This occurred because the flux of ions into the cathode increased, while the diffusion coefficient remained the same. The difference between the interfacial concentration and volume-averaged concentration for the 0.5 and 0.3 A / cm2cases after a delta ∆ ^^^^ ^^of 0.1 is 124.83 and 82.97 kg / m3, respectively. The time frame for the 1 A / cm2was considerably shorter but comparing the divergence of the interfacial concentration from the bulk concentration between the three current densities at the same molar fraction the concentration for 1 A / cm2was 86.3 kg / m3while it was 58.76 and 43.75 kg / m3for the 0.5 and 0.3 A / cm2cases respectively. Similarly, the large- capacity cell also exhibits higher concentration polarisation between the interface and bulk of the fluid at the same molar fraction, although this is caused by an increase in discharge time. These results are reflected in the literature multiple times.

[0101] These trends were not repeated in the modified LMB. In Figures 3(a) – (d) there was an initial transient period in which the concentration at the interface matched the diffusion cases. After this initial transient period, the flow induced by the coil mixed the cathode, clearing ions away from the interface. The design of the present invention had significantly lower concentration polarisations in the cathode; the divergence of the interfacial concentration decreased by 80.64% for the 0.3 A / cm2cases and 87.64% for the 0.5 A / cm2cases. Further, over the time frame of the computations, the concentration at the interface increased linearly as the volume averaged concentration increased. The mixing was unaffected by the density stratification due to the Pb(Li) alloy and the rate of mixing equalled the rate of ion flux. The two cases presented here have an areal capacity of 3.75 Ah / cm2and 7.5 Ah / cm2which is a 7.5 hour and 15 hour discharge time at 0.5 A / cm2. This indicates that if the flow remains unaffected, a LMB utilising this design could achieve complete capacity utilisation discharging at lengths suitable for long duration storage applications such as renewable energy arbitrage.

[0102] The results were analysed to see how the average surface interfacial concentration was affected by the changing discharge current density. After a ∆ ^^^^ ^^of 0.1, the difference between the interfacial and volume concentrations were 16.09 and 15.43 kg / m3for the 0.3 and 0.5 A / cm2cases, respectively. The surface averaged concentration at the final ∆ ^^^^ ^^for the 1 A / cm2case was 7.31 kg / m3compared to 13.94 and 17.63 kg / m3for the 0.3 and 0.5 A / cm2cases at the same molar fraction. From this, it is clear that the design of the present invention was unaffected by the increase in mass flux at higher current densities and, at 1 A / cm2, there is animprovement in the surface averaged concentration. This behaviour was unexpected but occurs because the mixing rate increased faster than the mass flux. Taking the scaling laws in literatures the velocity scales as either

[0103] Increasing the current density by a factor of 2 will also increase the magnetic field by a factor of 2 since the discharge current is channelled through the coil. Substituting these factors into the scaling laws, the velocity will increase by either 2.52 or 2.16, while doubling the discharge current will only lead to a doubling of the mass flow rate. This means that when discharging at higher current densities there is no additional mass-transport overpotential penalty.

[0104] In Figure 3(d) the larger capacity cell displays slightly higher interfacial concentrations than the other cases, but the coil still mixed the cathode successfully. The longer time to velocity saturation in the cathode due to the larger volume caused the higher concentrations. Before the velocity saturated, ions accumulated at the cathode-electrolyte interface until the mixing rate matched the mass flux rate.

