Simulating porous electrodes in flow batteries

Redox flow batteries are a type of electrochemical cell that can be used to store energy and convert between electrical and chemical energy. Flow batteries are a promising technology for grid scale energy storage and the ongoing clean energy transition. A critical component of flow batteries is a porous electrode, which is the site of electrochemical reactions and is often composed of carbon cloth in practice. In this talk, I will introduce a numerical simulation of porous electrodes. We model the system as a pair of loosely coupled phenomena. First, we simulate an incompressible fluid flow of the pumped electrolyte around solid fibers in the electrode. Then, we simulate advection, diffusion and the chemical source term using the Butler-Volmer equation. Our modeling approach uses embedded boundaries and cut cells and is based on the AmReX library. We have an MPI code that can run in parallel on multiple servers to simulate larger systems. The special case of greatest interest is steady state. I will demonstrate some novel techniques to accelerate solving steady state in a millimeter scale 2D system to a sub-micron resolution. With iterative upsampling, we solve the system at a coarse resolution and then interpolate the results as the initial guess for a simulation at a finer resolution. In the Nernst model, we take the limiting case of infinitely fast reaction kinetics. This allows us to treat the concentration of each species on the reactive surface as a boundary condition, obtained by solving the Nernst equation; we then simulate only advection and diffusion to find the steady state concentration field.