Shape optimization with Stokes constraints over the set of axisymmetric domains

International audienceIn this paper, we are interested in the study of shape optimizations problems with Stokes constraints within the class of axisymmetric domains represented by the graph of a function. Existence results with weak assumptions on the regularity of the graph are provided. We strongly use these assumptions to get some topological properties. We formulate the (shape) optimization problem using different constraints formulations: uniform bound constraints on the function and its derivative and/or volume (global) constraint. Writing the first order optimality conditions allows to provide quasi-explicit solutions in some particular cases and to give some hints for the treatment of the generic problem. Furthermore, we extend the (negative) result of [16] dealing with the non optimality of the cylinder

Shape optimization of fixed-bed reactors in process engineering

International audienceThis paper deals with geometric shape optimization of a parallelepipedic 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 which 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 opti- mal shape obtained allows 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