[0105] The changes to the interfacial concentrations in the design of the present invention have significant impacts on the electrochemical performance. Since mass transport overpotentials are coupled to the divergence of the concentration at the interface they are similarly reduced; there is a 78.31% reduction for the 0.3 A / cm2case and an 85.29% reduction for the 0.5 A / cm2case. This leads to an improvement in the voltage of the battery with the nominal OCV increasing by 6.32% and 9.55% for the 0.3 and 0.5 A / cm2cases, respectively. The difference between the references cases and the modified cases are much more significant at a ∆ ^^^^ ^^= 0.1 (see Tables 6 and 7) and if the full discharge cycle were modelled it can be expected that the differences would be much larger. The voltage increases should create much larger improvements in energy efficiency over a complete charge / discharge cycle. Table 6. Divergence of the interfacial concentration from the volume averaged concentration ∇ψ at ∆xLi= 0.1 ( ^^ ^^ / Decrease (%) Case ^^3) Diffusion 0.3 ^^ / ^^ ^^282.97 - 0.3 ^^ / ^^ ^^216.09 80.64 Diffusion 0.5 ^^ / ^^ ^^2124.83 - 0.5 ^^ / ^^ ^^215.43 87.64Table 7. Electrochemical performance of the reference cases and the design of the invention Nominal Coil Net Percent OCV at Percent Overpot Percent OCV (V) ohmic nominal increase ∆ ^^^^ ^^= increase entials decreas overpot OCV (V) (%) ^^. ^^ (%) = e (%) entialCase (V) Diffusion 0.4811 - 0.4811 - 0.4489 - 0.0590 - 0.3 ^^ / ^^ ^^20.3 0.5208 0.0093 0.5115 6.32 0.4859 8.24 0.0128 78.31 ^^ / ^^ ^^2Diffusion 0.4618 - 0.4618 - 0.4243 - 0.0836 - 0.5 ^^ / ^^ ^^20.5 ^^ 0.5214 0.0155 0.5059 9.55 0.4802 13.17 0.0123 85.29Flow Dynamics

[0106] This section will analyse the results from the 0.5 A / cm2case in depth as it had the most distinct dynamics. The flow induced by the coil and current collector created the improved operating conditions in the battery. As has been observed in past studies, the vertical magnetic field from the coil created a swirling flow which led to vigorous mixing. In typical swirling flows, the toroidal component of the velocity is an order of magnitude higher than the poloidal component. Here, the poloidal component of the flow dominated the dynamics. Figure 4(a) quantifies the magnitudes of the toroidal and poloidal components observed, showing that the poloidal flow was typically twice the magnitude of the toroidal component.

[0107] Figures 4(b) and 4(c) depict the flow morphology. It consisted of a rapidly rotating jet with a characteristic velocity of 0.067 m / s. The jet was dominated by a vertical action that created vortices that attached to the interface. These vortices removed ions from the interface, enhancing mixing in the cathode. The interfacial vortices' impact is visible on the interfacial concentration which oscillates in Figure 3.

[0108] The vortices were created by the centrifugal instability commonly observed in Taylor- Couette flow. During discharge the flow displayed cyclic behaviour. First, the fluid between the coil and current collector accelerated. This acceleration was driven by the Lorentz force from the vertical magnetic field and horizontal current and was mainly toroidal. The resulting centrifugal force pushed the flow out radially, leading to an acceleration in the poloidal velocity. This is evident in Figure 4(a) which shows that the maxima of the toroidal flow were out of phase with the maxima of the poloidal flow. Taylor vortices have been found to be present in swirling flows in the battery in past works. The main difference between those found in thiswork and that the past is that the geometrical configuration of the coil and current collector forced the vortices to travel along the interface.

[0109] Like the Taylor vortices studied in the literature, the vortices observed here have temporal coherence. There is a clear periodicity in the velocity fluctuations in Figure 4(a) as well as the interfacial fluctuations in Figure 3(b). A Fourier analysis was conducted on the data to capture the peak frequencies of the flow. First, the interfacial concentration was non- dimensionalised by dividing by the volumetric averaged concentration, ψ∗^^^^, with the result shown in Figure 4(d). Then, a fast Fourier transform of the data was performed and the result is plotted in Figure 4(e). There are two peak frequencies at 0.0637 and 0.0771 Hz. Two peak frequencies are found due to the small amount of data used to resolve the pattern and a longer sampling time would likely see these two frequencies collapse into a signal peak. These frequencies represent the rate at which the interfacial vortices are generated, clearing reactants away from the interface. While this section focussed on the data for the 0.5 A / cm2case, the oscillatory behaviour in the flow and concentration profiles can be observed at all current densities (see Figure 3). At 0.3 A / cm2the vortices were smaller and confined to a smaller central region in the cell. At 1 A / cm2, and in the large capacity cell, the vortices were generated at a higher frequency owing to the increased turbulence of the system. Prototyping and testing

[0110] To test the feasibility of the design a lab scale prototype was constructed. This allowed several aspects of the design to be evaluated, such as whether the coil can be easily electrically insulated from the liquid metal and whether the magnitudes of the flow shown in the numerical model are reproduced in an experiment. Using the method detailed above, PIV was carried out to quantitatively measure the flow induced by the coil.

