SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 1141-1165, January 2021.
This paper deals with geometric shape optimization of a parallelepiped shaped fixed-bed reactor with single phase liquid flow where a chemical reaction takes place. The packing is a sort of static mixer made up of solid cylindrical obstacles uniformly distributed in the reactor. The reactive flow is described by means of momentum and mass transport equations in laminar flow regime. The objective is to determine the shape of the packing that maximizes the reaction conversion rate subjected to some specified manufacturing constraints. The optimization approach developed is based on the adjoint system method and the results show that the optimal shape obtained allows one to significantly improve the reaction conversion rate. Furthermore, the optimal shape is printed by means of an additive manufacturing technique and several manufacturing constraints mainly related to the thickness of packing are considered.

中文翻译：

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工艺工程中固定床反应器的形状优化

SIAM 应用数学杂志，第 81 卷，第 3 期，第 1141-1165 页，2021 年 1 月。
本文涉及在发生化学反应的单相液流的平行六面体固定床反应器的几何形状优化。填料是一种由均匀分布在反应器内的实心圆柱状障碍物构成的静态混合器。反应流是通过层流状态中的动量和质量传输方程来描述的。目标是确定填料的形状，以在某些特定的制造限制条件下使反应转化率最大化。开发的优化方法基于伴随系统方法，结果表明获得的最佳形状可以显着提高反应转化率。此外，