Electrolyte Convection in Liquid Metal Batteries

Liquid metal batteries (LMBs) are
electrochemical energy storage devices featuring two liquid metal
electrodes divided by a fused salt electrolyte. Convection in the
electrolyte is typically assumed to be quite intense because it has
the by far lowest electrical conductivity of all three layers and is
therefore subject to strong Joule heating under typical current
densities. Given the central role of the electrolyte for the LMB's
performance characteristics and the consequences of typical
assumptions (e.g., no mass transport limitations for charge transfer),
it is worthwhile to investigate convection in this layer in detail.
Doing this by means of numerical simulations performed using the free
software library OpenFOAM is the
purpose of the contribution at hand.

Thermally driven convection in the electrolyte means first and
foremost internally heated convection that is of importance for topics
as diverse as mantle convection, nuclear reactor engineering, and
astrophysics. For a relatively recent comprehensive review see
Goluskin During charge, an additional source of
momentum is provided to the electrolyte via viscous coupling at the
positive electrode/electrolyte interface: solutal convection in the
positive electrode. Viscous coupling drives motion in the vicinity of
the lower electrolyte/electrode interface. The interplay of both
drivers (internal heating and viscous coupling) leads to interesting
dynamics. Already at quite low Rayleigh
numbers Ra , regular motion exists in the electrolyte
that modifies the temperature field there. Following Kulacki and
Goldstein , the quoted Rayleigh number is
based on the Joule heat release and the electrolyte layer's half
height. The convective cooling parameter defined by Peckover and
Hutchinson describes the ratio of the
maximum temperature that would occur if heat transport
were purely conductive, to the maximum value of the (height dependent)
temperature profile in the fully developed
flow averaged over time and in horizontal direction. For typical current densities occurring in LMBs , the dominant electrolyte convection mode
depends mainly on the electrolyte thickness. While thermal convection
does not develop in thin electrolyte layers, except for current
densities at the upper end of the range, thick electrolyte layers are
always dominated by thermally driven flow. As mentioned above, thin
electrolyte layers feature relatively regular convection cells during
charge. They extend over the full electrolyte height and are driven by
viscous coupling from the positive electrode. In contrast, the
Rayleigh numbers of thick electrolyte layers are well above the
critical ones for all cases considered. Averaged temperature profiles
show a pronounced asymmetry typical for penetrative convection. Nusselt numbers at the upper boundary of the
electrolyte layer exceed that at the lower
boundary for thick
electrolytes. The opposite holds true for thin electrolytes, where
viscous coupling drives the most intense flow at the lower boundary
and the cooling parameter is smaller than 0.5.