  This paper presents a three-dimensional topology optimization method for the
design of flow field in vanadium redox flow batteries (VRFBs). We focus on
generating a novel flow field configuration for VRFBs via topology
optimization, which has been attracted attention as a powerful design tool
based on numerical optimization. An attractive feature of topology optimization
is that a topology optimized configuration can be automatically generated
without presetting a promising design candidate. In this paper, we formulate
the topology optimization problem as a maximization problem of the electrode
surface concentration in the negative electrode during the charging process.
The aim of this optimization problem is to obtain a topology optimized flow
field that enables the improvement of mass transfer effect in a VRFB. We
demonstrate that a novel flow field configuration can be obtained through the
numerical investigation. To clarify the performance of the topology optimized
flow field, we investigate the mass transfer effect through the comparison with
reference flow fields---parallel and interdigitated flow fields---and the
topology optimized flow field. In addition, we discuss the power loss that
takes account of the polarization loss and pumping power, at various operating
conditions.
