Abstract: We present a topology optimization approach for the design of fluid-to-fluid heat exchangers which rests on an explicit meshed discretization of the phases at stake, at every iteration of the optimization process. The considered physical situations involve a weak coupling between the Navier--Stokes equations for the velocity and the pressure in the fluid, and the convection--diffusion equation for the temperature field. The proposed framework combines several recent techniques from the field of shape and topology optimization, and notably a level-set based mesh evolution algorithm for tracking shapes and their deformations, an efficient optimization algorithm for constrained shape optimization problems, and a numerical method to handle a wide variety of geometric constraints such as thickness constraints and non-penetration constraints. Our strategy is applied to the optimization of various types of heat exchangers. At first, we consider a simplified 2D cross-flow model where the optimized boundary is the section of the hot fluid phase flowing in the transverse direction, which is naturally composed of multiple holes. A minimum thickness constraint is imposed on the cross-section so as to account for manufacturing and maximum pressure drop constraints. In a second part, we optimize the design of 2D and 3D heat exchangers composed of two types of fluid channels (hot and cold), which are separated by a solid body. A non-mixing constraint between the fluid components containing the hot and cold phases is enforced by prescribing a minimum distance between them. Numerical results are presented on a variety of test cases, demonstrating the efficiency of our approach in generating new, realistic, and unconventional heat exchanger designs.

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).

Abstract: An efficient framework is described for the shape and topology optimization of realistic three-dimensional, weakly-coupled fluid-thermal-mechanical systems. At the theoretical level, the proposed methodology relies on the boundary variation of Hadamard for describing the sensitivity of functions with respect to the domain. From the numerical point of view, three key ingredients are used: (i) a level set based mesh evolution method allowing to describe large deformations of the shape while maintaining an adapted, high-quality mesh of the latter at every stage of the optimization process; (ii) an efficient constrained optimization algorithm which is very well adapted to the infinite-dimensional shape optimization context; (iii) efficient preconditioning techniques for the solution of large finite element systems in a reasonable computational time. The performance of our strategy is illustrated with two examples of coupled physics: respectively fluid--structure interaction and convective heat transfer. Before that, we perform three other test cases, involving a single physics (structural, thermal and aerodynamic design), for comparison purposes and for assessing our various tools: in particular, they prove the ability of the mesh evolution technique to capture very thin bodies or shells in 3D.