Solutal buoyancy and electrovortex flow in liquid metal batteries

Abstract

Solutal buoyancy has a large impact on the flow of the alloy phase composing the positive electrode in liquid metal batteries. During discharge solutal buoyancy creates a stabilizing stratification, during charge it creates a vigorous solutal convection. In this article we provide new physical understandings of the role of solutal buoyancy during both charge and discharge. In particular we find that during discharge the electrovortex mechanism is in general not strong enough to counter the stabilizing effect of solutal buoyancy, and therefore this mechanism cannot be used to mix the alloy as is sometimes suggested in the literature. We show that the mixing capability of a generic flow in the alloy phase can be estimated by comparing the typical flow magnitude U to two velocity scales: U p and U m . Below U p the flow cannot mix the alloy, and above U m the flow significantly opposes solutal buoyancy. Although we focus on Li||Pb-based batteries, these simple mixing criteria can be used during the discharging phase in other types of liquid batteries. We also present new, fully three-dimensional simulations of solutal convection during the charging cycle. These simulations suggest scaling laws for the magnitude of the convective flow, the time for the onset of solutal convection, and the typical inhomogeneity level in the alloy during charge. We propose physical arguments to explain these scaling laws.

Efficient mixing by swirling electrovortex flows in liquid metal batteries

“…The relevance of these velocity scales in the mixing problem has been supported by numerous numerical simulations in Herreman et al. (2020). Using this model together with a scaling law for the typical intensity of non-swirling electrovortex flows, we have verified that non-swirling electrovortex flows that are such that cannot enhance mixing during discharge.…”

“…2019; Herreman et al. 2020; Weber et al. 2020), we investigate in this paper how swirling electrovortex flows occurring in the alloy can enhance the mixing therein and, hence, prevent the formation of the inhomogeneous alloy layer at the alloy–salt interface.…”

“…The density difference can be as large as a few thousand (Herreman et al. 2020). This is a very large number compared to what thermal buoyancy could create.…”

“…In our first study (Herreman et al. 2020) we have investigated the mixing capabilities of non-swirling electrovortex flows in LMBs. Referring to figure 1( b ), the Lorentz force drives a predominantly poloidal electrovortex flow with when there is no external magnetic field ().…”

“…We finally combine this scaling law with the criterion for efficient mixing, , derived in Herreman et al. (2020) to find the minimal external magnetic field strength that yields enhanced mixing. Our numerical simulations show that this criterion is accurate.…”