[0111] For each experimental case a 32 A current, equivalent to the discharge current in the 0.5 A / cm2case, was supplied to the coil which was electrically connected in series to the current supply. The coil and current collector were implanted in a layer of Galinstan creating a flow that was initially axisymmetric as shown in Figure 5(a). The flow was concentrated in the central region confined by the current collector and rotated in a counter-clockwise direction with a velocity of 0.029 m / s. As the velocity in the layer accelerated the symmetry of the flow was broken as shown in Figure 5(b). This corresponded with a dip in the averaged velocity shown in Figure 5(c). This break in symmetry of the flow was caused by the flow achieving a higher azimuthal wave number than ^^ = 1 which is an axisymmetric wave number. Figure 5(c) shows the velocity at t=180s and it is clear that once the velocity in the layer saturated it still had a three-dimensional structure. In Figures 5(a) – 5(c) the eye of the vortex can be seen to belocated at different positions away from the origin. During the experiment it was found that the eye of the vortex precessed counter-clockwise, which matched the direction of the flow. It is possible that if this motion occurred in a cathode layer it could increase the mixing in the cathode. From these results it seems reasonable that a similar setup could be achieved in an LMB.

[0112] An axisymmetric model of the experiment was computed using the geometry presented in Figure 2. In Figures 5(d) and 5(e) the surface averaged velocity and maximum velocity from the experiment and simulation are presented. In the figures, the velocity in the experimental case fluctuates significantly more than the data from the axisymmetric model showing that the numerical data is much steadier than the PIV data.2D axisymmetry forces the flow to be symmetric when it may not be in a 3D model. This can cause the flow in the 2D model to have laminar boundary layers at higher Reynolds number than when they transition to turbulence in 3D models. There are also additional non-axisymmetric components to the model in the lab including the way the coil is mounted and the Earth’s background magnetic field which can have a large effect on magnetically driven flow.

[0113] However, axisymmetric models can still accurately capture the magnitude of the flow induced by a swirling flow even at high current densities and magnetic field strengths. To generate data from the numerical model that matched the experiment a slice was taken at ℎ = 0.011 m and the average was taken using a surface integral. It was found that at this height in the electrolyte layer, the average velocity was 0.0125 m / s which was lower than that found in the experiment, which oscillated between 0.014 m / s and 0.016 m / s. Despite the low aperture used, it seems likely that a perfect slice in the electrolyte was not captured but rather a volume. A volume average of the flow from ℎ = 0.011 − 0.012 m in the electrolyte layer yielded a much closer match to the experimental data with the average from the experiment oscillating around 0.015 m / s.

[0114] The maximum velocity at ℎ = 0.011 m compared much more favourably to the experiment. A weighted average filter was used with a window size of 25 values. This corresponded to the size of the interrogation windows used to analyse the flow. It was found that the maximum velocity in the simulations remained steady at 0.035 m / s. The maximum velocity in the experiment oscillated over a wide range of values with velocity from 0.03 to 0.04 m / s. The value from the simulations is clearly very close to the median value of the experiment. The oscillations in the experiment are caused by the unsteady three-dimensional nature of the flow. These results show that the numerical model used captures the magnitudes of the flow well.Battery module design

[0115] Figure 6 presents a battery module and cell stack (assembly) concept. Several components remain similar to current designs. The layers are still electrically isolated from the sidewalls through the use of an Al2O3 hollow cylindrical sleeve, the battery vessel is made from grade 304 stainless steel, the current collectors between vertically adjacent cells are coupled allowing the modules to be vertically stacked and the vessels can still make electrical contact through the sidewalls allowing them to operate in parallel. By maintaining these components of current designs existing production lines and cell construction methods can be leveraged.

[0116] To minimise additional manufacturing costs the current supply and coil could be manufactured at scale using sand or die casting. Both methods offer an efficiency at scale and are particularly suited to mass production for parts made using copper. This would allow for the low cell costs to be maintained. With the gains to the power density of LMBs utilising this coil there should be no increase to the costs per kilowatt hour.

[0117] The coil and current supply could foreseeably become a wear item in the cell as other works in DC electric arc furnaces have shown that electrodes exposed to liquid metal flows can be worn away over time. The ceramic coating, however, is identical to the insulation currently used in LMBs. It should be reasonable to expect that the batteries will maintain the same lifespan regardless of this modification.

[0118] If a coil fails or begins to short circuit by bolting on the top and bottom lids, the internal components of the cell remain accessible. A particularly advantageous aspect of current LMB cell-module designs is that they are modular. If a single cell fails, it can be removed and replaced with relative ease.

