Spring 2022 – Topology optimization of engineering systems

Abstract: This work is devoted to shape and topology optimization of multiphysics systems motivated by aeronautic industrial applications. Shape derivatives of arbitrary objective functionals are computed for a weakly coupled thermal fluid-structure model. A novel gradient flow type algorithm is then developed for solving generic constrained shape optimization problems without the need for tuning non-physical metaparameters. Motivated by the need for enforcing non-mixing constraints in the design of liquid-liquid heat exchangers, a variational method is developed in order to simplify the numerical evaluation of geometric constraints: it allows to compute line integrals on a mesh by solving a variational problem without requiring the explicit knowledge of these lines on the spatial discretization. All these ingredients allowed us to implement a variety of 2-d and 3-d multiphysics shape optimization test cases: from single, double or three physics problems in 2-d, to moderately large-scale 3-d test cases for structural design, thermal conduction, aerodynamic design and a fluid-structure interacting system. A final opening chapter derives high order homogenized equations for the Stokes system in a porous medium. These high order equations encompass the three classical homogenized regimes---namely Stokes, Brinkman and Darcy---associated with different obstacle's size scalings. They could allow, in future works, to develop new topology optimization methods for the design of fluid systems characterized by multi-scale patterns such as industrial heat exchangers.

Abstract: The purpose of these notes is to offer a comprehensive introduction to topology optimization for automated generation of complex heat exchanger designs, based on the methodof Hadamard whereby the design variable is the shape of the fluid-solid interfaces and is updated iteratively until convergence to a nearly optimal design. The material is intended to be an introductory exposure to our recent work (Feppon et al.(2021)) and PhD thesis (Feppon, 2019).