Ultrasound Velocity Measurement in a Liquid Metal Electrode

Liquid metal batteries are a promising technology for providing large-scale energy storage on worldwide electrical grids¹. These batteries offer high energy density, high power density, long cycle life, and low cost, making them ideal for grid-scale energy storage³. Introducing liquid metal batteries to the energy grid would allow peak shaving, improve grid stability, and enable much more widespread use of intermittent renewable sources like solar, wind, and tidal power. Liquid metal batteries are composed of two liquid metal electrodes separated by a molten salt electrolyte, as described in greater detail in prior work¹. Though many different combinations of metals and electrolyte can result in a working liquid metal battery, the principles of operation remain the same. The metals are chosen such that it is energetically favorable for them to form an alloy; thus alloying discharges the battery, and de-alloying charges it. The salt layer is chosen so that it allows metal ions to pass between the two electrodes, but blocks transport of neutral species, thereby affording electrochemical control of the system.

This work will advance liquid metal battery technology by quantifying and controlling mass transport effects. The methods described here are informed by electrochemical methods developed for liquid metal batteries by Sadoway et al.^1–4 as well as earlier liquid metal battery work at Argonne National Laboratory^5,6, and the work of the broader electrochemical community (Bard and Faulkner⁷ provide many relevant references). The methods described here also build upon prior fluid dynamics studies. Ultrasound velocimetry was developed and first used in water^8,9 and has since been applied to liquid metals including gallium^10,11, sodium^12,13, mercury¹⁴, lead-bismuth¹⁵, copper-tin¹⁵, and lead-lithium¹⁶, among others. Eckert et al. provide a useful review of velocimetry in liquid metals¹⁷.

Recent work using methods similar to the ones described here¹⁸ has shown that battery currents can enhance mass transport in liquid metal electrodes. Because mass transport in the positive electrode is the rate-limiting step in charge and discharge of liquid metal batteries, mixing therefore allows faster charge and discharge than would otherwise be possible. Moreover mixing prevents local inhomogeneities in the electrode, which can form solids that limit the cycle life of a battery. In ongoing work, we continue to study the role of fluid flow in the positive electrode of the liquid metal battery, which arises because of thermal and electromagnetic forces. Thermal gradients drive convective flow through buoyancy, and battery currents drive flow by interacting with the magnetic fields induced by the battery currents themselves. In experiments using the methods described below, we have observed flows with Reynolds number 50 < Re < 200, calculated from the electrode depth and root-mean-square velocity. A thorough experimental characterization is being undertaken and will use the resulting data set to build predictive battery models. The focus of this manuscript is on the experimental design and procedures required to produce such data. Ultrasound velocimetry provides the bulk of the measurements, and experimental conditions must be carefully controlled in order to use ultrasound successfully in liquid metal. High temperature, chemical activity, and electrical conductivity must all be managed carefully.

First, liquid metal batteries necessarily operate at high temperature, because both metals and the salt that separates them must be molten. One promising choice of materials, which uses lithium as the negative electrode, lead-antimony as the positive electrode, and a eutectic mix of lithium salts as the electrolyte, requires temperatures around 550 °C. Measuring the flow of an opaque fluid at such high temperatures is quite difficult. High-temperature ultrasound transducers, which separate the delicate electro-acoustic components from the test fluid with an acoustic waveguide, have been demonstrated¹⁵ and commercialized. However, because the transducers have insertion loss near 40 dB, and because of the general difficulty of working at such temperatures, a surrogate system has been chosen for initial study: a liquid metal battery may also be made using sodium as the negative electrode, eutectic 44% lead 56% bismuth (hereafter, ePbBi) as the positive electrode, and a triple eutectic mix of sodium salts (10% sodium iodide, 38% sodium hydroxide, 52% sodium amide) as the electrolyte. Such a battery is entirely molten above 127 °C, making it much more amenable to laboratory study. Because it is composed of three liquid layers separated by density, it is subject to the same physics as other liquid metal batteries. And it is compatible with readily available ultrasound transducers, which are rated to 230 °C, involve no waveguide losses, and cost much less than high-temperature transducers. These experiments typically take place at 150 °C. At that temperature, ePbBi has viscosity ν = 2.79 x 10^-7 m²/sec, thermal diffusivity κ = 6.15 x 10^-6 m²/sec, and magnetic diffusivity η = 0.8591 m²/sec, such that its Prandtl number is Pr = ν/κ = 4.53 x 10^-2 and its magnetic Prandtl number is Pm = ν/η = 3.24 x 10^-7.

Though this low-temperature liquid metal battery chemistry makes flow studies much easier than they would be in hotter batteries, temperature must nonetheless be managed carefully. Being delicate electro-acoustic devices, ultrasound transducers are susceptible to damage by thermal shock, and therefore must be heated gradually. High-quality ultrasound measurements also require careful temperature regulation. Ultrasound velocimetry works like sonar, as shown in Figure 1: the transducer emits a beep (here, the frequency is 8 MHz), then listens for echoes. By measuring the time of flight of the echo, the distance to the echoing body can be calculated, and by measuring the Doppler shift of the echo, one component of the body’s velocity can also be calculated. In water, tracer particles must be added to produce echoes, but no tracer particles are required in liquid metals, a fact that is not understood in detail but is typically attributed to the presence of small metal oxide particles. Each measurement is an average over all tracer particles in an interrogation volume; in this work, its minimum diameter is 2 mm, at a distance 30 mm from the probe. Though oxidation may eventually limit the duration of experiments, using the methods described below, we have made measurements continuously for as long as 8 hr.

