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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. [ABSTRACT FROM AUTHOR]

We consider the optimal shape design of polymer distributors used for industrial fiber spinning. In this laminar flow problem the residence time, the volume‐averaged age distribution of the fluid particles, has to be controlled to avoid material degradation. The residence time is modelled by an advection‐diffusion‐reaction equation with the fluid velocity being the transport field. This approach is more suitable for PDE‐constrained shape optimization than the Lagrangian particle‐tracking approach, where the observable is a finite set of trajectories. In order to develop an efficient shape optimization algorithm we derive the shape gradient of a tracking‐type cost functional by introducing the adjoint state. [ABSTRACT FROM AUTHOR]

The transport of gas‐solid suspensions in bended pipes can lead to erosion of the walls due to particle impact. In this context the numerical prediction of the erosion rate is usually based on an Eulerian flow description in combination with Lagrangian particle tracking, which however does not lend itself straightforwardly to the continuous adjoint approach of shape optimization. In order to find a pipe design, which is less prone to erosion, we therefore use a one‐way coupled Eulerian particle model. Upon formally computing the shape derivative of the resulting PDE‐constrained shape optimization problem, we minimize the erosion rate for a three‐dimensional tube bend under laminar flow conditions using a gradient descent method. [ABSTRACT FROM AUTHOR]

We introduce a new approach to solve shape optimization problems with state constraints. The problem is reformulated on a fixed reference domain using conformal pull-back. The shape dependence is then hidden in the conformal parameter. The problem is discretized using FEM and solved as an NLP. Finally the optimal shape can be reconstructed from the optimal conformal parameter. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]