  A method for density-based topology optimization of heat exchangers with two
fluids is proposed. The goal of the optimization process is to maximize the
heat transfer from one fluid to the other, under maximum pressure drop
constraints for each of the fluid flows. A single design variable is used to
describe the physical fields. The solid interface and the fluid domains are
generated using an erosion-dilation based identification technique, which
guarantees well-separated fluids, as well as a minimum wall thickness between
them. Under the assumption of laminar steady flow, the two fluids are modelled
separately, but in the entire computational domain using the Brinkman
penalization technique for ensuring negligible velocities outside of the
respective fluid subdomains. The heat transfer is modelled using the
convection-diffusion equation, where the convection is driven by both fluid
flows. A stabilized finite element discretization is used to solve the
governing equations. Results are presented for two different problems: a
two-dimensional example illustrating and verifying the methodology; and a
three-dimensional example inspired by shell-and-tube heat exchangers. The
optimized designs for both cases show an improved heat transfer compared to the
baseline designs. For the shell-and-tube case, the full freedom topology
optimization approach is shown to yield performance improvements of up to 113%
under the same pressure drop.