Calculating either distance or velocity requires knowing the speed of sound in the test fluid, and that speed varies with temperature. The work described here focuses on flow in the ePbBi negative electrode, where the speed of sound is 1,766 m/sec at 150 °C, 1,765 m/sec at 160 °C, and 1,767 m/sec at 140 °C ¹⁹. Thus inadequate temperature control would introduce systematic errors in the ultrasound measurements. A device was constructed to measure the speed of sound in ePbBi, finding values consistent with those published and accepted by the Nuclear Energy Agency¹⁹ (see below). Finally, since thermal convection is a primary driver of flow in liquid metal batteries, both the mean temperature and the temperature difference between the top and bottom of the ePbBi electrode directly affect observations. For consistent results, precise thermal control is essential.

Accordingly, temperature is measured continually with at least three K-type thermocouples, logging their measurements electronically with a computer-based acquisition device and a custom-written LabView program. The program also controls the power supply that provides battery current, via a USB connection; logs the battery current and voltage; and sends trigger pulses to the ultrasound instrument, so that its data can be synchronized with the other measurements. A system diagram is shown in Figure 2. Heat is provided by a custom-built furnace (also shown in Figure 2), which contains two 500-W industrial heating elements powered by a relay switched by a proportional-integral-differential (PID) controller. The base plate that supports battery cells is made of solid aluminum; because its thermal conductivity is an order of magnitude higher than the thermal conductivity of the stainless steel battery cell vessel and the ePbBi it contains¹⁹, the temperature of the furnace floor is approximately uniform. Moreover the aluminum base doubles as a path for the electrical currents passing through the electrode. Its electrical conductivity is also an order of magnitude higher than that of stainless steel or ePbBi, so the voltage of the furnace floor is also approximately uniform. Insulating legs separate the base from the bench top below, preventing burns and shorts. The sides of the battery vessel are insulated with silica ceramic insulation, cut to fit the vessel closely but leave room for accessing the cell’s ultrasound port. Finally, a polytetrafluoroethylene (PTFE) lid insulates the cell from above and holds the negative current collector and thermocouples in place. Though commercially-available hot plates can achieve the temperatures required for these experiments, our custom-built furnace maintains temperature with an order of magnitude less variation, and also allows us to measure heat power directly.

In addition to challenges associated with temperature, there are challenges associated with chemical activity. At 150 °C, an ePbBi positive electrode is chemically compatible with many common materials. A sodium negative electrode, however, corrodes many materials, oxidizes readily, and reacts vigorously with moisture. A lithium negative electrode is also aggressive, especially because lithium-based liquid metal batteries typically run at much higher temperatures. Though those higher-temperature systems are outside the scope of this work, many of the same measures for managing chemical activity are used here as in those systems. All experiments described here take place in an argon-filled glovebox containing only trace amounts of oxygen or moisture. The battery vessel is made from alloy 304 stainless steel, which corrodes minimally even with lithium at 550 °C. The thermocouples and negative current collector are also made from stainless steel. The vessel geometry is chosen to match vessels used for electrochemical testing of liquid metal batteries, to model as closely as possible the systems that are being commercialized. The vessel, shown in Figure 2, is cylindrical, with an 88.9 mm inner diameter and a 67 mm depth. All vessel walls are 6.4 mm thick. The vessel differs from those used for earlier experiments, however, in that it has an ultrasound port. The port passes through the side wall along a horizontal diameter of the cylinder, and the center of the port is 6.6 mm above the vessel floor. The port is 8 mm in diameter to accommodate an 8 mm ultrasound transducer, and seals around the transducer with a swage. In these experiments, the liquid metal electrode is just deep enough to cover the ultrasound transducer, typically 13 mm.

In order to achieve strong ultrasound signals, one requires good acoustic transmission between the ultrasound transducer and the fluid it probes (ePbBi). Maximum acoustic power is transmitted when the acoustic impedance of the transducer material and the test fluid are identical; when the impedances differ, signals suffer. Placing an ultrasound transducer in direct contact with clean ePbBi (as made possible by the port described above) provides ample signal, often for hours at a time. Metal oxides, however, have very different impedance, and may also interfere with wetting by altering the surface tension. If the ePbBi is substantially oxidized, ultrasound signals degrade and soon disappear. Again, an inert atmosphere is essential. If trace amounts of oxygen cause some oxidation nonetheless, the surface of the metal oxide is skimmed before transferring ePbBi into the battery vessel.

Finally, these experiments present challenges because of the presence of electrical currents. Though the currents are our central scientific and technological interest, they are large enough (30 A) to cause damage if incorrectly routed. Ungrounded thermocouples ensure that harmful electrical currents do not pass through the data acquisition device or the computer that supports it, because ungrounded thermocouples have no internal electrical connection from the protective sheath to either signal wire. Likewise it is essential to use ungrounded ultrasound transducers (Signal-Processing SA, TR0805LTH) to prevent stray current from damaging the valuable ultrasound instrument (Signal-Processing SA, DOP 3010). As mentioned previously, the base of the furnace serves to conduct electrical current, and must also be electrically isolated from its surroundings.

In the ePbBi electrode, current causes ohmic heating, potentially disrupting the temperature. Thus the automated thermal control system must be able to adjust to changes in heat input. Figure 3 shows how the temperature of the ePbBi electrode varies as current flows through it, and how the PID controller adjusts to compensate. Maintaining steady temperature with large currents (50 A = 800 mA/cm) would require additional cooling, but at the lower currents more realistic for liquid metal batteries in industrial applications (typically 17 A = 275 mA/cm ¹), the controller is able to compensate for ohmic heating and hold temperature variation to 2 °C.