Topology Optimization for Uniform Flow Distribution in Electrolysis Cells

TL;DR

The paper addresses achieving uniform flow distribution in the anode-side bipolar plate of a PEM electrolyzer by optimizing geometry with a Borvall–Petersson Stokes–Darcy model. It couples a smoothed velocity criterion, via a heat-equation-based $u_s$, with a level-set topology-optimization framework and derives a model-specific topological derivative $D_TJ(z)$ to drive design updates. Numerically, it demonstrates six-channel designs that realize near-uniform flow and shows how the smoothing parameter $\Delta t$ governs obstacle size and manufacturability, enabling tunable feature sizes. The approach provides a practical route to improve water distribution efficiency in PEM cells through topology optimization, with implementations using $\Delta t$-controlled smoothing and adjoint-based sensitivity analysis.

Abstract

In this paper we consider the topology optimization for a bipolar plate of a hydrogen electrolysis cell. We present a model for the bipolar plate using the Stokes equation with an additional drag term, which models the influence of fluid and solid regions. Furthermore, we derive a criterion for a uniform flow distribution in the bipolar plate. To obtain shapes that are well-manufacturable, we introduce a novel smoothing technique for the fluid velocity. Finally, we present some numerical results and investigate the influence of the smoothing on the obtained shapes.

Figures (3)

• Figure 1: Result of the topology optimization problem $(\ref{['optproblem']})$ with $\Delta t=10^{-3}$. In Figure a the final shape is displayed, in Figure b the corresponding norm of the velocity field and in Figure c the norm of the smoothed velocity field.
• Figure 2: Result of the topology optimization problem $(\ref{['optproblem']})$ with $\Delta t_1=5\cdot 10^{-3}$. In Figure a the final shape is displayed, in Figure b the corresponding norm of the velocity field and in Figure c the norm of the smoothed velocity field.
• Figure 3: Result of the topology optimization problem $(\ref{['optproblem']})$ with $\Delta t_2=5\cdot 10^{-4}$. In Figure a the final shape is displayed, in Figure b the corresponding norm of the velocity field and in Figure c the norm of the smoothed velocity field.

Theorems & Definitions (1)

• remark 1