[0119] Although the invention will be described with reference to specific examples it will be appreciated by those skilled in the art that the invention may be embodied in many other forms.

Claims

THE CLAIMS DEFINING THE INVENTION ARE AS FOLLOWS:- 1. A liquid metal battery, comprising: a negative current collector; a positive current collector; a liquid metal negative electrode in electrical communication with the negative current collector; a liquid metal positive electrode having a height and in electrical communication with the positive current collector; a liquid electrolyte in electrical communication with the negative electrode and the positive electrode; and a flow inducer configured to induce a swirl flow in the positive electrode by generating a magnetic field.

2. The liquid metal battery according to claim 1, wherein the flow inducer is embedded in the positive electrode.

3. The liquid metal battery according to claim 1 or claim 2, wherein the flow inducer comprises a metal coil.

4. The liquid metal battery according to claim 3, wherein the metal coil is a single loop metal wire.

5. The liquid metal battery according to claim 3 or claim 4, wherein the metal coil is a copper coil.

6. The liquid metal battery according to any one of claims 1 to 5, wherein the flow inducer and / or the positive current collector is at least partially coated with a coating having a magnetic permeability of at least about 1 x 10-4H / m, preferably between about 1 x 10-4to about 1.5 x 10-3H / m.

7. The liquid metal battery according to claim 6, wherein the coating comprises Nickel.

8. The liquid metal battery according to any one of claims 1 to 7, wherein the flow inducer is in electrical communication with the liquid metal battery.

9. The liquid metal battery according to claim 8, wherein the flow inducer is connected with the liquid metal battery in series to thereby generate the magnetic field from the battery’s discharge current.

10. The liquid metal battery according to any one of claims 2 to 9, wherein the flow inducer is embedded at same height of the positive electrode as the positive current collector extends in the positive electrode to.

11. The liquid metal battery according to any one of claims 2 to 10, wherein the flow inducer is embedded at about 10% to about 90% of the height of the positive electrode.

12. The liquid metal battery according to claim 11, wherein the flow inducer is embedded at about 30% to about 70% of the height of the positive electrode.

13. The liquid metal battery according to claim 12, wherein the flow inducer is embedded at about 50% of the height of the positive electrode.

14. The liquid metal battery according to any one of claims 1 to 13, wherein the positive current collector extends in the positive electrode to about 10% to about 90% of the height of the positive electrode.

15. The liquid metal battery according to claim 14, wherein the positive current collector extends in the positive electrode to about 30% to about 70% of the height of the positive electrode.

16. The liquid metal battery according to claim 15, wherein the positive current collector extends in the positive electrode to about 50% of the height of the positive electrode.

17. The liquid metal battery according to any one of claims 1 to 16, wherein the flow inducer is at least partially insulated from the positive electrode.

18. The liquid metal battery according to any one of claims 1 to 17, wherein thepositive current collector is at least partially insulated from the positive electrode.

19. The liquid metal battery according to claim 17 or claim 18, wherein the flow inducer and / or the positive current collector is insulated from the positive electrode using a ceramic coating.

20. The liquid metal battery according to any one of claims 1 to 19, wherein the negative electrode comprises an alkali or alkali earth metal.

21. The liquid metal battery according to any one of claims 1 to 20, wherein the positive electrode comprises a Group 12 element, Ga, In, Ti, Sn, Pb, Sb, Bi or Te.

22. The liquid metal battery according to any one of claims 1 to 21, wherein the electrolyte comprises an alkali metal halide or alkali earth metal halide.

23. The liquid metal battery according to any one of claims 1 to 22, having a discharge current density of between about 1000 to about 10000 A / m2.

24. The liquid metal battery according to any one of claims 1 to 23, having a discharge capacity of between about 200 to about 1000 Ah.

25. The liquid metal battery according to any one of claims 1 to 24, having an areal discharge capacity of between about 1 to about 50 Ah / cm2.

26. A battery assembly comprising a plurality of the liquid metal battery according to any one of claims 1 to 25.

27. A method of exchanging energy with an external device, comprising the steps of: i) providing an external energy exchanging device; ii) providing the liquid metal battery according to any one of claims 1 to 25, or the battery assembly according to claim 26; iii) providing electrical connections connecting the external energy exchanging device to the positive and negative current collectors; iv) inducing a swirl flow in the positive electrode by generating a magnetic field using the flow inducer.

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