A continuous adjoint cut‐cell formulation for topology optimization of bi‐fluid heat exchangers

Abstract

Purpose

This paper aims to present a topology optimization (TopO) method for designing heat exchangers (HEx) with two working fluids to be kept apart. The introduction of cut–cells gives rise to the cut-cell TopO method, which computes the optimal distribution of an artificial impermeability field and successfully overcomes the weaknesses of the standard density-based TopO (denTopO) by computing the fluid–solid interface (FSI) at each cycle. This allows to accurately solve the flow and conjugate heat transfer (CHT) problem by imposing exact boundary conditions on the computed FSI and results to correct performances computed without the need to re-evaluate the optimized solutions on a body-fitted grid.

Design/methodology/approach

The elements of an artificial impermeability distribution field defined on a background grid act as the design variables and allow topological changes to take place. Post-processing them yields two fields indicating the location of the two flow streams inside the HEx. At each TopO cycle, the FSIs computed based on these two fields are used as the cutting surfaces of the cut-cell grid. On the so-computed grid, the incompressible Navier–Stokes equations, coupled with the Spalart–Allmaras turbulence model, and the temperature equation are solved. The derivatives of the objective and constraint functions with respect to the design variables of TopO are computed by the continuous adjoint method, using consistent discretization schemes devised thanks to the “Think Discrete – Do Continuous” (TDDC) adjoint methodology.

Findings

The effectiveness of the cut-cell–based TopO method for designing HEx is demonstrated in 2D parallel/counter flow and 3D counter flow HEx operating under both laminar and turbulent flow conditions. Compared to the standard denTopO, its ability to compute FSIs along which accurate boundary conditions are imposed, increases the accuracy of the flow solver, which usually leads to optimal, rather than sub-optimal, solutions that truly satisfy the imposed constraints.

Originality/value

This work proposes a new/complete methodology for the TopO of two-fluid systems including CHT that relies on the cut-cell method. This successfully combines aspects from both TopO and Shape Optimization (ShpO) in a single framework thus overcoming the well-known downsides of standard denTopO regarding its accuracy or the need for a follow-up ShpO after TopO. Instead of adding the well-known Brinkman penalization terms into the flow equations, it computes the FSIs at each optimization cycle allowing the solution of the CHT problem on a cut-cell grid.