CFD-based geometrical shape optimization of a packed-bed reactor combining multi-objective and adjoint system methods

This paper presents the development of a geometric shape optimization methodology based on the so-called ”Hadamard boundary variation” method for performing very general domain deformations, and the related concept of domain differentiation. The resulting method is used to determine the optimal configuration of a two-dimensional packed-bed reactor that simultaneously optimizes its conversion rate and fluid energy dissipation, and where a homogeneous first-order reaction or a catalytic surface reaction takes place. The considered multi-objective optimization problem is subjected to four constraints: the process model constraints consisting of the Navier–Stokes, continuity and mass balance equations, an iso-volume and two manufacturing constraints. The approach to solve the problem is based on the linear scalarization method which converts the multi-objective problem into a single objective problem. The adjoint system method is used to compute the gradient of the performance indices and constraints. Since the indices are conflicting, the solution of the problem is a set of solutions, called Pareto front. Each optimal solution is evaluated using multi-attribute utility theory (MAUT) to determine the best optimal shape of the reactor. Finally, the resulting shape is fabricated using a 3D printing technique and will be experimentally validated.