A new multi-region solver for liquid metal batteries


A new multi-region solver for liquid metal batteries

Weber, N.; Galindo, V.; Stefani, F.; Weier, T.

Liquid metal batteries (LMBs) are a very innovative approach intending to fill the gap of grid-scale electricity storage, as induced by the expand of highly fluctuating renewable energies. Earth-abundant raw materials, simple construction and easy scalability allow for very cheap batteries – the biggest advantage of LMBs.
A LMB is made up of two liquid metals, separated by a liquid salt electrolyte. Properly chosen densities ensure a stable stratification. Taking a Na/Bi LMB, on dis-charge, the Na will lose one electron. The ion Na+ will pass the electrolyte layer and alloy with the Bi to NaBi.
The high resistivity of the salt requires a very thin electrolyte layer, but thick enough to avoid a short-circuit. Fluid flows in LMBs may involve the risk of displacing the electrolyte, resulting in a short-circuit. One of the most important sources of motion are electro vortex flows: the different cross-sections of feeding lines, current collectors and the battery itself induces Lorentz forces in the liquid metal, which are driving a fluid flow.
The fluid flow is governed by the incompressible Navier-Stokes equation (NSE) with the Lorentz force as source term. In order to obtain the latter, we solve a Laplace equation for the electric potential in the liquid metal as well as the current collectors and compute it's gradient giving the current density. With the help of the Biot-Savart law we can compute the magnetic field. The cross product of both is the desired Lorentz force.
Our solver is modeled analogous to chtMultiRegionFoam. We solve the NSE by the PISO algorithm as electro vortex flows are instationary. Solving the Laplace equation for the electric potential we alternate between the liquid and solid regions. The interface condition is given by the demand that there is no jump of the electric potential, and that the normal electric current must be continuous. We combine these two conditions to a single Dirichlet boundary condition for fastest Dirichlet-Neumann partitioning. We stop the iteration between the regions, when both boundary conditions are fulfilled at all interfaces.
The last step, the computation of the magnetic induction using the Biot-Savart law, is a N x N problem. In order to speed up the computation we propose a fast MPI implementation.
Finally, we present some exemplary results and show how electro vortex flows scale in LMBs with the applied current, the current collectors aspect ratio and it's conductivity.

Keywords: liquid metal battery; electro vortex flow; instability; OpenFOAM

  • Lecture (Conference)
    OpenFOAM User Conference, 07.-09.10.2014, Berlin, Deutschland

Permalink: https://www.hzdr.de/publications/Publ-20554
Publ.-Id: 20554